The total percent of the data falling between 62. 6 and 71. 8 is around 68%
Mean score = 67.2
Standard deviation = 4.6
Standardizing the values of interest by converting them into z-scores by -
z = (x - μ) / σ
where x is the score, μ is the mean, and σ is the standard deviation.
Calculating for the lower bound of 62.6:
z1
= (62.6 - 67.2) / 4.6
= - 4.6/4.6
= -1
Similarly,
Calculating for the upper bound of 71.8:
z2
= (71.8 - 67.2) / 4.6
= 4.6/4.6
= 1
Getting the area under curve between these two z-scores using a table of common normal probability. The normal distribution is symmetric, thus, the area between z1 and z2, can be then subtracted from the area to the left of z2. The Left of z1 is an area of 0.1587 and the left of z2 is an area of 0.8413. Therefore, the area between z1 and z2 is:
= 0.8413 - 0.1587
= 0.6826
Converting this area to a percentage -
0.6826 × 100%
= 68.26%
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A quantity m varies jointly with p and r. When p is 2 and r is 4, m is 1. What is the constant of variation?
One-eighth
One-half
2
8
The constant of variation is [tex]\frac{1}{8}[/tex].
What is variation?The discrepancy among an ideal and real scenario is referred to as the Law of Variation. The most frequent manifestations of variation or variability are changes in the data, anticipated results, or minor changes in the quality of the output.
The types of variation are given below-
Where a variable is a fixed multiple of another, this is known as direct variation. For instance, my income varies directly (or proportionally) with the amount of hours I put in.When one of the variables rises, the other one falls—this is known as inverse and indirect variation (product is constant). For instance, the length of time an air conditioner is operating has an indirect (equal or inverse) impact mostly on temperature in my home.Joint variation occurs when at least two factors are directly associated. For instance, a triangle's base and height are both related to the triangle's area.According to the question;
A quantity m varies jointly with p and r which shows that p and r in joint variation with m.
m ---> pr
m = kpr
where, k is the constant of variation.
m = 1, p = 2, r = 4.
Substitute the values in the relation,
1 = k(2)(4)
1 = 8k
k = 1/8
Therefore, the constant of variation is [tex]\frac{1}{8}[/tex].
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The constant of variation is 1/8, which is option A.
What is variation?
The way in which a quantity changes or varies with respect to another quantity. There are two types of variation: direct variation and inverse variation. Direct variation occurs when two quantities change in the same direction. In other words, if one quantity increases, the other quantity also increases.
y = kx, where y and x are the two quantities, and k is a constant of proportionality.
Inverse variation occurs when two quantities change in opposite directions. In other words, if one quantity increases, the other quantity decreases.
y = k/x, where y and x are the two quantities, and k is a constant of proportionality.
If m varies jointly with p and r, we can write the relationship as:
m = k * p * r
where k is the constant of variation.
We are given that when p is 2 and r is 4, m is 1. Substituting these values into the equation, we get:
1 = k * 2 * 4
Simplifying this equation, we get:
k = 1 / (2 * 4)
k = 1/8
Therefore, the constant of variation is 1/8, which is option A.
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The article "Well-Fed Crickets Bowl Maidens Over"† reported that female field crickets are attracted to males that have high chirp rates and hypothesized that chirp rate is related to nutritional status. The chirp rates for male field crickets were reported to vary around a mean of 60 chirps per second. To investigate whether chirp rate is related to nutritional status, investigators fed male crickets a high-protein diet for 8 days and then measured chirp rate. The mean chirp rate for the crickets on the high-protein diet was reported to be 103 chirps per second. Is this convincing evidence that the mean chirp rate for crickets on a high-protein diet is greater than 60 (which would then imply an advantage in attracting the ladies)? Suppose that the sample size and sample standard deviation are n = 32 and s = 35. You can test the relevant hypotheses to answer this question. A significance level of α = 0.01 will be used. (a) State the null and alternative hypotheses. 1)H0: μ < 60 Ha: μ > 60 2)H0: μ = 60 Ha: μ > 60 3)H0: μ = 60 Ha: μ < 60 4)H0: μ = 60 Ha: μ ≠ 60 (b)Calculate the test statistic. (Round your answer to two decimal places.) t = (c)Based onα = 0.01,what is the correct conclusion for the hypothesis test? (Use a table or technology.)
60
8.43
alternative hypothesis
(a) The hypotheses for this question are:
1) H0: μ = 60
Ha: μ > 60
2) H0: μ = 60
Ha: μ < 60
3) H0: μ = 60
Ha: μ ≠ 60
(b) The test statistic is calculated as:
t = (103-60)/(35/√32) = 8.43
(c) Based on a significance level of α = 0.01, the correct conclusion for the hypothesis test is that the mean chirp rate for crickets on a high-protein diet is greater than 60 chirps per second, as the test statistic (8.43) is greater than the critical value (2.58). Therefore, we can reject the null hypothesis and accept the alternative hypothesis.
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In a parallelogram, a diagonal of length 20 cm is perpendicular to one of the sides. Find the longer side of the parallelogram if its perimeter is 80 cm.
The longer side of the Quadrilateral/Parallelogram is approximately 16.28 cm.
what are quadrilaterals?
Quadrilaterals are geometric figures with four sides and four angles. They are two-dimensional shapes that can be classified based on their properties such as angles, side lengths, and symmetry.
Now,
Let's denote the shorter side of the parallelogram by x and the longer side by y. Since opposite sides of a parallelogram are congruent, the perimeter of the parallelogram is:
2x + 2y = 80
Simplifying this equation, we get:
x + y = 40
Now, let's consider the diagonal that is perpendicular to one of the sides. This diagonal divides the parallelogram into two right triangles. Let's denote the length of the altitude (or height) of each right triangle by h, as shown in the diagram below:
/|\
/ | \
/ | \
/______|______
20 cm
Using the Pythagorean theorem, we have:
h² + (x/2)² = 20²
Simplifying this equation, we get:
h² + x²/4 = 400
4h² + x² = 1600
Since h is also the height of the parallelogram, we know that h is perpendicular to the longer side y. Thus, we have:
h² + y² = (2h)²
h² + y² = 4h²
Substituting the value of h² from the first equation into the second equation, we get:
x²/4 + y² = 4(400 - x²/4)
x² + 4y² = 1600
Substituting x = 40 - y from the perimeter equation, we get:
(40 - y)² + 4y² = 1600
5y² - 80y + 400 = 0
y² - 16y + 80 = 0
Using the quadratic formula, we get:
y = (16 ± √(16² - 4*80))/2
y = 8 ± √(14)
Since y must be greater than x, we take the larger value of y:
y = 8 + √(14)
Therefore, the longer side of the parallelogram is approximately 16.28 cm.
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use the table and the situation given below to complete exercises 1-4
one month you write 5 checks and use bank's ATM machine 3 times you usr a non bank ATM twice and your debit card 8 times find the total amount of fees you would pay from rach bank
The total amount of fees for each bank is First state bank = $8, National bank = $12.50, and third city bank = $9.
What are arithmetic operations?The fundamentals of mathematics are arithmetic operations. Operations like addition, subtraction, multiplication, and division make up the majority of it. Sometimes referred to as mathematical operations, these. In daily life, we employ mathematical operations to calculate overall business revenue and costs, create monthly or yearly budgets, measure distances, and more. We use them nearly constantly throughout the day. For instance, we use them to calculate the overall amount of homework problems, time, money, the number of chocolates we ate, the total number of grades we received across all courses, etc.
Given that, one month you write 5 checks and use bank's ATM machine 3 times, you use a non bank ATM twice and your debit card 8 times
The total amount for first state bank is:
C = 5(1) + 3(1) = $8
The total amount for National bank is:
C = 12.50
The total amount for third city bank is:
C = 3(1) + 8(0.75) = 9
Hence, the total amount of fees for each bank is First state bank = $8, National bank = $12.50, and third city bank = $9.
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Differentiate the following functions: (a). 23x (b). 10(5−6n+n2) (c). 3x2+2 (d). t2t (e). x23x
The derivative of x23x is $\frac{2}{3}x^{-1/3}3^x+ x^{2/3} \ln(3)3^x$.
The functions are as follows: (a) 23x(b) 10(5−6n+n2)(c) 3x2+2(d) t2t(e) x23xDifferentiation is the process of finding the derivative of a function or equation. The derivative of a function, in calculus, is the rate at which it changes with respect to its independent variable.
In other words, it represents the slope of the tangent line at a particular point on the graph of the function. The following are the derivatives of the functions mentioned above: (a) 23x Solution:We know that, f(x) = 23xNow, differentiating both sides of the equation with respect to x we get, $\frac{d}{dx}(f(x))= \frac{d}{dx}(23x)$Here, $\frac{d}{dx}$ is the differential operator.
It implies that we need to find the derivative of the function with respect to x.Then, $\frac{d}{dx}(23x)= 23 \frac{d}{dx}(x)$Now, $\frac{d}{dx}(x)= 1$So, $\frac{d}{dx}(f(x))= 23$Therefore, the derivative of 23x is 23. (b) 10(5−6n+n2) Solution:We know that, f(x) = 10(5−6n+n2)Now, differentiating both sides of the equation with respect to x we get, $\frac{d}{dx}(f(x))= \frac{d}{dx}[10(5−6n+n^2)]$Here, $\frac{d}{dx}$ is the differential operator.
It implies that we need to find the derivative of the function with respect to x.Then, $\frac{d}{dx}(10(5−6n+n^2))= 10 \frac{d}{dx}(5−6n+n^2)$Now, $\frac{d}{dx}(5−6n+n^2)= \frac{d}{dx}(5)- \frac{d}{dx}(6n)+ \frac{d}{dx}(n^2)$Now, $\frac{d}{dx}(5)= 0$ because 5 is a constant, and its derivative is always 0. Hence, we can ignore it.Then, $\frac{d}{dx}(6n)= 6 \frac{d}{dx}(n)$Now, $\frac{d}{dx}(n)= 1$So, $\frac{d}{dx}(6n)= 6$Then, $\frac{d}{dx}(n^2)= 2n$Therefore, $\frac{d}{dx}(f(x))= 10 (0 - 6 + 2n) = 20n - 60$Therefore, the derivative of 10(5−6n+n2) is 20n - 60. (c) 3x2+2 Solution:We know that, f(x) = 3x2+2Now, differentiating both sides of the equation with respect to x we get, $\frac{d}{dx}(f(x))= \frac{d}{dx}(3x^2+2)$Here, $\frac{d}{dx}$ is the differential operator.
It implies that we need to find the derivative of the function with respect to x.Then, $\frac{d}{dx}(3x^2+2)= 3 \frac{d}{dx}(x^2)+ \frac{d}{dx}(2)$Now, $\frac{d}{dx}(x^2)= 2x$So, $\frac{d}{dx}(f(x))= 3(2x)+ 0 = 6x$Therefore, the derivative of 3x2+2 is 6x. (d) t2t Solution:We know that, f(x) = t2tNow, differentiating both sides of the equation with respect to x we get, $\frac{d}{dx}(f(x))= \frac{d}{dx}(\frac{t^2}{t})$Here, $\frac{d}{dx}$ is the differential operator.
It implies that we need to find the derivative of the function with respect to x.Then, $\frac{d}{dx}(\frac{t^2}{t})= \frac{d}{dx}(t^{2-1})$Now, $\frac{d}{dx}(t^{2-1})= 1 t^{2-1-1} \frac{d}{dx}(t)$So, $\frac{d}{dx}(t)= 0$ because t is a constant. Hence, we can ignore it.Then, $\frac{d}{dx}(f(x))= 1 t \frac{d}{dx}(t)= t$Therefore, the derivative of t2t is t. (e) x23x Solution:We know that, f(x) = x23xNow, differentiating both sides of the equation with respect to x we get, $\frac{d}{dx}(f(x))= \frac{d}{dx}(x^{2/3}3^x)$Here, $\frac{d}{dx}$ is the differential operator.
It implies that we need to find the derivative of the function with respect to x.Then, $\frac{d}{dx}(x^{2/3}3^x)= \frac{d}{dx}(x^{2/3})3^x+ x^{2/3} \frac{d}{dx}(3^x)$Now, $\frac{d}{dx}(x^{2/3})= \frac{2}{3}x^{-1/3}$Then, $\frac{d}{dx}(3^x)= \ln(3)3^x$So, $\frac{d}{dx}(f(x))= \frac{2}{3}x^{-1/3}3^x+ x^{2/3} \ln(3)3^x$Therefore, the derivative of x23x is $\frac{2}{3}x^{-1/3}3^x+ x^{2/3} \ln(3)3^x$.
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The board of directors of a corporation must select a president, a secretary, and a treasurer. In how many possible ways can this be accomplished if there are 23 members on the board of directors?
there are 10,626 possible ways to select a president, a secretary, and a treasurer from a board of directors with 23 members.
To solve this problem, we can use the formula for permutations, which is:
P(n, r) = n! / (n - r)!
where n is the total number of items, and r is the number of items selected.
In this case, we need to select 3 people from a group of 23, without replacement and order matters. Therefore, the number of ways to do this is:
P(23, 3) = 23! / (23 - 3)!
= 23! / 20!
= 23 x 22 x 21
= 10,626 possible ways
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The sum of two numbers is 58 and the difference is 20. What are the numbers?
Larger number:
Smaller number:
Answer:
Larger number: 39
Smaller number: 19
Step-by-step explanation:
Write two equations and solve the system of equations.
One number can be x. The other number can be y.
"sum" means adding.
x + y = 58
"difference" means subtracting.
x - y = 20
Take both equations, stack them and add them together from the top down.
x + y = 58
x - y = 20
_________
2x = 78
Divide by 2
x = 39
Use either original equation to find the other number.
x + y = 58
39 + y = 58
subtract 39
y = 19
The bigger number is 39 and the smaller number is 19.
Simplify: 5x2 +7y -6z, 4y + 3x2
, 9x2 +2z2
, 2z2
– 9y, 2y – 2x2
Answer:
Step-by-step explanation:
i don't know
A chemical company makes two brands of antifreeze. The first brand is 45% pure antifreeze, and the second brand is 70% pure antifreeze. In ord gallons of a mixture that contains 65% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Answer:
5 gallons of 70% antifreeze, 1 gallon of 45% antifreeze
Step-by-step explanation:
Many different combinations can be made to equal 65% pure antifreeze.
Essentially, this problem is asking us to find a combination that fits a mean of 65%. So, multiply 5 by 70 to get 350, and 1 x 45 to get 45. Add 350 + 45 together to get 395, and divide by the total amount of gallons used - 6.
395/6 = 65, which is the target value.
Mr. And Mrs. White and their son, Herbert, ignore the warnings about the danger of the supernatural. This foreshadowing helps develop the theme
The foreshadowing of Mr. and Mrs. White and Herbert ignoring the warnings about the danger of the supernatural helps to build suspense and create a sense of foreboding, thus helping to establish the theme of the story.
If that is the case, then yes, the White family ignoring the warnings about the danger of the supernatural helps develop the theme of the story. The story explores the consequences of tempting fate and meddling with the unknown, as the family's wishes on the cursed monkey's paw lead to tragic and horrifying outcomes.
The foreshadowing of danger through warnings and ominous hints, such as the Sergeant-Major's tales and the paw's sinister appearance, underscores the gravity of the situation and the potential consequences of the family's actions. However, the White family disregards these warnings and ultimately pays the price for their curiosity and greed.
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IF YOU GET THIS ONE QUESTION RIGHT, I'LL GIVE BRAINLIEST
Solve this equation.
√(x-10)^2=x-10
Valerie's class is attempting to recreate Van Gogh's
"'The Starry Night" on a tapestry to cover one of the
walls in the media center. The original painting was
28. 7 inches by 36. 25 inches. If they use a scale
factor Sin. : 2ft. , approximately how many square
feet will the tapestry cover? Round to the nearest
tenth
If they use a scale factor Sin : 2ft. , approximately 14.43 square feet will the tapestry cover.
The tapestry will cover approximately 57.4 square feet.
To calculate this, first multiply the width and the length of the painting (in inches) to find the area of the painting in inches squared.
28.7 inches x 36.25 inches = 1040.375 inches squared
Then, convert the inches squared to feet squared by dividing by 144.
1040.375/144 inches squared = 7.21354 feet squared
Finally, multiply the area of the painting in feet squared by the scale factor (2 feet) to find the area of the tapestry in feet squared.
7.21354 feet squared x 2 feet = 14.42708 feet squared
Finally, round the answer to the nearest hundredth to get the answer:
14.43 feet squared, or 57.4 square feet
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Three people are sitting on a bus. Barry is directly behind Julian and directly left of Dillon. If Julian and Barry are 5 feet apart, and Dillon and Julian are 8 feet apart, what is the distance between Barry and Dillon? If necessary, round to the nearest tenth.
Please respond.
Thank you!
Therefore , the solution of the given problem of unitary method comes out to be the distance between Barry and Dillon is roughly 6.2 feet.
What is an unitary method?Using the unilateral approach, the task can be completed by increasing the information obtained from such a nanosection by two. In essence, that whenever a wanted item emerges, the colour area of both the production runs were either skipped or the defined entity is set. For forty pens, a variable charge of Inr ($1.01) could have been required.
Here,
We can use a diagram to show the three passengers' locations on the bus in order to solve this issue:
Let x serve as a proxy for the separation between Barry and Dillon.
Using the knowledge provided, we can create two equations:
Barry is five steps away from Julian.
=> x² +d² = 5.
They are eight feet apart, Dillon and Julian.
Duplicate the formula
d = distance between Barry and Dillon (d = x² + 8² ).
The two formulae can be made equal to one another in order to find d:
=> x² + 5² = x² + 8²
=> 25 = 64 - x²
=> x² = 39
=> x ≈ 6.2
This means that, rounded to the closest tenth, the distance between Barry and Dillon is roughly 6.2 feet.
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Answer:
6.2 ft
Step-by-step explanation:
To find:-
The distance between Barry and Dillon .Answer:-
On drawing a figure representing the given situation , we get a right angled triangle . To find out the distance between Barry and Dillon we can use Pythagoras theorem, according to which;
[tex]\rm\implies h^2=a^2+b^2\\[/tex]
Here h is the longest side and a and b are two other sides. And in this question, hypotenuse is 8ft . One of the other side is 5ft .
On substituting the respective values , we have ;
[tex]\rm\implies 8^2 = 5^2+a^2 \\[/tex]
[tex]\rm\implies 64 = 25 + a^2\\[/tex]
[tex]\rm\implies 64 - 25 = a^2 \\[/tex]
[tex]\rm\implies 39 = a^2 \\[/tex]
[tex]\rm\implies a =\sqrt{39}\\[/tex]
[tex]\rm\implies \red{ a = 6.2 } \\[/tex]
Hence the distance between Barry and Dillon is 6.2 ft. (nearest tenth) .
You are designing an in-ground lap swimming pool with a volume of 2000 cubic feet. The width of the
pool should be 5 feet more than the depth, and the length should be 35 feet more than the depth. What
should the dimensions of the pool be?
The dimensions of the pool should be 8 feet deep, 13 feet wide, and 43 feet long.
How to calculate the dimension of the poolLet's assume that the depth of the pool is "x".
Given that the width is 5 feet more than the depth, then the width is x + 5.
Also, the length is 35 feet more than the depth, then the length is x + 35.
The volume of the pool is 2000 cubic feet, then:
length x width x depth = 2000
(x + 35) (x + 5) (x) = 2000
x^3 + 40x^2 + 175x - 2000 = 0
We can use trial and error or synthetic division to find that one of the roots of this cubic equation is x = 8.
Therefore, the depth of the pool is 8 feet.
The width is x + 5 = 8 + 5 = 13 feet.
The length is x + 35 = 8 + 35 = 43 feet.
So, the dimensions of the pool should be 8 feet deep, 13 feet wide, and 43 feet long.
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Which type of Raina's squash has a higher median length based on the box plot
The box plots show the average wind speeds, in miles per hour, for various cities in two different countries.
Box plots are graphical representations of data that summarize important features such as the center, spread, and shape of a distribution. In this case, the box plots show the average wind speeds, in miles per hour, for different cities in two different countries.
The box in the plot represents the middle 50% of the data, with the line inside the box showing the median. The whiskers extend to the minimum and maximum values of the data, excluding any outliers, which are shown as individual points outside the whiskers.
Comparing the box plots for the two countries, we can see that the average wind speeds for the cities in Country A are generally lower than those in Country B. The box in Country A is shorter and closer to the bottom of the plot, indicating less variability in the data. Meanwhile, the box in Country B is taller and more spread out, suggesting a wider range of wind speeds across the cities.
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Based on the box plot, which type of Raina's squash has a higher median length?
can someone plsss help me with this I’ll mark brainliest
Rewrite the expression as a product of two factors x²+x-2
we will multiply x by both terms in the parentheses, giving us x²+2x. Then, we will subtract 1 from this expression, leaving us with x²+2x-1. Therefore, the expanded expression is x²+2x-1.
x(x+2) - 1To rewrite the expression x²+x-2 as a product of two factors, we will use algebraic factoring. First, we will factor out the greatest common factor from the expression, which is x. We do this by dividing each term in the expression by x, leaving us with x+2 and -1. The expression can now be written as x(x+2) - 1. This expression is the product of two factors x and (x+2) - 1.
x²+2x-1 To expand the expression x(x+2) - 1, we will use the distributive property. First, we will multiply x by both terms in the parentheses, giving us x²+2x. Then, we will subtract 1 from this expression, leaving us with x²+2x-1. Therefore, the expanded expression is x²+2x-1.
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A runner sprinted for 447 feet . How many yards is this
Answer: 447/3
Feet to yards is every three feet is one yard
Step-by-step explanation:
447 divided by 3 equals 149 yards
A manufacturer finds that on average 1 in 200 light bulbs is defective. If the bulbs are shipped in boxes of 20 find the probability that a randomly selected box contains a) at least one defective bulb, b) at most one defective bulb
a) The probability that a randomly selected box contains at least one defective bulb is approximately 0.099. b) The probability that a randomly selected box contains at most one defective bulb is approximately 0.9998.
a) To find the probability that a randomly selected box contains at least one defective bulb, we can use the complement rule: the probability of the complement of the event (no defective bulbs) is easier to calculate. The probability that a bulb is not defective is 199/200, so the probability that all 20 bulbs in a box are not defective is (199/200)²⁰. Therefore, the probability that at least one bulb is defective is:
1 - (199/200)²⁰ ≈ 0.099
So the probability that a randomly selected box contains at least one defective bulb is approximately 0.099.
b) To find the probability that a randomly selected box contains at most one defective bulb, we can calculate the probability of each possible outcome (0, 1, or 2 defective bulbs) and add them up.
The probability of no defective bulbs is (199/200)²⁰ ≈ 0.9048.
The probability of exactly one defective bulb is:
20C1 * (1/200) * (199/200)¹⁹ ≈ 0.0950
where 20C1 is the number of ways to choose one defective bulb out of 20.
The probability of two defective bulbs is:
20C2 * (1/200)² * (199/200)¹⁸ ≈ 0.0002
where 20C2 is the number of ways to choose two defective bulbs out of 20.
Therefore, the probability of at most one defective bulb is:
0.9048 + 0.0950 ≈ 0.9998
So the probability that a randomly selected box contains at most one defective bulb is approximately 0.9998.
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To evaluate their products, the manager of an assembly line inspects the first 100 batteries that are produced out of 30,000 total batteries produced that day. He displays the results in the graph at the right and then releases it to a local newspaper.
95 batteries are in excellent condition, three batteries do not hold charge, two batteries are broken or they have cracked casing.
5. Identify any sampling errors( ways in which the when/ who of the data collected can lead to biased results)
The sample is large enough, random, and representative of the population being studied to avoid biased results.
The following list of potential sampling flaws that can result in biassed results is based on the information provided:
Limited sample size: Of the 30,000 batteries produced that day, the manager only examined 100 of them. It's possible that this sample size is insufficient to adequately represent the full population of batteries. A bigger sample size can yield more reliable results.
Non-random sampling: It's unclear how the manager decided to test 100 batteries. The outcomes might be skewed if the selection wasn't random or if there was any bias throughout the selection procedure.
Selection from a non-representative subset of the population: It is unclear if the 100 batteries that were subjected to inspection were drawn at random from the full population of batteries manufactured that day or merely from a particular section of the production line. The results might not be representative of the whole population of batteries manufactured that day if the batteries were only collected from a portion of the production line.
Confirmation bias: The manager's inspection procedure may have been prejudiced inadvertently, looking for more of what they anticipated to see. For instance, the management might have been more inclined to identify more batteries as being in good condition if they had expected the batteries to be of high quality, which could have skewed the results.
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Abc and acd are triangles. The area of acd is 108cm^2. Work out the area of abc. Give your answer to 3 significant figures
The area of the triangle ABC is 87.176 cm square.
A triangle is a polygon with three vertices and three sides. The internal angle of the triangle, which is 180 degrees, is built. It means that a triangle's internal angles sum to 180 degrees. It has the fewest sides of any polygon. Instead, a triangle is a three-sided, two-dimensional geometry with internal angles that are 180°.
A triangle with a right angle of 90 degrees is equivalent to one of a triangle's angles.
Triangles abc and acd. ACD is 108 cm square in size. Calculate ABC's area.
Given: ACD is 108 cm square in size.
Area of ACD = 108, thus calculate the area of ABC.
[tex]\frac{1}{2}*CD*AC=108\\\\\frac{1}{2}*16*AC=108\\\\8*AC=108\\\\AC=\frac{108}{8}\\\\Area\ (ABC)=\frac{1}{2}*AC*BC*sin38,\\ = \frac{1}{2}*\frac{27}{2}*21*sin38\\=87.176 cm^2[/tex]
[tex]\frac{1}{2}*CD*AC=108\\\\\frac{1}{2}*16*AC=108\\\\8*AC=108\\\\AC=\frac{108}{8}\\\\Area\ (ABC)=\frac{1}{2}*AC*BC*sin38,\\ = \frac{1}{2}*\frac{27}{2}*21*sin38\\=87.176 cm^2[/tex]
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The linear model represents the height f(x) of a water balloon thrown off a building over time, x, measured in seconds
a) Interval(s) of the domain in which the water balloon's height increasing is from x = 0 to x = 2.
b) Interval(s) of the domain in which the water balloon's height staying the same is from x = 2 to x = 4.
c) Interval(s) of the domain in which the water balloon's height decreasing the fastest is from x = 8 to x = 10.
d) The predicted height of the water balloon at 14 seconds is 82 feet.
a) The water balloon's height is increasing from x = 0 to x = 2 seconds, as the height goes from 26 feet to 34 feet.
b) The water balloon's height is staying the same from x = 2 seconds to x = 4 seconds, as the height remains at 34 feet.
c) The water balloon's height is decreasing the fastest from x = 8 seconds to x = 10 seconds, as the height drops from 30 feet to 0 feet over a span of only 2 seconds. During this interval, the balloon is likely hitting the ground.
d) To predict the height of the water balloon at 14 seconds, we need to find the corresponding value of f(x) on the linear model. Since the given ordered pairs only go up to x = 12 seconds, we need to use the equation of the line to extrapolate beyond that point.
We can first find the slope of the line using any two of the ordered pairs. Let's use (0, 26) and (2, 34):
slope = (34 - 26) / (2 - 0) = 4
Using the point-slope form of the equation, we can write the equation of the line as:
f(x) - 26 = 4(x - 0)
f(x) = 4x + 26
To predict the height at 14 seconds, we can simply substitute x = 14 into the equation:
f(14) = 4(14) + 26
f(14) = 82
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Complete question is:
The linear model represents the height, f(x), of a water balloon thrown off the roof of a building over time, x, measured in seconds:
A linear model with ordered pairs at 0, 26 and 2, 34 and 4, 34 and 8, 30 and 10, 0 and 12, 0. The x axis is labeled Time in seconds, and the y axis is labeled Height in feet.
a) During what interval(s) of the domain is the water balloon's height increasing? (2 points)
b) During what interval(s) of the domain is the water balloon's height staying the same? (2 points)
c) During what interval(s) of the domain is the water balloon's height decreasing the fastest? Use complete sentences to support your answer. (3 points)
d) Use the constraints of the real-world situation to predict the height of the water balloon at 14 seconds. Use complete sentences to support your answer. (3 points)
A tapered bar is 10. 0 inches long. The diameter of the circular cross section decreases linearly from 4. 0 inches at one end to 2. 0 inches at the other end. Determine the equation that expresses the cross-sectional area of the bar as a function of the position, x, along the length. The area of a circle is given by A=πr2.
what is the meaning of the cross-sectional area of the bar ? ( with drawing )
π/4 [2 + 1/5x] is the equation that expresses the cross-sectional area of the bar as a function of the position, x, along the length. The area of a circle is given by A=πr2.
Let us now consider a uniformly tapering circular bar having length,
L = 10 inches
and having diameter,
d₁ = 2 inches
at one end and
d₂ = 4 inches
at the other end, therefore we know that d₂ > d₁
let us consider a very short section xx of length kx and diameter dx, situated at a distance x from end A
now diameter, dx = d₁ + (d₂ - d₁)x
= d₁ + kx
where k = d₂ - d₁/ L
= 4-2/10 = 2/10 = 1/5
cross section area of the given circular bar 1
π/4 d₁²
π/4(d₁+Kx)
π/4 [2 + 1/5x]
here the cross section over 1x function of the given position of x, along the length.
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pinworm: in a prior sample of u.s. adults, the center for disease control (cdc), found that 11% of the people in this sample had pinworm but the margin of error for the population estimate was too large. they want an estimate that is in error by no more than 1.5 percentage points at the 95% confidence level. enter your answers as whole numbers. (a) what is the minimum sample size required to obtain this type of accuracy? use the prior sample proportion in your calculation. the minimum sample size is u.s. adults. (b) what is the minimum sample size required to obtain this type of accuracy when you assume no prior knowledge of the sample proportion? the minimum sample size is u.s. adults.
A minimum sample size of 1399 is required assuming a prior knowledge of the sample proportion of 11%, and a minimum sample size of 960 is required if no prior knowledge of the sample proportion is assumed.
To obtain an estimate of the percentage of U.S. adults with pinworm with an error of no more than 1.5 percentage points at a 95% confidence level, a minimum sample size of 1399 is required, assuming prior knowledge of the sample proportion of 11%.
However, if no prior knowledge of the sample proportion is assumed, a minimum sample size of 960 is required.
To calculate the minimum sample size, the formula n = (Z² * p * (1-p)) / E² is used, where n is the sample size, Z is the Z-value for the desired confidence level (1.96 for 95% confidence), p is the prior sample proportion, and E is the desired margin of error.
Therefore, assuming a prior knowledge of the sample proportion of 11%, a sample size of 1399 was needed. If no prior knowledge was assumed, a minimum sample size of 960 was required.
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Please help with these word problems!!!
The speed of the plane in still air is 87 mph and the speed of the wind is 29 mph.
The cost of one package of tulip bulbs is $10.8 and the cost of one bag of daffodil bulbs is $8.5.
A van can carry 14 students and a bus can carry 62 students.
There are 13 students in each van and 59 students in each bus.
How to calculate the speedLet the speed of the plane be p and the speed of the wind be w. Then we have the following system of equations:
p + w = d/t1 = 580/5 = 116
p - w = d/t2 = 580/10 = 58
Adding the two equations, we get:
2p = 174
p = 87 mph
Substituting this value into either equation, we get:
w = 29 mph
Therefore, the speed of the plane in still air is 87 mph and the speed of the wind is 29 mph.
Let the cost of one package of tulip bulbs be x and the cost of one bag of daffodil bulbs be y. Then we have the following system of equations:
6x + 12y = 198
7x + 6y = 127
Multiplying the second equation by 2 and subtracting it from the first equation, we get:
5x = 54
x = 10.8
Substituting this value into either equation, we get:
y = 8.5
Therefore, the cost of one package of tulip bulbs is $10.8 and the cost of one bag of daffodil bulbs is $8.5.
Let the number of students a van can carry be x and the number of students a bus can carry be y. Then we have the following system of equations:
16x + 8y = 752
5x + 5y = 380
Simplifying the second equation, we get:
x + y = 76
Multiplying this equation by 8 and subtracting it from the first equation, we get:
8x = 112
x = 14
Substituting this value into either equation, we get:
y = 62
Therefore, a van can carry 14 students and a bus can carry 62 students.
Let the number of students a van can carry be x and the number of students a bus can carry be y. Then we have the following system of equations:
16x + 5y = 417
10x + 8y = 480
Multiplying the first equation by 2 and subtracting it from the second equation, we get:
6x = 42
x = 7
Substituting this value into either equation, we get:
y = 51
Therefore, a van can carry 7 students and a bus can carry 51 students.
Let the number of students in each van be x and the number of students in each bus be y. Then we have the following system of equations:
14x + 16y = 1086
10x + 13y = 870
Multiplying the first equation by 13 and subtracting it from the second equation multiplied by 16, we get:
2x = 26
x = 13
Substituting this value into either equation, we get:
y = 59
Therefore, there are 13 students in each van and 59 students in each bus.
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7) A plane traveled 580 miles to Ankara and back. The trip there was with the wind. It took 5 hours. The trip back was into the wind. The trip back took 10 hours. Find the speed of the plane in still air and the speed of the wind.
8) Amanda and Ndiba are selling flower bulbs for a school fundraiser. Customers can buy packages of tulip bulbs and bags of daffodil bulbs. Amanda sold 6 packages of tulip bulbs and 12 bags of daffodil bulbs for a total of $198. Ndiba sold 7 packages of tulip bulbs and 6 bags of daffodil bulbs for a total of $127. Find the cost each of one package of tulips bulbs and one bag of daffodil bulbs.
9) The local amusement park is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 16 vans and 8 buses with 752 students. High School B rented and filled 5 vans and 5 buses with 380 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?
10) The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A rented and filled 16 vans and 5 buses with 417 students. High School B rented and filled 10 vans and 8 buses with 480 students. Every van had the same number of students in it as did the buses. How many students can a van carry? How many students can a bus carry?
11) The senior classes at High School A and High School B planned separate trips to the water park. The senior class at High School A rented and filled 14 vans and 16 buses with 1086 students. High School B rented and filled 10 vans and 13 buses with 870 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.
Write and solve an equation to find the product of 3 and (3)/(6). Assessment Write another expression that is equivalent to the product of 3 and (3)/(6).
The two expressions used to solve the product are 3 * (3/6) and (3/1) * (1/2). The product of the given expression is 3/2.
How do you multiply fractions and what is a fraction?A fraction is a number that expresses a portion of a total or the relationship between two quantities. Normally, it is written with a horizontal line separating the numerator from the denominator. The denominator represents the entirety or the second number, whereas the numerator represents a portion of the total or the first amount. The simplest way to multiply a fraction is to add the numerators and denominators together.
The product of 3 and (3/6), is:
3 * (3/6) = (3 * 3) / 6 = 9/6 = 3/2
Therefore, the product of 3 and (3/6) is 3/2.
Another expression that is equivalent to the product of 3 and (3/6) is:
3 * (3/6) = (3/1) * (1/2) = 3/2
This expression is equivalent to the previous one, as both represent the same value of 3/2.
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2. Solve each of the following then check:
a. 2^4x = 4^y+3
b. 9^4x = 27^x-1
Explain. What should the format of a problem be if using the Factoring Method? Can this method be applied for any quadratic problems? What are the limitations? Why do we make each factor equal to zero?
The factoring method is a technique used to solve quadratic equations of the form ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. To use the factoring method, we need to find two numbers that multiply to give c and add to give b. We then use these two numbers to factor the quadratic expression into two binomials, set each binomial equal to zero, and solve for x.
The format of a problem that can be solved using the factoring method should be in the form of ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable. The quadratic expression should be factorable into two binomials.
The factoring method can be applied to any quadratic problem that is in the correct format and is factorable. However, not all quadratic equations can be factored. In cases where the quadratic expression cannot be factored, we need to use other methods such as the quadratic formula or completing the square.
The main limitation of the factoring method is that it only works for quadratic equations that can be factored into two binomials. If the quadratic equation cannot be factored or if it has complex roots, then the factoring method cannot be used to solve the problem.
We make each factor equal to zero because if the product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for x to find the roots of the quadratic equation.
Find a formula for the exponential function passing through the points (5, 32567 ) and (4, 16
189). Use exact values, not decimals. f(x)=
As a result, the exponential function travelling between the points (5, 32567) and (4, 16189) has the following formula: function [tex]f(x) = 14000 * (1.007044628)^x[/tex]
what is function?Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.
f(x) = a * bx, where a and b are unknown constants. We have two places through which the function passes, which implies we have two equations:
[tex]f(5) = a * b^5 = 32567 f(4) = a * b^4 = 16189[/tex]
When we divide these two equations, we get:
[tex]b^5 / b^4 = 32567 / 16189 b = (32567 / 16189)^(1/1) = 1.007044628[/tex]
We may solve for a by substituting this value of b in any of the equations:
[tex]a = 16189 / b^4 = 16189 / (1.007044628)^4 = 14000[/tex]
As a result, the exponential function travelling between the points (5, 32567) and (4, 16189) has the following formula:
[tex]f(x) = 14000 * (1.007044628)^x[/tex]
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According to a survey by Accountemps, 48% of executives believe that employees are most productive on Tuesdays. Suppose 190 executives are randomly surveyed.
Appendix A Statistical Tables a. What is the probability that fewer than 85 of the executives believe employees are most productive on Tuesdays? b. What is the probability that more than 95 of the executives believe employees are most productive on Tuesdays? c. What is the probability that more than 79 of the executives believe employees are most productive on Tuesdays?
Therefore , the solution of the given problem of probability comes out to be P = 0.8236 , P= 0.0155 and P = 0.0203
What precisely is probability?The calculation of the probability that a statement is true or that a particular event will happen is the main objective of the patterns in the form known as hyperparameters. Chance can be represented by any number from range 0 and 1, where 1 typically signifies certainty and 0 typically signifies potential. A probability diagram illustrates the likelihood that a particular occurrence will take place.
Here,
Based on the survey findings, let p represent the likelihood that an executive thinks workers are most productive on Tuesdays: p = 0.48
Suppose there were n leaders who were surveyed: n = 190
Using Appendix A and the binomial distribution method, we can calculate:
=> P(X < 85) = P(X ≤ 84) = 0.0155
b. To determine the likelihood that more than 95 of the executives think that workers are most effective on Tuesdays, use Appendix A and the complement rule.
=> P(X > 95) = 1 - P(X ≤ 95) = 1 - 0.9797 = 0.0203
c. We need to compute P(X > 79) to determine the likelihood that more than 79 executives think workers are most productive on Tuesdays. This can be done using the complement rule and Appendix
A:
=> P(X > 79) = 1 - P(X ≤ 79) = 1 - 0.1764 = 0.8236
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