The initial number of bacteria in the colony was approximately 13.5.
The value of n, the number of bacteria at the start of the experiment, can be calculated using the formula n =
[tex](b/2)^(2/t),[/tex]
where b is the number of bacteria at any given time and t is the time in days.
Plugging in the given values, we get: n =
[tex](10,000/2)^(2/6)[/tex]
n =
[tex]2,500^(1/3)[/tex]
n ≈ 13.5. This formula is derived from the fact that the growth of bacteria is often modeled by an exponential function, where the rate of growth is proportional to the current population size.
In this case, the number of bacteria is doubling every 2 days (since [tex]2^(1/2) = 2^(2/4) = 2^(4/8) = ...),[/tex] so we can rewrite the original equation as n • [tex]2^(t/2)[/tex]. Using the given information that there are 10,000 bacteria 6 days after the experiment starts, we can plug in these values and solve for n using the derived formula.
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For the arithmetic sequence beginning with the terms (1, 4, 7, 10, 13, 16. },
what is the sum of the
first 19 terms?
The sum of the first 19 terms of the arithmetic sequence is 532.
We can find the sum of an arithmetic sequence by using the formula:
S = (n/2)(a1 + an)
where S is the sum of the first n terms of the sequence, a1 is the first term, and an is the nth term.
In this case, the first term is 1, and the common difference is 3 (since each term is 3 more than the previous term). So the nth term is:
an = a1 + (n - 1)d
an = 1 + (n - 1)3
an = 3n - 2
We want to find the sum of the first 19 terms, so:
n = 19
an = 3(19) - 2
an = 55
Now we can plug in the values into the formula:
S = (n/2)(a1 + an)
S = (19/2)(1 + 55)
S = 19(28)
S = 532
Therefore, the sum of the first 19 terms of the arithmetic sequence is 532.
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A teacher gave a 5 question multiple choice
quiz. Each question had 4 choices to select
from. If the a student completely guessed
on every problem, what is the probability
that they will have less than 3 correct
answers? (CDF)
A)0.896
B)0.088
C)0.984
D)0.264
Please help with my Aleks.
Answer:
64
Step-by-step explanation:
the total must be 60×4 =240
subtract the miles already given and that us your answer. You could also make an equation. (64+53+59+x)/4=
consider the -matrix and . we want to find the least-squares solution of the linear system using the projection onto the column space of . the projection of onto is 0 -1 -2 the least-square solution of is the solution of the linear system . thus is
The least-square solution H' is given by the solution vector in, resulting in H' = x = [0.6]. This solution minimizes the squared error between Ax and b and represents the best approximation for the given linear system.
The least-square solution of the linear system Ax = b can be found by projecting b onto the column space of A. Given the matrix A as [1 -1] and the vector b as [-2], the projection projcol(A)(b) of b onto Col(A) is approximately -0.3.
The least-square solution H' of Ax = b is obtained by solving the linear system Aîn = projcol(A)(b). In this case, the solution vector în is approximately [0.6]. Therefore, the least-square solution Ĥ for the given system is x = [0.6].
In order to find the least-square solution, we first compute the projection projcol(A)(b) of b onto the column space of A. This projection represents the closest point in the column space of A to the vector b. In this case, the projection is approximately -0.3. Next, we solve the linear system Aîn = projcol(A)(b), where A is the given matrix and în is the solution vector. By substituting the projection value, we get the equation [1 -1]în = -0.3. Solving this equation yields the value of în as approximately [0.6].
Therefore, the least-square solution H' is given by the solution vector în, resulting in H' = x = [0.6]. This solution minimizes the squared error between Ax and b and represents the best approximation for the given linear system.
Complete Question:
Finding the least square solution via projection ſi 1 0 Consider the 3 x 2-matrix A= 1 -1 and b= -2 We want to find the least-squares solution of the 1 0 -2 linear system Ax = b using the projection onto the column space of A. The projection projcol(A)(b) of b onto Col(A) is -0.3 projcol(A)(b) -2.3 x 0% 0.6 The least-square solution Ĥ of Ax = b is the solution of the linear system Aîn = projcol(A)(b). Thus în is 0.6 Â= ? x 0% 1.
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Can someone help me find the area of the regular polygons of numbers 1,2, and 3
To calculate the area of regular polygons with sides of length 1, 2, or 3 units, we need to calculate the Perimeter and Apothem using the appropriate formulas and then use the formula A = 1/2 * Perimeter * Apothem to obtain the area.
The area of a regular polygon can be calculated using the formula A = 1/2 * Perimeter * Apothem, where A is the area, Perimeter is the sum of all sides, and Apothem is the distance from the center of the polygon to the midpoint of any side.
For a regular polygon with sides of length 1, the Perimeter would be the product of the number of sides (also called the polygon's order) and the length of each side. Therefore, the Perimeter would be 1 x n, where n is the number of sides. The Apothem can be calculated using the formula Apothem = [tex]$\frac{1}{2}\left(\frac{1}{\tan\left(\frac{\pi}{n}\right)}\right)$[/tex], where π is pi and n is the number of sides. Substituting the values, we get Apothem = [tex]$\frac{1}{2}\left(\frac{1}{\tan\left(\frac{\pi}{n}\right)}\right)$[/tex]. Finally, we can use these values in the formula for area to get the area of the polygon.
Similarly, for a regular polygon with sides of length 2, we would use 2n as the Perimeter and the Apothem would be calculated using the same formula as before. For a polygon with sides of length 3, we would use 3n as the Perimeter and again calculate the Apothem using the same formula.
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Complete question:
What is the method for calculating the area of regular polygons with sides of length 1, 2, and 3 units?
A waterfall is 12. 8 km south of lake at a bearing of 242. How far away is the waterfall from the lake?
a news organization interested in chronicling winter holiday travel trends conducted a survey. of the 96 people surveyed in the eastern half of a country, 42 said they fly to visit family members for the winter holidays. of the 108 people surveyed in the western half of the country, 81 said they fly to visit family members for the winter holidays. use excel to construct a 99% confidence interval for the difference in population proportions of people in the eastern half of a country who fly to visit family members for the winter holidays and people in the western half of a country who fly to visit family members for the winter holidays. assume that random samples are obtained and the samples are independent. round your answers to three decimal places.
The 99% confident interval for the difference in population proportions of people in the eastern half and western half of the country who fly to visit family members for the winter holidays is between -0.407 and -0.013.
The following formula can be used to create a confidence interval for the difference in population proportions:
CI = (p1 - p2) ± z√((p1(1-p1)/n1) + (p2(1-p2)/n2))
where:
p1 = proportion of people in the eastern half who fly to visit family members
p2 = proportion of people in the western half who fly to visit family members
n1 = sample size from the eastern half
n2 = sample size from the western half
z = critical value for the appropriate level of confidence from the standard normal distribution
We want a 99% confidence interval, so z = 2.576.
Plugging in the values we have:
p1 = 42/96 = 0.4375
p2 = 81/108 = 0.75
n1 = 96
n2 = 108
CI = (0.4375 - 0.75) ± 2.576√((0.4375(1-0.4375)/96) + (0.75*(1-0.75)/108))
CI = (-0.407, -0.013)
Therefore, we have 99% confidence that the actual difference in population proportions of those traveling by plane to see family for the winter holidays in the eastern and western halves of the nation is between -0.407 and -0.013.
This shows that a bigger percentage of people go by plane to see family over the winter vacations in the western part of the country.
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please state the appropriate statistical test being used: I.e : (t - test for independent samples, z scores, single sample t test, t test for related samples, pearson correlation, Chi-square goodness of fit, Chi-square test for independence).
A graduate student in developmental psychology believes that there may be a relationship between birth weight and subsequent IQ. She randomly samples seven psychology majors at her university and gives them an IQ test. Next, she obtains the weight at birth of the seven majors from the appropriate hospitals (after obtaining permission from the students, of course).
The data are shown in the following table:
Student 1 2 3 4 5 6 7
Birth Weight (lbs) 5.8 6.5 8.0 5.9 8.5 7.2 9.0
IQ 122 120 129 112 127 116 130
What can the graduate student conclude? Use a = 0.05
State the appropriate statistical test:
H0:
H1:
df (if appropriate) and Critcal Value :
State Results, Decision, and Conclusions:
The graduate student cannot reject the null hypothesis that there is no significant correlation between birth weight and subsequent IQ among psychology majors at the university.
The appropriate statistical test to use in this scenario is the Pearson correlation coefficient.
H0: There is no significant correlation between birth weight and subsequent IQ.
H1: There is a significant correlation between birth weight and subsequent IQ.
df = n-2 = 7-2 = 5 (where n is the sample size)
Critical value (at alpha = 0.05 and df = 5) = ±2.571
Using a statistical software or calculator, we can find that the sample correlation coefficient is 0.758, with a p-value of 0.076.
Since the p-value is greater than the alpha level of 0.05, we fail to reject the null hypothesis. Therefore, we cannot conclude that there is a significant correlation between birth weight and subsequent IQ among psychology majors at the university.
In conclusion, the graduate student cannot reject the null hypothesis that there is no significant correlation between birth weight and subsequent IQ among psychology majors at the university.
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HELP need help ASAP (!!!!!!)
The value of component form and the magnitude of the vector v is,
v = √52
We have to given that;
Two points on the graph are, (3, 5) and (- 1, - 1)
Hence, We can formulate value of component form and the magnitude of the vector v is,
v = √ (x₂ - x₁)² + (y₂ - y₁)²
v = √(- 1 - 3)² + (- 1 - 5)²
v = √16 + 36
v = √52
Thus, The value of component form and the magnitude of the vector v is,
v = √52
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Perform the following operations and prove closure. Show your work.
x/x+3 + x+2/x+5
The value of simplify expression is,
⇒ (2x² + 10x + 6) / (x ² + 8x + 15)
We have to given that;
The expression is,
⇒ x/(x +3) + (x + 2) / (x+5)
Now, We can simplify as;
⇒ x (x + 5) + (x + 3) (x + 2) / (x+ 3) (x + 5)
⇒ (x² + 5x + x² + 3x + 2x + 6) (x² + 3x + 5x + 15)
⇒ (2x² + 10x + 6) / (x ² + 8x + 15)
Thus, The value of simplify expression is,
⇒ (2x² + 10x + 6) / (x ² + 8x + 15)
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When tossing a two-sided, fair coin with one side colored yellow and the other side colored green, determine P(yellow).
yellow over green
green over yellow
2
one half
The calculated value of the probability P(yellow) is 0.5 i.e. one half
How to determine P(yellow).From the question, we have the following parameters that can be used in our computation:
Sections = 2
Color = yellow, and green
Using the above as a guide, we have the following:
Yellow = 1
When the yellow section is selected, we have
P(yellow) = yellow/section
The required probability is
P(yellow) = 1/2
Evaluate
P(yellow) = 0.5
Hence, the value is 0.5
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How do you write 13 over five as a percentage
Answer this question You want to estimate the first derivative of f(x), given values of the function at discrete points x = 0, 0.1, 0.2, ..., 1. Which of these formulas is appropriate for estimating f'(1) if h > 0? 2h Select the correct answer A none B f'(x) =3f(x)+4 f(x +h)-f(x+2h)/2h C f'(x) =-3f(x)+4 f(x -h)-f(x-2h)/2h D f'(x)=f(x+h)-f(x-h) E f'(x) = f[(x+h)-f(x+2h)/ 2h
The appropriate formula for estimating f'(1) if h > 0 is D, which is f'(x) = f(x+h) - f(x-h). This is because the formula uses the values of the function at two points that are equidistant from the point at which the derivative is being estimated, which is x=1 in this case. Additionally, this formula uses a discrete difference approach, which is appropriate for estimating derivatives given discrete data points.
The step size h between the data points is defined as h = 1/n, where n is the number of discrete data points for the function f(x) for values of x from 0 to 1.
We must determine the values of the function at x = 1+h and x = 1-h in order to estimate the first derivative of f(x) at x = 1 using the central difference approach.
Depending on where the data points are located, we can extrapolate or interpolate using the given data points to predict the function value at x = 1+h and x = 1-h.
Once we know the values of the function at x = 1+h and x = 1-h, we may estimate the first derivative at x = 1 using the central difference approach and the formula D, which is f'(x) = f(x+h) - f(x-h).
The value of h should be big enough to prevent rounding errors while still being small enough to offer an accurate approximation of the derivative. H typically has a value of 0.001.
This formula only applies to smooth functions; it may not be effective for functions with abrupt corners or discontinuities. This is a crucial point to remember. Other techniques for determining the derivative might be more suitable in such circumstances.
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A store owner wants to buy a new rectanglar rug the rug must be between 55 aqnd 65 square feet and the side lenght must be less than 10 feet draw a rectangel that could repersent the new rug
A rectangle with a length less than 10 feet and an area between 55 and 65 square feet.
Let's call the length of the rectangle "l" and the width "w". We know that the area of a rectangle is given by the formula A = lw. We also know that the area of the rug must be between 55 and 65 square feet. Therefore:
55 ≤ lw ≤ 65
Since the length of the rectangle must be less than 10 feet, we have:
l < 10
We can use these two conditions to draw a rectangle that satisfies both requirements. For example, we could draw a rectangle with a length of 8 feet and a width of 7 feet, which gives an area of 56 square feet. This rectangle satisfies both conditions since 55 ≤ 56 ≤ 65 and 8 < 10.
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You want to estimate the average gas price in your city for a gallon of regular gas you take a random sample of the prices from 15 gas stations and find the average costs is $2:42 with a standard deviation of $0.017 create a 99% confidence interval for the mean price for a gallon of gasoline
Answer:
if being beautiful was a crime you would be innocent
Step-by-step explanation:
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Find an equation of the tangent line to the curve at the point (36,6). y = VxTo find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (36, 6), we know that (36, 6) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x = a can be found using the formula Mtan = lim f(x) - fla)/ x-a\a In this situation, the function is f(x) = ___
We can find its derivative and evaluate it at x=36 to find the slope of the tangent line, and then use the point-slope formula to find the equation of the line.
To find the derivative of y = Vx, we use the power rule, which states that if y = xn, then y' = nx^(n-1). In this case, y = Vx⁽¹/²⁾, so y' = V(1/2)x(-1/2) = V/(2sqrt(x)). Evaluating this at x=36, we get y' = V/12. Therefore, the slope of the tangent line is m = V/12. Using the point-slope formula, we get the equation of the tangent line as y - 6 = (V/12)(x - 36).
In summary, to find the equation of the tangent line to the curve at the point (36,6), we first found the derivative of the function y = [tex]Vx^{1/2}[/tex], which is y' = V/(2sqrt(x)). Evaluating this at x=36, we get y' = V/12, which is the slope of the tangent line. Using the point-slope formula, we then found the equation of the tangent line as y - 6 = (V/12)(x - 36).
To explain this answer in more detail, we can first note that the function
y = [tex]Vx^{1/2}[/tex] represents a square root function with a vertical stretch factor of V. This means that the graph of the function is a curve that starts at the origin and increases slowly at first, then more rapidly as x gets larger. The point (36,6) is on this curve, and we are asked to find the equation of the tangent line to the curve at this point.
To find the slope of the tangent line, we use the formula Mtan = lim f(x) - f(a)/ x-a\a, where f(x) is the function and a is the point where we want to find the tangent line. In this case, a = 36 and f(x) = Vx^(1/2), so we have [tex]Mtan=lim Vx^{1/2} - V(36)^{1/2}/ x-36/a[/tex]. We can simplify this expression by multiplying the numerator and denominator by the conjugate of the numerator, which is [tex]Vx^{1/2} +V(36)x^{1/2}[/tex] As x approaches 36, we can use L' Hopital's rule to evaluate the limit, which gives us Mtan = V/12.
Now that we have the slope of the tangent line, we can use the point-slope formula to find the equation of the line. The point-slope formula states that if the slope of a line is m and a point on the line is (x1,y1), then the equation of the line is y - y1 = m(x - x1). In this case, the point is (36,6) and the slope is V/12, so the equation of the tangent line is y - 6
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A number r has 8 added to it and the result is multiplied by 4
Is it:
8x4
4(r+8)
4r+8
8+rx4
r+8x4
Answer:
Step-by-step explanation:
A number r has 8 added to it
r+8
Then the result is multiplied by 4
To make sure the addition is done first, use PEMDAS
so add a parenthesis so addition goes before multiplication
(r+8) * 4
or 4*(r+8)
henry and liani have 200 feet of wood to frame a flower bed. henry wants the bed to be a square, while liani wants it to be a rectangle with dimensions of 55 feet and 45 feet. find the area of henry's flower bed. area
The area of Henry's flower bed would be 2500 square feet.
Let's start by finding the perimeter of Henry's flower bed since we know that he wants it to be a square. If we let s be the length of one side of the square, then the perimeter would be:
4s = 200
Simplifying this equation, we get:
s = 50
So Henry's flower bed will have sides of 50 feet each.
To find the area of the flower bed, we can use the formula:
Area = side^2
So in this case, the area would be:
Area = 50^2 = 2500 square feet
Therefore, the area of Henry's flower bed would be 2500 square feet.
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How do you Simplify the expression. –3x(4–5x) + (3x + 4)(2x – 7)
The simplified expression is [tex]21x^2 - 25x - 28[/tex] in the given case.
An expression in mathematics is a combination of numbers, symbols, and operators (such as +, -, x, ÷) that represents a mathematical phrase or idea. Expressions can be simple or complex, and they can contain variables, constants, and functions.
"Expression" generally refers to a combination of numbers, symbols, and/or operations that represents a mathematical, logical, or linguistic relationship or concept. The meaning of an expression depends on the context in which it is used, as well as the specific definitions and rules that apply to the symbols and operations involved. For example, in the expression "2 + 3", the plus sign represents addition and the meaning of the expression is "the sum of 2 and 3", which is equal to 5.
To simplify the expression, first distribute the -3x and (3x + 4) terms:
[tex]-3x(4 - 5x) + (3x + 4)(2x - 7) = -12x + 15x^2 + (6x^2 - 21x + 8x - 28)[/tex]
Next, combine like terms:
[tex]-12x + 15x^2 + (6x^2 - 21x + 8x - 28) = 21x^2 - 25x - 28[/tex]
Therefore, the simplified expression is [tex]21x^2 - 25x - 28.[/tex]
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Solve the system by substitution
y=-4x
y=x-5
Answer:
Point form:
(1,-4)
Equation form:
x=1,y=-4
Step-by-step explanation:
Answer:
Step-by-step explanation:
The solution to the system of equations by substitution is x = 1 and y = -4.
To solve the system of equations by substitution, we can substitute the expression for y from the first equation (-4x) into the second equation (y = x - 5), resulting in -4x = x - 5. By rearranging the equation and solving for x, we get x = 1. Substituting this value back into the first equation, we find y = -4.
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Solve the following equation for the variable given
Sole Y=mx+b for b
The solution for b is y-mx in the equation y=mx+b.
The given equation is y=mx+b
y equal r=to m times of x plus b
We need to solve for b in the equation
To solve we have to isolate b from the equation
Subtract mx from both sides
y-mx=b
Hence, the solution for b is y-mx in the equation y=mx+b.
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What is the preimage of (11.-4) using the translation (x,y) --------> (x-17, y+2)
The coordinate of the point after the translation will be (-6, -2).
Given that:
Point, (11, -4)
Transformation rule, (x - 17, y + 2)
The translation does not change the shape and size of the geometry. But changes the location.
The coordinate of the point after the translation is calculated as,
⇒ (x - 17, y + 2)
⇒ (11 - 17, -4 + 2)
⇒ (-6, -2)
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The value of a phone when it was purchased was $500. It loses 1/5 of its value a year. What is the value of the phone after 1 year?
Answer:
[tex]\huge\boxed{\sf \$400}[/tex]
Step-by-step explanation:
Value of phone = $500
Loss in price = 1/5 of total price
Loss in price:= 1/5 × 500 (of means to multiply)
= 1 × 100
= $100
Value of phone after one year:= Actual price - loss
= 500 - 100
= $400[tex]\rule[225]{225}{2}[/tex]
Find the absolute extrema of f(x) = x^6/7 on the interval (-2, -1]
The absolute maximum of f(x) =
[tex]x^( \frac{6}{7} )[/tex]
on the interval (-2, -1] occurs at x = -1, and the absolute maximum value is 1.
To find the absolute extrema of f(x) on the given interval, we need to evaluate the function at the endpoints and at the critical points within the interval. However, since the function is continuous and differentiable on the interval, the only potential critical point is where its derivative is equal to zero.
Taking the derivative of f(x), we get f'(x) =
[tex](6/7)x^( \frac{1}{7} )[/tex]
Setting this equal to zero, we get x = 0, which is outside the given interval.
Therefore, we only need to evaluate the function at the endpoints of the interval. Plugging in x = -2 and x = -1, we get f(-2) =
[tex](-2)^( \frac{6}{7})[/tex]
≈ 1.419 and f(-1) =
[tex](-1)^( \frac{6}{7} )[/tex]
= 1.
Since f(-1) = 1 is greater than f(-2), we have found the absolute maximum value of the function on the interval (-2, -1], and it occurs at x = -1.
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WHAT IS THE AREA OF A TRAPEZOID WITH COORDINATES (1,4) (1,-3) (6,6) (6,-5)
Answer:
THESE NUTS
Step-by-step explanation:
2. An organization has 20 male and 18 female members. In how many ways can five male and five female members be selected to sit on the board of directors? Explain your solution (12)
To determine the number of ways to select five male and five female members for the organization's board of directors, we'll use the combination formula C(n, r) = n! / (r! * (n-r)!). So, there are 132,819,072 ways to select five male and five female members for the organization's board of directors.
For the male members, n = 20 and r = 5. So, we'll calculate C(20, 5):C(20, 5) = 20! / (5! * (20-5)!)
C(20, 5) = 20! / (5! * 15!)
C(20, 5) = 15,504
For the female members, n = 18 and r = 5. So, we'll calculate C(18, 5):C(18, 5) = 18! / (5! * (18-5)!)C(18, 5) = 18! / (5! * 13!)C(18, 5) = 8,568Now, we'll multiply the number of ways to choose male and female members to get the total number of ways to form the board of directors:Total ways = 15,504 (male) * 8,568 (female)Total ways = 132,819,072know more about combination formula here: https://brainly.com/question/28065038
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What test to see if the difference between groups is statistically significant?
The level of significance, typically set at 0.05, is used to determine whether the observed difference is statistically significant or simply due to chance
To determine whether the difference between groups is statistically significant, you would typically use a hypothesis test such as a t-test, ANOVA (analysis of variance), or a chi-square test. These tests are used to compare the means or proportions of different groups and calculate the probability of obtaining the observed difference by chance. The level of significance, typically set at 0.05, is used to determine whether the observed difference is statistically significant or simply due to chance. To determine if the difference between groups is statistically significant, you can use a hypothesis test called the t-test. The t-test compares the means of two groups and takes into account the sample size and variance within each group. This test helps you determine if there is a significant difference between the groups or if the observed difference is due to random chance.
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a simple random sample of 100 8th graders at a large suburban middle school indicated that 84% of them are involved with some type of after school activity. find the 90% confidence interval that estimates the proportion of them that are involved in an after school activity. a) (0.700, 0.900) b) (0.780, 0.700) c) (0.780, 0.900) d) (0.830, 0.835) e) (0.680, 0.850) f) none of the above
The 90% confidence interval for the proportion of 8th graders involved in after school activities is c) (0.780, 0.900).
To find the confidence interval, we need to use the formula:
CI = p ± zα/2 * √(p(1-p)/n)
where:
p is the sample proportion (84% or 0.84 in decimal form)
zα/2 is the z-score for the desired confidence level (90% or 1.645 for a two-tailed test)
n is the sample size (100)
Substituting the values, we get:
CI = 0.84 ± 1.645 * √(0.84(1-0.84)/100)
CI = 0.84 ± 0.078
CI = (0.762, 0.918)
Rounding to three decimal places, we get the final answer of (0.780, 0.900) as the confidence interval for the proportion of 8th graders involved in after school activities. Therefore, the correct answer is (c).
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What is an obtuse angle?
Answer: An obtuse angle is an angle that measures between 90 and 180 degrees. An obtuse angle is wider than a right angle but narrower than a straight angle.
Step-by-step explanation:
Answer:
Obtuse angle is any angle greater than 90°: Straight angle is an angle measured equal to 180°: Zero angle is an angle measured equal to 0°: Complementary angles are angles whose measures have a sum equal to 90°: Supplementary angles are angles whose measures have a sum equal to 180°.
Question 1 Consider triangle ABC Not yet answered Marked out of 1.00 8 cm P Flag Question с B 15 cm What is the correct length of AB? Select one: O A 12.68 cm OB 23 cm OC 12.69 cm OD. 7 cm What is the perimeter and area of the triangle ABC? Question 2 Not yet answered A Marked out of 1.00 8 cm P Flag question C C B 15 cm Note: If you have not done so already, you will first need to determine the length of side AB in order to calculate these values. Select one: O A. 35.69 cm and 50.75 cm O B. 30 cm and 28 cm OC. 35.68 cm and 50.72 cm2 OD 46 cm and 92 cm2
The perimeter of triangle ABC is 40 cm and the area is 84.85 cm^2.
To get the length of AB in triangle ABC, we can use the Pythagorean theorem since we are given the lengths of sides BC and AC. Using the theorem, we get:
AB^2 = BC^2 + AC^2
AB^2 = 15^2 + 8^2
AB^2 = 225 + 64
AB^2 = 289
AB = √289
AB = 17 cm
Therefore, the length of AB is 17 cm.
To find the perimeter of triangle ABC, we need to add up the lengths of all three sides:
Perimeter = AB + BC + AC
Perimeter = 17 + 15 + 8
Perimeter = 40 cm
To get the area of triangle ABC, we can use the formula: Area = (1/2) x base x height
Since we do not know the height of triangle ABC, we can use the length of side AB as the base and draw a perpendicular line from point C to AB, creating a right triangle. This right triangle has base AB and height h, which we can solve for using the Pythagorean theorem:
h^2 = AC^2 - (AB/2)^2
h^2 = 8^2 - (17/2)^2
h^2 = 64 - 144.5
h^2 = -80.5 (not a possible value)
However, we can see that the height of triangle ABC is outside the triangle, meaning that the triangle is obtuse and the height extends beyond the opposite side. Therefore, we cannot use the formula for the area of a triangle with a right triangle base.
Instead, we can use Heron's formula, which is:
Area = √(s(s-a)(s-b)(s-c))
where s is the semi-perimeter (half of the perimeter), and a, b, and c are the lengths of the sides. In this case, we have:
s = (a + b + c)/2 = (17 + 15 + 8)/2 = 20
a = AB = 17
b = BC = 15
c = AC = 8
Plugging these values into the formula, we get: Area = √(20(20-17)(20-15)(20-8))
Area = √(20(3)(5)(12))
Area = √(7200)
Area = 84.85 cm^2
Therefore, the perimeter of triangle ABC is 40 cm and the area is 84.85 cm^2.
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