The volume of the object is 168.96 cubic units. The volume of the object can be found using the formula for volume of a solid with known cross-sections : [tex]V = ∫ A(x)dx[/tex], where [tex]A(x)[/tex] is the area of the cross-section at x.
In this case, the cross-sections are triangles with equal base and height. The area of a triangle is A = 1/2bh, so the area of the cross-section at x is [tex]A(x) = 1/2b^2.[/tex]
The base of the triangle is the distance between the two curves, which is [tex]6−3/8 x^2 - 0 = 6−3/8 x^2.[/tex] So the area of the cross-section is [tex]A(x) = 1/2(6−3/8 x^2)^2.[/tex]
Now we can find the volume by integrating the area function over the x-values of the base region. The base region is bounded by the curve [tex]y=6−3/8 x^2[/tex], so the x-values are the roots of this equation:
[tex]0 = 6−3/8 x^2 3/8 x^2 = 6 x^2 = 16 x = ±4[/tex]
So the volume is:
[tex]V = ∫[−4,4] 1/2(6−3/8 x^2)^2dx = 1/2 ∫[−4,4] (36 - 9/4 x^2 + 9/64 x^4)dx[/tex]
[tex]= 1/2 [(36x - 3/4 x^3 + 9/320 x^5)] from x=-4 to x=4 = 1/2 [(288 - 192 + 72.96) - (-288 + 192 - 72.96)] = 1/2 (576 - 384 + 145.92) = 1/2 (337.92)[/tex]
= 168.96 , So the volume of the object is 168.96 cubic units.
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A large company put out an advertisement in a magazine for a job opening. The first day the magazine was published the company got 125 responses, but the responses were declining by 24% each day. Assuming the pattern continued, how many total responses would the company get over the course of the first 8 days after the magazine was published, to the nearest whole number?
18 responses would the company get over the course of the first 8 days after the magazine was published.
What is a geometric sequence?
A geometric progression, often referred to as a geometric sequence, is a series of non-zero values where each term following the first is obtained by multiplying the preceding value by a constant, non-zero number known as the common ratio.
Here, we have
Given: A large company put out an advertisement in a magazine for a job opening. On the first day, the magazine was published the company got 125 responses, but the responses were declining by 24% each day.
We apply here geometric sequence.
aₙ = arⁿ⁻¹
where
aₙ = n^{th} term of the sequence
r = is the common ratio
a = the first term of the sequence
a = 125
r = 100% - 24% = 76% = 76/100 = 0.76
aₙ = (125)(0.76)⁸⁻¹
aₙ = 125(0.76)⁷
aₙ = 18
Hence, 18 responses would the company get over the course of the first 8 days after the magazine was published.
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Answer:
463 (to the nearest whole number)
Step-by-step explanation:
We can model the given scenario as a geometric sequence.
The first term, a, is the number of responses the company got on the first day:
a = 125The common ratio is the number you multiply by at each stage of the sequence. As the responses are declining by 24% each day, then each day the responses are 76% of the previous day's responses, since 100% - 24% = 76%. Therefore, the common ratio, r, is:
r = 0.76To calculate the total responses the company would get over the course of the first 8 days after the magazine was published, use the Geometric Series formula.
[tex]\boxed{\begin{minipage}{7 cm}\underline{Sum of the first $n$ terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]
Substitute a = 125, r = 0.76 and n = 8 into the formula and solve for S:
[tex]\implies S_8=\dfrac{125(1-0.76^8)}{1-0.76}[/tex]
[tex]\implies S_8=\dfrac{125(1-0.111303478...)}{0.24}[/tex]
[tex]\implies S_8=\dfrac{125(0.888696521...)}{0.24}[/tex]
[tex]\implies S_8=\dfrac{111.087065...}{0.24}[/tex]
[tex]\implies S_8=462.862771...[/tex]
[tex]\implies S_8=463[/tex]
Therefore, the total number of responses the company would get over the course of the first 8 days after the magazine was published is 463 to the nearest whole number.
Find the absolute maximum and minimum of the function on the given domain.
f(x,y)=7x^2+2y^2 on the closed triangular plate bounded by the lines x=0, y=0, y+2x=2 in the first quadrant
The absolute maximum is ?
The absolute minimum is ?
The absolute maximum of the function f(x,y)=7x^2+2y^2 on the given domain is 28 and the absolute minimum is 0.
The absolute maximum and minimum of the function f(x,y)=7x^2+2y^2 on the closed triangular plate bounded by the lines x=0, y=0, y+2x=2 in the first quadrant can be found by using the method of Lagrange multipliers.
First, we need to find the critical points of the function on the interior of the triangular plate. The gradient of the function is given by ∇f = <14x, 4y>. Setting ∇f = 0, we get x = 0 and y = 0. However, these points are on the boundary of the triangular plate, so they are not critical points on the interior.
Next, we need to find the critical points on the boundary of the triangular plate. We can use the method of Lagrange multipliers to do this. The constraint equation is given by g(x,y) = y + 2x - 2 = 0. The gradient of the constraint equation is given by ∇g = <2, 1>. Setting ∇f = λ∇g, we get the following system of equations:
14x = 2λ
4y = λ
y + 2x - 2 = 0
Solving this system of equations, we get two critical points: (2/3, 2/3) and (2, 0).
Finally, we need to evaluate the function at the critical points and at the corners of the triangular plate to find the absolute maximum and minimum. The function values at these points are:
f(0,0) = 0
f(2/3, 2/3) = 14/3
f(2,0) = 28
f(0,2) = 8
The absolute maximum is 28 and the absolute minimum is 0.
Therefore, the absolute maximum of the function on the given domain is 28 and the absolute minimum is 0.
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Which two statements are true???????
The statements that is true is option C FG ⊥ HB and FG ║ DE, that is FG is perpendicular to HB and parallel to DE.
What are perpendicular and parallel lines?Geometry's use of parallel and perpendicular lines is crucial, and their distinctive qualities make it simple to distinguish between them. If two lines are in the same plane, are spaced equally apart, and never cross one another, they are said to be parallel. Perpendicular lines are those that cross at an angle of 90 degrees. Two straight lines are said to be parallel if they are located in the same plane and never cross one another. On the other hand, two lines are said to be perpendicular when they cross each other at a 90° angle.
From the given figure we observe that, the angle between the segments FG and HB is 90 degrees thus,
FG ⊥ HB.
Also, DE ⊥ HB, thus the segments FG ║ DE.
Hence, the statements that is true is option C FG ⊥ HB and FG ║ DE, that is FG is perpendicular to HB and parallel to DE.
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Suppose we want to estimate the proportion of center party sympathizers with a 95% confidence interval with a statistical margin of error of at most 2% points. How large a sample do we need to take, if we assume that the percentage of centrists is about 6%?
sample=38
To calculate the size of the sample you need to take in order to estimate the proportion of center party sympathizers with a 95% confidence interval and a statistical margin of error of at most 2% points, you can use the formula n = (Zα/2/E)2 × p × (1-p), where n is the sample size, Zα/2 is the z-score of the desired confidence level (in this case, 1.96 for a 95% confidence interval), E is the margin of error (2%), and p is the population proportion (6%).
Plugging in the values from the question, we get n = (1.96/2)2 × 6% × (1 - 6%) = 38.4. Therefore, the sample size needed to estimate the proportion of center party sympathizers with a 95% confidence interval and a statistical margin of error of at most 2% points is 38.
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find number of conversion periods and rate of interest when compounded half-yearly for a sum of Rs 5000 is taken for 7 years and 9% p.a
The rate of interest when compounded half-yearly is 4.45% and there are 14 conversion periods.
Solving compounded interestThe formula for calculating the compound interest is:
A = P (1 + r/n)^(n*t)
Where:
A = Final amountP = Principal amountr = Annual interest rate (as a decimal)n = Number of times the interest is compounded per yeart = Time period (in years)In this case, P = Rs 5000, r = 9% p.a. and the interest is compounded half-yearly (i.e., n = 2).
To find the number of conversion periods, we need to multiply the number of years by the number of conversion periods per year:
Number of conversion periods = n*t = 2 * 7 = 14
So there are 14 conversion periods in 7 years.
To find the rate of interest when compounded half-yearly, we can rearrange the formula and solve for r:
A = P (1 + r/n)^(nt)
A/P = (1 + r/n)^(nt)
(1 + r/n) = (A/P)^(1/nt)
r/n = (A/P)^(1/nt) - 1
r = n[(A/P)^(1/n*t) - 1]
Substituting the given values, we get:
r = 2[(5000*(1 + 0.09/2)^(27))^(1/(27)) - 1]
= 0.0445 or 4.45%
Therefore, the rate of interest when compounded half-yearly is 4.45%.
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Please help me answer my homework in the image
Answer:
4 bc if u go by the side where a block counts u count it till that side ends and it will be 4
Quality Progress, February 2005, reports on improvements in customer satisfaction and loyalty made by Bank of America. A key measure of customer satisfaction is the response (on a scale from 1 to 10) to the question: "Considering all the business you do with Bank of America, what is your overall satisfaction with Bank of America?" Here, a response of 9 or 10 represents "customer delight." Suppose that the survey selected 350 customers. Assume that 48% of Bank of America customers would currently express customer delight. That is, assume p = .48.
Find the probability that the sample proportion obtained from the sample of 350 Bank of America customers would be within three percentage points of the population proportion. That is, find P(.45 < Picture < .51). (Round your answer to 4 decimal places. Do not round intermediate values. Round z-value to 2 decimal places.) P(.45 < Picture < .51) .7372
Find the probability that the sample proportion obtained from the sample of 350 Bank of America customers would be within six percentage points of the population proportion. That is, find P(.42 < Picture < .54). (Round your answer to 4 decimal places. Do not round intermediate values. Round z-value to 2 decimal places.) P(.42 < Picture < .54)
From the given data, the probability that the sample proportion is between 0.45 and 0.51 is approximately 0.7372 and between 0.42 and 0.54 is 0.9772.
To solve this problem, we can use the central limit theorem, which states that the distribution of sample proportions will be approximately normal for large sample sizes.
Given that the population proportion is p = 0.48 and the sample size is n = 350, we can calculate the standard error of the sample proportion as:
SE = √(p × (1 - p) / n) = √(0.48 × 0.52 / 350) = 0.025
We want to find the probability that the sample proportion is within three percentage points of the population proportion, or in other words, between 0.45 and 0.51. To do this, we can standardize the sample proportion using the standard error:
z = (P - p) / SE = (0.45 - 0.48) / 0.025 = -1.2
z = (P - p) / SE = (0.51 - 0.48) / 0.025 = 1.2
Using a standard normal distribution table or calculator, we can find the area under the curve between these two z-values, which represents the probability that the sample proportion is within three percentage points of the population proportion:
P(-1.2 < z < 1.2) = 0.7372
To find the probability that the sample proportion is within six percentage points of the population proportion, or between 0.42 and 0.54, we can use the same approach:
z = (P - p) / SE = (0.42 - 0.48) / 0.025 = -2.4
z = (P - p) / SE = (0.54 - 0.48) / 0.025 = 2.4
Again, using a standard normal distribution table or calculator, we can find the area under the curve between these two z-values:
P(-2.4 < z < 2.4) = 0.9772
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The soccer team plays every 4 days and the basketball team plays every 5 days. When will both teams have games on the same day again?
Answer:
Step-by-step explanation:
The soccer team:
1 2 3 4, 1 2 3 4, 1 2 3 4, 1 2 3 4, 1 2 3 4
The basketball team:
1 2 3 4 5, 1 2 3 4 5, 1 2 3 4 5, 1 2 3 4 5.
[ the bold number is the day of playing ]
Hope this helps.
Consider the following formulas.
a sin Bθ + b cos Bθ = a2 + b2 sin(Bθ + C), where C = arctan(b/a) and a > 0
a sin Bθ + b cos Bθ = a2 + b2 cos(Bθ − C), where C = arctan(a/b) and b > 0
Use the formulas given above to write the trigonometric expression in the form a sin Bθ + b cos Bθ.
11 cos (θ − π/ 4)
The trigonometric expression 11 cos (θ − π/4) in the form a sin Bθ + b cos Bθ is 11/√2 cos θ.
What is the trigonometric expression?
The write the trigonometric expression in the required, we can start by using the second formula:
a sin Bθ + b cos Bθ = a^2 + b^2 cos(Bθ − C)
where;
C = arctan(a/b) and b > 0Let a = 11 and b = 11/√2, and Bθ = θ − π/4.
Then C = arctan(a/b) = arctan(11/(11/√2)) = arctan(√2).
Substituting these values, we get:
11 cos (θ − π/4) = 11/√2 cos (θ − π/4 + arctan(√2))
= 11/√2 cos (θ - π/4 + π/4)
= 11/√2 cos θ
Thus, we have written the trigonometric expression 11 cos (θ − π/4) in the form a sin Bθ + b cos Bθ as 11/√2 cos θ.
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Test Prep: Simplify −5 (7 + x) + 2 5/6x.
Answer:
-35 - 5/6x
Step-by-step explanation:
Somebody please help me with my homework
The missing angle measures are 50 degrees, 100 degrees, and 80 degrees.
x = 50, we can substitute this value into the expressions for the other two angles:
2x = 2(50) = 100
x + 30 = 50 + 30 = 80
What are angles?When two rays are united at a common point, an angle is created. The two rays are referred to as the arms of the angle, while the common point is referred to as the node or vertex. The symbol stands for the angle. Angle is a derivative of the Latin word "Angulus."
The construction of an angle is a type of geometric shape made by connecting two rays at their termini. Three letters that make up the shape of the angle can alternatively be used to symbolize the angle, with the middle letter indicating the location of the angle (i.e.its vertex).
From the question:
The total of the measures of the angles in any triangle is always 180 degrees, as shown by the characteristics of triangle angles.
This knowledge allows us to construct an equation to account for the missing angle measurements:
x + 2x + 30 = 180
Combining like terms, we get:
3x + 30 = 180
Subtracting 30 from both sides, we get:
3x = 150
Dividing both sides by 3, we get:
x = 50
Knowing that x = 50, we can change the formulas for the remaining two angles to reflect this value:
2x = 2(50) = 100
x + 30 = 50 + 30 = 80
As a result, the missing angle measurements are 50, 100, and 80 degrees.
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alice wanted to buy 10 markers but was short of $5.20.Then she divided to buy 6 markers and used the remaining 4.40 to buy lunch. how much money did she have at first
Answer: k
Step-by-step explanation:
tddthvbkj
What is -5/6 divided -1/3? answers A -5/18 B -5/2 C 5/2 D 5/18
the numerators are both negative, the answer will be a negative number. The numerator of the first fraction (-5) divided by the numerator of the second fraction (5) is -1. Multiply this answer by the common denominator (18) to get the final answer: -5/2.
To solve this fraction division problem, first convert the fractions to have a common denominator. To do this, multiply the denominator of the first fraction (-1/3) by the denominator of the second fraction (6), and the denominator of the second fraction (6) by the denominator of the first fraction (-1/3). This will change the fractions to -5/18 and 5/18, respectively.
Next, divide the numerators of the fractions. Since the numerators are both negative, the answer will be a negative number. The numerator of the first fraction (-5) divided by the numerator of the second fraction (5) is -1.
Multiply this answer by the common denominator (18) to get the final answer: -5/2.
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The coordinates of the points A and B are (0, 6) and (8, 0) respectively. (i) Find the equation of the line passing through A and B. Given that the line y = x + 1 cuts the line AB at the point MÄUK (ii) the coordinates of M, (iii) the equation of the line which passes through M and is parallel to the x-axis, (iv) the equation of the line which passes through M and is parallel to the y-axis.
Therefore, the equation of this line is: x = 8/7.
What is equation?An equation is a mathematical statement that shows that two expressions are equal. It contains one or more variables, and the goal is to solve for the value(s) of the variable(s) that make the equation true.
Given by the question.
To find the equation of the line passing through points A and B, we need to determine the slope and the y-intercept of the line.
The slope of the line can be found using the formula:
slope = (change in y) / (change in x)
Using the coordinates of A and B, we have:
slope = (0 - 6) / (8 - 0) = -6/8 = -3/4
The y-intercept of the line can be found by substituting the coordinates of point A and the slope into the slope-intercept form of the equation of a line:
y = mx + b
where m is the slope and b are the y-intercept.
Using the coordinates of point, A and the slope we just calculated, we have:
6 = (-3/4) (0) + b
b = 6
Therefore, the equation of the line passing through points A and B is:
y = -3/4 x + 6
(ii) To find the coordinates of point M where the line y = x + 1 intersects the line AB, we need to solve the system of equations:
y = -3/4 x + 6 (equation of line AB)
y = x + 1 (equation of line y = x + 1)
Substituting y = x + 1 into the equation of line AB, we have:
x + 1 = -3/4 x + 6
Solving for x, we have:
x = 8/7
Substituting x = 8/7 into the equation of line y = x + 1, we have:
y = 8/7 + 1 = 15/7
Therefore, the coordinates of point M are:
M (8/7, 15/7)
(iii) The line passing through point M and parallel to the x-axis is a horizontal line with equation y = c, where c is the y-coordinate of point M. Therefore, the equation of this line is:
y = 15/7
(iv) The line passing through point M and parallel to the y-axis is a vertical line with equation x = c, where c is the x-coordinate of point M.
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Would a yardstick be a reeasonable tool to use to measure the length of a canoe paddle explain
In conclusion, a yardstick or ruler can be a reasonable tool to use to measure the length of a canoe paddle.
Then, move the yardstick along the length of the paddle, counting the marks until you reach the other end. This will give you an estimate of the length of the paddle in terms of the number of yardstick marks.
For a more precise measurement, you can also use a ruler. Place the zero mark of the ruler at the tip of the paddle and move the ruler along the length of the paddle, counting the small marks that correspond to 1/16th of an inch. This will give you a more precise estimate of the length of the paddle.
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In a class, we have 61 students of different majors. There are 23 chemistry majors (C), 12 math majors (M), 9 engineering majors (E), and 17 students who are undecided (U). Of these students, 4 of them have declared both math and engineering majors. A student will randomly be chosen to win a scholarship. Find the probability of awarding the scholarship to a student who is either a math major or an engineering major. 0.0290 0.7213 0.2787 0.3443
The probability of awarding the scholarship to a student who is either a math major or an engineering major is 0.2787 .Option (c) is the correct answer.
In this question, we are asked to find the probability of awarding the scholarship to a student who is either a math major or an engineering major. Total students (n) = 61 Chemistry majors (C) = 23 Math majors (M) = 12 Engineering majors (E) = 9 Undecided (U) = 17Students with declared majors in Math and Engineering (M ∩ E) = 4
We have to find P(A) = P(student is either a math major or an engineering major).To solve this problem, we will use the addition rule of probability. The addition rule states that the probability of event A or B occurring equals the probability of event A plus the probability of event B minus the probability of both A and B occurring. P(A) = P(M ∪ E) = P(M) + P(E) - P(M ∩ E)
Here, P(M) = probability that the student is a math major= number of math majors / total students = 12/61 P(E) = probability that the student is an engineering major= number of engineering majors / total students = 9/61 P(M ∩ E) = probability that the student has declared both math and engineering majors = 4/61So,P(A) = P(M ∪ E) = P(M) + P(E) - P(M ∩ E)P(A) = 12/61 + 9/61 - 4/61= 17/61≈ 0.2787
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Find the perimeter of the shape below:
Check the picture below.
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ S(\stackrel{x_1}{-2}~,~\stackrel{y_1}{7})\qquad R(\stackrel{x_2}{-1}~,~\stackrel{y_2}{3}) ~\hfill SR=\sqrt{(~~ -1- (-2)~~)^2 + (~~ 3- 7~~)^2} \\\\\\ ~\hfill SR=\sqrt{( 1 )^2 + ( -4)^2} \implies \boxed{SR=\sqrt{ 17}}[/tex]
[tex]R(\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad U(\stackrel{x_2}{-1}~,~\stackrel{y_2}{5}) ~\hfill RU=\sqrt{(~~ -1- (-1)~~)^2 + (~~ 5- 3 ~~)^2} \\\\\\ ~\hfill RU=\sqrt{( 0)^2 + ( 2)^2} \implies RU=\sqrt{ 4}\implies \boxed{RU=2} \\\\\\ U(\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\qquad T(\stackrel{x_2}{2}~,~\stackrel{y_2}{5}) ~\hfill UT=\sqrt{(~~ 2- (-1)~~)^2 + (~~ 5- 5~~)^2} \\\\\\ ~\hfill UT=\sqrt{( 3)^2 + ( 0)^2} \implies UT=\sqrt{ 9}\implies \boxed{UT=3}[/tex]
[tex]T(\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad S(\stackrel{x_2}{-2}~,~\stackrel{y_2}{7}) ~\hfill TS=\sqrt{(~~ -2- 2~~)^2 + (~~ 7- 5~~)^2} \\\\\\ ~\hfill TS=\sqrt{( -4)^2 + ( 2)^2} \implies \boxed{TS=\sqrt{ 20}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Perimeter} }{\sqrt{17}+2+3+\sqrt{20} }~~ \approx ~~ \text{\LARGE 13.6}[/tex]
Eleven percent of the products produced by an industrial process over the past several months fail to conform to specifications. The company modifies the process attempting to reduce the rate of noncomforties. In a trial run, the modified process produces 16 noncomforting items out of 300 produced. Construct and interpret a 95% ci for the proportion of noncomforming items
The 95% confidence interval for the proportion of nonconforming items is (0.093, 0.250). This indicates that there is a 95% chance that the true proportion of nonconforming items lies between 9.3% and 25%.
To calculate the 95% confidence interval for the proportion of nonconforming items, we first calculate the sample proportion p of nonconforming items: p = 16/300 = 0.053.
Next, we calculate the standard error of the sample proportion, which is SE = √(p(1-p)/n) = √(0.053(1-0.053)/300) = 0.01.
Finally, we calculate the lower and upper limits of the 95% confidence interval for the proportion of nonconforming items by subtracting and adding 1.96 x SE to the sample proportion, respectively. This gives us the confidence interval of (0.093, 0.250).
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The city of Irvine reported that approximately 75% of residents are over the age of 60. Let X be the number of Irvine residents over the age of 60.From a random sample of 500 Irvine residents, 350 were over the age of 60.What is the sampling distribution of the sample proportion for the sample size of 500?Using the distribution of X from above, what is the probability that at most 350 of the 500 Irvine residents selected will be over the age of 60?What is the probability that at least 350 of the 500 residents in the sample were over the age of 60?What is the probability that between 400 and 475 of the residents were over the age of 60?
The probability that at most 350 of the 500 Irvine residents selected will be over the age of 60 is 0.9292. The probability that at least 350 of the 500 residents in the sample were over the age of 60 is 0.0708. The probability that between 400 and 475 of the residents were over the age of 60 is 5.88.
The probability that at most 350 of the 500 Irvine residents selected will be over the age of 60 can be found by calculating the z-score for 350 and finding the corresponding probability from a normal distribution table. The z-score for 350 is (350-375)/17 = -1.47. The corresponding probability from a normal distribution table is 0.0708.
The sampling distribution of the sample proportion for the sample size of 500 is a normal distribution with a mean of 0.75 and a standard deviation of [tex]√[(0.75)(0.25)/500] = 0.017.[/tex]
The probability that at least 350 of the 500 residents in the sample were over the age of 60 can be found by calculating the z-score for 350 and finding the corresponding probability from a normal distribution table. The z-score for 350 is (350-375)/17 = -1.47. The corresponding probability from a normal distribution table is 1 - 0.0708 = 0.9292.
The probability that between 400 and 475 of the residents were over the age of 60 can be found by calculating the z-scores for 400 and 475 and finding the corresponding probabilities from a normal distribution table. The z-score for 400 is (400-375)/17 = 1.47 and the z-score for 475 is (475-375)/17 = 5.88.
The corresponding probabilities from a normal distribution table are 0.9292 and 1.0000, respectively. The probability that between 400 and 475 of the residents were over the age of 60 is 1.0000 - 0.9292 = 0.0708.
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Joshua has a ladder that is 19 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 15 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 75°. Will the ladder be safe at this height? Show your work and draw a diagram to support your answer.
Answer:
50.47°
Step-by-step explanation:
We can use the trigonometric function sine to determine the angle the ladder makes with the ground. Let's call this angle theta. We have:
sin(theta) = opposite/hypotenuse
where the opposite side is the height of the ladder on the wall (15 ft) and the hypotenuse is the length of the ladder (19 ft). Solving for theta, we get:
theta = sin^-1(15/19) ≈ 50.47°
Since this angle is less than 75°, the ladder will be safe at this height.
Please help me somebody
The surface area of the cone is 1,966.896 mm²
How to find the surface area of the cone?We can see that the surface area of a cone of slant height H and radius R is:
SA = pi*R² + pi*R*H
Here we can see that R = 27mm/2 = 13.5mm
And H = 32.9 mm
And we know that pi = 3.14
So, replacing that we will get:
SA = 3.14*(13.5mm)² + 3.14*13.5mm*32.9mm
SA = 1,966.896 mm²
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2.5 m³ of limestone has a mass of 6025 kg. a) Calculate the density of limestone in kg/m³. 3 b) Find the mass of 1.7 m³ of limestone in kg.
A wide receiver catches a ball and begins to run for the endzone following a path defined by (x-5, y-50) = t(0,10). A defensive player chases the receiver as soon as he starts running following a path defined by (x-10, y-54) = t(-0. 9, -10. 72)
Write Parametric equations for the path of each player.
A. Receiver: x=50,y=5-10t
Defensive: x=10-0. 9t, y=54-10. 72
B. Receiver: x=5, y=50-10t
Defensive: x=10-0. 9t, y=54-10. 72t
C. Receiver: x=5, y=50-10t
Defensive: x=54-10. 72t, y=10-0. 9t
D. Receiver: x=10-0. 9t, y=54-10. 72t
Defensive: x=5, y=50-10t
The correct answer is B Parametric equations for the path of each player is Receiver: x=5, y=50-10t Defensive: x=10-0. 9t, y=54-10. 72t
The given paths of the receiver and defensive player can be described parametrically, using the parameter t, as:
Receiver: x = 5, y = 50 - 10t
Defensive: x = 10 - 0.9t, y = 54 - 10.72t
We can use the parameter t to represent the time that has elapsed since they started moving. The parametric equations describe the x and y coordinates of each player as functions of t.
By plugging in different values of t, we can determine the positions of the players at different points in time. In this case, the receiver moves horizontally while the defensive player moves at an angle, so their equations are different.
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A small publishing company is releasing a new book. The production costs will include a one-time fixed cost for editing and an additional cost for each book
printed. The total production cost C (in dollars) is given by the function C = 18. 95N+750, where N is the number of books.
The total revenue earned (in dollars) from selling the books is given by the function R = 34. 60N.
Let P be the profit made (in dollars). Write an equation relating P to N. Simplify your answer as much as possible
If The total revenue earned (in dollars) from selling the books is given by the function R-34.60N. the equation relating P to N is P = 18.95N - 750.
Profit made (P) can be calculated by subtracting the total production cost (C) from the total revenue earned (R), so:
P = R - C
P = 34.60N - (18.95N + 750)
P = 34.60N - 18.95N - 750
P = 15.65N - 750
Therefore, the equation relating P to N is P = 18.95N - 750.
The equation shows that the profit made by the company is a linear function of the number of books printed. The slope of the line is the revenue per book (34.60 dollars), minus the cost per book (18.95 dollars), which is 18.95 dollars.
The intercept of the line is the fixed cost for editing (750 dollars). The equation can be used to estimate the profit for any given number of books printed, and to determine the break-even point, which is the number of books that need to be sold to cover the total production cost.
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Questions are in the following picture
1. If there were two people dividing the cost of the gift, each person would spend $180. If there were three people dividing the cost, each person would spend $120. If there were five people dividing the cost, each person would spend $72. If there were ten people dividing the cost, each person would spend $36. If there were one hundred people dividing the cost, each person would spend $3.60.
2. The function that could be used to model the amount each person would spend depending on the number of people contributing to the gift is:
cost per person = total cost / number of people
3. The table will be:
Number of people Amount per person
2. $180
3 $120
5. $72
10. $36
100. $3.60
The graph of the function would be a straight line passing through the points (2, $180), (3, $120), (5, $72), (10, $36), and (100, $3.60).
4. The domain of the function is all positive integers greater than zero, since you cannot have a fractional or negative number of people contributing.
How to explain the informationThe range of the function is all positive real numbers, since the cost per person can be any positive amount.
The function is decreasing, since the cost per person decreases as the number of people contributing increases.
There is no maximum or minimum value for the cost per person, since it can be any positive amount. The function is continuous, but the number of people contributing must be a discrete value (i.e., a whole number).
As the number of people contributing approaches infinity, the cost per person approaches zero. The y-intercept of the function is the cost of the gift, and the x-intercept is not applicable in this context.
There is a horizontal asymptote at y = 0, since the cost per person approaches zero as the number of people contributing approaches infinity.
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Chile is celebrating her Quinceañera. Hannah knows the perfect gift to buy Chile, but it costs $360. Hannah can't afford to pay for this on her own so thinks about asking some friends to join in and share the cost.
1. How much would each person spend if there were two people dividing the cost of the gift? How much would each person spend if there were three people dividing the cost? Five people? Ten? One hundred?
2. Determine the function that could be used to model the amount each person would spend depending on the number of people contributing to the gift.
3. Use multiple representations to show how the amount each person would contribute to the gift would change depending on the number of people contributing. Describe the connections between the representations.
4. Describe the features of the function based on the context (domain/range, increasing/decreasing, maxima/minima, discrete/continuous, end behavior, intercepts, asymptotes).
The sales tax on a $44.00 purchase is $2.42. At this rate, what would be the tax on goods worth $60.00?
Answer:
We can use proportions to find out the tax on goods worth $60.00:
Let x be the tax on goods worth $60.00.
Then, we can set up the following proportion:
tax/sales = tax rate
or
2.42/44 = x/60
To solve for x, we can cross-multiply and simplify:
44x = 2.42 * 60
44x = 145.20
x = 145.20/44
x = 3.3 (rounded to the nearest cent)
Therefore, the tax on goods worth $60.00 would be $3.30.
Step-by-step explanation:
Last month Carmen made $480 working for 30 hours this month she will get a 15% increase in the amount she earns per hour what will be her hourly rate in dollars after the increase enter your answer in the space provided
After the 15% increase in her hourly rate, Carmen's new hourly rate will be $18.40 per hour.
Carmen currently makes $480 in a month by working 30 hours. To find her hourly rate, we can divide her total earnings by the number of hours she worked:
Hourly rate = Total earnings ÷ Number of hours worked
So Carmen's current hourly rate is:
Hourly rate = $480 ÷ 30 = $16 per hour
If Carmen gets a 15% increase in her hourly rate, we can calculate her new hourly rate by multiplying her current hourly rate by 1.15 (since a 15% increase means the new rate is 115% of the current rate):
New hourly rate = Current hourly rate x 1.15
New hourly rate = $16 x 1.15
New hourly rate = $18.40 per hour
This means she will earn $2.40 more per hour than she did before the increase.
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Answer for this please!
Step-by-step explanation:
See image below
If 45% of a number is 153 and 10% of the same number is 34, find 55% of that number
Answer:
187
Step-by-step explanation:
We can calculate the number by doing 153/.45 to give us 340.
We can also do 34/.1 to give us 340.
Since we got 340 as our answer for the first two numbers, convert 55% to .55 and multiply by 340 to get 187.
The girl lifts a painting to a height of 0. 5 m in 0. 75 seconds. How much
power does she use? *
Answer:
and painting has 100kg or 1kg bcs thats not same