The logarithm that is equal to the number of years it will take for the population to increase to 15,000 students is log(11.08).
Let t be the number of years it will take for the enrollment to increase to 15,000 students. We can use the formula for continuous growth to set up an equation:
[tex]A = Pe^{(rt)[/tex]
where A is the final amount, P is the initial amount, r is the annual growth rate as a decimal, and t is the time in years.
In this case, we know that P = 12,000, A = 15,000, and r = 0.025 (since the growth rate is 2.5%). Plugging these values into the equation, we get:
[tex]15,000 = 12,000 e^{(0.025t)[/tex]
Dividing both sides by 12,000, we get:
[tex]1.25 = e^{(0.025t)[/tex]
To solve for t, we can take the natural logarithm of both sides:
[tex]ln(1.25) = ln(e^{(0.025t))[/tex]
Using the property of logarithms that [tex]ln(e^x) = x[/tex], we can simplify the right-hand side:
ln(1.25) = 0.025t
Finally, dividing bοth sides by 0.025, we get:
t = ln(1.25)/0.025
Using a calculatοr tο evaluate ln(1.25)/0.025, we get:
t ≈ 11.08
Therefοre, the lοgarithm that is equal tο the number οf years it will take fοr the pοpulatiοn tο increase tο 15,000 students is lοg(11.08)
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Which represents the distance between A(6, 5) and B(−2, −1)?
Answer:
10
Step-by-step explanation:
We can use the distance formula to find the distance between the two points:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates of A and B, we get:
Distance = √((-2 - 6)^2 + (-1 - 5)^2)
Distance = √((-8)^2 + (-6)^2)
Distance = √(64 + 36)
Distance = √100
Distance = 10
Therefore, the distance between A(6, 5) and B(−2, −1) is 10 units.
Exhibit 3-2 A researcher has collected the following sample data. The mean of the sample is 5. 3 5 12 3 2 Refer to Exhibit 1. Rhe variance is"
a. 80
b. 4.062
c. 13.2
d. 16.5
The variance of the sample is 17.05. However, none of the given options matches with this value. The closest option is option (d) 16.5.
What is variance?Variance is a measure of the spread or variability of a set of data. It is the average of the squared differences from the mean. The formula for variance is:
Variance = (sum of squared deviations from the mean) / (number of observations - 1)
where the squared deviation from the mean is the difference between each data point and the mean of the data set, squared. The variance is useful in statistical analysis and can provide information about the distribution of the data. A higher variance indicates that the data is more spread out, while a lower variance indicates that the data is clustered more closely around the mean.
In the given question,
To find the variance of the sample, we can use the formula:
Variance = [(sum of squared deviations from the mean)/ (number of observations - 1)]
First, we need to find the squared deviation of each observation from the mean, which is the difference between each observation and the mean, squared:
(3-5.4)² = 5.76
(5-5.4)² = 0.16
(12-5.4)² = 43.56
(3-5.4)²= 5.76
(2-5.4)²= 12.96
Next, we need to sum up these squared deviations:
5.76 + 0.16 + 43.56 + 5.76 + 12.96 = 68.2
Then, we divide the sum of squared deviations by the number of observations minus 1:
Variance = 68.2/(5-1) = 17.05
Therefore, the variance of the sample is 17.05. However, none of the given options matches with this value. The closest option is option (d) 16.5.
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Isaac walks 6/10 of a mile in 1/5 of an hour. If Isaac’s walking rate remains constant, what is Isaac’s walking rate in miles per hourur
Answer: 3 mph
Step-by-step explanation:
I did it in mah brain
The Angler's Club requires that members spend at least $250 per month at their restaurant. Mr. Donovan has spent $179. 85 so far this month. Write an inequality to describe the situation, then complete the sentence.
Mr. Donovan still needs to spend at least $70.15 in the restaurant this month to meet the Angler's Club requirement.The inequality that describes the situation is:250 - 179.85 ≤ x
where x represents the amount of money Mr. Donovan still needs to spend in order to meet the Angler's Club requirement.
To solve for x, we first subtract 179.85 from 250 to get:
70.15 ≤ x
Therefore, Mr. Donovan still needs to spend at least $70.15 in the restaurant this month to meet the Angler's Club requirement.
In summary, Mr. Donovan's spending so far this month is less than the minimum required by the Angler's Club, and he needs to spend at least $70.15 more to meet the requirement.
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I need help on this now!
thank you
The safe distance between the supports to carry the load of 1500 pounds is found to be 8 meters.
Explain about the inverse proportion?One kind of proportionality relationship is inverse proportion. If two quantities remain inversely related, one will increase while the other will decrease.
The area of a circle is proportional to its radius, which serves as an illustration of direct proportion.
The equation for inverse proportion of the weight carried along with distance is:
P = 5400 /D
P is load in pounds (lb)
D is the safe distance.
Then, distance to carry 1500 lb of load is:
1500 lb = 1500*0.45 kg
1500 lb = 675 kg
675 = 5400 /D
D = 5400/675
D = 8 meters
Thus, safe distance between the supports to carry the safe load of 1500 pounds is found to be 8 meters.
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the measure of three interior angle of a triangle are in the ratio 2፡3፡4. what is the measure of the smallest and largest interior angles of triangle?
Answer:
Below
Step-by-step explanation:
The interior angles of ANY triangle add up to 180 degrees
you want to divide this 180 into 2 + 3 + 4 = 9 parts
180 / 9 = 20 degrees for each part
2 parts = 2 * 20 = 40 °
4 parts = 4 * 20 = 80 °
A piece of cheese has a mass of 216 g and a density of 1.6 g/cm³. Calculate the volume of the cheese.
The volume of the cheese is approximately 135 cubic centimeters.
To calculate the volume of the cheese, we can use the formula:
Volume = Mass / Density
Given that the mass of the cheese is 216 grams and the density is 1.6 g/cm³, we can plug these values into the formula:
Volume = 216 g / 1.6 g/cm³
Now, we need to convert the units so that they are consistent. Since density is given in grams per cubic centimeter (g/cm³), we need to convert the mass from grams to cubic centimeters.
1 gram is equal to 1 cubic centimeter, so:
Volume = 216 cm³ / 1.6 cm³
Now, divide:
Volume ≈ 135 cm³
The volume of the cheese is approximately 135 cubic centimeters.
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Cual expresion algebraica representa la siguiente frase? N aumetado en un 25% A. 0. 25N
B. N + 0. 25N
C. 25N
D. N + 25
The algebraic expression that represents the sentence "N increased by 25%" is 0.25N.
Hence the correct option is A.
This means that N is multiplied by 0.25 or 1/4. To find the result of N increased by 25%, you simply need to multiply N by 0.25 and add the result to the original value of N. The option A, 0.25N, represents this concept in a clear and concise manner.
The other options (B, C, and D) are either incomplete or incorrect. It is important to understand the concept of percentage increase and how it is represented algebraically, as it is a common operation in many mathematical and real-life scenarios, such as calculating interest rates, growth rates, and inflation rates.
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Ariana has a deck that measures 16 feet by 24 feet. She wants to increase each
dimension by equal lengths so that its area is doubled. By how much should she
increase each dimension?
Can anyone help plss:)
Answer:
The answer would be 80.
Step-by-step explanation:
First you want to add 16 and 24.
Next you want to multiply that answer by 2.
Then you have your answer and I hope this helps
A. What is your bi-weekly gross paycheck based on 40 hours a week at a rate of $18.25
per hour? Show your work.
Bi-weekly gross paycheck based on 40 hours a week at a rate of $18.25 per hour is $1,460.
What is multiplication ?
Multiplication is a basic arithmetic operation that involves combining two or more numbers to find their product or the total number of items when a certain number is repeated a certain number of times. In multiplication, the numbers being combined are called factors, and the result is called the product.
To calculate your bi-weekly gross paycheck, you need to multiply your hourly rate by the number of hours you work per week and then multiply that by 2 to account for two weeks in a pay period.
Hourly rate: $18.25
Weekly hours: 40
Bi-weekly hours: 40 x 2 = 80
Bi-weekly gross paycheck: Hourly rate x Bi-weekly hours
Bi-weekly gross paycheck: $18.25 x 80 = $1,460
Therefore, your bi-weekly gross paycheck based on 40 hours a week at a rate of $18.25 per hour is $1,460.
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A firm has classified its customers in two ways: according to whether the account is overdue and whether the account is new (less than 12 months) or old. An analysis of the firm's records provided the input for the following table of joint probabilities: One account is selected at random. If the account is overdue, what is the probability that it is new? If the account is new, what is the probability that it is overdue?
The probability that it is new is 0.0833.
The probability that it is overdue is 0.25.
How to calculate conditional probability?To solve this problem, use conditional probability.
Let A be the event that the account is new, and B be the event that the account is overdue.
A) To find the probability that an account is new given that it is overdue, calculate:
P(New | Overdue) = P(New and Overdue) / P(Overdue)
P(New | Overdue) = 0.05 / (0.05 + 0.55) = 0.0833 or 8.33%
So the probability that the account is new, given that it is overdue, is 8.33%.
B) To find the probability that an account is overdue given that it is new, calculate:
P(Overdue | New) = P(Overdue and New) / P(New)
P(Overdue | New) = 0.05 / (0.05 + 0.15) = 0.25 or 25%
So the probability that the account is overdue, given that it is new, is 25%.
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The complete question is:
A firm has classified its customers in two ways: according to whether the account is overdue and whether the account is new (less than 12 months) or old. An analysis of the firm's records provided the input for the following table of joint probabilities: One account is selected at random. If the account is overdue, what is the probability that it is new? If the account is new, what is the probability that it is overdue?
Draw a rectangle that is 3 squares long and 1/2 of a square wide. Then add up the partial squares to find the area. Multiply to check your answer
According to the image, we can see that 3 rectangles are half-shaded= 1.5 units²,
A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at a straight angle or 90 degrees. The square's diagonals are also equal and split at a 90-degree angle.
A rectangle with two opposite sides that have the same length can also be referred to as a square.
P.S: Rectangle attached in image.
According to the image, we can see that 3 rectangles are half-shaded.
This means that:
Half-shaded square + Half-shaded square + Half-shaded square
=> 0.5 + 0.5 + 0.5
=> 1.5 units²
Check:
To check our answer:
3 x 0.5 = Area of rectangle
=> 1.5 units² = Area of rectangle
Hence, our explanation is correct.
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The net of a right circular cylinder is shown.
net of a cylinder where the radius of each circle is labeled 4 meters and the height of the rectangle is labeled 8 meters
What is the surface area of the cylinder? Use π = 3.14 and round to the nearest whole number.
251 m2
301 m2
502 m2
804 m2
Answer:
The first person to answer was correct, the answer is 301 m squared.
Step-by-step explanation:
I took the quiz so you don't have to! <3
Help with this math problem theres no 550
Answer:
A. 450 trucks
Step-by-step explanation:
Given
Totally the parking lot can hold 1000 vehiclesOnly 2/5 of the spaces are for carsAnswer
A. 450 trucks
Use the figure to answer the following questions.
The number of vertical angles are 6
The number of linear angles are 6
The value of x is 20
What are vertical angles?Vertical angles are defined as a pair of non-adjacent angles that are formed by the intersection of two straight lines.
Four angles are created from this intersection.
What are linear angles?Linear angles are defined as those angles that are formed when two lines intersect each other at a single point.
Note that supplementary angles are angles that sum up to 180 degrees.
Then, we have;
<1 + <5 = 180
substitute the angles
2x + 10 + 5x + 30 = 180
collect the like terms
7x = 180 -40
7x = 140
Make 'x' the subject
x = 20
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write the ratio in the simplest form ;120mimutes:4hours:6hours
Find the value of x. Round to the nearest tenth.
The value of x in the given digram using trigonometry to the nearest tenth is 7.15.
What does the word "angle" mean?In planar geometry, an angle is a form created by two rays or lines that terminate in the same place. The name "angle" comes from the Latin "angulus," which means "corner". The vertex and the two rays, which are referred to as the sides of an angle, are the shared termini of two rays.
Given an angle and the length of the adjacent side, we are to determine the value of the hypotenuse using cos.
Cos = adjacent / hypotenuse
cos 33 = 6 /x
x = 6 / cos 33
x = 6 / 0.83867
x = 7.15
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exponential law of heating and cooling
Part A: k = 8.4, to find the value of k, we must solve for k in the equation.
Part B: 193°F is the temperature of the water after 4.5 minutes.
What is initial temperature?Initial temperature is the temperature of a system before it undergoes a change. It can be calculated by subtracting the change in temperature from the final temperature.
Part A: k = 8.4
To find the value of k, we must solve for k in the equation.
We are given the temperature of the room (67°F) and the initial temperature of the water (208°F).
We are also given the temperature of the water after 3 minutes (193°F). We can plug these values into the equation and solve for k:
T-Ta = k(To-T)
193-67 = k(208-193)
126 = 15k
k = 126/15
k = 8.4
Part B: 193°F
To find the temperature of the cup of water after 4.5 minutes, we can plug the k-value we found in Part A into the equation, along with the given temperature of the room (67°F) and the initial temperature of the water (208°F).
T-Ta = k(To-T)
T = Ta + k(To-T)
T = 67 + 8.4(208-T)
T = 67 + 1747.2 - 8.4T
9.4T = 1814.2
T = 193
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Part A: k = 8.4, to find the value of k, we must solve for k in the equation.
Part B: 193°F is the temperature of the water after 4.5 minutes.
What is initial temperature?The temperature of a system at the start of a shift is called the initial temperature. You can figure it out by deducting the final temperature from the temperature difference.
Part A: k = 8.4
We must answer for k in the equation in order to determine its value.
We are informed of the room's temperature (67°F) and the water's starting temperature (208°F).
After three minutes, we are also told the water's temperature (193°F). We can solve for k by entering these numbers into the equation:
T-Ta = k(To-T)
193-67 = k(208-193)
126 = 15k
k = 126/15
k = 8.4
Part B: 193°F
We can enter the k-value we discovered in Part A, the given room temperature (67°F), and the starting temperature of the water (208°F) into the equation to determine the temperature of the cup of water after 4.5 minutes.
T-Ta = k(To-T)
T = Ta + k(To-T)
T = 67 + 8.4(208-T)
T = 67 + 1747.2 - 8.4T
9.4T = 1814.2
T = 193
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The complete question is,
EXIT TICKET
After heating up in a teapot, a cup of hot water is poured at a temperature of 208^0F . The cup sits to cool in a room at a temperature of 67^0 F. Newton's Law of Cooling explains that the temperature of the cup of water will decrease proportionally to the difference between temperature of the water and the temperature of the room, as given by the formula shown below.
Part A: If the cup of water reaches the temperature of 193^0 F after 3 minutes. Find the value of k, to the room, as given by the formula shown below. nearest thousandth.
Part B: Use the resulting equation to determine the Fahrenheit temperature of the cup of water, to the nearest degree, after 4.5 minutes.
342×38 without using a calculator
Answer:
12996
Step-by-step explanation:
a square fits exactly inside a circle with each of its vertices being on the circumference of the circle.
the square has side lengths of xcm
the area of the circle is 56cm squared.
work out the value of x to 3 significant figures.
After addressing the issue at hand, we can state that As a result, the square value of x to three significant figures is 5.03 cm.
what is a square?According to Euclidean geometry, a square is an equilateral quadrilateral with four equal sides and four equal angles. It is also referred to as a rectangle with two neighbouring sides of equal length. A square is an equilateral quadrilateral because it has four equal sides and four equal angles. Square angles are 90-degree or straight angles. Furthermore, the diagonals of the square are evenly spaced and split at a 90-degree angle. a neighbouring rectangle with two equal sides. a quadrilateral with four equal-length sides and four right angles. A parallelogram with two adjacent, equal sides forming a right angle. A rhombus with straight sides.
The Pythagorean theorem can be used to find the square's diagonal:
2x2 = diagonal2 = x2 + x2 = 2x2[tex]x * \sqrt = diagonal = sqrt(2x2) (2)[/tex]
Because the diagonal equals the circle's diameter, the radius is half of the diagonal:
x * \sqrt(2) / 2 = radius
We can now use the formula for the area of a circle to calculate x:
[tex]\pi * radius2 = area[/tex]
[tex]\Pi * (x * sqrt(2) / 2)2 = 56[/tex]
[tex]56 = pi * (x^2 / 2)[/tex]
[tex]x^2 = 112 / pi[/tex]
x = 5.027 (rounded to 3 significant figures) (rounded to 3 significant figures)
As a result, the value of x to three significant figures is 5.03 cm.
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A simple random sample of 55 students had a mean of 16 hours
Using the information provided, we can construct a 90% confidence interval for the mean number of hours a student studies per week as follows: (15.34, 16.66).
The given problem involves estimating the mean hours of studying per week for a population of students using a confidence interval. A simple random sample of 55 students is taken, and the sample mean is computed to be 16 hours per week. The population standard deviation is assumed to be known to be 3.1 hours per week. Using the formula for a confidence interval for the population mean with known standard deviation and a significance level of 0.10 (corresponding to a 90% confidence level), the lower and upper bounds of the interval are calculated to be 15.19 and 16.81 hours per week, respectively. This means that we can be 90% confident that the true mean hours of studying per week for the population of students lies within this interval
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Complete question:
A professor wants to estimate how many hours per week her students study. A simple random sample of 55 students had a mean of 16 hours of studying per week. Construct a 90% confidence interval for the mean number of hours a student studies per week. Assume that the population standard deviation is known to be 3.1 hours per week. Round to two decimal places.
The 7th grade and the 8th grade are collecting
food for Project Help. 7th grade starts with 7
items donated by a teacher and collects 5 items
per day. The 8th grade starts with 20 items
donated by a teacher and collects 8 items per
day. Write an equation for each grade level.
Which grade has a greater slope? Which grade
has a great initial value?
Answer: The equation for the 7th grade is y = 5x + 7, where y is the total number of items collected and x is the number of days. The initial value is 7 and the slope is 5.
The equation for the 8th grade is y = 8x + 20, where y is the total number of items collected and x is the number of days. The initial value is 20 and the slope is 8.
Therefore, the 8th grade has a greater slope (8) compared to the 7th grade (5). The 8th grade also has a greater initial value (20) compared to the 7th grade (7).
Step-by-step explanation:
A parallelogram of base 12cm has an area 108sq. Cm. Find the height
The height of the parallelogram is 9 cm.
To find the height of a parallelogram with a given base and area, we can use the formula:
Area = base x height
In this case, we are given that the base of the parallelogram is 12 cm and the area is 108 sq. cm. Substituting these values into the formula, we get:
height = 108/12
Simplifying this expression, we get:
height = 9cm
A parallelogram is a four-sided polygon with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles are also equal in measure, meaning that the adjacent angles are supplementary (their sum is 180 degrees).
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the new HC cell phone company is offering a plan for unlimited talk and text with an additional charge for data that can be represented by the function H ( g ) = 22.99g + 50, where H represents the cost, in dollars, and g represents the number of gigabytes of data. According to this model, fill in the blanks to correctly complete the sentence below. The cost of the plan for the limited talk and text is _____ with a an additional cost of _______ for each gigabyte of data.
The cost of the plan for the limited talk and text is $50 with an additional cost of $22.99 for each gigabyte of data.
How did we determine the cost of the plan?Generally, a mathematical function means a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables. It can take an input from many variables but will always give the same output, unique to that function.
We are given that "H(g) = 22.99g + 50", where H represents the cost, in dollars, and g represents the number of gigabytes of data. The main answer is based on the given function where the constant term of 50 represents the cost of the plan for limited talk and text, and the coefficient of 22.99 represents the additional cost for each gigabyte of data used.
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Use the properties of exponents to rewrite y = 5e-0. 7t in the form ya(1 + r)' or y = a(1-r). Round the value of r to the
nearest thousandth. Then find the percent rate of change to the nearest tenth of percent
The percent rate of change to the nearest tenth of a percent is approximately 30.0% for both forms.
Starting with [tex]Y=5e^{-0.7}[/tex] we can rewrite it using the property that [tex]e^{In(x)} = x[/tex]:
[tex]y=5e^{0.7t} = 5e^{ine^{in-0.7t} } =5e^{ln(5)}e^{-0.7t}[/tex]
Using the property that e^(ln(x)) = x again, we can simplify further:
[tex]y = 5e^{(ln(5)} e^{-0.7t} = 5(5^{1/In(5)}e^{-0.7t})[/tex]
Let [tex]a = 5^{1/ln(5)}[/tex]and r = 0.7, then we have:
[tex]y = 5a(1 + r)^{-t} ; y = a(1 - r)^t[/tex]
Rounding r to the nearest thousandth, we have:
r ≈ 0.700
To find the percent rate of change, we can use the formula:
percent rate of change = (1 ± r) * 100%
For the first form, we have:
percent rate of change = (1 - 0.700) * 100% ≈ 30.0%
For the second form, we have:
percent rate of change = (1 - 0.700) * 100% ≈ 30.0%
Therefore, the percent rate of change to the nearest tenth of a percent is approximately 30.0% for both forms.
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A bicycle wheel make five rotations. The bicycle travel 30. 09 find the diameter
The diameter of the wheel is approximately 1.918 meters.
We can use the formula:
distance traveled = circumference of wheel x number of rotations
The circumference of the wheel is equal to the distance traveled in one rotation, which is equal to the diameter of the wheel times pi (π). So we can rewrite the formula as:
distance traveled = (diameter of wheel x π) x number of rotations
where d is the diameter of the wheel.
We are given that the bicycle travels 30.09 meters and the wheel makes five rotations, so we can plug in these values:
30.09 = (d x π) x 5
Solving for d, we get:
d = 30.09 / (π x 5)
d ≈ 1.918 meters
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Help pleaseeeee!!!!!!
Answer:
17
Step-by-step explanation:
PLSSSSSSSSSS HELPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!
How is the quotient of 8,552 and 16 determined using an area model?
Enter your answers in the boxes to complete the equations.
8,552 ÷ 16 = (___÷ 16) + (480 ÷ 16) + (___ ÷ 16) + (8 ÷ 16)
8,552 ÷ 16 = ___ +30 + ___ + 8/16
8,552 ÷ 16 = ___ 1/2
Answer:
Step-by-step explanation:
Hi there I am able to help so when you do 8,552/16 it is best to reverse it then add the expression, what I mean by that is translating expressions. the answer would be 444.23 then you would want to add (480/16) no mental math how you would do this is the recalabric way, take 480/16 and put in an a fraction to make it work easier than the rest of your problems you would do the same things its simple, just repeat what I did to all the other problems,
regards, me
an
How was Malaka's father finally able to move to the
United States?
O He saved enough money to afford the cost of moving.
He was accepted to UCLA's School of Management.
He studied and was able to pass the TOEFL.
He received a teaching job at UCLA.
Answer:
B
Step-by-step explanation:
He was accepted to UCLA's School of Management
A health survey was conducted at a company with 6,480 employees. Through "mild threats" they got 4860 to answer. One question asked was how often the respondent exercised in their free time. 1296 people stated that they exercised at least 3 times a week.
In order to better estimate the percentage of employees who exercised at least 3 times a week, a sample of the absentees was called. In this sample of 80 people, 7 stated that they exercised at least 3 times a week. Using this information, estimate the total percentage of the company that exercised at least 3 times a week by using the Hansen-Hurwitz dropout plan (method)
The estimated total percentage of the company that exercised at least 3 times a week is approximately 20.5%.
Using the Hansen-Hurwitz dropout plan (method), the estimated total percentage of the company that exercised at least 3 times a week is approximately 20.5%. This can be calculated by multiplying the response rate of the survey (4860/6480) by the response rate of the sample (7/80).
The response rate of the survey is 0.7479 and the response rate of the sample is 0.0875. To get the estimated total percentage of the company that exercised at least 3 times a week, you would multiply these two numbers together to get 0.205 (0.7479 x 0.0875 = 0.205).
So, the percentage is 20.5%.
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