The total profit P(x)(in thousands of dollars) from the sale of x hundred thousand automobile tires is approximated by P(x) = -x + 15x + 72x - 300, x ≥ 5.
Find the number of hundred thousands of tires that must be sold to maximize profit. Find the maximum profit.

Answers

Answer 1

The maximum profit is $1,892,250.

How to find the maximum profit?

The profit function is given by[tex]P(x) = -x^2 + 15x + 72x - 300 = -x^2 + 87x - 300.[/tex]

To find the number of hundred thousands of tires that must be sold to maximize profit, we need to find the value of x that maximizes P(x).

We can do this by finding the critical point of P(x) and then checking whether it corresponds to a maximum or a minimum.

The derivative of P(x) is:

P'(x) = -2x + 87

Setting this equal to zero to find critical points, we get:

-2x + 87 = 0

Solving for x, we get:

x = 43.5

Since the problem specifies that x must be at least 5, we know that the critical point x = 43.5 corresponds to a maximum.

Therefore, the number of hundred thousands of tires that must be sold to maximize profit is 43.5.

To find the maximum profit, we substitute x = 43.5 into the profit function:

[tex]P(43.5) = -43.5^2 + 87(43.5) - 300 = 1892.25[/tex]

Therefore, the maximum profit is $1,892,250.

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Related Questions

An amusement park charges $4. 25 for admission, plus $1. 50 for each ride ticket. Chase has $30 to spend on admission and ride tickets. What is the greatest number of ride tickets Chase can buy?

Answers

The greatest number of ride tickets Chase can buy is 17 and spend $30 for total cost of admission.

To solve this problem, we need to use algebraic equations. Let x be the number of ride tickets that Chase can buy. We know that the total amount of money Chase can spend on admission and ride tickets is $30, so we can write:

4.25 + 1.5x = 30

To solve for x, we can isolate the variable by subtracting 4.25 from both sides and then dividing by 1.5:

1.5x = 25.75
x = 17.17

Since Chase can't buy a fractional number of ride tickets, we need to round down to the nearest whole number. Therefore, Chase can buy a maximum of 17 ride tickets with his $30 budget.

To double-check our answer, we can calculate the total cost of admission and 17 ride tickets:

4.25 + 1.5(17) = 29.25

This is less than $30, so it is indeed possible for Chase to buy 17 ride tickets within his budget.

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On a baseball diamond, home plate and second base lie on the perpendicular bisector of the line segment that joins first and third base. First base is 90 feet from home plate. How far is it from third base to home plate? Sketch a baseball diamond on a separate sheet of paper, labeling home plate as point A
, first base as B
, second base as C
, and third base as D. Label the intersection of AC⎯⎯⎯⎯⎯
and BD⎯⎯⎯⎯⎯
as E. Using the Perpendicular Bisector Theorem, determine how far it is from third base to home plate. Describe your conclusion in the context of the situation

Answers

Using the Perpendicular Bisector Theorem, the distance from third base to home plate is 90 feet. This means that all the bases are equidistant from home plate, which is a fundamental property of a baseball diamond.

To find the distance from third base to home plate, we need to use the Perpendicular Bisector Theorem, which states that if a point lies on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.

First, we draw a baseball diamond with points A, B, C, and D labeled as described in the problem.

Next, we draw the line segment that joins first base (B) and third base (D), and we construct the perpendicular bisector of this segment by drawing a line through the midpoint of BD and perpendicular to BD. Let's label the point where the perpendicular bisector intersects the line that connects home plate (A) and second base (C) as E.

Since E lies on the perpendicular bisector of BD, it is equidistant from B and D. We know that first base (B) is 90 feet from home plate (A), so the distance from home plate to E must also be 90 feet. Therefore, the distance from third base (D) to home plate (A) is also 90 feet.

In conclusion, using the Perpendicular Bisector Theorem, we determined that the distance from third base to home plate is 90 feet.

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A cylindrical jar of peanut butter has a height of 4 inches and a diameter of 3 inches. How many cubic inches of peanut butter can the jar hold? Use π = 3.14.

28.26 in3
37.68 in3
113.04 in3
150.72 in3

Answers

The jar can hold 28.26 cubic inches of peanut butter

How to calculate the amount of cubic inches of peanut butter?

The first step is to write out the parameters

A cylindrical jar of peanut has a height of 4 inches

The diameter is 3 inches

The next step is to calculate the radius, this is done by dividing the diameter by 2

radius= 3/2

= 1.5

The formula used to calculate the cubic inches of peanut butter is

V= πr²h

= 3.14 × 1.5² × 4

= 3.14 × 2.25 × 4

= 28.26

Hence the jar can hold 28.26 cubic inches of peanut butter

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28 is the geometric mean of 13 and another number. Find the number and round your answer to the nearest hundredth

Answers

To find the number when 28 is the geometric mean of 13 and that number, we'll use the formula for the geometric mean: √(a * b) = GM, where a and b are the two numbers, and GM is the geometric mean. In this case, a = 13, GM = 28.

Step 1: Substitute the given values into the formula:
√(13 * b) = 28

Step 2: Square both sides to get rid of the square root:
(√(13 * b))^2 = 28^2
13 * b = 784


Step 3: Divide both sides by 13 to isolate b:
b = 784 / 13
b ≈ 60.31


So, the other number is approximately 60.31 when rounded to the nearest hundredth. In summary, 28 is the geometric mean of 13 and 60.31, as √(13 * 60.31) ≈ 28.

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Solve problems 1 and 4 ONLY with the rules given on the paper.

Answers

The solution to the equations obtained using inverse trigonometric function values are;

1. x ≈ 0.65

4. x ≈ 0.95

What are trigonometric functions?

Trigonometric functions indicates the relationships between the angles in a right triangle and two of the sides of the triangle. Trigonometric functions are periodic functions.

The value of x is obtained from the inverse trigonometric function of the output value of the trigonometric function, as follows;

The inverse function for sine is arcsine

The inverse function for cosine is arccosine

The inverse function for the tangent of an angle is arctangent

1. sin(x) = 0.6051

Therefore; x = arcsine(0.6051) ≈ 0.65 radians

The value of x in the interval [0·π, 2·π] is x ≈ 0.65

4. tan(x) = 1.3972

Therefore, x = arctan(1.3972) ≈ 0.95

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Which corectly renames 7/8 and 5/6 using a common denominator

Answers

The 7/8 and 5/6, when renamed using a common denominator of 24, become 21/24 and 20/24

How we find the common denominator?

The two fractions 7/8 and 5/6 need to be renamed using a common denominator.

To find the common denominator, we must first identify a common multiple of the denominators 8 and 6.

The smallest common multiple of 8 and 6 is 24. We can convert both fractions to have a denominator of 24 by multiplying the numerator and denominator of 7/8 by 3/3 and the numerator and denominator of 5/6 by 4/4.

This results in 21/24 and 20/24, respectively.  

Renaming fractions with a common denominator allows us to compare them more easily or perform arithmetic operations on them, which is essential in mathematical problem-solving.

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Lucinda has already earned $30 walking dogs. She earns $3 per dog walked, and she needs at least $80 to buy more leashes. Write and solve an inequality to determine how many more dogs Lucinda will need to walk to have at least $80.

Answers

I would say she has to walk 17 dogs, im not sure if that's correct though

Let's assume that Lucinda needs to walk "x" more dogs to have at least $80. Then, the amount of money she will earn from walking those "x" dogs can be calculated by multiplying the number of dogs by the amount of money earned per dog, which is $3:

Amount of money earned from walking "x" dogs = $3x

To determine how many more dogs Lucinda needs to walk to have at least $80, we can write the following inequality:

$30 + $3x ≥ $80

Simplifying the inequality, we get:

$3x ≥ $50

Dividing both sides by 3, we get:

x ≥ 16.67

Since we can't walk a fraction of a dog, we need to round up to the nearest whole number. Therefore, Lucinda needs to walk at least 17 more dogs to have at least $80.

Find the slope of the line

Answers

Answer:

m = -2

Step-by-step explanation:

We Know

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (-3,2) (-2,0)

We see the y decrease by 2, and the x increase by 1, so the slope is

m = -2

The slope is -2 that’s the answer

Ruth has a street lamp in front of her house, represented by AB . Her mom insists that at night she only plays within its light. If AB = 54,

Answers

Using trigonometry, the length that Ruth has to play in if she plays between her friend's house (point D) and the edge of the lighted area (point C) is 6.72 feet. Option C is the correct answer.

To solve this problem, we need to use trigonometry. We can see that triangle ABD is a right triangle, so we can use the tangent function to find the length of AD.

First, we need to find the length of BD. We can use the right triangle trigonometry again to find it.

tan(27) = BD/AB

BD = AB × tan(27)

BD = 54 × tan(27)

BD ≈ 24.12

Now, we can use the right triangle trigonometry on triangle BCD to find the length of CD.

tan(41) = CD/BD

CD = BD × tan(41)

CD ≈ 18.85

Finally, we can use the Pythagorean theorem on triangle ACD to find the length of AD.

AD² = AC² - CD²

AD² = 20² - 18.85²

AD ≈ 6.72

Therefore, the length that Ruth has to play is approximately 6.72 feet.

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The question is -

Ruth has a street lamp in front of her house, represented by Segment AB The street Lamp is 20 feet tall. Her mom insists that at night she only plays within its light. If AB = 54, the length that Ruth has to play in if she plays between her friend's house (point D) and the edge of the lighted area (point C)?

Options are:

a. 1.7 feet

b. 2.2 feet

c. 6.7 feet

d. 5.9 feet

A three digit number is such that twice the hundreds digit is more than the tens digit by 2. The unit digit is thrice the hundred digit. When the digits are reversed the number is increased by 594. Find the number.(5 marks)

Answers

Answer:

Step-by-step explanation:

Let the three-digit number be represented as $abc$, where $a$ is the hundreds digit, $b$ is the tens digit, and $c$ is the units digit.

From the problem, we have two equations:

Equation 1: $2a=b+2$

Equation 2: $c=3a$

We can use these equations to solve for $a$, $b$, and $c$.

Starting with Equation 1, we can isolate $b$ to get $b=2a-2$.

Next, we can substitute Equation 2 into Equation 1 to get $2a=3a-6+2$, which simplifies to $a=8$.

Using this value of $a$, we can now find $b$ and $c$. From Equation 2, we have $c=3a=24$. And from Equation 1, we have $b=2a-2=14$.

Thus, the original three-digit number is $abc=824$.

When we reverse the digits to get $cba=428$, we increase the number by 594, so we have $cba=abc+594=824+594=1418$.

Therefore, the answer is $\boxed{824}$.

The probability that Sam parks in a no-parking zone and gets a parking ticket is 0. 07,and the probability that Sam Connor finr a legal parking space and has to park in the no-parking zone is 0. 50. On Monday,Sam arrives at school and has to park in a no-parking zone. Find the probability that he will get a parking ticket.

Answers

The probability that Sam will get a parking ticket given that he has to park in a no-parking zone on Monday is approximately 0.1308 or 13.08%.

We can use Bayes' theorem to solve this problem. Let A be the event that Sam gets a parking ticket and B be the event that Sam parks in a no-parking zone. Then, we want to find P(A|B), which is the conditional probability of A given B.

Bayes' theorem states that P(A|B) = P(B|A)*P(A)/P(B), where P(B|A) is the probability of B given A, P(A) is the prior probability of A, and P(B) is the prior probability of B.

From the problem, we know that P(A) = 0.07, P(B|A) = 1 (since if Sam parks in a no-parking zone, he will definitely get a parking ticket), and P(B|not A) = 0.50 (since if Sam finds a legal parking space, he has a 0.50 probability of parking in a no-parking zone).

To find P(B), we can use the law of total probability, which states that P(B) = P(B|A)*P(A) + P(B|not A)*P(not A), where P(not A) = 1 - P(A).

Therefore, P(B) = 10.07 + 0.50(1-0.07) = 0.5351.

Finally, we can use Bayes' theorem to find P(A|B):

P(A|B) = P(B|A)P(A)/P(B) = 10.07/0.5351 ≈ 0.1308.

Therefore, the probability that Sam will get a parking ticket given that he has to park in a no-parking zone on Monday is approximately 0.1308 or 13.08%.

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Asako’s employer covers 90% of the cost of a $3,500 per year disability insurance plan and 60% of a $1,300 per year disability insurance plan. If Asako gets paid monthly, what is the total amount deducted frok her gross income health and disability insurance during each pay period

Answers

The total amount deducted from her gross income health and disability insurance during each pay period is $72.50.

To calculate the total amount deducted from Asako's gross income for health and disability insurance during each pay period, we need to first determine the cost of each insurance plan after the employer's coverage.

For the $3,500 per year disability insurance plan, Asako's employer covers 90% of the cost, which means Asako is responsible for 10% of the cost.

10% of $3,500 is $350, so Asako's cost for the $3,500 per year disability insurance plan is $350 per year.

For the $1,300 per year disability insurance plan, Asako's employer covers 60% of the cost, which means Asako is responsible for 40% of the cost.

40% of $1,300 is $520, so Asako's cost for the $1,300 per year disability insurance plan is $520 per year.

Since Asako gets paid monthly, we need to divide the annual cost of each insurance plan by 12 to determine the cost per pay period.

For the $3,500 per year disability insurance plan, Asako's cost per pay period is $350 / 12 = $29.17.

For the $1,300 per year disability insurance plan, Asako's cost per pay period is $520 / 12 = $43.33.

Therefore, the total amount deducted from Asako's gross income for health and disability insurance during each pay period is $29.17 + $43.33 = $72.50.

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Ralph's t-shirt company sells custom t-short for $5. 00 each plus a $20 shipping and design fee. Frank's t-shirt company sells t-shirts for $10 each with no additional fees

Answers

To compare Ralph's and Frank's t-shirt companies, let's calculate the total cost of buying a certain number of t-shirts from each company.

1. Ralph's t-shirt company:

- Price per t-shirt: $5.00

- Shipping and design fee: $20.00

Total cost for Ralph's t-shirts = (number of t-shirts * $5.00) + $20.00

2. Frank's t-shirt company:

- Price per t-shirt: $10.00

- No additional fees

Total cost for Frank's t-shirts = number of t-shirts * $10.00

Now you can compare the total costs for each company depending on the number of t-shirts you want to buy.

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Luna and ger friend maka sandwiches with 1/3 of a baguette. They sahre the baguette equally

Answers

Luna and her friend Maka decided to make sandwiches using 1/3 of a baguette. To ensure fairness, they agreed to divide the baguette equally between them. They carefully measured the baguette and cut it into two equal parts, ensuring each of them received an equal portion.

Luna and Maka then began assembling their sandwiches. They spread their preferred fillings on their respective portions of the baguette, adding layers of vegetables, meats, and condiments to create delicious sandwiches.

After completing their sandwich preparation, Luna and Maka sat down together to enjoy their culinary creations. They appreciated the taste and quality of their sandwiches, delighted by the shared experience and the equal distribution of the baguette.

As they savored each bite, Luna and Maka cherished their friendship and the simple joy of sharing a meal together. They found contentment in the realization that even the smallest things, like a shared baguette, could strengthen their bond and create lasting memories.

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Here is a set of data showing the test scores for US History class:


56, 88, 70, 72, 90, 85, 99, 65, 66, 54, 74, 85, 91, 92, 72, 88, 97, 62, 88 Create a stem and leaf plot to show this data. Hint: Decide how many stems you will need.


can somebody help me ?

Answers

Hi! I'd be happy to help you create a stem and leaf plot using the provided set of data for US History class test scores.

Step 1: Arrange the data in ascending order.


54, 56, 62, 65, 66, 70, 72, 72, 74, 85, 85, 88, 88, 88, 90, 91, 92, 97, 99

Step 2: Determine the range of the data.


The data ranges from 50s to 90s, so we will need 5 stems: 5, 6, 7, 8, and 9.

Step 3: Create the stem and leaf plot using the stems and corresponding leaves (the units digits of the data).

5 | 4 6
6 | 2 5 6
7 | 0 2 2 4
8 | 5 5 8 8 8
9 | 0 1 2 7 9

Here is the completed stem and leaf plot for the US History class test scores. The stems represent the tens digits (50s, 60s, 70s, 80s, 90s), and the leaves represent the units digits of the scores in each range.

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Find the area of the polygon.
18 m
29 m
36 m
The area of the polygon is 14
14 m
square meters.

Answers

The total area of the composite figure is 576 square meters

Calculating the area of the polygon figure

From the question, we have the following parameters that can be used in our computation:

The composite figure

The total area of the composite figure is the sum of the individual shapes

So, we have

Surface area = Rectangle + Trapezoid

Using the area formulas, we have

Surface area = 29 * 16 + 1/2 *(14 + 18) * (36 - 29)

Evaluate

Surface area = 576

Hence. the total area of the figure is 576 square meters

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Complete question

Find the area of the polygon.

See attachment

The area of the polygon is ____ square meters.

The chart below represents the number of marbles in a jar.

Answers

The probability that a marble selected from the jar is green, P(green) = 5/19. The correct option is therefore;

5/19

What is the theoretical probability of an event occurring?

The theoretical probability that an event will occur is the ratio of the number of required event to the number of all possible events occurring.

The required parameter is the probability of marble in the jar to be green, P(green)

The number of each color of marbles in the jar are;

Red = 5, Yellow = 11, Blue = 7, Green = 10, Brown = 5

The total number of marbles in the jar is therefore;
5 + 11 + 7 + 10 + 5 = 38

The probability that a marble in the jar is green, P(green) = 10/38 = 5/19

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How to find the area of this whole figure? Please help me

Answers

The area of the whole figure is 31.5 sq. units.

What is the area of a figure?

The area of a given figure connotes its expanse in a 2 dimensional plane. The shape and size of a given figure determines how to calculate its area.

From the given question, the figure given can be likened to a rhombus. So that;

area of a rhombus = (diagonal 1 * diagonal 2)/ 2

Then,

area of the figure = (diagonal 1 * diagonal 2)/ 2

where: diagonal 1 = 7.5, and diagonal 2 = 8.4

So that;

area of the figure = (7.5*8.4)/ 2

                             = 63/ 2

                             = 31.5

The area of the whole figure is 31.5 sq. units.

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A credit card had a APR of 33. 01% all of last year and compounded interest daily. What was the credit card’s effective interest rate last year?

Answers

The credit card's effective interest rate for the year is [tex]40.51%.[/tex]%

To solve this problem

We can use the following formula:

Effective annual interest rate is calculated as[tex](1 + APR/365)365 - 1.[/tex]

The interest is compounded everyday in this case and the APR is 33.01 percent. When we enter these values into the formula, we obtain:

Effective annual interest rate =[tex](1 + 0.3301/365)^365 - 1[/tex]

Effective annual interest rate =[tex]1.4051 - 1[/tex]

Effective annual interest rate =[tex]1.4051 - 1[/tex]

So the credit card's effective interest rate for the year is[tex]40.51%.[/tex]%

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A pyramid has a base that is a regular hexagon with each side measuring 10 units. The base of the pyramid is shown below.If the pyramid has a height of 12 units, what is the approximate volume of the pyramid?

Answers

Answer:

Step-by-step explanation:

The volume of a pyramid can be calculated using the formula:

V = (1/3) * Base Area * Height

To calculate the volume of this pyramid, we need to first find the area of its regular hexagonal base. The formula for the area of a regular hexagon is:

A = (3√3/2) * s^2

where s is the length of one side of the hexagon. Substituting s = 10, we get:

A = (3√3/2) * 10^2 = 259.80 square units (approx)

Now we can use the formula for the volume of a pyramid to find the volume of this pyramid:

V = (1/3) * 259.80 * 12 = 1039.20 cubic units (approx)

Therefore, the approximate volume of the pyramid is 1039.20 cubic units.

A) What internal goods does mathematics offer? Discuss how these goods multiply when you share them with others. B) Discuss creative power and coercive power that you have witnessed in mathematical settings. C) How can teachers affirm their students' dignity as creative human beings in the ways they do mathematics?

Answers

A) Internal goods in mathematics include problem-solving skills, logical thinking, analytical reasoning, and a deep understanding of mathematical concepts.

B) Coercive power, on the other hand, might manifest when individuals impose their methods or beliefs on others, potentially stifling creativity and discouraging alternative perspectives.
C) Teachers affirm their students' dignity as creative human beings in the ways they do mathematics by creating a safe space, encourage exploration and expression, value the learning process, celebrate creativity and originality in problem-solving

A) When you share these goods with others, they multiply in the sense that others also develop these skills, fostering collaboration, and generating new ideas, ultimately contributing to the overall progress in the field of mathematics.
B) Creative power in mathematical settings can be seen when individuals or teams come up with innovative solutions to problems, develop new theories, or find unique ways to apply mathematics to real-world situations.
C) Teachers can affirm their students' dignity as creative human beings in the ways they do mathematics by:
1. Encouraging students to explore multiple solution methods and strategies, allowing them to find the approach that best suits their thinking style.
2. Valuing each student's input, ideas, and questions, creating a safe and supportive environment for them to express their thoughts.
3. Challenging students with open-ended problems that require creativity and critical thinking, emphasizing the importance of understanding concepts over rote memorization.
4. Recognizing and celebrating each student's unique strengths and contributions to the learning process, promoting a growth mindset and a sense of accomplishment.

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4. Use the data below for the calculations.
Average hours sleeping per weeknight: 4, 5, 8, 12, 10, 6, 7, 9, 8, 8, 6, 6, 4, 3, 9
Mean:

Median:

Mean Absolute Deviation:


Absolute Deviation from Median:

Answers

The mean is 7

The median is the middle value, which is 7.

Mean Absolute Deviation: 2

How to solve for the mean absolute deviation

Step 3: Find the absolute deviation of each value from the mean:

|4-7.067|, |5-7.067|, |8-7.067|, |12-7.067|, |10-7.067|, |6-7.067|, |7-7.067|, |9-7.067|, |8-7.067|, |8-7.067|, |6-7.067|, |6-7.067|, |4-7.067|, |3-7.067|, |9-7.067|

These absolute deviations are: 3.067, 2.067, 0.933, 4.933, 2.933, 1.067, 0.067, 1.933, 0.933, 0.933, 1.067, 1.067, 3.067, 4.067, 1.933.

Step 4: Find the mean of these absolute deviations to find the mean absolute deviation:

Mean Absolute Deviation = (3.067+2.067+0.933+4.933+2.933+1.067+0.067+1.933+0.933+0.933+1.067+1.067+3.067+4.067+1.933) / 15 = 2

Step 5: Find the absolute deviation of each value from the median:

|4-8|, |5-8|, |6-8|, |6-8|, |6-8|, |7-8|, |8-8|, |8-8|, |8-8|, |9-8|, |9-8|, |10-8|, |12-8|, |8-8|, |3-8|

These absolute deviations are: 4, 3, 2, 2, 2, 1, 0, 0, 0, 1, 1, 2, 4, 0, 5.

Therefore, the absolute deviation from the median is 5.

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I NEED HELP PLEASE!

1. 3 statements about limiting frictional force between two surfaces are given below.


A - Nature of surfaces in contact affects to limiting frictional force.

B - Normal reaction between them affects to limiting frictional force.

C - Area of surfaces in contact affects to limiting frictional force.


Correct statement / statements from above A, B, C is/ are,

(1) A

(2) B

(3) A and C

(4) A, B and C

Answers

The correct statement is (3) A and C.

The limiting frictional force between two surfaces is dependent on the nature of the surfaces in contact and the area of the surfaces in contact. The normal reaction between them is not a factor affecting the limiting frictional force.
Let's analyse the options:Option 1: Statement A is correct. The nature of surfaces in contact determines the friction between them. Rough and irregular surfaces have higher friction than smooth surfaces.Option 2: Statement B is incorrect. The normal reaction between the surfaces does not affect the limiting frictional force. Only the maximum static friction depends on the normal reaction.Option 3: Statements A and C are correct. Both nature of surfaces and area of contact determine the friction between them.Option 4: All statements A, B and C are incorrect. Nature of surfaces, normal reaction and area of contact affect the limiting frictional force between two surfaces.

The limiting frictional force depends only on:

A. The nature of surfaces in contact: Rough and irregular surfaces have higher friction than smooth surfaces. C. The area of surfaces in contact: Larger the contact area, higher is the friction between the surfaces.(3) A and C is the right option

The dean of students at a large college is interested in learning about their opinions regarding the percentage of


first-year students who should be given parking privileges in the main lot. He sends out an email survey to all


students about this issue. A large number of first-year students reply but very few sophomores, juniors, and seniors


reply. Based on the responses he receives, he constructs a 90% confidence interval for the true proportion of


students who believe first-year students should be given parking privileges in the main lot to be (0. 71, 0. 79). Which


of the following may have an impact on the confidence interval, but is not accounted for by the margin of error?


O response bias


O nonresponse bias


O sampling variation


O undercoverage bias


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Answers

The dean of students at a large college is interested in learning about their opinions regarding the percentage of students who are satisfied with their academic experience. This is an important question for the dean to consider, as it can help them identify areas for improvement and ensure that they are meeting the needs of their students.

To gather this information, the dean may choose to conduct a survey or hold focus groups with students to hear their feedback. They may also review data on student retention rates and academic performance to get a sense of how satisfied students are with their experience at the college.

Once the dean has gathered this information, they can use it to make informed decisions about how to improve the academic experience for their students. This may involve investing in new programs or resources to better support students, or making changes to existing programs based on feedback from students.

Ultimately, by taking the time to gather and listen to student opinions about their academic experience, the dean can create a more student-centered learning environment that meets the needs and expectations of their diverse student population.

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Use a calculator to find the values of the inverse trigonometric functions. Round to the nearest degree.

Answers

The values of the inverse trigonometric functions are 72°, 76° and 85°.

How to explain the steps

The range of the inverse trigonometric function is limited to a certain interval based on the domain of the original trigonometric function.

Its also important to identify the trigonometric ratio that corresponds to the given value.

The value on degree for inverse of sin (2/3) will be 41.81° which is 42°. Also, inverse of tan(4) is 76° using the calculator.

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Use a calculator to find the values of the inverse trigonometric functions. Round to the nearest degree.

inverse of sin (2/3)

inverse of tan(4)

inverse of tan (0.1)

A string has a length of 80 cm. It is cut into pieces in the ratio 1: 4: 5. Calculate the length of the longest piece.

Answers

First, we need to find the total number of parts in the ratio 1:4:5:

1 + 4 + 5 = 10

This means that the string is divided into 10 equal parts. To find the length of each part, we divide the total length of the string by the number of parts:

80 cm ÷ 10 = 8 cm

Now, we can find the length of the longest piece, which is 5 times the size of each part:

8 cm x 5 = 40 cm

Therefore, the length of the longest piece is 40 cm.

This trapezoid-based right prism has a volume of 30 cm


6 cm


5 cm


1 cm


What is the area of the base of the prism?

Answers

The area of the base of the prism is,

Area = 5.5 cm²

We have to given that,

This trapezoid-based right prism has a volume of 30 cm³.

We have;

Here we assume

a = 6

b = 5

c = 1

Now we know that

Area = (a + b) c / 2

Area = (6 + 5) 1 /2

Area = 11/2

Area = 5.5 cm²

Thus, The area of the base of the prism is,

Area = 5.5 cm²

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Jack bought 540 shares of Sound Foundations stock years ago for $44.50 per share. He sold them yesterday for $49.54 per share. What was the percent capital gain for the 540 shares, rounded to the nearest percent?

Answers

Answer:

11.325 %

Step-by-step explanation:

44.50 . . ... .. 100%

0.445. . . . . . . . .1 %

49.54 . . . . . . . .?%

49.54 : 0.445=111.325 %

111.325-100 = 11.325%

Answer:

Step-by-step explanation:

Jamal winchester invested 75,000 in to a property. He expects his annual expenses to be 18,000. If Jamal wants to earn 8% annual income on his capital investment, what monthly rent must he charge?​

Answers

Jamal must charge a monthly rent of 2,000 to earn an 8% annual income on his capital investment.

It is given that Jamal Winchester invested 75,000 in to a property and he expects his annual expenses to be 18,000. Jamal wants to earn 8% annual income on his capital investment. Hence, the monthly rent he must charge is determined as follows.

1. Calculate the desired annual income:

75,000 (capital investment) x 0.08 (8% annual income) = 6,000.

2. Add the annual expenses:

6,000 (desired annual income) + 18,000 (annual expenses) = 24,000.

3. Divide by 12 months to find the monthly rent: 24,000 ÷ 12 = 2,000.

Jamal must charge a monthly rent of 2,000.

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The figure below has semicircles on each side of a 40 meter by 40 meter square. Find the area of the enclosed figure. Round to the nearest tenth

Answers

The area enclosed by the circle is given as 7494.12 m² and the mistake Frank have made is he subtracted the area of the square and the area of 4 semi-circles.

We are given that the figure is made by attaching semicircles to each side of a 54 dash m​-by-54 dash m square. Frank says the area is 1 comma 662.12 m squared.

We have to find the error made by Frank,

Area of the square = Side of the square x Side of the square

In the question; the side of the square given is 54 m and this would also be the diameter of the semicircle attached to each side of a square.

So, the radius of the semicircle = diameter /2  = 54/2 = 27 m

Now, the area of the square = 54 x 54 = 2916 m².

Also, the area of the semi-circle = [tex]\frac{\pi r^2}{2}[/tex] = [tex]\frac{3.14*27^2}{2}[/tex] = 1144.53 m² .

As there are a total of 4 semi-circles attached to the square, so the area of all the 4 semi-circles = 4 x 1144.53  = 4578.12

Now, the total area of the figure = Area of the square + Area of 4 semi-circles

                = 2916 + 4578.12

                = 7494.12 m².

The error made by Frank was that he subtracted the area of the square and the area of 4 semi-circles to find the area of the whole figure as (4578.12  - 2916  = 1662.12 ).

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Complete question:

Frank needs to find the area enclosed by the figure. The figure is made by attaching semicircles to each side of a 54 m​-by-54 m square. Frank says the area is 1662.12 meter squared. Find the area enclosed by the figure. Use 3.14 for pi. What error might Frank have​ made?

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