4.5.36
A smoke jumper jumps from a plane that is 1500 ft above the ground. The function h= - 16t^2+ 1500 gives the jumper's height h in feet during the free fall att seconds
a. How long is the jumper free fall if the parachute opens at 1000 ft?
b. How long is the jumper in free fall if the parachute opens at 940 ft?
c. What is a reasonable domain and range for the function h?

Answers

Answer 1

We have a jumper that jumps from 1500ft above the ground, such that its height as a function of time is given by:

h(t) = -16*t^2 + 1500

The solutions are:

A) 5.59 seconds

B) 5.91 seconds

C) D = (0s, 9.68s)

    R = [0ft, 1500ft]

Notice that when t = 0, h = 1500, then at the initial time (t = 0) the height is 1500 (in ft), which means that the zero of the height is the ground.

a) How long is the jumper free fall if the parachute opens at 1000 ft?

Here we need to solve:

h = 1000 = -16*t^2 + 1500

Now we just need to solve this for t:

16*t^2 = 1500 - 1000 = 500

t^2 = 500/16 = 31.25

t = √31.25 = 5.59

So it takes 5.59 seconds to open the parachute.

B) similar to before, this time we need to solve:

h = 940 = -16*t^2 + 1500

16*t^2  =1500 - 940 = 560

t^2 = 560/16 = 35

t = √35 = 5.91

So it takes 5.91 seconds to open the parachute.

C) The domain is the set of inputs that we can use in the function.

The minimum of the domain is t = 0, when the jumper jumps.

To find the maximum of the domain we need to find the maximum time at which he could open the parachute, that is when h = 0ft, just in the ground.

Then we solve:

h = 0 = -16*t^2 + 1500

16*t^2 = 1500

t = √(1500/16) = 9.68

Then a reasonable domain is (0s, 9.68s)

And the range is the set of possible outputs, which will be all the possible heights of the jumper. We know that all of these are between 0ft and 1500ft, thus the range is [0ft, 1500ft]

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Related Questions

Grady is excavating the foundation of a house. If the hole will be
40 feet long, 24 feet wide, and 4 feet deep, how many cubic feet
of dirt must be removed from the site?

Answers

Answer:

3,840 cubic feet

Step-by-step explanation:

V=LWH

V= 40X24X4

V=3,840 cubic feet

How many moles are 1.20 x 1025 atoms of phosphorous?

Answers

Answer:

19.93 moles

Step-by-step explanation:

Select the table of values that you would use to graph f(x) = 3x2 – 4.
Hello Please help.

Select the table of values that you would use to graph f(x) = 3x2 4.Hello Please help.

Answers

The the table of values that you would use to graph \(f(x) = 3x^{2} -4\)  is option "B"

What is point on graph?

A point is the basic relationship displayed on a graph. Each point is defined by a pair of numbers containing two coordinates. A coordinate is one of a set of numbers used to identify the location of a point on a graph.

According to the question

Points on graph for equation :

\(f(x) = 3x^{2} -4.\)  

Now,

Table of points on graph

x                  y

-2                8

-1                 -1

0                 -4

1                   -1

2                   8

Hence, The the table of values that you would use to graph \(f(x) = 3x^{2} -4\)  is option "B" .

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Type the correct answer in the box. Use the information from the image to complete the table then determine the total number of bacteria after the first hour(60 minutes).​

Type the correct answer in the box. Use the information from the image to complete the table then determine

Answers

Answer:

Number of Bacteria, B(t)   2    4      8      16

Step-by-step explanation:

To find the B(t) values when t equals 0 through 3, look at the diagram and count the number of bacteria: when t is 0, B(t) is 2, when t is 1, B(t) is 4; when t is 2, B(t) is 8; and when t is 3, B(t) is 16.

Every second of video time equals 20 minutes of real time. So, one hour, or 60 minutes, of real time is 3 seconds of video time, which results in 16 bacteria.

Number of Bacteria, B(t)   2    4      8      16

The total number of bacteria after the first hour(60 minutes) is 16.

What is unitary method?

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

According to the question

He is taking screenshots of the video after every second of video time, with each second of video time correlating to 20 minutes of real time.

In the video, each bacteria cell splits into two cells with each passing second, as seen in the images from the video.

To find the B(t) values when t equals 0 through 3, look at the diagram and count the number of bacteria: when t is 0, B(t) is 2, when t is 1, B(t) is 4; when t is 2, B(t) is 8; and when t is 3, B(t) is 16.

Every second of video time equals 20 minutes of real time. So, one hour, or 60 minutes, of real time is 3 seconds of video time, which results in 16 bacteria.

Number of Bacteria, B(t)   2    4      8      16

Hence,

The total number of bacteria after the first hour(60 minutes) is 16.

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14. What is the constant of proportionality (unit rate) shown in the table?
Pounds of Apples
1
2
3
4
5
Cost
$0.78
$1.56
$2.34
$3.12
$3.90
O
A. $0.39
O
B. $0.78
O
C. $2.34
O
D. $3.90

14. What is the constant of proportionality (unit rate) shown in the table?Pounds of Apples12345Cost$0.78$1.56$2.34$3.12$3.90OA.

Answers

Answer:

B. $0.78

Step-by-step explanation:

Constant of proportionality = 0.78/1 = 1.56/2 = 0.78



Tito purchased sandwiches and a gallon of milk for himself and his friends. Each

sandwich cost $9. The gallon of milk cost $6. The total cost of the meal was $33.

Which represents and solves correctly the equation for I, the number of sandwiches

that Tito purchased?

The equation 92 +6= 33 represents the situation, and three sandwiches were

purchased.

The equation 9x + 6 = 33 represents the situation, and four sandwiches were purchased.

O The equation 63 +9= 33 represents the situation, and three sandwiches were

purchased.

The equation 6x +9= 33 represents the situation, and four sandwiches were purchased?

Answers

Answer:

The equation 9x + 6 = 33 represents the situation, and three sandwiches were purchased.

Step-by-step explanation:

Each sandwich cost $9.

The gallon of milk cost $6.

The total cost of the meal was $33.

Let us represent the number of sandwiches that Tito bought as x

The equation is:

$9 × x + $6 = $33

9x + 6 = 33

Collect like terms

9x = 33 - 6

9x = 27

x = 27/9

x = 3

Hence,

The equation 9x + 6 = 33 represents the situation, and three sandwiches were purchased.

PLEASE HELP FAST !!!!!!!!
Identify the equation that represents a quadratic relationship

PLEASE HELP FAST !!!!!!!!Identify the equation that represents a quadratic relationship

Answers

Answer:

Step-by-step explanation:

Quadratic means squared equation so

the first one is your answer.

y= 4x²

Two baseball teams are playing each other twice. Enter the values to complete the possible outcomes for one team. Use W for a win and L for a loss. Then enter the number of outcomes in the sample space.

Answers

First game: W second W
First game W second L
First game L second L
First game L second W

Answer:

2+2+2 x 2 so 12

Step-by-step explanation:

well since there’s two teams either of thme could win or lose or tie I think I’m I wrong though I’m really tired so

Hello I need help not sure if I got it incorrectly

Hello I need help not sure if I got it incorrectly

Answers

Answer:  (-4, 1)

The first row of the table shows (x,y) = (-4,2). If we add in (-4,1), then we will re-use x = -4 a second time. The input x = -4 leads to multiple outputs of 2 and 1 at the same time. Visually the two points stack on each other to form a vertical line, therefore failing the vertical line test.

The second answer choice (1,-4) looks like your teacher might be trying to trick you or place out a trick/trap answer due to how similar it looks. This point can be added and the function is still valid because x = 1 hasn't been used yet in the table.

x/2 - 4=-16 wha would x equal

Answers

Answer: -24

Step-by-step explanation:

x/2= -16+4

x/2= -12

x= -12 x 2

x= -24

Answer:

x = -24

Step-by-step explanation:

Add the same term to both sides of the equation

Simplify

Multiply all terms by the same value to eliminate fraction denominators

Simplify

Solve for x.

Show work

Solve for x.Show work

Answers

Answer:

x=11.34

Step-by-step explanation:

x / -5.4 = -2.1

Multiply -5.4 in both sides

x = 11.34

Have a good day ^^

Given the equation of the parabola - 36y = ?

The focus of the parabola is:

(0,9)

(-9,0)

(0,-9)

Answers

Correct question is ;

Given the equation of the parabola x² = -36y

The focus of the parabola is:

Answer:

Option C - Focus = (0,-9)

Step-by-step explanation:

The equation of the parabola is:

x² = -36y

Thus, y = - x²/36

Using the vertex form,

y = a(x − h)² + k, to determine the values of a, h, and k.

We will have;

y = (-1/36)(x − 0)² + 0

Thus,

a = - 1/36

h = 0

k = 0

The distance (p) from the vertex to a focus of the parabola is gotten by using the following formula.

p = 1/4a

So, p = 1/(4*(-1/36))

p = - 1/(1/9)

p = -9

Now, The focus of a parabola can be found by adding p to the y-coordinate k if the parabola opens up or down.

Focus is (h, k+p)

Plugging in the relevant values, we have;

Focus = (0, (0 + (-9))

Focus = (0,-9)

Do beavers benefit beetles? Researchers laid out 23 circular plots, each 4 meters in diameter, in an area where beavers were cutting down cottonwood trees. In each plot, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle larvae. Ecologists think that the new sprouts from stumps are more tender than other cottonwood growth, so that beetles prefer them. If so, more stumps should produce more beetle larvae. The table contains the data 2 213 3 4 3125 10 30 12 24 36 40 43112756 18 40 2 1 2 2 11 4 12 1 25 8 2114166 5491314 50 13 Stumps Beetle larvae 4 Stumps Beetle larvae To access the complete data set, click the link for your preferred software format Excel Minitab JMP SPSS TI R Mac-TXT PC-TXT CSV CrunchIt! Analyze these data to see if they support the "beavers benefit beetles" idea. Follow the four-step process in reporting your work STATE: Choose the statement that best describes the goal of the research. The number of tree stumps is the explanatory variable, and we expect an increase in the number of tree stumps to induce a decrease in the response variable, the number of beetle larvae. The number of tree stumps is the explanatory variable, and we expect an increase in the number of tree stumps to induce an increase in the response variable, the number of beetle larvae. Beetle larvae are the explanatory variable, and we expect an increase in beetle larvae to induce a decrease in the response variable, the number of tree stumps. Beetle larvae are the explanatory variable, and we expect an increase in beetle larvae to induce an increase in the response variable, the number of tree stumps. PLAN: Make a scatterplot of the data and examine the pattern. Choose the statement that best describes your findings: There is a weak negative linear relationship The relationship doesn't seem to be linear There is a positive linear relationship. There is a strong negative linear relationship SOLVE: Calculate the correlation for the data. Also calculate the slope and intercept of the regression line. Drag the correct answers to the appropriate bins Correlation Slope Intercept Answer Bank 1.286 11.89 0.839 1.661 0.916 3.452 -0.916 -1.286 CONCLUDE: Calculate the fraction of the variation in the values of the number of beetle larvae that is explained by the least-squares regression with the number of tree stumps. Enter your answer as a decimal rounded to three decimal places Which of the choices correctly describes whether the association supports the idea that beavers benefit beetles? Yes, the weak negative association supports the idea that beavers benefit beetles. Yes, the strong positive association supports the idea that beavers benefit beetles No, the strong negative association does not support the idea that beavers benefit beetles There is not enough information to tell No, the strong positive association does not support the idea that beavers benefit beetles.

Answers

.No, the strong negative association does not support the idea that beavers benefit beetles.

The solution is as follows:

The number of tree stumps is the explanatory variable, and we expect an increase in the number of tree stumps to induce an increase in the response variable, the number of beetle larvae.

There is a weak negative linear relationship.

Correlation is : -0.916; Slope: -1.286; Intercept: 3.452

The fraction of the variation in the values of the number of beetle larvae that is explained by the least-squares regression with the number of tree stumps is 0.839. This indicates that the strong negative association does not support the idea that beavers benefit beetles.

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Trent announced to his class that 15) is -5 and |- 5| is 5. Heather disagreed with him. She said that |- 5| and 151 are both 5. Who, if either, is correct? *

Answers

Answer:

Step-by-step explanation:

Looks like Heather is right. Absolutely value bars (the straight up and down lines around the 5 or the -5) dont change the number inside to the opposite sign. Absolute value just makes the number positive. |5| = 5 and |-5| = 5

Solve for y. 2(y-2) -6y=-28​

Answers

Answer:

y = -8

Step-by-step explanation:

2(y-2)- 6y-28 = 0

2y - 4 -6y - 28 = 0

-4y = 32

y = -8

the total surface area of a closed cylinder is 5000cm squared. find the dimensions of the cylinder that maximizes its volume

Answers

The dimensions of the cylinder that maximizes its volume are radius = 16.29 cm and height = 32.57 cm

Total surface area of a cylinder

The total surface area of a cylinder is given by A = 2πr² + 2πrh where

r = radius of cylinder and h = height of cylinder.

Since the total surface area of the cylinder A = 5000 cm². So,

A = 2πr² + 2πrh

5000 = 2πr² + 2πrh

Making h subject of the formula, we have

h = 2500/πr - r

Volume of a cylinder

Since the volume of the cylinder V = πr²h where

r = radius of cylinder and h = height of cylinder.

Substituting h into V, we have

V = πr²h

V = πr²(2500/πr - r)

V = 2500r - πr³

Maximizing the volume

Since we want to maximize V, we differentiate with respect to r and equate to zero.

So, dV/dr = d(2500r - πr³)/dr

dV/dr = 2500 - 3πr²

Equating dV/dr to zero, we have

dV/dr = 0

2500 - 3πr² = 0

2500 = 3πr²

Dividing both sides by 3π, we have

r² = 2500/3π

Findng the radius of the cylinder

Taking square root of both sides, we have

r = √(2500/3π)

r = 50/√(3π) cm

r = 50/√(9.4247) cm

r = 50/3.07

r = 16.29 cm

Value of radius that gives maximum volume

We need to determine if this value of r gives a maximum for V. So, we differentiate dV/dr.

So, d(dV/dr)/dr = d²V/dr²

d²V/dr² = d(2500 - 3πr²)/dr

d²V/dr² = 0 - 6πr

d²V/dr² = - 6πr

Substituting the value of r into the equation, we have

d²V/dr² = - 6πr

d²V/dr² = - 6π(50/√(3π))

d²V/dr² = - 6π(50/√(3π))

Since d²V/dr² = - 6π(50/√(3π)) < 0. V is maximum at r = 50/√(3π) cm

Finding the height of the cylinder

Substituting the value of r into h, we have

h = 2500/πr - r

h = 2500/π(16.29) - 16.29

h = 2500/51.17 - 16.29

h = 48.86 - 16.29

h = 32.57 cm

So, the dimensions of the cylinder that maximizes its volume are radius = 16.29 cm and height = 32.57 cm

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A student is graduating from college in 12 months but will need a loan in the amount of $11,650 for the last two semesters. The student may receive either an unsubsidized Stafford Loan
or a PLUS Loan. The terms of each loan are:
Unsubsidized Stafford Loan: annual interest rate of 5.95%, compounded monthly, and a payment grace period of six months from time of graduation
PLUS loan: annual interest rate of 6.55%, compounded monthly, with a balance of $12,436.41 at graduation
Which loan will have a lower balance, and by how much, at the time of repayment?
O The PLUS loan will have a lower balance by $298.35 at the time of repayment.
O The Stafford loan will have a lower balance by $298.35 at the time of repayment.
O The PLUS loan will have a lower balance by $527.14 at the time of repayment.
O The Stafford loan will have a lower balance by $527.14 at the time of repayment

Answers

Based on the information, the Stafford loan will have a lower balance by $527.14 at the time of repayment

How to calculate the loan

Using the formula for compound interest, the total cost of the loan can be calculated as follows:

Total cost of Stafford loan = $11,650 x (1 + 0.0595/12)^(12*0.5) = $12,652.14

Total cost of PLUS loan = $12,436.41 x (1 + 0.0655/12)^12 = $13,179.28

Therefore, the Stafford loan will have a lower balance at the time of repayment by $527.14 ($13,179.28 - $12,652.14).

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A kids pool had a small opening through which water sometimes leaked out. Water was poured into the pool from time to time. The graph shows the amount of water in the pool (y), in gallons, at certain times (x), in hours.

Which of the following statements best describes the amount of water in the pool ?

1) it is increasing during the time interval 4
2) it is increasing during the time interval 10
3) it is decreasing during the time interval 4
4) it is decreasing during the time interval 10

A kids pool had a small opening through which water sometimes leaked out. Water was poured into the pool

Answers

The best statement that describes the amount of water in the pool is that it is decreasing during the time interval 4. That is option 3.

How to determine the the interval of the water in the pool?

To determine the time interval of the water in the pool the following is carried out.

At 0 hour, the water is at the level of = 40 gallons

At 1 hour, the water decreased to = 25 gallons.

At 2 hours, the water decreased to = 10 gallons.

The water remained at a constant level till 4 hours.

Therefore, the amount of water in the pool is that it is decreasing during the time interval 4.

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please help 3/4 divided by 1/8

Answers

Answer:

6

Step-by-step explanation:

please help 3/4 divided by 1/8

3/4 : 1/8 =

3/4 x 8 =

24/4 =

6

what is the answer to 4x - 6 ≥ 6x - 20

Answers

Answer: x ≤ 7

Step-by-step explanation:

Answer:

x\(\leq\)7

Step-by-step explanation:

4x-6\(\geq\)6x-20

First get x on one side.

So substract 6x on each side to get:

4x-6x-6\(\geq\)-20

Then add 6 on each side to get:

4x-6x\(\geq\)-14

Simplify.

-2x\(\geq\)-14

Divide each side by -2 to get x alone.

*Remember that when dividing by a negative sign is fliped.

x\(\leq\)-14/-2

Simplify.

x\(\leq\)7

What is (123
) ÷ (18
)?

Answers

Answer:

6.8333333333 or 41/6

Step-by-step explanation:

Find the limit of the function by using direct substitution. limit as x approaches zero of quantity x squared plus eleven.

Answers

Answer:  11

Step-by-step explanation:

\(\displaystyle \lim_{x \to 0} x^2+11 \qquad =(0)^2+11\qquad =\large\boxed{11}\)

The exponential model A=302.5e^0.0211 describes the​ population, A, of a country in​ millions, t years after 2003. Use the model to determine the population of the country in 2003.

Answers

The population of the country in 2003 is 302.5 million

How to determine the population of the country in 2003.

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

Exponential model, A = 302.5e^0.0211t

Where i is the number of years after 2003

In the year 2003, the value of t is 0

i.e. 0 years after 2003

So, we have

A = 302.5e^(0.0211 * 0)

Evaluate the products

A = 302.5 * 1

So, we have the following result

A = 302.5

Hence, the population is 302.5 million

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I need help with geometry! I need to find x and y, please help asp

I need help with geometry! I need to find x and y, please help asp

Answers

Here you go, hope this helped
I need help with geometry! I need to find x and y, please help asp

Check the picture below.

I need help with geometry! I need to find x and y, please help asp

Find the area of the figure

Find the area of the figure

Answers

Answer:

104ft

Step-by-step explanation:

First - find the area of triangles.

h = hight

b = base
h • b / 2

5 • 8 /2 = 20ft

And

4 • 6 /2 = 12ft

And then area of the rectangle.
l • w


9 • 8 = 72 ft

Than add. Them all together

Consider the ordinary differential equation (answer questions in picture)

Consider the ordinary differential equation (answer questions in picture)

Answers

a. Given the 2nd order ODE

\(y''(x) = 4y(x) + 4\)

if we substitute \(z(x)=y'(x)+2y(x)\) and its derivative, \(z'(x)=y''(x)+2y'(x)\), we can eliminate \(y(x)\) and \(y''(x)\) to end up with the ODE

\(z'(x) - 2y'(x) = 4\left(\dfrac{z(x)-y'(x)}2\right) + 4\)

\(z'(x) - 2y'(x) = 2z(x) - 2y'(x) + 4\)

\(\boxed{z'(x) = 2z(x) + 4}\)

and since \(y(0)=y'(0)=1\), it follows that \(z(0)=y'(0)+2y(0)=3\).

b. I'll solve with an integrating factor.

\(z'(x) = 2z(x) + 4\)

\(z'(x) - 2z(x) = 4\)

\(e^{-2x} z'(x) - 2 e^{-2x} z(x) = 4e^{-2x}\)

\(\left(e^{-2x} z(x)\right)' = 4e^{-2x}\)

\(e^{-2x} z(x) = -2e^{-2x} + C\)

\(z(x) = -2 + Ce^{2x}\)

Since \(z(0)=3\), we find

\(3 = -2 + Ce^0 \implies C=5\)

so the particular solution for \(z(x)\) is

\(\boxed{z(x) = 5e^{-2x} - 2}\)

c. Knowing \(z(x)\), we recover a 1st order ODE for \(y(x)\),

\(z(x) = y'(x) + 2y(x) \implies y'(x) + 2y(x) = 5e^{-2x} - 2\)

Using an integrating factor again, we have

\(e^{2x} y'(x) + 2e^{2x} y(x) = 5 - 2e^{2x}\)

\(\left(e^{2x} y(x)\right)' = 5 - 2e^{2x}\)

\(e^{2x} y(x) = 5x - e^{2x} + C\)

\(y(x) = 5xe^{-2x} - 1 + Ce^{-2x}\)

Since \(y(0)=1\), we find

\(1 = 0 - 1 + Ce^0 \implies C=2\)

so that

\(\boxed{y(x) = (5x+2)e^{-2x} - 1}\)

6.a) The differential equation for z(x) is z'(x) = 2z(x) + 4, z(0) = 3.

6.b) The value of z(x) is \(z(x) = 5e^{2x} - 2\).

6.c) The value of y(x) is \(y(x) = \frac{5e^{2x}}{4} - \frac{1}{4e^{2x}} -1\).

The given ordinary differential equation is y''(x) = 4y(x) + 4, y(0) = y'(0) = 1 ... (d).

We are also given a substitution function, z(x) = y'(x) + 2y(x) ... (z).

Putting x = 0, we get:

z(0) = y'(0) + 2y(0),

or, z(0) = 1 + 2*1 = 3.

Rearranging (z), we can write it as:

z(x) = y'(x) + 2y(x),

or, y'(x) = z(x) - 2y(x) ... (i).

Differentiating (z) with respect to x, we get:

z'(x) = y''(x) + 2y'(x),

or, y''(x) = z'(x) - 2y'(x) ... (ii).

Substituting the value of y''(x) from (ii) in (d) we get:

y''(x) = 4y(x) + 4,

or, z'(x) - 2y'(x) = 4y(x) + 4.

Substituting the value of y'(x) from (i) we get:

z'(x) - 2y'(x) = 4y(x) + 4,

or, z'(x) - 2(z(x) - 2y(x)) = 4y(x) + 4,

or, z'(x) - 2z(x) + 4y(x) = 4y(x) + 4,

or, z'(x) = 2z(x) + 4y(x) - 4y(x) + 4,

or, z'(x) = 2z(x) + 4.

The initial value of z(0) was calculated to be 3.

6.a) The differential equation for z(x) is z'(x) = 2z(x) + 4, z(0) = 3.

Transforming z(x) = dz/dx, and z = z(x), we get:

dz/dx = 2z + 4,

or, dz/(2z + 4) = dx.

Integrating both sides, we get:

∫dz/(2z + 4) = ∫dx,

or, {ln (z + 2)}/2 = x + C,

or, \(\sqrt{z+2} = e^{x + C}\),

or, \(z =Ce^{2x}-2\) ... (iii).

Substituting z = 3, and x = 0,  we get:

\(3 = Ce^{2*0} - 2\\\Rightarrow C - 2 = 3\\\Rightarrow C = 5.\)

Substituting C = 5, in (iii), we get:

\(z = 5e^{2x} - 2\).

6.b) The value of z(x) is \(z(x) = 5e^{2x} - 2\).

Substituting the value of z(x) in (z), we get:

z(x) = y'(x) + 2y(x),

or, 5e²ˣ - 2 = y'(x) + 2y(x),

which gives us:

\(y(x) = \frac{5e^{2x}}{4} - \frac{1}{4e^{2x}} -1\) for the initial condition y(x) = 0.

6.c) The value of y(x) is \(y(x) = \frac{5e^{2x}}{4} - \frac{1}{4e^{2x}} -1\).

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look at picture below

look at picture below

Answers

i’m pretty sure it’s 60 because if you look at angle 1 is next to the angle that measures 120 degrees and 60+120= 180

A soccer team is planning to sell candy bars to spectators at their games. They will buy two-pound bags of candy. The number of candy bars per bag has mean 12 and standard deviation 2. They will sell each candy bar for $1.25. (Assume that all of the candy in a bag will be sold.)
1. What is the expected value and the standard deviation for the amount of money that would be made selling all of the candy in one bag of candy?

Answers

The expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

What exactly is a standard deviation?

The standard deviation is a measurement of how widely apart a set of numbers or statistics are from their mean.

The expected value for the amount of money made selling all of the candy in one bag can be found by;

Expected value = mean number of candy bars per bag x price per candy bar

Expected value = 12 x $1.25 = $15

Formula for the standard deviation of a product of random variables:

\(SD (XY) = \sqrt{((SD(X)^2)(E(Y^2)) + (SD(Y)^2)(E(X^2)) + 2(Cov(X,Y))(E(X))(E(Y)))}\)

where X and Y are random variables, SD is the standard deviation, and Cov is the covariance.

X is the number of candy bars in a bag, which has a mean of 12 and a standard deviation of 2. Y is the price per candy bar, which is a constant $1.25. So we have:

E(Y²) = $1.25² = $1.5625

E(X²) = (SD(X)²) + (E(X)²) = 2² + 12² = 148

Cov (X,Y) = 0 (because X and Y are independent)

Using these values, we can calculate the standard deviation for the amount of money made selling all of the candy in one bag:

\(SD = sqrt((2^{2} )(148) + (0)(12)(1.25)^{2} + 2(0)(2)(12)(1.25))\)

SD = √(592)

SD ≈ $24.33

Therefore, the expected value for the amount of money made selling all of the candy in one bag is $15, and the standard deviation is approximately $24.33.

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On average, Nathaniel drinks
4/5 of a 10-ounce glass of water in
2 2/5​
hours. How many glasses of water does he drink in one hour? Enter your answer as a whole number, proper fraction, or mixed number in simplest form.

Answers

Nathaniel drinks 3 glasses of water in one hour.

To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.

In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.

Let's convert the mixed number of hours to an improper fraction:

\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)

\(=\frac{12}{5}\)

Now, we can set up a proportion to find his drinking rate per hour.

We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.

Let's assign "x" as the number of glasses he drinks in one hour.

The proportion is then

\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)

Cross-multiplying gives us

\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)

Simplifying, we get

\(\frac{12}{5} =\frac{4}{5}\times x\)

Dividing both sides by \(\frac{4}{5}\), we find x:

\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)

\(x=\frac{12}{4}\)

\(x = 3.\)

Therefore, Nathaniel drinks 3 glasses of water in one hour.

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what is the formula for finding the area of a sphere​

Answers

Answer: \(4\pi r^{2}\)

Step-by-step explanation:

Area of a circle is pi r squared

it’s 4 pi r squared
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