Is the binomial a factor of the polynomial function?

f(x)=x^3+4x^2−25x−100

(I'm not sure if the highlighted answers are correct, help!!!)

Answer:

a) 4.387

b) Yes, because np & npq are greater than 10.

c) = 0.017          

Step-by-step explanation:

Give data:

p = 0.69

n = 90

a) a

E(X) = np = 62.1

[tex]SD(X) = \sqrt{(np(1-p))}[/tex]

          [tex]=\sqrt{90\times 0.69(1- 0.69)}[/tex]

          = 4.387

b)

np = 62.1  

q = 1 - p  = 1 - 0.69 = 0.31

npq = 19.251

Yes, because np & npq are greater than 10.

c.

[tex]P(X \geq 72   ) = P(X > 71.5)[/tex] [continuity correction]

[tex]=    P(Z> \frac{((71.5-62.1)}{ 4.387})[/tex]

= P(Z> 2.14 )      

= 1 - P(Z<2.14)              

= 1 - 0.983   (using table)          

= 0.017          

Final answer:

The tennis player is expected to have an average of 62.1 successful first serves with a standard deviation of 4.573 in 90 attempts. A normal model is appropriate for this distribution. The probability that she makes at least 7272 first serves is approximately [tex]\( 1 - 0.9908 \approx 0.0092 \)[/tex], or about 0.92%.

Explanation:

A certain tennis player makes a successful first serve 69% of the time. If the tennis player serves 90 times in a match, we can calculate the mean and standard deviation of the number of good first serves expected, and determine if a normal model can be used to approximate the distribution.

a) Mean and Standard Deviation

The mean (μ) of the number of successful first serves can be calculated using the formula μ = n*p, where n is the total number of serves, and p is the probability of success on each serve. For 90 serves with a 69% success rate, the mean is 90*0.69 = 62.1 serves.

The standard deviation (σ) can be calculated using the formula σ = √(n*p*(1-p)). Therefore, the standard deviation for our scenario is √(90*0.69*0.31) = 4.573.

b) Normal Model Appropriateness

To determine if a normal model can approximate the distribution, we check if np and n(1-p) are both greater than 10. Here, np = 62.1 and n(1-p) = 27.9, both of which are greater than 10, indicating a normal model is appropriate.

c) Probability of At Least 72 First Serves

Given the large number of trials (9090) and the high probability of success (0.6969), we can approximate the binomial distribution with a normal distribution using the central limit theorem. The mean of the binomial distribution is [tex]\( \mu = np = 9090 \times 0.6969 \approx 6340.8841 \)[/tex] and the standard deviation is [tex]\( \sigma = \sqrt{np(1-p)} = \sqrt{9090 \times 0.6969 \times (1-0.6969)} \approx 39.9549 \).[/tex]

Now, to find the probability that she makes at least 7272 first serves, we'll use the normal approximation with continuity correction. We'll first standardize X = 7272 to find the corresponding z-score:

[tex]\[ z = \frac{X - \mu}{\sigma} = \frac{7272 - 6340.8841}{39.9549} \approx 2.3333 \][/tex]

Using a standard normal distribution table or calculator, the probability associated with z = 2.3333 is approximately 0.9908.

Thus, the probability that she makes at least 7272 first serves is approximately [tex]\( 1 - 0.9908 \approx 0.0092 \)[/tex], or about 0.92%.

Answer:

The time that the hose can complete the job alone is 18.513 hour.

The time that the inlet pipe can complete the job alone is 17.513 hours.

Step-by-step explanation:

Let the number of hours required to fill the pond by hose alone = x

Then the number of hours required to fill the pond by inlet pipe alone = x-1

This means that in 1 hour, the hose alone can fill 1/x of the pond.

Similarly, in 1 hour, the inlet pipe can fill 1/(x-1) if the pond.

Taken together,in 1 hour, the hose and inlet pipe can together fill:

[tex]\[\frac{1}{x} + \frac{1}{(x-1)}\][/tex] of the pond.

But this actually corresponds to 1/9 of the pond.

[tex]\[\frac{1}{x} + \frac{1}{(x-1)} = \frac{1}{9}\][/tex]

Solving:

[tex]\[\frac{x-1+x}{x(x-1)} = \frac{1}{9}\][/tex]

=> [tex]\[18x-9 = x^{2}-x\] [/tex]

=> [tex]\[x^{2}-19x+9=0\][/tex]

=> x= 18.513,0.486 ( roots of the quadratic equation)

Of these values, x=18.513 is relevant since x-1 must be non-negative.

So, the number of hours required to fill the pond by hose alone is 18.513 hours

Similarly, the number of hours required to fill the pond by inlet pipe alone is 17.513 hours

The time that the hose can complete the job alone is (-9 + √(109))/18 hour. The time that the inlet pipe can complete the job alone is (-9 + √(109))/18 + 1 hours.

Let x be the time it takes for the hose alone to complete the job. Therefore, the inlet pipe can complete the job in x + 1 hour.

From the given information, we know that the inlet pipe and the hose together can fill the pond in 9 hours.

Using the formula for work done, we can set up the following equation:

1/((x + 1) + 1/((1/x)) = 1/9

Simplifying the equation, we get:

1/(x + 1) + x = 1/9

Multiplying all terms by 9(x + 1) to eliminate the fractions, we get:

9 + 9x(x + 1) = (x + 1)

Simplifying further, we get:

9 + 9x(x + 1) = (x + 1)

9x^2 + 9x - 7 = 0

Using the quadratic formula, we can solve for x:

x = (-b ± √(b^2 - 4ac))/(2a) = (-9 ± √(9^2 - 4(-7)))/(2(9))

Simplifying, we get:

x = (-9 ± √(81 + 28))/18 = (-9 ± √(109))/18

Since the time cannot be negative, we take the positive square root:

x = (-9 + √(109))/18

Therefore, the time that the hose can complete the job alone is (-9 + √(109))/18 hour.

The time that the inlet pipe can complete the job alone is (x + 1) = (-9 + √(109))/18 + 1 hours.

Answer:

I think the answer is 3/52

The intensity of sound is I=7.943 × 10⁻¹¹ Wm⁻²

Step-by-step explanation:

The intensity level in dB of a sound of intensity I is given as

(10dB)log₁₀ (I/I₀), where I₀ is the intensity of threshold of hearing

The intensity of threshold of hearing I₀= 1×10⁻¹² Wm⁻²

In this question;

I=?

I₀=1×10⁻¹² Wm⁻²

Sound intensity in dB = 19 dB

Substitute values in the equation

(10dB)log₁₀ (I/I₀)= 19

(10)log₁₀ (I/1×10⁻¹²)=19

log₁₀ (I/1×10⁻¹²) =19/10

log₁₀ (I/1×10⁻¹²) =1.9

(I/1×10⁻¹²)=10^1.9

(I/1×10⁻¹²)=79.43

(I/1×10⁻¹²)=79.43

I=79.43 * 10⁻¹²

I=7.943 *10⁻¹¹ Wm⁻²

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For this case we have the following expression:

[tex](c ^ 4) ^ 6 = c^{24}[/tex]

By definition of power properties we have to meet:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

This property is known as "high power to power."

Answer:

The property shown is:

High power to power.

Answer:

The answer to your question is letter C. [tex]t = \frac{30}{7}[/tex]

Step-by-step explanation:

                               [tex]\frac{2}{3} t - \frac{1}{5} t = 2[/tex]

                               [tex]\frac{10t - 3t}{15} = 2[/tex]

                               [tex]\frac{7t}{15} = 2[/tex]

                                              7t = 30

                                                [tex]t = \frac{30}{7}[/tex]

Answer:

14.5

Step-by-step explanation:

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The area of smaller mp3 player is 4.5 square inches

Solution:

Given that ratio of corresponding side lengths of two similar MP3 players is 4:3

The area of the larger MP3 player is 8 square inches

To find: area of the smaller MP3 player

If two MP3 players are similar, then their corresponding sides are proportional.

To find the area ratios, raise the side length ratio to the second power

[tex]\frac{\text {area of larger mp3}}{\text {area of smaller mp3}}=\left(\frac{4}{3}\right)^{2}[/tex]

From given information,

area of larger mp3 = 8 square inches

Let the area of smaller mp3 = x

So the above ratio becomes,

[tex]\frac{8}{x}=\left(\frac{4}{3}\right)^{2}\\\\\frac{8}{x} = \frac{16}{9}\\\\16x = 9 \times 8\\\\16x = 72\\\\x = 4.5[/tex]

Thus the area of smaller mp3 player is 4.5 square inches

Final answer:

The area of the smaller MP3 player is 128/9 square inches.

Explanation:

The area of the larger MP3 player is 8 square inches and the ratio of corresponding side lengths of the two MP3 players is 4:3. To find the area of the smaller MP3 player, we need to use the ratio of the side lengths squared. Since the ratio is 4:3, the area ratio will be (4/3)^2 = 16/9. Given that the area of the larger MP3 player is 8 square inches, we can find the area of the smaller MP3 player by multiplying 8 by the area ratio: (8) * (16/9) = 128/9 square inches.

Answer: $21,000

Step-by-step explanation:

Cleaning expense is only related to the floor space occupied by the department.

If the company spend a total of $30,00 on cleaning each year.

And Department B occupies 70% of the company floor.

Therefore, the company spends 70% of their cleaning expense on department B

Hence, the cleaning expense on department B is given as;

= 70% of $30,000

= $21,000

Department B should be allocated $21,000 for cleaning expenses, as it occupies 70% of the floor space and the total cleaning expense is $30,000.

To determine how much cleaning expense should be allocated to Department B at Calico Company, you should consider the proportion of floor space occupied by the department. Since cleaning expenses are primarily based on vacuuming the carpet, it's reasonable to use floor space as the basis for allocation.

Department B occupies 70% of the company's floor space. With a total annual cleaning expense of $30,000, we can calculate Department B's share of the expense by multiplying the total expense by the percentage of space that Department B occupies:

Allocated expense to Department B = Total cleaning expense × Department B's percentage of floor space

Allocated expense to Department B = $30,000 × 70%

Allocated expense to Department B = $30,000 × 0.70

Allocated expense to Department B = $21,000

Therefore, $21,000 should be allocated to Department B for cleaning expenses.

Kendal bought 7 boxes of cookies, kept 2 boxes for herself and brought 60 cookies to the party.

Let x represent the number of boxes of cookies bought by Kendal.

Each box has 12 cookies, hence:

number of cookies = 12x

Kendal brings 60 cookies to the party. She keeps 2 boxes for herself. To find the number of boxes we use:

12x = 60 + 12(2)

12x = 84

x = 7

Therefore Kendal bought 7 boxes of cookies, kept 2 boxes for herself and brought 60 cookies to the party.

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Final answer:

To find the number of boxes, x, Kendal bought, we can set up an equation based on the information given. The equation (x - 2) * 12 = 60 can be used to find the number of boxes Kendal bought.

Explanation:

To find the number of boxes, x, Kendal bought, we can set up an equation based on the information given. Kendal initially buys x boxes of cookies. Each box contains 12 cookies. She decides to keep two boxes for herself and brings 60 cookies to the party.

The number of cookies Kendal brings to the party can be calculated by multiplying the number of boxes she bought minus the number of boxes she kept for herself by the number of cookies in each box. So, the equation to find x would be:

(x - 2) * 12 = 60

Solving this equation will give us the value of x, which represents the number of boxes Kendal bought.

Answer:

Multiplying the mass of ice by the specific latent heat of fusion of ice

Step-by-step explanation:

The heat energy required to completely melt 100 grams can be calculated by multiplying the mass of ice (100g) by the specific latent heat of fusion of ice (336J/g)

Answer:

[tex]\Omega = \{ 1HH, 1HT, 1TH, 1TT, 2H, 2T, 3HH, 3HT, 3TH, 3TT, 4H, 4T,\\5HH , 5HT, 5TH, 5TT, 6H, 6T \}[/tex]

The probability is 3/12. The third option is correct.

Step-by-step explanation:

The sample space is

[tex]\Omega = \{ 1HH, 1HT, 1TH, 1TT, 2H, 2T, 3HH, 3HT, 3TH, 3TT, 4H, 4T,\\5HH , 5HT, 5TH, 5TT, 6H, 6T \}[/tex]

Note that this sample space is not equally probable.

The probability of getting a given number followed is the probability of getting an even number from the 6 numbers (3/6) multiplied by the probability of getting a head after getting that even number, that is 1/2, because is equally probable to get heads or tails from one single coin toss (note that we are assuming that the dice was even, thats why there is a single coin toss).

Therefore, the probability of getting an even number and a head is

P( D in {2,4,6} , H = 1) = P(D in {2,4,6}) * P(H=1 | D in {2,4,6}) = 3/6 * 1/2 = 3/12.

The sample space S can be constructed by listing all possible outcomes. The probability of getting an even number on the die followed by one head is 1/4.

The sample space S can be constructed by listing all possible outcomes. Since there are 6 possible outcomes for the die and 2 possible outcomes for the coin flip, the total number of outcomes is 6 * 2 = 12. The sample space S is {1HH, 1HTT, 2H, 2HTT, 3HH, 3HT, 4H, 4HTT, 5HH, 5HTT, 6H, 6HTT}.

The probability of getting an even number on the die followed by one head can be found by counting the number of favorable outcomes (even number on the die followed by one head) and dividing it by the total number of outcomes. From the sample space, we can see that there are 3 favorable outcomes: 2H, 4H, and 6H. Therefore, the probability is 3/12, which can be simplified to 1/4.

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Answer:

12.47 is the correct answer

Answer:

a) the vector equation is r(x,y) = (35cos27°t, 16t^2 -35sin27° - 4)

b) Maximum height = 7.945ft

c) Time of flight = 1.201 secs and range = 37.45ft

d) when t = 0.74, the distance above the ground = 14.37ft

When t = 0.254, the distance above the ground = 26.53ft

e) if the ball is raised to 8ft, the ball won't be able to reach it. This is because the maximum height is 7.954ft

Step-by-step explanation:

a) From the diagram

x0 = 0

y0= 4

V0(initial velocity) = 35

α= 27°

y = 4 + 35sin27°t - 16t^2

y = -16t^2 + 35sin27°t+ 4

y = 16t^2 - 35sin27°t - 4

x = 35cos27°t

Vector equation for the path of the volleyball = r(x,y)

r(x,y) = (35cos27°t, 16t^2 -35sin27° - 4)

b) the ball reaches maximum when dy/dt = 0

y = 16t^2 - 35sin27°t - 4

dy/dt = 32 - 35sin27°

0 = 32 - 35sin27°t

-32 = -35sin27°t

t = -32 / -35sin27°

t = 0.4966 seconds

Put t = 0.4966 into y = 16t^2 - 35sin27°t - 4

y = 16(0.4966)^2 - 35sin27°(0.4966) - 4

y = 7.945 ft

The maximum height is 7.945 ft

c) To find the range and flight time, put y= 0

0 = 16t^2 - 35sin27°t - 4

0 = 16t^2 - 15.89t - 4

Using quadratic equation general formula,

[-b +/- √b^2 -4ac] / 2a

a = 16, b = -15.89, c = -4

= [-(-15.89) +/- √ (-15.89)^2 - 4(16)(-4)] /2(16)

= [15.89 +/- √(15.89)^2 + 256] / 32

= (15.59 +/- 22.55) / 32

= (15.89 + 22.55) / 32 or (15.89 - 22.55) / 32

= 1.201 or -0.208

Time of flight = 1.201 secs

Range = x = 35cos27°t

Range = 32cos27°(1.201)

= 37.45 ft

d) when the volley is 7ft above ground, y = 7

Recall that y = 16t^2 - 35sin27°t - 4

7 = 16t^2 - 35sin27°t - 4

0 = 16t^2 - 35sin27°t - 4 +7

0 = 16t^2 - 35sin27°t + 3

0 = 16t^2 - 15.89t + 3

Using quadratic equation general formula,

[-b +/- √b^2 -4ac] / 2a

a = 16, b = -15.89, c = 3

= [-(-15.89) +/- √ (-15.89)^2 - 4(16)(3)] /2(16)

= [15.89 +/- √(15.89)^2 - 192] / 32

= (15.59 +/- 7.7778) / 32

= (15.89 + 7.7778) / 32 or (15.89 - 7.7778) / 32

= 0.74 or 0.254

When t = 0.74,

x = 35cos27°t

x = 35cos27°(0.74)

x = 23.08 ft

Therefore , R - x(0.74)

= 37.45 - 23.08

= 14.37ft

When t = 0.254,

x = 35cos27°t

x = 35cos27°(0.254)

x = 7.92 ft

Therefore R - x(0.254) =

37.45 - 7.92 = 29.53ft

e) if the ball is raised to 8ft, the ball won't be able to reach it. This is because the maximum height is 7.954ft

Answer:

A

[tex]h = -16t^2 + 192t[/tex]

B

Vertex=(6,576)

Step-by-step explanation:

The problem gives us the following data:

[tex]v_o=192\ ft/s,\ h_o=0[/tex]

A.

Thus the function is

[tex]h = -16t^2 + 192t[/tex]

The graph of h has the shape of an inverted parabola. Recall if the coefficient of the quadratic term is negative, the parabola is concave down, so it has a maximum value.

Part B

Let's take the function of h

[tex]h = -16t^2 + 192t[/tex]

Factoring by -16

[tex]\displaystyle h = -16(t^2 - 12t)[/tex]

Completing squares

[tex]\displaystyle h = -16(t^2 - 12t+36-36)[/tex]

[tex]\displaystyle h = -16(t^2 - 12t+36)+576[/tex]

Factoring

[tex]\displaystyle h = -16(t-6)^2+576[/tex]

Rearranging

[tex]\displaystyle h -576= -16(t-6)^2[/tex]

We can get the coordinates of the vertex from this standard form of the parabola.

Vertex=(6,576)

The maximum value means that at t=6 seconds, the firework will be 576 feet high and then it will start falling back to the ground.

Answer:

  46°

Step-by-step explanation:

The exterior angle marked 69° is the sum of the remote interior angles 23° and x. So ...

  69° = 23° +x

  x = 69° -23°

  x = 46°

Answer:

46 degrees

Step-by-step explanation:

see attached

Answer:

the recommended number of caories for a 11 year old male = 220.

Step-by-step explanation:

it is given that frank consumes 660 calories during breakfast.

660 calories is the 30 percent of recommended calories for a day.

let the number of calories required for a day be x.

therefore 30 percent of x = 660

therefore [tex]\frac{30}{100}[/tex]×x = 660

30x= 660×100

x=660×[tex]\frac{100}{30}[/tex]

x= [tex]\frac{10}{3}[/tex]×660

x= 2200

solving the equation we get x= 2200

there the recommended number of caories for a 11 year old male = 220.

Answer:$1109.23 will be in the account after 9 years

Step-by-step explanation:

Initial amount deposited into the account is $400 This means that the principal

P = 400

It was compounded annually. This means that it was compounded once in a year. So

n = 1

The rate at which the principal was compounded is 12%. So

r = 12/100 = 0.12

It was compounded for 9 years. So

n = 9

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. Therefore

A = 400 (1+0.12/1)^1×9

A = 400(1.12)^9 = 1109.23$

Answer:

17.37

Step-by-step explanation:

y varies inversely as the square root of x

Mathematically:

y = k.root x

We first find k here

To find k, we were made to know that y is 21 and x = 361

k = y/root.x

k = 21/root. 361

k = 21/19

now what is y when x = 247

From y = k.root x

y = 21/19 * root 247

y= 21/19 * 15.72

y = 17.37

Answer:

The arithmetic average return would be 3.96%

Step-by-step explanation:

Given,

The returns in 5 years are,

-​9.7%, -​8.1%, ​15%, 7.2%, and​ 15.4%

We know that,

[tex]\text{Arithmetic average}=\frac{\text{Sum of all observations}}{\text{Number of observations}}[/tex]

Hence,

The arithmetic average return of the investment = [tex]\frac{-9.7-8.1+15+7.2+15.4}{5}[/tex]

[tex]=\frac{19.8}{5}[/tex]

= 3.96%

Answer:

It will cost him $616 for 160 gallons of gas.

Step-by-step EXPLANATION FIRST YOU HAVE TO MULTIPLY 3.25 BY 160 TO GET $520, THEN JUST ADD IT BY $96 TO GET $616.

It will cost Lee $520 to purchase 160 gallons of gas.

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division. The priority of these opeartors in a given expression can be determined by PEDMAS. Each letter represents one operation as P for Parenthesis, E for exponential, D for division, M for Multiplication, A for Addition and S for Subtraction.

The price of gas per gallon is $3,25.

The cost of 160 gallons can be calculated as follows,

Number of gallons × Price per gallon

⇒ 160 × 3.25

⇒ 520

Hence, the price of 160 gallons is given as $520.

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Answer:

5.5 years old.

Step-by-step explanation:

Let D represent present age of Robert's dog and C represent present age of Karen's cat.

We have been given that Robert's dog is 4 years older than Karen's cat. We can represent this information in an equation as:

[tex]D=C+4...(1)[/tex]

We are also told that in 3 years, the sum of the ages of Robert's dog and Karen's cat will be 13. After 3 years age of dog and cat would be [tex]D+3[/tex] and [tex]C+3[/tex] respectively.

We can represent this information in an equation as:

[tex]D+3+C+3=13...(2)[/tex]

From equation (1), we will get:

[tex]C=D-4[/tex]

Upon substituting this value in equation (2), we will get:

[tex]D+3+D-4+3=13[/tex]

Combine like terms:

[tex]2D+2=13[/tex]

[tex]2D+2-2=13-2[/tex]

[tex]2D=11[/tex]

[tex]\frac{2D}{2}=\frac{11}{2}[/tex]

[tex]D=5.5[/tex]

Therefore, Robert's dog is 5.5 years old right now.

Answer:

The answer is True.

Step-by-step explanation:

Sales variance is computed in same manner as cost variance that is computing both price and volume variance. However interpretation of end result will not be same. For example in material price variance if

A = actual purchase price = $ 4, B = standard purchase price= $ 5 and Qt= quantity purchased = 500 units then

Material price varaince = 500 (5-4) = 500,

This gives us favourable price variance of 500 dollars. However in sales price variance if

A = actual sales price = $ 4, B = standard sale price= $ 5 and Qt= quantity sold = 500 units then

Sale price varaince = 500 (5-4) = (500)

This gives us unfavourable sales price variance of 500 dollars.

This show that formulas to compute variances are same but sale price decrease give us un favorable variance and cost price decrease gives us favorable price variance and vice versa.

Answer:

3.4286 hours or 3 hours 26 minutes

Step-by-step explanation:

Well, it is considered that there are 5 different pumps (A, B, C, a and b). Pumps A and B are not same with pumps a and b.

Let us solve it. Well, it says a and b pump could empty a pool for 8 hours. So in 1 hour, pumps a and b empty 1/8 part of the pool.

And pumps A, B and C could empty a pool for 6 hours. Then A, B and C pumps empty 1/6 part of pool in 1 hour.

5 pumps (A, B, C, a and b) altogether can empty 7/24 parts (1/6+1/8=7/24) of a pool in 1 hour.

To drain whole pool, it will take 24/7=3.4286 hours or 3 hours 26 minutes.

Answer:the percent of increase in price is 7.69%

Step-by-step explanation:

The yearbook was sold for $26 at the beginning of the year. This means that the initial price of the year book was $26.

The price has increased to $28. The amount by which it was increased would be the current price - the initial price. It becomes

28 - 26 = $2

The percent of increase in price would be

Increase/initial price × 100

It becomes

2/26 × 100 = 7.69%

Answer:

Part 1) [tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex]

Part 2) [tex]\frac{a}{b}=\frac{2}{3}[/tex]

Part 3) [tex]\frac{a^3}{b^3}=\frac{8}{27}[/tex]

Step-by-step explanation:

Part 1) Find the ratio Area I/Area II  

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

The ratio of the areas is equal to divide the surface area cylinder I by the surface area cylinder II

Let

a^2 -----> the surface area cylinder I

b^2 ----> the surface area cylinder II

we have

[tex]a^2= 8\pi\ in^2[/tex]

[tex]b^2= 18\pi\ in^2[/tex]

Find the ratio

[tex]\frac{a^2}{b^2}=\frac{8\pi }{18\pi}[/tex]

Simplify

[tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex]

That means

[tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex] --->[tex]4b^2=9a^2[/tex]

Four times area cylinder II is equal to nine times the surface area of cylinder  I.  

Part 2) Find the ratio a/b

we know that

If two figures are similar, then the ratio of its corresponding sides is equal to the scale factor.

In this problem

[tex]\frac{r_1}{r_2}=\frac{h_1}{h_2}=\frac{a}{b}[/tex] ----> scale factor

we have

[tex]\frac{a^2}{b^2}=\frac{4}{9}[/tex]

so

square root both sides

[tex]\frac{a}{b}=\frac{2}{3}[/tex]

That means

[tex]\frac{r_1}{r_2}=\frac{2}{3}[/tex] --->[tex]2r_2=3r_1[/tex]

Two times radius cylinder II (r_2) is equal to three times radius cylinder I (r_1)

[tex]\frac{h_1}{h_2}=\frac{2}{3}[/tex] --->[tex]2h_2=3h_1[/tex]

Two times height cylinder II is equal to three times height cylinder I

Part 3) Find the ratio Volume I/Volume II  

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

we have

[tex]\frac{a}{b}=\frac{2}{3}[/tex] ----> scale factor

[tex]\frac{Volume\ I}{Volume\ II}=\frac{a^3}{b^3}[/tex]

substitute the values

[tex]\frac{Volume\ I}{Volume\ II}=\frac{2^3}{3^3}[/tex]

[tex]\frac{Volume\ I}{Volume\ II}=\frac{8}{27}[/tex]

[tex]8Volume\ II=27Volume\ I[/tex]

8 times volume cylinder II is equal to 27 times volume cylinder I

Answer:

[tex]H_{0}: \mu \leq 600\text{ dollars}\\H_A: \mu > 600\text{ dollars}[/tex]

Step-by-step explanation:

We are given the following in the question:

Manager's claim: The mean guest bill for a weekend is $600 or less.

A member of the hotel’s accounting staff noticed that the total charges for guest bills have been increasing in recent months.

A sample of weekend guest bills were collected to test the manager’s claim.

We design the null and alternate hypothesis in the following manner:

[tex]H_{0}: \mu \leq 600\text{ dollars}\\H_A: \mu > 600\text{ dollars}[/tex]

Conclusion when null hypothesis cannot be rejected:

When we fail to reject the null hypothesis and accept the null hypothesis, thus, we have enough evidence to support the manager's claim that the mean guest bill for a weekend is $600 or less.

Conclusion when null hypothesis can be rejected:

When the null hypothesis is rejected, we accept the alternate hypothesis.

Thus, there are not sufficient evidence to support the manager's claim  that the mean guest bill for a weekend is $600 or less.

Answer:

answer is the first option

Step-by-step explanation:

Answer:

  A: 6 and 24

  B: 4 times as great; the rate of change increases exponentially

Step-by-step explanation:

Part A: The average rate of change on the interval [a, b] is given by ...

  average rate of change = (h(b) -h(a))/(b -a)

On the interval [1, 2], the rate of change is ...

  (h(2) -h(1))/(2 -1) = (12 -6)/1 = 6

On the interval [3, 4], the rate of change is ...

  (h(4) -h(3))/(4 -3) = (48 -24)/1 = 24

For Section A, the average rate of change is 6; for Section B, the average rate of change is 24.

__

Part B: The ratio of the rates of change on the two intervals is ...

  (RoC on [3,4]) / (RoC on [1,2]) = 24/6 = 4

The average rate of change of Section B is 4 times that of Section A.

__

The rate of change is exponentially increasing, so an interval of the same width that starts at "d" units more than the previous one will have a rate of change that is 2^d times as much.

Answer:  Expected value of the daily cost of operating the machine is 235.264.

Step-by-step explanation:

Since we have given that

E[x]= 0.96 repairs per day

And Var[x] = 0.96 repairs per day.

[tex]C=160+40x^2[/tex]

[tex]E[c]=160+40E[x^2]\\\\E[c]=160+40(Var[x]+(E[x])^2)\\\\E[c]=160+40(0.96+0.96^2)\\\\E[c]=235.264[/tex]

Hence, Expected value of the daily cost of operating the machine is 235.264.

The expected value of the daily cost of operating the machine is $235.264.

To find the expected value of the daily cost of operating the machine, we need to calculate the expected value of C = 160 + 40X^2, where X is the number of repairs the machine needs per day. Since X follows a Poisson distribution with a mean of 0.96, we can use the formula for the expected value of a function of a random variable:

E(C) = E(160 + 40X^2) = 160 + 40E(X^2)

To calculate E(X^2), we need to find the variance of X first.

The variance of X is Var(X) = λ = 0.96.

Then, E(X^2) = Var(X) + [E(X)]^2 = 0.96 + (0.96)^2 = 0.96 + 0.9216 = 1.8816.

Now, we can calculate the expected value of the daily cost:

E(C) = 160 + 40E(X^2) = 160 + 40(1.8816) = 160 + 75.264 = 235.264.

Therefore, the expected value of the daily cost of operating the machine is $235.264.

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Answer: Major special revenue funds with legally adopted budgets.

Step-by-step explanation: GASB ( Governmental accounting standards board) is a private organization based in Norwalk,that tries to regulates Government accounting process in the United States of America by giving specific standards to ensure proper accounting.

Governmental accounting standards board (GASB) requires a budget to actual comparison in the financial statements for the general fund and major special revenue funds with legally adopted budgets.