The number of events is 29​, the number of trials is 298​, the claimed population proportion is​ 0.10, and the significance level is 0.05. Use technology to identify the test statistic for this hypothesis​ test, rounding to two decimal places.

Answer:

12.47 is the correct answer

Answer:

Expected net gain is -$0.75. Not a fair game. Appropriate price is $2.25.

Step-by-step explanation:

There is 1 in 600 chance to win the grand price (1/600)

There are 2 in 600 chance to win the 2nd price (2/600 = 1/300)

There are 5 in 600 chance to win the 3rd price (5/600 = 1/120)

We can use these probability to calculate the expected gain from this game

[tex]E_g = 700\frac{1}{600} + 200*\frac{1}{300} + 50*\frac{1}{120} = \$2.25[/tex]

Since the cost to play is $3, the expected net gain from this game is

$2.25 - $3 = -$0.75

So this game is not fair as the player is losing money. The appropriate price should instead be $2.25

The expected value of $1.91 is less than the cost of $3 per ticket, indicating it is not a fair game. To make it fair, the price per ticket should be set at $1.91.

Determining Fairness:

The expected value of $1.91 is less than the cost of $3 per ticket, indicating it is not a fair game. To make it fair, the price per ticket should be set at $1.91.

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:

Step-by-step explanation:

Given

Circle has radius [tex]r=5 in.[/tex]

Area of the sector is given by

[tex]A_s=\frac{\theta }{2\pi }\times \pi r^2[/tex]

if [tex]A_s[/tex] is one-sixth  of area of circle then

[tex]A_s=\frac{\pi r^2}{6}[/tex]

[tex]\frac{\pi r^2}{6}=\frac{\theta }{2\pi }\times \pi r^2[/tex]

[tex]\theta =\frac{2\pi }{6}=\frac{\pi }{3}\ radian[/tex]

If [tex]A_s[/tex] is one-fourth of area of circle then

[tex]A_s=\frac{\pi r^2}{4}[/tex]

[tex]\theta =\frac{2\pi }{4}[/tex]

[tex]\theta =\frac{\pi }{2}[/tex]

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:

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:

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:

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 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.

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:

Option C.

Step-by-step explanation:

The vertices of triangle PQR are P(3, −6), Q(6, −9), and R(−15, 3).

It is given that triangle PQR dilated by a scale factor of 3 to obtain triangle P′Q′R′.

We know that a figure and its image after dilation are similar. It means triangle PQR and triangle P′Q′R′

If a figure dilated by factor k about the origin then

[tex](x,y)\rightarrow (kx,ky)[/tex]

PQR dilated by a scale factor of 3, so

[tex](x,y)\rightarrow (3x,3y)[/tex]

Using this rule we get

[tex]P(3,-6)\rightarrow P'(3(3),3(-6))=P'(9,-18)[/tex]

[tex]Q(6,-9)\rightarrow Q'(3(6),3(-9))=Q'(18,-27)[/tex]

[tex]R(-15,3)\rightarrow R'(3(-15),3(3))=R'(-45,9)[/tex]

The vertices of image are P'(9,-18), Q'(18,-27) and R'(-45,9).

Therefore, the correct option is C.

Answer:

C

Step-by-step explanation:

Answer:

A) quantitative

Step-by-step explanation:

A data that can be counted or expressed numerically constitute quantitative data. Quantitative data collection method is capturing statistical data in numbers, figures, or values. Quantitative data collection usually answered the questions of “how many?”, "how much?" and “how often?” are the occurrence of a particular data. These questions are quantitative data collection methods based on numbers and mathematical calculations. Quantitative data collection methods are based on random sampling and structured data collection. Some of the quantitative data collection methods are surveys, questionnaires, quizzes, interviews and direct observation.

Final answer:

To represent the total amount Abigail's parents will pay both Abigail and her sister for working the same number of hours, you could use the algebraic expressions 5h + 3h or (5 + 3)h, where h is the number of hours worked.

Explanation:

Abigail's parents pay her for weeding the yard and pay her little sister for raking leaves. If both of them work for the same amount of hours, we can represent the total amount their parents will pay using algebraic expressions. Let h be the number of hours they work.

One way to write the expression is: 5h + 3h, where 5 represents the dollars per hour for Abigail and 3 represents the dollars per hour for her sister.

Another way to represent this is: (5 + 3)h, which simplifies the expression by adding the hourly wages first and then multiplying by the number of hours worked, h.

Both expressions will give us the total amount paid to Abigail and her sister for the same number of hours worked, h.

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:

The three questions about the given triangle has been answered below.

Step-by-step explanation:

We are given a right angled triangle whose sides are of length 20, 21 and 29.

(1) sin(B) = [tex]\frac{side opposite to B}{hypotenuse}[/tex]

              = [tex]\frac{21}{29}[/tex]

              = 0.72

(2) sin(A) = [tex]\frac{20}{29}[/tex]

     sin(A)  = 0.689

     ∠CAB = [tex]sin^{-1}(0.689)[/tex]

     ∠CAB = 43.551°

(3) We suppose that cosA < sinA and we haveto find which all angles will satisfy this condition.For this the angle A should be greater than 45°.

From the given options the angles that satisfy this are 55 , 66 and 75.

45 is not included as then sinA = cosA and that condition is not there.

We can use sine and cosine trigonometric ratios to calculate the ratio and measures of angles.

A: The ratio equivalent to sin(B) is  [tex]\dfrac{21}{29}[/tex]

B: The measure of angle  ∠CAB is  [tex]43.6^\circ[/tex]

C: The possible measures of angle A can be: 55, 66 or 75

A: The ratio equivalent to sin(B) is:

[tex]sin(B) = \dfrac{CA}{AB} = \dfrac{21}{29}\\[/tex]

B: The measure of angle ∠CAB is calculated as:

[tex]sin(A) = \dfrac{CB}{BA} = \dfrac{20}{29} = 0.69\\\\A = arcsin(0.69) = 43.6^{\circ}\\\\\angle CAB = 43.6^{\circ}[/tex]

C: When sin A > cos A, the measures of angle A from 25,35,45,55,66,75 are:

55, 65 and 75:

The reason for the angles possible are 55, 66 ,75 is that:

[tex]\theta \leq 45\\sin(\theta) \leq cos(\theta)[/tex]

Thus, we have:

A: The ratio equivalent to sin(B) is  [tex]\dfrac{21}{29}[/tex]

B: The measure of angle  ∠CAB is  [tex]43.6^\circ[/tex]

C: The possible measures of angle A can be: 55, 66 or 75

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Answer:

  0.5

Step-by-step explanation:

We assume your function is

  [tex]f(x)=\sqrt{4-x}[/tex]

The distance formula can be used to find the distance from the point on the curve (x, f(x)) to the origin:

  d^2 = (x)^2 + (f(x))^2 = x^2 + (4 -x)

Written in vertex form, this is ...

  d^2 = (x -1/2) + 3.75

This has a minimum at x=1/2, so that is the x-coordinate of the point closest to the origin.

In the function f(x) = √(4-x), the x-coordinate of the point on the graph that is closest to the origin is x=0 because the function exists in the first quadrant, meaning the shortest distance to the origin is along the y-axis.

The function described is f(x) = √(4-x). We're looking for the x-coordinate of the point on the graph of this function that is closest to the origin. The distance from any point (x, y) to the origin (0, 0) is given by D=√(x²+y²). For this function, y=f(x) = √(4-x), so the distance can be written as D=√(x²+(4-x)²). To find the minimum distance, we take the derivative of this distance function with respect to x, set it equal to zero and solve for x. However, because this function lives in the first quadrant (y is always equal to or greater than 0), the shortest distance to the origin would be along the y-axis. Thus, the solution is x=0, and that is the x-coordinate of the point on the function's graph that is closest to the origin.

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Answer: there are 10 multiple choice questions and 15 short-answer questions

Step-by-step explanation:

Let x represent the number of multiple choice questions in the test.

Let y represent the number of short-answer questions in the test.

If the test has 25 questions, it means that

x + y = 25

Multiple-choice questions are worth 2 points, and short-answer questions are worth 4 points. The test is worth a total of 80 points. It means that

2x + 4y = 80 - - - - - - - -1

Substituting x = 25 - y into equation 1, it becomes

2(25 - y) + 4y = 80

50 - 2y + 4y = 80

- 2y + 4y = 80 - 50

2y = 30

y = 30/2 = 15

x = 25 - y = 25 - 15 = 10

A. The number of multiple-choice questions plus the number of short-answer questions is 25.

Answer:

A makes the most sense

Step-by-step explanation:

as if you don't get tricked and notice that C and D are not true but between A and B are two answers but B isn't correct if you go over what it means without getting tricked and A is to be the right answer

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:

Step-by-step explanation:

I'm going to paint you a picture in words of what this looks like on paper.  We have a train leaving from a point on your paper heading straight west.  We have another train leaving from the same point on your paper heading straight east.  This is the "opposite directions" that your problem gives you.  

Now let's make a table:

                 distance       =        rate      *       time

Train 1

Train 2

We will fill in this table from the info in the problem then refer back to our drawing.  It says that one train is traveling 12 mph faster than the other train.  We don't know how fast "the other train" is going, so let's call that rate r.  If the first train is travelin 12 mph faster, that rate is r + 12.  Let's put that into the table

               distance        =        rate        *        time

Train 1                                        r

Train 2                                    (r + 12)

Then it says "after 2 hours", so the time for both trains is 2 hours:

               distance        =        rate        *        time

Train 1                                        r           *          2

Train 2                                  (r + 12)       *          2

Since distance = rate * time, the distance (or length of the arrow pointing straight west) for Train 1 is 2r.  The distance (or length of the arrow pointing straight east) for Train 2 is 2(r + 12) which is 2r + 24.  The distance between them (which is also the length of the whole entire arrow) is 232.  Thus:

2r + 2r + 24 = 232 and

4r = 208 so

r = 52

This means that Train 1 is traveling 52 mph and Train 2 is traveling 12 miles per hour faster than that at 64 mph

Answer: its A    ^3^❤

Step-by-step explanation:

that guy above me probably got yall confused

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:

Option (b) is correct.

The correlation between age and weight  shown in the table is positive.

Step-by-step explanation:

According to the given values, it is found that there is a positive correlation between age and weight.

In this problem, when the age increases, so does the weight, hence they have positive correlation.

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Answer:

h=12, w=24, t=8

Step-by-step explanation:

System of Linear Equations

We have 3 unknown variables and 3 conditions between them. They form a set of 3 equations with 3 variables.

We have the following data, being  

w = price of a sweatshirt

t = price of a T-shirt

h = price of a pair of shorts

19.

The first condition states the price of a sweatshirt is twice the price of a pair of shorts. We can write it as

[tex]\displaystyle w=2h[/tex]

The second condition states the price of a T-shirt is $4 less than the price of a pair of shorts. We can write it as

[tex]\displaystyle t=h-4[/tex]

The final condition states Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for $136, thus

[tex]\displaystyle 3w+2h+5t=136[/tex]

This is the system of equations we need to solve for w,t,h

20.

To solve the system, we replace w in terms of h and t in terms of h. Those relations have been already written, so

[tex]\displaystyle 3(2h)+2h+5(h-4)=136[/tex]

Operating

[tex]\displaystyle 6h+2h+5h-20=136[/tex]

[tex]\displaystyle 13h=156[/tex]

Solving for h

[tex]\displaystyle h=12[/tex]

The other two variables are

[tex]\displaystyle w=2h=24[/tex]

[tex]\displaystyle t=12-4=8[/tex]

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:

Eugene friend will have more pie than Eugene.

Eugene friend has [tex]\frac{3}{5}[/tex] more pie than Eugene.

Step-by-step explanation:

Given:

Amount of pie Eugene has = 3

Amount of Pie given to friend  = [tex]1\frac{4}{5}[/tex]

[tex]1\frac{4}{5}[/tex] can be Rewritten as [tex]\frac{9}{5}[/tex]

We need to find who has pie and how much more.

We will first find the amount of pie Eugene is left with.

The amount of pie Eugene is left with is equal to Amount of pie Eugene had minus Amount of pie given to friend.

Framing the equation we get;

The amount of pie Eugene is left = [tex]3-\frac{9}{5}[/tex]

We will take LCM to solve the same.

The amount of pie Eugene is left = [tex]3-\frac{9}{5} = \frac{3\times5}{5}-\frac{9}{5} =\frac{15}{5}-\frac{9}{5} = \frac{15-9}{5} =\frac{6}{5}[/tex]

Now  [tex]\frac{9}{5} = 1.8[/tex] and  [tex]\frac{6}{5} = 1.2[/tex]

Hence  [tex]\frac{9}{5}[/tex] is greater than  [tex]\frac{6}{5}[/tex]

Hence Eugene friend will have more pie than Eugene.

Now we will find amount more pie Eugene friend has.

Amount More Eugene friend has can be calculate by Subtracting Amount of of Eugene has with Amount of pie his friend has.

Amount More Eugene friend has =[tex]\frac{9}{5} - \frac{6}{5} =\frac{9-6}{5}= \frac{3}{5}[/tex]

Hence Eugene friend has [tex]\frac{3}{5}[/tex] more pie than Eugene.

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:

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: 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.

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.