Write the equation of the graph obtained when the graph of y -
is compressed vertically by a factor of 0.25, translated 4 units
right, and then translated 3 units up.

Answer:

a) probability of choosing the mean amount of sleep for adult as  μ < 9 hours when it is μ = 8.5 hours is 0.4038

b) There is a 0.5962 probability of failing to choose that the mean amount of sleep for adult is  μ < 9 hours when it is μ = 8.5 hours

Step-by-step explanation:

a) Interpret the value of the power

The power of an hypothesis is the probability of rejecting the null hypothesis when the alternative hypothesis is valid. It is a type 1 error

Power = 0.4038

From the hypothesis test,

the null hypothesis, μ = 8.5 hours

Alternative hypothesis, μ < 9 hours

Sine the power is the probability of rejecting the null hypothesis, it means that the probability of choosing the mean amount of sleep for adult as  μ < 9 hours when it is μ = 8.5 hours is 0.4038

b)

Power + β = 1

β = 1 - Power

β = 1 - 0.4038

β = 0.5962

β, type 2 error, is the probability of not rejecting the null hypothesis even when it is false.

It means that there is a 0.5962 probability of failing to choose that the mean amount of sleep for adult is  μ < 9 hours when it is μ = 8.5 hours

The power of a test (0.4038 in this case) is the probability that we correctly reject the null hypothesis, given the actual population mean is 8.5 hours. Beta (1 - Power, or 0.5962 in this case) is the probability of committing a type II error, which is incorrectly accepting the null hypothesis.

In the context of hypothesis testing in statistics, the power of a test refers to the probability that the test will correctly reject the null hypothesis when the alternative hypothesis is true. In this specific scenario, the power of the test is 0.4038. This means that there is a 40.38% chance that we would correctly conclude that the mean sleep for adults is less than 9 hours, assuming that the actual population mean is 8.5 hours.

The value of beta represents the probability of committing a type II error, which is the error of not rejecting a null hypothesis when it should be rejected; in other words, incorrectly concluding that the mean sleep for adults is not less than 9 hours when it actually is. The value of beta can be calculated as 1 minus the power of the test, so in your case it would be 1 - 0.4038 = 0.5962. This means there is a 59.62% chance of committing a type II error.

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Answer:

The Correct answer is C

Step-by-step explanation:

because i just took it.

Answer:

c

Step-by-step explanation:

Answer:52

Step-by-step explanation:

Answer:

248cm

Step-by-step explanation:

Answer:

0.8937

Step-by-step explanation:

This is a case of binomial probability with n = 64, p = 0.10 and x = 3.  This means that the probability of a cancellation is 10%.  Here, we can find the probability that more than 3 cancellations or no shows will occur by finding binompdf(64,0.10, 0) + binompdf(64,0.10, 1) + binompdf(64,0.10, 2) + binompdf(64,0.10, 3) and then subtracting this sum from 1.000.  

We get:    0.0012 + 0.0084 + 0.0293 + 0.0674 = sum = 0.1063

Then the desired probability is 1.0000 - 0.1063 = 0.8937

The probability that more than 3 cancellations and/or no-shows will occur during the next week is: 0.8937

This involves binomial probability distribution with the formula;

P(X = x) = ⁿCₓ × pˣ × q⁽ⁿ ⁻ ˣ⁾

We are given;

p = 10% = 0.1

n = 64

q = 1 - p = 1 - 0.1

q = 0.9

We want to find the probability that more than 3 cancellations and/or no-shows will occur during the next week is given by;

P(X > 3) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X =3))

From online binomial probability calculator;

P(0) = 0.0012

P(1) = 0.0084

P(2) = 0.0293

P(3) = 0.0674

Thus;

P(X > 3) = 1 - (0.0012 + 0.0084 + 0.0293 + 0.0674 )

P(X > 3) = 1 - 0.1063

P(X > 3) = 0.8937

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Answer:

-10

Step-by-step explanation:

combine like terms -5x+9=59 subtract 9 from both side and get -5x=50 so x=-10

Answer:

-10

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−t+9−4t=59

−t+9+−4t=59

(−t+−4t)+(9)=59(Combine Like Terms)

−5t+9=59

−5t+9=59

Step 2: Subtract 9 from both sides.

−5t+9−9=59−9

−5t=50

Step 3: Divide both sides by -5.

−5t −5 = 50−5

t=−10

Answer:

504 in.

Step-by-step explanation:

6 · 12 · 7 = 504

Answer:

504in^3

Step-by-step explanation:

voluke of rectangular prism formula: LWH

where l=length(7)

w=width(12)

h=height(6)

so

7*12*6=504

504in^3

Angle Zc measures 90° as it is supplementary to the given 90° angle. Therefore, Zc = 90°.

To find the measure of angle Zc, we need to use the properties of angles formed by intersecting lines.

Given:

- Angle Zc is supplementary to angle 90°.

- Angle 90° is formed by the intersection of lines, let's denote them as line AB and line CD.

- Angle 90° is bisected by line EF, forming two congruent angles.

Step-by-step explanation:

1. Since angle Zc is supplementary to angle 90°, we subtract the measure of angle 90° from 180° to find the measure of angle Zc.

  Measure of angle Zc = 180° - 90°

                                     = 90°

So, angle Zc measures 90°.

Answer:

Step-by-step explanation:

The answer is 10 bananas and 2 apples

The number of apples are 2 and number of bananas is 10.

Two or more expressions with an Equal sign is called as Equation.

Given that Hattie is making fruit baskets, which includes apples and bananas, to send to some of her real estate clients.

She wants each basket to have 12 pieces of fruit, but the fruit should weigh no more than 80 ounces total.

On average, each apple weighs 5 ounces, and each banana weighs 7 ounces.

Let Bananas is denoted by B and Apples are represented by A.

A+B=12...(1)

5A+7B<80...(2)

A=12-B

Substitute in equation 2.

5(12-B)+7B=80

60-5B+7B=80

60+2B=80

Subtract 60 on both sides.

2B=80-60

2B=20

Divide both sides by 2.

B=10

A+B=12

A+10=12

A=2

Hence, the number of apples are 2 and number of bananas is 10.

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The correct value of the angle of rotation is 3π/5

Answer:

Distance travelled ≈ 22.6 ft

Step-by-step explanation:

We are given;

Radius;r = 12 ft

Angle of rotation; θ = 3π/5

The formula for calculating distance travelled is;

Distance travelled = rθ

So, plugging in the relevant values;

Distance travelled = 12 x 3π/5

Distance travelled ≈ 22.6 ft

Answer:

its 280

Step-by-step explanation:

Answer:

(a) 0.85

(b) 0.7225

Step-by-step explanation:

(a) The point estimate for the proportion of all such components that are not defective is given by the number of non-defective units in the sample divided by the sample size:

[tex]p=\frac{80-12}{80}\\p=0.85[/tex]

The proportion is 0.85.

(b) Assuming that the sample is large enough to accurately provide a point estimate for the whole population, this can be treated as a binomial model with probability of success (non-defective part) p = 0.85. Since both components must be non-defective for the system to work, the probability of two successes in two trials is:

[tex]P(x=2) = 0.85^2\\P(x=2) = 0.7225[/tex]

An estimate of 0.7225 for the proportion of all such systems that will function properly.

Answer:

8. 11 packets

Step-by-step explanation:

8. If the machine makes 88 pieces in 1 minute and puts 8 pieces in each snack packet 88÷8=11 so, 11 packets are filled each minute.

I cannot read 9. as it is cut off, so i can't answer it :)

Final answer:

In an economy with 100 workers who can produce either four cakes or three shirts, they can make 400 cakes or 300 shirts, respectively, when all are dedicated to one task.

Explanation:

Calculating Production Output

If an economy has 100 identical workers with each one capable of producing either four cakes or three shirts, we can calculate the total production of each good. When all workers are cooking, the number of cakes that can be produced in this economy is 400 cakes (100 workers × 4 cakes per worker).

Conversely, if all workers are sewing shirts, then the total number of shirts produced is 300 shirts (100 workers   ×3 shirts per worker).

Answer:

37

Step-by-step explanation:

all triangle's angle measures add up to 180

180-98-45 = x

x = 37

Answer:

Step-by-step explanation:

All triangles = 180 degrees

^ That is known.

98 + 45 = 143

     ^ These 2 angles are given (98 and 45)

180 - 143 = 37

          ^ This was the total.

37 is the final answer.

I hope I helped you!

Answer:

  volume is 3 1/2 units³

Step-by-step explanation:

The question asks for area, but the answers have dimensions of volume.

__

The volume is the product of the length, height, and width dimensions:

  V = LWH = (2)(1)(1 3/4) = 2 6/4 = 3 1/2 . . . . units³

The volume is 3 1/2 cubic units.

Answer:

  -1

Step-by-step explanation:

The required relation is ...

  7n = n^2 -8

  0 = n^2 -7n -8 . . . . put in standard form

  0 = (n -8)(n +1) . . . . factor

Solutions are n=8 and n=-1.

The negative solution is -1.

Answer: 0.66

Step-by-step explanation:

The United States senate had 57 Democrats and 43 Republicans which makes the total numerous of senators 100.

38 Democrats had served in the military while 28 Republicans has served in the military which makes the total number of senators that had served in the military 66.

Probability of a Republican senator that had served in the military will be:

Answer:

0.011

Step-by-step explanation:

let's see so first

first you line the numbers on the right (DO NOT ALINE DECIMAL POINTS)

second, starting from on the right multiply each digit in the top number by each digit in the bottom number just as whole numbers .

after add the products

Answer:

Required probability is 0.2262

Step-by-step explanation:

given data

mean length = 170 millimeters

standard deviation = 10 millimeters

sample n = 299

population mean by greater than = 0.7 millimeters

solution

we consider here batch of steel rod produced = x

probability that mean length sample that differ than the population mean greater than 0.7  required probability is

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 1 - P (  [tex]\bar {x} -\mu[/tex] ≤ 0.7 )   .................1

so we take here value

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 1 - [  P ( -0.7 ≤  [tex]\bar {x} -\mu[/tex] ≤ 0.7 ) ]

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 1 -  [  P (     [tex]\frac{-0.7}{\frac{10}{\sqrt{299}}}[/tex]    ≤   [tex]\frac{\bar {x} -\mu}{\frac{\sigma }{\sqrt{n}}}[/tex]    ≤    [tex]\frac{0.7}{\frac{10}{\sqrt{299}}}[/tex]    )  

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 1 [ P ( - 1.21  ≤  Z  ≤ 1.21 ) ]

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 1 ( P ( Z ≤ 1.21 ) - P ( Z ≤ - 1.21 ) )

we use here excel function that

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 1 - { (=NORMSDiST (1.21) - (=NORMSDiST (-1.21)  }

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 1 - ( 0.8869 - 0.1131 )

P ( [tex]\bar {x} -\mu[/tex] > 0.7  ) = 0.2262

so required probability is 0.2262

To find the probability that the sample mean length of steel rods differs from the population mean by more than 0.7 millimeters, we calculate the standard error, convert 0.7 mm to a z-score, and then find the two-tailed probability using the standard normal distribution.

To calculate the probability that the mean length of a sample of steel rods will differ from the population mean by more than 0.7 millimeters, we must use the Central Limit Theorem, which states that the sampling distribution of the sample mean will be normally distributed as the sample size gets larger (which holds true in this case since we have 299 rods).

We can apply this theorem to find the standard error of the mean (SEM), which is the standard deviation of the sample mean distribution, calculated as σ/√n (population standard deviation/square root of sample size).

With σ = 10 millimeters and n = 299, the SEM is 10/√299 = 0.5787 millimeters. To find the probability that the sample mean differs from the population mean by more than 0.7 millimeters, we convert 0.7 millimeters to a z-score by dividing by the SEM: z = 0.7/0.5787 = 1.2096.

Using the standard normal distribution, we find the probability for the corresponding z-score and then calculate the two-tailed probability, as we are looking for the probability that the sample mean is either above or below the population mean by 0.7 millimeters. However, to provide the exact figure, we would need a z-table or software to get the precise probability.

Finally, we find that the distribution of the sample mean will have higher probabilities closer to the population mean, as described in the provided information.

Answer:

P(X>17) = 0.979

Step-by-step explanation:

Probability that a camera is defective, p = 3% = 3/100 = 0.03

20 cameras were randomly selected.i.e sample size, n = 20

Probability that a camera is working, q = 1 - p = 1 - 0.03 = 0.97

Probability that more than 17 cameras are working P ( X > 17)

This is a binomial distribution P(X = r) [tex]nCr q^{r} p^{n-r}[/tex]

[tex]nCr = \frac{n!}{(n-r)!r!}[/tex]

P(X>17) = P(X=18) + P(X=19) + P(X=20)

P(X=18) = [tex]20C18 * 0.97^{18} * 0.03^{20-18}[/tex]

P(X=18) = [tex]20C18 * 0.97^{18} * 0.03^{2}[/tex]

P(X=18) = 0.0988

P(X=19) = [tex]20C19 * 0.97^{19} * 0.03^{20-19}[/tex]

P(X=19) = [tex]20C19 * 0.97^{19} * 0.03^{1}[/tex]

P(X=19) = 0.3364

P(X=20) = [tex]20C20 * 0.97^{20} * 0.03^{20-20}[/tex]

P(X=20) = [tex]20C20 * 0.97^{20} * 0.03^{0}[/tex]

P(X=20) = 0.5438

P(X>17) = 0.0988 + 0.3364 + 0.5438

P(X>17) = 0.979

The probability that there are more than 17 working cameras should be 0.979 for the company to accept the whole batch

Answer:

C

Step-by-step explanation:

A cube has 6 square faces

Each face: 5² = 25

Surface area: 6(25) = 150 in²

Answer:

the answer is 3/2

Step-by-step explanation:

because when you divide it you have to do keep change flip so you change 4/9 to 9/4 and divide it by 2/3 to get 3/2 so you put it in the equation to see if it is correct

The equation is a linear function, and the value of n that makes the 2/3 times n equals 4/9 true is 2/3

The equation in the question implies that:

2/3 of n equals 4/9

This equation can be expressed as:

2/3 * n = 4/9

Multiply both sides by 3

3 * 2/3 * n = 3 * 4/9

Evaluate the product

2 * n = 4/3

Divide both sides by 2

n = 2/3

Hence, the value of n that makes the 2/3 times n equals 4/9 true is 2/3

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Answer:

[tex]f(a) = \frac{(a+5)}{(a-1)}[/tex]

Step-by-step explanation:

Given : [tex]f(x) = \frac{(3+x)}{(x-3)}[/tex]

In order to find [tex]f(a+2)[/tex] we will substitute [tex](a+2)[/tex] for [tex]x[/tex] in the given function, that is :

[tex]f(a) = \frac{(3+a+2)}{(a+2-3)}[/tex]

[tex]f(a) = \frac{(a+5)}{(a-1)}[/tex]

Answer:

A) f(x) = –16x2 + 99x + 6

Step-by-step explanation:

ed2021 :)

Answer:

2

Step-by-step explanation:

6×2=12

That is how I got the answer.

Answer:

2

Step-by-step explanation:

Answer:

7/12

Step-by-step explanation:

Probability is a ratio defined by the number of possible outcome to the number of total outcome. The probability that an event will happen added to the probability that the event will not happen gives 1. In other words, the outcome of a probability cannot exceed 1.

The probability that an event a will happen or that another independent event  b will happen is the sum of the probability that a will happen to the probability that b will happen.

For the 2 dies, the outcomes possible when rolled are as shown below  

O   1     2     3    4    5     6

1    2    3     4     5    6    7

2   3    4     5    6    7     8

3   4    5    6    7      8    9

4   5    6    7     8    9    10

5   6     7   8    9    10    11

6   7    8    9    10    11    12    

From the table, there are 36 possible outcomes but only 21 outcomes are less than 8 hence the probability required

= 21/36

= 7/12      

Answer:

Adding 254 to both sides.

This is an inverse operation.

On the right side of the equation, there is a -254, which you need to get rid of in order to isolate p. (You have to isolate p to find the value)

So, since it is -254, you would do +254 on BOTH sides of the equation. Hope this helps!!

The inverse operation needed to solve for p in the equation 765 = p - 254 is addition.

To solve for p in the equation 765 = p - 254, we need to isolate p on one side of the equation. To do this, we can use the inverse operation of subtraction, which is addition. By adding 254 to both sides of the equation, we get:

765 + 254 = p - 254 + 254

Simplifying the equation gives us:

1019 = p

Therefore, the inverse operation needed to solve for p is addition.

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Answer:

Step-by-step explanation:

Given that,

A rectangular prism with a volume of 8 cubic units, V = 8 cubic units

The rectangular prism is filled with a cube twice.

First one

A cube with ½ length unit, we should know that a cube have equal length

Then, L = ½ units

Volume of a cube is L³

V = L³

V1 = (½)³ = ⅛ cubic units

Second cube

A cube with ⅓ length unit, we should know that a cube have equal length

Then, L = ⅓ units

Volume of a cube is L³

V = L³

V1 = (⅓)³ = 1 / 27 cubic units

So, to know number of times cube one will filled the rectangular prism

V = nV1

Where V is the volume of rectangular prism

n is the number of times the cube will be able to matched up with the volume of the rectangular prism

Then, n_1 = V / V1

n_1 = 8 / ⅛

n_1 = 64 times

Also,

n_2 = V / V2

n_2 = 8 / 1 / 27

n_2 = 8 × 27 = 216 times

So, the we need more of ⅓units and we will need (216 - 64) = 152 times

We need 152 more of ⅓units

You need 152 more cubes with side lengths of 1/3 unit than cubes with side lengths of 1/2 unit to fill a rectangular prism with a volume of 8 cubic units.

To determine how many more cubes with side lengths of 1/3 unit are needed to fill the rectangular prism compared to cubes with side lengths of 1/2 unit, we first need to find the number of each type of cube that fits into the prism.

The volume of the rectangular prism is given as 8 cubic units.

First, let's calculate the volume of one small cube:

Next, determine how many of each type of cube are needed to fill the prism:

The difference in the number of cubes needed is:

216 (1/3-unit cubes) - 64 (1/2-unit cubes) = 152 more 1/3-unit cubes.

Answer:

7.28 7.29  c

Step-by-step explanation:

The square root of 53 can be found to lie between the values of 7.28 and 7.29.

The square root function can only have non negative values. If we take thee square root of a number, we obtain a value that can be multiplied by itself to obtain the number.

The square root of 53 can be found to lie between the values of 7.28 and 7.29.

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