The EverGlow nuclear power plant releases water into Lake Fishbegone every afternoon at 4:51 p.m. Environmental researchers are concerned that fish are being driven away from the area around the plant. They believe that the temperature of the water discharged may be a factor. The data table below gives the temperature of the water released by the plant and the measured distance (in meters) from the outflow pipe of the plant to the nearest fish found in the water on several randomly chosen afternoons. A scatterplot of the data and the least-squares regression line are given.
What is the slope of the least-squares regression line? *
A. -74.704
B. 5.791
C. 12.196
D. 0.946

Answer:

72 dollars

Step-by-step explanation:multiplrf the two

Answer:

1

Step-by-step explanation:

The expected value for the given case is $-4.75.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lies in the close interval of 0 and 1 [0,1].

Given that,

The probability of winning $76 is 1/20.

And, the probability of losing $9 is 19/20.

The expected value for the given probability can be given by taking the product of the probability and the wining or losing amount and then substracting them as,

Expected value = 1/20 × 76 - 19/20 × 9

                          = 3.8 - 8.55

                          = -4.75

Hence, the expected value of amount for losing and winning the game is $-4.75.

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Answer:

15 divided by 1/5 is equal to 1.

Answer:

f(4) - g(2) = 10

Step-by-step explanation:

[tex]f(x) = 2x + 4 \\ f(4) = 2 \times 4 + 4 = 8 + 4 = 12 \\ \\ g(x) = 6x - 10 \\ g(2) = 6 \times 2 - 10 = 12 - 10 = 2 \\ \\ f(4) - g(2) = 12 - 2 \\ \\ \huge \red{ \boxed{ f(4) - g(2) = 10}}[/tex]

Answer:

answer what???

Step-by-step explanation:

Answer:

0.1

Step-by-step explanation:

Answer:

-3.25

Step-by-step explanation:

Answer:

To find the points, remember the definition of distance or difference.

First, the 5 is easy to find, is in the extreme right.

Now, the next number is 3.

The difference between 3 and 5 is:

3 - 5 =  - 2

This means that the place of the 3 will be 2 units at the left of the 5.

The next number is -2

The difference between -2 and 5 is:

-2 - 5 = -7

This means that the -2 is located 7 units at the left of the 5.

Below is an image of the located points in a number line.

Answer:

y=14

Step-by-step explanation:

measure of a=50degrees b=50 degrees c=(5(14)+10) =80

50+50+80=180

Answer:

Y= 14

Step-by-step explanation:

a=50degrees

b=50 degrees

c=(5(14)+10) =80

50+50+80=180

Answer:

The derivative is [tex]\frac{dR}{dM} = CM - M^2[/tex]

Step-by-step explanation:

From the question we are told that

The equation representing the reaction is [tex]R = M^2 (\frac{C}{2} - \frac{M}{3} )[/tex]

Generally this equation can be represented as

[tex]R = \frac{C M^2}{2} - \frac{M^3}{3}[/tex]

Generally [tex]\frac{dR}{dM}[/tex] as a function of M is mathematically represented as

[tex]\frac{dR}{dM} = 2 * \frac{C M^{2 - 1 }}{2} + 3 * \frac{M^{3-1}}{3}[/tex]

=> [tex]\frac{dR}{dM} = CM - M^2[/tex]

Answer:

The answer is 270.

Step-by-step explanation:

This is the answer is because:

If you let the number be x.

x divided by 3 is equal to x divided by 10 plus 63.

x/3 = x/10 +63

So...

x divided by 3 plus x divided by 10 is equal to 63

x/3 +x/10 = 63

Then if you make a commmon denominator...

10x divided 30 plus 3x divided by 30 is equal to 63

10x/30 + 3x/30 = 63

Then...

7x divided by 30 is equal to 63

7x/30 = 63

After that...

x is equal to ( 63 * 30 ) divided by 7

x = (63*30) / 7

So...

x is equal to 9*30

x = 9*30

Finally...

x is equal to 270

x = 270

Step-by-step explanation:

(7x)^2 - 2×7x×1 +1^2 =0

(7x-1)^2 =0

7x-1=0

7x=1

x= 1\7

Answer:

G. 6 months

Step-by-step explanation:

1. 495-165 to remove the one-time payment = 330

2. 330/55 to find the number of months = 6

Barbara receive 6 months of dance lessons from Dance Unlimited

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, Barbara signed up for dance lessons at Dance Unlimited. She was charged $55 per month for lessons and a one-time recital fee of $165.

Let m be the no of months and f(m) is the total cost.

∴ f(m) = 55m + 165.

The equation represents the $495 total cost,

∴ 495 =  55m + 165.

55m = 330.

m = 330/55.

m = 6.

Barbara receives 6 months of dance lessons from Dance Unlimited.

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Answer:

The sum of two irrational numbers, in some cases, will be irrational. However, if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational.

Answer:

mDE = 9

Step-by-step explanation:

mCD and mDE must add up to mCE

Step 1: Set up equation

mCD + mDE = mCE

5x + 1 + 3x + 3 = 20

Step 2: Solve for x

Step 3: Find mDE

mDE = 3x + 3

mDE = 3(2) + 3

mDE = 6 + 3

mDE = 9

Answer:

7

The difference between 9 a positive number and - 2 a negative number is 7 because the question States 9 - 2.

Answer:

230

Step-by-step explanation:

The answer is 230 because if you add 123 and 108 together you get 231 but since we are rounding to the nearest 10 it would be 230 because 231 is closer to 230 than it is to 240.

Answer:

82

Step-by-step explanation:

59 + 23 = 82

The sum of 59 and 23 is  82

Answer: 7 and a 1/2

Step-by-step explanation: 1 and 1/4 times4 = 5 plus 2 and a 1/2 = 7 and a 1/2

Answer:

7.5

Step-by-step explanation:

Answer:

7.5

Step-by-step explanation:

I am a senior so I am right

Answer:

Step-by-step explanation:

Given the simultaneous equation

4x-5y+16 =0  ....... 1

2x+y-6 =0  ...... 2

Let us solve to get the variable x and y:

The equation becomes

4x-5y =-16   ........ * 1

2x+y =6 ...... *2

Using Elimination method

Multiply eqn 1 by 1 and eqn 2 by 2

4x-5y =-16

4x+2y =12

Subtract resulting equation

-5y-2y = -16-12

-7y = -28

solve for y

-7y/-7 = -28/-7

y = 4

Substitute y = 4 into equation 2 to get x

2x+y =6

2x + 4 = 6

2x = 6-4

2x = 2

x = 2/2

x = 1

hence x is 1, y is 4

Answer:

51

Step-by-step explanation:

Answer: 51

Step-by-step explanation:

Evaluate

Answer:

3960 feet

Step-by-step explanation:

Answer:

3,960 feet long

Step-by-step explanation:

1 mile = 5,280 feet

5,280 feet ÷ 4 (because the denominator is 4) = 1,320 feet

1,320 x 3 (the numerator is 3) = 3,960 feet

3/4 of a mile = 3,960 feet

Answer:

(a) 0.94

(b) 0.20

(c) 90.53%

Step-by-step explanation:

From a population (Bernoulli population), 90% of the bearings meet a thickness specification, let [tex]p_1[/tex] be the probability that a bearing meets the specification.

So, [tex]p_1=0.9[/tex]

Sample size, [tex]n_1=500[/tex], is large.

Let X represent the number of acceptable bearing.

Convert this to a normal distribution,

Mean: [tex]\mu_1=n_1p_1=500\times0.9=450[/tex]

Variance: [tex]\sigma_1^2=n_1p_1(1-p_1)=500\times0.9\times0.1=45[/tex]

[tex]\Rightarrow \sigma_1 =\sqrt{45}=6.71[/tex]

(a) A shipment is acceptable if at least 440 of the 500 bearings meet the specification.

So, [tex]X\geq 440.[/tex]

Here, 440 is included, so, by using the continuity correction, take x=439.5 to compute z score for the normal distribution.

[tex]z=\frac{x-\mu}{\sigma}=\frac{339.5-450}{6.71}=-1.56[/tex].

So, the probability that a given shipment is acceptable is

[tex]P(z\geq-1.56)=\int_{-1.56}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}}=0.94062[/tex]

Hence,  the probability that a given shipment is acceptable is 0.94.

(b) We have the probability of acceptability of one shipment 0.94, which is same for each shipment, so here the number of shipments is a Binomial population.

Denote the probability od acceptance of a shipment by [tex]p_2[/tex].

[tex]p_2=0.94[/tex]

The total number of shipment, i.e sample size, [tex]n_2= 300[/tex]

Here, the sample size is sufficiently large to approximate it as a normal distribution, for which mean, [tex]\mu_2[/tex], and variance, [tex]\sigma_2^2[/tex].

Mean: [tex]\mu_2=n_2p_2=300\times0.94=282[/tex]

Variance: [tex]\sigma_2^2=n_2p_2(1-p_2)=300\times0.94(1-0.94)=16.92[/tex]

[tex]\Rightarrow \sigma_2=\sqrt(16.92}=4.11[/tex].

In this case, X>285, so, by using the continuity correction, take x=285.5 to compute z score for the normal distribution.

[tex]z=\frac{x-\mu}{\sigma}=\frac{285.5-282}{4.11}=0.85[/tex].

So, the probability that a given shipment is acceptable is

[tex]P(z\geq0.85)=\int_{0.85}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}=0.1977[/tex]

Hence,  the probability that a given shipment is acceptable is 0.20.

(c) For the acceptance of 99% shipment of in the total shipment of 300 (sample size).

The area right to the z-score=0.99

and the area left to the z-score is 1-0.99=0.001.

For this value, the value of z-score is -3.09 (from the z-score table)

Let, [tex]\alpha[/tex] be the required probability of acceptance of one shipment.

So,

[tex]-3.09=\frac{285.5-300\alpha}{\sqrt{300 \alpha(1-\alpha)}}[/tex]

On solving

[tex]\alpha= 0.977896[/tex]

Again, the probability of acceptance of one shipment, [tex]\alpha[/tex], depends on the probability of meeting the thickness specification of one bearing.

For this case,

The area right to the z-score=0.97790

and the area left to the z-score is 1-0.97790=0.0221.

The value of z-score is -2.01 (from the z-score table)

Let [tex]p[/tex] be the probability that one bearing meets the specification. So

[tex]-2.01=\frac{439.5-500 p}{\sqrt{500 p(1-p)}}[/tex]

On solving

[tex]p=0.9053[/tex]

Hence, 90.53% of the bearings meet a thickness specification so that 99% of the shipments are acceptable.

The manufactures bearings.

As per the question, the process that a manufacturer bears 90% of the bearings and meet the thickness specifications. The shipment consists of 500 bearings. The shipment if taken has a least 440 and 500 bearings.

the answer is 0.94, 0.20, and 90.53%.

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Answer:

(a) [tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]

(b) P(1) = 0.740, P(2) = 0.192, and P(3) = 0.050.

(c) The probability that n ≥ 4 is 0.018.

(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is 3.

Step-by-step explanation:

We are given that on the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry.

Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

(a) We can observe that the above situation can be represented through the geometric distribution because the geometric distribution states that we will keep on going with the trials until we achieve our first success,

Here also, n represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.

So, the probability distribution of the geometric distribution is given by;

[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]

where, p = probability that the residents are of Hawaiian ancestry = 74%

(b) The probabilities that n = 1, n = 2, and n = 3 is given by;

[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1}[/tex]

P(1) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{1-1}[/tex] = 0.74

P(2) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{2-1}[/tex] = 0.192

P(3) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{3-1}[/tex] = 0.050

(c) The probability that n ≥ 4 is given by = P(n ≥ 4)

     P(n ≥ 4) = 1 - P(n = 1) - P(n = 2) - P(n = 3)

                   = 1 - 0.74 - 0.192 - 0.050

                   = 0.018

(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is given by = E(n)

We know that the mean of the geometric distribution is given by;

           Mean = [tex]\dfrac{p}{1-p}[/tex] = [tex]\dfrac{0.74}{1-0.74}[/tex]

                     = [tex]\dfrac{0.74}{0.26}[/tex] = 2.85 or 3 (approx).

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Answer:

The answer is,2094.75

Step-by-step explanation:

Percentage decrease = 5% × 2,205

2,205 - Percentage decrease =

2,205 - (5% × 2,205) =

2,205 - 5% × 2,205 =

(1 - 5%) × 2,205 =

(100% - 5%) × 2,205 =

95% × 2,205 =

95 ÷ 100 × 2,205 =

95 × 2,205 ÷ 100 =

209,475 ÷ 100 =

2,094.75

Or to be simpler

You find 5% of 2,205 which is 110.25 then subtract it from 2205 which is 2,094.75 and that 5% of 2,205

Answer:

B

Step-by-step explanation: