geometry math help plz answer all questions

Answer:

a. The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57

b. Yes

c. The power of the test is 0.03836

d. The sample size can be considered adequate

Step-by-step explanation:

a. The given data in the study

Catalyst 1: 57.9, 66.2, 65.4, 65.4, 65.2, 62.6, 67.6, 63.7, 67.2, 71.0

Catalyst 2: 66.4 , 71.7, 70.3, 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.8

Using the Average, Standard Deviation function from Microsoft Excel, we have;

The mean for Catalyst 1, [tex]\overline x_1[/tex] = 65.22

The standard deviation for catalyst 1, σ₁ = 3.444416

The mean for Catalyst 2, [tex]\overline x_2[/tex] = 68.42

The standard deviation for catalyst 2, σ₂ = 2.22401

The 95% confidence interval on the difference in mean is given as follows;

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]

The critical-z for a 95% confidence interval = 1.96

Therefore, we have;

[tex]\left (65.22-68.42 \right ) \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}}[/tex]

Therefore, we have;

The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57

The test statistics is given as follows;

[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]

Therefore we have;

[tex]z=\dfrac{(65.22-68.42)}{\sqrt{\dfrac{3^{2} }{10}+\dfrac{3^{2}}{10}}} = -2.385[/tex]

The p-value = P(Z<-2.39 or Z > 2.39) = 2P(Z<-2.39) = 2 × 0.00842 = 0.01684

b. From the confidence interval which range from approximately -5.83 to -0.57 and does not include 0, therefore, there is a difference in mean active concentration which depends on the choice of catalyst

c. The power of the test

 The sample mean difference is given as follows;

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]

Therefore, we have;

[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}} = \pm 2.6296[/tex]

The z-value is given as follows;

[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]

μ₁ - μ₂ = 5

When [tex]\bar{x}_1-\bar{x}_{2} = 2.6296[/tex]

[tex]z=\dfrac{2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -1.7667918[/tex]

When [tex]\bar{x}_1-\bar{x}_{2} = -2.6296[/tex]

[tex]z=\dfrac{-2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -5.686768[/tex]

The power of the test is given by P = P(Z<-5.69) + P(Z>-1.77) = 0 + 0.03836 = 0.03836

The power of the test = 0.03836

d. The sample size is statistically adequate because the confidence interval of -5.83 < μ₁ - μ₂ < -0.57 has a value of -5 as a possible population difference in mean

The assumption of normality seems adequate because the confidence interval obtained by using the sample standard deviation is given as follows;

(-5.74, -0.66) which also contains -5 which is the difference in the population mean

Answer:

55

Step-by-step explanation:

Answer:

A sample of 595 should be obtained.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

Estimate of 0.55

This means that [tex]\pi = 0.55[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

What sample size should be obtained if she wishes the estimate to be within a margin of error of 0.04?

This is n for which M = 0.04. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.04 = 1.96\sqrt{\frac{0.55*0.45}{n}}[/tex]

[tex]0.04\sqrt{n} = 1.96\sqrt{0.55*0.45}[/tex]

[tex]\sqrt{n} = \frac{1.96\sqrt{0.55*0.45}}{0.04}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96\sqrt{0.55*0.45}}{0.04})^2[/tex]

[tex]n = 594.2[/tex]

Rounding up,

A sample of 595 should be obtained.

Answer: x=3, elimination method

Step-by-step explanation:

x=3

-7x-2y=-13    ->  -7x-2y=-13

-(x-2y=11)      ->   -x+2y=-11

                        -----------------

                          -8x=-24

                              x = 3

elimination method

because you can easily eliminate one variable (y) using the elimination method

Answer:

0.8 of a chocolate bar

Step-by-step explanation:

Bc 5 divided by 6 is 0.8

Answer:

Sum is 4/8

Difference is 2/8

Step-by-step explanation:

Sum is adding so add the numerators and denominators would be the same

Difference is subtraction

Answer:

1.45

Step-by-step explanation:

I don't really know if this is right

9514 1404 393

Answer:

  $3633.96

Step-by-step explanation:

The monthly payment is given by the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

monthly payment for principal P at annual rate r for t years.

  A = $672096(0.04/12)/(1 -(1 +0.04/12)^(-12·24)) = $3633.96

The monthly payment for the mortgage is $3633.96.

9514 1404 393

Answer:

  no

Step-by-step explanation:

The slope formula is ...

  m = (y2 -y1)/(x2 -x1)

We can use the values ...

  (x1, y1) = (1, -19)

  (x2, y2) = (-2, -7)

Putting these into the formula gives ...

  m = (-7 -(-19))/(-2 -1) = 12/-3 = -4

The slope is -4, not -1/4. Mark is incorrect.

Answer:

If they water the plants in the garden together then it will take about 15 minutes because when they do it seperatly it takes about 30 minutes. So if they do it together, they are cutting work in half. And half of 30 is 15.

Step-by-step explanation:

32 rounded is 30.

25 rounded is 30.

30/ 2 = 15

Answer:

B

Step-by-step explanation:

Answer:

r=13

Step-by-step explanation:

81.64/3.14=26(diameter)

26/2=13(radius)

Answer:

26%

Step-by-step explanation:

To find the percentage of a number, I find it's often helpful to first write it as a fraction:  [tex]\frac{104}{400}[/tex] .

Percentages can be represented as a fraction by putting them over 100, eg. 25% is [tex]\frac{25}{100}[/tex]

.

Therefore, to get [tex]\frac{104}{400}[/tex] into a percentage, we need to change that 400 on the bottom to 100. How do we do that? Divide by four. However, anything we do to the bottom of a fraction, we must do to the top, so we divide both by four:

[tex]\frac{\frac{104}{4} }{\frac{400}{4} }[/tex] = [tex]\frac{26}{100}[/tex]

As we saw earlier, if a fraction has 100 at the bottom, then the top of the fraction is the percentage. So 104 is 26% of 400.

Answer:

Domain: (−∞,∞),{x|x∈R}

Step-by-step explanation:

the domain will be Domain: (−∞,∞),{x|x∈R} because

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Answer: Option C: (−∞,∞)

Step-by-step explanation:

answer is for plato

Answer:

Verifal angles I think but I'm not necessarily sure!!!

Answer:

1) Congruent

2) Vertical angles

3) 12x - 18 = 8x + 10

4) x = 7

Step-by-step explanation:

1)

Congruent because they're vertical angles.

2)

Vertical angles

3)

12x - 18 = 8x + 10

4)

12x - 18 = 8x + 10

12x - 8x = 10 + 18

4x = 28

x = 7

Answer:

yeah my boy i think your right

Step-by-step explanation:

Answer:

0.9644

Step-by-step explanation:

Answer:

Its only 5 point but ok

its $3.44 per quart

Step-by-step explanation:

Answer:

g=1

Step-by-step explanation:

6g+3g=-3g+9+3g, add 3g to both sides and you get closer to the answer

Answer:

g=1

Step-by-step explanation:

solved and got the same answer

Answer:

f(x) = 4*(5/2)^x

Step-by-step explanation:

First, we know that our function has the points:

(0, 4)

(1, 10)

(2, 25)

The first one (0, 4) means that:

f(0) = 4.

Then you can evaluate the four given functions in x = 0 and see which ones meet this condition (have the outcome equal to 4)

Here we can discard the function f(x) = 15*x - 5 because:

f(0) = 15*0 - 5 = -5

Then this function is discarded.

Now let's look at the second point, (1, 10)

This means that f(1) = 10

Then you can evaluate the remaining functions in x = 1, and see if the outcome is equal to 10.

Here we can discard the first function f(x) = (x + 2)^2 because:

f(1) = (1 + 2)^2 = 3^2 = 9

So the output is not 10 as we wanted.

(while for the other two functions we have)

for f(x) = 6*x + 4

f(1) = 6*1 + 4 = 10

for f(x) = 4*(5/2)^x

f(1) = 4*(5/2)^1 = 4*(5/2) = (4/2)*5 = 10

Now we use the last point, (2, 25)

This means that when x = 2, the outcome needs to be equal to 25.

For the function f(x) = 6*x + 4 we have:

f(2) = 6*2 + 4 = 12 + 4 = 16

So we can discard this one.

Then we could conclude that the remaining option is the correct one, but let's ceck.

f(x) = 4*(5/2)^x

then for x = 2

f(2) = 4*(5/2)^2 = 4*(25/4) = 25

correct.

Then the correct option is f(x) = 4*(5/2)^x

Answer:

Option #2: 32 ÷2

Step-by-step explanation:

Take Note: There are 2 cups in a pint.

Since we are converting cups TO pints.... the number should (logically) be smaller. That eliminates the last two options.

Referring back to our note, it is only sensible to eliminate the first option since there are only 2 cups per pint, NOT 4.

In the end, you should have gotten option 2 which is 32÷2.

Answer:

2 : 5

Step-by-step explanation:

4/10 = 8.6/21.5 = 10/25 because all ratios equal 2/5

Answer:

2:5

Step-by-step explanation:

all the ratios are equal

Answer:

Both pools will have the same amount of water after 11 minutes and 32 seconds.

Step-by-step explanation:

Since Team Sunshine is filling an inflatable kiddie pool from a garden hose, and the pool has 30 gallons in it and Team Sunshine is adding 8 gallons per minute with a garden hose, while next door, Team Breeze's pool is already filled with 180 gallons of water, and they are emptying the pool at 5 gallons per minute with buckets, to determine how long it will take until both pools have the same amount of water, the following calculation must be performed:

Team Sunshine:

30 + (8X) = T

30 + 8x10 = 110

30 + 8x11 = 118

30 + 8x12 = 126

30 + 8x11.5 = 122

30 + 8x11.6 = 122.8

30 + 8x11.55 = 122.4

30 + 8x11.54 = 122.3

Team Breeze:

180 - (5X) = T

180 - 5x11 = 125

180 - 5x12 = 120

180 - 5x11.5 = 122.5

180 - 5x11.6 = 122

180 - 5x11.55 = 122.25

180 - 5x11.54 = 122.3

1 = 60

0.54 = X

0.54 x 60 = X

32.4

Thus, both pools will have the same amount of water after 11 minutes and 32 seconds.

Answer:

x=1,y=4

Step-by-step explanation:

x=1,y=4

Answer:

Cd equals the square root of 3

Answer: 2 square root 3

Step-by-step explanation:

other user's answer

Answer:X=10

Step-by-step explanation: 3x-2=2x+8 If that's what you're looking for

Answer:

25/500 or 5% said 'other'

Step-by-step explanation:

55% = 275 (dog)

1/10 = 50 (cat)

0.3 = 150 (bird)

Total = 475

475 out of 500 (95%) gave an answer other than 'other'

Answer:

help him

Step-by-step explanation:

Paying a $2,500 down payment on an automobile would normally benefit Jim. He reduces the total amount of the loan for the vehicle he will need to take out by making a down payment, which reduces the cost of his monthly payments and the amount of interest he will have to pay over the life of the loan. Furthermore, having a down payment increases his chances of getting approved for a loan or receiving a cheaper interest rate.

A down payment is an upfront cash payment made when purchasing a significant ticket item like a car or a house. The down payment is often a proportion of the total cost of ownership and is made in order to lower the amount of financing required. Lower monthly payments or a shorter loan term are sometimes the outcome of a higher down payment.

A down payment is an initial up-front payment in part for the purchase of a large item or service, such as a car or a house. It is normally paid in cash or in the form of an equivalent at the time the transaction is completed. The balance of the payment is then financed by a loan of some kind.

Therefore, paying a $2,500 down payment on an automobile would normally benefit Jim.

Learn more about Down payment, here:

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