The pH scale measures the amount of alkalinity or acidity in a liquid and ranges from 0-14. The ideal pH for a swimming pool is 7.2. A pH that is too high or low can cause discomfort for the swimmers, especially in the eyes. High variability in the pH readings across the swimming pool can be problematic. The following data shows seven pH readings that were taken at the Wilson Community Pool from different locations at 10 a.m. this morning. The average pH reading from this sample was 7.02 with a sample standard deviation of 0.40. Using α= 0.05 and the critical value approach, determine if correctiveaction is needed at this pool to adjust the pH value.

Required:
State your conclusion.

a. Because calculated t statistic is greater than t critical value, we reject the null hypothesis. Therefore, Wilson Community Pool cannot conclude that the pH value is not equal to 7.2. Based on this sample, corrective action needs to be
taken.
b. Because calculated t statistic is less than critical t value, we reject the null hypothesis. Therefore, Wilson Community Pool cannot conclude that the pH value is not equal to 7.2. Based on this sample, corrective action needs to be
taken.
c. Because the t calculated is greater than the critical t, we fail to reject the null hypothesis. Therefore, Wilson Community Pool conclude that the pH value is equal to 7.2. Based on this sample, no corrective action is needed.
d. Because the t calculated is less than the critical t, we fail to reject the null hypothesis. Therefore, Wilson Community Pool conclude that the pH value is equal to 7.2. Based on this sample, no corrective action is needed.

Answer:

[tex]\bar X=\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And replacing we got:

[tex] \bar X= 58.33[/tex]

[tex]s= 10.78[/tex]

Then we can fin the limits for one deviation within the mean like this:

[tex]\mu -\sigma = 58.33-10.78= 47.55[/tex]

[tex]\mu -\sigma = 58.33+10.78= 69.11[/tex]

And then we see that the number of values between the limits are: 69, 64, 54,47 who represent 4 and then the percentage would be:

[tex]\% =\frac{4}{6}*100 =66.7\%[/tex]

Step-by-step explanation:

First we need ot calculate the mean and deviation with the following formulas:

[tex]\bar X=\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

And replacing we got:

[tex] \bar X= 58.33[/tex]

[tex]s= 10.78[/tex]

Then we can fin the limits for one deviation within the mean like this:

[tex]\mu -\sigma = 58.33-10.78= 47.55[/tex]

[tex]\mu -\sigma = 58.33+10.78= 69.11[/tex]

And then we see that the number of values between the limits are: 69, 64, 54,47 who represent 4 and then the percentage would be:

[tex]\% =\frac{4}{6}*100 =66.7\%[/tex]

Answer:

Step-by-step explanation:

[tex]3p - 11 = 19[/tex]

Move constant to R.H.S and change its sign

[tex]3p = \: 19 + 11[/tex]

Add the numbers

[tex]3p = 30[/tex]

Divide both sides of the equation by 3

[tex] \frac{3p}{3} = \frac{30}{3} [/tex]

Calculate

[tex]p = 10[/tex]

Hope this helps..

Best regards!!

Answer:

p = 10

Step-by-step explanation:

Solve for p (make p the subject)

3p -11 =19  (add 11 to both sides)

3p = 30 (divide by 3)

p = 10

I HOPE THIS HELPED :)

The division -240 by 8 gives the quotient is -30.

The division is one of the four introductory fine operations, the other three being addition, deduction, and addition. In simple words, division can be defined as the splitting of a large group into lower groups similar that every group will have an equal number of particulars. It's an operation used for equal grouping and equal sharing in calculation.

We have to divide -240 by 8.

So, the division is

                              8 | -240 | 30

                                     24

                                    ____

                                      00

Thus, the quotient is -30.

Learn more about Division here:

https://brainly.com/question/21416852

#SPJ2

Answer:

Step-by-step explanation:

[tex] - \frac{1}{2} + c = \frac{31 }{4} \\ \\ c = \frac{31}{4} + \frac{1}{2} = \frac{31 - 2}{4} \\ \\ c = \frac{29}{4} [/tex]

Hope this helps you

Answer:

The impact on the objective function is that it is increased by 50.

Step-by-step explanation:

In this case we have that the value of the objective function is 150, and they tell us that 10 more units of resource one are added, but they tell us that the shadow price ranges from 1 to 5, therefore:

10 * 5 = 50

Which means that the impact on the objective function is that it is increased by 50.

Answer:

Step-by-step explanation:

a) For private colleges,

Mean = (52.8 + 30.6 + 43.2 + 45.8 + 45.0 + 37.8 + 33.3 + 50.5 + 44.0 + 42.0)/10 = 42.5

x1 = 42.5 × 1000 = 42500

Standard deviation = √(summation(x - mean)²/n

n = 10

Summation(x - mean)² = (52.8 - 42.5)^2 + (30.6 - 42.5)^2 + (43.2 - 42.5)^2 + (45.8 - 42.5)^2 + (45.0 - 52.5)^2 + (37.8 - 42.5)^2 + (33.3 - 42.5)^2 + (50.5 - 42.5)^2 + (44.0 - 42.5)^2 + (42.0 - 52.5)^2 = 598.56

standard deviation = √(598.56/10 = 7.74

s1 = 7.74 × 1000 = 7740

For public colleges,

Mean = (20.3 + 22.8 + 22.0 + 25.8 + 28.2 + 18.5 + 15.6 + 25.6 + 24.1 + 14.4 28.5 + 21.8)/12 = 22.3

x2 = 22.3 × 1000 = 22300

n2 = 12

Summation(x - mean)² = (20.3 - 22.3)^2 + (22.8 - 22.3)^2 + (22 - 22.3)^2 + (25.8 - 22.3)^2 + (28.2 - 22.3)^2 + (18.5 - 22.3)^2 + (15.6 - 22.3)^2 + (25.6 - 22.3)^2 + (24.1 - 22.3)^2 + (14.4 - 22.3)^2 + (28.5 - 22.3)^2 + (21.8 - 22.3)^2 = 225.96

standard deviation = √(225.96/12 = 4.34

s2 = 4.34 × 1000 = 4340

b) The point estimate is the difference between the sample means

Point estimate = 42500 - 22300 = 20200

The best guess for the difference in population mean annual cost of attending private and public colleges is $20200. The range of the value is determined by the margin of error.

c) Confidence interval = point estimate ± margin of error

Margin of error = z√(s²/n1 + s2²/n2)

Where z is the test score for 95% confidence level from the t distribution table. To find the test score, we would first find degree of freedom, df

df = (n1 - 1) + (n2 - 1) = (10 - 1) + (12 - 1) = 20

From the t distribution table,

z = 2.086

Margin of error = 2.086√(7.74²/10 + 4.34²/12) = 4.84

4.84 × 1000 = 4840

Confidence interval = 20200 ± 4840

Answer:

[tex]296.693\leq x\leq 319.307[/tex]

Step-by-step explanation:

The confidence interval for the population mean x can be calculated as:

[tex]x'-z_{\alpha /2}\frac{s}{\sqrt{n} } \leq x\leq x'+z_{\alpha /2}\frac{s}{\sqrt{n} }[/tex]

Where x' is the sample mean, s is the population standard deviation, n is the sample size and [tex]z_{\alpha /2}[/tex] is the z-score that let a proportion of [tex]\alpha /2[/tex] on the right tail.

[tex]\alpha[/tex] is calculated as: 100%-99%=1%

So, [tex]z_{\alpha/2}=z_{0.005}=2.576[/tex]

Finally, replacing the values of x' by 308, s by 17, n by 15 and [tex]z_{\alpha /2}[/tex] by 2.576, we get that the confidence interval is:

[tex]308-2.576\frac{17}{\sqrt{15} } \leq x\leq 308+2.576\frac{17}{\sqrt{15} }\\308-11.307 \leq x\leq 308+11.307\\296.693\leq x\leq 319.307[/tex]

Answer:

28π cm²

Step-by-step explanation:

Circumference Formula: C = 2πr

Simply plug in r into the formula:

C = 2π(14)

C = 28π or 87.9646

Answer:

28π cm

Step-by-step explanation:

The circumference of a circle has the formula 2πr.

2 × π × r

Where r is the radius.

2 × π × 14

28 × π

= 28π

The circumference is 28π and the unit is centimeters.

Answer:

B ). IF = IT

Step-by-step explanation:

IG is perpendicular to FT, means that the line IG divides the line FT into two equal parts without remainder.

Line IG does not only divide line FT, it also bisect the arc FT into two equally parts also.

It also divide the segment of the circle FIT into two equal parts.

So to the correct answer to the question, IF = IT

Answer:

D

Step-by-step explanation:

jtrsytexjgfcgvhjbkjnhgfdsasdfghjhgrertyu

Answer:

Correct answer is D

Step-by-step explanation:

Answer:

[tex]\huge\boxed{x=\sqrt{30}}[/tex]

Step-by-step explanation:

ΔABC and ΔBDC are similar (AAA).

Therefore the corresponding sides are in proportion:

[tex]\dfrac{AC}{BC}=\dfrac{BC}{CD}[/tex]

substitute

[tex]AC=7+3=10\\{BC}=x\\CD=3[/tex]

[tex]\dfrac{10}{x}=\dfrac{x}{3}[/tex]           cross multiply

[tex](10)(3)=(x)(x)\\\\30=x^2\\\\x^2=30\to x=\sqrt{30}[/tex]

Step-by-step explanation:

2x+y=15x-y=3

then u group like terms

2x-15x= -y+y=3

then ur answer

13x=3

Answer:

Use the formula

a

n

=

a

1

r

n

−

1

to identify the geometric sequence.

Step-by-step explanation:

a

n

=

64

4

n

−

1 hope this helps you :)

Answer: The answer is in the steps.

Step-by-step explanation:

f(1)= 64  

f(n)=1/4(n-1)      n in this case is the nth term.

Answer:

1/17

Step-by-step explanation:

There are 13 diamond cards in a standard 52-card deck.

First drawing:

13 diamonds

52 total cards

After the first drawing you already took a diamond, so there are 12 diamonds left out of 51 total cards.

p(diamond and diamond) = 13/52 * 12/51 = 1/4 * 4/17 = 1/17

Answer:

99% confidence interval for the proportion of married young adults aged 18-29.

(0.1779 , 0.2287)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 964

Given data a random sample of 964 young adults aged 18-29, it was found that 196 of them were married

sample proportion

                           [tex]p^{-} = \frac{196}{964} = 0.2033[/tex]

Step(ii):-

99% confidence interval for the proportion of married young adults aged 18-29.

[tex](p^{-} - Z_{0.05} \sqrt{\frac{p^{-}(1-p^{-} ) }{n} } ,p^{-} +Z_{0.05} \sqrt{\frac{p^{-}(1-p^{-} ) }{n} })[/tex]

[tex](0.2033 -1.96 \sqrt{\frac{0.2033(1-0.2033 ) }{964} } ,0.2033 +1.96\sqrt{\frac{0.2033(1-0.2033 ) }{964} })[/tex]

(0.2033 -  0.02540 , 0.2033 +0.02540)

(0.1779 , 0.2287)

Conclusion:-

99% confidence interval for the proportion of married young adults aged 18-29.

(0.1779 , 0.2287)

Answer:

It is 90º

Step-by-step explanation:

Looking at the picture, we realize that the angle direcly beside it, EGD, is 90º. Now, both angles form a straight line, which equals 180º. 180-90= 90º.

Answer: A 40 B 50 C 90 D 130

where they go: B goes under A, D goes under the whole thing, just like E (although that doesn't want to be answered) and C goes under B

hope this helped

Answer:

a. z=3.09. Yes, it can be concluded that the population mean is greater than 50.

b. z=1.24. No, it can not be concluded that the population mean is greater than 50.

c. z=2.22. Yes, it can be concluded that the population mean is greater than 50.

Step-by-step explanation:

We have a hypothesis test for the mean, with the hypothesis:

[tex]H_0: \mu\leq50\\\\H_a:\mu> 50[/tex]

The sample size is n=55 and the population standard deviation is 6.

The significance level is 0.05.

We can calculate the standard error as:

[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{55}}=0.809[/tex]

For a significance level of 0.05, the critical value for z is zc=1.644. If the test statistic is bigger than 1.644, the null hypothesis is rejected.

a. If the sample mean is M=52.5, the test statistic is:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{52.5-50}{0.809}=\dfrac{2.5}{0.809}=3.09[/tex]

The null hypothesis is rejected, as z>zc and falls in the rejection region.

b. If the sample mean is M=51, the test statistic is:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{51-50}{0.809}=\dfrac{1}{0.809}=1.24[/tex]

The null hypothesis failed to be rejected, as z<zc and falls in the acceptance region.

c. If the sample mean is M=51.8, the test statistic is:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{51.8-50}{0.809}=\dfrac{1.8}{0.809}=2.22[/tex]

The null hypothesis is rejected, as z>zc and falls in the rejection region.

Answer:

The variance is "9475" and standard deviation is "97.3396112".

Step-by-step explanation:

Let's all make the assumption that X seems to be the discrete uniformly distributed random indicating demand for units, and that f(x) has been the corresponding probability.

The expected value of the monthly demand will be:

⇒  [tex]E(X)=\sum_{x} x\times f(x)[/tex]  

⇒            [tex]=00\times 0.20+400\times 0.30+500\times 0.35+600\times 0.15[/tex]

⇒            [tex]=445 \ units[/tex]

The variance will be:

⇒  [tex]Var(X)=E(X^2)-{E(X)}^2[/tex]

⇒  [tex]E(X^2)=\sum_{x} x^2\times f(x)[/tex]

                [tex]=(300)^2\times 0.20+(400)^2\times 0.30+(500)^2\times 0.35+(600)^2\times 0.15[/tex]

                [tex]=207500[/tex]

⇒  [tex]Var(X)=207500 - (445)^2[/tex]

                  [tex]=9475[/tex]

The standard deviation will be:

⇒  [tex]X=\sqrt{var(X)}[/tex]

         [tex]=97.3396112[/tex]

Answer:

(a) Yes, Fredrick’s data set contains an outlier.

(b) No, the median value is not 12 home runs.

(c) Yes, the mean value is about 12.6 home runs.

(d) Yes, the median describes Fredrick’s data more accurately than the mean.

(e) No, the mean value doesn't stay the same when the outlier is not included in the data set.

Step-by-step explanation:

We are given that Fredrick hit 14, 18, 13, 12, 12, 16, 13, 12, 1, and 15 home runs in 10 seasons of play.

Firstly, arranging our data set in ascending order we get;

1, 12, 12, 12, 13, 13, 14, 15, 16, 18.

(a) The statement that Fredrick’s data set contains an outlier is true because in our data set there is one value that stands out from the rest of the data, which is 1.

Hence, the outlier value in the data set is 1.

(b) For calculating median, we have to first observe that the number of observations (n) in the data set is even or odd, i.e;

                    Median  =  [tex](\frac{n+1}{2})^{th} \text{ obs.}[/tex]

                    Median  =  [tex]\frac{(\frac{n}{2})^{th} \text{ obs.}+(\frac{n}{2}+1)^{th} \text{ obs.} }{2}[/tex]

Here, the number of observations in Fredrick's data set is even, i.e. n = 10.

SO,  Median  =  [tex]\frac{(\frac{n}{2})^{th} \text{ obs.}+(\frac{n}{2}+1)^{th} \text{ obs.} }{2}[/tex]

                      =  [tex]\frac{(\frac{10}{2})^{th} \text{ obs.}+(\frac{10}{2}+1)^{th} \text{ obs.} }{2}[/tex]

                      =  [tex]\frac{(5)^{th} \text{ obs.}+(6)^{th} \text{ obs.} }{2}[/tex]

                      =  [tex]\frac{13+13 }{2}[/tex]  = 13 home runs

So, the statement that the median value is 12 home runs is not correct.

(c) The mean of the data set is given by;

          Mean =  [tex]\frac{1+ 12+ 12+ 12+ 13+ 13+14+ 15+ 16+ 18}{10}[/tex]

                     =  [tex]\frac{126}{10}[/tex]  = 12.6 home runs

So, the statement that the mean value is about 12.6 home runs is correct.

(d) The statement that the median describes Fredrick’s data more accurately than the mean is correct because even if the outlier is removed from the data set, the median value will remain unchanged but the mean value gets changed.

(e) After removing the outlier, the data set is;

12, 12, 12, 13, 13, 14, 15, 16, 18.

Now, the mean of the data =  [tex]\frac{12+12+ 12+ 13+ 13+ 14+ 15+ 16+ 18}{9}[/tex]

                                             =  [tex]\frac{125}{9}[/tex]  =  13.89

So, the statement that the mean value stays the same when the outlier is not included in the data set is incorrect.

Answer:

Fredrick’s data set contains an outlier.

The mean value is about 12.6 home runs.

The median describes Fredrick’s data more accurately than the mean.

Step-by-step explanation:

Answer:

1 1/2 > - 4 1/2  and                                                                                                      Manuela scored more points against the Canada Moose than against the China Dragons.

Answer:Priya ran 19 miles last week

Step-by-step explanation:

4 x 3 = 12

12 + 7 = 19

Answer:

(9, -1)

Step-by-step explanation:

Midpoint Formula: [tex](\frac{x1+x2}{2}, \frac{y1+y2}{2} )[/tex]

Since we already have 1 endpoint and the midpoint, all we need to do is set the equation up to find the other endpoint:

12.5 = (16 + x)/2

25 = 16 + x

x = 9

-4 = (-7 + y)/2

-8 = -7 + y

y = -1

Answer:

(9, -1)

Step-by-step explanation:

(16 + x)/2= 12.5

16 + x = 25

x = 9

(-7 + y)/2 = -4

-7 + y = -8

y = -1

Answer:

Step-by-step explanation:

In 1968, vehicle emission standards allowed 6.3 hydrocarbons released per mile driven and by 1980, the

standards allowed only 0.41 hydrocarbons per mile driven. This means that the change in the amount of hydrocarbons released per mile driven as allowed by the vehicle emission standards between 1968 and 1980 is

6.3 - 0.41 = 5.89

Therefore, the percentage rate of change in the amount of hydrocarbons released per mile driven as allowed by the vehicle emission standards between 1968 and 1980 would be

5.89/6.3 × 100 = 93.49%

Hey there!

If everything is on the same horizontal level, it is at the same elevation, or height. On a graph, the elevation is the y-value. So, if we want the points to on the same horizontal line, they have to have the same y-value.

The points that all share the y-value of -1 are (7,-1), (2,-1), and (-3,-1). Since (-3,9) is at a different y-value it is not on the horizontal line of y=-1.

Have a wonderful day!

Answer:

A (7,-1)

B (2,-1)

D (-3,-1)

Step-by-step explanation:

Well lets plot the following points on a graph first,

A (7,-1)

B (2,-1)

C (-3,9)

D (-3,-1)

Look at the image below ↓

By looking at the graph we can tell that points,

A, B, and D lie on the same horizontal line.

Thus,

points A, B, and D lie on the same horizontal line.

Hope this helps :)

Answer:

b. 14

Step by step explanation:

Answer:

The 20th digit is 6.

Step-by-step explanation:

1. Add 2/9 and 1/7.

2/9 + 1/7 = 23/63

2. Convert to a decimal.

23 ÷ 63 = 0.365079...

If you continue to divide, you will notice that the number repeat. So, the decimal would be 0.365079365079...

3. Find the 20th digit.

0.365079365079365079365079

Answer:

6

Step-by-step explanation:

Aops question

We have $\frac29 + \frac17 = \frac{14}{63} + \frac{9}{63} = \frac{23}{63}$. Expressing $\frac{23}{63}$ as a decimal using long division, we find $\frac{23}{63}=0.\overline{365079}$. Therefore, every 6th digit after the decimal point is a 9. So, the 18th digit is a 9; the 20th digit is 2 decimal places later, so it is a $\boxed{6}$.

It's in Latex

Answer:

y = 2x/3 - 15

Step-by-step explanation:

Step 1: Find slope of perpendicular line

Take the negative reciprocal of the other line

m = 2x/3

Step 2: Rewrite equation (You already found b because it gave you y-int)

y = 2x/3 - 15

Answer:

1234567891234567890

Answer: 25 years

Step-by-step explanation:

t = I / Pr

t = 5700 / ( 3800 × 0.06 ) = 25

t = 25 years

Answer:

96 ways

Step-by-step explanation:

Let´s call flags of countries from Africa as  A₁,  A₂, A₃, A₄, and from Europe as  E₁, E₂, E₃ and E₄

We have to display the flags always beginning with one flag from Africa let´s take A₁

For that flag, we have 4! possibilities Then 4! is:

4*3*2*1  = 24

As we have 4 different Flags from Africa, we will have

4*24 = 96  possibilities

Answer:

six single scoops icecream cones