A certain manufactured product is supposed to contain 23% potassium by weight. A sample of 10 specimens of this product had an average percentage of 23.2 with a standard deviation of 0.2. If the mean percentage is found to differ from 23, the manufacturing process will be recalibrated.
a. State the appropriate null and alternate hypotheses.
b. Should the process be recalibrated? Explain.
c. Compute the P-value.

Answers

Answer 1

Answer:

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 23%    

    Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 23%

(b) We conclude that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated.

(c) P-value is 0.6%.

Step-by-step explanation:

We are given that a certain manufactured product is supposed to contain 23% potassium by weight.

A sample of 10 specimens of this product had an average percentage of 23.2 with a standard deviation of 0.2.

Let [tex]\mu[/tex] = mean percentage of potassium by weight.

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 23%      {means that the mean percentage is equal to 23 and the manufacturing process will not be re-calibrated}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 23%     {means that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated}

The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;

                                T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean percentage = 23.2

            s = sample standard deviation = 0.2

            n = sample of specimens = 10

So, the test statistics  =  [tex]\frac{23.2-23}{\frac{0.2}{\sqrt{10} } }[/tex]  ~ [tex]t_9[/tex]

                                     =  3.162

The value of t test statistic is 3.162.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of -2.262 and 2.262 at 9 degree of freedom for two-tailed test.

(b) Since our test statistic doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated.

(c) The P-value of the test statistics is given by;

            P-value = P( [tex]t_9[/tex] > 3.162) = 0.006 or 0.6%

Answer 2

(a) Null Hypothesis,  [tex]H_o:\mu[/tex]: = 23%    

   Alternate Hypothesis, [tex]H_A:\mu\neq[/tex] : 23%

(b) We conclude that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated.

(c) P-value is 0.6%.

What is a null hypothesis?

The hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.

We are given that a certain manufactured product is supposed to contain 23% potassium by weight.

A sample of 10 specimens of this product had an average percentage of 23.2 with a standard deviation of 0.2.

Let  = mean percentage of potassium by weight.

(a) Null Hypothesis, [tex]H_o:\mu[/tex]:  = 23%      {means that the mean percentage is equal to 23 and the manufacturing process will not be re-calibrated}

Alternate Hypothesis,  [tex]H_A:\mu\neq[/tex]:   23%     {means that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated}

The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;

[tex]TS=\dfrac{X-\mu}{\frac{s}{\sqrt{n}}}[/tex]   ~ [tex]t_{n-1}[/tex]

where,  = sample mean percentage = 23.2

           s = sample standard deviation = 0.2

           n = sample of specimens = 10

So, the test statistics  =   [tex]\dfrac{23.2-23}{\frac{0.2}{\sqrt{10}}}[/tex] ~ [tex]t_g[/tex]

                                    =  3.162

The value of t test statistic is 3.162.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of -2.262 and 2.262 at 9 degree of freedom for two-tailed test.

(b) Since our test statistic doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated.

(c) The P-value of the test statistics is given by;

           P-value = P( [tex]t_g[/tex] > 3.162) = 0.006 or 0.6%

Hence ,

(a) Null Hypothesis,  [tex]H_o:\mu[/tex]: = 23%    

   Alternate Hypothesis, [tex]H_A:\mu\neq[/tex] : 23%

(b) We conclude that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated.

(c) P-value is 0.6%.

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Related Questions

Lori rented a booth at the craft fair for $200 to sell baskets she made. The cost of the materials for each basket was $8. Lori sells the baskets for $20 each. How many baskets does she have to sell to make a profit?

Answers

Answer:

15 baskets

Step-by-step explanation:

If 4/3 * 3/4 = 5k, then k =

Answers

Answer:

1/5

Step-by-step explanation:

switch sides, delete both common factors and your stuck with 5k=1. then you put both in a fraction and it gets you 1/5

True or False: As the value of cos(x) approaches 1 and the value of sin(x) approaches 0, the value of tan(x) approaches infinity

Answers

Answer: False

Step-by-step explanation:

We can write tan(x) = sin(x)/cos(x)

if cos(x) tends to 1, and sin (x) tends to 0 (this happens aronund the point x = 0)

then we have:

Tan(x) = 0/1 = 0

Then the statement is false, as cos(x) approaches 1 and sin(x) approaches 0, tan(x) also approaches 0.

I run 200m in 32 seconds, how long will it take to run 5000m

Answers

Answer:

It will take 800seconds to you to run 5000m

Step-by-step explanation:

Let time taken to run 5000m is x

Using ratio and proportion

200:32=5000:x

200/32=5000/x

200*x=5000*32

200x=160000

x=800seconds

In a randomly selected sample of 500 Phoenix residents, 445 supported mandatory sick leave for food handlers. Legislators want to be very confident that voters will support this issue before drafting a bill. What is the 99% confidence interval for the percentage of Phoenix residents who support mandatory sick leave for food handlers?

Answers

Answer:

The 99% confidence interval for the percentage of Phoenix residents who support mandatory sick leave for food handlers is between 85.40% and 92.60%.

Step-by-step explanation:

Confidence interval for the proportion:

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].

For this problem, we have that:

[tex]n = 500, \pi = \frac{445}{500} = 0.89[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.89 - 2.575\sqrt{\frac{0.89*0.11}{500}} = 0.8540[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.89  + 2.575\sqrt{\frac{0.89*0.11}{500}} = 0.9260[/tex]

For the percentage:

Multiply the proportion by 100.

0.8540*100 = 85.40%

0.9260*100 = 92.60%

The 99% confidence interval for the percentage of Phoenix residents who support mandatory sick leave for food handlers is between 85.40% and 92.60%.

What’s the correct answer for this question?

Answers

Answer:

A. Schaid draws a white sock and a green sock. It did not talk about no green sock

Step-by-step explanation:

Brainliest AppreciatEd

What is the difference?
х
4
x2-2x-15 x² + 2x-35
x2 + 3x+12
(x-3)(x-5)(x+7)
x(x+3-12)
(x+3)(x-5)(x+7)
x2 + 3x+12
(x+3)(x-5)(x+7)
x2 + 3x-12
(x+3)(x-5)(x+7)

Answers

The difference of the equation is A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Let the first equation be P = x / ( x² - 2x - 15 )

Let the second equation be Q = 4 / x² + 2x - 35 )

Now , A = P - Q

On simplifying , we get

A = x / ( x² - 2x - 15 ) - 4 / x² + 2x - 35 )

Taking the LCM , we get

A = x ( x + 7 ) - 4 ( x + 3 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )

A = x² + 7x - 4x + 12 / ( x + 3 ) ( x - 5 ) ( x + 7 )

A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )

Therefore , the value of A is ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )

Hence , the equation is A = ( x² - 3x - 12 ) / ( x + 3 ) ( x - 5 ) ( x + 7 )

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Solve the problem.
If a boat uses 25 gallons of gas to go 73 miles, how many miles
can the boat travel on 75 gallons of gas?
24 mi
438 mi
219 mi
239 mi

Answers

Answer:

For this problem we can use the following proportional rule:

[tex] \frac{73 mi}{25 gal}= \frac{x}{75 gal}[/tex]

Where x represent the number of miles that we can travel with 75 gallons. For this case we can use this proportional rule since by definition [tex] D=vt[/tex]. If we solve for x we got:

[tex] x =75 gal (\frac{73 mi}{25 gal}) =219mi[/tex]

And the best answer would be:

219 mi

Step-by-step explanation:

For this problem we can use the following proportional rule:

[tex] \frac{73 mi}{25 gal}= \frac{x}{75 gal}[/tex]

Where x represent the number of miles that we can travel with 75 gallons. For this case we can use this proportional rule since by definition [tex] D=vt[/tex]. If we solve for x we got:

[tex] x =75 gal (\frac{73 mi}{25 gal}) =219mi[/tex]

And the best answer would be:

219 mi

A line has a slope of -


Which ordered pairs could be points on a line that is perpendicular to this line? Select


Which ordered pairs coul


two options

Answers

Answer:

(a) -2,0 and 2,5 and (b) 2,-1 and 10,9

Question:

The question is incomplete without the answer choice. Let's consider the following:

A line has a slope of -4/5. Which ordered pairs could be points on a line that is perpendicular to this line? select two options

a) -2,0 and 2,5

b) -4,5 and 4,-5

c) -3,4 and 2,0

d) 1,-1 and 6,-5

e) 2,-1 and 10,9

Step-by-step explanation:

The ordered pairs that could be points on a line that is perpendicular to this line would have same slope as that of the line.

Let's check out the slope of the options.

The line has slope = -4/5

Slope = m = (y subscript 2 -y subscript 1)/(x subscript 2 - x subscript 1)

The coordinates is in the form of (x,y)

Find attached the workings.

a) -2,0 and 2,5

m = 5/4

b) -4,5 and 4,-5

m = -5/4

c) -3,4 and 2,0

m = -4/5

d) 1,-1 and 6,-5

m = -4/5

e) 2,-1 and 10,9

m = 5/4

Two lines are perpendicular if (m subscript 1) × (m subscript 2) = -1

In other words, the slopes

of the two lines must be negative reciprocals of each other.

If 1st slope = -4/5

For the lines to be perpendicular, the slope of every other line = 5/4

2nd slope = 5/4

The ordered pairs that are points on the line perpendicular to the line:

(a) -2,0 and 2,5 and (b) 2,-1 and 10,9

Answer:AandE

Step-by-step explanation:

Simplify the following expression:
-5[(x^3 + 1)(x + 4)]​

Answers

Answer:

[tex]-5x^{4} -20x^{3} -5x-20[/tex]

Step-by-step explanation:

[tex]-5[(x^{3} +1)(x+4)][/tex]

Use the FOIL method for the last two groups.

[tex]-5(x^{4} +4x^{3} +x+4)[/tex]

Now, distribute the -5 into each term.

[tex]-5x^{4} -20x^{3} -5x-20[/tex]

help asap giving branlist!!!

Answers

Answer:

Option 2

Step-by-step explanation:

So you know that you have to START with 16 gallons, so you can eliminate options 3 and 4.

Then calculate how long you can drive on 16 gallons. 75 * 4 = 300

It's option 2

Answer:

Option 2

Step-by-step explanation:

The slope will have to be negative since the amount of gas decreases as the miles traveled increased. If the car travels 75 miles on 4 gallons of gas it travels 75 * 4 = 300 miles on 16 gallons of gas, meaning (300, 0) is a point on the line. The only line that satisfies this is Option 2.

The functions f(x) and g(x) are graphed.

On a coordinate plane, a curved red line with an upward arc, labeled g of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).



Which represents where f(x) = g(x)?

f(2) = g(2) and f(0) = g(0)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
f(2) = g(4) and f(1) = g(1)

Answers

Answer: first answer choice

Step-by-step explanation:

They give us that f(0) and g(0) = 4 and f(2) = g(2) = 0, so the answer is simply the first one. When x=0, y=4 for both and when x=2, y=0 for both.

Hope that helped,

-sirswagger21

Answer:

A

Step-by-step explanation:

on edge

"Children under the age of 13 are not allowed to operate a boat." Part A: Write an inequality to show the age of children who are allowed to operate a boat. (5 points) Part B: Describe in words how you can show the solution to this inequality on a number line. (5 points)

Answers

Answer:

X ≤ 13

Step-by-step explanation:

Part A: X ≤ 13

Part B:  Draw a closed circle from 13 and up on the number line.

Make the arrow look like this >.

The inequality will be x ≥ 13. The age of the person should be greater than or equal to 13.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Children under the age of 13 are not allowed to operate a boat.”

Let x be the age of the person.

The inequality to show the age of children who are allowed to operate a boat will be

x ≥ 13

The age of the person should be greater than or equal to 13.

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Find the measure of angle b

Answers

Answer: The measure of angle B is 31 degrees.

Step-by-step explanation:

180 -149 = 31

Answer:

31 degrees

Step-by-step explanation:

We can see that 149 degrees and b are on a line. If they are next to each other they are called adjacent angles. There is a rule that adjacent angles add up to 180 degrees. So we subtract 149 from 180 and we get 31 degrees for angle b.

Hope this helps! :)

i have a problem on statistics
5. Data on household vehicle miles of travel (VMT) are compiled annually by the Federal Highway Administration and are published in National Household Travel Survey, Summary of Travel Trends. Independent random samples of 15 midwestern households and 14 southern households provided the following data on last year’s VMT, in thousands of miles. At the 5% significance level, does there appear to be a difference in last year’s mean VMT for midwestern and southern households? Use both p-value and critical value approach. Assume population variance to be equal

Midwest
16.2 , 14.6 , 11.2 , 24.4 , 9.4 12.9 , 18.6 , 16.6 , 20.3 ,15.1 , 17.3 , 10.8 , 16.6 , 20.9 , 18.3
South
22.2, 19.2 , 9.3 , 24.6 ,20.2 , 15.8, 18.0 , 12.2 , 20.1 , 16.0 , 17.5 , 18.2 , 22.8 , 11.5

Answers

Answer:

Step-by-step explanation:

Hello!

The objective is to  compare the VMT of mid western households and southwestern households. For this two independent random samples of households from both areas and their VMT were recorded:

Be

X₁: VMT of a mid western household

Midwest

16.2 , 14.6 , 11.2 , 24.4 , 9.4 12.9 , 18.6 , 16.6 , 20.3 ,15.1 , 17.3 , 10.8 , 16.6 , 20.9 , 18.3

n₁= 15

∑X₁= 243.20

∑X₁²= 4175.98

X[bar]₁= 16.21

S₁²= 16.64

S₁= 4.08

X₂: VMT of a southwestern household

22.2, 19.2 , 9.3 , 24.6 ,20.2 , 15.8, 18.0 , 12.2 , 20.1 , 16.0 , 17.5 , 18.2 , 22.8 , 11.5

n₂= 14

∑X₂= 247.60

∑X₂²= 4633.24

X[bar]₂= 17.69

S₂²= 19.56

S₂= 4.42

The parameters of study are the population means, if the claim is that the VMT of households is different in both areas, then you'd expect the population means to be different too.

The hypotheses are:

H₀: μ₁ = μ₂

H₁: μ₁ ≠ μ₂

α: 0.05

Assuming both populations are normal and since both population variances are equal the test to apply is an independent samples t test pooled variance:

[tex]t= \frac{(X[bar]_1-X[bar]2)-(Mu_1-Mu_2)}{Sa*\sqrt{\frac{1}{n_1} +\frac{1}{n_2} } } ~~t_{n_1+n_2-2}[/tex]

[tex]Sa^2= \frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2} = \frac{14*16.67+13*19.56}{15+14-2}= \frac{487.66}{27} = 18.06[/tex]

Sa= 4.249= 4.25

[tex]t_{H_0}= \frac{(16.21-17.69)-0}{4.25*\sqrt{\frac{1}{15} +\frac{1}{14} } }= -0.937= -0.94[/tex]

Critical value approach:

This test is two-tailed, this means that the rejection region is divided in two tails:

[tex]t_{n_1+n_2-2; \alpha /2}= t_{27; 0.025}= -2.052[/tex]

[tex]t_{n_1+n_2-2; 1-\alpha /2}= t_{27; 0.975}= 2.052[/tex]

The decision rule is:

If [tex]t_{H_0}[/tex] ≤ -2.052 or if [tex]t_{H_0}[/tex] ≥ 2.052, reject the null hypothesis.

If -2.052 < [tex]t_{H_0}[/tex] < 2.052, do not reject the null hypothesis.

The calculated value is within the "no rejection region" so the decision is to not reject the null hypothesis.

Using the p-value approach:

The p-value is the probability of obtaining a value as extreme as the calculated value of the statistic under the null hypothesis ([tex]t_{H_0}[/tex]). Just as the significance level, the p-value is two tailed, you can calculate it as:

P(t₂₇ ≤ -0.93) + P(t₂₇ ≥ 0.93)= P(t₂₇ ≤ -0.93) + (1 - P(t₂₇ < 0.93)= 0.1796 + ( 1 - 0.8204)= 0.1796*2= 0.3592

p-value= 0.3592

The p-value is always compared to the significance level, the decision rule for this approach is:

If the p-value ≤ α, reject the null hypothesis.

If the p-value > α, do not reject the null hypothesis.

The p-value is greater than α, so the decision is to not reject the null hypothesis.

At a 5% significance level, there is no significant evidence to reject the null hypothesis. You can conclude that the population means of the VMT for households of the Midwest  South ers households.

I hope this mhelps!

Jenn uses 6 cups of flour to bake 40 muffins. How many muffins can she can bake if she has 15 cups of flour?

Answers

Answer:

100 muffins

Step-by-step explanation:

We can use a ratio to solve

6 cups          15 cups

-------------   = -----------

40 muffins     x muffins

Using cross products

6x = 40*15

Divide each side by 6

6x/6 = 40*15/6

x =100

100 muffins

Answer:

100 muffins

Step-by-step explanation:

If she could bake 40 muffins with 6 cups, then she could bake 80 muffins with 12 cups. Then, we have 3 cups left over, which is half of 6, meaning she can only bake half of her regular amount with 3 cups, which would be 20. 80+20=100

40+40+20=100

36°

I

80°

w

m

What equation can be used to calculate the measure of angle ? Describe, in words, the

process you would use to find

Answers

Answer:

44°

Step-by-step explanation:

A pair of angles formed from the intersection of two lines opposite to each other at the point of intersection (vertex) is called vertically opposite angles. These vertically opposite angles are congruent to each other (that means they are equal).

Since opposite angles are equal, the equation needed to calculate w is given as:

80° = 36° + w

w = 80° - 36°

w = 44°

The Tennessean, an online newspaper located in Nashville, Tennessee, conducts a daily poll to obtain reader opinions on a variety of current issues. In a recent poll, readers responded to the following question: "If a constitutional amendment to ban a state income tax is placed on the ballot in Tennessee, would you want it to pass? Possible responses are yes or no,or not sure.

Required:
a. What was the sample size for this poll?
b. Are the data categorical or quantitative?
c. Would it make more sense to use averages or percentages as a summary of the data for this question?
d. Of the respondents, 67% said Yes, they would want it to pass. How many individuals provided this response?

Answers

Answer:

Step-by-step explanation:

a. The sample size for the poll would be at most 10% of the total readers of the tennessean.

b. Categorical data...data collected in groups or categories.

c. Yes it would make more sense to use percentages as this gives a better estimate for proportion.

d. The number of individual that provided this response is 67% of the sample size (which is at most 10% of the total population of readers of the online newspaper).

Factor 12q^2+34q-28. Include list of factors.

Answers

Answer:

2(2q+7)(3q-2)=0

Step-by-step explanation:

lets set up the equation equal to 0:

12q^2+34q-28=0

now, lets factor:

2(6q^2+17q-14)=0

2(2q+7)(3q-2)=0

now, lets find the solutions:

2q+7=0

2q=-7

q=-3.5

3q-2=0

3q=2

q=2/3

Use the compound interest formulas A = Pert and A = P(1 + ) to solve. Suppose that you have $11,000 to invest. Which investment yields the greater return over 10 years: 6.25% compounded continuously or 6.3% compounded semiannually? Show your work

Answers

Answer:

Continuously

Step-by-step explanation:

Compounded continuously:

A = Pe^(rt)

A = 11,000 e^(0.0625 × 10)

A = 20,550.71

Compounded semiannually (twice per year):

A = P(1 + r)^t

A = 11,000 (1 + 0.063/2)^(2×10)

A = 11,000 (1 + 0.0315)^20

A = 20,453.96

What is the volume of a rectangular prism with a length of 12ft, a width of 10ft, and a height of 18ft?

Answers

Answer:

2160ft³

Step-by-step explanation:

V=whl=10·18·12=2160ft³

What is a unit rate?
A) a rate with one in the numerator
B) a rate in which the numerator and the denominator are equal
C) a rate with one in the denominator
D) a rate in which the denominator is greater than the numerator

Answers

A unit rate is a rate with 1 in the denominator. If you have a rate, such as price per some number of items, and the quantity in the denominator is not 1, you can calculate unit rate or price per unit by completing the division operation: numerator divided by denominator.

Hey there! Welcome to Brainly! I"m happy to help!

The unit rate is how much there is of something per  one unit. The word per basically means divided or a fraction. So, if something was a, the unit rate would be a/1.

Therefore, the unit rate is C) a rate with one in the denominator.

I hope that this helps! Have a wonderful day!

can someone please help me it’s urgent!!!!!

Answers

Answer:

6/4

Explanation:

If Alex can file the papers in the cabinets for 6 hours and 4 hours with Millie, then the fraction to represent the papers filed with Millie would be 6/4.

Hope this helps!

the sum of two rational numbers is 8 if one of the numbers is -5/6 find the other

Answers

Answer:53/6

Step-by-step explanation:

Let X be the other rational number

-5/6+X=8

Add 5/6 to both sides

-5/6+5/6+X=8+5/6

0+X= 53/6 (inverse property)

X=53/6. (Identity property)

A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures wide. The biologist estimates she will need of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit into the air tank. Write your answer in atmospheres. Round your answer to significant digits.

Answers

The complete question is;

A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures 78.0 cm wide. The biologist estimates she will need 2600 L of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit in to the air tank. Write you answer in atmospheres

Answer:

10.5 atm

Step-by-step explanation:

Formula for Volume of a sphere is;

V = (4/3)πr³

r = 78/2 = 39 cm

V = (4/3)π(39)³

V = (4/3)*π*59319

V = 248475 cm³

Now, from conversions, 1000 cm³ = 1L

So,

V = 248475/1000

V = 248.5 L

This is the volume of the storage tank

If we assume that the 2600 L of air is measured at 1 atmosphere pressure, then we will obtain the following relationship:

From Boyles law,

P1 × V1 = P2 × V2

Thus;

(1 atm) × (2600 L) = (P2) × (248.5 L)

P2 = 2600/248.5

P2 = 10.463 atmospheres

Approximating to 3 significant figures is; P2 = 10.5 atm

What’s the correct answer for this question?

Answers

Answer:

C

Step-by-step explanation:

A cylinder is formed when rotating the 3-D figure around y-axis

(DONT REPORT OR ANSWER) pls don’t (what is -2 plus -2)

Answers

Answer:

I think it’s -4

Step-by-step explanation:

-2 plus -2 is -4

since 2 plus 2 is 4

Hope this helps ;)

Answer:

It is -4

Step-by-step explanation:

It is because 2 plus 2 is 4

so -2 plus -2 is -4

hth!

Which graph has a slope of 1/4?

Answers

Answer:Please include images of the graphs!

Step-by-step explanation:

Look at each graph given. Ensure that there is a line, and that you can locate two points on the line given.

Use the following equation to get the slope:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Note that you can obtain the numbers for the equation by getting two points on the number line. Plug in the numbers by variables:

(x₁ , y₁) & (x₂ , y₂)

In this equation, make sure that the slope (m) will equal 1/4 (given).

The full equation that you will use is:

1/4 =  (y₂ - y₁)/(x₂ - x₁)

Find the graph that will satisfy this equation.

Mr. Dylan asks his students throughout the year to record the number of hours per week they spend practicing math at
home. At the end of the year, he creates a scatter plot that models the relationship between exam score and time spent
practicing. Which line of best fit will give Mr. Dylan the most accurate linear equation in order to make predictions about
this relationship?​

Answers

Answer:

  see the attachment

Step-by-step explanation:

A "line of best fit" generally has about as much data above the line as below it. If the data has any trend, it generally follows the trend.

The best choice here is B.

Answer:Answer:

 see the attachment

Step-by-step explanation:

A "line of best fit" generally has about as much data above the line as below it. If the data has any trend, it generally follows the trend.

The best choice here is B.

Step-by-step explanation:

Please answer this correctly

Answers

Answer:

17.85 feet.

Step-by-step explanation:

Area = 1/4 * 3.14 * r^2  where r is the radius

So r^2 = 19.625 / (1/4 * 3.14)

r^2 = 25

r = 5 feet.

The perimeter = 2r + 1/4 * 2* 3.14*r

= 2*5 + 7.85

= 17.85 feet.

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