How do I solve this using the Pythagorean theorem

Answer:

The 99.9% confidence interval for the difference between these results is between 12.09 and 25.91 hours per week.

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction of normal variables:

When two normal variables are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of variances.

Ohio had an average of 52, standard deviation of 7.22, sample of 40.

This means that [tex]\mu_O = 52, s_O = \frac{7.22}{\sqrt{40}} = 1.1416[/tex]

Pennsylvania had an average of 33, standard deviation of 10.11, sample of 33.

This means that [tex]\mu_P = 33, s_P = \frac{10.11}{\sqrt{33}} = 1.76[/tex]

Distribution of the difference:

[tex]\mu = \mu_O - \mu_P = 52 - 33 = 19[/tex]

[tex]s = \sqrt{s_O^2 + s_P^2} = \sqrt{1.1416^2 + 1.76^2} = 2.1[/tex]

Confidence interval:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.999}{2} = 0.0005[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.0005 = 0.9995[/tex], so Z = 3.29.

Now, find the margin of error M as such

[tex]M = zs[/tex]

[tex]M = 3.29*2.1 = 6.91[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 19 - 6.91 = 12.09 hours per week

The upper end of the interval is the sample mean added to M. So it is 19 + 6.91 = 25.91 hours per week.

The 99.9% confidence interval for the difference between these results is between 12.09 and 25.91 hours per week.

Answer:

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Answer:

13.5

Step-by-step explanation:

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Or 13 with a remainder of 5

13R5

or

13 5/8

The quotient is 13 and the remainder is 4 for the given statement.

When we divide 108 by 8, we find:

108 ÷ 8 = 13 remainder 4

The quotient is 13 and the remainder is 4.

Therefore, 108 divided by 8 is equal to 13 with a remainder of 4.

Learn more about Mathematical operations here:

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Answer:

c as they give the line of the graph

Answer:

Th final equation is [tex]Y = 2X^2 -3[/tex]

The graph is attached

Step-by-step explanation:

Given

[tex]X = \sqrt{t} \\t = X^2[/tex] --- Eq (1)

and [tex]Y = 2t -3[/tex] --- Eq (2)

Substituting the value of "t" from Eq (1) into Eq (2), we get -

[tex]Y = 2X^2 -3[/tex]

The graph for the equation is attached here with

The Cartesian form of the parametric equation is y = 2x² – 3 and the graph will be a parabola.

A parametric equation in mathematics specifies a set of numbers as functions of one or more independent variables known as parameters.

We have parametric functions:

x = √t ⇒ x² = t

y = 2t—3

Plug t = x² in the other equation, we get:

y = 2x² - 3

The graph will be a parabola.

Thus, the Cartesian form of the parametric equation is y = 2x² – 3 and the graph will be a parabola.

Learn more about the parametric function here:

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Answer:

The Black Stallion, known as the Black or Shêtân, is the title character from author Walter Farley's bestselling series about the Arab stallion and his young owner, Alec Ramsay. The series chronicles the story of a sheikh's prized stallion after he comes into Alec's possession, although later books furnish the Black's backstory. Shaytan (under various transliterations) is the Arabic word for "devil".

Answer:

Susan spilled 1/6 of a gallon of lemonade.

Step-by-step explanation:

Since Susan was carrying a pitcher that contained 2/3 of a gallon of lemonade to the table for lunch, and she slipped and spilled 1/4 of the lemonade in the pitcher, to determine what fraction of a gallon of lemonade did she spill the following calculation must be performed:

2/3 = 0.6666

0.666666 x 1/4 = X

0.166666 = X

0.166666 = 1/6

Therefore, Susan spilled 1/6 of a gallon of lemonade.

Answer:

enlarged

Step-by-step explanation:

imagine there are two figures, figure A and B.  figure A has a length of 10cm and the scale factor is 1.2

the length of figure B = 10 X 1.2 = 12

Figure B has a longer length than figure A. thus figure B is an enlarged version of figure A.

Conversely, if the factor is 0.2

the length of figure B = 10 X 0.2 = 2cm

the length of figure B is less than that of figure A. Thus, figure B is a scaled image of A

Answer:

a

Step-by-satep explanation:

Answer:

1/6

Step-by-step explanation:

just did on edg

Answer:

288.62

Step-by-step explanation:

Answer:

74,611,399

Step-by-step explanation:

Percentage of obese children and adolescent = 19.3%

19.3% = 14.4 million

The overall number of children and adolescent equals a total percentage of 100%

Hence,

If 19.3 % = 14.4 million

100% = x

Cross multiply :

19.3% x = 100% * 14.4 million

0.193x = 14400000

x = 14400000 / 0.193

x = 74611398.964

Total number of children and adolescent = 74,611,399

Answer:

i got B for my answer

Answer:

8730

Step-by-step explanation:

Answer:

Mean: 89

Median: 89

Mode: 89

Range: 22

Step-by-step explanation:

Answer:

89

Step-by-step explanation:

Mean-89

Median-89

Mode-89

Answer: C

Step-by-step explanation: Hope this help :D

Answer:

t=7seconds or 5seconds

Step-by-step explanation:

s=-16t^2 +192t

let s=560ft

560=-16t^2 +192t

16t^2 -192t+560=0

16(t^2-12t+35)=0

(t^2 -12t +35)=0

factoring it ,it will give

(t-7)(t-5)=0

solving for t

t-7=0 or t-5=0

t=7s or t=5s

Answer:

So, the coefficient of the x^2 -term is 80

Step-by-step explanation:

so we need to simplify it:

#10(x^2)(2^3) = 10(x^2)(8) = 80x^2

Answer:

x > -6

Step-by-step explanation:

1) Divide both sides by -4

      x > - [tex]\frac{24}{4}[/tex]

2) Simplify and solve to get answer.

 x > -6.

Step-by-step explanation:

work is on the paper for you, somthing that might help you with your future with math is PEMDAS always do exponents first when it's an equation like your first, second, and third question. I hope this helped.

Answer:

40x^20

Step-by-step explanation:

Each sequence the x value doubles.

Each sequence the x exponent goes up by 5

Answer:

[tex] {4x}^{2} - 12x[/tex]

Answer:

4x² - 12x

Step-by-step explanation:

Multiply 4x by each term inside the parentheses

4x(x) = 4x²

4x(-3) = -12x

Put the terms back into order

4x² - 12x

Answer:

Step-by-step explanation:

The steps in the photo above

I hope that is useful for you :)

Answer:

it will take 4 workers 27 hours to build 3 playsets.

Step-by-step explanation:

Given;

two works to build 1 play set in 18 hours

If a worker works at the same rate, he will finish a playset as follows;

2 worker ---------> 18 hours

1 worker -----------> ?

1 worker = 2  x 18 hours = 36 hours for 1 playset

4 workers  will take  ³⁶/₄ hours for 1 playset

4 workers --------------> 9 hours for 1 playset

For 3 playsets, 4 workers will take 3 x 9 hours = 27 hours.

Therefore, it will take 4 workers 27 hours to build 3 playsets.

Answer:

The answer is Option D

Step-by-step explanation:

Option D is the right answer since 85° is a acute angle. Acute angles are angles below 90°

Hope this helps!

Have a good day

Answer:

[tex]x + 3y > 9 \\ 3y > - x + 9 \\ y > - \frac{1}{3} x + 3 \\ y - intercept \: is \: 3 \\ first \: point = 3 \\ second \: point \: = 9[/tex]

Answer:

-x^2+3x+3

Step-by-step explanation:

if the evaluated answer is correct (but my answer above is correct)  it would be -4+6+3 then the answer would be 5 but I am not sure

Answer:

2v+2

Step-by-step explanation: