Special right triangles.
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Answer:

1) The null and alternative hypotheses.

H0: Hours of sleep per night is independent of age.

Ha: Hours of sleep per night is not independent of age.

Test Statistics χ²=4.009

The corresponding p-value for the test at χ²= 4.009 is 0.2604

Step-by-step explanation:

1) The null and alternative hypotheses.

H0: Hours of sleep per night is independent of age.

Ha: Hours of sleep per night is not independent of age.

2) The data is

                              ≤ 39           ≥ 40              Total

6 hours                    36               34                70

6.9-7 hours              60              57               117

7- 7.9 hours              79              77               156

8 hours or more       65              92              157

Total                       240           260             500

3) The expected values are computed as follows

260×70/500=36.4

240×117/500 =56.16

260×117/500 =60.84

240×156/500 =74.88

260×156/500 =81.12

240×157/500=75.36

260×157/500 =81.64

4) The squared distances are calculated as

{(36 - 33.6)^2}/{ 33.6} = 0.171

{(34 - 36.4)^2}{ 36.4} = 0.158

{(60 - 56.16)^2}/{ 56.16} = 0.263

{(57 - 60.84)^2}/{ 60.84} = 0.242

{(79 - 74.88)^2}/{ 74.88} = 0.227

{(77 - 81.12)^2}/{ 81.12} = 0.209

{(65 - 75.36)^2}/{ 75.36} = 1.424

{(92 - 81.64)^2}{ 81.64} = 1.315

5) The significance level is set at α=0.05 for df = (4 - 1) (2 - 1) =3

degrees of freedom.

6) The critical region for this test is χ² = χ² >7.815

7) Test Statistics

χ²=i=∑(O ij −Eij )2/Eij

=0.171+0.263+0.227+1.424+0.158+0.242+0.209+1.315

= 4.009

8) Conclusion

As the calculated value χ² =4.009 does not lie in the critical region ≤χ² =7.815, null hypothesis is not rejected.

Therefore, we conclude that there is not enough evidence to accept the alternate hypothesis , at the α=0.05 significance level.

The p-value for the test at χ²= 4.009 is 0.2604

Answer:

B) y=1/2x

Step-by-step explanation:

y=1/2x

The percentage of the total finance charge on the loan that the service charge will be is about 15.65%. Option D is correct.

D. 15.56%

A loan is an item borrowed for a charged amount, such as an amount borrowed to be repaid with a specified interest fee.

The compound interest formula for the semiannual interest rate is presented as follows;

A = P·[1 + R/n]^(n·t)

Where;

P = The initial amount borrowed on loan = $15,360

t  = The interest rate on the loan = 9.58% = 0.0958

n = The number of periods in a year = 2 for semiannual interest rate

t = The duration of the loan = 8 years

The equal semi annual installment (ESI) formula is presented as follows;

[tex]ESI = P\times \dfrac{\dfrac{r}{2} \times\left(1 + \dfrac{r}{2} \right)^n }{\left(1+\dfrac{r}{2} \right)^n-1}[/tex]

Therefore;

ESI = 15360 × ((0.0958/2)×(1 + 0.0958/2)¹⁶)/((1 + 0.0958/2)¹⁶-1) ≈ 1396.16

The total amount Sam pays = 16 × 1396.16 ≈ 22338.6

The finance charge ≈ 22338.6 - 15360 = 6978.6

The percentage of the finance charge represented the service charge is therefore;

(1294.64/(6978.6 + 1294.64))×100 ≈ 15.65%

The percentage of the total finance charge represented by the service charge is therefore about 15.65%

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Therefore , the solution of the given problem of expression comes out to be probably 4 slices.

In mathematics, it is possible can multiply, division, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression. Expressions and phrases can be contrasted.

Here,

you figure if a toaster takes about 1-2 minutes to toast a piece of bread  and a toaster usually can fit 2 slices at a time i would say 4.

Preheat oven broil to high. Move oven rack to highest position.

Place sliced bread on an ungreased baking sheet. 4 slices of bread.

Broil bread for 1 minute, or until golden brown, then flip and broil for another 20-30 seconds. ...

Top with butter, jam, or any other favorite topping!

The temperature needed for the hot ambient air in a toaster, which makes the bread turn brown, is around 310°F (146°C). The heating element inside a toaster is a nickel-chromium alloy. The electrical current that runs through it heats it to make it red hot, with a temperature of 1,100°F to 1,200°F (519°C to 566°C).

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The number of houses left to be sold is 12

There are 90 new houses built in the neighbourhood

2/5 were sold last month

2/5 × 90

= 18 × 2

= 36

1/3 of the remaining were sold this month

1/3 × 36

=12

Hence there are 12 houses left to be sold

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On solving the provided question, we can say that - the value of the given polynomials domain will be ( - infinity, 0)

The range of values a function may accept is referred to as its domain. These numbers represent the x-values of a function like f. (x). The range of values that a function may operate on is referred to as its domain. The value that the function returns following the insertion of the x value is this set. A function containing the independent variable x and the dependent variable y is said to be y = f(x). A value of x is said to be in the domain of a function f if it can be used to successfully create a single value y utilizing the value of x for that purpose.

domain will be ( - infinity, 0)

range = (-infinity, +infinity)

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Answer:

-4

Step-by-step explanation:

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Answer:

-4

Step-by-step explanation:

So we can start with -2 + 3, (negatives mean -, and positives mean +)

= 1

Then, 1 - 4

= -3

-3 - 1

= -4

hope this helps :)

Answer:

D

Step-by-step explanation:

3[tex]\frac{3}{8}[/tex] + 4[tex]\frac{3}{4}[/tex]  Use the common denominator of 8 Multiply [tex]\frac{3}{4}[/tex] x [tex]\frac{2}{2}[/tex]

3[tex]\frac{3}{8}[/tex] + 4[tex]\frac{6}{8}[/tex]

7[tex]\frac{9}{8}[/tex]

7 + [tex]\frac{8}{8}[/tex] + [tex]\frac{1}{8}[/tex]  Another name for [tex]\frac{8}{8}[/tex] is 1

7 + 1 + [tex]\frac{1}{8}[/tex]

8[tex]\frac{1}{8}[/tex]

Answer:

Its B they are structural isomers

Step-by-step explanation:

Answer:

B) They are structural isomers.

Step-by-step explanation:

Got it right on Edge :D

The value of the function f(x) at x = - 2, - 1, 0, 1 are - 4, - 1, 2, 5.

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, A function f(x) = 3x + 2.

Now,

At x = - 2, f(x) = 3(-2) + 2 ⇒ f(x) = - 4.

At x = - 1, f(x) = 3(-1) + 2 ⇒ f(x) = - 1.

At x = 0, f(x) = 3(0) + 2 ⇒ f(x) = 2.

At x = 1, f(x) = 3(1) + 2 ⇒ f(x) = 5.

This can also be written in the form of ordered pairs

(- 2, - 4), (- 1, - 1), (0, 2), (1, 5).

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Answer:

the answer is 51

Step-by-step explanation:

a triangle has 180 degree in total

180-124=56

73+56+x= 180

x= 51

Answer:

51

Step-by-step explanation:

➝x+73=124

➝x=124-73

➝x=51

Answer:

522 square feet

Step-by-step explanation:

Area is the term used to define the amount of space taken up by a 2D shape or surface. We measure area in square units : cm² or m². Area is calculated by multiplying the length of a shape by its width, so you mutiply 18 by 29 and got 522

Answer:

522

Step-by-step explanation:

Area of a rectangle = width times length

The length in this case is 29 feet, and the width is 18 feet.

29 times 18 = 522 square feet

So on solving the provided question, we can say that the function g(x) is equal to g(x) = [tex]\sqrt{2x}[/tex]

The mathematical procedure known as "function composition" takes two functions, f and g, and creates a function, h = g f, such that h(x) = g. This process involves applying the function g to the outcome of applying the function f to x. When the result of one function is utilized as the input for another, this is known as a composite function. The function f g (x) fg(x) fg(x) fg(x), also known as "f of g of x" or "f g fg fg of x," is the composition of the two functions if we have a function f and another function g.

f(f(x)) = [tex]\frac{x}{\sqrt{6} }[/tex]

f(x) = 3x^2

g(f(x)) = [tex]\frac{3x^2}{\sqrt{6} }[/tex]

g(x) = [tex]\sqrt{2x}[/tex]

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Answer:

11.0325 J

Step-by-step explanation:

The formula for calculating Potential Energy is:

P.E. = mass * acceleration due to gravity * height

where mass is in kg

acceleration due to gravity is a constant at the surface of the earth = 9.8 m/sec^2

and height is in meters

Here:

P.E. = 0.75 kg * 9.8 meters/sec^2 * 1.5 meters

P.E. = 11.0325 kg*m^2/sec^2

Now kg*m^2/sec^2 = joules

so the answer is 11.0325 joules

The required potential energy of the jar is 11.0325 joules.

Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases.

Given that,

The height of self h = 1.5 m.

The mass of cookie jar m = 0.75 kg.

To find the potential energy of jar,

Use formula of Potential Energy

Potential Energy = m × g × h

where m = mass is in kg

Ang g is gravity.

And the value of g at the surface of the earth = 9.8 m/sec²

and height is in meters

Substitute the values here,

Potential energy = 0.75 kg * 9.8 meters/sec² * 1.5 meters

Potential energy = 11.0325 kg x m²/sec²

Since, kg x m²/sec² = joules

Potential energy = 11.0325 joules.

Hence the required answer is 11.0325 joules.

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On solving the provided question, we can say that In still water, a family must paddle at a speed of 2.125 miles per hour.

Speed is the amount of distance traveled by an object in one unit of time when it is in motion.

Given that, a family is paddling a boat (with the current). Their average speed in relation to the riverbanks is 2.75 miles per hour. On the way back, they paddle upstream (against the current), moving toward the riverbank at an average speed of 1.5 miles per hour.

Here, Let the family's speed on still water be x and the current's speed be y. Upstream speed is calculated using the formula 1.5 = x - y - - - - (1)

2.75 downstream speed = x + y - - - - (1)

Equations 1 and 2 are solved as follows: 2x = 4.25 and x = 2.125 miles per hour In still water, a family must paddle at a speed of 2.125 miles per hour.

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Answer:

25.95 + 36

Step-by-step explanation:

You don't have any options so the answer I would say is 25.95 + 36, or the other way around.

Hope this helped :]

Answer: Your answer is 60 divided by 13 = 4.165.

Step-by-step explanation: You would have to divide 12 out of 50, and that would be a decimal of 4.166666666666667 So you need an aditional 10 items but then another additional suitcase there is an answer to this but it would come out as a decimal or fraction, so you would have to specify what type of object is going into these suitcases, most people would just deal with it and carry it in the hands lol.  

Answer:

its letter A.

[tex] \frac{2}{x + 1} [/tex]

Answer:

No

Step-by-step explanation:

The ratio used should have been 6 parts yellow paint to 2 parts blue paint

hope this helps

Using the Central Limit Theorem, the sampling distribution of the sample mean wait time for random samples of size 84 has mean of 11.4 minutes and standard deviation of 0.28 minutes.

The Central Limit Theorem establishes 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].

In this problem, the population has:

Samples of 84 are taken, thus, by the Central Limit Theorem:

[tex]n = 84, s = \frac{2.6}{\sqrt{84}} = 0.28[/tex]

The sampling distribution of the sample mean wait time for random samples of size 84 has mean of 11.4 minutes and standard deviation of 0.28 minutes.

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The solution to the equation is given as [tex]a = \frac{2n}{(d + g)}[/tex]

The equation is given as 2n= a(d+g), we are to make a the subject of the equation

in order to have a stand on its own we would have to divide the two sides of the equation by d + g

hence we would have:

[tex]\frac{2n}{(d + g)} =\frac{a(d+g)}{(d+g)}[/tex]

this would cancel out on the right hand side such that we would have:

[tex]\frac{2n}{(d + g)} =a[/tex]

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Answer: 12

Step-by-step explanation: There are about 12 grams of carbohydrates in a 8 fluid ounce (240 mL) glass of whole milk. The amount of carbohydrates in milk can vary slightly depending on the type of milk you are drinking. For example, skim milk has slightly fewer carbohydrates (about 11 grams per 8 fluid ounces) than whole milk because the fat has been removed. On the other hand, milk that is high in fat, such as heavy cream, has even more carbohydrates (about 4 grams per fluid ounce).

Answer:

3x²

Step-by-step explanation:

3x²

They would all reduce to 1, 2x^4, and -4x

Answer:

1.7$

Step-by-step explanation:

To solve this, first subtract the coffee from the total cost, and then divide the cost by the amount of granola bars.

So first, subtract 7$ from 24(the coffee from the total cost):

24-7

=

17

Next divide the 17$ by the 10 granola bars:

17/10

=

1.7

So we know that the answer is each granola bar cost 1.7$

Hope this helps!

Answer:

multinational banking operations help a bank prevent the erosion of its traveler's check, tourist, and foreign business markets from foreign bank competition.

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Answer:=Answer1 has the regression analysis with all 4 independent variables. Using the stepwise method, we toss the one with the largest non-significant p-value which is Senior Present. Then do another regression analysis with only 3 independent variables. Answer2 has this. From this analysis we can toss education (has the largest non-significant p-value) and do another analysis which is in Answer3. In this analysis we see that Income is not quite significant (p=.0586) at the 0.05 level so we can toss it and do an analysis with Family Size as the only independent variable. This result is given in Answer4. The final regression equation has Family Size as the only independent variable and it can stay in the regression equation because it is statistically significant (p=.0003). The prediction equation is given at the bottom of Answer4. This should answer your question. If not let me know.

Step-by-step explanation:

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Answer:

B. 434.89

Step-by-step explanation:

A basketball is a sphere and the volume formula is:

V = 4/3πr³

Given:

d = 9.4

r = 9.4/2

r = 4.7

Work:

V = 4/3πr³

V = 4/3π(4.7)³

V = 4/3π(103.823)

V = 434.89