what is the area of the rectangular piece of wood?

Answer:

The test statistic is t = 3.24.

Step-by-step explanation:

We want to test the hypothesis that the fuel additive has mean mpg less than the mean mpg without the additive.

This means that the null hypothesis is that the difference is less than 0, while the alternate hypothesis is that the difference is 0 or more.

The test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]s[/tex] is the standard deviation of the sample and n is the size of the sample.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

Randomly select 10 cars

This means that [tex]n = 10[/tex]

The sample mean difference in gas mileage (mpg with additive - mpg without additive) is 0.41 mpg with a sample variance of 0.16.

This means that [tex]X = 0.41, s = \sqrt{0.16} = 0.4[/tex]

Calculate the test statistic.

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{0.41 - 0}{\frac{0.4}{\sqrt{10}}}[/tex]

[tex]t = 3.24[/tex]

The test statistic is t = 3.24.

Answer:

(3)(c) + 43 ≥ 100

Step-by-step explanation:

Given:

Total number of friends = 3 friends

Number of card already have = 43

Total number of card at least want to collect = 100

Find:

Inequality

Computation:

Assume;

Same number of card each friend collect = c

Total number of card at least want to collect ≤ (Total number of friends)(Same number of card each friend collect) + Number of card already have

Total number of card at least want to collect ≤ (3)(c) + 43

100 ≤ (3)(c) + 43

(3)(c) + 43 ≥ 100

Answer:

4

Step-by-step explanation:

20 ÷ 5 = 4

Answer:

27 cards left to be signed

Answer:

27 cards

Step-by-step explanation:

first we need to find what 1/4 of 84 is which will be 21 then we need to find what 3/7 of 84 is which will be 36 now we add the two getting 57 and then subtract 57 from 84 leaving us with 27 cards left. hope this helps.

Answer:

The volume is 588 ft³

Step-by-step explanation:

[tex]v = a {}^{2} \frac{h}{3} = 14 {}^{2} \times \frac{9}{3} = 588[/tex]

Answer:

254.6 ft3 F

Step-by-step explanation:

To find the volume of the pyramid, first calculate the area of the base.

As the pyramid is the regular triangular pyramid, the base is an equilateral triangle.

To find the area of the equilateral triangle, calculate the length of the height.

Since the triangle is equilateral, each angle in the triangle equals 60°.

The height forms a 30°- 60°- 90° triangle. One leg of this triangle is equal to half of the side of the large triangle, or 7 ft. The other leg of the triangle is equal to 73‾√ ft by the 30°- 60°- 90° Triangle Theorem.

Therefore, the length of the height of the triangle is 73‾√ ft.

To find the area of the base of the pyramid, B, use the formula for the area of a triangle, B=12bh.

Substitute 14 for b and 73‾√ for h.

B=12⋅14⋅73‾√

Simplify.

B=493‾√ ft2

To find the volume of the pyramid, use the formula for the volume of a pyramid, V=13Bh.

Substitute 493‾√ for B and 9 for h.

V=13⋅493‾√⋅9

Simplify.

V=1473‾√

Use a calculator to approximate.

V≈254.6 ft3

Therefore, the volume of the regular triangular pyramid is about 254.6 ft3.

Answer:

C. 6(104)=624

Step-by-step explanation:

edge quiz

The equivalent expression of [tex]\sum \limits^{104}_{n = 1} {6}[/tex] is 6(104) = 24

The sigma notation is given as:

[tex]\sum \limits^{104}_{n = 1} {6}[/tex]

The above means that we add 6 in 104 places.

i.e. 6₁ + 6₂ + ................ + 6₁₀₄

The expression can be expressed using the following product

[tex]\sum \limits^{104}_{n = 1} {6} = 6 * 104[/tex]

Evaluate the product

[tex]\sum \limits^{104}_{n = 1} {6} = 624[/tex]

Hence, the equivalent expression of [tex]\sum \limits^{104}_{n = 1} {6}[/tex] is 6(104) = 24

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If ur trying to find the rate its 12.7252%

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

A. 2,4,1,3

B. 2,1,3,4

C. 2,1,3,4

D. 1,2,4,3

Step-by-step explanation:

its always cell the simplest among the choices then tissue which is comprised of cells then organs which comprised of tissues and lastly the systems in our body that is comprised of organs

Answer: 8.6

Step-by-step explanation:

Using pythagorean theorem, c²=a²+b² you can find the distance between AB.

c²=7²+5²

c²=74

√c²=√74

c=8.6

Answer:

i think that the correct answer is 12 for the least common denominator

Answer:

1033.2 g or 1.033 kg

Step-by-step explanation:

(620/12)(20) = 1033.2 g

Answer:

(7x+3)(-x-3)

Step-by-step explanation:

-7x²-24x-9 would be the same thing as (7x+3)(-x-3) because 7x*-x=-7x², +3*-3=-9, and 7x*-3 - 3x = -24x

9514 1404 393

Answer:

Step-by-step explanation:

Assuming you're interested in the number of each that were sold, the system of equations will express the relation for total sold, and the relation for total revenue. We have used the variable c and p to represent numbers of cakes and pies sold, respectively. Your choices may use x and y, instead.

__

The solution can be found by subtracting 6 times the first equation from the second. That tells you 6 cakes were sold, hence 4 pies.

Answer:

Number of total arrangement of beads = 2,520

Step-by-step explanation:

Given:

Number of beads in necklace = 8 beads

Find:

Number of total arrangement of beads

Computation:

Changing beads is a cyclic permutation,

So,

Formula to find number of total arrangement in cyclic permutation

(n-1)!/2 , where n = number of item

So,

(n-1)!/2

Number of total arrangement of beads = (8-1)!/2

Number of total arrangement of beads = (7)!/2

Number of total arrangement of beads = (7 x 6 x 5 x 4 x 3 x 2 x 1) / 2

Number of total arrangement of beads = 5,040 / 2

Number of total arrangement of beads = 2,520

Answer:

1335.7

Step-by-step explanation:

f(5)= 9e^x

Substitute x for 5 and solve

The value of the equation f ( x ) = 9eˣ , when x = 5 is  1335.7

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 f ( x ) = 9eˣ

The equation is an exponential form , and the value of x is substituted in the equation

When the value of x is 5

The value of e = 2.7182

x = 5

So , substituting the value of x in f ( x ) , we get

f ( x ) = 9eˣ

f ( 5 ) = 9 x e⁵

Now , e⁵ = 148.4131

And ,

The equation f ( 5 ) = 9 x 148.4131

                                = 1335.718

                                ≈ 1335.7

Hence , the value of the equation f ( x ) = 9eˣ , when x = 5 is  1335.7

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Answer:

50 students

Step-by-step explanation:

20 is 40% of 50

because 50 x .40 = 20

Hope this helps!

Answer:

30

Step-by-step explanation:

40%/2=20%

20/2=10

100%-40%=60%

60%/3=20%

10x3=30

Answer:

the ration of 3:5. 5 x 4 gives you 20 so, 3x4 gives you 12.

Answer:

probably 6 thats one of the missing ones

Answer:

$50.

Step-by-step explanation:

To find your answer, divide 250 by 5.

250/5 = 50.

You can use inverse operation to check your answer.

50⋅5 = 250.

Therefore, Tom got $50 each day.

Answer:

[tex]x - 8 + 4x - 7 = 180 \\ \\ 5x - 15 = 180 \\ \\ 5x = 180 + 15 \\ \\ 5x = 195 \\ \\ x = 195 \div 5 \\ \\ x = 39 \\ [/tex]

Answer:

17.6

Step-by-step explanation:

But im not sure if u can use decimals

Answer:

i dont know because you have not really explained it

Step-by-step explanation:

The quotient of the division of 145413 by 321 is 453.

Division is one of the operation in mathematics where number is divideD into equal parts as that of a definite number.

We are using long division method here.

For that dividend is 145413 and divisor is 321.

First take the first some digits of dividend which is greater than 321.

That is the first four digits, 1454.

The multiple of 321 closest to 1454 is 1284 which is equal to 4 × 321

So the first digit of quotient is 4.

1454 - 1284 = 170

Now 170 is less than 321.

Add the next digit of the dividend to 170.

It becomes 1701.

Multiple of 321 closest to 1701 is 1605 which is equal to 5 × 321.

The next digit of the quotient is 5.

1701 - 1605 = 96

Again since 96 less than 321, take the next digit of the dividend and the number becomes 963.

Now 963 is a multiple of 321, where 963 = 3 × 321

So the next digit of the  quotient is 3.

Quotient = 453

Hence the quotient of the given division is 453.

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Answer:

5. 4        6. 6

Step-by-step explanation:

Number 5

[tex]10-2\sqrt{9}[/tex]

[tex]2\sqrt{9}=6[/tex]

[tex]=10-6[/tex]

Subtract the numbers: 10 - 6 = 4

[tex]=4[/tex]

Number 6

[tex]70-\left(\sqrt[3]{64}\right)^3[/tex]

[tex]\left(\sqrt[3]{64}\right)^3=64[/tex]

[tex]=70-64[/tex]

Subtract the numbers: 70 - 64 = 6

[tex]=6[/tex]