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3 years ago

What is the area of this trapezoid?

Mathematics

1 answer:

lbvjy [14]3 years ago

3 0

Answer:

A. $12 \frac{1}{4} \: {cm}^{2}$

Step-by-step explanation:

Area Of of the trapezoid

$= \frac{1}{2} (7 + 5 \frac{1}{4} )2 \\ \\ = 7 + \frac{21}{4} \\ \\ = \frac{28 + 21}{4} \\ \\ = \frac{49}{4} \\ \\ = 12 \frac{1}{4} \: {cm}^{2}$

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The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $3.94 (U

tekilochka [14]

Answer:

a) 25

b) 49

c) 97

Step-by-step explanation:

The sample size is calculated using the formula, n = $(\frac{\sigma\times z}{\textup{Margin of error}})^2$

Now,

for 95% confidence level value of z-factor = 1.96

Given:

Mean = $3.94

standard deviation = $0.25

thus,

a) for margin of error = $0.10

n = $(\frac{\sigma\times z}{\textup{Margin of error}})^2$

n = $(\frac{0.25\times1.96}{\textup{0.10}})^2$

n = 4.9²

n = 24.01 ≈ 25 (Rounded off to next integer)

b) for margin of error = $0.07

n = $(\frac{\sigma\times z}{\textup{Margin of error}})^2$

n = $(\frac{0.25\times1.96}{\textup{0.07}})^2$

n = 7²

n = 49

c) for margin of error = $0.05

n = $(\frac{\sigma\times z}{\textup{Margin of error}})^2$

n = $(\frac{0.25\times1.96}{\textup{0.05}})^2$

n = 9.8²

n = 96.04 ≈ 97 (Rounded off to next integer)

6 0

3 years ago

What mixed<br> number represents thirty-eighths?

Anvisha [2.4K]

Answer:

............... 3 6/8

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3 years ago

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2x-3y=9<br> Find slope-<br> x-intercept-<br> y-intercept-

Readme [11.4K]

get the equation in slope intercept form

2x-3y=9

subtract 2x from each side

-3y = -2x +9

divide by -3

y = 2/3 x -3

slope = 2/3

y intercept = -3

x intercept set y=0 and solve

0 = 2/3 x -3

add 3 to each side

3 = 2/3 x

multiply each side by 3/2

9/2 = x

the x intercept is 9/2 or 4 1/2

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3 years ago

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Re write the expression 8^6 x 8^3/ 8^5 as an exponential expression with a single base

Arada [10]

Answer:

8^4

Step-by-step explanation:

Here we have:

8^6 · 8³

-------------

8^5

That's multiplication in the numerator. The appropriate rule of exponents states that:

8^a·8^b = 8^(a+b), so the numerator is equivalent to 8^(6 + 3) = 8^9.

Now we have

8^9

------

8^5

and the appropriate rule for division here is

8^a / 8^b = 8^(a - b)

So our:

8^9

--------- 8^(9-5) = 8^4

8^5

4 0

2 years ago

A researcher compares the effectiveness of two different instructional methods for teaching physiology. A sample of 178 students

xxTIMURxx [149]

Answer:

critical value = 1.645

The 90% confidence interval = ( -22.62, -17.58)

Step-by-step explanation:

Given that:

the sample size $n_1$ = 178

the sample size $n_2$ = 226

the sample mean $\overline x_1$ = 54.4

the sample mean $\overline x_2$ = 74.5

population standard deviation $\sigma_1$ = 18.58

population standard deviation $\sigma_2$ = 9.52

level of significance ∝ = 1 - 0.90 = 0.10

The critical value for $Z_{\alpha/2} = Z _{0.10/2} = Z_{0.005}$ is 1.645

For the construction of our confidence interval, we use 90% since that is used to find the critical value.

∴

The margin of error = $Z \times\sqrt{\dfrac{\sigma_1^2}{n_1} + \dfrac{\sigma_2^2}{n_2}}$

$1.645 \times\sqrt{\dfrac{18.58^2}{178} + \dfrac{9.52^2}{226}}$

$1.645 \times\sqrt{\dfrac{345.2164}{178} + \dfrac{90.6304}{226}}$

$1.645 \times\sqrt{2.34042}$

$\simeq$ 2.52

The lower limit = $( \overline x_1 - \overline x_2) - (M.O.E)$

= ( 54.4-74.5) - (2.52)

= -20.1 - 2.52

= -22.62

The upper limit = $( \overline x_1 - \overline x_2) + (M.O.E)$

= ( 54.4-74.5) + (2.52)

= -20.1 + 2.52

= -17.58

The 90% confidence interval = ( -22.62, -17.58)

6 0

3 years ago