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3 years ago

Alana took a math quiz last week. She got 12 out of 20 problems correct. What percentage did Alana get correct?

Mathematics

1 answer:

Deffense [45]3 years ago

4 0

Answer:

60%

Step-by-step explanation:

The fraction 12/20 in simplest form would be 6/10 which come be converted to a percentage. (6x10)/(10x10)=60/100 or 60%.

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Need help with this

defon

Let n be the larger integer and n-2 be the smaller integer.

n² - (n - 2)²

= n² - (n - 2)(n - 2)

= n² - (n² - 4n - 4)

= n² - n² + 4n + 4

= 4n + 4

= 4(n + 1)

No matter what value n is, it will always be a multiple of 4.

4 0

3 years ago

Farmer Ed has 8,000 meters of fencing & wants to enclose a rectangular plot that borders a river. If farmer Ed does not fenc

attashe74 [19]

Answer:

largest area that can be enclosed = 8,000,000 m²

Step-by-step explanation:

Since it is a rectangle plot, the area is expressed as; A = xy, where x is length and y is width.

Because it is next to the river, he only needs to fence three sides, so amount of fencing; F = x + 2y.

Since we know the amount of fencing available is 8000m, we get:

8000 = x + 2y

solving for x, we have;

x = 8000 - 2y

substitute 8000 - 2y for x into the area equation to give;

A = (8000 - 2y)y distribute

A = -2y² + 8000y

Now, due to the negative sign next to 2, this will be a parabola which opens down, meaning that the point of maximum area will be at the vertex,

Thus; y = -b/2a = -8000/[2(-2)] = 2000

x = 8000 - 2(2000) = 4000

A = 4000(2000) = 8,000,000 m²

8 0

4 years ago

The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years

inn [45]

Answer:

b. The null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0$

c. Student's t distribution, as it is a two-sample test for the difference between means.

d. Test statistic t = 5.42.

P-value = 0

e. They appear to be significantly different, as the sample data gives strong evidence that the difference is greater than 0.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that the mean life spans in the county is significantly different for whites and nonwhites.

Then, the null and alternative hypothesis are:

$H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0$

The significance level is 0.05.

The sample 1 (white), of size n1=124 has a mean of 45.3 and a standard deviation of 12.7.

The sample 2 (non-white), of size n2=82 has a mean of 34.1 and a standard deviation of 15.6.

The difference between sample means is Md=11.2.

$M_d=M_1-M_2=45.3-34.1=11.2$

The estimated standard error of the difference between means is computed using the formula:

$s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{12.7^2}{124}+\dfrac{15.6^2}{82}}\\\\\\s_{M_d}=\sqrt{1.301+2.968}=\sqrt{4.269}=2.066$

Then, we can calculate the t-statistic as:

$t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{11.2-0}{2.066}=\dfrac{11.2}{2.066}=5.42$

The degrees of freedom for this test are:

df=n_1+n_2-2=124+82-2=204

This test is a two-tailed test, with 204 degrees of freedom and t=5.42, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=2\cdot P(t>5.42)=0.0000002$

As the P-value (0.0000002) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the mean life spans in the county is significantly different for whites and nonwhites.

4 0

3 years ago

How to solve the equation 8b - 12 = 5b

Virty [35]

Answer:

b = 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Equality Properties

Step-by-step explanation:

Step 1: Define equation

8b - 12 = 5b

Step 2: Solve for b

Subtract 5b on both sides: 3b - 12 = 0
Add 12 on both sides: 3b = 12
Divide 3 on both sides: b = 4

Step 3: Check

Plug in b to verify it's a solution.

Substitute: 8(4) - 12 = 5(4)
Multiply: 32 - 12 = 20
Subtract: 20 = 20

And we have our final answer!

4 0

3 years ago

Find the total surface area of the prism. 8x7x8x5x5

ale4655 [162]

The prism of the surface area is 11200

5 0

3 years ago

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