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Lelu [443]
3 years ago
6

Clare has a set of cubes with a volume of 1 cm³ each. She also has a box with a volume of 24 cm³. Exactly two layers of cubes ca

n fit in this box. How many cubes must be in each layer? its a school problem I'm having trouble with
Mathematics
1 answer:
Damm [24]3 years ago
5 0

Answer:

12 cubes

Step-by-step explanation:

If the total volume of the box is 24 cm³ and the volume of each cube is 1 cm³ then that means that 24 total cubes can fit perfectly inside the box. Since there can only be two layers of cubes then we simply need to divide the total amount of cubes that will fit in the box by 2 to find the number of cubes in each layer...

24 / 2 = 12 cubes

Finally, we can see that each layer within the box will contain 12 cubes

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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
Which two ratios form a proportion?
Alex17521 [72]

Step-by-step explanation:

4 and 5 is one 20/25

3 0
3 years ago
Read 2 more answers
Which of the numbers below belong to both the set of natural numbers and the set of integers?
VladimirAG [237]
15  -  natural (1,2,3...15....) and integers (...-2,-1,0, 1,2,...15,...)
8 0
3 years ago
Their are two boxes at the bottom that I couldn’t fit in, but the answer would go in those two boxes.
valkas [14]

Answer:

3x+8=68 degrees

6x-8= 112 degrees

Step-by-step explanation:

3x+8+6x-8=180

9x=180

x=20

3*20+8=68

6*20-8=112

8 0
3 years ago
What is the equation of the line that is parallel to the line 12x + 15y = 10 and passes through the point (5, −2)
Aleonysh [2.5K]

Answer:

The slope of the given line and a line parallel to it is 5/2.

Step-by-step explanation:

Explanation:

Given:

5

x

−

2

y

=

11

is the standard form of a linear equation.

A line parallel to this line has the same slope. To determine the slope, solve for

y

to change the equation to slope-intercept form:

y=mx+b, where: m is the slope and b is they intercept.5x−2y=11      

Subtract 5x from both sides. −2y=−5x+11

Divide both sides by −2. y=−5/−2x+11/2

Simplify. y=5/2 x −11/2

The slope of the given line and a line parallel to it is 5/2.

.

7 0
2 years ago
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