What does the ratio pi represent in any circle?

A rectangular box has interior dimensions 6-inches by 5-inches by 10-inches. The box is filled with as many solid 3-inch cubes a

Arte-miy333 [17]

Answer: The box would have 99% of its volume taken up.

Step-by-step explanation: The box has dimensions as follows;

Length = 6 inches

Width = 5 inches

Height = 10 inches

Therefore the volume of the box shall become

Volume = L x W x H

Volume = 6 x 5 x 10

Volume = 300 cubic inches

Also a 3 inch cube would have its volume given as follows (

Volume = 3 x 3 x 3 (All sides of a cube has equal lengths)

Volume = 27 cubic inches

To find out how many of 3-inch cubes can fit in, divide 300 by 27 and that equals 11.11.

Hence you can have at most 11 cubes in the box. The total volume of 11 cubes is given as 11 x 27 which equals 297. Therefore, the percentage of the box taken up completely by the cubes is given as;

Percentage = (Volume of cubes/Volume of box) x 100

Percentage = (297/300) x 100

Percentage = 99

Therefore the box would have 99% of its volume taken up by the cubes.

8 0

3 years ago

-6a-4= -4 (1+7a) Solve for a.

soldi70 [24.7K]

Answer:

$a = 0$

Step-by-step explanation:

On the right side of the = multiply -4 through

$- 6a - 4 = - 4 - 28a$

add 28a and add 4 to both sides

$28a - 6a = 4 - 4$

$22a = 0$

divide both sides by 22

$a = 0$

6 0

3 years ago

Read 2 more answers

URGENTTT! CAN SOMEONE PLEASE HELP?

miskamm [114]

Answer:

Hey there!

We have tangent 29=h/400

Thus, tangent 29 times 400=h

h=221.7 feet.

The height of the kite is 221.7 feet.

Hope this helps :)

8 0

4 years ago

A study was recently conducted at a major university to estimate the difference in the proportion of business school graduates w

sveta [45]

Answer:

$(0.1875-0.274) - 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.1412$

$(0.1875-0.274) + 1.96 \sqrt{\frac{0.1875(1-0.1875)}{400} +\frac{0.274(1-0.274)}{500}}=-0.0318$

And the 95% confidence interval would be given (-0.1412;-0.0318).

We are confident at 95% that the difference between the two proportions is between $-0.1412 \leq p_A -p_B \leq -0.0318$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_A$ represent the real population proportion for business

$\hat p_A =\frac{75}{400}=0.1875$ represent the estimated proportion for Business

$n_A=400$ is the sample size required for Business

$p_B$ represent the real population proportion for non Business

$\hat p_B =\frac{137}{500}=0.274$ represent the estimated proportion for non Business

$n_B=500$ is the sample size required for non Business

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.