A box has a length of 5 feet, width of 4 feet, be a height of 8 inches. what is the volume of the box in cubic inches

What is the exact value of tan 30° ? enter your answer, as a simplified fraction, in the box?

attashe74 [19]

In this question , we have to find the value of tan 30 and we need to write the answer in simplified form .

$tan x = \frac{sin x}{ cos x}$

Substituting the values of sin (30) and cos(30, we will get

$tan (30) = \frac{1/2}{ \sqrt{3} /2}$

Multiplying both numerator and denominator by 2, we will get

$tan(30 ) = \frac{1}{ \sqrt3}$

TO simplify it, we need to multiply both numerator and denominator by square root 3.

$tan(30) = \frac{ \sqrt 3}{ \sqrt3 * \sqrt 3} = \frac{ \sqrt 3}{3}$

6 0

3 years ago

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The angle of elevation to the sun is 24°. What is the length of the shadow cast by a person 1.82 m tall? A. 0.81 m B. 1.99 m C.

Zanzabum

Answer:

C. 4.09 m

Step-by-step explanation:

Let the length of the shadow cast by a person be x m.

$\tan \: 24 \degree = \frac{height \: of \: person}{length \: of \: the \: shadow} \\ \\ 0.4452286853 = \frac{1.82}{x} \\ \\ x = \frac{1.82}{0.4452286853} \\ \\ x = 4.08778693 \: m \\ x = 4.09 \: m$

7 0

3 years ago

A rucksack can hold a maximum of 3 kg.

devlian [24]

Answer:

4 textbooks

Step-by-step explanation:

3 kg = 3000 g

3000 ÷ 650 = 4.61......

Maximum number is 4 as 0.61... book being carried is not possible

Hope this helped and brainliest please

4 0

2 years ago

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How many times bigger is 80000000 than 20000

Elis [28]

Answer:
4000 times greater

8 0

3 years ago

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Men are believed to have a slightly longer average length of short hospital stays than women; 5.2 days versus 4.5 days respectiv

Georgia [21]

Answer:

Since our calculated value is lower than our critical value, $z_{calc}=2.02$ , we have enough evidence to FAIL to reject the null hypothesis at 1% of singificance. So there is not nough evidence to conclude that mean for men it's significantly higher than the mean for female.

Step-by-step explanation:

1) Data given and notation

$\bar X_{1}=5.2$ represent the mean for group men

$\bar X_{2}=4.5$ represent the mean for group women

Assuming these values for the remaining data:

$\sigma_{1}=1.2$ represent the population standard deviation for the sample men

$\sigma_{2}=1.5$ represent the population standard deviation for the sample women

$n_{1}=32$ sample size for the group men

$n_{2}=30$ sample size for the group women

z would represent the statistic (variable of interest)

$p_v$ represent the p value

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the mean for men it's higher than the mean for women, the system of hypothesis would be:

H0: $\mu_{1} \leq \mu_{2}$

H1: $\mu_{1} > \mu_{2}$

If we analyze the size for the samples both are higher than 30, and we know the population deviation's, so for this case is better apply a z test to compare means, and the statistic is given by:

$z=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

3) Calculate the statistic

We have all in order to replace in formula (1) like this:

$z=\frac{5.2-4.5}{\sqrt{\frac{1.2^2}{32}+\frac{1.5^2}{30}}}=2.02$

4) Find the critical value

In order to find the critical value we need to take in count that we are conducting a right tailed test, so we are looking on the normal standard distribution a value that accumulats 0.01 of the area on the right and 0.99 of the area on the left. We can us excel or a table to find it, for example the code in Excel is:

"=NORM.INV(1-0.01,0,1)", and we got $z_{critical}=2.33$

5) Statistical decision

Since our calculated value is lower than our critical value, $z_{calc}=2.02$ , we have enough evidence to FAIL to reject the null hypothesis at 1% of significance. So there is not nough evidence to conclude that mean for men it's significantly higher than the mean for female.

6 0

3 years ago