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2 years ago

A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground.

Mathematics

2 answers:

jeka57 [31]2 years ago

8 0

Answer:

angle made by the ladder with the ground is 59°.

Step-by-step explanation:

Ladder AC is placed 30 inches from a wall

It touches the wall as a height of 50 meters from the ground.

We have to find ∠C.

From the right angle triangle ABC.

Tan C = $\frac{50}{30}$

Tan C = $(\frac{5}{3})$

C = $Tan^{-1}(\frac{5}{3})$

= 59°

Therefore, angle made by the ladder with the ground is 59°.

kati45 [8]2 years ago

7 0

I don't know if you need the answer to how long the ladder is or what degree the ladder and ground form so I am going to give you both.

The ladder is 58.31 inches
The degree is 59.04

If you have any question let me know

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oee [108]

Answer:

$f(g(x))=6x^3+4$ , it is the amount of money earned per number of hours of work, x

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Here we have two functions:

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This function represents the amount of money (the earning) per unit x

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$g(x)=\sqrt{3x^3}$

which represents the number of gallons of ice cream that Barrett makes per hour, where x is the number of hours he works.

Here we want to find the composite function

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which means that we use the output of $g(x)$ as input for $f(x)$ . In this context, this means that the function $f(g(x))$ represents the amount of money earned per number of hours of work, x.

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2 years ago

Samuel was riding in the back seat of the station wagon on the way home after a long and tiring day at the

ki77a [65]

Answer: One fourth of the entire trip.

Step-by-step explanation:

The initial distance is D.

" He fell asleep halfway home."

Then he fells asleep when the distance between his actual position and his house was half of D, or:

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"He didn't wake up until he still had half as far to go as he had already

gone while asleep."

So he wakes up when his actual position is a fourth of the initial distance:

(D/2)/2 = D/4.

Then if the entire trip has a distance D, and he was sleeping between:

D/2 - D/4 = 2D/4 - D/4 = D/4.

in a trip of a distance D, he was asleep a distance of D/4.

Then, returning to the question:

How much of the entire trip home was Samuel asleep?

This is equal to the quotient between the distance that he travels asleep and the total distance:

r = (D/4)/D = 1/4.

Then he was asleep in 1/4 of the entire trip.

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2 years ago

Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, and then state the concl

never [62]

Answer:

a) Failed to reject the null hypothesis (P-value=0.09).

b) The 95% CI for the difference in proportions is:

$-0.0599\leq\pi_1-\pi_2\leq0.0124$

Step-by-step explanation:

a) We have to perform a hypothesis test for the difference of proportions.

The null and alternative hypothesis are:

$H_0: \pi_1\geq\pi_2\\\\H_1: \pi_1$

The significance level is 0.05.

The proportion of the passenger cars owners is:

$p_1=\frac{239}{2142} =0.1116$

The proportion of commercial truck owners is:

$p_2=\frac{54}{399}=0.1353$

The weigthed average p is

$p=\frac{n_1p_1+n_2p_2}{n_1+n_2}=\frac{239+54}{2142+399}=0.1153$

The estimated standard deviation is

$s=\sqrt{\frac{p(1-p)}{n_1}+\frac{p(1-p)}{n_2}} =\sqrt{\frac{0.1153(1-0.1153)}{2142}+\frac{0.1153(1-0.1153)}{399}} =0.0174$

We can calculate the z-value as:

$z=\frac{\Delta p}{s}=\frac{0.1116-0.1353}{0.0174}=-1.362$

The P-value for z=-1.362 is P=0.0866.

The P-value (0.09) is greater than the significance level (0.05), so it failed to reject the null hypothesis. There is no enough evidence to prove that commercial trucks owners violate laws requiring front license plates at a higher rate than owners of passenger cars.

b) We can construct a 95% CI, according to the significance level of 0.05.

The z-value for this CI is 1.96.

We have to recalculate the standard deviation:

$\sigma=\sqrt{\frac{p_1(1-p_1)}{n_1} +\frac{p_2(1-p_2)}{n_2}} =\sqrt{\frac{0.1116(1-0.1116)}{2142} +\frac{0.1353(1-0.1353)}{399}} =0.0184$

The lower limit is then:

$LL=(p_1-p_2)-z*\sigma=(0.1116-0.1353)-1.96*0.0184=-0.0238-0.0361\\\\LL=-0.0599$

The upper limit is:

$UL=(p_1-p_2)+z*\sigma=(0.1116-0.1353)+1.96*0.0184=-0.0238+0.0361\\\\UL=0.0124$

The 95% CI for the difference in proportions is:

$-0.0599\leq\pi_1-\pi_2\leq0.0124$

In this case, we can conclude that the difference between the proportions, with 95% confidence, can still be equal or greater than zero, meaning that it is possible passenger car owners violate laws more than truck owners.

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2 years ago