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3 years ago

MATH HELP PLEASE!!!!! 15 POINTS WILL MARK BRAINLIEST PLEASE ANSWER THESE 5 QUESTIONS BELOW

Mathematics

2 answers:

rusak2 [61]3 years ago

8 0

The answer is B(-5,13), (1,1), (2,-1)

Elodia [21]3 years ago

3 0

The answer to it is (-5,13),(1,1),(2,-1)

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The Pythagorean Theorem can be used to find the missing side length of a triangle when two other side lengths are known.

lubasha [3.4K]

Answer:

The value of b is 21

Step-by-step explanation:

29=√20^2+b^2

or, 29=√400+b^2

or, 841=400+b^2

or, 841-400=b^2

or, √441=b

b=21

5 0

2 years ago

Random samples of size 64 are taken from an infinite population whose mean and standard deviation are 24 and 6.4, respectively.

umka2103 [35]

Answer:

Mean 24, standard error 0.8

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation, also called standard error $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 24, \sigma = 6.4, n = 64$

What are the mean and the standard error of the sample mean?

By the Central Limit Theorem, mean 24 and standard error $s = \frac{6.4}{\sqrt{64}} = 0.8$

7 0

3 years ago

A ladder 10 m long,leans against a vertical wall at an angle of 70° to the ground.if the ladder slips down the wall 4m,find,corr

lina2011 [118]

Answer:

(a) the new angle the ladder makes with the ground is $32.7^o$

(b) the ladder slipped back about 5 meters

Step-by-step explanation:

Notice that the ladder doesn't change its length in the process.

So let's start from the initial situation , finding the distance from the ground at which the ladder touches the wall when the angle with the ground is 70^o. Notice that this situation is represented by a right angle triangle with the right angle between the wall and the ground (see attached image), and that we can use the sine function to find the side opposite to the 70 degree angle:

$sin(70^o)=\frac{opposite}{hypotenuse} \\sin(70^o)=\frac{h}{10}\\h=10\, sin(70^o) \approx 9.4 \,\,m$

therefore 9.4 meters is approximately the height at which the ladder touches the wall initially.

Now, if the tip of the ladder goes down the wall 4 meters, it is now at 9.4 m - 4 m = 5.4 m from the ground. We can therefore use again the sine function to solve for the new angle:

$sin(x)=\frac{opposite}{hypotenuse} \\sin(x)=\frac{5.4}{10} \\sin(x)=0.54\\x=arcsin(0.54)\\x= 32.7^o$

To answer the second question we need to find the original distance from the wall that the bottom of the ladder was originally, and for that we can use the cosine function:

$cos(70^o)=\frac{adjacent}{hypotenuse} \\cos(70^o)=\frac{x}{10}\\x=10\,cos(70^o)\\x\approx 3.4 \,\,m$