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2 years ago

An angle measures eleven more than four times a number. Its compliment is

Mathematics

1 answer:

Rus_ich [418]2 years ago

7 0

Answer:

35 and 55 degrees

Step-by-step explanation:

Let's use n for the number

Angle 1 = 4n+11

Angle 2 = 3n+2

Since it states that these angles are complimentary, they add up to 90 degrees

So we can write an equation using what is given.

Angle 1 + Angle 2 = 90

4n+11+3n+2 = 90

Combine like terms

7n+13 = 90

Subtract 13 from each side

7n = 77

n = 11

Now we plug eleven in for n and solve for the measure of each angle.

Angle 1 = 4(11)+11

Angle 1 = 44+11

Angle 1 = 55

Angle 2 = 3(11)+2

Angle 2 = 33+2

Angle 2 = 35

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Consider this equation:

alexandr1967 [171]

Answer:

we are given the function –2x – 4 + 5x = 8 and is asked in the problem to solve for the variable x in the function. In this case, we can first group the like terms and put them in their corresponding sides:

-2x + 5x =8+4

Then, do the necessary operations.

3x = 12

x = 4.

The variable x has a value of 4.

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

AYUDAAA porfavorrrr primera urna 6 bolas verdes y 3 rojas segunda urna 3 verdes, 3 blancas y 3 rojas tercera urna 6 verdes, 1 bl

marin [14]

We have the following information:

first urn: 6 green balls and 3 red ones

total: 6 + 3 = 9

second urn: 3 green, 3 white and 3 red

total: 3 + 3 + 3 = 9

third urn: 6 green, 1 white and 2 red

total: 6 + 1 + 2 = 9

a) A green ball is more likely to be obtained, since there are more green balls than red balls, which makes the probability higher.

b) probability of drawing a green, red and white ball.

first urn:

green = 6/9 = 66.66%

red = 3/9 = 33.33%

white = 0/9 = 0%

second urn:

green = 3/9 = 33.33%

red = 3/9 = 33.33%

white = 3/9 = 33.33%

third urn:

green = 6/9 = 66.66%

red = 2/9 = 22.22%

white = 1/9 = 11.11%

c) it would be chosen where the probability of drawing green would be the highest, which means that it would be possible both in the first and in the third ballot box, the probability is equal 66.66%

d) without a green ball, the third ballot box would look like this:

5 green balls, 2 red balls and 1 white ball, with a total of 8.

The probability of drawing would be:

green = 5/8 = 62.5%

red = 2/8 = 25%

white = 1/8 = 12.5%

7 0

2 years ago

The amount of coffee that a filling machine puts into an 8-ounce jar is normally distributed with a mean of 8.2 ounces and a sta

nordsb [41]

Answer:

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 8.2, \sigma = 0.18, n = 100, s = \frac{0.18}{\sqrt{100}} = 0.018$

What is the probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce?

This is the pvalue of Z when X = 8.2 + 0.02 = 8.22 subtracted by the pvalue of Z when X = 8.2 - 0.02 = 8.18. So

X = 8.22

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{8.22 - 8.2}{0.018}$

$Z = 1.11$

$Z = 1.11$ has a pvalue of 0.8665

X = 8.18

$Z = \frac{X - \mu}{s}$

$Z = \frac{8.18 - 8.2}{0.018}$

$Z = -1.11$

$Z = -1.11$ has a pvalue of 0.1335

0.8665 - 0.1335 = 0.7330

73.30% probability that the sampling error made in estimating the mean amount of coffee for all 8-ounce jars by the mean of a random sample of 100 jars will be at most 0.02 ounce

8 0

2 years ago

Find the circumference of the circle. Then, find the length of each bolded arc. Use appropriate notation

Vaselesa [24]

Answer:

$\text{1) }\\\text{Circumference: }24\pi \text{ m}},\\\text{Length of bolded arc: }18\pi \text{ m}\\\\\text{3)}\\\text{Circumference. }4\pi \text{ mi},\\\text{Length of bolded arc: } \frac{3\pi}{2}\text{ mi}$

Step-by-step explanation:

The circumference of a circle with radius $r$ is given by $C=2\pi r$ . The length of an arc is makes up part of this circumference, and is directly proportion to the central angle of the arc. Since there are 360 degrees in a circle, the length of an arc with central angle $\theta^{\circ}$ is equal to $2\pi r\cdot \frac{\theta}{360}$ .

Formulas at a glance:

Circumference of a circle with radius $r$ : $C=2\pi r$
Length of an arc with central angle $\theta^{\circ}$ : $\ell_{arc}=2\pi r\cdot \frac{\theta}{360}$

<u>Question 1:</u>

The radius of the circle is 12 m. Therefore, the circumference is:

$C=2\pi r,\\C=2(\pi)(12)=\boxed{24\pi\text{ m}}$

The measure of the central angle of the bolded arc is 270 degrees. Therefore, the measure of the bolded arc is equal to:

$\ell_{arc}=24\pi \cdot \frac{270}{360},\\\\\ell_{arc}=24\pi \cdot \frac{3}{4},\\\\\ell_{arc}=\boxed{18\pi\text{ m}}$

<u>Question 2:</u>

In the circle shown, the radius is marked as 2 miles. Substituting $r=2$ into our circumference formula, we get:

$C=2(\pi)(2),\\C=\boxed{4\pi\text{ mi}}$

The measure of the central angle of the bolded arc is 135 degrees. Its length must then be:

$\ell_{arc}=4\pi \cdot \frac{135}{360},\\\ell_{arc}=1.5\pi=\boxed{\frac{3\pi}{2}\text{ mi}}$

8 0

2 years ago

SOMEONE HELP PLEASE

Alborosie

I’m sorry but I can’t understand what the question is saying

4 0

2 years ago