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2 years ago

Answer the question please

Mathematics

1 answer:

givi [52]2 years ago

5 0

Answer:

(d) 108°

Step-by-step explanation:

An inscribed angle is half the measure of the arc it subtends. Conversely, the arc is twice the measure of the inscribed angle it subtends.

<h3>using the relation</h3>

We can define the vertex of the marked angle as point Q. Arc XY is twice the measure of inscribed angle XQY:

arc XY = 2(54°) = 108°

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Solve the equation or formula for the indicated variable. S=3r^4t, for t

algol [13]

we are given

$S=3r^{4t}$

Since, we have to solve for t

so, we will isolate t on anyone side

divide both sides by 3

$\frac{S}{3} =r^{4t}$

now, we can take ln both sides

$ln(\frac{S}{3}) =ln(r^{4t})$

we can simplify it

$ln(\frac{S}{3}) =4tln(r)$

divide both sides by 4ln(r)

$t=\frac{ln(\frac{S}{3})}{4ln(r)}$ ..............Answer

4 0

3 years ago

Two less than three times a number is equal to 19. What is the number?

EastWind [94]

The best way to approach a word problem like this

is to break it down into pieces, so we can understand it fully.

In this problem, we have a number, which we don't know.

We can use any variable to represent it.

So let's use the variable <em>n</em> to represent it.

"Two less than three times a number" means 3n - 2.

A common mistake is for students to put 2 - 3n.

However, the word "less than" switches the order around.

So we have 3n - 2 = 19.

Solving from here, we add 2 to both sides to get 3n = 21.

Now divide both sides of the equation by 3 and we have n = 7.

So the number is 7.

8 0

3 years ago

Ronald scores 700 on the math section of the SAT exam. The distribution of SAT scores is approximately normal with a mean of 500

Artist 52 [7]

Answer:

a) Due to the higher z-score, Ronald performed better relative to his peers on the test.

b) Ronald needed a grade of at least 732.5, and Rubin of at least 33.58.

c) 95% of the population fall between graded of 4.868 and 31.132 on the ACT.

95% of the population fall between graded of 304 and 696 on the SAT.

Step-by-step explanation:

Normal probability distribution

When the distribution is normal, we use 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.

In this question:

(a) Relative to their peers who also took the tests, who performed better on his test? Explain.

We have to find whoever has the higher z-score.

Ronald:

Ronald scores 700 on the math section of the SAT exam. The distribution of SAT scores is approximately normal with a mean of 500 and a standard deviation of 100. So the z-score is found when $X = 700, \mu = 500, \sigma = 100$ . So

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

$Z = \frac{700 - 500}{100}$

$Z = 2$

Rubin:

Rubin takes the ACT math exam and scores 31 on the math portion. ACT scores are approximately normally distributed with a mean of 18 and a standard deviation of 6.7. So the z-score is found when $X = 31, \mu = 18, \sigma = 6.7$ . So

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

$Z = \frac{31 - 18}{6.7}$

$Z = 1.94$

Due to the higher z-score, Ronald performed better relative to his peers on the test.

(b) A certain school will only consider those students who score in the top 1% in the math section. What grades would Ronald and Rubin have to receive on their respective tests to be considered for admission?

They have to be in the 100 - 1 = 99th percentile, that is, they need a z-score with a pvalue of at least 0.99. So we need to find for them X when Z = 2.325.

Ronald:

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

$2.325 = \frac{X - 500}{100}$

$X - 500 = 232.5$

$X = 732.5$

Rubin:

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

$2.325 = \frac{X - 18}{6.7}$

$X - 18 = 15.58$

$X = 33.58$

Ronald needed a grade of at least 732.5, and Rubin of at least 33.58.

(c) Between what two grades does 95% of the population fall for the ACT and the SAT exams?

They fall between the 100 - (95/2) = 2.5th percentile and the 100 + (95/2) = 97.5th percentile, that is, they fall between X when Z = -1.96 and X when Z = 1.96.

ACT:

Lower bound:

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

$-1.96 = \frac{X - 18}{6.7}$

$X - 18 = -1.96*6.7$

$X = 4.868$

Upper bound:

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

$1.96 = \frac{X - 18}{6.7}$

$X - 18 = 1.96*6.7$

$X = 31.132$

95% of the population fall between graded of 4.868 and 31.132 on the ACT.

SAT:

Lower bound:

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

$-1.96 = \frac{X - 500}{100}$

$X - 500 = -196$

$X = 304$

Upper bound:

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

$1.96 = \frac{X - 500}{100}$

$X - 500 = 196$

$X = 696$

95% of the population fall between graded of 304 and 696 on the SAT.

7 0

3 years ago

Fill in the other coordinate for the line 3x-3y=9 (2,

Delicious77 [7]

We have that

<span>the function of the line is
3x-3y=9
clear y
3x-9=3y
y=(3x-9)/3
y=x-3
for x=2
y=x-3----->y=2-3------> y=-1

the point is (2,-1)

the answer is
the y coordinate is -1</span>

4 0

3 years ago

eli takes a typing test and types all 300 words in 1/10 hour.he takes the test a second time and types the words in 1/12 hour wa

Leokris [45]

He typed faster the second time because if you multiple 60 minutes by 1/10 and 1/12 of and hour separately, you get a smaller answer with 1/12 than by 1/10, and thereby a smaller answer.

Hope this helps!

5 0

3 years ago

Answer the question please ​

Answer the question please