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3 years ago

An equilateral triangle has an apothem of 5cm. Find the perimeter of the triangle to the nearest centimeter

1 answer:

5 0

The apothem is the distance from which the altitudes of the triangle to one of its sides. It can be calculated through the equation below,
tan 30° = apothem / 0.5(length of side)
Substituting the known values,
tan 30° = 5 / 0.5x
The value of x from the equation above is 17.32. Multiplying this value by 3 (because a triangle has 3 sides), we get an answer of 51.96 cm or approximately equal to 52. Thus, the answer is letter B.

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I'll mark as brainliest if it lets me;-;<br>please answer B. & C. with solution:)

san4es73 [151]

Answer:

B. AC = 22, BC = 22, AB = 44

C. AC = 30, BC = 30, AB = 60

Step-by-step explanation:

$radius \: \overline {OR} \perp chord \: \overline {AB}$ at C. (given)

$\therefore AC = BC$ (perpendicular dropped from the center of the circle to the chord bisects the chord)

$\therefore 2x - 6 = x + 8$

$\therefore 2x - x= 6 + 8$

$\therefore x= 14$

$AC = 2x-6=2(14)-6=28-6= 22$

$BC= x + 8=14 + 8= 22$

AB = AC + BC = 22 + 22 = 44

$radius \: \overline {OR} \perp chord \: \overline {AB}$ at C. (given)

$\therefore BC = AC$ (perpendicular dropped from the center of the circle to the chord bisects the chord)

$\therefore 7x-5=4x+10$

$\therefore 7x - 4x= 5 + 10$

$\therefore 3x= 15$

$\therefore x= \frac{15}{3}$

$\therefore x= 5$

$AC = 4x+10=4(5)+10=20+10= 30$

$BC= 7x - 5=7(5)-5=35-5= 30$

AB = AC + BC = 30 + 30 = 60

7 0

3 years ago

Suppose that the national average for the math portion of the College Board's SAT is 515. The College Board periodically rescale

nasty-shy [4]

Answer:

a) 16% of students have an SAT math score greater than 615.

b) 2.5% of students have an SAT math score greater than 715.

c) 34% of students have an SAT math score between 415 and 515.

d) $Z = 1.05$

e) $Z = -1.10$

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the empirical rule.

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.

Empirical rule

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

$\mu = 515, \sigma = 100$

(a) What percentage of students have an SAT math score greater than 615?

615 is one standard deviation above the mean.

68% of the measures are within 1 standard deviation of the mean. The other 32% are more than 1 standard deviation from the mean. The normal probability distribution is symmetric. So of those 32%, 16% are more than 1 standard deviation above the mean and 16% more then 1 standard deviation below the mean.

So, 16% of students have an SAT math score greater than 615.

(b) What percentage of students have an SAT math score greater than 715?

715 is two standard deviations above the mean.

95% of the measures are within 2 standard deviations of the mean. The other 5% are more than 2 standard deviations from the mean. The normal probability distribution is symmetric. So of those 5%, 2.5% are more than 2 standard deviations above the mean and 2.5% more then 2 standard deviations below the mean.

So, 2.5% of students have an SAT math score greater than 715.

(c) What percentage of students have an SAT math score between 415 and 515?

415 is one standard deviation below the mean.

515 is the mean

68% of the measures are within 1 standard deviation of the mean. The normal probability distribution is symmetric, which means that of these 68%, 34% are within 1 standard deviation below the mean and the mean, and 34% are within the mean and 1 standard deviation above the mean.

So, 34% of students have an SAT math score between 415 and 515.

(d) What is the z-score for student with an SAT math score of 620?

We have that:

$\mu = 515, \sigma = 100$

This is Z when X = 620. So

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

$Z = \frac{620 - 515}{100}$

$Z = 1.05$

(e) What is the z-score for a student with an SAT math score of 405?

We have that:

$\mu = 515, \sigma = 100$

This is Z when X = 405. So

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

$Z = \frac{405 - 515}{100}$

$Z = -1.10$

3 0

3 years ago

Find the percent of increase.<br> Original number: 45 books<br> New number: 63 books

BARSIC [14]

Answer:

Step-by-step explanation:

first you multiply 45 by .40 you multiply by .40 because that is the percent increase.

45*.40=18

then you just add the 18 to 45 which get you 63.

answer:40%

7 0

3 years ago

3. What is the scale factor of Figure B to Figure A?

xxMikexx [17]

Answer:

2.5

Step-by-step explanation:

From the diagram, figure B was enlarged to obtain figure A.

The two figures are therefore similar.

The corresponding sides are in the same proportion. That constant value of the proportion is called scale factor.

It is given by:

$k = \frac{image \: length}{corresponding\:object \: length}$

Figure B is the image of A

$k = \frac{10}{4} = \frac{25}{10} = \frac{21.5}{8.6} = 2.5$

Therefore the scale factor is 2.5

4 0

3 years ago

How do I write three and one fourth as a percent

tatiyna

U can write 3 and one fourth as 325

3 0

3 years ago

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