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3 years ago

PLsss help 15 points!

Mathematics

2 answers:

Lubov Fominskaja [6]3 years ago

6 0

Answer:

90 square cm.

Step-by-step explanation:

For similar figures, the length of corresponding sides are proportional.

So we can write 4k = 6 where k is the proportionality constant.

Note: In terms of area, the scale factor would be k^2 and in terms of volume, it would be k^3y

Solving 4k = 6, we see that k = 6/4 or 3/2

We need area, so we multiply area of ABC by k^2 to get area of PQR.

$40(\frac{3}{2})^2\\=40(\frac{9}{4})\\=90$

Area of PQR = 90 cm^2

S_A_V [24]3 years ago

5 0

Answer:

The area of △PQR is $90\ cm^{2}$

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Let

z-----> the scale factor

x---> the corresponding side triangle PQR

y---> the corresponding side triangle ABC

$z=\frac{x}{y}$

substitute the values

$z=\frac{6}{4}=1.5$

step 2

Find the area of triangle PQR

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

x---> the area of triangle PQR

y---> the area of triangle ABC

$z^{2} =\frac{x}{y}$

we have

$z=1.5$

$y=40\ cm^{2}$

substitute the values

$1.5^{2} =\frac{x}{40}$

$x=40(1.5^{2})=90\ cm^{2}$

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CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars

velikii [3]

Answer:

P(939.6 < X < 972.5) = 0.6469

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 normal distributions can be 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.

CNNBC recently reported that the mean annual cost of auto insurance is 965 dollars. Assume the standard deviation is 113 dollars.

This means that $\mu = 965, \sigma = 113$

Sample of 57:

This means that $n = 57, s = \frac{113}{\sqrt{57}} = 14.97$

Find the probability that a single randomly selected policy has a mean value between 939.6 and 972.5 dollars.

This is the pvalue of Z when X = 972.5 subtracted by the pvalue of Z when X = 939.6. So

X = 972.5

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

By the Central Limit Theorem

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

$Z = \frac{972.5 - 965}{14.97}$

$Z = 0.5$

$Z = 0.5$ has a pvalue of 0.6915

X = 939.6

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

$Z = \frac{939.6 - 965}{14.97}$

$Z = -1.7$

$Z = -1.7$ has a pvalue of 0.0446

0.6915 - 0.0446 = 0.6469

P(939.6 < X < 972.5) = 0.6469

3 0

2 years ago

18n squared + 57n -10

aniked [119]

Most people use the decomposition method but i dont know how to do that so i use the Joes method a method similar to decomp. but easier.
canadian way

Find gcf: None
complet trinomial: 18n^2+57-10
find the product=10(18)
=-180
find the sum =57
-3 and 60 goes into both meaning if you multiply 3 and60 you get -180 and if you add them you get 57.

so (n-3)(n+60)
divide by a in this case it 18
so (n-3)(n+60)
18 18
do not divide. treat it like a fraction so you reduce it to lowest terms
(n-3)(n-3)
 18 10
 at this point its reduced to lowest terms so now you take the deniminator and move it beside the "n"

=(18n-3)(10n-3)

therefore your answer is (18n-3)(10n-3)
I hoped this helped :)

3 0

3 years ago

Answers: A.5 B.9 C.10 D.13 Need the answer ASAP

maw [93]

Answer:

x = 5

Step-by-step explanation:

See attached image.

8 0

2 years ago

Complete the inequality statement. 8 ___ 8 > < =

murzikaleks [220]

Answer:

8 = 8

Step-by-step explanation:

If the numbers are the same, they are equal ( = )

7 0

2 years ago

Use the given information to solve the triangle for A = 150°, b = 4.8, a = 9.4

ELEN [110]

Well you can start by drawing a triangle with the information

the size of angle B can be found using the Law of Sine

$\frac{sin(150)}{9.4)} = \frac{sin(B)}{4.8}$

the size of angle C can be found using angle sum of a triangle.

The length of side c can be found using the Law of Cosines

$c^2 = 4.8^2 + 9.4^2 - 2 \times4.8\times9.4\times cos(C)$

hope it helps

7 0

3 years ago