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3 years ago

The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second.

Mathematics

1 answer:

pickupchik [31]3 years ago

5 0

Answer: first option.

Step-by-step explanation:

The ratio of the area of the triangles can be calculated as following:

$ratio_{(area)}=(\frac{l_1}{l_2})^2$

Where $l_1$ is the lenght of the given side of the smaller triangle and $l_2$ is the lenght of the given side of the larger triangle.

Therefore:

$ratio_{(area)}=(\frac{28}{32})^2=\frac{49}{64}$

It can be written as following:

$ratio_{(area)}=49:64$

The ratio of the perimeter is:

$ratio_{(perimeter)}=\frac{l_1}{l_2}$

Where $l_1$ is the lenght of the given side of the smaller triangle and $l_2$ is the lenght of the given side of the larger triangle.

Therefore:

$ratio_{(perimeter)}=\frac{28}{32}=\frac{7}{8}$

It can be written as following:

$ratio_{(perimeter)}=7:8$

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Consider a game in which players roll a number cube to determine the number of points earned. If a player rolls a prime number,

Aleksandr-060686 [28]

Answer:

The expected value of the points earned on a single roll in this game is $\dfrac{1}{6} = 0.1667$ .

Step-by-step explanation:

We are given that consider a game in which players roll a number cube to determine the number of points earned. If a player rolls a prime number, that many points will be added to the player’s total. Any other roll will be deducted from the player’s total.

Assuming that the numbered cube is a dice with numbers (1, 2, 3, 4, 5, and 6).

Here, the prime numbers are = 1, 2, 3 and 5

Numbers which are not prime = 4 and 6

This means that if the dice got the number 1, 2, 3 or 5, then that many points will be added to the player’s total and if the dice got the number 4 or 6, then that many points will get deducted from the player’s total.

Here, we have to make a probability distribution to find the expected value of the points earned on a single roll in this game.

Note that the probability of getting any of the specific number on the dice is $\dfrac{1}{6}$ .

Numbers on the dice (X) P(X)

+1 $\frac{1}{6}$

+2 $\frac{1}{6}$

+3 $\frac{1}{6}$

-4 $\frac{1}{6}$

+5 $\frac{1}{6}$

-6 $\frac{1}{6}$

Here (+) sign represent the addition in the player's total and (-) sign represents the deduction in the player's total.

Now, the expected value of X, E(X) = $\sum X \times P(X)$

= $(+1) \times \frac{1}{6} +(+2) \times \frac{1}{6} +(+3) \times \frac{1}{6} +(-4) \times \frac{1}{6} +(+5) \times \frac{1}{6} +(-6) \times \frac{1}{6}$

= $\frac{1}{6} + \frac{2}{6} + \frac{3}{6} - \frac{4}{6} + \frac{5}{6} - \frac{6}{6}$

= $\frac{1+2+3-4+5-6}{6}$

= $\frac{11-10}{6}= \frac{1}{6}$

Hence, the expected value of the points earned on a single roll in this game is $\frac{1}{6} = 0.1667$ .

4 0

3 years ago

Please help and thank you

s2008m [1.1K]

Answer:

Answer is(-1,-1)

Step-by-step explanation:

$given \: points \: are \:( 1, - 6) \: and \: ( - 3,4) \\ midpoint \: = (\frac{x1 + x2}{2} , \frac{y1 + y2}{2} ) \\ =( \frac{1 - 3}{2} , \frac{ - 6 + 4}{2} ) \\ (\frac{ - 2}{2} , \frac{ - 2}{2} ) \\ midpoint \: = ( - 1, - 1)$

 

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THANKS FOR GIVING ME THE OPPORTUNITY TO ANSWER YOUR QUESTION. 

3 0

3 years ago

you're 495 miles from home and you are driving toward home at an average of 45mph. How long will it take to drive home if you ma

LenaWriter [7]

11 hours because I did the math

7 0

3 years ago

What is the value of y in the equation 6 + y = −3?

oee [108]

The value of y is -9

6 0

3 years ago

A bag of potato chips is packaged at sea level (1.00 atm) and has

serg [7]

Answer:

406 ml

Step-by-step explanation:

P1V1 = P2V2

(1) (.315) = (.775)(V2)

V2 = .406

3 0

2 years ago