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AveGali [126]
3 years ago
14

Devon made a scale drawing of a triangle. He used a scale factor of 1/4 to draw the new triangle. How does each side of the new

triangle compare to the original?
A.Each side of the new triangle is 4 times shorter than the original.
B.Each side of the new triangle is 12 times shorter than the original.
C.Each side of the new triangle is 4 times longer than the original.
D.Each side of the new triangle is 12 times longer than the original.
Mathematics
2 answers:
Charra [1.4K]3 years ago
7 0
The answer is Option A.
Scale Factors
If the Scale Factor IS 1, the polygon stays the SAME.
(If an equilateral triangle has a side length of 8 and the scale factor is 1, the sides will stay at 8)
If the Scale Factor is MORE THAN 1, the polygon's sides INCREASE depending on what the scale factor is.
(If a square has a side length of 3 and the scale factor is 4, the sides will increase to 12)
If the Scale Factor is LESS THAN 1, the polygon's sides DECREASE depending on what the scale factor is.
(If a square has a side length of 5 and the scale factor is 1/2, the side lengths will decrease down to 0.5)
Therefore each side length of the new triangle is 4 times shorter than the original (Option A)
Viktor [21]3 years ago
7 0

Answer:

the answer is.......

A

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A circle with radius of 2cm sits inside a circle with radius of 4cm What is the area of the shaded region
Klio2033 [76]

ANSWER

12\pi \:  {cm}^{2}

EXPLANATION

We want to find the area of the shaded region.

We find the area of the smaller circle and subtract from the area of the larger circle.

Area of smaller circle is

a = \pi \: \times   2^{2}  = 4\pi

Area of larger circle is

A = \pi \:   \times {4}^{2}  = 16\pi

The area of the shaded region is:

16\pi - 4\pi = 12\pi

5 0
3 years ago
Jill’s bowling scores are approximately normally distributed with mean 170 and standard deviation 20, while Jack’s scores are ap
miss Akunina [59]

Answer:

a) The probability of Jack scoring higher is 0.3446

b) They probability of them scoring above 350 is 0.2119

Step-by-step explanation:

Lets call X the random variable that determines Jill's bowling score and Y the random variable that determines jack's. We have

X \simeq N(170,400)\\Y \simeq N(160,225)

Note that we are considering the variance on the second entry, the square of the standard deviation.

If we have two independent Normal distributed random variables, then their sum is also normally distributed. If fact, we have this formulas:

N(\lambda_1, \sigma^2_1) + N(\lambda_2, \sigma^2_2) = N(\lambda_1 + \lambda_2,\sigma^2_1 + \sigma^2_2) \\r* N(\lambda_1, \sigma^2_1) = N(r\lambda_1,r^2\sigma^2_1)  

for independent distributions N(\lambda_1, \sigma^2_1) , N(\lambda_2, \sigma^2_2) , and a real number r.

a) We define Z to be Y-X. We want to know the probability of Z being greater than 0. We have

Z = Y-X = N(160,225) - N(170,400) = N(160,225) + (N(-170,(-1)^2 * 400) = N(-10,625)

So Z is a normal random variable with mean equal to -10 and vriance equal to 625. The standard deviation of Z is √625 = 25.

Lets work with the standarization of Z, which we will call W. W = (Z-\mu)/\sigma = (Z+10)/25. W has Normal distribution with mean 0 and standard deviation 1. We have

P(Z > 0) = P( (Z+10)/25 > (0+10)/25) = P(W > 0.4)

To calculate that, we will use the <em>known </em>values of the cummulative distribution function Φ of the standard normal distribution. For a real number k, P(W < k) = Φ(k). You can find those values in the Pdf I appended below.

Since Φ is a cummulative distribution function, we have P(W > 0.4) = 1- Φ(0.4)

That value of Φ(0.4) can be obtained by looking at the table, it is 0.6554. Therefore P(W > 0.4) = 1-0.6554 = 0.3446

As a result, The probability of Jack's score being higher is 0.3446. As you may expect, since Jack is expected to score less that Jill, the probability of him scoring higher is lesser than 0.5.

b) Now we define Z to be X+Y Since X and Y are independent Normal variables with mean 160 and 170 respectively, then Z has mean 330. And the variance of Z is equal to the sum of the variances of X and Y, that is, 625. Hence Z is Normally distributed with mean 330 and standard deviation rqual to 25 (the square root of 625).

We want to know the probability of Z being greater that 350, for that we standarized Z. We call W the standarization. W is s standard normal distributed random variable, and it is obtained from Z by removing its mean 330 and dividing by its standard deviation 25.

P(Z > 350) = P((Z  - 330)/25 > (350-330)/25) = P(W > 0.8) = 1-Φ(0.8)

The last equality comes from the fact that Φ is a cummulative distribution function. The value of Φ(0.8) by looking at the table is 0.7881, therefore P(X+Y > 350) = 1 - Φ(0.8) = 0.2119.

As you may expect, this probability is pretty low because the mean value of the sum of their combined scores is quite below 350.

I hope this works for you!

Download pdf
6 0
3 years ago
Baily has been measuring the growth of a flower. It has grown ¾ of an inch each week. It is now 3 inches tall. How many weeks ha
finlep [7]

Answer:

Step-by-step explanation:

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6 0
2 years ago
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Caden exercises daily by walking on a treadmill. He sets the machine so that he will walk at a steady rate of 3.6 miles per hour
babunello [35]

Answer:

a) d = 3.6t

b) 10.8 miles

c) 1.2 hours

Step-by-step explanation:

For part a:

Slope of a line: y = mx + b

In this case, the equation would be: d = mt,

where m represents the speed Caden is walking at.

Note: b = 0 in this case because when Caden starts walking on the treadmill, he hasn't really covered any distance yet.

Therefore, plugging in a speed of 3.6 miles per hour, the equation is:

d = 3.6t

For part b:

This is a simple instance of plugging in 3 hours for our t value.

Therefore, d = 3.6 (3)

d = 10.8 miles

For part c:

In this case, we are given that d = 4.32 miles.

Therefore, 4.32 = 3.6t

Dividing both sides by 3.6, we get

t = 1.2 hours

5 0
3 years ago
A shelf is built on a wall, as shown below. What is the value of x?<br> (2x+1) + (3x-1)
Hoochie [10]

Answer:

x = 18

Step-by-step explanation:

We need to find the value of x.

We know that the sum of angles of a triangle is equal to 180°. So, using this property,

2x+1+3x-1+90 = 180

2x+3x = 180-90

5x = 90

x = 18

So, the value of x is equal to 18.

6 0
2 years ago
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