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Paladinen [302]
3 years ago
13

Pre image ABCD was dilated to produce image A’B’C’D why is the scale factor from the pre image? Enter your answer in the box as

a fraction

Mathematics
1 answer:
shepuryov [24]3 years ago
7 0

The scale factor of the dilation from ABCD to A′B′C′D′ is 3.

Step-by-step explanation:

Step 1:

In the pre-image ABCD, the length of one of the sides is given as 14 units.

For the other shape A′B′C′D′, the same side as the previous shape is given as 8 units.

Step 2:

To determine the scale factor, we divide the measurement after scaling by the same measurement before scaling.

In this case, it is the given length of the sides CD and C′D′.

So the scale factor = \frac{C^{1} D^{1} }{CD} = \frac{8}{14} = \frac{4}{7} .

So the shape ABCD is dilated by a scale factor of \frac{4}{7} to produce the shape A′B′C′D′.

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I need help on B and C. Not sure how I can solve those. Can someone please help me out here? Thank you for your help!
Valentin [98]

Nice job with part A on getting those correct answers.

====================================================

Part B

  • mu = mean = 43
  • sigma = standard deviation = 3

Let's calculate the z score for the raw score x = 37

z = (x - mu)/sigma

z = (37 - 43)/3

z = -6/3

z = -2

A negative z score tells us we're below the mean. Specifically, we are exactly 2 standard deviations under the mean.

If you repeat those steps for x = 46 (not changing mu or sigma), then you should get z = 1. So we're now 1 standard deviation above the mean.

Ultimately, we want to know the area under the standard normal curve (aka z curve) from z = -2 to z = 1.

Refer to the chart below which is a breakdown of the Empirical Rule. The pink areas are within 1 standard deviation of the mean. We have two regions taking up roughly 34% of the full area under the curve, so they combine to 34+34 = 68%

Then we add on another 13.5% which is the blue area on the left (between z = -2 and z = -1)

So 13.5+68 = 81.5% of the area under the curve is between z = -2 and z = 1.

<h3>Answer: 81.5</h3>

Note: the percent sign is already taken care of for us, so there's no need to type it in. But the answer above of course means 81.5% and that answer is approximate.

====================================================

Part C

Let's find the z score for x = 34. The values of mu and sigma are the same as before.

z = (x - mu)/sigma

z = (34-43)/3

z = -9/3

z = -3

So computing P(X > 34) is the same as P(Z > -3)

Notice how adding up all of the values in the chart mentioned gets us:

2.35+13.5+34+34+13.5+2.35 = 99.7

which means 99.7% of the distribution is within 3 standard deviations of the mean. The remaining 100% - 99.7% = 0.3% is the combined area of both tails. So each tail is (0.3%)/2 = 0.15%

In short, 0.15% of the area under the curve is to the left of z = -3

Therefore, 100% - 0.15% = 99.85% of the widgets are going to have z values larger than -3, which in turn means they have values larger than 34.

<h3>Answer: 99.85</h3>

Again you don't have to worry about the percent sign. Like before, the answer is approximate.

5 0
3 years ago
What is the union sets M= (1,7,10,11,15) and N=(5,15)?
katen-ka-za [31]

Answer: <em>(1,5,7,10,11,15)</em>

To get the union of two sets of numbers, all you do is combine the numbers from least to greatest. If a number repeats in the 2 sets, you only put it once.

7 0
3 years ago
Read 2 more answers
A youth club organizer is plannning a day trip for the club members. The cost of the trip is $330 and club has already saved $75
alexgriva [62]

Answer:

Step-by-step explanation:

330 = 21x + 75

7 0
3 years ago
PLEASE ANSWER At a basketball game, 75% of people attending were supporting the home team, while 25% were supporting the visitin
Rufina [12.5K]

75% = 0.75

750 people / 0.75 = 1,000 people

There were 1,000 total people attending the game

6 0
3 years ago
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Is 33, 56, and 66 and right triangle
GenaCL600 [577]

Answer:

No

Step-by-step explanation:

If you mean they are the sides lengths,

33^2+ 56^2 != 66^2

3136 != 4356

7 0
3 years ago
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