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IRISSAK [1]
3 years ago
8

The length of CD is 12 units C’D’ is the image of CD under a dilation with a scale factor of n.Which of these are true?

Mathematics
1 answer:
Korvikt [17]3 years ago
8 0

Answer: FIrst option, Fourth option and Fifth option.

Step-by-step explanation:

First it is important to know the definition of "Dilation".

A Dilation is defined as a transformation in which the Image (which is the figure obtained after the transformation) and the Pre-Image (this is the original figure, before the transformations) have the same shape, but their sizes are different.

If the length of CD is dilated with a scale factor of "n" and it is centered at the origin, the length C'D' will be:

C'D'=nCD=(n)(12\ units)

Therefore, knowing this, you can determine that:

1. If n=\frac{3}{2} , you get:

C'D'=(\frac{3}{2})(12\ units)=18\ units

2. If n=4, then the length of C'D' is:

C'D'=(4)(12\ units)=48\ units

3. If n=8, then:

C'D'=(8)(12\ units)=96\ units

4. If n=2, then, you get that the lenght of C'D' is:

C'D'=(2)(12\ units)=24\ units

5. If n=\frac{3}{4}, the length of C'D' is the following:

C'D'=(\frac{3}{4})(12\ units)=9\ units

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The midpoint of AB is M(-5,1). If the coordinates of A are (-4,-5), what are the coordinates of B?
Elenna [48]

<u>ANSWER:</u>

The midpoint of AB is M(-5,1). The coordinates of B are (-6, 7)

<u>SOLUTION: </u>

Given, the midpoint of AB is M(-5,1).  

The coordinates of A are (-4,-5),  

We need to find the coordinates of B.

We know that, mid-point formula for two points A(x_{1}, y_{1}) and B (x_{1}, y_{2}) is given by

M\left(x_{3}, y_{3}\right)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)

Here, in our problem, \mathrm{x}_{3}=-5, \mathrm{y}_{3}=1, \mathrm{x}_{1}=-4 \text { and } \mathrm{y}_{1}=-5

Now, on substituting values in midpoint formula, we get

(-5,1)=\left(\frac{-4+x_{2}}{2}, \frac{-5+y_{2}}{2}\right)

On comparing, with the formula,

\frac{-4+x_{2}}{2}=-5 \text { and } \frac{-5+y_{2}}{2}=1

-4+\mathrm{x}_{2}=-10 \text { and }-5+\mathrm{y}_{2}=2

\mathrm{x}_{2}=-6 \text { and } \mathrm{y}_{2}=7

Hence, the coordinates of b are (-6, 7).

5 0
3 years ago
16. A telemarketer makes six phone calls per hour and is able to make a sale on 30% of these contacts. During the next two hours
Reika [66]

Answer:

a) 23.11% probability of making exactly four sales.

b) 1.38% probability of making no sales.

c) 16.78% probability of making exactly two sales.

d) The mean number of sales in the two-hour period is 3.6.

Step-by-step explanation:

For each phone call, there are only two possible outcomes. Either a sale is made, or it is not. The probability of a sale being made in a call is independent from other calls. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

A telemarketer makes six phone calls per hour and is able to make a sale on 30% of these contacts. During the next two hours, find:

Six calls per hour, 2 hours. So

n = 2*6 = 12

Sale on 30% of these calls, so p = 0.3

a. The probability of making exactly four sales.

This is P(X = 4).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 4) = C_{12,4}.(0.3)^{4}.(0.7)^{8} = 0.2311

23.11% probability of making exactly four sales.

b. The probability of making no sales.

This is P(X = 0).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{12,0}.(0.3)^{0}.(0.7)^{12} = 0.0138

1.38% probability of making no sales.

c. The probability of making exactly two sales.

This is P(X = 2).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{12,2}.(0.3)^{2}.(0.7)^{10} = 0.1678

16.78% probability of making exactly two sales.

d. The mean number of sales in the two-hour period.

The mean of the binomia distribution is

E(X) = np

So

E(X) = 12*0.3 = 3.6

The mean number of sales in the two-hour period is 3.6.

4 0
3 years ago
Assume that the amount of beverage in a randomly selected 16-ounce beverage can has a normal distribution. Compute a 99% confide
ioda

Answer:

The question is incomplete, but the step-by-step procedures are given to solve the question.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.99}{2} = 0.005

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.005 = 0.995, so Z = 2.575.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 2.575\frac{\sigma}{\sqrt{n}}

The lower end of the interval is the sample mean subtracted by M.

The upper end of the interval is the sample mean added to M.

The 99% confidence interval for the population mean amount of beverage in 16-ounce beverage cans is (lower end, upper end).

7 0
3 years ago
The first discount on a camera was 18%. The second discount was 20%. After these two discounts the price was $328. What was the
Artyom0805 [142]

Answer:

$500

Step-by-step explanation:

We can find the original price of the camera through a proportion. A proportion is an equation where two ratios or fractions are equal. The ratios or fractions compare like quantities.

<u>Second Discount</u>

20% off means we paid 80%. We know we paid $328 of some price.

\frac{80}{100} =\frac{328}{y}

I can now cross-multiply by multiplying numerator and denominator from each ratio.

80y=100(328)\\80y=32800

I now solve for y by dividing by 80.

\frac{80y}{80} =\frac{32800}{80} \\y= $410

The price after the first discount was $410.

<u>First Discount</u>

We will repeat the steps above with $410. 18% off means we paid 82%.

\frac{82}{100} =\frac{410}{y}

I can now cross-multiply by multiplying numerator and denominator from each ratio.

82y=100(410)\\82y=41000

I now solve for y by dividing by 82.

\frac{82y}{82} =\frac{41000}{82} \\y= $500

The original price was $500.


5 0
3 years ago
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(a-b)(a+b) because when you reverse the sum you do axa and ax-b xx
5 0
3 years ago
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