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2 years ago

BF is dilated to created WH. The center of dilation is point A where BF=15, WH=20

Mathematics

2 answers:

LekaFEV [45]2 years ago

7 0

Answer:

The scale factor is 4/3

Step-by-step explanation:

Let x = the scale factor

15x = 20 Divide both sides by 15

x =20/15 Which simplifies to 4/3

denis-greek [22]2 years ago

5 0

The scale factor that was used to create WH will be 4/3.

<h3>What is the scale factor?</h3>

The scale factor is defined as the proportion of the new image's size to that of the previous image decision-making. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

Given that BF is dilated to create WH. The center of dilation is point A where BF=15, WH=20

The scale factor will be calculated as below:-

Let x = the scale factor

15x = 20

Divide both sides by 15

x =20/15

Which simplifies to 4/3.

x = 4 / 3

Therefore, the scale factor that was used to create WH will be 4/3.

To know more about scale factors follow

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Sofia and Diego drive to work. Sofia drives 72 miles in 1.5 hours. Diego drives 126 km in 2 hour 30 min. Work out the difference

sdas [7]

Answer:

26.4 km/hr

Step-by-step explanation:

Sofia and Diego drive to work.

For Sofia

We convert miles to km

Sofia drives 72 miles in 1.5 hours.

1 mile = 1.6 km

72 miles = x

x = 72 × 1.6 km

x = 115.2 km

We find the speed in km/hr

Speed = Distance /Time

= 115.2km/1.5 hours

= 76.8 km/hr

For Diego

Diego drives 126 km in 2 hour 30 min.

Speed = Distance/Time

Time = 2 hour 30 min = 2.5 hours

Speed = 126km/2.5 hours

= 50.4 km/hr

The difference between their average speeds in km/h is calculated as:

76.8 km/hr - 50.4 km/hr

= 26.4 km/hr

5 0

3 years ago

Use a normal approximation to find the probability of the indicated number of voters. In this case, assume that 104 eligible vot

crimeas [40]

Answer:

The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed 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.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this case, assume that 104 eligible voters aged 18-24 are randomly selected.

This means that $n = 104$ .

Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.

This means that $p = 0.22$

Mean and standard deviation:

$\mu = 104*0.22 = 22.88$

$\sigma = \sqrt{104*0.22*0.78} = 4.2245$

Probability that exactly 27 voted

By continuity continuity, 27 consists of values between 26.5 and 27.5, which means that this probability is the p-value of Z when X = 27.5 subtracted by the p-value of Z when X = 26.5.

X = 27.5

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

$Z = \frac{27.5 - 22.88}{4.2245}$

$Z = 1.09$

$Z = 1.09$ has a p-value of 0.8621

X = 26.5

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

$Z = \frac{26.5 - 22.88}{4.2245}$

$Z = 0.86$

$Z = 0.86$ has a p-value of 0.8051

0.8621 - 0.8051 = 0.057

The probability that exactly 27 of 104 eligible voters voted is 0.057 = 5.7%.

5 0

3 years ago

At the start of the school year, students in Mr. Pi’s class were asked the

kupik [55]

Answer:

No, there is not enough information to determine how many students were absent that particular morning.

Explanation:

The probability of randomly selecting a student who answered the question “yes” is the number of students that responded yes divided by the number of students present. Thus, it was:

21/30 = 7/10

The probability of randomly selecting a student who answered the question “no” is the number of students who answered "no" divided by the number of students present. Thus, it was:

9/30 = 3/10

On one particular morning later in the year, the probability of randomly selecting a student who had answered the question “yes” was 3/4

The equivalent ratios to 3/4 will tell you the possible combinations of students that answered yes and students present on that particular morning.

For instance: 3/4 = 6/8

6/8 would mean that there were 6 students that answered yes and 8 total students on that particular morning.

Since more than half of class was present, the total number of students was greater than 15. Then, you must find a ratio with a denominator greater than 15 (and less than 30).

The other equivalent ratios to 3/4 are: 9/12, 12/16, 15/20, 18/24, 21/28, 24/32, ...

That means that the only possibilities with more than 15 and less than 30 present students are 12/16, 15/20, 18/24, and 21/28.

The total number of absents might have been:

30 - 28 = 2
30 - 24 = 6
30 - 20 = 10
30 - 16 = 14

Since at least one of the students who had answered “yes” was absent and at least one of the students who had answered “no” was absent, all the above possibilities are valid: there is not enough information to determine how many students were absent that particular morning; they could be 2, 6, 10, or 14.

7 0

3 years ago

Solve each system of linear equations by substitution

mariarad [96]

Answer:

x=-6-3y/2

Step-by-step explanation:

5 0

3 years ago

3. The average distance from the sun to the planet Jupiter is about 483,800.000. The average

MArishka [77]

Answer:

The answer to your question is:

a) sun to jupiter = 4.838 x 10 ⁸ miles

sun to earth = 9.296 x 10 ⁷ miles

b) 5.2 times

Step-by-step explanation:

distance sun to jupiter = 483 800 000 miles

distance sun to earth = 92 960 000 miles

sun to jupiter = 4.838 x 10 ⁸ miles just move the decimal point eight places to the left.

sun to earth = 9.296 x 10 ⁷ miles just move the decimal point seven places to the left.

divide distance sun to jupiter by distance sun to earth =

= 4.838 x 10 ⁸ / 9.296 x 10 ⁷

First divide 4.838 by 9.296 or 4.838 / 9.296 = 0.52

Then we substract the powers: 8 minus 7 or 8 -7 = 1

So we get 0.52 x 10¹ or 0.52 x 10 = 5.2 times

5 0

3 years ago