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dusya [7]
3 years ago
7

F(x) = { x + 7 and g(x) = -x + 7 What transformation occurs from function f to function g?

Mathematics
1 answer:
Triss [41]3 years ago
5 0
<h3>Answer:  Reflect over the y axis</h3>

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

Explanation:

We have these two given functions

  • f(x) = x+7
  • g(x) = -x+7

The change is that the x has been replaced with -x

We can say

f(x) = x+7

f(-x) = -x+7 ... replace each x with -x

g(x) = f(-x)

g(x) = -x+7

When we replace x with -x, we're flipping the x inputs from positive to negative, and vice versa. This visually will reflect the line over the vertical y axis. A point like (1,8) on f(x) reflects over to (-1,8) on g(x).

As another example, the point (-5,2) on f(x) reflects over the y axis to arrive at (5,2) on the g(x) function.

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3 years ago
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Graph the image of this figure after a dilation with a scale factor of 2 centered at (2, 2).
Maru [420]

Answer:

(-6,6), (0,12), (4,8)

Step-by-step explanation:

To dilate an object, we need to multiply the x and y values by the given scale factor.

In this case the scale factor is 2 --> 2(x, y)

Before-> After dilation

2(-3,3) = (-6,6)

2(0,6) = (0,12)

2(2,4) = (4,8)

Please leave a 'thanks' if this helps!

6 0
3 years ago
the average starting salary for this year's graduates at a large university (lu) is $55,000 with a standard deviation of $6,000.
alexira [117]

0.84% of the graduates will receive the tax break

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean  and standard deviation , the z-score of a measure X is given by:

Z = x - μ / σ

Z-scores are used to measure how far a measure is from the mean. We find the p-value associated with this Z-score by looking at the z-score table after finding the Z-score. The p-value represents the probability that the measure is smaller than X, which is the percentile of X. The probability of the measure being greater than X is calculated by subtracting 1 from the pvalue.

μ = $55,000 σ = $6,000

This is the pvalue of Z when X = $39,600. So

z = 39600 - 55000 / 6000

z = -2.5

z = -2.5 has a o value of 0.0084

0.84% of the graduates will receive the tax break.

To learn more about similar tax break:

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7 0
1 year ago
2. In your own words, explain HOW to find the standard deviation of this data set. (20 points) 3. What does the standard deviati
Ket [755]

Answer:

\sigma = 11.28 --- Standard deviation

Step-by-step explanation:

Given

See attachment for graph

Solving (a): Explain how the standard deviation is calculated.

<u>Start by calculating the mean</u>

To do this, we divide the sum of the products of grade and number of students by the total number of students;

i.e.

\bar x = \frac{\sum fx}{\sum f}

So, we have:

\bar x = \frac{50 * 1 + 57 * 2 + 60 * 4 + 65 * 3 +72 *3 + 75 * 12 + 77 * 10 + 81 * 6 + 83 * 6 + 88 * 9 + 90 * 12 + 92 * 12 +95 * 2 + 99 * 4 + 100 * 5}{1 + 2 + 4 + 3 +3 + 12 + 10 + 6 + 6 + 9 + 12 + 12 +2 + 4 + 5}

\bar x = \frac{7531}{91}

\bar x = 82.76

Next, calculate the variance using the following formula:

\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f}

i.e subtract the mean from each dataset; take the squares; add up the squares; then divide the sum by the number of dataset

So, we have:

\sigma^2 = \frac{1 * (50 - 82.76)^2 +...................+ 5 * (100 - 82.76)^2}{91}

\sigma^2 = \frac{11580.6816}{91}

\sigma^2 = 127.26

Lastly, take the square root of the variance to get the standard deviation

\sigma = \sqrt{\sigma^2}

\sigma = \sqrt{127.26}

\sigma = 11.28 --- approximated

<em>Hence, the standard deviation is approximately 11.28</em>

Considering the calculated mean (i.e. 82.76), the standard deviation (i.e. 11.28) is small and this means that the grade of the students are close to the average grade.

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2 years ago
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Alinara [238K]
Answer: X=12
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