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2 years ago

If f(x) = x^2 is vertically stretched by a factor of 6 to g(x) and reflected over the x-axis, what is the equation for g(x)?

Mathematics

1 answer:

Orlov [11]2 years ago

4 0

Answer:

Option B

$g(x) = -6x^2$

Step-by-step explanation:

If the graph of the function $g(x)=cf(x)$ represents the transformations made to the graph of $y= f(x)$ then, by definition:

If $0$ then the graph is compressed vertically by a factor c.

If $|c| > 1$ then the graph is stretched vertically by a factor c

If $c$ then the graph is reflected on the x axis.

In this problem we have the function $f(x)=x^2$

We now that this function is vertically stretched by a factor of 6 to g(x) and reflected over the x-axis

Then $|c| =6 >0$ and $c=-6$

Therefore the graph of $g(x)$ is $g(x) = -6f(x)$

$g(x) = -6x^2$

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What is the equation of the line passing through (-2,-7) (4,23)

malfutka [58]

Answer:

The equation of line Passing through (2,3) and (4,7)

The slope of line is

4−2

7−3

The equation of line is y−7=2(x−4)

y−7=2x−8

2x−y−1=0

Step-by-step explanation:

5 0

2 years ago

The estimated daily living costs for an executive traveling to various major cities follow. The estimates include a single room

Alexandra [31]

Answer:

$\bar x = 260.1615$

$\sigma = 70.69$

The confidence interval of standard deviation is: $53.76$ to $103.25$

Step-by-step explanation:

Given

$n =20$

See attachment for the formatted data

Solving (a): The mean

This is calculated as:

$\bar x = \frac{\sum x}{n}$

So, we have:

$\bar x = \frac{242.87 +212.00 +260.93 +284.08 +194.19 +139.16 +260.76 +436.72 +355.36 +.....+250.61}{20}$

$\bar x = \frac{5203.23}{20}$

$\bar x = 260.1615$

$\bar x = 260.16$

Solving (b): The standard deviation

This is calculated as:

$\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}$

$\sigma = \sqrt{\frac{(242.87 - 260.1615)^2 +(212.00- 260.1615)^2+(260.93- 260.1615)^2+(284.08- 260.1615)^2+.....+(250.61- 260.1615)^2}{20 - 1}}$ $\sigma = \sqrt{\frac{94938.80}{19}}$

$\sigma = \sqrt{4996.78}$

$\sigma = 70.69$ --- approximated

Solving (c): 95% confidence interval of standard deviation

We have:

$c =0.95$

So:

$\alpha = 1 -c$

$\alpha = 1 -0.95$

$\alpha = 0.05$

Calculate the degree of freedom (df)

$df = n -1$

$df = 20 -1$

$df = 19$

Determine the critical value at row $df = 19$ and columns $\frac{\alpha}{2}$ and $1 -\frac{\alpha}{2}$

So, we have:

$X^2_{0.025} = 32.852$ ---- at $\frac{\alpha}{2}$

$X^2_{0.975} = 8.907$ --- at $1 -\frac{\alpha}{2}$

So, the confidence interval of the standard deviation is:

$\sigma * \sqrt{\frac{n - 1}{X^2_{\alpha/2} }$ to $\sigma * \sqrt{\frac{n - 1}{X^2_{1 -\alpha/2} }$

$70.69 * \sqrt{\frac{20 - 1}{32.852}$ to $70.69 * \sqrt{\frac{20 - 1}{8.907}$

$70.69 * \sqrt{\frac{19}{32.852}$ to $70.69 * \sqrt{\frac{19}{8.907}$

$53.76$ to $103.25$

8 0

2 years ago

You spin a spinner numbered 1 through 10. Find the probability of landing on an even<br> number.

DENIUS [597]

Answer:

probability of landing on purple and pink. Find the missing probability. get ... numbered 1 through 5. Predict how many times out of 240 spins the spinner is most likely to stop on an odd number. odd ... Answer: red marbles. D. 10 total blue marbles green marbles. 1 2 2 2 2 ... You receive a less expensive prize if you spin and.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A study dealing with health care issues plans to take a sample survey of 1500 Americans to estimate the mean dollar amount that

frutty [35]

Answer:

The population parameter of this study is the population mean.

Step-by-step explanation:

A population parameter is a numerical measure representing a certain characteristic of the population. For example, population mean, population variance, population proportion, and so on.

The population parameter is computed using all the values of the population.

The population parameter can be estimated using the sample statistic. If the value of the population parameter is not known, then a random sample of large size, say <em>n</em> ≥ 30 can be selected from the population and the statistic value can be computed. This statistic value is considered as the point estimate of the parameter. It is also known as the unbiased estimator of the parameter.

In this case the survey involved sampling of 1500 Americans to estimate the mean dollar amount that Americans spent on health care in the past year.

The sample selected is used to compute the sample mean dollar amount that Americans spent on health care.

So, the population parameter of this study is the population mean.

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2 years ago

What value can be written on the blank line to make the expressions equivalent?

KIM [24]

Hello!

I believe the number that can be written in the blank space above is 6.

48+54=6'(8+9)

The number written in the blank space is 6 because when you divide 48 and 54 by their numbers, 8 and 9, you will get an answer of 6 for both numbers.

48/8=6
54/9=6

So the number in the blank space would be 6.

I hope this helps!

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3 years ago

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