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Marina CMI [18]
3 years ago
9

Question 7 PLEASE HELP Describe the transformation from the graph of f(x) =x to the graph of g(x)=1/5x+4 A: The transformations

are a rotation and a translation. B: The transformations are a translation, A reflection, and a rotation. C The transformations are a translation and a reflection. D The transformations are a rotation and a reflection

Mathematics
1 answer:
Elis [28]3 years ago
7 0

Answer:

  A: The transformations are a rotation and a translation.

Step-by-step explanation:

The function f(x) is shown in the attachment as a dashed red line. The function g(x) is shown as the blue line.

The two lines have different slopes. The change in slope can be accomplished by horizontal or vertical scaling, or by rotation. The offered answer choices only include <em>rotation</em> as an option for changing the slope.

The two lines have different intercepts. To move the line from one intercept to another, generally translation is involved.

The simplest transformation is rotation and translation.

_____

<em>Comment on the answer choices</em>

If the reflection is done across a line other than an axis, or if the rotation is done about a point other than the origin, then <em>any combination of rotation, reflection, and translation can be used to make the transformation seen</em>. (Translation alone is not sufficient.)

For example, reflecting the line across the bisector of the angle between the lines (a line with a slope of (√13 -2)/3 through (5, 5)) will give the desired transformation in one step.

Similarly, a rotation of about 33.69° about the point (5, 5) will give the transformation in on step. (That angle is 45°-arctan(1/5).)

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The answer in binary is 10
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2 years ago
How many 3/4 -centimeter cubes do you need to create a cube with an edge length of 12 centimeters?
zzz [600]
To make a LINE that is 12 cm long, you'd need (12 / .75) cubes or sixteen cubes.
To make a CUBE you'd need 16^3 cubes or 16*16*16 cubes or 4,096 three quarter centimeter cubes.

3 0
3 years ago
Do the ratios 10/8 and 16/20 form a proportion<br><br> Yes or no?
ziro4ka [17]

Answer:

No. Reduce 10/8 by dividing by 2. 10/8= 5, 8/2= 4. 10/8= 5/4. Reduce 16/20 by dividing by 4. 16/4= 4 , 20/4= 5. 16/20= 4/5.

6 0
3 years ago
Suppose the horses in a large stable have a mean weight of 975lbs, and a standard deviation of 52lbs. What is the probability th
Lubov Fominskaja [6]

Answer:

0.8926 = 89.26% probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

\mu = 975, \sigma = 52, n = 31, s = \frac{52}{\sqrt{31}} = 9.34

What is the probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable?

pvalue of Z when X = 975 + 15 = 990 subtracted by the pvalue of Z when X = 975 - 15 = 960. So

X = 990

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{990 - 975}{9.34}

Z = 1.61

Z = 1.61 has a pvalue of 0.9463

X = 960

Z = \frac{X - \mu}{s}

Z = \frac{960 - 975}{9.34}

Z = -1.61

Z = -1.61 has a pvalue of 0.0537

0.9463 - 0.0537 = 0.8926

0.8926 = 89.26% probability that the mean weight of the sample of horses would differ from the population mean by less than 15lbs if 31 horses are sampled at random from the stable

7 0
3 years ago
Need answer for this ratios question
Tom [10]

Answer: 4:1

Step-by-step explanation: I think the answer is 4:1. I think this because 20% of 2500, would be 500. So 2500-500=2000. So the ratio would be 2000:500. Then we simplify 2000:500, by dividing 2000 by 500, and dividing 500 by 500. 500 / 500 = 1. 2000 / 500 = 4, so the answer is 4:1. (I am sorry if I am incorrect)

7 0
2 years ago
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