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BlackZzzverrR [31]
2 years ago
8

Which one is steeper? y=3x+7 y=1/2x+9

Mathematics
1 answer:
Nutka1998 [239]2 years ago
8 0

Option a is more steeper

The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept form formula is used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).

According to the slope intercept form of equation

   y = mx + c

where m = slope of the line

            c = y-intercept

the steeping of the graph is determined by the slope of the line on the graph. The more is the value of the slope the more steeper the graph will be of the given line.

In option a: m=3 whereas option b: m=1/2

So y=3x+7 is more steeper

Learn more about slopes and straight lines here :

brainly.com/question/28453709

#SPJ9

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Power +, Inc. produces AA batteries used in remote-controlled toy cars. The mean life of these batteries follows the normal prob
Novay_Z [31]

Answer:

a) By the Central Limit Theorem, it is approximately normal.

b) The standard error of the distribution of the sample mean is 1.8333.

c) 0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d) 0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours

e) 0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

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 normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score 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 p-value, 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.

Mean of 36 hours and a standard deviation of 5.5 hours.

This means that \mu = 36, \sigma = 5.5

a. What can you say about the shape of the distribution of the sample mean?

By the Central Limit Theorem, it is approximately normal.

b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)

Sample of 9 means that n = 9. So

s = \frac{\sigma}{\sqrt{n}} = \frac{5.5}{\sqrt{9}} = 1.8333

The standard error of the distribution of the sample mean is 1.8333.

c. What proportion of the samples will have a mean useful life of more than 38 hours?

This is 1 subtracted by the pvalue of Z when X = 38. So

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

By the Central Limit Theorem

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

Z = \frac{38 - 36}{1.8333}

Z = 1.09

Z = 1.09 has a pvalue of 0.8621

1 - 0.8621 = 0.1379

0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.

d. What proportion of the sample will have a mean useful life greater than 34.5 hours?

This is 1 subtracted by the pvalue of Z when X = 34.5. So

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

Z = \frac{34.5 - 36}{1.8333}

Z = -0.82

Z = -0.82 has a pvalue of 0.2061.

1 - 0.2061 = 0.7939

0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.

e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?

pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So

0.8621 - 0.2061 = 0.656

0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours

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Would you rather have 1 of 8 slices from a 10" pizza or 1 of 10 slices from a 14" pizza?
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1 8 of a pizza you get more
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Garth estimated the height of the door ti his classroom in meters. what is a reasonable estimate?
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2 because 3 meters is labor 6 feet and 2 is above 5'9'' so it's kinda understandable
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What is the slope of the line through (1,0) and (3,8)
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Slope = (y2 - y1)/(x2 - x1)

Slope = (8 - 0)/(3 - 1)

Slope = 8/2

Slope = 4


Answer

4

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Luda [366]

We need to graph the given piecewise function.

To graph any piecewise function we do that into parts

Let's graph upper part first which is

f(x)=x^2+2

restriction for that is -5 \leq x < 3

that means we are free to pick any number for x that is between -5 and 3, including 3.

So we will find few points by plugging random numbers between -5 and 3.

Let's use x=-5, we get:

f(-5)=(-5)^2+2=25+2=27

so first point is (-5,27).

similarly we can find other points like (0,2), (2,6), (-1,3) etc.

Now we join those points by a curved line.

-5 \leq x means we use a close circle at -5

x<3 means use open circle at 3


------------

Repeat same process for 2nd part f(x)=x-4

choose any number between 3 and 7 like x=3, 4 etc

so we get points (3,-1), (4,0) etc

Now graph them

So the final graph will look like:


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