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sattari [20]
3 years ago
12

The United States Census Bureau uses demographic information to set a poverty threshold that is used in to determine how many Am

ericans are living in poverty based on annual income. For an individual on her own, the poverty threshold was $4,190 in 1980 and has increased by about $220 per year since then.
1. Which piece of information in the problem is a rate of change? What would that represent in a linear function modeling the poverty threshold?
2. When modeling information that changes with time, we almost never use the actual time--whether it's clock time or year--as input. Instead, we chose a beginning time for the problem and call that x=0. In this case, we would decide that x=0 corresponds to 1980 since that's the earliest time we have information for. In that case, what is the y-intercept for our function?
3. Write a linear function that describes the poverty threshold in dollars in terms of years after 1980. Then use your function to estimate the poverty threshold in 2010, and the year that it will pass $15,000 per year.
4. Use the Internet to find the most recent poverty threshold as set by the census bureau, and discuss how accurately your model predicted that value.
Mathematics
1 answer:
Svetlanka [38]3 years ago
7 0

Answer:

Increment in property per year ;

Slope of a linear function

Kindly check explanation for the rest of the answers.

Step-by-step explanation:

The rate of change is the increment in property value per year ; $220

Thsi corresponds to the gradient or slope of a linear function

If 1980 = x and x = 0

Recall :

y = bx + c

Where, b = slope = 220

x = year

y = property threshold

c = intercept value

In 1980, x = 0

y - intercept.

Put x = 0 into the equation :

4190 = 220x + c

4190 = 220(0) + c

4190 = c

3.)

The linear function becomes :

y = 220x + 4190

Property threshold in 2010:

x = 2010 - 1980 = 30

y = 220(30) + 4190

y = 6600 + 4190

y = 10,790

Property threshold in 2010

Year it will exceed 15000

15000 = 220x + 4190

15000 - 4190 = 220x

10810 = 220x

x = 10810 / 220

x = 49.136

That is, property threshold will exceed 15000 after 50 years

1980 + 50 = 2030

Year 2030

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Stels [109]

Answer:

P(X > 25) = 0.69

Step-by-step explanation:

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 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.

The sale prices for a particular car are normally distributed with a mean and standard deviation of 26 thousand dollars and 2 thousand dollars, respectively.

This means that \mu = 26, \sigma = 2

Find P(X>25)

This is 1 subtracted by the pvalue of Z when X = 25. So

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

Z = \frac{25 - 26}{2}

Z = -0.5

Z = -0.5 has a pvalue of 0.31

1 - 0.31 = 0.69.

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P(X > 25) = 0.69

4 0
3 years ago
Dean has a spinner that is divided into 4 equal sections are labeled 1, 2, 3, and 4. Dean spun the spinner 60 times. He recorded
ICE Princess25 [194]

Answer:

B

Step-by-step explanation:

Dean recorded the results of spinning the spinner 60 times:

  • Number  1 spun 12 times
  • Number  2 spun 17 times
  • Number  3 spun 15 times
  • Number  4 spun 16 times

The <u>experimental probability</u> is the ratio of the number of times an event occurs to the total number of trials or times the activity is performed.

Find all experimental probabilities:

P_{1}=\dfrac{12}{60}=\dfrac{1}{5}\\ \\P_{2}=\dfrac{17}{60}\\ \\P_3=\dfrac{15}{60}=\dfrac{1}{4}\\ \\P_4=\dfrac{16}{60}=\dfrac{4}{15}

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Inessa05 [86]

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Step-by-step explanation:

Cosatana

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2 years ago
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AlekseyPX

Answer:

B

C

F

D

H

A

G

E

Step-by-step explanation:

Ok. They are trying to reconstruct the smaller looking triangle in the bigger triangle using angle A as the common angle.

The first statement is always the given.

Second they constructed line segment XY into the bigger triangle so that XY is parallel to BC.

Third, from the construction of the parallel lines we can now find corresponding angles that are congruent. This would be the use of F.

Since we have all three angles in triangle AXY and triangle ABC, then the construction of the smaller triangle we made inside the bigger triangle is similar to the bigger triangle. So we have the triangles are similar. You could say E or D here in my opinion. This is choice D.

Fifth the creation of those fractions of sides being equal comes from us knowing the corresponding sides of similar triangles are proportional. This is choice H.

Things looked cut off for the sixth thing so I can't fully read it, but it is possible a substitution has occured.

The seventh thing is a congruence statement which can be proven by a congruence postulate. The only one listed is SAS. So that is G.

The last thing, since the triangle construction is congruent to the smaller triangle then we know the smaller triangle is also similar to the bigger triangle since the bigger one is also similar to the construction we made. I really think E and D is interchangeable. Choice E goes here.

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Answer:

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Step-by-step explanation:

3 0
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