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Aleks [24]
3 years ago
14

The population of a small town in central Florida has shown a linear decline in the years 1992-2000. In 1992 the population was

48000 people. In 2000 it was 44880 people.
A) Write a linear equation expressing the population of the town P
P
in terms of t
t
, the number of years since 1992.
Answer: c

B) If the town is still experiencing a linear decline, what will the population be in 2003?
Mathematics
1 answer:
wlad13 [49]3 years ago
7 0

Answer:

  • P = -390t +48,000
  • P = 43,710 in 2003

Step-by-step explanation:

A) We are given two pairs of (t, P): (0, 48000), (8, 44880). We can use these with the 2-point form of the equation of a line:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  P = (44880 -48000)/(8 -0)(t -0) +48000

  P = -3120/8t +48000

  P = -390t +48000

__

B) In 2003, t = 11, so we have ...

  P = -390(11) +48000 = 43710

The population in 2003 is predicted to be 43,710.

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Suppose the speeds of cars along a stretch of I-40 is normally distributed with a mean of 70 mph and standard deviation of 5 mph
neonofarm [45]

Answer:

a) 68%.

b) 84%.

c) Approximately 2.5% of cars are traveling at a speed greater than or equal to 80 mph.

d) Approximately 2.5% of cars are traveling at a speed greater than or equal to 80 mph.

e) Between 60 mph and 80 mph.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean of 70 mph, standard deviation of 5 mph.

(a) Approximately what percent of cars are travelling between 65 and 75 mph?

70 - 5 = 65

70 + 5 = 75

Within 1 standard deviation, so approximately 68%.

(b) If the speed limit on this stretch of highway is 65 mph, approximately what percent of cars are traveling faster than the speed limit?

The normal distribution is symmetric, which means that 50% of the measures are below the mean, and 50% are above.

65 is one standard deviation below the mean, so of the cars below the mean, 68% are above 65 mph.

0.68*50% + 50% = 34% + 50% = 84%.

84%.

(c) What percent of cars are traveling at a speed greater than or equal to 80 mph?

80 = 70 + 2*10

2 standard deviations above the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean. Due to the symmetry of the normal distribution, of the other 5%, 2.5% is at least 2 standard deviations below the mean and 2.5% is at least 2 standard deviations above the mean. Then:

Approximately 2.5% of cars are traveling at a speed greater than or equal to 80 mph.

(d) What percent of cars are traveling at a speed greater than 80 mph?

Same as item c, as in the normal distribution, the probability of an exact value is considered to be 0.

(e) 95% of cars are traveling between what two speeds?

Within two standard deviations of the mean.

70 - 2*5 = 60 mph

70 + 2*5 = 80 mph.

Between 60 mph and 80 mph.

6 0
2 years ago
Solve 2w^2– 16w = 12W – 48 by factoring. Select the solution(s)
UkoKoshka [18]

Answer:

w=12 or w=2

Step-by-step explanation:

2w^2-16w=12w-48

2w^2-28w=-48

2w^2-28w+48=0

2(w^2-14w+24)=0

2(w-12)(w-2)=0

(w-12)(w-2)=0

w=12 or w=2

3 0
2 years ago
Celia ate 5/8 of a pizza what decimal is equivalent to the fraction of pizza celia ate
Naddik [55]

Answer:

0.625

Step-by-step explanation:

5÷8=0.625

This is equal to the number of pizzas Celia ate.

plz mark me as brainliest.

8 0
2 years ago
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the lombaro family went out to dinner and the cost of their meal was 62% if they left a 20% tip how much did they leave
swat32

Answer:

they left a $1.24 tip

Step-by-step explanation:


3 0
3 years ago
Violet contributes 12% of her $55,700 annual salary to her 401(k) plan. What is her pretax income?
NikAS [45]
You have that:

 - Her contribution from her salary <span>to her 401(k) plan, </span>is: 12%.
 - Her annual salary is: $55,700.

 Then, to solve this problem and calculate her pretax income, you must following the steps below:

 1. You must calculate the amount that Violet contributed to her 401(k) plan. So, you have:

 12%/100=0.12

 ($55,700x0.12)=$6,684 

 2. Now, you must subtract her annual pay ($55,700) by the amount obtained ($6,684), as below:

 Pretax income= $55,700-$6,684
<span> Pretax income=$49,016
</span><span>
 What is her pretax income?

 The answer is: Her pretax income is </span>$49,016
7 0
3 years ago
Read 2 more answers
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