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3 years ago

Three years after purchase, a car is estimated to be worth

1 answer:

7 0

Y - value
x - year

$24000=a\cdot3+b\\
19000=a\cdot5+b\\\\
24000=3a+b\\
-19000=-5a-b\\
---------\\
5000=-2a\\
a=-2500\\\\
b+3\cdot(-2500)=24000\\
b-7500=24000\\
b=31500\\\\
\boxed{y=-2500x+31500}

$

a)
$f(x)=-2500x+31500\\
f(x+1)=-2500(x+1)+31500\\
f(x+1)=-2500x-2500+31500\\
f(x+1)=-2500x+29000\\\\
f(x)-f(x+1)=-2500x+31500-(-2500x+29000)\\
f(x)-f(x+1)=-2500x+31500+2500x-29000\\
f(x)-f(x+1)=\boxed{2500}$

b)
$f(0)=-2500\cdot0+31500=\boxed{31500}$

c)
$f(10)=-2500\cdot10+31500\\
f(10)=-25000+31500\\
f(10)=\boxed{6500}$

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2. To estimate the mean age for a population of 4000 employees, a simple random sample of 40 employees is selected. a. Would you

ANEK [815]

Answer:

Step-by-step explanation:

Size of the population, N = 4000

Size of the sample, n = 40

n/N = 40/4000 = 0.01

0.01 is less than 0.05 and hence we would not us the finite population correction factor in calculating the standard error of the mean.

Population standard deviation is σ = 8.2

So, the standard error of x’ using the finite population correction factor is give by

σ(x’) = √[(N - n)/(N - 1)] x (sigma/√n)

σ(x’) = √[(4000 - 40)/(4000 - 1)] x (8.2/√40)

σ(x’) = 1.29

Standard error of x’ without using the finite population correction factor is

σ(x’) = σ/√n

σ(x’) = 8.2/√40 = 1.2965

There is little difference between the two values of the standard error. So we can ignore the population correction factor.

Let the population mean be μ

Probability that the sample mean will be within =-2 of the population mean is

P(μ– 2 < x’ < μ + 2)

At x’ = μ – 2 , we have

z = (μ – 2 – μ)/1.2965

z = -1.54

at x’ = μ + 2, we have

z = (μ + 2 – μ)/1.2965

z = 1.54

So the required probability is

P(μ – 2 < x’ < μ + 2) = p(-1.54< z < 1.54)

P(μ – 2 < x’ < μ + 2) = p(z < 1.54) – p(z < -1.54)

P(μ – 2 < x’ < μ + 2) = 0.9382 – 0.0618

P(μ – 2 < x’ < μ + 2) = 0.8764

7 0

3 years ago

Is 9.55x10 to the 3rd power greater than less than or equal to 5,900

erastovalidia [21]

Answer:

See below.

Step-by-step explanation:

9.55 * 10^3 = 9550.

So it is greater than 5,900.

5 0

3 years ago

Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 68 miles per hour, with a standard

Vladimir79 [104]

About 99.7% of vehicles whose speeds are between 59 miles per hour and 77 miles per hour.

Empirical rule states that for a normal distribution, 68% lie within one standard deviations, 95% lie within two standard deviations, and 99.7% lie within three standard deviations of the mean.

Given that mean (μ) = 68 miles per hour, standard deviation (σ) = 3 miles per hour.

68% lie within one standard deviation = (μ ± σ) = (68 ± 3) = (65, 71).

Hence 68% of the vehicle speed is between 65 miles per hour and 71 miles per hour.

95% lie within two standard deviation = (μ ± 2σ) = (68 ± 2*3) = (62, 74).

Hence 95% of the vehicle speed is between 62 miles per hour and 74 miles per hour.

99.7% lie within three standard deviation = (μ ± 3σ) = (68 ± 3*3) = (59, 77).

Hence 99.7% of the vehicle speed is between 59 miles per hour and 77 miles per hour.

Find out more at: brainly.com/question/14468516

3 0

2 years ago

Read 2 more answers

A certain hybrid car has a mileage rating of 57 miles per gallon. if the car makes a trip of 293 miles, how many gallons of gaso

dlinn [17]

To determine the number of gallons of gasoline that is used, we need to know the rate of usage of gasoline. This rate would describe the number of gasoline in units of volume that is being used per distance in units of length. In this case, we need the rate in units of miles per gallon. From what is asked and the given values, we simply divide the rate to the the total distance that was traveled by the car. We calculate as follows:

Gallons of gasoline = 293 miles / 57 miles / gallon
Gallons of gasoline = 5.14 gallons

Therefore, about 5 gallons of gasoline was consumed by the hybrid car for a distance of 57 miles.

4 0

3 years ago

How do i figure out 9 1/6 - 8 5/6 and 10 3/4 - 6 4/4?

Westkost [7]

Answer:

1) $9\frac{1}{6}-8\frac{5}{6}=\frac{1}{3}$

2) $10\frac{3}{4}-6\frac{4}{4}=3\frac{3}{4}$

Step-by-step explanation:

You can convert he mixed numbers to improper fractions:

1. Multiply the whole number part by the denominator of the fraction.

2. Add the product obtained to the numerator.

3. The denominator does not change.

Then:

$9\frac{1}{6}=\frac{54+1}{6}=\frac{55}{6}\\\\8\frac{5}{6}=\frac{48+5}{6}=\frac{53}{6}\\\\10\frac{3}{4}=\frac{40+3}{4}=\frac{43}{4}\\\\6\frac{4}{4}=\frac{24+4}{4}=\frac{28}{4}$

Observe that, in each subtraction, the denominators are equal, then you can rewrite the denominator and subtract the numerators:

$1)\ \frac{55}{6}-\frac{53}{6}=\frac{55-53}{6}= \frac{2}{6}=\frac{1}{3} \\\\2)\ \frac{43}{4}-\frac{28}{4}=\frac{43-28}{4}= \frac{15}{4}$

Divide 15 by 4. The quotient will be 3 and the remainder 3.

Then:

$\frac{15}{4}=3\frac{3}{4}$

6 0

2 years ago