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2 years ago

15

the U.S. Census Bureau states that in 2010 the average commute time for Wake County workers was 23.9 minutes and in 2016 the ave

rage was 25 minutes. What was the percentage increase in average commute times between these years? Write your answer as a percentage rounded to two decimal places, but do not include the % symbol.

1 answer:

DIA [1.3K]2 years ago

3 0

<h3>Answer: 4.60%</h3>

====================================================

Explanation:

We'll ignore the year numbers (2010 and 2016).

The difference in time values is 25-23.9 = 1.1 minutes

Divide this over the first time value to get (1.1)/(23.9) = 0.046025

Moving the decimal point over to the right 2 spots gets us 4.6025% which then rounds to 4.60% when rounding to two decimal places.

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

As a way to verify the answer:

4.60% of 23.9 = 0.046*23.9 = 1.0994

Increasing by 4.60% means the time value has increased by roughly 1.0994 minutes. So we go from 23.9 to 23.9+1.0994 = 24.9994 which is fairly close to 25 minutes. There's a bit of rounding error, but we have effectively confirmed the answer.

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Sarah competes in a long jump competition Her first jump is 4.25m Her best jump is 12% more than this However, her best jump is

ad-work [718]

>First jump = 4.25 m

>Best jump = 1.12 * First jump

Best jump = 1.12 * (4.25 m)

Best jump = 4.76 m

>Best jump = 0.85 * Winning jump

Hence,

Winning jump = Best jump / 0.85

Winning jump = 4.76 m / 0.85

<span>Winning jump = 5.6 m</span>

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2 years ago

Assume the sample variances to be continuous measurements. Find the probability that a random sample of 25observations, from a n

konstantin123 [22]

Answer:

a) $P(4S^2 > 4*9.1) = P(\chi^2_{24} >36.4) = 0.0502$

b) $P(13.848$ Step-by-step explanation:

Previous concepts

The Chi Square distribution is the distribution of the sum of squared standard normal deviates .

For this case we assume that the sample variance is given by $S^2$ and we select a random sample of size n from a normal population with a population variance $\sigma^2$ . And we define the following statistic:

$T = \frac{(n-1) S^2}{\sigma^2}$

And the distribution for this statistic is $T \sim \chi^2_{n-1}$

For this case we know that n =25 and $\sigma^2 = 6$ so then our statistic would be given by:

$\chi^2 = \frac{(n-1)S^2}{\sigma^2}=\frac{24 S^2}{6}= 4S^2$

With 25-1 =24 degrees of freedom.

Solution to the problem

Part a

For this case we want this probability:

$P(S^2 > 9.1)$

And we can multiply the inequality by 4 on both sides and we got:

$P(4S^2 > 4*9.1) = P(\chi^2_{24} >36.4) = 0.0502$

And we can use the following excel code to find it: "=1-CHISQ.DIST(36.4,24,TRUE)"

Part b

For this case we want this probability:

$P(3.462 < S^2$

If we multiply the inequality by 4 on all the terms we got:

$P(3.462*4 < 4S^2 < 4*10.745)= P(13.848< \chi^2$ And we can find this probability like this: $P(13.848$ And we use the following code to find the answer in excel: "=CHISQ.DIST(42.98,24,TRUE)-CHISQ.DIST(13.848,24,TRUE)"

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2 years ago

using compound interest, how long does it take to double a 1000 dollar investment that pays 6.5% annual interest, compounded mon

KonstantinChe [14]

Answer:

11 years approx

Step-by-step explanation:

Given data

P=$1000

A=2000

R=6.5%

T= ?

Calculate time, solve for t

t = ln(A/P) / r

substitute

t=ln(2000/1000)/0.065

t=ln(2)/0.065

t=0.693/0.065

t=10.66

Hence the time is 11 years approx

3 0

3 years ago

(with steps please) Find the inverse Laplace transform, f(t), of the function: 16/(s-4)^3

Stells [14]

Answer: The required inverse transform of the given function is

$f(t)=8t^2e^{4t}.$

Step-by-step explanation: We are given to find the inverse Laplace transform, f(t), of the following function :

$F(s)=\dfrac{16}{(s-4)^3}.$

We have the following Laplace formula :

$L\{t^ne^{at}\}=\dfrac{n!}{(s-a)^{n+1}}\\\\\\\Rightarrow L^{-1}\{\dfrac{1}{(s-a)^{n+1}}\}=\dfrac{t^ne^{at}}{n!}.$

Therefore, we get

$f(t)\\\\=L^{-1}\{\dfrac{16}{(s-4)^3}\}\\\\\\=16\times\dfrac{t^{3-1e^{4t}}}{(3-1)!}\\\\\\=\dfrac{16}{2}t^2e^{4t}\\\\\\=8t^2e^{4t}.$

Thus, the required inverse transform of the given function is

$f(t)=8t^2e^{4t}.$

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3 years ago

Santa gave kittens to 13 boys and girls. What is the ratio of kitten ears to kitten tails?

SVEN [57.7K]

Answer:

$Ratio = 2 : 1$

Step-by-step explanation:

Given

$Population = 13$ --- Boys & Girls

Required

Determine the ratio of the kitten ears to the tails

A kitten has 1 tail and 2 ears.

Assume each individual got 1 kitten each

This implies that,

$Number\ of\ tails= 1 * 13$

$Number\ of\ tails= 13$

$Number\ of\ ears= 2* 13$

$Number\ of\ ears= 26$

The ratio of ears to tail is then calculated as follows:

Ratio = Number of ears : Number of tails

This gives

$Ratio = 26 : 13$

Divide by 13

$Ratio = 26/13 : 13/13$

$Ratio = 2 : 1$

8 0

3 years ago