Ask question

Ask question

All categories

2 years ago

9

Theresa has hired Chuck and Diana to paint a fence. Diana can paint 150 fence posts in the same time it takes Chuck to paint 130

fence posts, which can be shown using the following relationship where d and c are the respective rates at which Diana and Chuck can paint fence posts: 150 over d equals 130 over c Also, Diana can paint 10 fence posts more per hour than Chuck. How many fence posts can Chuck paint per hour?

1 answer:

Alenkasestr [34]2 years ago

4 0

Answer: Chuck can paint 65 posts per hour.

Step-by-step explanation:

The data we have here is:

Diana can paint 150 fence posts in a time T

Chuck can pint 130 fence posts in a time T.

In one hour, Diana can paint 10 more fence posts than Chuck.

If D is the hourly rate of Daian, and C is the hourly rate for Chuck, we have:

D = 150/T

C = 130/T

D = C + 10

we can replace the last equation in the first one and geT:

C + 10 =150/T

C = 130/T

Now we can replace the bottom equation in the above one:

130/T + 10 = 150/T

10 = 150/T - 130/T = 20/T

T*10 = 20

T = 20/10 = 2

So T is 2 hours, then whe have:

D = 150post/2hours = 75 posts per hour.

C = 130 posts/2hours = 65 posts per hour.

You might be interested in

A new car has a sticker price of $20,950, while the invoice price paid was $18,750. What is the percentage markup?

stich3 [128]

About 12% (rounded up)

8 0

2 years ago

Read 2 more answers

A brewery produces cans of beer that are supposed to contain exactly 12 ounces. But owing to the inevitable variation in the fil

MArishka [77]

Answer:

$T \sim N (\mu = 6*12=72 , \sigma= \sqrt{6} *0.3=0.735)$

$P(T \leq 72) = P(Z< \frac{72-72}{0.735}) = P(Z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solutio to the problem

Let X the random variable that represent the amount of beer in each can of a population, and for this case we know the distribution for X is given by:

$X \sim N(12,0.3)$

Where $\mu=12$ and $\sigma=0.3$

For this case we select 6 cans and we are interested in the probability that the total would be less or equal than 72 ounces. So we need to find a distribution for the total.

The definition of sample mean is given by:

$\bar X = \frac{\sum_{i=1}^n X_i}{n} = \frac{T}{n}$

If we solve for the total T we got:

$T= n \bar X$

For this case then the expected value and variance are given by:

$E(T) = n E(\bar X) =n \mu$

$Var(T) = n^2 Var(\bar X)= n^2 \frac{\sigma^2}{n}= n \sigma^2$

And the deviation is just:

$Sd(T) = \sqrt{n} \sigma$

So then the distribution for the total would be also normal and given by:

$T \sim N (\mu = 6*12=72 , \sigma= \sqrt{6} *0.3=0.735)$

And we want this probability:

$P(T\leq 72)$

And we can use the z score formula given by:

$z = \frac{x-\mu}{\sigma}$

$P(T \leq 72) = P(Z< \frac{72-72}{0.735}) = P(Z$

6 0

2 years ago

A car travels 17 miles on one gallon of gas.

ehidna [41]

Answer:

$y$ ranges from 2890 miles to 5780 miles.

Step-by-step explanation:

Let us call $y$ the number of miles the car travels, and $x$ the number of gallons of gas that are used, then we have the relationship

$y=17x$ <em>(this says the car travels 17 miles for each gallon of gas).</em>

Now, when $x=170$ , we have

$y=17(170)$

$y=2890\: miles$

and when $x=340$ , we have

$y=17(340)$

$y=5780\:miles$

So, when $x$ goes from 170 to 340, $y$ goes from $2890$ to $5780$ .

Therefore, when $x$ ranges from 170 to 340 gallons, the distance traveled ranges from 2890 to 5780 miles.

5 0

2 years ago

Suppose that you want to estimate the mean pH of rainfalls in an area that suffers from heavy pollution due to the discharge of

labwork [276]

Answer:

The number of rainfalls is $n =96$

The answer to the second question is no it will not be valid this because from the question we are told that the experiment require one pH reading per rainfall so getting multiply specimens(used for the pH reading) from one rainfall will make the experiment invalid.

Step-by-step explanation:

from the question we are told that

The standard deviation is $\sigma = 0.5$

The margin of error is $E = 0.1$

Given that the confidence level is 95% then we can evaluate the level of significance as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha =0.05$

Next we will obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table , the value is $Z_{\frac{\alpha }{2} } = 1.96$

Generally the sample size is mathematically represented as

$n = [\frac{Z_{\frac{\alpha }{2} * \sigma }}{ E} ]^2$

substituting values

$n = [\frac{1.96 * 0.5 }{ 0.1} ]^2$

$n =96$

The answer to the second question is no the validity is null this because from the question we are told that the experiment require one pH reading per rainfall so getting multiply specimens(used for the pH reading) from one rainfall will make the experiment invalid

5 0

2 years ago

Hannah and Corrine are playing a game by rolling two cubes, each numbered 1 through 6. If the sum of the numbers on the cubes is

Katarina [22]

Answer:

D. Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.

Step-by-step explanation:

To get a sum of 7 by rolling two cubes, we need to get one of the combinations from the list below:

1 on the first cube, 6 on the second cube

or

6 on the first cube, 1 on the second cube

2 on the first cube, 5 on the second cube

or

5 on the first cube, 2 on the second cube

3 on the first cube, 4 on the second cube

or

4 on the first cube, 3 on the second cube

Therefore, the correct answer option is D. Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.

7 0

2 years ago