Turner mesuares 3/4 foot of a ribbon for a coustume. He needs 9 pieces of ribbon with the same length

Sully is having a party and wants to fill his swimming pool. If he only uses his hose, it takes 3 hours more than if he only use

coldgirl [10]

Answer:

It takes the neighor's hose 3 hours to fill the pool and it takes Sully's hose 6 hours to fill the pool if each filled alone.

Step-by-step explanation:

This is a work problem, and the way these are done is to figure the amount that each can do based on how much can get done in a single hour.

First thing, in order to have only one variable, we have to put one hose in terms of the other hose.

We know that it takes the neighbor's hose a certain amount of time (there's our unknown) to fill the pool and that it takes Sully's hose that same time plus 3 hours.

neighbor's hose can get the job done in x time

Sully's hose can get the job done in x + 3 time

Now we will figure out how much each can do in a single hour.

If the neighbor's hose takes x hours to fill the pool, then it can get

of the pool filled in 1 hour.

If Sully's hose takes x + 3 hours to fill the pool, then it can get

of the pool filled in 1 hour.

The sum of these takes 2 hours total and 1/2 of the pool gets filled in 1 hour.

Our equation then is:

This equation states in words:

"the amount of the pool that the neighbor's hose can fill in an hour plus the amount of the pool that Sully's hose can fill in an hour will fill half the pool".

Solving for x will give us that time.

Begin to solve this by finding the LCM of those denominators and getting rid of the fractions by reducing. The LCM will be 2x(x + 3). Multiplying each term by that LCD looks like this:

In the first term the x's cancel out, in the second term the (x + 3) cancels out, and in the last term the 2's cancel out leaving us with:

and simplifying gives us:

This is a quadratic that will have to be factored to solve for those values of x. Combine like terms and get everything on one side to get:

Factor this however you find easiest to get the values:

x = 3 hours and x = -2 hours

We all know that the 2 things in math that will never EVER be negative are times and distances/measures, so we can disregard the -2 and say that

x = 3 hours.

To answer our question, then;

It takes the neighbor's hose 3 hours to fill the pool; it takes Sully's hose 3+3 hours = 6 hours to fill the pool.

5 0

3 years ago

36 out of 100 randomly selected taxpayers knew about tax incentives for installing energy-saving furnaces. Find a 90% confidence

tresset_1 [31]

Answer:

The 90% confidence interval for the population proportion who knew about the incentives is (0.28, 0.44).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 100, \pi = \frac{36}{60} = 0.6$

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so $Z = 1.645$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.36 - 1.645\sqrt{\frac{0.36*0.64}{100}} = 0.28$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.36 + 1.645\sqrt{\frac{0.36*0.64}{100}} = 0.44$

The 90% confidence interval for the population proportion who knew about the incentives is (0.28, 0.44).

7 0

4 years ago

On a coordinate plane, 3 triangles are shown. Triangle B C D has points (1, 4), (1, 2), (5, 3). Triangle B prime C prime D prime

Tresset [83]

The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y ⇒ last answer

Step-by-step explanation:

Let us revise the reflection across the y-axis , horizontal translation

and vertical translation

1. If point (x , y) is reflected across the y-axis, then its image is (-x , y)

2. If point (x , y) is translated h units to the right, then its image is

(x + h , y), if translated h units to the left, then its image is (x - h , y)

3. If point (x , y) is translated k units up, then its image is (x , y + k),

if translated k units down, then its image is (x , y - k)

∵ The vertices of triangle BCD are (1 , 4) , (1 , 2) , (5 , 3)

∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)

∵ The x-coordinates of the vertices of Δ B'C'D' have the same

magnitude of x-coordinates of Δ BCD and opposite signs

∴ Δ B'C'D' is the image of Δ ABC after reflection across the y-axis

∵ The vertices of triangle B'C'D' are (-1 , 4) , (-1 , 2) , (-5 , 3)

∵ The vertices of triangle B''C''D'' are (5 , -1) , (5 , -3) , (1 , -2)

∵ The image of -1 is 5 and the image of -5 is 1

∴ The x-coordinates of the vertices of triangle B'C'D' are added by 6

∵ The image of 4 is -1 , image of 2 is -3 and the image of 3 is -2

∴ The y-coordinates of the vertices of triangle B'C'D' are subtracted

by 5

∴ Δ B"C"D" is the image of Δ B'C'D' by translate 6 units to the right

and 5 units down ⇒ (x + 6 , y - 5)

The rule which describe the composition of transformations that

maps ΔBCD to ΔB"C"D" is:

Reflection across the y-axis composition translation of 6 units x,

negative 5 units y

Learn more:

You can learn more about reflection in brainly.com/question/11203617

#LearnwithBrainly

3 0

3 years ago

Read 2 more answers

Complete the square and write the quadratic equation in vertex form please show steps

nasty-shy [4]

Answer:

Square: $(x-10)^{2} -68$

Vertex: (10,-68)

Step-by-step explanation:

5 0

3 years ago

PLEASE HURRY!! I HAVE TO GET THIS DONE NOW AND IM STUCK ON IT A LITTLE. MAKE SURE TO ANSWER THEM ALL PLEASE! THXS

Sphinxa [80]

Answer:

v = 2419200in³

Step-by-step explanation:

v=l*b*h

=240*84*120

=2419200in³

3 0

2 years ago

Read 2 more answers