Solve the system of linear equations using elimination.

Hank's pickup can travel 100 miles on 5 gallons of gas. How many gallons will Hank's pickup need to travel 80 miles?

Orlov [11]

Answer:

the answer is 4

Step-by-step explanation:

because there are 20 5's is 100 and 100 - 20 is 80 that eighty makes the five four.

7 0

3 years ago

Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the disp

fenix001 [56]

Now, it look like there is some information missing in the answer. The whole problem should look like this:

Alicia Keys's new album As I Am is climbing the charts, and the manager of Tip Top Tunes expects to sell a lot of copies. Because she has limited shelf space, she can't put out all her copies of the CD at once. On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold. On Tuesday morning, she counted the number of copies left and then added that many more to the shelf. In other words, she doubled the number that was left in the display. At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday. On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday. Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty. How many copies of the As I Am CD did she sell each day?

Answer:

She sold 24 copies of the cd each day.

Step-by-step explanation:

In order to solve this problem we must first set our variable up. In this case, since we need to know what the number of sold cd's per day is, that will just be our variable:

x= Number of copies sold.

So we can start setting our equation up. So we take the first part of the problem:

"On Monday morning, she stocked the display with 40 copies. By the end of the day, some of the copies had been sold."

This can be translated as:

40-x

where this expression represents the number of copies left on the shelf by the end of monday.

"On Tuesday morning, she counted the number of copies left and then added that many more to the shelf."

so we represent it like this:

(40-x)+(40-x)

"In other words, she doubled the number that was left in the display."

so the previous expression can be simplified like this:

2(40-x)

"At the end of the day, she discovered that she had sold the exact same number of copies as had been sold on Monday."

so the expression now turns to:

2(40-x)-x this is the number of copies left by the end of tuesday.

"On Wednesday morning, the manager decided to triple the number of copies that had been left in the case after Tuesday."

this translates to:

3[2(40-x)-x]

This is the number of copies on the shelf by the begining of Wednesday.

"Amazingly, she sold the same number of copies on Wednesday as she had on each of the first two days! But this time, at the end of the day the display case was empty."

this piece of information lets us finish writting our equation:

3[2(40-x)-x] -x = 0

since there were no copies left on the shelf, then the equation is equal to zero.

So now we proceed and solve the equation for x:

3[2(40-x)-x] -x = 0

We simplify it from the inside to the outside.

3[80-2x-x]-x=0

3[80-3x]-x = 0

we now distribute the 3 so we get:

240-9x-x=0

we combine like terms so we get:

240-10x=0

we move the 240 to the other side of the equation so we get:

-10x=-240

and divide both sides into -10 so we get:

x=24

so she sold 24 copies each day.

5 0

4 years ago

Circle R is shown. Line segments Q R and S R are radii. The length of Q R is 18. Sector Q R S is shaded.

hoa [83]

The answer is b

Answer my questions plz

6 0

3 years ago

Read 2 more answers

a scuba diver descends 48 feet in 4 min. What is the divers average change in position per min. relative to where she started?

Black_prince [1.1K]

With this you need to find the unit rate so divide 48 by 4 to get 12, so the scuba diver descended 12 ft. per min.

6 0

3 years ago

Read 2 more answers

The following observations were made on fracture toughness of a base plate of 18% nickel maraging steel (in ksi √in, given in in

Grace [21]

Answer:

A 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

Step-by-step explanation:

We are given the following observations that were made on fracture toughness of a base plate of 18% nickel maraging steel below;

68.6, 71.9, 72.6, 73.1, 73.3, 73.5, 75.5, 75.7, 75.8, 76.1, 76.2, 76.2, 77.0, 77.9, 78.1, 79.6, 79.8, 79.9, 80.1, 82.2, 83.7, 93.4.

Firstly, the pivotal quantity for finding the confidence interval for the standard deviation is given by;

P.Q. = $\frac{(n-1) \times s^{2} }{\sigma^{2} }$ ~ $\chi^{2} __n_-_1$

where, s = sample standard deviation = $\sqrt{\frac{\sum (X - \bar X^{2}) }{n-1} }$ = 5.063

$\sigma$ = population standard deviation

n = sample of observations = 22

Here for constructing a 90% confidence interval we have used One-sample chi-square test statistics.

So, 90% confidence interval for the population standard deviation, $\sigma$ is ;

P(11.59 < $\chi^{2}__2_1$ < 32.67) = 0.90 {As the critical value of chi at 21 degrees

of freedom are 11.59 & 32.67}

P(11.59 < $\frac{(n-1) \times s^{2} }{\sigma^{2} }$ < 32.67) = 0.90

P( $\frac{ 11.59}{(n-1) \times s^{2}}$ < $\frac{1}{\sigma^{2} }$ < $\frac{ 32.67}{(n-1) \times s^{2}}$ ) = 0.90

P( $\frac{(n-1) \times s^{2} }{32.67 }$ < $\sigma^{2}$ < $\frac{(n-1) \times s^{2} }{11.59 }$ ) = 0.90

90% confidence interval for $\sigma^{2}$ = [ $\frac{(n-1) \times s^{2} }{32.67 }$ , $\frac{(n-1) \times s^{2} }{11.59 }$ ]

= [ $\frac{21 \times 5.063^{2} }{32.67 }$ , $\frac{21 \times 5.063^{2} }{11.59 }$ ]

= [16.48 , 46.45]

90% confidence interval for $\sigma$ = [ $\sqrt{16.48}$ , $\sqrt{46.45}$ ]

= [4.06 , 6.82]

Therefore, a 90% confidence interval for the standard deviation of the fracture toughness distribution is [4.06, 6.82].

5 0

3 years ago