Two mechanics worked on a car. The first mechanic worked for 10 hours, and the second mechanic worked for 15 hours. Together they charged a total of $2475 . What was the rate charged per hour by each mechanic if the sum of the two rates was $200 per hour?

He answered 16 questions correctly, and got 3 wrong answers.

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Explanation:

Let

x,y,z are nonnegative whole numbers.

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Since there are 20 questions total, this means the first equation to set up is:

x+y+z = 20

Solving for y leads to

x+y+z = 20

y+z = 20-x

y = 20-x-z

We'll use this later.

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Another equation to set up is 7x-4y = 100 because Eric earns 7 points per correct answer and loses 4 points for each incorrect answer, and all that leads to 100 points total which was his quiz score. We'll ignore the questions he left blank since they add 0 points.

Let's plug the equation in which we isolated y

7x-4y = 100  

7x-4(20-x-z) = 100

7x-80+4x+4z = 100

7x+4x+4z = 100+80

11x+4z = 180

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Now we can guess and check to see which pair of x and z values will make that last equation above true. I suggest starting with the smallest possible value of x and using that x value to solve for z.

If x = 0, then,

11x+4z = 180

11(0)+4z = 180

4z = 180

z = 180/4

z = 45

So if Eric got 0 correct answers, then he left 45 questions blank. But that isn't possible because there are only 20 questions total. So we'll ignore the case that x = 0.

If we increase x by 4, and decrease z by 11, then we get another ordered pair solution to this equation

So another solution is (x,z) = (4,34)

Note that

11x+4y = 180

11(4) + 4(34) = 180

But like before, z = 34 isn't possible since 20 is the max.

Increase x by 4 again, and drop z by 11 to get (x,z) = (8,23). Again we run into the same issue as before.

Increase x by 4 again, and decrease z by 11 to get (x,z) = (12, 12). Now we have both x and z smaller than 20, but note how x+z = 12+12 = 24 which exceeds the total number of questions. So we rule this case out as well.

Do another round of "increase x by 4, decrease z by 11" to get to (x,z) = (16, 1). This is the only case left because anything beyond this, z will be negative.

Luckily, this final case does work. If Eric answers x = 16 questions correctly, then he left z = 1 of them blank. That must mean y = 20-x-z = 20-16-1 = 3 questions were incorrect.

We can see that:

7x-4y = 7(16)-4(3) = 112-12= 100

meaning that (x,y) = (16,3) is a solution to 7x-4y = 100.

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To summarize, we found that the only possible solution is (x,y,z) = (16, 3, 1)

Meaning x = 16 questions were correct, y = 3 were wrong, and z = 1 question was left blank.

Step-by-step explanation:

a_n=6-n

➜a_1=6-1

➜,a_2=6-2

➜a_3=6-3

➜a_20=6-20

Answer:

asasasdcvxcvszs

Step-by-step explanation:dsadsdasz

Answer:

y = -3x - 2

Step-by-step explanation:

to find slope use m= y2-y1/x2-x1

m= -4-2/6-4

m= -6/2

m=-3

then use point slope formula (y-y1) =m(x-x1)

(y-2) = -3(x-4)

simplify

y-2 = -3x - 4

turn into slope intercept form

y = -3x - 2

Answer: factors of 10 are 1, 2, 5, and 10.

Step-by-step explanation: You can also look at this the other way around: if you can multiply two whole numbers to create a third number, those two numbers are factors of the third. 2 x 5 = 10, so 2 and 5 are factors of 10.

Answer:

1,2,5,10

Step-by-step explanation:

1 x 10 = 10

2 x 5 = 10

10 x 1 = 10

Answer:

false..................

Answer:46%

Step-by-step explanation:

Answer:

23/50 or 46%

Step-by-step explanation:

I just added red and purple out of the total(red+purple/total=11+12/50=23/50)

then I multiplied the fraction by 2 to get out of 100 for the percentage(23/50*2=46/100=46%)

Answer:

R = 12

L = 84

Step-by-step explanation:

R + L =96

L = 7R

R = 1R

L = 7R

1 R + 7R = 8R

R = 12

L = 84

hope it helps,

Answer:

5 bottles

Step-by-step explanation:

a total of $0.80 was paid

6 $0.05 bottles were returned= $0.05×6= $0.30

remainder= $0.80-$0.30= $0.50

amount of $0.10 bottles returned= $0.50÷$0.10= 5

Answer:

The exact value of sin-1(√32) sin -1 ( 3 2 ) is π3 .

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

We know that the slope of a line passing through the points ( x ₁ , y₁) and ( x₂ , y₂ ) is ,

→ Slope ( m ) = ( y₂ - y₁) / ( x₂ - x ₁ )

→ m = -3 - y / -7 - (-1)

→ 1 = -(3+y)/ -7+1

→ 1 = -(3+y) / -6

→ 6 = 3 + y

→ y = 6 - 3

→ y = 3

Answer:

hope this helps

Step-by-step explanation:

Answer:

1. <

2. <

Step-by-step explanation:

Have a good day :)

Answer:

269.46

Step-by-step explanation:

sin(theta) = opposite / adjacent

adjacent = opposite / sin(theta)

adjacent = 1425*sin(10.9)

adjacent = 269.4610063

Answer:

0.056

Step-by-step explanation:

Answer:

56/1000 = .056

Step-by-step explanation:

56/100 = .56

56/1000 = .056

56/10000 = .0056

Answer:

B

Step-by-step explanation:

Answer:

Exact form:

[tex]x=\sqrt{17} +3,-\sqrt{17} +3[/tex]

Step-by-step explanation:

Take the root of both sides and solve.

Answer:

Hello! answer: 25

Step-by-step explanation:

x = 56 because... 56 - 31 = 25 56 + 43 = 99 and x = 56 so 56 + 25 + 99 = 180 Hope that helps!

Answer:

72°

Step-by-step explanation:

The interior angles of a triangle sum to 180°. Since there are two angles at 54°, we can use the equation x = 180 - 54 - 54 or x = 180 - 2(54), which will give us 72°.

Answer:

[tex]x=\frac{7}{15}[/tex]

Step-by-step explanation:

[tex]5x-\frac{1}{5} =\frac{7}{3}[/tex]

[tex]5x - \frac{3}{15} = \frac{35}{15}[/tex]

[tex]5x - \frac{3}{15} + \frac{3}{15} = \frac{35}{15} + \frac{3}{15}[/tex]

[tex]5x=\frac{35}{15}[/tex]

[tex]\frac{5x}{5} } =\frac{\frac{35}{15}}{5}[/tex]

[tex]x=\frac{7}{15}[/tex]

c = 22.3 km

Step-by-step explanation:

You can solve this problem using cosine law:

[tex] {c}^{2} = {a}^{2} + {b}^{2} - 2ab \cos( \gamma ) [/tex]

where a and b are the legs of the triangle, c is the unknown length and the angle gamma is the angle opposite length c. We know that

a = 50 km

b= 52.4 km

gamma = 25°

c^2 = (50 km)^2 + (52.4 km)^2 -2(50)(52.4)cos25°

= 496.707 km^2

or

c = 22.3 km

Answer:

I think Its D I'm not sure though because when it comes to maths I'm not smart

Answer:

the correct answer is A x<-2

Step-by-step explanation:

2x<1/2x-3

4x<x-6

4x-x<-6

3x<-6

x<-2

Answer:

Step-by-step explanation:

Answer: it would be  P=4n

Answer: B. 23.07755 has 7 significant digits

Step-by-step explanation: