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kow [346]
3 years ago
8

Let ŷ represent the profit (in thousands of dollars) for a certain company x years after 1970. A statistician calculates a linea

r model ŷ = 0.66 x + 12 Use the model to estimate the profit in 1978. Your answer should be in dollars, not thousands of dollars.
Mathematics
1 answer:
Anika [276]3 years ago
5 0

Answer:

$17,280

Step-by-step explanation:

The model for profit (y), in thousands of dollars, as a function of time (x), in years after 1970 is:

y=0.66x +12

The corresponding value of x in 1978 is:

x= 1978-1970\\x=8

Estimating the profit (in thousands of dollars) in 1978:

y(8)=0.66*8 +12\\y(8) = 17.28

Converting it to dollars:

P = \$1,000*y(8)= \$1,000*17.28\\P= \$17,280

The estimated profit in 1978 is $17,280.

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Answer:

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Step-by-step explanation:

9x^2−45yx+8x−40y

Do the grouping 9x^2−45yx+8x−40y=(9x^2−45yx)+(8x−40y), and factor out 9x in the first and 8 in the second group.

9x(x−5y)+8(x−5y)

Factor out common term x−5y by using distributive property.

(x−5y)(9x+8)

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Rachel has 60 scones. She sells them to Robbie, Cameron, Louis, Tom and
Nutka1998 [239]
We can start by writing all that we know about the problem. Let us write down how many scones each boy has:
R_{o} : x
C_{a} : x+k
L_{o} : x+2k
T_{o} : x+3k
C_{h} : x+4k
Note that k is the increase, we know it's a constant. This is not a system of equations, please keep that in mind. We will use rest of the information given to build the system. We have two variables x (the number of cookies the first boy bought) and k( the increase), that means we need to have two equations to solve this problem. 
We know that total amount of scones is 60, so we can use that information to build our first equation. We sum all of the scones and we get 60. 
R_{o}+C_{a}+L_{o}+T_{o}+C_{h}=60
5x+10k=60
We know that Robbie and Cameron combined have 3/7 of <span>Louis, Tom and Charlie combined. We can use this information to build our second equation.
</span>R_o+C_a= \frac{3}{7} (L_o+T_o+C_h)
2x+k= \frac{3}{7} (x+2k+x+3k+x+4k)
2x+k= \frac{3}{7} (3x+9k)
14x+7k=9x+27k
5x=20k
x=4k
Now this piece of information alows us to solve the first equation that we made and this will solve our problem. We simply plug in x=4k into 5x+10k=60.
5(4k)+10k=60
30k=60
k=2
Now we can plug this information into the same equation 5x+10k=60 and get x.
5x+10(2)=60
5x=40
x=8
And that's it. Now we can write out how many cookies each boy has bought.
R_{o} : x=8
C_{a} : x+k=10
L_{o} : x+2k=12
T_{o} : x+3k=14
C_{h} : x+4k=16
If you add them all up you get 60.
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I think the answer is 10 since that is the largest number they can both be divided by
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