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sashaice [31]
3 years ago
12

The system of equations can be solved using linear combination to eliminate one of the variables. 2x − y = −4→10x − 5y = −20 3x

5y = 59→3x 5y = 59 13x = 39 which equation can replace 3x 5y = 59 in the original system and still produce the same solution? 2x – y = –4 10x – 5y = –20 7x = 39 13x = 39
Mathematics
2 answers:
tester [92]3 years ago
6 0

Answer:

Option D is correct.

13x = 39

Step-by-step explanation:

The system of equation is given:

2x-y = -4             ....[1]

3x+5y = 59         .....[2]

Multiply equation [1] by 5 to both sides we have;

10x-5y = -20              .....[3]

Using elimination method:

Add [2] and [3] equations to eliminate y and solve for x, we have;

13x = 39

Divide both sides by 13 we get;

x = 3

Substitute x in [1] we have;

2(3)-y = -4

6-y = -4

Subtract 6 from both sides we have;

-y = -10

Divide both sides by -1 we have;

y = 10

⇒Solution: (3, 10)

Therefore, an equation can replace 3x+5y = 59 in the original system and still produce the same solution is,

13x = 39

guapka [62]3 years ago
4 0

Answer:

13x=39

Step-by-step explanation:

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Jensen Tire & Auto is in the process of deciding whether to purchase a maintenance contract for its new computer wheel align
sasho [114]

Answer:

Step-by-step explanation:

Hello!

The given data corresponds to the variables

Y:  Annual Maintenance  Expense ($100s)

X: Weekly Usage  (hours)

n= 10

∑X= 253; ∑X²= 7347; \frac{}{X}= ∑X/n= 253/10= 25.3 Hours

∑Y= 346.50; ∑Y²= 13010.75; \frac{}{Y}= ∑Y/n= 346.50/10= 34.65 $100s

∑XY= 9668.5

a)

To estimate the slope and y-intercept you have to apply the following formulas:

b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} } = \frac{9668.5-\frac{253*346.5}{10} }{7347-\frac{(253)^2}{10} }= 0.95

a= \frac{}{Y} -b\frac{}{X} = 34.65-0.95*25.3= 10.53

^Y= a + bX

^Y= 10.53 + 0.95X

b)

H₀: β = 0

H₁: β ≠ 0

α:0.05

F= \frac{MS_{Reg}}{MS_{Error}} ~~F_{Df_{Reg}; Df_{Error}}

F= 47.62

p-value: 0.0001

To decide using the p-value you have to compare it against the level of significance:

If p-value ≤ α, reject the null hypothesis.

If p-value > α, do not reject the null hypothesis.

The decision is to reject the null hypothesis.

At a 5% significance level you can conclude that the average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.

b= 0.95 $100s/hours is the variation of the estimated average annual maintenance expense of the computer wheel alignment and balancing machine is modified when the weekly usage increases one hour.

a= 10.53 $ 100s is the value of the average annual maintenance expense of the computer wheel alignment and balancing machine when the weekly usage is zero.

c)

The value that determines the % of the variability of the dependent variable that is explained by the response variable is the coefficient of determination. You can calculate it manually using the formula:

R^2 = \frac{b^2[sumX^2-\frac{(sumX)^2}{n} ]}{[sumY^2-\frac{(sumY)^2}{n} ]} = \frac{0.95^2[7347-\frac{(253)^2}{10} ]}{[13010.75-\frac{(346.50)^2}{10} ]} = 0.86

This means that 86% of the variability of the annual maintenance expense of the computer wheel alignment and balancing machine is explained by the weekly usage under the estimated model ^Y= 10.53 + 0.95X

d)

Without usage, you'd expect the annual maintenance expense to be $1053

If used 100 hours weekly the expected maintenance expense will be 10.53+0.95*100= 105.53 $100s⇒ $10553

If used 1000 hours weekly the expected maintenance expense will be $96053

It is recommendable to purchase the contract only if the weekly usage of the computer is greater than 100 hours weekly.

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Answer:

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