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qwelly [4]
2 years ago
11

30 POINTS! Combine the like terms of the 2 questions below:

Mathematics
1 answer:
astraxan [27]2 years ago
5 0

Answer:

\tt 1)\: \boxed{\tt 4y+10}

\tt 2)\:\boxed{\tt 0.5x^4+10.5}

Step-by-step explanation:

1) y + 4 + 3(y + 2)

Expand:-

\tt y+4+3y+6

Combine like terms:-

\tt y+3y+4+6

\boxed{\tt 4y+10}

__

2) 0.5(x⁴ - 3) + 12

Expand:-

\tt 0.5x^4-1.5+12

Add/Subtract Numbers:-

\boxed{\tt 0.5x^4+10.5}

___________________

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Help! <br> Which expression is equivalent? <br> On edge
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Answer: Choice B

x^{1/8}y^{8}

======================================================

Explanation:

The two rules we use are

(a*b)^c = a^c*b^c

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When applying the first rule to the expression your teacher gave you, we can say that:

\left(x^{1/4}y^{16}\right)^{1/2} = \left(x^{1/4}\right)^{1/2}*\left(y^{16}\right)^{1/2}

Then applying the second rule lets us say

\left(x^{1/4}\right)^{1/2}*\left(y^{16}\right)^{1/2} = x^{1/4*1/2}*y^{16*1/2} = x^{1/8}y^{8}

Therefore,

\left(x^{1/4}y^{16}\right)^{1/2}  = x^{1/8}y^{8}

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In short, we just multiplied each exponent inside by the outer exponent 1/2.

So that explains why the exponents go from {1/4,16} to {1/8,8} for x and y in that exact order.

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3 years ago
Which equations describes a line that has a y-intercept of 4 and a slope of 3?
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Which expression shows the prime<br> factorization of 66?<br> A 32 x 11<br> B 2x 3 x 11<br> C 6 x 11
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Step-by-step explanation:

good luck have a nice day

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Jensen Tire &amp; 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.

4 0
3 years ago
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