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vredina [299]
3 years ago
6

A company produces items in small batches. The machinery needs to warm up before the items can be produced. The scatterplot show

s the time needed to produce batches of different numbers of items.
Line of best fit= y=8x+20

Based on the line of best fit, which of the following statements is true?
A. As the number of items in a batch increases by 1, the production time increases by 8 minutes.
B. It takes about 60 minutes for the equipment to warm up
C. It takes about 44 minutes for the equipment to warm up.
D. As the number of items in a batch increases by 1, the production time increases by 20 minutes.
Mathematics
2 answers:
Lerok [7]3 years ago
7 0

Answer:

The correct option is A.

Step-by-step explanation:

The equation of best fit is

y=8x+20

Where, y is time needed to produce batches of different numbers of items and x is number of items in a batch.

The slope intercept form of a line is

y=mx+b

Where, m is slope and b is y-intercept.

On comparing both equations we get m=8 and b=20.

It means initial time is 20 or it takes about 20 minutes for the equipment to warm up.

Since m=8, so the production time increases by 8 minutes as the number of items in a batch increases by 1.

Therefore, the correct option is A.

loris [4]3 years ago
6 0
Its <span>A.) As the number of items in a batch increases by 1, the production time increases by 8 minutes.
</span>
-apex :)
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The quadratic function g(x) = a.ca + bx+c has the
Mumz [18]

<em>The value of b is 14 and the value of c is 65</em>

<h2>Explanation:</h2>

The quadratic function is a function of the form:

f(x)=ax^2+bx+c

Here we know that the leading coefficient a=1 so we reduce our equation to:

g(x)=x^2+bx+c

The roots are those values at which g(x)=0

So:

x^2+bx+c=0 \\ \\ First \ root: \\ \\ (-7+4i)^2+b(-7+4i)+c=0 \\ \\ (-7)^2-2(7)(4i)+(4i)^2-7b+4bi+c=0 \\ \\  49-56i+16i^2-7b+4bi+c=0 \\ \\ \\ Simplifying: \\ \\ 49-56i+16(-1)-7b+4bi+c=0 \\ \\ 49-56i-16-7b+4bi+c=0 \\ \\ 33-56i-7b+4bi+c=0 \\ \\ \\

Second \ root: \\ \\ (-7-4i)^2+b(-7-4i)+c=0 \\ \\ (-1)^2(7+4i)^2+b(-7-4i)+c=0 \\ \\ (7)^2+2(7)(4i)+(4i)^2-7b-4bi+c=0 \\ \\  49+56i+16i^2-7b-4bi+c=0 \\ \\ \\ Simplifying: \\ \\ 49+56i+16(-1)-7b-4bi+c=0 \\ \\ 49+56i-16-7b-4bi+c=0 \\ \\ 33+56i-7b-4bi+c=0

So we have:

(1) \ 33-56i-7b+4bi+c=0 \\ \\ (2) \ 33+56i-7b-4bi+c=0 \\ \\ \\ Subtract \ 2 \ from: \\ \\ 33-56i-7b+4bi+c-(33+56i-7b-4bi+c)=0 \\ \\ 33-56i-7b+4bi+c-33-56i+7b+4bi-c=0 \\ \\ \\ Combine \ like \ terms: \\ \\ 33-33-56i-56i-7b+7b+4bi+4bi+c-c=0 \\ \\ -112i+8bi=0 \\ \\ Isolating \ b: \\ \\ b=\frac{112i}{8i} \\ \\ \boxed{b=14}

Finding c from (1):

33-56i-7b+4bi+c=0 \\ \\ \\ Substituting \ b: \\ \\ 33-56i-7(14)+4(14)i+c=0 \\ \\ 33-56i-98+56i+c=0 \\ \\ -65+c=0 \\ \\ \boxed{c=65}

<h2>Learn more:</h2>

Complex conjugate: brainly.com/question/2137496

#LearnWithBrainly

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