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Tomtit [17]
3 years ago
11

A small company borrows money and remains in debt to its lenders for a period of time. The function f(x)=−6x2+8x+50 represents t

he amount of debt the company has, in thousands of dollars, x years after opening its business. Approximately how many years after opening its business will the company be out of debt?
A. 2.9
B. 3.2
C. 3.6
D. 4.2
Mathematics
1 answer:
Marysya12 [62]3 years ago
5 0
Given that the debt has been represented by the function:
f(x)=-6x^2+8x+50
To get the number of years, x that it would take for the company to be debt free we proceed as follows:
we solve the equation for f(x)=0
hence:
0=-6x^2+8x+50
solving for x using the quadratic formula we get:
x=[-b+/-sqrt(b^2-4ac)]/2a
x=[-8+/-sqrt(8^2-4*(-6)*50)]/(-6*2)
x=[-8+/-√1264]/(-12)
x=27.552
x~28

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Five widgets and three gadgets cost $109. 90.
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Answer:

one gadget costs $15.80

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Let g = cost of one gadget

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Answer:

(a) The correct option is: <em>H₀</em>: <em>p</em> = 0.02 vs. <em>Hₐ</em>: <em>p</em> < 0.02.

(b) Explained below.

(c) The better value of <em>α</em> will be 0.10.

Step-by-step explanation:

An automobile manufacturer is considering using robots for part of its assembly process only if there is strong evidence that the proportion of defective installations is less for the robots than for human assemblers.

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The alternate hypothesis is the claim or the statement that is being tested.

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(c)

The power of the test is the probability of rejecting a false null hypothesis.

The power of the test sis affected by the significance level of the test (<em>α</em>).

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So higher the value of <em>α</em> the higher is the probability of making a correct decision.

Thus, the better value of <em>α</em> will be 0.10.

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