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Taya2010 [7]
3 years ago
10

The function f(x) = –x2 + 20x – 75 models the profit from one customer, in dollars, a shop makes for printing photos, where x is

the number of photos printed, and f(x) is the amount of profit.
Part A: Determine the vertex. What does this calculation mean in the context of the problem? (5 points)

Part B: Determine the x-intercepts. What do these values mean in the context of the problem? (5 points)

Mathematics
1 answer:
trasher [3.6K]3 years ago
8 0
The function is graphed as shown below

Part A:

We use the formula - \frac{b}{2a} to find the vertex of the function. A quadratic function of the form of a x^{2} +bx+c and equating this form to the given function - x^{2} +20x-75, we have
b=20 and a=-1.

Substituting a and b into the vertex formula, we have
x=- \frac{20}{2(-1)}=10, as shown in the graph

This calculation means that the highest profit is achieved when the number of photo printed equals to ten photos

Part B:

We can find solution to this equation by factorising

- x^{2} +20x-75=0
-( x^{2} -20x+75)=0
x^{2} -20x+75=0
(x-5)(x-15)=0
x=5 and x=15, as shown in the graph

The two values means that the company makes no profit when they either produce 5 or 15 photos

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Step-by-step explanation:

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\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}

Given : Sample size : n= 314 , which is a large sample , so we apply z-test .

Sample mean : \overline{x}=346

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Significance level : \alpha=1-0.95=0.05

Critical value : z_{\alpha/2}=1.96

Now, a confidence interval at the 95% level of confidence will be :-

346\pm(1.96)\dfrac{86}{\sqrt{314}}\\\\\approx346\pm9.51\\\\=(346-9.51,\ 346+9.51)\\\\=(336.49,\ 355.51)

8 0
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What percent is 24 of 96
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Can 12m, 35m and 37m make a right triangle
antoniya [11.8K]

Answer:

YES

Step-by-step explanation:

Explanation:

If this is a right triangle we can then substitute the sides of the triangle (12 and 35) and the hypotenuse (37) into the Pythagoras Theorem and the two sides of the equation will be equal. If this is not a right triangle the two sides of the equation will not be equal.

The Pythagoras Theorem is  

a

2

+

b

2

=

c

2

Substituting we get:

12

2

+

35

2

=

37

2

12

⋅

12

+

35

⋅

35

=

37

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37

144

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1225

=

1369

1369

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Because these are equal this is a right triangle.

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Step-by-step explanation:

The slope of AB is ...

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The slope of BC is ...

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We want the product of these slopes to be -1:

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  -(q-1)/(6 -p) = -1 . . . . cancel factors of 3

  q -1 = 6 -p . . . . . multiply by -(6 -p)

  q + p = 7 . . . . . matches choice D

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2 years ago
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