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Nataly [62]
2 years ago
14

In a survey of 400 seniors, x percent said that they plan on majoring in physics. One university has used this data to estimate

the number of physics majors it expects for its entering class of 3,300 students. If the university expects 66 physics majors, what is the value of x
Mathematics
1 answer:
azamat2 years ago
8 0

Answer:

2 percent

Step-by-step explanation:

We can use two separate fractions, one representing the amount of physics majors expected and the amount of seniors expected in physics majors by the university.

\frac{400x}{66} = \frac{400}{3600}

Now cross multiply.

\frac{66*400}{400x * 3600}

x will be removed.

\frac{26400}{1320000}

Simplifying this fraction will get you \frac{1}{50}, which in percentage form, will be 2 percent.

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If you ask the first 50 females who enter a restaurant to complete a survey about their experience, who is the sample?
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Explain how to evaluate f(g(0)).
alekssr [168]

Answer as a fraction:  17/6

Answer in decimal form: 2.8333  (approximate)

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

Work Shown:

Let's use the two black points to determine the equation of the red f(x) line.

Use the slope formula to get...

m = slope

m = (y2-y1)/(x2-x1)

m = (4-0.5)/(2-(-1))

m = (4-0.5)/(2+1)

m = 3.5/3

m = 35/30

m = (5*7)/(5*6)

m = 7/6

Now use the point slope form

y - y1 = m(x - x1)

y - 0.5 = (7/6)(x - (-1))

y - 0.5 = (7/6)(x + 1)

y - 0.5 = (7/6)x + 7/6

y = (7/6)x + 7/6 + 0.5

y = (7/6)x + 7/6 + 1/2

y = (7/6)x + 7/6 + 3/6

y = (7/6)x + 10/6

y = (7/6)x + 5/3

So,

f(x) = (7/6)x + 5/3

We'll use this later.

---------------------

We ultimately want to compute f(g(0))

Let's find g(0) first.

g(0) = 1 since the point (0,1) is on the g(x) graph

We then go from f(g(0)) to f(1). We replace g(0) with 1 since they are the same value.

We now use the f(x) function we computed earlier

f(x) = (7/6)x + 5/3

f(1) = (7/6)(1) + 5/3

f(1) = 7/6 + 5/3

f(1) = 7/6 + 10/6

f(1) = 17/6

f(1) = 2.8333 (approximate)

This ultimately means,

f(g(0)) = 17/6 as a fraction

f(g(0)) = 2.8333 as a decimal approximation

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