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3 years ago

What is the range of the function on the graph?

Mathematics

1 answer:

Hitman42 [59]3 years ago

6 0

Answer:

The range is all real numbers greater than or equal to 2

Step-by-step explanation:

we know that

Observing the graph

The solution for the variable y is

$y\geq 2$

therefore

The range is the interval -----> [2,∞)

All real numbers greater than or equal to 2

You might be interested in

Give a rule for finding the first of four consecutive odd integers if you know the sum of the four integers.

Artemon [7]

This ones a bit of a trick question, since whether the integers are even or odd doesn't really matter. What does matter, is that consecutive odd integers are 2 numbers apart (as are consecutive even integers).

So again, if the first of the odd integers is the variable n

the consecutive odd integers after it can be written as:

n+2 , n+4, etc...

So the sum of four consecutive odd integers can be written as:

sum = n + (n+2) + (n+4) + (n+6)

Simplify:

sum = 4n + 12

And finally rearrange to solve for n:

$\frac{sum-12}{4}$ = n

This can also be written as:

$\frac{sum}{4}$ - 3 = n

Whichever way you prefer.

6 0

2 years ago

Read 2 more answers

A factory makes car batteries. The probability that a battery is defective is 1/14. If 400 batteries are tested, about how many

Rufina [12.5K]

Answer:

28.6, that is, about 29 are expected to be defective

Step-by-step explanation:

For each battery, there are only two possible outcomes. Either it is defective, or it is not. The probability of a battery being defective is independent of other betteries. So the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$

The probability that a battery is defective is 1/14.

This means that $p = \frac{1}{14}$

400 batteries.

This means that $n = 400$

How many are expected to be defective?

$E(X) = np = 400*\frac{1}{14} = 28.6$

28.6, that is, about 29 are expected to be defective

3 0

3 years ago

These are the cost and revenue functions for a line of trumpets sold at a music store:

Maslowich

Answer:

168 trumpets for $1702

Step-by-step explanation:

Profit is the measure to be maximized. We are given revenue and cost relationships as a function of units, x (trumpets). Profit is the difference:

Profit = Revenue[R(x)] - Cost[C(x)]

Profit = (76x – 0.25x^2) - (-7.75x + 5,312.5)

Profit = 76x - 0.25x^2 + 7.75x - 5,312.5

Profit = - 0.25x^2 + 83.75x - 5312.5

At this point we can find the trumpets needed for maximum profit by either of two approaches: algebraic and graphing. I'll do both.

Mathematically

The first derivative will give us the slope of this function for any value of x. The maximum will have a slope of zero (the curve changes direction at that point). Take the first derivative and set that equal to 0 and solve for x.

First derivative:

d(Profit)/dx = - 2(0.25x) + 83.75

d(Profit)/dx = - 0.50x + 83.75

0 = - 0.50x + 83.75

0.50x = 83.75

x = 167.5 trumpets

Graphically

Plot the profit function and look for the maximum. The graph is attached. The maximum is 167.5 trumpets.

Round up or down to get a whole trumpet. I'll go up: 168 trumpets.

Maximum Profit

Solve the profit equation for 168 trumpets:

Profit = - 0.25x^2 + 83.75x - 5312.5