All categories

4 years ago

The table below shows the squares of different numbers:

1 answer:

6 0

Part A:

Yes this is a function of x. Specifically the function is f(x) = x^2
The inputs (x) are squared to get the outputs (y).
For example,
f(x) = x^2
f(-3) = (-3)^2 <<--- input is x = -3
f(-3) = 9 <<--- output is 9
The pair of values -3 and 9 are shown in the table (column on the very right side)

The fact that each input leads to exactly one output is what makes this a function. If we had an input lead to multiple outputs, then it wouldn't be a function.

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

Part B

Replace every x with 150 and then use the order of operations PEMDAS to simplify

f(x) = 20+3x
f(x) = 20+3*x
f(150) = 20+3*150 <<--- x has been replaced with 150
f(150) = 20+300
f(150) = 320
So the value of f(150) is 320
The input is 20
The output is 320
x is the number of hours
y or f(x) is the total cost

So this means f(150) = 320 represents the idea that 150 hours of renting the rowboat leads to a total cost of $320

You might be interested in

Solve the equation 3y + 9 2/5 = 28. explain the steps and properties you used. :)

Brut [27]

Answer: division properties

Step-by-step explanation:

8 0

3 years ago

Can someone explain to me how to solve problem 32?

krok68 [10]

Ok so parallel equations mean they have equal slope, but different y intercepts. Here, we can solve and get the equation:

y=2/5x-7/5

5 0

3 years ago

Is y=800(6/5)t exponential growth or exponential decay?

marin [14]

Answer:

It is exponential growth.

Step-by-step explanation:

6/5 is greater than 1.

5 0

3 years ago

Read 2 more answers

What is the constant of y= 3/4x ??

Xelga [282]

the constant is -4 because Y is proportional to x

5 0

3 years ago

The age of the children in kindergarten on the first day of school is uniformly distributed between 4.8 and 5.8 years old. A fir

Kazeer [188]

Answer:

(1) (c) 5.30 years.

(2) (b) 0.289.

(3) (b) 0.80.

(4) (d) 0.50.

(5) (a) 5.25 years.

Step-by-step explanation:

Let X = age of the children in kindergarten on the first day of school.

The random variable X follows a continuous Uniform distribution with parameters a = 4.8 years and b = 5.8 years.

The probability density function function of X is:

$f_{X}(x)=\left \{ {{\frac{1}{b-a}} ;\ a$

(1)

The expected value of a Uniform random variable is:

$E(X)=\frac{1}{2}(a+b)$

Compute the mean of X as follows:

$E(X)=\frac{1}{2}(a+b)=\frac{1}{2}\times (4.8+5.8)=5.3$

Thus, the mean of the distribution is (c) 5.30 years.

(2)

The standard deviation of a Uniform random variable is:

$SD(X)=\sqrt{\frac{1}{12}(b-a)^{2}}$

Compute the standard deviation of X as follows:

$SD(X)=\sqrt{\frac{1}{12}(b-a)^{2}}=\sqrt{\frac{1}{12}\times (5.8-4.8)^{2}}=0.289$

Thus, the standard deviation of the distribution is (b) 0.289.

(3)

Compute the probability that a randomly selected child is older than 5 years old as follows:

$P(X>5)=\int\limits^{5.8}_{5} {\frac{1}{5.8-4.8}}\, dx\\$

$=\int\limits^{5.8}_{5} {1}\, dx\\=[x]^{5.8}_{5}\\=(5.8-5)\\=0.8$

Thus, the probability that a randomly selected child is older than 5 years old is (b) 0.80.

(4)

Compute the probability that a randomly selected child is between 5.2 years and 5.7 years old as follows:

$P(5.2$

$=\int\limits^{5.7}_{5.2} {1}\, dx\\=[x]^{5.7}_{5.2}\\=(5.7-5.2)\\=0.5$

Thus, the probability that a randomly selected child is between 5.2 years and 5.7 years old is (d) 0.50.

(5)

It is provided that a randomly selected child is at the 45th percentile.

This implies that:

P (X < x) = 0.45

Compute the value of x as follows:

$P (X < x) = 0.45$

$\int\limits^{x}_{4.8} {\frac{1}{5.8-4.8}}\, dx=0.45$

$\int\limits^{x}_{4.8} {1}\, dx=0.45$

$[x]^{x}_{4.8}=0.45$

$x-4.8=0.45\\$

$x=0.45+4.8\\x=5.25$

Thus, the age of the child at the 45th percentile is (a) 5.25 years.

6 0

3 years ago