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horsena [70]
2 years ago
6

Which situation shows a constant rate of change

Mathematics
1 answer:
damaskus [11]2 years ago
5 0

Answer: the amount a person pays for gas compared with the number of gallons purchased

Step-by-step explanation:

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What is the solution to the system of equations below? -4x+6y=-18 and y=-2x+21
Verdich [7]

Answer:

x=9 and y=3

Step-by-step explanation:

Let's solve your system by substitution.

−4x+6y=−18 and y=−2x+21

Rewrite equations:

y=−2x+21;−4x+6y=−18

Step: Solve  y=−2x+21for y:

y=−2x+21

Step: Substitute−2x+21foryin−4x+6y=−18:

−4x+6y=−18

−4x+6(−2x+21)=−18

−16x+126=−18(Simplify both sides of the equation)

−16x+126+−126=−18+−126(Add -126 to both sides)

−16x=−144

−16x

−16

=

−144

−16

(Divide both sides by -16)

x=9

Step: Substitute9forxiny=−2x+21:

y=−2x+21

y=(−2)(9)+21

y=3(Simplify both sides of the equation)

Answer:

x=9 and y=3

3 0
3 years ago
3. Which of the following are the roots of the quadratic function below?
sergejj [24]

Answer:

x = ± 12

Step-by-step explanation:

Given

f(x) = x² - 144

To find the roots set f(x) = 0, that is

x² - 144 = 0 ( add 144 to both sides )

x² = 144 ( take the square root of both sides )

x = ± \sqrt{144} = ± 12

4 0
2 years ago
Read 2 more answers
An insurance company has 25,000 automobile policy holders. If the yearly claim of a policy holder is a random variable with mean
telo118 [61]

Answer:

P(T>8300000)=1-P(T

Step-by-step explanation:

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Data given

n = 25000 represent the automobile policy holders

\mu= 320 represent the population mean

\sigma =540 represent the population standard deviation

Let T the variable that represent the total of interest on this case. We can assume that the random variable for an individual policy holder is given by:

X\sim N(\mu = 540, \sigma=540)

From the central limit theorem we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

Solution to the problem

First we need to find the distribution for the random variable T like this:

\bar X = \frac{\sum_{i=1}^n x_i}{n}

And the total T is given by:

T=\sum_{i=1}^n X_i =n \bar X

We can find the expected value, variance and deviation for this random variable like this:

E(T)= n E(\bar X) = n \mu = 25000*320=8000000

Var(T)= Var(n\bar X)= n^2 Var(\bar X) = n^2 \frac{\sigma^2}{n}=n \sigma^2 =25000*(540^2)=7290000000

Sd(T)=\sqrt{7290000000}=85381.497

And we are interested on this probability:

P(T>8300000)

And we can use the Z score formula given by:

Z=\frac{T-E(T)}{\sigma_T}

P(T>8300000)=1-P(T

6 0
3 years ago
A certain connected graph has 68 vertices and 72 edges. Does it have a circuit?
OLEGan [10]

Answer:

Yes.

Step-by-step explanation:

If a graph G doesn't have a circuit, we must have that

|E(G)|=|V(G)|-1

where |E(G)| is the number of edges of the graph and |V(G)| the number of vertices. However, in this case it holds that

|E(G)|=72>68=|V(G)|.

5 0
3 years ago
I urgently need help
Pepsi [2]

Answer: 75/8=9.37500

6 0
3 years ago
Read 2 more answers
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