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2 years ago

Find the slope of any line parallel to the lien through the given points (3,2),(3,1)

Mathematics

1 answer:

Alborosie2 years ago

8 0

Answer:

m = undefined

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)
Parallel lines have the same slope but different y-intercepts
An undefined line is a vertical line
Slope Formula: $\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

Step-by-step explanation:

Step 1: Define

Point (3, 2)

Point (3, 1)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute in points [Slope Formula]: $\displaystyle m=\frac{1-2}{3-3}$
[Fraction] Subtract: $\displaystyle m=\frac{-1}{0}$
Simplify: m = undefined

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alexgriva [62]

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1 year ago

A number increased by 4 is the same as 19 minus 2 times the number

ElenaW [278]

Hello from MrBillDoesMath!

Answer:

n = 5

Discussion:

Let the original number be "n" Translating the problem statement to mathematical symbolism:

n + 4 = 19 - 2n => add 2n to both sides

n + 2n + 4 = 19 - 2n + 2n => combine like terms

3n + 4 = 19 => subtract 4 from both sides

3n = 19 -4 = 15 => divide both sides by 3

n = 15/3 =5

Check: Does 5 +4 = 19 - 2(5)? Does 9 = 9? Yes. so the value for n is confirmed correct.

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2 years ago

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attashe74 [19]

Answer:

a) Null hypothesis: $\mu \leq 30.2$

Alternative hypothesis: $\mu > 30.2$

b) $X \sim N(\mu=32.12, \sigma=4.83)$

And the distribution for the random sample is given by:

$\bar X \sim N(\mu=32.12, \frac{\sigma}{\sqrt{n}}=\frac{4.83}{\sqrt{50}}=0.683)$

c) $t=\frac{32.12-30.2}{\frac{4.83}{\sqrt{50}}}=2.81$

$p_v =P(t_{(49)}>2.81)=0.0035$

d) If we compare the p value and the significance level assumed $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 30.2.

e) The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. And for this case is a value to accept or reject the null hypothesis.

Step-by-step explanation:

1) Data given and notation

$\bar X=32.12$ represent the sample mean

$s=4.83$ represent the sample standard deviation

$n=50$ sample size

$\mu_o =30.2$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

a. Define the parameter and state the hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 30.2 mpg, the system of hypothesis would be:

Null hypothesis: $\mu \leq 30.2$

Alternative hypothesis: $\mu > 30.2$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

b. Define the sampling distribution (mean and standard deviation).

Let X the random variable who represent the variable of interest. And we know that the distribution for X is:

$X \sim N(\mu=32.12, \sigma=4.83)$

And the distribution for the random sample is given by:

$\bar X \sim N(\mu=32.12, \frac{\sigma}{\sqrt{n}}=\frac{4.83}{\sqrt{50}}=0.683)$

c. Perform the test and calculate P-value

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{32.12-30.2}{\frac{4.83}{\sqrt{50}}}=2.81$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=50-1=49$

Since is a one right tailed test the p value would be:

$p_v =P(t_{(49)}>2.81)=0.0035$

d. State your conclusion.

If we compare the p value and the significance level assumed $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is significantly higher than 30.2.

e. Explain what the p-value means in this context.

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. And for this case is a value to accept or reject the null hypothesis.

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2 years ago

Solve the system.

Alex777 [14]

Answer:

{x,y,z} = {-18,4,2}

Step-by-step explanation:

Solve equation [2] for the variable x

x = -10y + 2z + 18

Plug this in for variable x in equation [1]

(-10y+2z+18) + 9y + z = 20

- y + 3z = 2

Plug this in for variable x in equation [3]

3•(-10y+2z+18) + 27y + 2z = 58

- 3y + 8z = 4

Solve equation [1] for the variable y

y = 3z - 2

Plug this in for variable y in equation [3]

- 3•(3z-2) + 8z = 4

- z = -2

Solve equation [3] for the variable z

z = 2

By now we know this much :

x = -10y+2z+18

y = 3z-2

z = 2

Use the z value to solve for y

y = 3(2)-2 = 4

Use the y and z values to solve for x

x = -10(4)+2(2)+18 = -18

6 0

2 years ago