All categories

4 years ago

The ordered pairs in the table below represent a linear function.

Mathematics

2 answers:

Dmitriy789 [7]4 years ago

5 0

Answer:

slope = 2

Step-by-step explanation:

The ordered pairs are (2,3) and (5,9).

It is given that the function is linear.

Since it is linear, the graph of the function is a straight line.

Slope of the straight line is constant at all points lying on it.

Slope of a straight line containing the points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is given by:

$\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$ .

Slope of the straight line containing (2,3) and (5,9) is given by:

$\frac{9-3}{5-2}=\frac{6}{3}=2$ .

Basile [38]4 years ago

3 0

Answer:

Step-by-step explanation:

To find slope you use the formula Y2-Y1/X2-X1, so it would be (9-3)/(5-2) which equals 6/3

You then reduce to get 2

You might be interested in

Jim is designing a seesaw for a children’s park

dsp73

Do you have a question or is that the problem cause that’s not enough information to solve the problem. :/

6 0

4 years ago

Mrs.flossi is having

Thepotemich [5.8K]

Answer:

Step-by-step explanation:

5 0

3 years ago

Type the expression that results from the following series of steps start with 5 and subtract p

azamat

Answer:

5-p

Step-by-step explanation:

8 0

3 years ago

Test the claim that the mean GPA of night students is larger than 2 at the .025 significance level. The null and alternative hyp

exis [7]

Answer:

$H_0: \, \mu = 2$ .

$H_1:\, \mu > 2$ .

Test statistics: $z \approx 2.582$ .

Critical value: $z_{1 - 0.025} \approx 1.960$ .

Conclusion: reject the null hypothesis.

Step-by-step explanation:

The claim is that the mean $\mu$ is greater than $2$ . This claim should be reflected in the alternative hypothesis:

$H_1:\, \mu > 2$ .

The corresponding null hypothesis would be:

$H_0:\, \mu = 2$ .

In this setup, the null hypothesis $H_0:\, \mu = 2$ suggests that $\mu_0 = 2$ should be the true population mean of GPA.

However, the alternative hypothesis $H_1:\, \mu > 2$ does not agree; this hypothesis suggests that the real population mean should be greater than $\mu_0= 2$ .

One way to test this pair of hypotheses is to sample the population. Assume that the population mean is indeed $\mu_0 = 2$ (i.e., the null hypothesis is true.) How likely would the sample (sample mean $\overline{X} = 2.02$ with sample standard deviation $s = 0.06$ ) be observed in this hypothetical population?

Let $\sigma$ denote the population standard deviation.

Given the large sample size $n = 60$ , the population standard deviation should be approximately equal to that of the sample:

$\sigma \approx s = 0.06$ .

Also because of the large sample size, the central limit theorem implies that $Z= \displaystyle \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}}$ should be close to a standard normal random variable. Use a $Z$ -test.

Given the observation of $\overline{X} = 2.02$ with sample standard deviation $s = 0.06$ :

$\begin{aligned}z_\text{observed}&= \frac{\overline{X} - \mu_0}{\sigma / \sqrt{n}} \\ &\approx \frac{\overline{X} - \mu_0}{s / \sqrt{n}} = \frac{2.02 - 2}{0.06 / \sqrt{60}} \approx 2.582\end{aligned}$ .

Because the alternative hypothesis suggests that the population mean is greater than $\mu_0 = 2$ , the null hypothesis should be rejected only if the sample mean is too big- not too small. Apply a one-sided right-tailed $z$ -test. The question requested a significant level of $0.025$ . Therefore, the critical value $z_{1 - 0.025}$ should ensure that $P( Z > z_{1 - 0.025}) = 0.025$ .

Look up an inverse $Z$ table. The $z_{1 - 0.025}$ that meets this requirement is $z_{1 - 0.025} \approx 1.960$ .

The $z$ -value observed from the sample is $z_\text{observed}\approx 2.582$ , which is greater than the critical value. In other words, the deviation of the sample from the mean in the null hypothesis is sufficient large, such that the null hypothesis needs to be rejected at this $0.025$ confidence level in favor of the alternative hypothesis.

3 0

3 years ago

Which equations represents a line that is parallel to 3x-4y=7 and passes through the point (-4,-2)

insens350 [35]

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 3x - 4y = 7 into this form

Subtract 3x from both sides

- 4y = - 3x + 7 ( divide all terms by - 4 )

y = $\frac{3}{4}$ x - $\frac{7}{4}$ ← in slope- intercept form

with slope = $\frac{3}{4}$

• Parallel lines have equal slopes, hence

y = $\frac{3}{4}$ x + c ← is the partial equation of the parallel line

To find c substitute (- 4, - 2) into the partial equation

- 2 = - 3 + c ⇒ c = - 2 + 3 = 1

y = $\frac{3}{4}$ x + 1 ← in slope- intercept form

Multiply all terms by 4

4y = 3x + 4 ( subtract 4 from both sides )

4y - 4 = 3x ( subtract 4y from both sides )

- 4 = 3x - 4y, that is

3x - 4y = - 4 ← in standard form

6 0

4 years ago