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2 years ago

Find the slope of the given line, if it is defined.

Mathematics

1 answer:

il63 [147K]2 years ago

8 0

Answer: A. The slope is $-\dfrac{4}{3}$ .

Step-by-step explanation:

The slope of a line helps to specify the direction of the line.

The slope of a line that passes through (a,b) and (c,d) is given by :-

$\text{Slope}=\dfrac{d-b}{c-a}$

Then the slope of a line passes through origin i.e. (0,0) and (-9,12) is given by :-

$\text{Slope}=\dfrac{12-0}{-9-0}\\\\\Rightarrow\ \text{Slope}=\dfrac{12}{-9}\\\\\Rightarrow\ \text{Slope}=-\dfrac{4}{3}$

Hence, the slope is $-\dfrac{4}{3}$ .

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Country Financial, a financial services company, uses surveys of adults age and older to determine if personal financial fitness

Yakvenalex [24]

Complete Question

Country financials, a financial services company, uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. In February 2012, a sample of 1000 adults showed 410 indicating that their financial security was more that fair. In Feb 2010, a sample of 900 adults showed 315 indicating that their financial security was more than fair.

State the hypotheses that can be used to test for a significant difference between the population proportions for the two years.

What is the sample proportion indicating that their financial security was more that fair in 2012?In 2010?

Conduct the hypothesis test and compute the p-value.At a .05 level of significance what is your conclusion?

Answer:

The null hypothesis is $H_o : p_1 = p_2$

The alternative hypothesis is $H_a : p_1 \ne p_2$

in 2012 $\r p_1 =0.41$

in 2010 $\r p_2 =0.35$

The p-value is $p-value = 0.0072$

The conclusion is

There is sufficient evidence to conclude that the proportion of those indicating that financial security is more fair in Feb 2010 is different from the proportion of those indicating that financial security is more fair in Feb 2012.

Step-by-step explanation:

From the question we are told that

The sample size in 2012 is $n_1 = 1000$

The number that indicated that their finance was more than fail is k = 410

The sample size in 2010 is $n_2 = 900$

The number that indicated that their finance was more than fail is u = 315

The level of significance is $\alpha = 0.05[/ex]The null hypothesis is [tex]H_o : p_1 = p_2$

The alternative hypothesis is $H_a : p_1 \ne p_2$

Generally the sample proportion for 2012 is mathematically represented as

$\r p_1 = \frac{k}{n_1}$

=> $\r p_1 = \frac{410}{1000}$

=> $\r p_1 =0.41$

Generally the sample proportion for 2010 is mathematically represented as

$\r p_2 = \frac{u}{n_2}$

=> $\r p_2 = \frac{315}{900}$

=> $\r p_2 =0.35$

Generally the pooled sample proportion is mathematically represented as

$\r p = \frac{k + u }{n_1 + n_2}$

=> $\r p = \frac{410 + 315 }{1000+ 900}$

=> $\r p = 0.3816$

Generally the test statistics is mathematically represented as

$z = \frac{( \r p_1 - \r p_2 ) - 0}{\sqrt{\r p (1 - \r p ) ( \frac{1}{n_1} +\frac{1}{n_2} )} }$

$z = \frac{( 0.41 -0.35 ) - 0}{\sqrt{0.3816 (1 - 0.3816 ) ( \frac{1}{1000} +\frac{1}{900} )} }$

$z = 2.688$

Generally the p- value is mathematically represented as

$p-value = 2 P(Z >2.688 )$

From the z -table

$P(Z > 2.688) = 0.0036$

$p-value = 2 *0.0036$

$p-value = 0.0072$

So from the p-value obtained we see that p-value < $\alpha$ so we reject the null hypothesis

Thus there is sufficient evidence to conclude that the proportion of financial security is more fair in Feb 2010 is different from the proportion of financial security is more fair in Feb 2012.

5 0

3 years ago

Dan drove 845 miles in 13 hours. At the same rate, how many miles would he drive in 11 hours

denis23 [38]

845 miles / 13 hours = 65 miles per hour

65 miles per hour x 11 hours = 715 miles

6 0

3 years ago

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

mrs_skeptik [129]

2(2x − 1) > 6 or x + 3 ≤ −6

2(2x − 1) > 6

4x - 2 > 6

4x > 8

x > 2

x + 3 ≤ −6

x ≤ - 9

Solution: x ≤ - 9 or x > 2

(- ∞ , - 9] or (2 , + ∞)

Answer is the first one

(- ∞ , - 9] or (2 , + ∞)

8 0

2 years ago

A map has the scale 0.5 of an inch equals 180 miles. The distance from Springfield to Glenview is 4 inches. How many actual mile

Amiraneli [1.4K]

180 multiplied by 4 is the answer.

6 0

3 years ago

How do I graph that

nika2105 [10]

Start by finding the vertex, which is the point the parabola turns. The x value is -b/2a, which you have in your notes here. b = -8 and a = 2 and therefore the x value of the vertex is 2. Plug that in to find the y value, which is -2.

Start by plotting this point and the y intercept, which is 6. The parabola will be a U shape, which goes upwards starting at the vertex. If you draw that using the side with the y intercept, you can just mirror it on the other side of the vertex.

7 0

2 years ago