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2 years ago

The line represented by the equation 3x + 5y = 2 has a slope of -3/5 . Which shows the graph of this equation?

Mathematics

2 answers:

Westkost [7]2 years ago

8 0

Answer:

Here, The given equation of the line,

3 x + 5 y = 2 -------(1)

Since, x-intercept of the line is ( 0.667, 0)

And, y-intercept of the line is (0,0.4)

Also, Slope of the line is -3/5.

Since, Put x = -1 in equation (1)

We get, -3 + 5 y =2⇒ 5 y = 5 ⇒ y = 1

And, put x = 4 in equation (1),

We get, 12 + 5 y = 2

⇒ 5y = -10

⇒ y = -2

Thus, the point of the lines are (4,-2) and (-1,1)

Thus, from the above information we can plot the graph of the given line. ( Which is shown below)

Kazeer [188]2 years ago

8 0

Answer:

The graph is shown in the attachment.

Step-by-step explanation:

In order to obtain the graph of a linear equation, you have to calculate the x-axis intercept, the y-axis intercept and the slope.

A linear equation has the form:

Y=mX+b

where m is the slope and b is the y-axis intercept.

To calculate the x-axis intercept, replace y=0 in the equation:

3x+5(0)=2

Dividing by 3 both sides:

x=2/3

The point is (2/3,0)

To calculate the y-axis intercept, replace x=0

3(0)+5y=2

Dividing by 5 both sides:

y=2/5

The point is (0,2/5)

You have to graph the intercept points and trace a line containing those points to obtain the graph, which is shown in the attachment.

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Show how to make a ten to solve 13-7. Write the number sentence.

VARVARA [1.3K]

-7 + 3 + 10 = -4 + 10 = 10 - 4 = 6.

To turn 13 into 10, you need to break it up into 10 + 3, which does not change the value of 13. Then, you add 3 to -7, which results in -4. Next, you add -4 to 10 (or rather, subtract 4 from 10), which results in 6.

5 0

2 years ago

The manufacturer of hardness testing equipment uses steel-ball indenters to penetrate metal that is being tested, however, the m

masha68 [24]

Answer:

$1.667-2.31\frac{1.803}{\sqrt{9}}=0.2789$

$1.667+2.31\frac{1.803}{\sqrt{9}}=3.055$

So on this case the 95% confidence interval would be given by (0.2789;3.055)

The 95% confidence interval to judge whether the two indeners result in different measurements is?

Yes the confidence interval not contains the value 0 so we can conclude that the values for Diamond are significantly higher than the values for Steel Ball at 5% of significance.

Step-by-step explanation:

We have the following dataset:

specimen 1 2 3 4 5 6 7 8 9

Steel Ball 51 57 61 70 68 54 65 51 53

Diamond 53 55 63 74 69 56 68 51 56

If we calculate the differences diamond-steel ball we have this datase:

d: 2, -2, 2, 4, 1, 2, 3, 0, 3

The second step is calculate the mean difference

$\bar d= \frac{\sum_{i=1}^n d_i}{n}=1.667$

The third step would be calculate the standard deviation for the differences, and we got:

$s_d =\frac{\sum_{i=1}^n (d_i -\bar d)^2}{n-1} =1.803$

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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 confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=9-1=8$

Since the confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,9)".And we see that $t_{\alpha/2}=2.31$ .

Now we have everything in order to replace into formula (1):

$1.667-2.31\frac{1.803}{\sqrt{9}}=0.2789$

$1.667+2.31\frac{1.803}{\sqrt{9}}=3.055$

So on this case the 95% confidence interval would be given by (0.2789;3.055)

The 95% confidence interval to judge whether the two indeners result in different measurements is?

Yes the confidence interval not contains the value 0 so we can conclude that the values for Diamond are significantly higher than the values for Steel Ball at 5% of significance.

4 0

2 years ago

According to the Vivino website, suppose the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating

Natali [406]

Answer:

a) Null and alternative hypothesis

$H_0: \mu=32.48\\\\H_a:\mu< 32.48$

b) Test statistic t=-1.565

P-value = 0.0612

NOTE: the sample size is n=65.

c) Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

d) Null and alternative hypothesis

$H_0: \mu=32.48\\\\H_a:\mu< 32.48$

Test statistic t=-1.565

Critical value tc=-1.669

t>tc --> Do not reject H0

Do not reject H0. We cannot conclude that the price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

Then, the null and alternative hypothesis are:

$H_0: \mu=32.48\\\\H_a:\mu< 32.48$

The significance level is 0.05.

The sample has a size n=65.

The sample mean is M=30.15.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=12.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{12}{\sqrt{65}}=1.4884$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{30.15-32.48}{1.4884}=\dfrac{-2.33}{1.4884}=-1.565$

The degrees of freedom for this sample size are:

$df=n-1=65-1=64$

This test is a left-tailed test, with 64 degrees of freedom and t=-1.565, so the P-value for this test is calculated as (using a t-table):

$\text{P-value}=P(t$

As the P-value (0.0612) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

At a significance level of 0.05, there is not enough evidence to support the claim that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48.

<u>Critical value approach</u>

<u></u>

At a significance level of 0.05, for a left-tailed test, with 64 degrees of freedom, the critical value is t=-1.669.

As the test statistic is greater than the critical value, it falls in the acceptance region.

The null hypothesis failed to be rejected.

6 0

2 years ago

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Anon25 [30]

Here is how to do that conversion...