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3 years ago

Select the correct answer. A triangle has vertices (-1, 2), (3, 1), and (7, 2). What is the approximate perimeter of th...

Mathematics

1 answer:

Eva8 [605]3 years ago

5 0

Answer:

16.24 Units

Step-by-step explanation:

The perimeter of the triangle is the sum of the length of the sides of the triangle. Given the points on the vertices, the length of each side may be found using the formula

Length = √(x2 - x1)^2 + (y2 - y1)^2

Considering the pair (-1, 2), (3, 1), the length of that side

= √(3 -- 1)^2 + (1-2)^2)

= √(16 + 1)

= √17 units

Considering the pair (-1, 2), (7, 2), the length of that side

= √(7 -- 1)^2 + (2-2)^2)

= √(64)

= 8

Considering the pair (3, 1), and (7, 2), the length of that side

= √(7 - 3)^2 + (2 - 1)^2

= √(16 + 1)

= √17

Hence the perimeter of the triangle

= √17 + 8 + √17

= 4.12 + 8 + 4.12

= 16.24 Units

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$n\geq 23$

Step-by-step explanation:

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$ME$ is the desired margin of error.

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Three runners are training for a marathon. One day, they all run about ten miles, each at their own constant speed. Which of the

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Step-by-step explanation:

The first one we need to find the slope

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A recipe uses 1/4 teaspoon of salt and 2 1/2 teaspoons of sugar. What is the ratio of salt to sugar in this recipe?

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Step-by-step explanation:

the ratio we can it is

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What is the slope and the point based on the equation: (y-2) = 5(x - 4)

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Step-by-step explanation:

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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.

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