Find the coordinates of the midpoint of the segment given the endpoints p( -3,-7) and q (3, -5)

Rhombus EFGH is shown. What is the length of EF ? A. 3 B. 6 C. 8 D. 9

liubo4ka [24]

Answer:

D

Step-by-step explanation:

The diagonals of a rhombus bisect each other, thus

FJ = JH, that is

y + 5 = 4x ( subtract 5 from both sides )

y = 4x - 5 → (1)

In a rhombus all sides are congruent, thus

HG = EF, substitute values

3x + y = 2x + y + 2 ( subtract y from both sides )

3x = 2x + 2 ( subtract 2x from both sides )

x = 2

Substitute x = 2 into (1)

y = 4(2) - 5 = 8 - 5 = 3

Thus

EF = 2x + y + 2 = 2(2) + 3 + 2 = 4 + 3 + 2 = 9 → D

4 0

3 years ago

What is the value of x if 2x - 3 = 15?

dedylja [7]

X=9

You add 3 to both sides which leaves you with 2x=18 and then divide by two and that gives you x=9

6 0

3 years ago

I need help!!!!!!!!!!!!!!

stira [4]

The answer would have to be d

7 0

3 years ago

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The space shuttle travels at about 28,000 km per hour. Using that information, estimate how many hours it will take the shuttle

dem82 [27]

Answer:

It depends on the location of the Earth and Saturn. Depending on whether the earth is between sun and saturn, or sun is between earth and saturn, the distance from earth to saturn varies. Obviously, if the earth is between the Sun and Saturn, the shortest distance will be. We will understand that the gap between Earth and Saturn is:

Step-by-step explanation:

s = 1 275 000 000 km

The time required to travel that distance is:

t = s/v = 45535 hours or 1897.3 days

5 0

3 years ago

A maker of a certain brand of low-fat cereal barsclaims that the average saturated fat content is 0.5gram. In a random sample of

finlep [7]

Answer:

$t=\frac{0.475-0.5}{\frac{0.183}{\sqrt{8}}}=-0.386$

$p_v =2*P(t_{(7)}$

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 0.5 at 5% of signficance. So then the claim makes sense

Step-by-step explanation:

Previous concepts

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

The mean calculated for this case is $\bar X=0.475$

The sample deviation calculated $s=0.183$

We need to conduct a hypothesis in order to check if the true mean is 0.5 or no, the system of hypothesis would be:

Null hypothesis: $\mu = 0.5$

Alternative hypothesis: $\mu \neq 0.5$

If we analyze the size for the sample is < 30 and 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".

Calculate the statistic

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

$t=\frac{0.475-0.5}{\frac{0.183}{\sqrt{8}}}=-0.386$

P-value

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

$df=n-1=8-1=7$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(7)}$

Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to fail reject the null hypothesis, so we can't conclude that the true mean is different from 0.5 at 5% of signficance. So then the claim makes sense

4 0

3 years ago

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