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3 years ago

If dh = 3x -3 and fh = x+7, find the value of x for which defg must be a parallelogram.

Mathematics

2 answers:

rosijanka [135]3 years ago

4 0

Answer:

Option c is correct

x = 5

Step-by-step explanation:

Properties of parallelogram:

Opposites sides are congruent.

Opposites angle are congruent

Diagonal of parallelogram bisect each other.

As per the statement:

In the given DEFG parallelogram,

DH = 3x-3 units

FH=x+7 units

by properties of parallelogram we have;

DH = FH

$3x-3 = x+7$

Subtract x from both sides we have;

$2x-3 =7$

Add 3 to both sides we have;

$2x=10$

Divide both sides by 2 we have;

x = 5

Therefore, the value of x for which DEFG must be a parallelogram is, 5

Ugo [173]3 years ago

3 0

parallelogram
DH = FH
3x -3 = x + 7
2x = 10
x = 5

Answer
c. 5

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A balloon rose 32 feet in the air. Then it fell to the ground.

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A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a variance of

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Answer:

The probability that the mean battery life would be greater than 533.2 minutes (in a sample of 75 batteries) is $\\ P(z>0.48) = P(x>533.2) = 0.3156$

Step-by-step explanation:

The main thing we have to take into account in this question is that we are about to find the probability of a sample mean. The distribution for sample means follows a normal distribution with mean $\\ \mu$ and standard deviation $\\ \frac{\sigma}{\sqrt{n}}$ . Mathematically

$\\ \overline{x} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

For values of the sample $\\ n \ge 30$ , no matter the distribution the data come from.

And the variable z follows a standard normal distribution, and, as we can remember, this distribution has a mean = 0 and a standard deviation = 1. Mathematically

$\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [1]

That is

$\\ z \sim N(0, 1)$

We have a variance of 3364. That is, a standard deviation of

$\\ \sigma^2 = 3364; \sigma = \sqrt{3364} = 58$

The population mean is

$\\ \mu = 530$

The sample size is $\\ n = 75$

The sample mean is $\\ \overline{x} = 533.2$

With all this information, we can solve the question

The probability that the mean battery life would be greater than 533.2 minutes

Using equation [1]

$\\ z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ z = \frac{533.2 - 530}{\frac{58}{\sqrt{75}}}$

$\\ z = \frac{3.2}{\frac{58}{8.66025}}$

$\\ z = \frac{3.2}{6.69726}$

$\\ z = 0.47780$

With this value of z we can consult a cumulative standard normal table (or use some statistic program) to find the cumulative probability for z (and remember that this variable follows a standard normal distribution).

Most standard normal tables have values for z for only two decimals, so we can round the previous value for z as z = 0.48.

Then

$\\ P(z$

However, in the question we are asked for $\\ P(z>0.48) = P(x>533.2)$ . As well as all normal distributions, the standard normal distribution is symmetrical around the mean, and we have

$\\ P(z>0.48) = 1 - P(z$

Thus

$\\ P(z>0.48) = 1 - 0.68439$

$\\ P(z>0.48) = 0.31561$

Rounding to four decimal places, we have

$\\ P(z>0.48) = 0.3156$

So, the probability that the mean battery life would be greater than 533.2 minutes is (in a sample of 75 batteries) $\\ P(z>0.48) = P(x>533.2) = 0.3156$ .

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4 years ago

I need some help on this

andrew-mc [135]

Answer:

b, k = -4

Step-by-step explanation:

3/2 = k + 11/2

=> 3/2 - 11/2 = k

=> -8/2 = k

=> k = -4

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