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3 years ago

What is the value of x? The answer can be a decimal! (5x - 25) ° (3x + 9°

Mathematics

2 answers:

bixtya [17]3 years ago

4 0

5x - 25 + 3x + 9 = 180
8x - 16 = 180
8x = 196
x = 24.5

Nesterboy [21]3 years ago

3 0

Answer:

24.5

Step-by-step explanation:

5x-25+3x+9=180

8x-16=180

8x=196

196/8=24.5

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ABC is a right triangle with AB = AC. Bisector of ∠A meets BC at D. prove that ∆ ABC ≅ ∆DEF

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Answer:

Triangles ABC and DEF have the following characteristics :B and E are right angles A=D, BC=EF which congruence theorem can be used to prove ABC =DEF

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3 years ago

Solve the inequality 3m - 3(m + 8) > 3m

OlgaM077 [116]

Answer:

m<−8

Step-by-step explanation:

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3 years ago

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I am once having trouble solving an equation. 6x2 - 2x = 19

brilliants [131]

Answer:

X=1 9/10

Step-by-step explanation:

6X multiply 2 - 2X=19

Calculate the product

12X-2X=19

Collect the like terms

10X=19

Divide both sides of the equation by 10

X=19/10

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4 years ago

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

iris [78.8K]

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) $\\ P(z>0.48) = P(x>533.2) = 0.3156$ .

5 0

3 years ago

Multiply -4/9 x -7/8 Write fractions in simplest form.

Ray Of Light [21]

Answer:

7/18

Step-by-step explanation:

-4 × -7

9 × 8

28/72, which would simplify to 7/18

8 0

3 years ago