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3 years ago

11

which of the following demonstrates how the first 21 on the left side of the triangle is calculated using the combination patter

n?

1 answer:

d1i1m1o1n [39]3 years ago

7 0

Answer:

d

Step-by-step explanation:

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How do you solve 6 1/2 x 16?

balu736 [363]

Answer:

Step-by-step explanation:

Make 6 1/2 an irrational fraction: 13/2 (I dunno know if its called that )

divide 16 by 2: 8

multiply that by 13: 104

Tell me if this helps or not bc I'm not really sure, but I really hope I helped!

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2 years ago

Olga had more than 6 aces in what percent of tennis matches

Tanya [424]

Answer:

50%

Step-by-step explanation:

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3 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 <em>sample mean</em>. The distribution for <em>sample means</em> follows a <em>normal distribution</em> 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 <em>z</em> follows a <em>standard normal distribution</em>, 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 <em>standard deviation</em> 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 <em>cumulative standard normal table</em> (or use some statistic program) to find the cumulative probability for <em>z</em> (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

What is the least common multiple of 8 and 10

Vika [28.1K]

Answer:

Pretty sure it's 2 :)

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

find the fraction of the area of a triangle that is occupied by the largest rectangular that can be drawn in the triangle (with

gogolik [260]

Answer:

½

Step-by-step explanation:

Draw a picture of the triangle with the rectangle inside it.

Let's say the width and height of the triangle are w and h (these are constants).

Let's say the width and height of the rectangle are x and y (these are variables).

The area of the triangle is ½ wh.

The area of the rectangle is xy.

Using similar triangles, we can say:

(h − y) / h = x / w

x = (w/h) (h − y)

So the rectangle's area in terms of only y is:

A = (w/h) (h − y) y

A = (w/h) (hy − y²)

We want to maximize this, so find dA/dy and set to 0:

dA/dy = (w/h) (h − 2y)

0 = (w/h) (h − 2y)

0 = h − 2y

y = h/2

So the width of the rectangle is:

x = (w/h) (h − y)

x = (w/h) (h − h/2)

x = (w/h) (h/2)

x = w/2

That means the area of the rectangle is:

A = xy

A = ¼ wh

The ratio between the rectangle's area and the triangle's area is:

(¼ wh) / (½ wh)

½

So no matter what the dimensions of the triangle are, the maximum rectangle will always be ½ its area.

6 0

3 years ago