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3 years ago

Complete this factor tree to find the prime factors of 492

Mathematics

2 answers:

AVprozaik [17]3 years ago

5 0

Answer:

Yesh it's 3 then 41 I got it right on time4learning

Ik I'm the best

damaskus [11]3 years ago

4 0

Answer:

246

Step-by-step explanation:

next time use a calculator

divide 492 by 2 and you get 246

divide that by 2 and you get 123

and divide that by 3 and you get 41

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The mean number of words per minute (WPM) read by sixth graders is 8888 with a standard deviation of 1414 WPM. If 137137 sixth g

Bingel [31]

Noticing that there is a pattern of repetition in the question (the numbers are repeated twice), we are assuming that the mean number of words per minute is 88, the standard deviation is of 14 WPM, as well as the number of sixth graders is 137, and that there is a need to estimate the probability that the sample mean would be greater than 89.87.

Answer:

"The probability that the sample mean would be greater than 89.87 WPM" is about $\\ P(z>1.56) = 0.0594$ .

Step-by-step explanation:

This is a problem of the distribution of sample means. Roughly speaking, we have the probability distribution of samples obtained from the same population. Each sample mean is an estimation of the population mean, and we know that this distribution behaves normally for samples sizes equal or greater than 30 $\\ n \geq 30$ . Mathematically

$\\ \overline{X} \sim N(\mu, \frac{\sigma}{\sqrt{n}})$ [1]

In words, the latter distribution has a mean that equals the population mean, and a standard deviation that also equals the population standard deviation divided by the square root of the sample size.

Moreover, we know that the variable Z follows a normal standard distribution, i.e., a normal distribution that has a population mean $\\ \mu = 0$ and a population standard deviation $\\ \sigma = 1$ .

$\\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$ [2]

From the question, we know that

The population mean is $\\ \mu = 88$ WPM
The population standard deviation is $\\ \sigma = 14$ WPM

We also know the size of the sample for this case: $\\ n = 137$ sixth graders.

We need to estimate the probability that a sample mean being greater than $\\ \overline{X} = 89.87$ WPM in the distribution of sample means. We can use the formula [2] to find this question.

The probability that the sample mean would be greater than 89.87 WPM

$\\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$\\ Z = \frac{89.87 - 88}{\frac{14}{\sqrt{137}}}$

$\\ Z = \frac{1.87}{\frac{14}{\sqrt{137}}}$

$\\ Z = 1.5634 \approx 1.56$

This is a standardized value and it tells us that the sample with mean 89.87 is 1.56 standard deviations above the mean of the sampling distribution.

We can consult the probability of P(z<1.56) in any cumulative standard normal table available in Statistics books or on the Internet. Of course, this probability is the same that $\\ P(\overline{X} < 89.87)$ . Then

$\\ P(z$

However, we are looking for P(z>1.56), which is the complement probability of the previous probability. Therefore

$\\ P(z>1.56) = 1 - P(z$

$\\ P(z>1.56) = P(\overline{X}>89.87) = 0.0594$

Thus, "The probability that the sample mean would be greater than 89.87 WPM" is about $\\ P(z>1.56) = 0.0594$ .

5 0

3 years ago

Write the equation of a line that is perpendicular to the line that passes through (4,−3)and (−7,8).

masha68 [24]

Line perpendicular to a given line is = 1/m

To find m, use m =y2-y1/x2-x1 formula

m = (8-(-3))/(-7-4)

m = 11/-11,

m = -1

Use y= mx+c to find equation of line

Plug in a pair of values,

-3= -1(4)+ c

c= 1

Thus, equation is:

y = -x+1

Equation of line perpendicular to this line is:

y= x+1

Hope it helps :)

Pls mark it as Brainliest :)

3 0

3 years ago

You need a 50% solution. On hand, you have a 200 mL of a 35% alcohol mixture. You also have 70% alcohol mixture. How much of the

CaHeK987 [17]

Answer:

150 mL

Step-by-step explanation:

We need a mixture that is at 50%, now we have 200 mL at 35% and another mixture that is at 70%, that is, we must calculate how much of this mixture is added, by the following equation

200 * 35% + x * 70% = 50% (x + 200)

70 + 0.7 * x = 0.5 * x + 100

0.7 * x - 0.5 * x = 100 - 70

0.2 * x = 30

x = 30 / 0.2

x = 150

150 mL must be added so that the mixture is 50%.

6 0

3 years ago

Cate and Elena were playing a card game. The stack of cards in the middle had 24 cards in it to begin with. Cate added 8 cards t

Yuki888 [10]

You start with 24, there are 8 added, there are 12 taken away, then 9 are taken away. The equation looks like:
24 + 8 - 12 - 9 = 11

7 0

3 years ago

During a test period, an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO2 emission

Aleksandr-060686 [28]

Answer:

Probably unequal ( B )

Step-by-step explanation:

experimental group = 10

using 85% ethanol gasoline

mean = 240 pounds per 100 miles

standard deviation = 20 pounds

control group = 14 vehicles

using regular gasoline

mean = 252 pounds per 100 miles

standard deviation = 15 pounds

comparing the sample variance of each group shows that they are probably unequal using the equation below

Variance for a sample set of data = ∑ ( x - X ) ^2 / n - 1

where n = number of events

X = mean value

x = value of events

8 0

3 years ago