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3 years ago

Find the triangle of the following figure: A. 30cm2 B: 36cm2 C. 18cm2 D. 15cm2

Mathematics

1 answer:

hram777 [196]3 years ago

8 0

Answer:

D. 15cm2

Step-by-step explanation:

To find the area of a triangle, you multiply the base (10cm) and height of the triangle (3cm) and divide that by 2. So 10×3=30. Then, you need to divide this by 2. Since 30 is an even number, you won't get a decimal. So 30/2=15. And dont forget your units!

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Assume the random variable X is normally distributed with mean

nignag [31]

Answer:

$P(34$

And we can find this probability with this difference and using the normal standard table or excel:

$P(-2.286$

And the result is illustrated in the figure attached.

Step-by-step explanation:

Previous concepts

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:

$X \sim N(50,7)$

Where $\mu=50$ and $\sigma=7$

We are interested on this probability

$P(34$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(34$

And we can find this probability with this difference and using the normal standard table or excel:

$P(-2.286$

And the result is illustrated in the figure attached.

5 0

3 years ago

Two random samples were taken to determine how often people in a community listen to the local radio station each month. The fir

leonid [27]

Answer:

The answers to this question are 1,2,4,6. Hope this helps you

Step-by-step explanation:

3 0

4 years ago

Sierra wants to train for a marathon. Right now she can run 4 miles. She plans to add half a mile each week

Monica [59]

Answer:

go on.Need more info how many weeks does she need to reach her goal?

6 0

3 years ago

The total sales were $200 more than the manager's prediction. If x represents the manager prediction, write an expression to rep

OverLord2011 [107]

Answer:

$y = 200 + x$

Step-by-step explanation:

Given

$Prediction = x$

$Sales = \$200\ more$

Required

Determine the actual sales

Represent the actual sales with u

$y = Sales + Prediction$

$y = 200 + x$

Hence, the total sales can be expressed using y = 200 + x

4 0

3 years ago

A computer company claims that the batteries in its laptops last 4 hours on average. A consumer report firm gathered a sample of

klemol [59]

Answer:

a) We can reject the null hypothesis and conclude that average battery time is shorter than 4 hours at a = 0.05

b) 95% confidence interval of the mean battery time is 230±11.55. That is between 218.45 min and 241.55 min.

c) If you were to test H0: µ =240 minutes vs. H1: µ ≠ 240 minutes, we can conclude that we fail to reject the null hypothesis, because confidence interval includes 240 min.

d) We made a correct decision at c, if study establishes that in fact, a population mean is 4 hours.

Step-by-step explanation:

H0: µ=240

H1: µ<240

Test statistic can be found using the equation

$t=\frac{X-M}{\frac{s}{\sqrt{N} } }$ where

X = 230 min. (3 hours 50 minutes)

M is the lasting time of laptop batteries claimed in null hypothesis (240 min.)

s is the sample standard deviation (20 minutes)

N is the sample size (16)

$t=\frac{230-240}{\frac{20}{\sqrt{16} } }$ = -2

One tailed p-value of t=-2 for 15 degrees of freedom is ≈ 0.032

Since 0.032<0.05, the result is significant. We can reject the null hypothesis and conclude that average battery time is shorter than 4 hours at a = 0.05

b) 95% confidence interval of the mean battery time can be calculated using M± $\frac{t*s}{\sqrt{n}}$ where

M is the sample average lasting time (230 min)

t is the two tailed statistic for 95% confidence level and 15 degrees of freedom (2.13)

s is the sample standard deviation (20 min.)

n is sample size (16)

230± $\frac{2.31*20}{\sqrt{16}}$ that is 230±11.55

c) If you were to test H0: µ =240 minutes vs. H1: µ ≠ 240 minutes, from 95% confidence interval which is between 218.45 min and 241.55 min, we can conclude that we fail to reject the null hypothesis, because confidence interval includes 240 min.

d) We made a correct decision at c, if study establishes that in fact, a population mean is 4 hours.

4 0

3 years ago

Read 2 more answers