MATHEMATICS COLLEGE

Find the area of the right triangle.

Answers

Answer 1

Answer:

Answer:

area is 28 units²

Step-by-step explanation:

find the area of the rectangle with sides 7 and 8 and divide it in half

A=7*8/2= 56/2=28

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Suppose that the US plans to send a shipment of "rovers" to Mars. These are mobile robots, programmed to collect rock and soil samples, and then return to the landing site. The rovers operate independently of each other. The mean weight a rover is programmed to collect is 50 pounds, and the standard deviation of weights is 5 pounds. Weights collected by rovers are approximately normally distributed. If the US sends 10 rovers, what is the probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds? What sampling distribution should we use to compute this probability?

Answers

Answer:

79.24% probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds

We use the sampling distribution of the sample means of size 10 to solve this question, by the Central Limit Theorem. They are normally distributed with mean 50 and standard deviation 1.58.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = (\sigma)/(√(n))$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 50, \sigma = 5, n = 10, s = (5)/(√(10)) = 1.58$

What is the probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds?

This is the pvalue of Z when X = 52 subtracted by the pvalue of Z when X = 48. So

X = 52

$Z = (X - \mu)/(\sigma)$

By the Central Limit Theorem

$Z = (X - \mu)/(s)$

$Z = (52 - 50)/(1.58)$

$Z = 1.26$

$Z = 1.26$ has a pvalue of 0.8962

X = 48

$Z = (X - \mu)/(s)$

$Z = (48 - 50)/(1.58)$

$Z = -1.26$

$Z = -1.26$ has a pvalue of 0.1038

0.8962 - 0.1038 = 0.7924

79.24% probability that the average weight of rock and soil brought back by these rovers will be between 48 pounds and 52 pounds

What sampling distribution should we use to compute this probability?

We use the sampling distribution of the sample means of size 10 to solve this question, by the Central Limit Theorem. They are normally distributed with mean 50 and standard deviation 1.58.

Jamie ordered 200 business cards and paid $23. She ordered 500 business cards and few months later and paid $35. WRITE and SOLVE a linear equation to find the cost to order 700 business cards.

Answers

Find the unit rate of the previous two. use that to plug in 700

There are 500 employees in a firm, 45% are female. a sample of 60 employees is selected randomly. the probability that the sample proportion of females is between 0.40 and 0.55 is

Answers

Let X be the number of female employee. Let n be the sample size, p be the probability that selected employee is female.

It is given that 45% employee are female it mean p=0.45

Sample size n=60

From given information X follows Binomial distribution with n=50 and p=0.45

For large value of n the Binomial distribution approximates to Normal distribution.

Let p be the proportion of female employee in the given sample.

Then distribution of proportion P is normal with parameters

mean =p and standard deviation = $\sqrt{(p(1-p))/(n)}$

Here we have p=0.45

So mean = p = 0.45 and

standard deviation = $\sqrt{(0.45(1-0.45))/(60)}$

standard deviation = 0.0642

Now probability that sample proportions of female lies between 0.40 and 0.55 is

P(0.40 < P < 0.45) = $P((0.40 - 0.45)/(0.0642) < (P-mean)/(standard deviation) < (0.55- 0.45)/(0.0642) )$

= P(-0.7788 < Z < 1.5576)

= P(Z < 1.5576) - P(Z < -0.7788)

= P(Z < 1.56) - P(Z < -0.78)

= 0.9406 - 0.2177

= 0.7229

The probability that the sample proportion of females is between 0.40 and 0.55 is 0.7229

Final answer:

To find the probability that the sample proportion of females is between 0.40 and 0.55, convert the sample proportions to z-scores and use the z-table to find the probabilities.

Explanation:

To find the probability that the sample proportion of females is between 0.40 and 0.55, we need to find the z-scores associated with these proportions and use the z-table to find the probabilities.

First, we need to convert the sample proportions to z-scores using the formula: z = (p - P) / √(P(1-P) / n), where p is the sample proportion, P is the population proportion, and n is the sample size.

Once we have the z-scores, we can use the z-table to find the probabilities. The probability that the sample proportion of females is between 0.40 and 0.55 is the difference between the probabilities associated with the z-scores for 0.40 and 0.55.

Learn more about Probability here:

brainly.com/question/32117953

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Ms Adams shares out 36 pencils between Niamh and jack in the ratio 4:8 How many pencils does each get?

Answers

Answer:

Niamh gets 12 and Jack gets 24.

Step-by-step explanation:

4:8 is equal to 1:2. 1 part + 2 parts is equal to 3 parts, which is equal to the whole. 36 is the whole, so 36/3 is equal to 12. 1 * 12 is equal to 12, and 2 * 12 is equal to 24.

Answer:Adam gets 12 and nidam gets 24..

Step-by-step explanation:feel pleasure to help u..

Please use statement and reason, not sin cos or tan. In rectangle ABCD the diagonals intersect each other at point O and ABD = 30. Find BC if AC = 16 in. Include a picture if you can, but you don't have to.

Answers

Answer:

8 in

Step-by-step explanation:

Rectangle has properties:
Diagonals are congruent
Opposite sides are congruent
All angles are right

Given

m∠ABD = 30°
AC = 16 in
BC = ?

Solution

As per properties mentioned above we have:

BC = AD
BD = AC = 16 in

ΔABD is right triangle with ∠B - 30°, ∠A- 90°, ∠D - 60°

Side opposite to 30 is half of the length of the hypotenuse

AD is opposite to ∠B and BD is the hypotenuse, then:

AD = 1/2*BD
AD = 1/2(16)
AD = 8 in

and

BC = AD = 8 in

Help with this problem (20 points)

Answers

Answer:

what problem? i dont see it

No problem here! Are you sure?

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