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3 years ago

How do you identify the constant of proportionality when given an equation?

1 answer:

8 0

The constant of proportionality k is given by k=y/x where y and x are two quantities that are directly proportional to each other. Once you know the constant of proportionality you can find an equation representing the directly proportional relationship between x and y, namely y=kx, with your specific k. (i looked up this explanation but not sure if it’s right.. if it’s wrong let me know:) )

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the jedi have a weapon that can shoot a projectile 20 miles. find the area that the projectile can land in.

kifflom [539]

Answer:

The area he can cover with that weapon is 1,256 miles².

Step-by-step explanation:

Assuming that the Jedi won't move and that he can shoot in every direction, he'd be shooting at a circle with a radius of 20 miles. Therefore the are that he can cover with that weapon is the area of the circle, which is shown below:

area = pi*r²

area = 3.14*(20)²

area = 3.14*400

area = 1,256 miles²

The area he can cover with that weapon is 1,256 miles².

5 0

4 years ago

How many grams are in 8 kilograms?

shutvik [7]

I believe it is 8,000 grams :).

5 0

3 years ago

The mean of a population is 74 and the standard deviation is 15. The shape of the population is unknown. Determine the probabili

Lena [83]

Answer:

a) 0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

b) 0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c) 0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

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 normal distributions can be solved using the z-score formula.

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

$Z = \frac{X - \mu}{\sigma}$

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 p-value, 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 $s = \frac{\sigma}{\sqrt{n}}$ .

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

The mean of a population is 74 and the standard deviation is 15.

This means that $\mu = 74, \sigma = 15$

Question a:

Sample of 36 means that $n = 36, s = \frac{15}{\sqrt{36}} = 2.5$

This probability is 1 subtracted by the pvalue of Z when X = 78. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{78 - 74}{2.5}$

$Z = 1.6$

$Z = 1.6$ has a pvalue of 0.9452

1 - 0.9452 = 0.0548

0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

Question b:

Sample of 150 means that $n = 150, s = \frac{15}{\sqrt{150}} = 1.2247$

This probability is the pvalue of Z when X = 77 subtracted by the pvalue of Z when X = 71. So

X = 77

$Z = \frac{X - \mu}{s}$

$Z = \frac{77 - 74}{1.2274}$

$Z = 2.45$

$Z = 2.45$ has a pvalue of 0.9929

X = 71

$Z = \frac{X - \mu}{s}$

$Z = \frac{71 - 74}{1.2274}$

$Z = -2.45$

$Z = -2.45$ has a pvalue of 0.0071

0.9929 - 0.0071 = 0.9858

0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c. A random sample of size 219 yielding a sample mean of less than 74.2

Sample size of 219 means that $n = 219, s = \frac{15}{\sqrt{219}} = 1.0136$

This probability is the pvalue of Z when X = 74.2. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{74.2 - 74}{1.0136}$

$Z = 0.2$

$Z = 0.2$ has a pvalue of 0.5793

0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

5 0

3 years ago

Why can't a trapezoid have 4 obtuse angles

In-s [12.5K]

Hello there, and thank you for posting your question here on brainly.

A trapezoid is not possible to have for obtuse because it would look more like a diamond. Also, if it had 4 obtuse angles, it would have 6 sides.

Hope this helped!! ☺♥

7 0

3 years ago

Read 2 more answers

Find the volume................

Sauron [17]

Answer:

$1) v= 400 ft^{2}$

$2) v=1093.3m^{3}$

Step-by-step explanation:

1) v= 1/3 ab ×h

v= 1/3 (10)(10)×√13²-5²

v= 400 ft²

-------------------

2) v= πr² h/3

v= 1/3 × π×(6)²×29

v= 1/3×π×12×29

v= 348π

v= 1093.27

≈1093.3

---------------

hope it helps...

have a great day!!

5 0

3 years ago