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3 years ago

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Into a triangle, with a base of 30cm and height of 10cm, has been drawn a right triangle (90°), such that it's hypotenuse is par

allel to the given triangles base, and the 90° corner in the triangle is at its base. Calculate the hypotenuse of that 90° triangle.
Please help!

1 answer:

zavuch27 [327]3 years ago

3 0

Answer:

31.62

Step-by-step explanation:

If we know it's a right triangle, we can use the Pythagorean Theorem to solve this problem.

10^2 + 30^2 = 1000

Find the square root of 1000 and get your answer of 31.62.

Hope this Helps!

Good Luck!

<em>-kiniwih426</em>

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Andrew plans to retire in 32 years. He plans to invest part of his retirement funds in stocks, so he seeks out information on pa

Debora [2.8K]

Answer:

a) 0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

b) 0.4129 = 41.29% probability that the mean return will be less than 8%

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.

Mean 8.7% and standard deviation 20.2%.

This means that $\mu = 8.7, \sigma = 20.2$

40 years:

This means that $n = 40, s = \frac{20.2}{\sqrt{40}}$

(a) What is the probability (assuming that the past pattern of variation continues) that the mean annual return on common stocks over the next 40 years will exceed 13%?

This is 1 subtracted by the pvalue of Z when X = 13. So

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

By the Central Limit Theorem

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

$Z = \frac{13 - 8.7}{\frac{20.2}{\sqrt{40}}}$

$Z = 1.35$

$Z = 1.35$ has a pvalue of 0.9115

1 - 0.9115 = 0.0885

0.0885 = 8.85% probability that the mean annual return on common stocks over the next 40 years will exceed 13%.

(b) What is the probability that the mean return will be less than 8%?

This is the pvalue of Z when X = 8. So

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

$Z = \frac{8 - 8.7}{\frac{20.2}{\sqrt{40}}}$

$Z = -0.22$

$Z = -0.22$ has a pvalue of 0.4129

0.4129 = 41.29% probability that the mean return will be less than 8%

8 0

3 years ago

suppose you have a bag that holds 30 pieces of candy 11 blueberry 5 lemon and 14 cream soda you reach into the bag pull out one

kumpel [21]

Okay, so if you have 30 pieces of candy. 14 of them are cream soda flavored, so, right away, you can eliminate those. 30-14=16. 16 pieces are not cream soda flavored. So put the number of non cream soda flavored pieces as the numerator over the total number of candy pieces as the denominator. 16/30. However, we can simplify this. take the numerator and divide it by 2, to get 8. take the denominator and divide it by 2, to get 15. So the simplified fraction is 8/15. So there is an 8 out of 15 chance that you will pull out a candy that is not cream soda flavored.

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3 years ago

1/6b=7.4 please help

Alex17521 [72]

1/6b=74/10
b=74/10 / 1/6
b=74/10 *6/1
b=222/5
b=44.4

7 0

4 years ago

What is √2323 in simplest form as a radicand and a number outside the radicand

bazaltina [42]

Since 2323 = 23*101 has no perfect square factors, this means we cannot simplify $\sqrt{2323$ into the form $a\sqrt{b}$

It seems like your teacher may have made a typo. I would double check with them.

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

I'll show you how to simplify a different problem. Let's say we want to simplify $\sqrt{232}$

Find the prime factorization of the radicand:

232 = 2^3*29

we can rewrite the "2^3" as "2^2*2" to pull out the perfect square factor, which helps us simplify as such:

$\sqrt{232} = \sqrt{2^3*29}$

$\sqrt{232} = \sqrt{2^2*2*29}$

$\sqrt{232} = \sqrt{2^2*58}$

$\sqrt{232} = \sqrt{2^2}*\sqrt{58}$

$\sqrt{232} = 2*\sqrt{58}$

For the last two steps I used these square root rules

$\sqrt{x*y} = \sqrt{x}*\sqrt{y}$

$\sqrt{x^2} = x$ where x is nonnegative

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3 years ago

A rectangular parking lot has a perimeter of 820 ft. The area of the parking lot measure SL 42,000 ft

horsena [70]

Answer:

a= 200

b = 210

Step-by-step explanation:

My assumption is, we have to find the length of sides of rectangle

Given

perimeter = 2a + 2b = 820 ft (i) (here a is smaller side and b is larger side)

area = a*b = 42,000 ft^2 (ii)

from eq (1)

2a + 2b = 820

=> 2(a+b) = 820

=> a+b = 820/2

=> a + b = 410

=> a = 410-b (iii)

putting the value of a in eq(ii), we get

(410-b) *b = 42,000

410b - b^2 = 42,000

0 = b^2 - 410b + 42000

b^2 - 410b + 42000 = 0

b^2- 200b- 210b + 42000 = 0

b(b-200)-210(b-200) = 0

(b-200)(b-210) = 0

or

b= 210 and b = 200

if b is larger side than b =210

By putting value of b in eq(iii),

a = 410 -210 = 200

6 0

3 years ago