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3 years ago

Help pls! I need the answer quickly and pls explain. thank you!

Mathematics

1 answer:

riadik2000 [5.3K]3 years ago

5 0

Answer:

h = 6 $\sqrt{3}$

Step-by-step explanation:

The given is the special right triangle with angle measures : 90-60-30

and the side lengths for the given angles are represented by :

2a-a $\sqrt{3}$ -a

the side length that sees 60 degrees is represented by a $\sqrt{3}$ (h in this case)

the area of a triangle is calculated by multiplying height and base and that is divided by 2

a $\sqrt{3}$ *a/2 = 18 $\sqrt{3}$ multiply both sides by 2

a^2 $\sqrt{3}$ = 36 $\sqrt{3}$ divide both sides by $\sqrt{3}$

a^2 = 36 find the roots for both sides

a = 6

since h sees angle measure 60 and is represented by a $\sqrt{3}$

h = 6 $\sqrt{3}$

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What are the steps for this problem<br> 2/6m+2=6

beks73 [17]

$\frac{2}{6} m+2=6\\ \frac{1}{3} m=4\\ m =12$

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3 years ago

Describe the relationship between n and 4 that will make the value of the expression 6 x n/4 greater than 6.

KatRina [158]

Answer:

n is greater than 4

Step-by-step explanation:

We have to find the relation between n and 4 for which $(6\times \frac{n}{4})$ is greater 6.

Converting this verbal expression into algebraic expression,

$(6\times \frac{n}{4})>6$

$(6\times \frac{n}{6\times 4})>\frac{6}{6}$

$\frac{n}{4}>1$

$\frac{n}{4}\times 4>1\times 4$

n > 4

Therefore, relation between n and 4 is "n is greater than 4".

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3 years ago

What is the percent of change from 74 to 112? rounded to the nearest percent

ruslelena [56]

Answer:

The percent of change from 74 to 112 is 51%.

Step-by-step explanation:

Given:

The percent of change from 74 to 112.

Now, the difference between the numbers $112-74=38$ .

Then, calculating the percentage of the result by $74$ .

$\frac{38}{74}\times100$

$=0.5135\times100$

$=51.35%$ .

Round to the nearest percent of $51.35%$ is $51%$ .

Therefore, the percent of change from 74 to 112 is 51%.

4 0

3 years ago

Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose t

worty [1.4K]

Answer:

a) $P(X \leq 100) = 1- e^{-0.01342*100} =0.7387$

$P(X \leq 200) = 1- e^{-0.01342*200} =0.9317$

$P(100\leq X \leq 200) = [1- e^{-0.01342*200}]-[1- e^{-0.01342*100}] =0.1930$

b) $P(X>223.547) = 1-P(X\leq 223.547) = 1-[1- e^{-0.01342*223.547}]=0.0498$

c) $m = \frac{ln(0.5)}{-0.01342}=51.65$

d) $a = \frac{ln(0.05)}{-0.01342}=223.23$

Step-by-step explanation:

Previous concepts

The exponential distribution is "the probability distribution of the time between events in a Poisson process (a process in which events occur continuously and independently at a constant average rate). It is a particular case of the gamma distribution". The probability density function is given by:

$P(X=x)=\lambda e^{-\lambda x}$

Solution to the problem

For this case we have that X is represented by the following distribution:

$X\sim Exp (\lambda=0.01342)$

Is important to remember that th cumulative distribution for X is given by:

$F(X) =P(X \leq x) = 1-e^{-\lambda x}$

Part a

For this case we want this probability:

$P(X \leq 100)$

And using the cumulative distribution function we have this:

$P(X \leq 100) = 1- e^{-0.01342*100} =0.7387$

$P(X \leq 200) = 1- e^{-0.01342*200} =0.9317$

$P(100\leq X \leq 200) = [1- e^{-0.01342*200}]-[1- e^{-0.01342*100}] =0.1930$

Part b

Since we want the probability that the man exceeds the mean by more than 2 deviations

For this case the mean is given by:

$\mu = \frac{1}{\lambda}=\frac{1}{0.01342}= 74.516$

And by properties the deviation is the same value $\sigma = 74.516$

So then 2 deviations correspond to 2*74.516=149.03

And the want this probability:

$P(X > 74.516+149.03) = P(X>223.547)$

And we can find this probability using the complement rule:

$P(X>223.547) = 1-P(X\leq 223.547) = 1-[1- e^{-0.01342*223.547}]=0.0498$

Part c

For the median we need to find a value of m such that:

$P(X \leq m) = 0.5$

If we use the cumulative distribution function we got:

$1-e^{-0.01342 m} =0.5$

And if we solve for m we got this:

$0.5 = e^{-0.01342 m}$

If we apply natural log on both sides we got:

$ln(0.5) = -0.01342 m$

$m = \frac{ln(0.5)}{-0.01342}=51.65$

Part d

For this case we have this equation:

$P(X\leq a) = 0.95$

If we apply the cumulative distribution function we got:

$1-e^{-0.01342*a} =0.95$

If w solve for a we can do this:

$0.05= e^{-0.01342 a}$

Using natural log on btoh sides we got:

$ln(0.05) = -0.01342 a$

$a = \frac{ln(0.05)}{-0.01342}=223.23$

5 0

3 years ago

Write an equation:Three sisters went shopping for Mother’s Day. Each sister bought a gift for their mom. Maggie spent 3 times as

masya89 [10]

Answer:

Karen spent $ 10 , Jasmine spent $20 , Maggie spent $30

When x disappears from the equation and the two sides of the equation not equal each other , then the equation has no solution

When x disappears from the equation and the two sides of the equation equal each other , then the equation has infinite solutions

Step-by-step explanation:

* Lets read the problem and solve it

- There are three sisters ⇒ Maggie , Karen , Jasmine

- Each sister bought a gift for their mom

- Maggie spent 3 times as much as Karen

- Karen spent half as much as Jasmine

- Altogether, they spent $60

- Let Jasmine spent x

∵ Karen spent half as much as Jasmine

∴ Karen spent 1/2 x

∵ Maggie spent 3 times as much as Karen

∴ Maggie spent 3 × 1/2 x = 3/2 x

∵ Altogether, they spent $60

∴ x + 1/2 x + 3/2 x = 60

∴ 3x = 60 ⇒ divide both sides by 3

∴ x = 20

* Lets find the share of each one

∵ Jasmine spent x

∴ Jasmine spent $20

∵ Karen spent 1/2 x

∴ Karen spent 1/2 × 20 = $10

∵ Maggie spent 3/2 x

∴ Maggie spent 3/2 x 20 = $30

* Karen spent $ 10 , Jasmine spent $20 , Maggie spent $30

* Lets describe what happens when an equation has no solution

- "No solution" means that there are no values of x satisfy the equation

- When x disappears from the equation and the two sides of the

equation not equal each other , then the equation has no solution

- Ex: solve the equation 2 + 2x – 8 = 7x + 5 – 5x

∵ 12 + 2x – 8 = 7x + 5 – 5x ⇒ add the like terms

∴ 4 + 2x = 2x + 5 ⇒ subtract 2x from both sides

∴ 4 = 5 ⇒ the two sides not equal

∴ There is no value of x satisfy this equation

∴ There is no solution

* Lets describe what happens when an equation has infinite solutions

- "Infinite solutions" means all numbers are solutions.

- When x disappears from the equation and the two sides of the

equation equal each other , then the equation has infinite solutions

- Ex: solve the equation 2x + 3 = x + x + 3

∵ 2x + 3 = x + x + 3 ⇒ add the like terms

∴ 2x + 3 = 2x + 3 ⇒ subtract 2x from both sides

∴ 3 = 3 ⇒ the two sides are equal

∴ All values of x satisfy the equation

∴ There are infinite solutions

3 0

4 years ago