Simplify the expression below (4x)3

What is the equation of a line with a slope of -8 and an ordered pair (4,-3)?

lisabon 2012 [21]

You can solve this easily using point slope form: y-y1 = m(x-x1)
Substitute the given y value in for y1 and the given x for x1, and substitute the slope in for m.
To put it in slope intercept form, isolate y.
Hope this helps!

6 0

3 years ago

Mallory is 2 years older than three times her brother Jake’s age. Let j represent Jake’s age. During the Strategize step of the

DedPeter [7]

Let j = Jake's age.
Because Mallory is 2 years older than three times Jake, Mallory's age is
3j + 2.

Answer: Mallory's age is 3j + 2

6 0

4 years ago

-10 + 15xy = 20 Direct and inverse variation. constant of variation (k)

lozanna [386]

Answer:

This is an inverse variation, and the constant of variation is k = 2.

Step-by-step explanation:

Direct variation is something like:

y = k*x

Where k is the constant of variation.

So as x increases also increases y.

Inverse variation is something like:

y = k/x

k is the constant of variation.

In this case, if x increases, y decreases.

Now let's look at the equation:

-10 + 15*x*y = 20

Let's isolate y in one side of the equation:

15*x*y = 20 + 10 = 30

15*x*y = 30

y = 30/(15*x) = (30/15)/x = 2/x

y = 2/x

Then we can conclude that this is an inverse variation, with a constant of variation equal to 2.

4 0

4 years ago

A health statistics agency in a certain country tracks the number of adults who have health insurance. Suppose according to the

Nana76 [90]

Answer:

a) There is a 15.3% probability that a randomly selected person in this country is 65 or older.

b) Given that a person in this country is uninsured, there is a 2.2% probability that the person is 65 or older.

Step-by-step explanation:

We have these following percentages:

5.3% of those under the age of 18, 12.6% of those ages 18–64, and 1.3% of those 65 and older do not have health insurance.

22.6% of people in the county are under age 18, and 62.1% are ages 18–64.

(a) What is the probability that a randomly selected person in this country is 65 or older?

22.6% are under 18

62.10% are 18-64

The rest are above 65

So

100% - (22.6% + 62.10%) = 15.3%

There is a 15.3% probability that a randomly selected person in this country is 65 or older.

b) Given that a person in this country is uninsured, what is the probability that the person is 65 or older?

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

$P = \frac{P(B).P(A/B)}{P(A)}$

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

So, what is the probability that a person is 65 and older, given that the person is uninsured.

P(B) is the probability that a person is 65 and older. From a), we have that $P(B) = 0.153$

P(A/B) is the probability is uninsured, given that that person is 65 and older. So $P(A/B) = 0.013$

P(A) is the probability that a person is uninsured. That is the sum of 5.3% of 22.6%, 12.6% of 62.1% and 1.3% of 15.3%. So:

$P(A) = 0.053*(0.226) + 0.126*(0.621) + 0.013*(0.153) = 0.0922$

So

$P = \frac{P(B).P(A/B)}{P(A)} = \frac{0.153*0.013}{0.0922} = 0.022$

Given that a person in this country is uninsured, there is a 2.2% probability that the person is 65 or older.

6 0

3 years ago

HELP ASAP!!! A man is 6 feet 2 inches tall. To find the height of a tree, the shadow of the man and the shadow of the tree were

Whitepunk [10]

1 ft = 12 inches

6 ft = 72 inches (multiply both sides by 6)

6 ft + 2 inches = 72+2 = 74 inches

6 ft, 2 inches = 74 inches

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

1 ft = 12 inches

2 ft = 24 inches

2 ft + 1 in = 24+1 = 25 inches

2 ft, 1 in = 25 inches

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

1 ft = 12 inches

3 ft = 36 inches

3 ft + 7 in = 36+7 = 43 inches

3 ft, 7 in = 43 inches

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

To rewrite the problem a bit in equivalent form, we have a man who is 74 inches cast a shadow that is 25 inches long. The tree has a shadow of 43 inches. We want to find the height of the tree, which for now we'll call x

(tree height)/(tree shadow) = (person height)/(person shadow)

x/43 = 74/25

25x = 43*74

25x = 3182

x = 3182/25

x = 127.28 inches

The tree is 127.28 inches tall which is the same as 10 ft, 7.28 inches

because 127/12 = 10 remainder 7, then we add on the 0.28 portion

8 0

3 years ago