A 2012 Gallup survey of a random sample of 1014 American adults indicates that American families spend on average $151 per week

Answer:

The exponential equation can be expressed as A = 600(1.04)^15

After 15 years, the value of the mutual fund will be $1,081

Step-by-step explanation:

The worth of the mutual fund after a specific number of years can be represented by the compound interest formula shown below;

A = P(1 + r/n)^nt

In this formula, A stands for the mutual fund's value after 15 years, P represents the principal amount invested, which is $600, r denotes the interest rate at 4% or 0.04 (thus, 4% = 4/100 = 0.04), n indicates the number of times compounding occurs per year (in this case, it is done once a year), and t represents the number of years, which is 15.

Now, substituting in these values gives us;

A = 600(1 + 0.04/1)^15

A = 600(1.04)^15

A = $1,081 approximately

Response:

The likelihood that fewer than 8 of the sampled adults use glasses or contact lenses is 0.4745.

Detailed explanation:

We have the following information:

Considering adults wearing glasses or contact lenses a success.

P(Adults use glasses or contact lenses) = 75% = 0.75

Hence, the number of adults follows a binomial distribution, represented as:

with n as total observations, x as successful outcomes, and p as success probability.

For our case, n = 10

We need to calculate:

P(fewer than 8 adults wear glasses or contact lenses)

0.4745 is the probability of having fewer than 8 of the selected adults utilizing glasses or contact lenses.

Brother is liable for 4/7 of the total cost.

Detailed solution:

The price of solid paper is $1.75 each

Printed paper is priced at $2.50 each

Information provided:

Ben's total is $43.50 (12 rolls of solid paper and 9 rolls of printed paper)

Joel's total is $51.50 (8 rolls of solid paper and 15 rolls of printed paper)

Let x represent solid paper

Let y represent printed paper

The equations are: 12x + 9y = 43.50

 8x + 15y = 51.50

To find x:

8x + 15y = 51.50

Solving for x gives: 8x = 51.50 - 15y

Thus, x = (51.50 - 15y)/8

Next, substitute x:

12x + 9y = 43.50

Replacing x results in: 12(51.50 - 15y)/8 + 9y = 43.50

Which expands to: (618 - 180y)/8 + 9y = 43.50

Multiplying through by 8 yields: 618 - 180y + 72y = 348

Rearranging gives us: -108y = 348 - 618

This simplifies to: -108y = -270

Dividing by -108 results in: y = 2.50

Using the expression for x:

x = (51.50 - 15y)/8

Substituting y, we get: x = (51.50 - 15(2.5))/8

Thus, x = (51.50 - 37.50)/8

This simplifies to: x = 14/8

Final value is: x = 1.75

Verification: x = 1.75; y = 2.5

Substituting into the first equation: 12x + 9y = 43.50

12(1.75) + 9(2.5) = 43.50

Calculating gives: 21 + 22.50 = 43.50

This confirms: 43.50 = 43.50

Substituting into the second equation: 8x + 15y = 51.50

8(1.75) + 15(2.5) = 51.50

Calculating yields: 14 + 37.50 = 51.50

This also confirms: 51.50 = 51.50

This is an exercise in fact families. A fact family consists of four related facts: two addition sentences and two subtraction sentences. The task asks for the subtraction fact written two ways.

First way. Start with 10 objects—imagine 10 triangles:

Δ Δ Δ Δ Δ
Δ Δ Δ Δ Δ

If you remove 3 triangles, how many remain? Seven remain:
Δ Δ Δ Δ Δ
Δ Δ 

So subtracting 3 from 10 gives:


Second way. Again begin with the same 10 triangles:Δ Δ Δ Δ Δ
Δ Δ Δ Δ Δ

This time remove 7 triangles; the leftovers are 3:
Δ Δ Δ

Thus subtracting 7 from 10 yields: