Part of Abernathy’s divorce settlement involves setting aside money today for college tuition for their daughter who enters college in 10 years. They estimate that the cost of four years’ tuition and fees at the state university their daughter will attend will be $40,000. Find the amount of interest earned at 4% interest compounded semiannually

Answer:

\(\tt 1)\: \boxed{\tt 4y+10}\)

\(\tt 2)\:\boxed{\tt 0.5x^4+10.5}\)

Step-by-step explanation:

1) y + 4 + 3(y + 2)

Expand:-

\(\tt y+4+3y+6\)

Combine like terms:-

\(\tt y+3y+4+6\)

\(\boxed{\tt 4y+10}\)

__

2) 0.5(x⁴ - 3) + 12

Expand:-

\(\tt 0.5x^4-1.5+12\)

Add/Subtract Numbers:-

\(\boxed{\tt 0.5x^4+10.5}\)

___________________

The option that describes the end behavior of the graphed function is the second one.

f(x) → ∞ as x →-∞

f(x) →∞ as x →∞

For any function y = f(x), we define the end behavior as the behavior of the function as x tends to negative infinity and positive infinity.

If we look at the left side of the graph, we can see that the function goes upwards.

Then we can assume that as x tends to negative infinity, the function tends to infinity (because it keeps going up) this is written as:

f(x) → ∞ as x →-∞

On the right side we can see the same thing, then when x goes to infinity we can write:

f(x) →∞ as x →∞.

So the end behavior of the function is:

f(x) → ∞ as x →-∞

f(x) →∞ as x →∞.

So the correct option is the second one.

Learn more about end behavior by reading:

https://brainly.com/question/1365136

#SPJ1

Answer:

Yes

Step-by-step explanation:

To know if a table is a function or not, we have to see if 1 input only has 1 output.

Looking at the table each input only has 1 output, so it is a function.

Answer:

y = -4/3x - 8

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Slope Formula: \(m=\frac{y_2-y_1}{x_2-x_1}\)

Step 1: Define points

x-intercept is (-6, 0)

y-intercept is (0, -8)

Step 2: Find slope m

\(m=\frac{-8-0}{0-(-6)}\)

\(m=\frac{-8}{0+6}\)

\(m=\frac{-8}{6}\)

\(m=\frac{-4}{3}\)

y = -4/3x + b

Step 3: Find y-intercept b

We are given (0, -8)

Step 4: Write linear equation

y = -4/3x - 8

If an auto body shop repaired 22 cars and trucks and there were 8 fewer cars than trucks, 15 trucks were repaired.

Let's assume the number of trucks repaired is "x". We know that the total number of cars and trucks repaired is 22. Since there were 8 fewer cars than trucks, the number of cars repaired must be x-8. Therefore, we can set up the following equation:

x + (x-8) = 22

Simplifying, we get:

2x - 8 = 22

Adding 8 to both sides:

2x = 30

Dividing by 2:

x = 15

We can check this by plugging x back into the equation and verifying that the number of cars repaired is 7, which is 8 fewer than 15.

To learn more about equation click on,

https://brainly.com/question/3298560

#SPJ1

Answer:

180

Step-by-step explanation:

-5= -a/36

-5*36= -a

-180= -a

180 = a

Using a linear function and a quadratic function, the system of equations that can be used to model this situation is:

The linear equation is given by:

h(t) = h(0) + v(0)t.

In which:

Hence, for Graham, the equation is:

h(0) = 18, v(0) = 1.5t.

Then:

h(t) = 18 + 1.5t.

The equation is:

h(t) = -16t² + v(0)t + h(0).

For Hunter, the parameters are:

v(0) = 24, h(0) = 5.

Hence the equation is:

h(t) = -16t² + 24t + 5.

The system is:

More can be learned about a system of equations at https://brainly.com/question/24342899

#SPJ1

The degree of the polynomial is 14

The polynomial is given as:

y^2+7x^14-10x^2

Here, we assume that the variable of the polynomial is x

The highest power of x in the polynomial y^2+7x^14-10x^2 is 14

Hence, the degree of the polynomial is 14

Read more about polynomial at

https://brainly.com/question/4142886

#SPJ1

Answer:

B)

Step-by-step explanation:

Because it says that Alex wants to spend exactly $30 so you want to have 30 as the total (  = 30 )

and it says 18 plus, you only add 18 one time ( 18 + )

and then it says 0.12 per mile, so you need to do something times 0.12 + 18 and get exactly 30. so you do ( 0.12x ) in this case we're not solving it we're just doing the equation so it's just 0.12x instead of a specific number

Put it all together and you get 18 + 0.12x = 30

Hope this helps dude

Solution

To get equation B from A

Distributive property

a(b + c) = ab + ac

=>3(x + 2) = 18

=>3x + 6 = 18.

D. Rewrite one side (or both) using the distributive property.

(a) The algebraic expression, -5x - 2 + 5x + 2 is simplified as 0.

(b) The algebraic expression, 5x -2  - (5x + 2) is simplified as -4.

The given algebraic expression is simplified by adding similar terms together, as it will make the expression to be in simplest form.

The given algebraic expressions are;

-5x - 2 + 5x + 2

5x -2  - (5x + 2)

The first algebraic expression is simplified as follows;

-5x - 2 + 5x + 2

collect similar terms;

(-5x + 5x) + (-2 + 2)

= 0 + 0

= 0

The second algebraic expression is simplified as follows;

5x - 2 - (5x + 2)

= 5x - 2 - 5x - 2

collect similar terms;

= (5x - 5x) + (-2 - 2)

= 0 - 4

= - 4

Learn more about simplification here: https://brainly.com/question/28008382

#SPJ1

Answer:

B. $65.31

Step-by-step explanation:

first you have to multiply 3.68 times 14.25 to get the cost of the ribbon that she bought, then you add 12.87 because she also purchased that, which totals 65.31

The expression that represents the perimeter and the of the rectangle is: 14.6q - 13.4.

A rectangle's perimeter if the length of its surrounding borders. Thus, the perimeter of a rectangle is the sum of all the length of the sides of the rectangle which can be calculated using the formula below:

Perimeter of a rectangle = 2(length + width).

Given the following:

Therefore, substitute the expression for the width and length of the rectangle into the perimeter of the rectangle formula:

Perimeter of rectangle = 2(9.6q - 3.6 + 4.3q - 3.1)

Combine like terms

Perimeter of rectangle = 2(7.3q - 6.7)

Perimeter of rectangle = 14.6q - 13.4

Learn more about the perimeter of rectangle on:

https://brainly.com/question/24571594

#SPJ1

The new function g(x) which is equal to f(2x) will be stretched or compressed by the factor 2.

It is defined as a special type of relationship and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function f(x) shown in the coordinate plane.

The function g(x) = f(2x)

As we can see in the new function g(x) it is the transformation of the f(x).

Transformation is applied as below:

x → 2x   (x is replaced by the twice of it)

= f(x)

= f(2x)

= g(x)

When the function is multiplied by a positive number it will be stretched or compressed according to that factor vertically and in the given function the factor is 2 which means the g(x) will be stretched or compressed according to that factor.

Thus, the new function g(x) which is equal to f(2x) will be stretched or compressed by the factor 2.

Learn more about the function here:

brainly.com/question/5245372

The domain for f(x) is all real numbers greater than or equal to -4

The equation of the function is given as

g(x) ≥ -2√(1/2x + 2)

For the function to have real values,

We need to set the radical to at least 0

This means that we set 1/2x + 2 to greater than or equal to 0

So, we have the following representation

1/2x + 2 ≥ 0

Subtract 2 from both sides

1/2x ≥ -2

Multiply both sides by 2

x ≥ -4

Hence, the domain is all real numbers that are at least -4

Read more about domain at

brainly.com/question/2264373

#SPJ1

Answer:

There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours. (P-value = 0).

The null and alternative hypothesis are:

\(H_0: \mu=4\\\\H_a:\mu< 4\)

Step-by-step explanation:

The question is incomplete: To test this claim a sample or population standard deviation is needed.

We will estimate that the sample standard deviation is 2 hours, and use a t-test to test that claim.

NOTE (after solving): The difference between the sample mean and the mean of the null hypothesis is big enough to reject the null hypothesis, even when we have a sample standard deviation of 3.5 hours, which can be considered bigger than the maximum standard deviation for the sample.

This is a hypothesis test for the population mean.

The claim is that the batteries power the laptops for significantly less than 4 hours.

Then, the null and alternative hypothesis are:

\(H_0: \mu=4\\\\H_a:\mu< 4\)

The significance level is 0.05.

The sample has a size n=500.

The sample mean is M=3.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=2.

The estimated standard error of the mean is computed using the formula:

\(s_M=\dfrac{s}{\sqrt{n}}=\dfrac{2}{\sqrt{500}}=0.0894\)

Then, we can calculate the t-statistic as:

\(t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{3.5-4}{0.0894}=\dfrac{-0.5}{0.0894}=-5.5902\)

The degrees of freedom for this sample size are:

\(df=n-1=500-1=499\)

This test is a left-tailed test, with 499 degrees of freedom and t=-5.5902, so the P-value for this test is calculated as (using a t-table):

\(P-value=P(t<-5.5902)=0\)

As the P-value (0) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the batteries power the laptops for significantly less than 4 hours.

Answer:

144

Step-by-step explanation:

Length of 1 side is 12 so area is 12*12

Given A rectangular print is 36 inches long and 24 inches wide.

And a rectangular frame that is 2 inches wide on all sides.

so, the rectangular frame will be 38 inches long and 26 inches wide.

The area of the rectangular print = 36 x 24 = 864 square inches

The area of the rectangular frame = 38 x 26 = 988 square inches

The area when the print is inside the frame will be the area of the frame

So, the answer will be 988 square inches

Answer:

Total amount receive each day = 1250 mg per day

Number of dosage = 1250 / 4 = 312.5 mg per meal

Step-by-step explanation:

Given:

Weight of patient = 110 lb

Dosage = 25 mg/kg/day

Find:

Total amount receive each day

Computation:

Weight of patient = 110 lb

1 lb = 0.453592

Weight of patient = 110 (0.453592)

Weight of patient = 49.89

Weight of patient = 50 kg (Approx)

Total amount receive each day = 50 kg × 25 mg/kg/day

Total amount receive each day = 1250 mg per day

Number of dosage = 1250 / 4 = 312.5 mg per meal

Answer:

\(y+6=\frac{-8}{7} (x-7)\)

Step-by-step explanation:

To find the slope of the equation use \(\frac{y_2-y_1}{x_2-x_1}\).

So, \(\frac{-6-2}{7-0}\) = \(\frac{-8}{7}\). Now we can use our slope and any of the two points to write in point-slope form, which is \(y-y_1=m(x-x_1)\). Using the point (7,-6), the formula will give \(y+6=\frac{-8}{7} (x-7)\).

To check, you can plug in this equation and the points into a calculator to graph. The line passes through both points.

the diagram of situation is given as follows

so by using the right-angle property.

so the height of the tree is 44

This identities are known as Pythagorean identities because this can be represented and solved using the pythagoras theorem. Let's remind the theorem:

Now, we also should know that the trigonometric functions can be written using the sides of a triangle. For the tangent and secant, we know:

In the next step I will substitute this identities to the given equation:

Which satisfy the Pythagoras Theorem.

Answer: D.42⁰

Ok done. Thank to me :>

Answer:

25%

Step-by-step explanation:

Given the following question:

0.25 = 25__

To find the answer simply convert the decimal into a percent by multiplying the decimal by a hundred.

0.25 = 25_
\(0.25 \times100=25\)
\(=25\)

0.25 is equal to "25%."

Hope this helps.

Answer:

100

Step-by-step explanation:

25/100=.25

Hope this helps you! (:

Answer:

n=639.48

Step-by-step explanation:

Answer:

639.48

Step-by-step explanation:

Given:

The probability that a baseball team goes to the city playoffs is 0.20.

The probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.10.

Required:

Find the probability that a randomly selected team from Littletown goes to the city and state playoffs.

Explanation:

Apply the following probability formula:

Final answer:

Thus option (B) is the correct answer.

The solution is,  the domain is: x ∈ (-∞, ∞).

Here, we have,

When we have two functions, f(x) and g(x), the composite function:

(f°g)(x)

is just the first function evaluated in the second one, or:

f( g(x))

And the domain of a function is the set of inputs that we can use as the variable x, we usually start by thinking that the domain is the set of all real numbers, unless there is a given value of x that causes problems, like a zero in the denominator, for example:

f(x) = 1/(x + 1)

where for x = -1 we have a zero in the denominator, then the domain is the set of all real numbers except x = -1.

Now, we have:

f(x) = x^2

g(x) = x + 9

then:

(f ∘ g)(x) = (x + 9)^2

And there is no value of x that causes problems here, so the domain is the set of all real numbers, that, in interval notation, is written as:

x ∈ (-∞, ∞)

(g ∘ f)(x)

this is g(f(x)) = (x^2) + 9 = x^2 + 9

And again, here we do not have any problem with a given value of x, so the domain is again the set of all real numbers:

x ∈ (-∞, ∞)

(f ∘ f)(x) = f(f(x)) = (f(x))^2 = (x^2)^2 = x^4

And for the domain, again, there is no value of x that causes a given problem, then the domain is the same as in the previous cases:

x ∈ (-∞, ∞)

(g ∘ g)(x) = g( g(x) ) = (g(x) + 9) = (x + 9) +9 = x + 18

And again, there are no values of x that cause a problem here,

so the domain is:

x ∈ (-∞, ∞)

To learn more on domain click:

brainly.com/question/2622299

#SPJ1

complete question:

Consider the following functions. f(x) = x2, g(x) = x + 9 Find (f ∘ g)(x). Find the domain of (f ∘ g)(x). (Enter your answer using interval notation.) Find (g ∘ f)(x). Find the domain of (g ∘ f)(x). (Enter your answer using interval notation.) Find (f ∘ f)(x). Find the domain of (f ∘ f)(x). (Enter your answer using interval notation.) Find (g ∘ g)(x). Find the domain of (g ∘ g)(x). (Enter your answer using interval notat

Answer:

17

Step-by-step explanation:

Answer:

it is 17

Step-by-step explanation:

I tested it out.