If $4,000 is invested in an account, find the value of the investment at the end of 20 years if the interest
is 6% compound interest, compounded quarterly. Round your answers to the nearest cent.

Answer:

$2.48

Step-by-step explanation:

29.75/12 =2.479

We are given:

f(x) = 3x + 8

g(x) = -x³

__________________________________________________________

The Concept:

We have to find the values of f(g(3)), which means that we have to apply the function g() on 3 and apply the function f() on the value we get.

Finding f(g(3)):

Finding g(3):

g(x) = -x³

g(3) = -(3)³

g(3) = -27

Finding f(g(3)):

f(x) = 3x + 8

f(g(3)) = 3(g(3)) + 8

f(g(3)) = 3(-27) + 8

f(g(3)) = -81 + 8

f(g(3)) = -73

Hence, f(g(3)) = -73

Answer: Sin θ =

Step-by-step explanation:

In the figure attached, ABC is a right angle triangle.

Sides of this triangle are AB = 12 BC = 5 and CA = 13

Angle opposite to the side having length = 12 is θ.

Now we have to calculate sin θ.

Since Sinθ =

=

Therefore, ratio which represents sinθ will be

Step-by-step explanation:

Answer:

1.42 hours

Step-by-step explanation:

In this case we must take into account that the speed would be to fill a pool for a time, that this case is in hours, therefore it would be like this:

1/5 for the first pipe

1/2 for the second pipe

Now, we will use both at the same time, therefore:

1/5 + 1/2 = 1 / x

0.7 = 1 / x

x = 1 / 0.7

x = 1.42

That is to say that if we use both we will take a total of 1.42 hours

The cups of giardia-laced lemonade that Wiyot will have sold by the time his parents get a call from county health officials on day 8 is 75 cups.

From the information, Wiyot sells 33 lemonades on the first day, and 6 additional lemonades each day as the summer heats up.

This is an arithmetic sequence and will be expressed as:

= a + (n - 1)d

a = first term = 33

d = common difference = 6

n = 8

This will be:

= a + (n - 1)d

= 33 + (8 - 1)6

= 33 + (7 × 6)

= 33 + 42

= 75

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The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes, hence it is the same as a relative frequency.

The total number of periods is given as follows:

5 + 6 + 4 = 15.

The frequency of each class is given as follows:

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Answer:

the numbers are 8 and 3.

Answer:

NO

Step-by-step explanation:

6312/8= 789

here, 6312 is devisable by 8.

Therefore, there will not be any water left in the tank.

The mean of the data set is 82.77

If we want to find the mean, we would have to put it at the back of our minds that the mean is the same as the average. As such, we would have to take the sum of all the values that have been listed in the data set and divide by the total number of the data.

The first step is to arrange the data set orderly from smallest to largest;

70, 71,79, 82,88,85,87,91,92

We have nine values in the data set thus the mean is;

70+71+79+82+88+85+87+91+92/9= 745/9= 82.77

Hence the mean of the data set is 82.77

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Answer:

1/x

Step-by-step explanation:

The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.

The expression "F = {(x, y) :  φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function  φ, which takes the variables x, y, and p as inputs.

To fully understand the meaning of F, we need to delve into the function  φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.

For instance, let's consider a specific example where vraphi(x, y, p) is defined  φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.

It is important to note that the specific meaning and implications of F heavily rely on the nature of the function  φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.

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Answer:

none of the choices is correct

Step-by-step explanation:

To find the length of the side of square 1, divide the perimeter, 104÷4 = 27

That is the hypotenuse of the triangle.

The square of 27 is 729

Subtract the given square of Square 2, 576

729 - 576 = 153

Take the square root of 153 to find the length of the side of Square 3

√153= 12.37

I hope this helps. It's just a bit more challenging version of Pythagorean Theorem: a² + b² = c²

Answer:

y=2x+9

Step-by-step explanation:

I got y-2x+9 because if you add 8-1 that equals 7 and if u do 7-5 that equals 2 so y2x and then 7 Plus 2 equals 9 so it all adds up to Y=2x+9?.

The algorithm justifies the answer of 3/5 as the fraction each person gets.

Representation of the fractions on the second row:

From what you described, two of the loaves were divided into thirds.

This means each person receives one third, and there is one third remaining. Then, this remaining third from the second loaf was further divided into fifths.

Therefore, each person receives one fifth from this remaining third.

So, the representation of the fractions on the second row would be:

Each person receives 1/3 (one third) from the two loaves.

Each person receives 1/5 (one fifth) from the remaining third.

Algorithm/Abstract strategy to justify the 3/5 found as the answer:

To find the final answer of 3/5, we can follow the steps you provided:

Divide two loaves into thirds, giving each person 1/3.

Divide the remaining third from the second loaf into fifths, giving each person 1/5.

Combining the fractions, each person has 1/3 + 1/5.

To add these fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 5 is 15. We can convert 1/3 and 1/5 to have a denominator of 15:

1/3 = 5/15 (multiplying numerator and denominator by 5)

1/5 = 3/15 (multiplying numerator and denominator by 3)

Now, we can add the fractions:

5/15 + 3/15 = 8/15

Therefore, each person receives 8/15 of a loaf.

Simplifying this fraction, we get 3/5.

Hence, the algorithm justifies the answer of 3/5 as the fraction each person gets.

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Answer:

y=-3x+1

Step-by-step explanation:

Have a good one.

The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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The adjusting entry for deferred revenue at its year-end of December 31 is $1,150

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

\(I = \dfrac{P \times R \times T}{100}\)

We are given that;

The amount of payment=$3,450
Now,

The adjusting entry for deferred revenue at its year-end of December 31

Debit: Deferred Revenue $1,150 (which is one-third of the total payment received)

Credit: Revenue $1,150 (which represents the portion of the service that has been provided in December)

Therefore, by the given interest answer will be $1,150

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Answer:

\(P(R\ or\ odd\ Numbered)=5/7\)

Step-by-step explanation:

From the question we are told that:

Number of Red Marble \(n_r=6\)

Number of Blue Marble \(n_b=8\)

Sample size \(n=n_r+n_b\)

\(n=6+8\)

\(n=14\)

And

No of red or Odd numbered \(x= 6+4 = 10\)

Generally the equation for  probability the marble is red or odd numbered. is mathematically given by

\(P(R or odd Numbered)=x/n\)

\(P(R or odd Numbered)=10/14\)

\(P(R\ or\ odd\ Numbered)=5/7\)

Answer:

The sampling distribution of the sample proportion of people who answer yes to the question is approximately normal with mean of 0.75 and standard deviation of 0.0791.

Step-by-step explanation:

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

In this question:

\(p = 0.75, n = 30\)

So

\(\mu = 0.75, s = \sqrt{\frac{0.75*0.25}{30}} = 0.0791\)

The sampling distribution of the sample proportion of people who answer yes to the question is approximately normal with mean of 0.75 and standard deviation of 0.0791.

Answer:

5 1/7 or 36/7

Step-by-step explanation:

11 8/7+3 5/1-x=15

12 1/7+8-x=15

12 1/7+8-15=x

20 1/7-15=x

5 1/7=x

Answer:

so yeah here is the answer and working!!!

Answer:

  7290

Step-by-step explanation:

Put 5 in the formula and evaluate.

  a(5) = 90·3^(5-1) = 90·81 = 7290

There will be 7290 bacteria at the beginning of hour 5.

Answer:

$0.50

50 cents per ounce.

Step-by-step explanation:

To get the unit price, you take the cost of the package divided by the parts it has. Since Marissa has a package of yogurt that costs $3.50 and there are seven ounces in the package we have this equation:

($3.50)/(7 ounces)= $0.50 = 50 cents = the second answer available.

Answer:

Step-by-step explanation:

The interest to be paid is $99

Simple interest is an interest charge that borrowers pay lenders for a loan. It is calculated using the principal only and does not include compounding interest. Simple interest relates not just to certain loans. It's also the type of interest that banks pay customers on their savings accounts.

Simple Interest = P×R×T/100

where P is the principal,

R is the rate

and T is the time

P = $900

R = 11%

T= 1

I = 900× 11/100

I = $99

therefore the interest to be paid is $99

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Answer:

\(\displaystyle \int {\frac{2}{(1 + \sqrt{x})^5}} \, dx = \frac{-(4\sqrt{x} + 1)}{3(\sqrt{x} + 1)^4} + C\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

Antiderivatives - Integrals

Integration Constant C

U-Substitution

Integration Rule [Reverse Power Rule]:                                                               \(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)

Integration Property [Multiplied Constant]:                                                         \(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Integration Property [Addition/Subtraction]:                                                       \(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)

Step-by-step explanation:

Step 1: Define

\(\displaystyle \int {\frac{2}{(1 + \sqrt{x})^5}} \, dx\)

Step 2: Identify Variables

Find the variables u-solve using u-substitution.

U-Substitution

\(\displaystyle u = 1 + \sqrt{x}\)

\(\displaystyle du = \frac{1}{2\sqrt{x}}dx\)

U-Solve

\(\displaystyle x = (u - 1)^2\)

\(\displaystyle dx = 2\sqrt{x}du\)

Step 3: Integration

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Integration

Book: College Calculus 10e

Answer:

100/150 simplified to lowest terms is 2/3.

Step-by-step explanation:

2:3 answer is correct

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