Sam invests a sum of money in a retirement account with a fixed annual interest rate of 7%
compounded quarterly. After 13 years, the balance reaches $19,280.02. What was the amount of
the initial investment? ROUND YOUR ANSWER TO THE NEAREST DOLLAR (do NOT put a dollar
sign $ in your answer)

The answer of u/4 + 3/5 is as a single fraction in its simplest form is

5u + 13 / 20.

Here, we have,

given that,

u/4 + 3/5

Convert the given fractions into like fractions.

To do so, Take the L.C.M ( Least Common Multiple ) of 5 and 4.

To find out the L.C.M of given numbers,

First of all, find the prime factors of each numbers.

5 = 5 × 1

4 = 2 × 2 × 1

Take out the common prime factor i.e 1

Also take out the other remaining prime factors i.e 2 , 2 and 5

Now, multiply those all prime factors and obtain L.C.M

= 1 × 2 × 2 × 5 = 20

L.C.M of 5 and 4 = 20

so, we get,

u/4 + 3/5 = 5u + 13 / 20

To earn more on addition click:

brainly.com/question/29560851

#SPJ1

To determine if a function has a vertical asymptote, you need to consider its behavior as the input approaches certain values.

A vertical asymptote occurs when the function approaches positive or negative infinity as the input approaches a specific value. Here's how you can determine if a function has a vertical asymptote:

Check for restrictions in the domain: Look for values of the input variable where the function is undefined or has a division by zero. These can indicate potential vertical asymptotes.

Evaluate the limit as the input approaches the suspected values: Calculate the limit of the function as the input approaches the suspected values from both sides (approaching from the left and right). If the limit approaches positive or negative infinity, a vertical asymptote exists at that value.

For example, if a rational function has a denominator that becomes zero at a certain value, such as x = 2, evaluate the limits of the function as x approaches 2 from the left and right. If the limits are positive or negative infinity, then there is a vertical asymptote at x = 2.

In summary, to determine if a function has a vertical asymptote, check for restrictions in the domain and evaluate the limits as the input approaches suspected values. If the limits approach positive or negative infinity, there is a vertical asymptote at that value.

know more about vertical asymptote.

https://brainly.com/question/29260395

#SPJ11

Susan has more candy in weight compared to Isabel.

To compare the candy weights between Susan and Isabel, we need to ensure that both weights are in the same unit of measurement. Let's convert Isabel's candy weight to ounces for a fair comparison.

Given:

Susan: 4 bags x 6 ounces/bag = 24 ounces

Isabel: 1 bag x 16 ounces/pound = 16 ounces

Now that both weights are in ounces, we can see that Susan has 24 ounces of candy, while Isabel has 16 ounces of candy. As a result, Susan is heavier on the candy scale than Isabel.

for such more question on weight

https://brainly.com/question/24191825

#SPJ8

The given system of equations is expressed as

5x - 2y = 14

6x - 3y = 15

We would apply the method of elimination. We would make the coefficient of y to be equal in both equations by multiplying the first equation by 3 and the second equation by 2. It becomes

15x - 6y = 42

12x - 6y = 30

If we subtract the fourth equation from the third equation, it becomes

15x - 12x - 6y - - 6y = 42 - 30

3x - 6y + 6y = 12

3x = 12

x = 12/3

x = 4

Substituting x = 4 into the first equation, it becomes

5 * 4 - 2y = 14

20 - 2y = 14

2y = 20 - 14

2y = 6

y = 6/2

y = 3

To know if we are correct, we would substitute x = 4 and y = 3 into any of the equations. Substituting into the second equation, it becomes

6 * 4 - 3 * 3 = 15

24 - 9 = 15

15 = 15

This is correct

A decrease in the price of cotton can have positive effects on the affordability and availability of socks in the market, benefiting consumers by potentially offering lower prices and a wider range of choices.

If the price of cotton falls in the market for a bag of socks, it is likely to have an impact on the overall cost and availability of socks. Cotton is a common material used in the production of socks, and its price plays a significant role in determining the cost of manufacturing.

When the price of cotton falls, it reduces the cost of raw materials for sock manufacturers. As a result, manufacturers may experience lower production costs. This can lead to several outcomes:

1. Decrease in sock prices: With lower production costs, manufacturers have the option to reduce the prices of socks to attract customers. This can result in more affordable socks for consumers, making them more accessible.

2. Increase in sock supply: Lower production costs may incentivize manufacturers to increase their sock production. As a result, the supply of socks in the market could rise, leading to a greater availability of socks for consumers.

3. Potential for improved quality or additional features: Manufacturers may choose to invest the cost savings from lower cotton prices into enhancing the quality of socks or adding extra features. This can result in socks with improved durability, comfort, or design, providing more options for consumers.

It's important to note that the impact of falling cotton prices on sock prices and availability may also depend on other factors, such as production and distribution costs, market competition, and consumer demand. Additionally, the extent to which the price reduction in cotton translates into lower sock prices may vary among different brands and retailers.

Overall, a decrease in the price of cotton can have positive effects on the affordability and availability of socks in the market, benefiting consumers by potentially offering lower prices and a wider range of choices.

Learn more about affordability here

https://brainly.com/question/32019057

#SPJ11

a) The total cost of producing the first 6 units is 198 dollars.

b) The total cost of producing the next 6 units is 660 dollars.

a) To find the total cost of producing the first 6 units, we need to integrate the marginal cost function from 0 to 6:

C(q) = ∫C'(q) dq = ∫(11q + 4) dq = [11q^2/2 + 4q] from 0 to 6

C(6) = 11(6)^2/2 + 4(6) - [11(0)^2/2 + 4(0)] = 198 dollars

Therefore, the total cost of producing the first 6 units is 198 dollars.

b) To find the total cost of producing the next 6 units, we need to integrate the marginal cost function from 6 to 12:

C(q) = ∫C'(q) dq = ∫(11q + 4) dq = [11q^2/2 + 4q] from 6 to 12

C(12) - C(6) = [11(12)^2/2 + 4(12)] - [11(6)^2/2 + 4(6)] = 858 dollars - 198 dollars = 660 dollars

Therefore, the total cost of producing the next 6 units is 660 dollars.

To know more about marginal cost refer here:

https://brainly.com/question/7781429

#SPJ11

Answer:

8

Step-by-step explanation:

Each coin Collin collects is worth 25 points. His goal is 200 points. Divide 200 by 25. The answer is 8, Collin needs to collect 8 coins.

Angle ABC is equal to 1/2 x, proved as required.

To prove that ABC = 1/2 x, we will use the following reasoning:

∴ ∠ OAB = ∠OBA = (180 - x)/2 (the sum of angles in a triangle is 180 degrees and ∠ AOB is twice the size of ∠ OAB)

∠ABC  = ∠OBC - ∠OBA.  (the sum of angles in a triangle is 180 degrees).

∠OBC is a right angle, since it is the angle between a radius and a tangent to the circle at B.

∴, ∠OBC = 90 ⁰

Substituting in the values we have found, we get:

ABC = OBC - OBA

ABC = 90 - (180 - x)/2 = x/2.

Therefore, ABC = 1/2 x, as required.

Learn more about proof of angles here: https://brainly.com/question/26119418

#SPJ1

The probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15

For given question,

A research center poll showed that 85 percent of people believe that it is morally wrong to not report all income on tax returns.

so, the probability that someone have this belief is P = 0.85

We know that in probability,

p = 1 - q

where;

p is probability of success

q is probability of failure.

Thus the probability that someone does not have this​ belief would be,

= 1 - P

= 1 - 0.85

= 0.15

Therefore, the probability that someone does not believe that it is morally wrong to not report all income on tax returns is = 0.15

Learn more about the probability here:

https://brainly.com/question/3679442

#SPJ4

18 root

2

Step-by-step explanation:

In this question imagine there is no y

It will be 10 root2 +5 root2 +3 root 2 it will be 18 root 2

Answer:

627% 6.285 6. 28 21 6 3

Step-by-step explanation:

Um.. I did it from greatest to least but here it is!

To solve the first equation, f(x) = x^2 - 7x^2 + 2x + 9 = 0, we can use the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, the equation is x^2 - 7x^2 + 2x + 9 = 0, so a = 1, b = -7, and c = 2.

Plugging in these values into the quadratic formula, we have:

x = (-(-7) ± √((-7)^2 - 4(1)(2))) / (2(1))

Simplifying further:

x = (7 ± √(49 - 8)) / 2

x = (7 ± √41) / 2

Now, let's approximate the roots up to 4 significant digits:

x ≈ (7 + √41) / 2 ≈ 6.7053

x ≈ (7 - √41) / 2 ≈ 1.3259

Therefore, the roots of the equation f(x) = 0 are approximately x = 6.7053 and x = 1.3259.

For the second equation, x^2 + 2x + 4 = 0, we can also use the quadratic formula. In this case, a = 1, b = 2, and c = 4.

Applying the quadratic formula:

x = (-2 ± √(2^2 - 4(1)(4))) / (2(1))

x = (-2 ± √(4 - 16)) / 2

x = (-2 ± √(-12)) / 2

Since the term under the square root is negative, we have complex roots. Simplifying further:

x = (-2 ± √(12)i) / 2

x = -1 ± √3i

Therefore, the roots of the equation x^2 + 2x + 4 = 0 are approximately x = -1 + √3i and x = -1 - √3i.

learn more about quadratic here

https://brainly.com/question/22364785

#SPJ11

Answer:

Step-by-step explanation:

The values of x and y are required.

and

From the given figure the sides and are equal.

Also, and are equal.

So,

Hence, and

To find (f o g)(-4), we substitute -4 into g(x) to get -4, and then substitute -4 into f(x) to get -11.

The question asks us to find (f o g)(-4), where f(x) = 3x + 1 and g(x) = x. To find (f o g)(-4), we need to substitute -4 into g(x) and then take that result and substitute it into f(x).

First, let's find g(-4) by substituting -4 into g(x):
g(-4) = -4

Now, let's substitute g(-4) into f(x):
f(g(-4)) = f(-4)

Substituting -4 into f(x):
f(-4) = 3(-4) + 1
       = -12 + 1
       = -11

Therefore, (f o g)(-4) = -11.

In mathematics, a function is an expression, rule, or law that specifies a connection between two variables (the independent variable and the dependent variable). Functions are common in mathematics and are required for the formulation of physical connections in the sciences.

For more questions on function

https://brainly.com/question/11624077

#SPJ8

Answer:

maybe $825

Step-by-step explanation:

Im not sure but I think Its accurate

Valve guides can be measured for roundness and diameter using a micrometer or a bore gauge. Both of these tools are commonly used in the automotive industry to measure the dimensions of engine parts such as valve guides.

A micrometer is a precision measuring tool that uses a calibrated screw to measure the diameter of an object with high accuracy. It can be used to measure the diameter of the valve guide at different points along its length to check for roundness. A bore gauge, also known as an inside micrometer, is a specialized tool used to measure the inside diameter of a cylinder, such as the bore of an engine block or the valve guide. It consists of a probe that is inserted into the cylinder and expands to take a measurement. A bore gauge is particularly useful for measuring the internal dimensions of complex shapes like valve guides, which can have irregular or non-circular profiles. Both micrometers and bore gauges come in various sizes and types, and the specific tool used will depend on the size and shape of the valve guide being measured.

Learn more about Valve guides here

https://brainly.com/question/28497905

#SPJ11

Answer: The combined amount of kids and adult meals sold = 36

Step-by-step explanation:

Let the number of kids meals sold = 5x and the number of adult meals = 4x

Since total kids meals sold = 20

Then, 5x= 20

⇒ x =4

Adult meals = 4(4) = 16

Combined meals sold  =  kids meals + Adult meals

= 20+ 16

= 36

Hence, the combined amount of kids and adult meals sold = 36

Answer:

Step-by-step explanation:

Any value of x not equal to zero decreases the function from its maximum of 5 when x=0. So the range of the function is (-oo, 5] So all real numbers less than or equal to five.

The sun would more frequently be reaching the ground at a high angle at latitude 0° (the equator). Option A is correct.

What is latitude?

Latitude is the angle north or south of the equator and extends horizontally over the globe. Longitude, on the other hand, runs from east to east and runs vertically across the globe.

On any given day, only points on Earth's surface that are located along a single line of latitude can experience sunlight at a 90-degree angle. Lower levels of sunshine are present everywhere else. The sun's beams are typically strongest at the equator and weakest at the poles.

Option A is correct,0° (the equator).

Learn more about the latitude here,

https://brainly.com/question/28606059

#SPJ4

Answer:

C

Step-by-step explanation:

it would be C because their is an increase in which is walking to school, a level place, which is being at the school, then a decrease which would be walking home afterwards

The given scatter plot shows a negative association.

Therefore, the given scatter plot shows a negative association.

Learn more about scatter plot on:

https://brainly.com/question/6592115

Answer:

Negative

Step-by-step explanation:

Answer:

\(4x - 9 < 5x - 2\)

The probability of NOT drawing a face card from a standard deck of 52 cards is 10 over 13.

First determine the total number of face cards and non-face cards in a standard deck of 52 cards.                                   In a standard deck, there are 12 face cards (3 face cards per suit: Jack, Queen, and King, and 4 suits: Hearts, Diamonds, Clubs, and Spades). This means there are 52 - 12 = 40 non-face cards.

Now, we'll calculate the probability of NOT drawing a face card:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Probability of NOT drawing a face card = (Number of non-face cards) / (Total number of cards)
Probability = 40 / 52

Simplify the fraction by dividing the numerator and denominator by their greatest common divisor (4):
Probability = (40/4) / (52/4)
Probability = 10 / 13

So, the probability of NOT drawing a face card from a standard deck of 52 cards is 10/13. Your answer: 10 over 13.

Learn more about standard deck here: brainly.com/question/31494408

#SPJ11

An algebraic expression which models the given context would be written as s + 0.02s = 1.05s.

Price can be define as an amount of money which is primarily set by the seller of a good (product), and it must be paid by a buyer to the seller, so as to enable the acquisition of this good (product).

An algebraic expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

Let s represent the price of a pair of shoes.

Therefore, an algebraic expression which models the given context would be written as follows:

s + 0.02s = 1.05s.

Read more on algebraic expression here: https://brainly.com/question/17615109

#SPJ4

Answer:

The balance of the savings account in 15 years will be $1,750.24.

The required transformation of the function is 1 unit left and 5 unit down.

Given that,
To determine the transformation of the parent function y=|x|. y=|x-1|-5.

The graph is a demonstration of curves which gives the relationship between the x and y-axis.

Here,
The function y=|x| is an absolute function,
when we add 1 unit left and 5 unit down to the function, the function arises as y=|x-1|-5. It implies the transformation of function as -1 on the x-axis and -5 units on the y-axis.

Thus, the required transformation of the function is 1 unit left and 5 unit down.

Learn more about graphs here:

branily.com/question/16608196

#SPJ1

Answer:

surface area is A≈394.08

not so sure about volume

Step-by-step explanation:

The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

Visit here to learn more about differential equation  : https://brainly.com/question/14620493
#SPJ11

Answer:

0.85.

Step-by-step explanation:

20)17.00 (0.85

-    160

       100

      -100

          ......

Answer:

2400

Step-by-step explanation:

since the ratio is 3:2, you take 3600 and divide it by 3 and x it by 2 to find the women