What amount will Chris and Allison report for taxable interest on their Form 1040? The couple's partially completed Form 1040, page 1, is shown below. You may use the form to assist you in answering this question.

The time taken for the money to grow to $8670 at compound interest is approximately 9.24 years.

Given the amount of money that is the principal = $6000

Rate = 4% compounded quarterly.

Time = t

Amount = $8670

Now we know that the amount is calculated by the formula:

A = P(1+r/4)ⁿ

8670 = 6000(1+0.01)ⁿ

Hence

log 1.445 = n log 1.01

or, n = 36.99

Number of years = 36.99 / 4 = 9.24 years.

The interest that is added to a loan or deposit is referred to as compound interest. Compound interest is computed for a sum utilizing both the principal and interest already paid. The main distinction between compound interest and simple interest is this.

If we look at our bank statements, interest is usually credited to our account once a year. While the principle remains constant, the interest changes annually.

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The inverse element of the binary operation is given by  (20-7a)/9 .

The binary operation is defined by a * b = 2a + 3b - 5

Now let us first find the identity element of the operation.

let e be the identity element.

Hence we know that a * e = a

Therefore a * e = 2a + 3e - 5

or, a = 2a + 3e - 5

or, a - 2a = 3e - 5

or, -a = 3e - 5

or, e = (5-a) / 3

Now we know that the inverse of the operation will be such that

a * a⁻¹ = e

or,  a⁻¹ = (20-7a) / 9

Therefore the inverse of the operation is given by (20-7a) / 9  .

A binary operation or dyadic operation is a rule that combines two elements (referred to as operands) to produce a third element. Formally, a binary operation is a two-arity operation.

An internally binary operation on a set is a binary action with the same set as its two domains or codomain. Examples include addition, multiplication, and other basic mathematical operations.

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If top opens at a cross section parallel to the base of  the rectangular pyramid, then the shape of the opening of the base will be rectangle

The shape of the jewelry box = Rectangular pyramid

The top opens at a cross section parallel to the  base

The parallel lines are defined as the  the coplanar straight line  that are equal distance from each other and never meet.

The shape of the base of the rectangular pyramid is rectangle and open at a cross section parallel to the base, then the shape of the opening of the base will be same as the base

The shape  of the opening of the base will be rectangle

Hence, if top opens at a cross section parallel to the base of  the rectangular pyramid, then the shape of the opening of the base will be rectangle

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Answer:

The quadratic function has the following sets of values below: (0,8) (2,10) (3,1). The quadratic functions represented as follows: f(x) = ax² + bx + c. using (0,8) 8 = a(0)² + b(0) + c. 8 = c. Therefore, using (2, 10)(3 , 1). f(x) = ax² + bx + c.

Answer:

25%

Step-by-step explanation:

got it right on my quiz .

The triangle has a hypothenuse 9.21 units and the graph it's attached below

The distance between any two points is the length of the line segment joining the points. There is only one line passing through two points. So, the distance between two points can be calculated by finding the length of this line segment connecting the two points.

The formula of distance between two points is given as

d = √(y₂ - y₁)² + (x₂ - x₁)²

The two points are

Substituting the values into the formula above;

d = √(2 -(-7))² + (-6-(-8))²

d = √85

d = 9.21 units

The hypothenuse of the triangle is 9.21 units

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Answer:

[tex]g(x)=(x+4)^2-5[/tex]

Step-by-step explanation:

The graph of [tex]f[/tex] was shifted 4 units left and 5 units down,

Answer:

We have to prove the triangles ΔXYW and ΔZYW are similar. We can do this by showing that they have two equal/in-ratio corresponding sides with the same angle between them (SAS/side-angle-side), or by showing they have two equal corresponding angles (AA/angel-angle), or by showing their sides are in ratio (SSS).

We are told XY=ZY, so we already know the triangles share an equal side.

Both triangles also share YW as a side.

Because YW bisects <XYZ, we know <XYW = <ZYW, so we know the angle between the triangle's corresponding sides are the same.

Therefore, since the triangles have two equal corresponding sides with the same angle between them (SAS), we can say they are similar.

Hope this helps :)

Answer: Though there is not enough information to be sure, a table to complete this ratio could be one include the sets of numbers (5,3) (10,6) and (15, 9)

Step-by-step explanation:

The number of ways  that five out of seven patients are called to remind them of their appointment is 21 ways

Total number of patients = 7

Number of patients that called to remind them of their appointments = 5

To find the total number of ways we have to use the combination methods

The combination is the method of selection of elements from the collection. In the combination order of the selection does not matters

Total number of ways = [tex]7C_5[/tex]

= 7! / (5!(7 - 5)!)

Subtract the terms

= 7! / 5! × 2!

= (7×6×5!) /  (5!×2!)

= 7 × 6 / 2 × 1

= 42 / 2

= 21 ways

Hence, the number of ways  that five out of seven patients are called to remind them of their appointment is 21 ways

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According to the solving the value of the Quadratic equation are as follows:

x = 0

x = 2

We can answer any quadratic equation using the quadratic formula. The first step is to change the equation's form to ax2+bx+c=0, where a, b, but instead c are the coefficients. The formula (-b(b2-4ac))/(2a) is then used to enter these coefficients. View instances of the formula being used to solve various equations.

Make a video of the pupils utilizing one technique to solve a quadratic equation. Allowing pupils to pick is an option, but you can also direct them to utilize the quadratic equation, factoring, or square-rooting.

f(x) = 2x² – 3x

x- (2x² – 3x) = 0

x - 2x² + 3x = 0

4x - 2x²= 0

x = 0

x = 2

According to the solving the value of the Quadratic equation are as follows:

x = 0

x = 2

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Answer:

[tex]h=2[/tex]

Step-by-step explanation:

[tex]A=bh \\ \\ 14=7h \\ \\ h=2[/tex]

Answer:

h = 2

Step-by-step explanation:

A = 14; b = 7

A = bh

14 = 7h

7h = 14

Divide both sides by 7.

h = 14/7

h = 2

The probability that a random sample of 30 smoke detectors will have a mean lifetime between 57 and 62 months is 0.8945.

Let x represent the lifespan of smoke detectors manufactured by a business.

We assume that the lifetime of smoke detectors manufactured by a business is normally distributed.

Given: The average lifetime of a company's smoke detectors is 5 years, or 60 months, with an 8-month standard deviation.

μ = 60, σ = 8 and samle size n = 30

The probability that a random sample of 30 smoke detectors will have a mean lifetime of 57 to 62 months is :

P(57 < P < 62) = P{(57-60)/(8/√30) < ((x-μ)/σ)/(σ/√n) < (62-60)/(8/√30)}

P(57 < P < 62) = P(-1.37 < z < 2.05)

= P(z<2.05) - P(z< -1.37)

= P(<2.05)-(1-P(<1.37)) P(Z) = 1 − P(Z < 2)]

= 0.9798178-(1-0.9146565) [By using p-value table for z]

= 0.8944743≈ 0.8945

Hence, the probability that a random sample of 30 smoke detectors will have a mean lifetime between 57 and 62 months is 0.8945.

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The kilograms of sugar that were used for cherry jam is 9kg.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

Since there are 40 kg of sugar in the bag. Strawberry jam was used which was 4 kg. The remaining kilograms will be:

= 40kg - 4kg

= 36 kg

Since 1/4 of the remaining sugar was used, the amount used will be:

= Fraction × Total amount

= 1/4 × 36

= 9kg.

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The probability of randomly choosing a green marble after you have chosen red is 4.4%

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Given

A jar has 20 marbles: 3 green, 12 blue, 5 red.

Probability;

In probability theory, an event is a set of outcomes of an experiment or a subset of the sample space.

The total number of marbles = 20

The number of green marbles= 3

The number of blue marbles = 12

The number of red marbles = 5

The probability of choosing a red marble = Number of red marbles / Total number of marbles

= 5/20

The probability of choosing a green marble is =  Number of green marbles / New total number of marbles

= 3/19

Therefore,

The probability of randomly choosing a green marble after you have chosen red is;

= 5/20 * 3/19

= 3/68

percentage = 3/68 * 100 = 4.4%

Hence, the probability of randomly choosing a green marble after you have chosen red is 4.4%

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Answer:

x=6

Step-by-step explanation:

11x-3=4x+39

-4x     -4x

7x-3=39

   +3  +3

7x=42

______

7      7

x=6

11(6)-3=66-3=63

4(6)+39=63

yw hope it helps

Answer:

252

Step-by-step explanation:

The second and third smallest factors must add to 5. The only possibility is that these factors are 2 and 3.

The second and third largest factors must add to [tex]462-N[/tex]. These factors are [tex]N/2[/tex] and [tex]N/3[/tex].

[tex]462-N=\frac{N}{2}+\frac{N}{3} \\ \\ 462-N=\frac{5N}{6} \\ \\ 462=\frac{11N}{6} \\ \\ N=252[/tex]

The cost of each friend's meal in terms of a is 35/a.  

The cost of each friend's meal when the number of friends is 5 is $7.

We are given that;

Total amount that they can spend on food bill = $41 including delivery charge of $6

The equation is given as;

6 + ax = 41

Where;

a is the number of people

x is the cost of each friend's meal.

Thus;

ax = 41 - 6

ax = 35\

x = 35/a

So it will be the cost of each friend's meal in terms of a.

Now,

If the number of friends = 5

Then,

a = 5

Thus;

x = 35/5 = $7

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Complete question is;

A group of friends are ordering food. The total amount that they can spend on their food bill is $41, including the delivery charge of $6. The equation below represents the situation, where x is the cost of each friend's meal.

The cost of each friend's meal in terms of a is

.

The cost of each friend's meal when the number of friends is 5 is $

The statement that would be true if the data in the data in the stem-and-leaf plot is shown in a line plot is: D. We could calculate the range and median.

A line plot is a graph that shows individual data in a data set with the use of dots. Each dot represents a data plot.

In a line plot, we can easily find the middle of the data distribution which is the median of the data and also we can determine the highest and lowest value which enables us to find the range of the data.

Thus, using the stem-and-leaf plot in the diagram, below, write out each data points given, which are:

68, 70, 80, 86, 88, 88, 96, 96, 97, 97, 98, 98, 99, 100, 100, 100, 100, 100

The line plot for these data would have the following frequency for each data point:

68 - 1 dot

70 - 1 dot

80 - 1 dot

86 1 dot

88 - 2 dots

96 - 2 dots

97 - 2 dots

98 - 2 dots

99 - 1 dot

100 - 5 dots

The line plot is shown in the diagram below.

Range = 100 - 68 = 32

Median = 97

Therefore, the answer is: D. We could calculate the range and median.

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Answer:

answer for first one is 8

for 2nd one is [tex]2(x+5)/3x^2-7[/tex]

for 3 rd one is [tex](x-5)/x[/tex]

for 4th one is [tex]3x^{2} n^{2} (7n-9)/7x-9[/tex]

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

It can not be a or b because the figure is upside-down.

It cannot be d because the figure would literally fly off the grid shown.

It must be C because the figure rotates 90° counterclockwise and moves 4 units to the right.

The value after differentiate will be;

⇒ [tex]\frac{dy}{dx} = 3x^2 3^{x^{3} } log_{e} 3[/tex]

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The function is,

⇒ [tex]y = 3^{x^{3} }[/tex]

Now,

Differentiate the function with respect to x as;

The function is,

⇒ [tex]y = 3^{x^{3} }[/tex]

⇒ [tex]\frac{dy}{dx} = 3^{x^{3} } log_{e} 3 \frac{d}{dx} (x^3)[/tex]

⇒ [tex]\frac{dy}{dx} = 3^{x^{3} } log_{e} 3 * 3x^2[/tex]

⇒ [tex]\frac{dy}{dx} = 3x^2 3^{x^{3} } log_{e} 3[/tex]

Thus, The value after differentiate will be;

⇒ [tex]\frac{dy}{dx} = 3x^2 3^{x^{3} } log_{e} 3[/tex]

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When the population standard deviation, is unknown, a hypothesis test for the population mean is conducted the same way as if the population standard deviation were known. The t-distribution is used instead of the conventional normal distribution, which is the only distinction (z-distribution).

The distance around the given triangle is [tex]\cfrac{13x}{12}[/tex].

We are asked to calculate the distance around the triangle, commonly known as the perimeter.

The perimeter is the sum of all side lengths in any shape. For a triangle, you add up all the side lengths and that is your perimeter.

Now we need to add up all these side lengths.

[tex]\cfrac{x}{2} +\cfrac{x}{3} +\cfrac{x}{4}[/tex]

We have fractions with unlike denominators. We need to get common denominators in order to solve. To do this, we need to obtain the GCF (Greatest Common Factor) of the numbers 2, 3, and 4.

This number is 12.

By changing the fractions so they all have denominators of 12, we retrieve our new equation:

[tex]\cfrac{6x}{12} +\cfrac{4x}{12} +\cfrac{3x}{12}[/tex]

Now we add them:

[tex]\cfrac{6x+4x+3x}{12}=\cfrac{13x}{12}[/tex]

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Step-by-step explanation:

(2/5x − 1) − (1/4x + 2)

2/5x − 1 − 1/4x - 2

8/20x - 1  - 5/20x - 2

3/20x - 1 - 2

3/20x - 3

As per the given population function, the growth function is written as, P = 13000(1.05)ˣ

Population function:

Population function refers the positive change in a particular population as a function of time. And this growth is not linear, but exponential, and so the formula for population growth can be found by starting with the premise that P (population) multiplies by a rate r over time.

Given,

A population numbers 13,000 organisms initially and grows by 5% each year. Suppose P represents population and t represents the number of years of growth. An exponential model for the population can be written in the form P = abˣ

Now, we have to find the population growth function for this situation.

From the given question, 'we have the following details,

Population numbers = 13,000

So, the value of a in the population function is 13,000

And it grows every year as 5%.

So, in decimal form in can be 0.05.

So, the value of b is calculated as,

=> b = 1 + 0.05

=> b = 1.05

Now, we have to apply these values on the function,

Then we get,

=> P = 13000(1.05)ˣ

Therefore, the population growth function is been identified

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Step-by-step explanation:

g(7)=

[tex] {7}^{2} + n[/tex]

[tex]49 + n[/tex]

f(g(7))=n

[tex]f(g(7)) = \sqrt{49 + n + 1} [/tex]

[tex]f(g(7)) = \sqrt{n + 50} [/tex]

[tex]9 = \sqrt{n + 50} [/tex]

[tex]81 = n + 50[/tex]

[tex]n = 31[/tex]

So

[tex]g(31) = 31 {}^{2} + 31[/tex]

[tex] = 992[/tex]

Answer:

576482670576482670576482670576482670576482670576482670576482670576482670576482670576482670

Step-by-step explanation: