if 1=0+1;2=1+1;3=2+1... so
0=a+1,a=?

After 18 ​years, the investment compounded periodically will be worth (future value) ​$534.55 more than the investment compounded annually.

The future value is the compounded present value of an investment using an interest rate.

The future value can be computed using an online finance calculator.

N (# of periods) = 72 quarters (18 years x 4)

I/Y (Interest per year) = 6%

PV (Present Value) = $8,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $23,369.26

Total Interest = $15,369.26

N (# of periods) = 18 years

I/Y (Interest per year) = 6%

PV (Present Value) = $8,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $22,834.71

Total Interest = $14,834.71

Difference in future value = $5,34.55 ($23,369.26 - $22,834.71)

Thus, compounding an investment quarterly yields a greater future value than annual compounding.

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The equation of the line with gradient of 1 / 2 and passes through (4, -2) is  y = 1 / 2 x - 4.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, the equation of the line has a gradient or slope of 1 / 2 and it passes through (4, -2).

y = 1 / 2 x + b

let's find the y-intercept using (4, -2)

-2 = 1 / 2(4) + b

-2 - 2 = b

b = -4

Therefore, the equation is y = 1 / 2 x - 4

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Answer:

12.43 pounds of chocolate with 13 pounds of trail mix

Step-by-step explanation:

To find the amount of chocolate that needs to be mixed with the trail mix, we need to set up the following equation:

(cost of chocolate per pound * pounds of chocolate) + (cost of trail mix per pound * pounds of trail mix) = cost per pound of mixture * (pounds of chocolate + pounds of trail mix)

We can plug in the given values to get the following equation:

($20.80/pound * pounds of chocolate) + ($3.50/pound * 13 pounds) = $11.80/pound * (pounds of chocolate + 13 pounds)

We can then solve this equation to find the number of pounds of chocolate that should be mixed with the trail mix.

($20.80/pound * pounds of chocolate) + $46.50 = $11.80/pound * (pounds of chocolate + 13 pounds)

$20.80/pound * pounds of chocolate = $11.80/pound * (pounds of chocolate + 13 pounds) - $46.50

$20.80/pound * pounds of chocolate = $11.80/pound * pounds of chocolate + $11.80/pound * 13 pounds - $46.50

$9.00/pound * pounds of chocolate = $158.40 - $46.50

$9.00/pound * pounds of chocolate = $111.90

pounds of chocolate = $111.90 / $9.00/pound

pounds of chocolate = 12.43 pounds

Thus, the store owner should mix 12.43 pounds of chocolate with 13 pounds of trail mix to create a mixture worth $11.80 per pound.

Answer:

12 pound of chocolate

Step-by-step explanation:

Let x pounds of chocolate costing $20.80 per pound, mixed with 13 pounds of trail mix costing $3.50 per pound to create a mixture worth $11.80,

The total quantity of trail mix = ( x + 13 ) pounds,

Also, the cost of x pounds of chocolate + the cost of 13 pounds of trail mix = the cost of the resultant trail mix.

total cost = number of pounds × price per pound

20.80x + 3.50(13) = 11.80(x + 13)

20.80x + 45.5 = 11.80x + 153.53

9x + 45.5 = 153.53

9x = 108.03

x = 12 pound

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The cost to Alex to put molding around his living room, given the molding costs per foot and the dimensions of the living room, is $ 87. 72

The molding cost can be found by multiplying the cost per foot, by the number of feet of his living room . In other words, the perimeter of Alex's living room in feet .

Given that this is a living room, it is most likely of rectangular shape which means that the perimeter of the living room would be :
= 16 + 18 + 16 + 18

= 68 feet

This means that the cost of putting molding around the living room to Alex, would be :

= Cost per feet of molding x Number of feet around living room

= 1. 29 x 68

= $ 87. 72

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The height, in feet, of the fifth bounce=2.7579

On the 1st bounce, height = 6.1 feet

We were not given the initial height of the ball before the 1st bounce

2nd bounce:

height = 0.82 of the previous bounce

height = 0.82(6.1)

height=5.002

3rd bounce:

height = 0.82 of the previous bounce

previous bounce = 0.82(6.1)

height = 0.82(0.82 × 6.1)

height=4.10164

We can derive a formula for the nth bounce:

height=6.1(0.82)^n-1

h(n)=6.1(0.82)^n-1

To verify consider n=1

h(1)=6.1(0.82)^1-1

h(1)=6.1

To calculate the fifth bounce:

h(5)=6.1(0.82)^5-1

considering n=5

h(5)=6.1(0.45212176)

h(5)=2.7579

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Isosceles triangle the vertex angle is twice either base angle is the right statement. Isosceles triangle is a triangle which has two sides of equal length or value.

Isosceles triangle is a triangle that has two side of same value. It is mean that isosceles triangle has to fulfill this condition : two sides of triangle has to be congruent to each other; the third side of isosceles triangle that has not same length to the another side is called the base of the isosceles triangle; the two angles opposite has the same sides are congruent to one another.

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Eric's regular hourly pay is $14.05.

Pay is a term used to describe the compensation received for providing goods or services. It may be in the form of wages, salary, commission, bonus, tips, piece rate pay, or other forms of compensation. Pay is often based on the amount of time worked, or on the amount of work completed. Pay is a key component of the employer-employee relationship, and labor laws often regulate pay to ensure fairness and compliance.

To calculate Eric’s regular hourly pay, we can use the following equation:

Regular hourly pay = (Total pay - Overtime pay) / (Regular hours + Overtime hours)

In this case, we would plug in the following values:

Regular hourly pay = ($852.5 - (10 x 1.5 x Regular hourly pay)) / (40 + 10)

Regular hourly pay = ($852.5 - $150) / 50

Regular hourly pay = $702.5 / 50

Regular hourly pay = $14.05

Therefore, Eric's regular hourly pay is $14.05.

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Answer:

B True

Step-by-step explanation:

The cuneiform was a system of writing that used wedge-shaped symbols, and it was developed by the ancient Sumerians in Mesopotamia, which is often referred to as "the land between the rivers" because it is located between the Tigris and Euphrates rivers. Cuneiform was used for a variety of purposes, including recording laws, keeping track of business transactions, and recording historical events. It was one of the earliest systems of writing in the world, and it continued to be used in various forms for over three thousand years.

57 beads out of 100 beads are brown in colour.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Brennan ordered a set of beads

He received 100 beads

57% of 100 beads were brown.

we need to find the number of beads which are brown.

Convert 57 % to the decimal value.

57/100=0.57

Now multiply 0.57 with 100

0.57×100=57

Hence, 57 beads out of 100 beads are brown in colour.

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The domain and range of the function whose vertex is (3,-2) are (-∞, +∞) and (-∞, 2] respectively.

What is a graph?

A graph is a diagram that depicts the relationship between two variables, usually measured along opposite axes in a pair, is used.

In the given graph, the vertex is (3, -2).

Since, the domain of the function shows the values of x,

The values of x can be all real numbers,

So, domain = (-∞, +∞)

And the range of the function shows the value of y,

In the graph, the value of y is less than or equal to 2,

So, range = (-∞, 2].

Therefore, the domain of the function is (-∞, +∞) and the range of the function is (-∞, 2].

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The formula of the sinusoidal function is given as follows:

y = 3sin(0.6πx) - 6.

The sinusoidal function intersects the midline at x = 0, meaning that it is modeled by a sine function.

The standard definition of the sine function is given as follows:

y = Asin(Bx) + C.

For which the parameters are given as follows:

The midline is at y = -6, while the minimum point is at y = -9, hence the amplitude of the function is given as follows:

A = -6 - (-9)

A = 3.

A sinusoidal function with amplitude 3 should oscillate between -3 and 3, while it oscillates between -3 and -9, hence the vertical shift is given as follows:

C = -6.

The distance from the midline to the minimum value is of 3/4 of the period, hence the period is of:

3/4P = 2.5

P = 4 x 2.5/3

P = 10/3.

This means that the parameter b is obtained as follows:

2π/B = 10/3

10B = 6π

B = 0.6π

This means that the function is defined as follows:

y = 3sin(0.6πx) - 6.

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The estimated solution of the system of equations is (55/13, 87/6).

The graph of the system of equations is given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

y = 3x - 6 _____(1)

y = (2/5)x + 5 ______(2)

From (1) and (2) we get,

3x - 6 = (2/5)x + 5

3x - (2/5)x = 5 + 6

(15x - 2x) / 5 = 11

13x / 5 = 11

13x = 55

x = 55/13 substituting in (1)

y = 3 x 55/13 - 6 = 165/13 - 6 = (165 - 78) / 6 = 87/6

The solution is (55/13, 87/6)

The graph is given below.

Thus,

The solution is (55/13, 87/6).

The graph is given below.

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To verify:

cos⁴x+sin⁴x=1-2sin²xcos²x​

we have,

LHS= sin⁴x+cos⁴x

=(sin²x)²+(cos²x)² +2sin²x cos²x - 2sin² cos²x

(by adding and subtracting 2sin²x cos²x)

=(sin²x +cos²x )² - 2 sin²x cos²x

=1-2sin²x cos²x =RHS

Therefore LHS=RHS

The study of angles and the angular relationships of planar and three-dimensional figures is known as trigonometry. It is the branch of mathematics concerned with specific functions of angles and their application to calculations.

Trigonometry as the name suggests is all about triangles. More specifically, it is about right-angled triangles.

The trigonometry functions (also called the circular functions) comprising trigonometry are the cosecant, cosine(cos), secant, sine(sin), and tangent(tan).

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The value of x will be;

⇒ x = - 3

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 expression is,

⇒ 8 × 2²ˣ + 4 × 2ˣ × 2 = 1 + 2ˣ

Now,

Since, The expression is,

⇒ 8 × 2²ˣ + 4 × 2ˣ × 2 = 1 + 2ˣ

Solve for x as;

⇒ 8 × 2²ˣ + 8 × 2ˣ = 1 + 2ˣ

⇒ 8 × 2ˣ (2ˣ + 1) = 1 + 2ˣ

⇒ 8 × 2ˣ = (1 + 2ˣ) / (1 + 2ˣ)

⇒ 8 × 2ˣ = 1

⇒ 2ˣ = 1/8

⇒ 2ˣ = 2⁻³

By comparing, we get;

⇒ x = - 3

Thus, The value of x = - 3

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The number of different combinations of five can the teacher choose from the eight study questions will be 56.

Combination and permutation are two different ways of grouping elements of a set into subsets in mathematics. The elements of the subset can be listed in any order in a combination. The elements of the subset are listed in a specific order in a permutation.

Given that your history teacher gives you a list of eight study questions. Five of the eight will be on the next test.

The combination will be calculated as,

Combination = ⁸C₅

Combination = ( 8!) / ( 5! x 3! )

Combination = ( 8 x 7 x 6 x 5!) / ( 5! x 3 x 2 )

Combination = ( 8x 7 )

Combination = 56

Hence, the combination will be 56.

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Store of Value: people are willing to hold onto it because they're confident that it will keep its value over time.

In Economics, money can be defined as any formally recognized economic unit that is universally accepted as a medium of exchange for goods (products) and services, as well as repayment of debts such as taxes, levies, fees, and loans, across the world.

Generally speaking, money is universally accepted as a medium of exchange because it possesses six (6) essential characteristics and these include the following:

In conclusion, we can reasonably infer and logically deduce that store of value is a measure of the durability of money.

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Simpson's Paradox makes this claim possible.

The phenomenon whereby particular trends are prevalent in small data portions but are not evident or an inverse trend is observed when the portions are joined together is known as Simpson's paradox.

Whereby the data for calculating the batting averages as found online are given as follows:

Season                      Derek Jeter                           David Justice

1995                           12/48 = 0.250                         104/411 ≈ 0.253

1996                           183/582 ≈ 0.314                      45/140 ≈ 0.321

The overall hits to the overall bat's ratio are:

(183 + 12)/(582 + 48) ≈0.310   (104+45)/(411+140) = 0.27

This shows that  Derek Jeter's overall average was better than Justice's average.

Thus, Simpson's Paradox makes this claim possible.

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As per the given average, the team statistician claims Jeter's overall average was better than Justice's average is 0.27

Here we have given that the following table of data is presented

Time,                       Score of Derek Jeter               Score of David Justice

At 1995,                         ≈  0.250                                     ≈ 0.253

At 1996,                          ≈ 0.314                                      ≈ 0.321

Then the overall score for Derek Jeter is calculated by

=>  (183 + 12)/(582 + 48) ≈0.310  

And the overall score for  David Justice is calculated as

=> (104+45)/(411+140) = 0.27

Here the resulting values shows that  Derek Jeter's overall average was better than Justice's average  

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The two true options about the ratio between the hours he works and the neckties he produces among the given statements are (c) and (d).

Given that Diante can make 5 neckties in 4 hours. ratio

Hence,

Number of neckties Diante can make in an hour = 5/4 = 1.25 per hour.

Hence, (d) is correct.

As in (b), it is written that Diante can make 4/5 of a necktie in an hour hence it is incorrect.

We can also say that:-

Number of hours taken to make a necktie = 4/5 hour.

Hence, (c)  is correct.

As in (a), it is written that Diante can make 1 necktie in 1.25 hours, hence it is incorrect.

complete question

Diante can make 5 neckties in 4 hours.

select the two true statements about the ratio between the hours he works and the neckties he produces.

a. it takes diante 1.25 hours to make one necktie.

b. diante makes 45 of a necktie per hour.

c. it takes diante 45 hour to make a necktie.

d. diante makes 1.25 neckties per hour.

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The solution that is correct is B. Amy is correct because adding the decimals and then adding the exponents is not the correct procedure for adding numbers in scientific notation.

Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It is also called standard form or standard index form e.g  1000000 = 10⁶ and 0.0001 = 10⁻⁴

(8.0 × 10⁷) + (6.2 × 10³) = (80000 × 10³) + (6.2 × 10³)

                                     = (80000 + 6.2) × 10³

                                     = 80006.2 × 10³

                                     = 8.00062 × 10⁷

Thus, Amy is correct because adding the decimals and then adding the exponents is not the correct procedure for adding numbers in scientific notation.

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Multiple triangles are possible with three different side lengths. The relationships between the side lengths and the lengths of the sides determine the number of triangles.

For instance, only one triangle can be formed if the lengths of the three sides are the same. Two triangles can be formed if the lengths of two sides are equal. It is possible to form three triangles if the lengths of the three sides differ.

In general, it is possible to form a triangle if the three side lengths satisfy the triangle inequality theorem. The sum of any two sides of a triangle must be greater than the sum of the third side, according to this theorem. For instance, since 3 + 4 is greater than 5, a triangle can be formed if the three side lengths are 3, 4, and 5. A triangle cannot be formed if the sum of any two sides is not greater than the third side.

The angle relationships between the sides also play a role in determining how many distinct triangles can be formed.

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Answer:

Buffy is correct

Step-by-step explanation:

To start off, we know that if we buy 1 pen, the cost of the singular pen will be 1.5, which isn't a whole number. Therefore we can eliminate Bonnie, meaning the domain of the situation is by positive real numbers (real numbers meaning decimal, fraction AND whole numbers)

The population of interest is: A. all people in Emerald, Queensland.

The population of interest refers to the group of individuals that the research is trying to draw inferences about. In this case, the international fast food chain is looking to assess the level of interest in opening a franchise in Emerald, Queensland.

Therefore, the population of interest is all people who live in Emerald, Queensland, as they are the group that the research is trying to understand. The sample of 100 addresses that the research firm selected is just a subset of this population and the questionnaires are being sent to them to infer about the entire population.

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Please find attached herewith the solutions of your questions.

Hope it helps.

If you have any query, feel free to ask.

Answer:

[tex]\textsf{8.} \quad \textsf{B.}\;8x^3y[/tex]

[tex]\textsf{9.} \quad \textsf{D.}\;81x^8[/tex]

[tex]\textsf{10.} \quad \textsf{A.}\;10t^{-7}[/tex]

[tex]\textsf{11.} \quad \textsf{C.}\;\dfrac{3m^2}{x^3}[/tex]

[tex]\textsf{12.} \quad \textsf{B.}\;\dfrac{1}{3m^9}[/tex]

Step-by-step explanation:

Exponent Rules

[tex]\textsf{Product rule}: \quad a^b \cdot a^c=a^{b+c}[/tex]

[tex]\textsf{Power rule}: \quad (a^b)^c=a^{bc}[/tex]

[tex]\textsf{Quotient rule} \quad \dfrac{a^b}{a^c}=a^{b-c}[/tex]

[tex]\textsf{Power of a Product rule}: \quad (ab)^c=a^{c} \cdot b^c[/tex]

[tex]\textsf{Negative exponent rule} \quad a^{-n}=\dfrac{1}{a^n}[/tex]

[tex]\begin{aligned}\left(2x^2y^3\right)\left(4xy^{-2}\right)&=2 \cdot 4 \cdot x^2 \cdot x \cdot y^3 \cdot y^{-2}\\&=8\cdot x^{(2+1)}\cdot y^{(3-2)}\\&=8 \cdot x^3 \cdot y^1\\&=8x^3y\end{aligned}[/tex]

[tex]\begin{aligned}\left(3x^2\right)^4&=3^4 \cdot (x^2)^4\\&=81 \cdot x^{(2 \cdot 4)}\\&=81x^8\end{aligned}[/tex]

[tex]\begin{aligned}5t^{-2} \cdot 2t^{-5}&=5 \cdot 2 \cdot t^{-2} \cdot t^{-5}\\&=10 \cdot t^{(-2-5)}\\&=10t^{-7}\end{aligned}[/tex]

[tex]\begin{aligned}\dfrac{6m^{10}x^4}{2m^8x^7}&=\dfrac{6}{2} \cdot \dfrac{m^{10}}{m^8} \cdot \dfrac{x^4}{x^7}\\\\&=3 \cdot m^{(10-8)} \cdot x^{(4-7)}\\\\&=3m^2x^{-3}\\\\&=\dfrac{3m^2}{x^3}\end{aligned}[/tex]

[tex]\begin{aligned}\dfrac{m^{-3}}{3m^6}&=\dfrac{1}{3} \cdot \dfrac{m^{-3}}{m^{6}}\\\\&=\dfrac{1}{3} \cdot m^{(-3-6)}\\\\&=\dfrac{1}{3} \cdot m^{-9}\\\\&=\dfrac{1}{3m^9}\end{aligned}[/tex]

Answer: y=mx+b

Step-by-step explanation:

So there are 5 raspberries in the bowl.

The unitary approach involves calculating the value of a single unit, from which we may calculate the values of the necessary number of units.

Two quantities are compared to form a ratio. An equality of two ratios is a percentage. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.

We know that for every 3 raspberries, there are 5 blackberries.

We can set up an equation to represent this relationship:

5 blackberries = 3 raspberries

We also know that there are a total of 15 blackberries in the bowl.

We can use the equation to find the number of raspberries in the bowl:

15 blackberries = 3 raspberries

15 blackberries / 3 raspberries = 5 raspberries

So there are 5 raspberries in the bowl.

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The equations of the line in slope-intercept form are listed below:

4) y = - x / 2 + 3

5) y = (5 / 2) · x + 1

6) y = - 4 · x + 5

7) y = - x + 2

8) y = 2 · x / 3 + 4

9) y = x

Lines are described by first order polynomials of the form:

y = m · x + b

Where:

Where the slope of the line is found by secant line formula:

m = Δy / Δx

Where:

The complete procedure is summarized below:

Case 4

(x₁, y₁) = (0, 3), (x₂, y₂) = (6, 0)

m = (0 - 3) / (6 - 0)

m = - 1 / 2

b = y - m · x

b = 0 - (- 1 / 2) · 6

b = 3

y = - x / 2 + 3

Case 5

(x₁, y₁) = (0, 1), (x₂, y₂) = (2, 6)

m = (6 - 1) / (2 - 0)

m = 5 / 2

b = y - m · x

b = 6 - (5 / 2) · 2

b = 6 - 5

b = 1

y = (5 / 2) · x + 1

Case 6

(x₁, y₁) = (- 2, 3), (x₂, y₂) = (0, - 5)

m = (- 5 - 3) / [0 - (- 2)]

m = - 4

b = y - m · x

b = - 5 - (- 4) · 0

b = - 5

y = - 4 · x + 5

Case 7

(x₁, y₁) = (0, 2), (x₂, y₂) = (2, 0)

m = (0 - 2) / (2 - 0)

m = - 1

b = y - m · x

b = 0 - (- 1) · 2

b = 2

y = - x + 2

Case 8

(x₁, y₁) = (0, - 4), (x₂, y₂) = (6, 0)

m = [0 - (- 4)] / (6 - 0)

m = 2 / 3

b = y - m · x

b = 0 - (2 / 3) · 6

b = 4

y = 2 · x / 3 + 4

Case 9

(x₁, y₁) = (0, 0), (x₂, y₂) = (1, 1)

m = (1 - 0) / (1 - 0)

m = 1

b = y - m · x

b = 1 - 1 · 1

b = 0

y = x

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