In a recipe for fizzy grape juice, the ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1

[tex]~~~~~~~~~~~~\stackrel{\textit{payments at the beginning of the period}}{\textit{Future Value of an annuity due}} \\\\ A=pmt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]\left(1+\frac{r}{n}\right)[/tex]

[tex]\qquad \begin{cases} A=\textit{accumulated amount} \\ pmt=\textit{periodic payments}\dotfill & 4500\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &10 \end{cases}[/tex]

[tex]A=4500\left[ \cfrac{\left( 1+\frac{0.04}{1} \right)^{1 \cdot 10}-1}{\frac{0.04}{1}} \right]\left(1+\frac{0.04}{1}\right) \\\\\\ A=4500\left[ \cfrac{(1.04)^{10}-1}{0.04} \right](1.04) \implies A \approx 56188.58[/tex]

so every year you were putting in 4500 bucks, so for 10 years that'd be a total deposits for 4500*10 = 45000, so let's squeeze out the 45000 from the the total, that gives us 56188.58 - 45000 ≈ 11188.58.

so, if we take 56188.58 to be the 100%, what's 11188.58 off of it in percentage?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 56188.58 & 100\\ 11188.58& x \end{array} \implies \cfrac{56188.58}{11188.58}~~=~~\cfrac{100}{x} \implies 56188.58x=1118858 \\\\\\ x=\cfrac{1118858}{56188.58}\implies x\approx \stackrel{\%}{19.91}[/tex]

The concurrent parts in ABDE are Side AB ≅ Side ED and Side AE ≅ Side BD.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create a similar appearance. They are in alignment with one another when moved. The symbol ≅ used for concurrence.

Here we have,

ABDE is an isosceles trapezoid.  

If we draw two diagonals in a given trapezoid as given picture

Then the diagonal  will divide the trapezoid into 4 triangles

Here ΔAOB, ΔBOD, ΔEOD, and AOE

Here ΔAOB and ΔEOD will be two concurrent triangles

And ΔBOD and AOE will be two concurrent triangles

From ΔAOB and ΔEOD

Side AB ≅ Side ED  

From ΔBOD and AOE

Side AE ≅ Side BD    

Therefore,

The concurrent parts in ABDE are Side AB ≅ Side ED and Side AE ≅ Side BD      

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Area of composite figure is 48 square feet.

What do you mean by composite figure?

A compound shape or figure is a two-dimensional figure made up of basic two-dimensional shapes such as triangles, rectangles, circles, and semicircles.

To find the perimeter of a compound 2D shape, add the lengths of the sides. Find individual regions for each part of the compound shape. The area of ​​a composite shape is the sum of its individual areas.

Let the given composite figure be divided into four rectangles A,B,C and D having dimension 3 and 4

Area of rectangle A = 3 × 4 = 12

Area of rectangle A = area of rectangle B = area of rectangle C = area of rectangle D = 12 square feet.

Total area = Area of rectangle A + area of rectangle B + area of rectangle C + area of rectangle D = 12 + 12 + 12 + 12 =48 square feet

Therefore, area of composite figure is 48 square feet.

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The equation of the line is y = x - 2.

What is the equation of the line?

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Key Concept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

We have,

y-intercept(c) = −2 and

the line is equally inclined to the axis i.e., the same angle to the x-axis and y-axis(say)=θ

but the angle between the axes is 90°

2θ = 90° ⇒ θ = 45°

As slope and y-intercept are given.

The equation of a line is y = mx + c

c = -2 and

m = tan45°

as the line is equally inclined to the axes.

c = -2 and m = 1

Hence, the equation of the line is y = x - 2.

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What is a NPV  net present value ?

The difference between the current value of cash inflows and withdrawals over a period of time is known as net present value (NPV). To evaluate the profitability of a proposed investment or project, NPV is used in capital budgeting and investment planning.

Using the appropriate discount rate, computations are performed to determine the current value of a stream of future payments, or NPV. Projects that have a positive NPV are generally worthwhile pursuing, whereas those that have a negative NPV are not.

1.

NPV of project A = [tex]-50+\frac{8}{/(1.10)^1} +\frac{8}{(1.10)^2} \frac{8}{(1.10)^3} +\frac{8}{(1.10)^4} +\frac{8}{(1.10)^5} +\frac{8}{(1.10)^6} +\frac{8}{(1.10)^7} +\frac{8}{(1.10)^8} +\frac{8}{(1.10)^9} +\frac{8}{(1.10)^1^0} +\frac{8}{(1.10)^1^1} +\frac{8}{(1.10)^1^2} +\frac{8}{(1.10)^1^3} +\frac{8}{(1.10)^1^4} +\frac{8}{(1.10)^1^5} +\frac{8}{(1.10)^1^6} +\frac{8}{(1.10)^1^7} +\frac{8}{(1.10)^1^8} +\frac{8}{(1.10)^1^9} +\frac{8}{(1.10)^2^0}[/tex]

=$18.11

2.

NPV of project B  = [tex]-15+\frac{3.4}{/(1.10)^1} +\frac{3.4}{(1.10)^2} \frac{3.4}{(1.10)^3} +\frac{3.4}{(1.10)^4} +\frac{3.4}{(1.10)^5} +\frac{3.4}{(1.10)^6} +\frac{3.4}{(1.10)^7} +\frac{3.4}{(1.10)^8} +\frac{3.4}{(1.10)^9} +\frac{3.4}{(1.10)^1^0} +\frac{3.4}{(1.10)^1^1} +\frac{3.4}{(1.10)^1^2} +\frac{3.4}{(1.10)^1^3} +\frac{3.4}{(1.10)^1^4} +\frac{3.4}{(1.10)^1^5} +\frac{3.4}{(1.10)^1^6} +\frac{3.4}{(1.10)^1^7} +\frac{3.4}{(1.10)^1^8} +\frac{3.4}{(1.10)^1^9} +\frac{3.4}{(1.10)^2^0}[/tex]

= $13.95

Use function IRR in excel as = IRR(-50,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8)

= 15.03% is the IRR for A.

Use function IRR in excel as = IRR(-15,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4,3.4)

= 22.26% is the IRR for B.

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The rate of change is 7 more of function A than the slope of function B.

Slope is calculated as the ratio of "vertical change" to "horizontal change" between any two points on a line, or any two points. When the ratio is expressed as a quotient ("rise over run"), the same number is provided for every two distinct locations on the same line. There is a negative "rise" on a descending line.

Since y=8x+3,

The rate of change in equation A is equal to the slope m m=8.

The rate of change, m=1, is given in equation B.

y=mx+ is the solution to equation B.

By substituting the values we get,

y=x+4

Calculate the difference between the rates of change of function A and function B.

8-1=7

Therefore, the rate of change is 7 more of function A than the slope of function B.

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Answer:

n = 45

m = 135

Step-by-step explanation:

The sum of the interior angles of a triangle is 180

180 - 55 - 80 = 45

m = the sum of 55 + 80

n= 45°;

m= 135.

The sum of all interior angles of a triangle must equa 360°. Hence, the value of n is given by the following expression:

[tex]n+55+80=180\\ \\n=180-55-80\\\\ n=45[/tex]

Since "m" and "n" are opposites angles and, since there's a straight line adjacent to them, the sum of m and n should equal 180 (check the attached image). Find m with the following expression:

[tex]45+m=180\\ \\m=180-45\\ \\m=135.[/tex]

The measure of the side QR is 58.72 if the sides KL=11, NM=17 and OP=38

Having four edges (sides) and four corners, a quadrilateral is a four-sided polygon in geometry (vertices). The term is derived from the Latin terms quadri, a four-letter version, and latus, which means "side." In comparison to other polygons, it is also known as a tetragon. Tetragon is a Greek word that means "four" and "gon" is a word that means "corner" or "angle" (e.g. pentagon). A quadrangle, or 4-angle, is the equivalent term as "gon" denotes "angle." There are four closed sides to a quadrilateral. These shapes below are quadrilaterals: with Raphael, a creation. a four-sided form. One set of parallel sides make up the shape, and there are no right angles.

From the both figures,

KL/NM=OP/QR

11/17=38/QR

QR=(17×38)/11

QR=58.72

Therefore, the measure of the side QR is 58.72 if the sides KL=11, NM=17 and OP=38.

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The roots of a quadratic function are the values of x that make the function is 0. These roots can be found by solving the equation f(x) is 0.

A quadratic function is a type of mathematical function that can be written in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a is not equal to 0. This type of function is called a quadratic function because the highest power of x in the function is 2.

The graph of a quadratic function is a parabola, which is a U-shaped curve. The shape of the parabola is determined by the value of the constant a. If a is positive, the parabola opens upwards and if a is negative, the parabola opens downwards.

The roots of a quadratic function are the values of x that make the function equal to 0. These roots can be found by solving the equation f(x) = 0. To solve this equation, we can use the quadratic formula, which is:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

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82.9 score should be assigned for A’s and 74.4 should be assigned for B’s

In this question we have been given the scores of students on a test are normally distributed with a mean score of 70 points and a standard deviation of 10 points.

It is decided to give A’s to 10 percent of the students and B’s to 23 percent of the students.

We need to find what scores should be assigned A’s and B’s.

μ = 70, σ = 10

Using standard normal table,

P(X > x) = 10%

P(X > x) = 0.10

1 - P(X ≤ x) = 0.10

P(X ≤ x) =1−0.10

             =0.90

Using standard normal z table,

(x - 70)/10 = 1.29

x = 82.9 (score for A’s)

Now, P(X > x) = 33% (top 33% = 10% for A’s+23 % for B’s)

P(X>x) = 0.33

1 - P(X ≤ x) = 0.33

P(X ≤ x) = 1 - 0.33

             = 0.67

Using standard normal z table,

(x - 70)/10 = 0.44

x = 74.4 (score for B’s)

Therefore, the score for A = 82.9 and the score for B = 74.4

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The total years taken to double the money according to Compounding will be 12.5  years.

What is compound interest?

Compound interest is that the interest on savings calculated on each the initial principal and therefore the accumulated interest from previous periods.

Main body:

Given :

rate = 6%

amount = $900

Total amount = $1800

Compounded monthly,

so formula becomes,

Total amount = amount (1+r/1200)^12t

T = A[tex](1+r/1200)^{12t[/tex]

1800 = 900 (1+6/1200)^12t

2 = (1+1/200)^12t

2 = 1.005^12t

taking log on both sides

log 2 = 12t *log 1.005

0.3/0.002 = 12t

t = 12.5 years

Hence the time taken to double the money is 12.5 years.

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After 25 years, Sample left will be 100g if nearest hundred...ig...

The equation of the line that is normal to the curve y² + ln(x) = 19 at the point (e³, -4) is given as follows:

y + 4 = -8e³(x - e³).

The equation of the line normal to a curve follows the point-slope definition of a linear function, given as follows:

y - y' = m(x - x').

The derivative of the function is found applying implicit differentiation, as follows:

2y dy/dx + 1/x = 0

dy/dx = -1/(2xy).

At x = e³, y = -4, the numeric value of the derivative is given as follows:

dy/dx = e^(-3)/8.

The normal line is perpendicular to the tangent line, hence it's slope is calculated as follows:

m x e^(-3)/8 = -1.

m = -8e³.

Then the equation of the line normal to the curve at the point is given as follows:

y + 4 = -8e³(x - e³).

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The answers to all the parts are given below.

We have a function h = -16t² + 1800, that gives the height of the person at time [t] seconds.

[A] -

For [x] = 1000ft, we can write -

1000 = -16t² + 1800

16t² = 800

t² = (800/16)

t² = 50

t = 7.07 seconds

[B] -

For [x] = 950ft, we can write -

950 = -16t² + 1800

16t² = 850

t² = 53.125

t² = √(53.125)

t = 7.29 seconds

[C] -

The domain of the function will be -

0 ≤ x ≤ 10

[D] -

The range of the function will be -

0 ≤ h ≤ 1800

Therefore, the answers to all the parts are given above.

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Present Value of Annuity = $4,000 × 26.1948  = $104779.2

What is a present value?

The worth of an anticipated revenue stream assessed as of the valuation date is known as the present value in the fields of economics and finance.

Here, we have

Where , Annuity Amount = $4,000            

n = No. of periods = 8 years × 4 quarters per year = 32 periods but since the first payment is at beginning of the quarter,

Then, n = 31 when considered for PVAF

r  = 5.4% / 4 quarters = 1.35%,

Present value of Annuity  = Annuity Amount × Present Value Annuity Factor i.e. PVAF (n, r)

PVAF(n₀,r) when the first payment is at beginning of n i.e.

n₀ = 1 + { [1-(1+r)^ -n ]/r }

= 1 + { [1-(1+0.0135)^ {-31}]/0.0135 }

= 1 + [ (1 - 0.65987 ) ] / 0.0135]

= 1 + 25.1948

= 26.1948

PVAF(32,35%) = 26.1948

Hence, Present Value of Annuity = $4,000 × 26.1948  = $104779.2

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Answer:

  a.  18.5 million

  b.  2002

Step-by-step explanation:

Given that A = 18.5·e^(0.1708t) models a population t years after 2000, you want to know the population in 2000 and when it will reach 26.6 million.

The year 2000 is 0 years after 2000, so we can find the population using t=0 in the given equation.

  A = 18.5·e^(0.1708·0) = 18.5·e^0 = 18.5

The population in 2000 was 18.5 million.

We can solve for t to find the year in which the population reached 26.6 million:

  26.6 = 18.5·e^(0.1708t)

  26.6/18.5 = e^(0.1708t)

  ln(266/185) = 0.1708t

  t = ln(266/185)/0.1708 ≈ 2.13 . . . . . . 2.13 years after 2000

The population will reach 26.6 million in the year 2002.

__

Additional comment

The population of 26.6 million represents about a 44% increase over the initial population of 18.5 million. The exponential term tells you the rate of growth is 17.08% compounded continuously. Thus we expect the larger population to be reached in a time slightly less than 44/17 ≈ 2.6 years.

(These numbers were found using a calculator. It is sufficient to do the estimating by realizing that 1.50·18 = 27, and 17·3 = 51, so the growth to 26.6 from 18.5 is less than 50% and will take less than 3 years.)

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Answer: 5.25>1 3/4>-5/2>-8.345

Step-by-step explanation:

Answer:

  1/3log₂(x) +1/3log₂(y) +1/3log₂(z)

Step-by-step explanation:

You want the complete expansion of ...

  [tex]\log_2{\sqrt[3]{x\cdot y\cdot z\vphantom{b}}}[/tex]

The rules of logs and exponents relevant to this expansion are ...

  [tex]\log_b{(xy)}=\log_b{(x)}+\log_b{(y)}\\\\\log_b{(x^a)}=a\cdot\log_b{(x)}\\\\\sqrt[n]{\vphantom{b}a}=a^{\frac{1}{n}}[/tex]

Applying these rules to the given expression, we get ...

  [tex]\log_2{\sqrt[3]{x\cdot y\cdot z\vphantom{b}}}=\log_2{((xyz)^{\frac{1}{3}})}=\dfrac{1}{3}\log_2{(xyz)}\\\\=\boxed{\dfrac{1}{3}\log_2{(x)}+\dfrac{1}{3}\log_2{(y)}+\dfrac{1}{3}\log_2{(z)}}[/tex]

G(1) has a value of 3,The collection of all possible inputs and outputs constitutes a function's domain and range, respectively.

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The cost of each apple and each orange will be $2.5 and $1.75, respectively. The cost of 1 apple and 1 orange will be $4.25.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

9 apples and 6 oranges cost $33 and 18 apples and 20 oranges cost $80.

Let 'x' be the cost of each apple and 'y' be the cost of each orange. Then the equations are given as,

9x + 6y = 33               ...1

18x + 20y = 80          ...2

Multiply equation 1 by negative 2, then we have

-18x - 12y = - 66          ...3

Add equations 2 and 3, then we have

20y - 12y = 80 - 66

8y = 14

y = $1.75

Then the cost of each apple is calculated as,

9x + 6(1.75) = 33

9x = 33 - 7.5

9x = 22.5

x = $2.5

The cost of each apple and each orange will be $2.5 and $1.75, respectively.

The cost of 1 apple and 1 orange will be given as,

⇒ $2.5 + $1.75

⇒ $4.25

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Answer: Slants upwards.

Step-by-step explanation:

     This is a positive slope, so the line with this given slope will slant upwards. For every increase of one in y, there is a positive change of 2 in x. See attached for a visual example, if the graph was y = ½x.

Answer:

[tex]x = 3, -1[/tex]

Explanation:

math

Answer:

y=3x^2 - 2x + 5

Step-by-step explanation:

The easiest way to find the answer to this question would be to just plug the different x values into the equations. If you take the equations and plug in x and it gives out the correct f(x) value, then the answer would be correct.

For example, plugging -3 into y=3x^2 - 2x + 5 gives you 10. Plugging in 0 gives 5. Plugging in 2 gives 13.

The quadratic equation will be written as F(x) = -2x² - 4x + 1.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

The point from which the quadratic equation passes are,

(0,1), (-1,3), and (-2,1).

The quadratic equation will be written as,

y =ax²+ bx +c

For point (0,1)

1 = 0 + 0 + c

c = 1

For points (-1,3),

3 = a - b + c

3 = a - b + 1

a - b = 2

For point (-2,1),

1 = 4a - 2b + c

1 = 4a - 2b + 1

4a = 2b

b = 2a

calculate the values of a and b,

a - b = 2

a  - 2a = 2

-a = 2

a = -2

b = 2a = 2 x -2 = -4

The quadratic equation will be written as,

F(x) = -2x² - 4x + 1

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Step-by-step explanation:

chances of winning $20=7/20

chances of winning $30=3/20

chances of winning $15=1/2

Answer:-1.34

Step-by-step explanation:

Answer: n=11 m=3

Step-by-step explanation:

2n+2=3n-9

n=11

3m+6=n+4

3m+6=11+4

3m+6=15

3m=9

m=3