An insurance company offers an ordinary annuity that earns 6.5% interest compounded annually. A couple plans to make equal annual deposits into this account for 30 years and then make 20 equal annual withdrawals of €25,000, reducing the balance of the account to zero.

(i) Compute the value of the fund based on the withdrawals required. [5 marks]

(ii) Compute the amount of each deposit needed in order to maintain the fund. [5 marks]

(iii) Compute the total interest earned over the entire 50 years. [5 marks]​

The radius of the circle is 35.98 in, the diameter is 71.96 in. and the area of the circle is 4066.98 sq. in.

Here, the circumference of circle is C=226.08 in

We know that the formula for the circumference of circle is C = 2πr

Using this formula we find the value of radius 'r',

C = 2πr

226.08 = 2πr

r = 226.08 / 2π

r = 35.98 in

And the diameter of the circle would be,

d = 2r

d = 2 × 35.98

d = 71.96 in.

And the area of the circle would be,

A = π × r²                                                                  

A = π × 35.98²

A = 4066.98 sq. in.

Therefore, the required area is  4066.98 sq. in.

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The complete question is:

Solve for radius and diameter then what is the area of the circle if the circumference of circle is C=226.08 in.

The theoretical probability of drawing a green or red ticket is 1/2 or 0.5.

We have,

There are a total of 3 + 4 + 5 + 6 = 18 tickets in the basket.

The probability of drawing a yellow ticket.

= 4/18

Since there are 4 yellow tickets out of 18 total tickets.

The probability of not drawing a yellow ticket is equal to the probability of drawing a green, blue, or red ticket.

There are 3 + 5 + 6 = 14 tickets that are not yellow.

The probability of not drawing a yellow ticket.

= 14/18

= 7/9

To find the probability of drawing a green or red ticket, we need to add the probabilities of drawing a green ticket and a red ticket.

The probability of drawing a green ticket.

= 3/18

The probability of drawing a red ticket.

= 6/18

Now,

The probability of drawing a green or red ticket is

= 3/18 + 6/18

= 9/18

= 1/2

Thus,

The theoretical probability of drawing a green or red ticket is 1/2 or 0.5.

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A line on the graph which could represent this scenario is shown in the image attached below.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about this line, it can be modeled by this equation:

y = mx + c

y = 2x/3 + (-6)

y = 2x/3 - 6

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Answer:5.03

1.26 are correct

Step-by-step explanation:We can solve this quadratic equation in cos(θ) by using the substitution u = cos(θ):

5u^2 - 8u + 2 = 0

We can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 5, b = -8, and c = 2. Substituting these values, we get:

u = (8 ± sqrt(64 - 40)) / 10

u = (8 ± 2sqrt(6)) / 10

Therefore, either:

Answer:

[tex]\huge\boxed{\sf x = 10\°}[/tex]

Step-by-step explanation:

According to the statement,

92° + x + 78° = 180°

170° + x = 180°

x = 180° - 170°

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

(a)  

16

36

​

=

4

9

​

36:16=9:4

(b)  

144

324

​

=

4

9

​

324:144=9:4

(c)  

1125

125

​

=

1125

125

​

=

45

5

​

=

9

1

​

∴125:1125=1:9

Answer:

Please help me by marking me the brainliest.

The area of the triangle is 9 units^2

Step-by-step explanation:

Area of triangle = 1/2(6*3)

                          =1/2(18)

                          =9

Answer:

Answer:

= 6 R 25

= 6 25/27

187 divided by 27 equals

6 with a remainder of 25

Step-by-step explanation:

The area of the circular pateo is 50.24 square yards.

Remember that for a circle of radius R, the area is given by the formula:

A = pi*R²

Where pi = 3.14

Here we know that the patio is circular, and it has a diameter of 4 yards, then the radius is:

R = 4yd/2

R = 2 yd

Replacing that in the area formula we will get:

A = 3.14*(2yd)²

A = 50.24 yd²

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The probability of passing at least one will be 0.70.

We know that,

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

here, we have,

Probability of passing history course = 0.59

Probability of passing math course = 0.60

Probability of passing both courses = 0.49

so, we get,

Probability of passing at least one will be

⇒ 0.59 + 0.60 – 0.49

⇒ 0.70

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complete question:

A student is taking two courses, history and math. the probability the student will pass the history course is 0.59, and the probability of passing the math course is 0.60. the probability of passing both is 0.49. what is the probability of passing at least one?

Answer:

C) 23/32

Step-by-step explanation:

count how many lines there are in all

32

Then count from beginning to X

23

The distance of X is 23/32

The Height of the given rectangular prism is:  (x + 1) - 4/(x³ + 3x² + 8)

In algebra, polynomial long division is defined as an algorithm used in dividing a polynomial by another particular polynomial of the same or even lower degree, which is a generalized version of the common arithmetic technique called long division. It can be done easily by hand, because it separates a supposedly complex division problem into smaller ones.

We are given:

Volume of a rectangular prism =  (x⁴ + 4x³ + 3x² + 8x + 4), and the area of its base is (x³ + 3x² + 8)

Thus, height is:

                   x + 1

x³ + 3x² + 8|x⁴ + 4x³ + 3x² + 8x + 4

                -  x⁴ + 3x³ + 0   + 8x

                           x³ + 3x² + 4

                         - x³ + 3x² + 8

                                        -4

Thus:

Height = (x + 1) - 4/(x³ + 3x² + 8)

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The two expressions "8m+4-3m" and "3+ m+2m+1+2m​" are equivalent because they simplify to the same-value.

To determine if the two expressions are equivalent, we can simplify each expression and then compare them.

Simplifying the first -expression,

We have,

⇒ 8m + 4 - 3m can be simplified by combining like terms;

⇒ 8m - 3m + 4 = 5m + 4

Next, Simplifying the second-expression,

we have,

⇒ 3 + m + 2m + 1 + 2m can also be simplified by combining like-terms:

⇒ (1 + 3) + (m + 2m + 2m) = 4 + 5m

So we have:

(i) 8m + 4 - 3m = 5m + 4

(ii) 3 + m + 2m + 1 + 2m = 4 + 5m

Since both simplified expressions are equal to "5m + 4", we can conclude that the two original expressions are equivalent.

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The rate at which the temperature of the compound rose was 5¹/₄ degrees per hour.

To find the rate at which the temperature of the compound rose, we need to divide the change in temperature by the time interval during which the change occurred.

The temperature rose 3¹/₂ degrees every 2/3 of an hour. To write this as a fraction, we can first convert 3¹/₂ to an improper fraction:

3¹/₂= 7/2

Now, we can write the rate of change as a fraction:

Rate of change = (7/2) / (2/3)

To divide by a fraction, we can multiply by its reciprocal:

Rate of change = (7/2) x (3/2)

Simplifying, we get:

Rate of change = 21/4

Therefore, the rate at which the temperature of the compound rose was 5¹/₄ degrees per hour.

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The correct statement regarding whether the graph represents a function is given as follows:

No, it is not a function.

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.

In the graph, we have that at x = 0 = y-axis, the function has three numeric values, which is a case of vertically aligned points, hence the graph does not represent a function.

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a) An equation that represents the amount of money that Gilberto

receives during a school year:  y = 5 + (0.5) x

b) The number of correct answers Gilberto needs to buy a new shirt that costs $25 = 40

Let us assume that y represents the amount of money and x represents the number of correct answers.

We know that One dollar = 100 cents.

so, 50¢ = 0.5 dollars

From the described informtaion, we can write the equation that represents the amount of money that Gilberto receives during a school year as: y = 5 + (0.5) x

Now we need to find the number of correct answers Gilberto needs to buy a new shirt that costs $25

i.e., for y = 25, we need to find the value of x.

Substitute y = 25 in above equation.

25 = 5 + (0.5) x

We solve this equation for x

(0.5) x = 20

x = 20 / (0.5)

x = 40

This means that he needs to give 40 correct answers.

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The complete question is:

Gilberto's  grandfather gives Gilberto $5 and then 50¢ for each math question he answers correctly on his math exams for the year.

a. Write an equation that represents the amount of money that Gilberto

receives during a school year. Explain what the variables and numbers mean.

b. Use the equation to find the number of correct answers Gilberto needs to buy a new shirt that costs $25. Show your work.

Answer:

18. The end behavior of the graph of f(x) = x³ + 2x² - 5x + 1 is as follows: as x approaches negative infinity, the function f(x) approaches negative infinity, and as x approaches positive infinity, the function f(x) approaches positive infinity. This is because the leading term of the polynomial is x³, which has a positive coefficient, so the graph of the function will have a "smile" shape, with the ends of the graph pointing upwards.

19. The end behavior of the graph of g(x) = -2x³ - 8x² + 18x + 72 is as follows: as x approaches negative infinity, the function g(x) approaches negative infinity, and as x approaches positive infinity, the function g(x) approaches negative infinity. This is because the leading term of the polynomial is -2x³, which has a negative coefficient, so the graph of the function will have a "frown" shape, with the ends of the graph pointing downwards.

Step-by-step explanation:

Answer:

Rs 2150.81.

Step-by-step explanation:

The interest rate for the first two years is 6% per annum, which is halved for each six-month period. Therefore, the interest for the first two years would be (6950*(1+(0.03))^8) - 6950 = Rs 1373.53.

For the third year, the interest rate is 9% per annum, which is also halved for each six-month period. Therefore, the interest for the third year would be (6950*(1+0.045))^2 - 6950 = Rs 777.28.

Hence, the total compound interest for three years would be Rs 2150.81.

Answer:

Step-by-step explanation:

You want the number of day passes sold for $61 and weekend passes sold for $110 if 257 more day passes were sold, and sales totaled $307745.

Let w represent the number of weekend passes sold. Then w+257 is the number of day passes sold. The total revenue is ...

  61(w+257) +110(w) = 307745

Simplifying the equation, we have ...

  171w +15677 = 307745

  171w = 292068 . . . . . . . . subtract 15677

  w = 1708 . . . . . . . . . . . divide by 171

  w+257 = 1965 . . . day passes sold

1965 day passes and 1708 weekend passes were sold.

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Answer: A' will be at (-2,0)

Step-by-step explanation:

Reflecting things over a line can be done in several different ways, I will try to explain the one I use and the easiest one. What I use is to look at it and find the shortest distance between the line and A, in this case, the shortest distance is at (-.5,1.5), since A is at (1,3) the distance between them is (-1.5,-1.5) If you double this change you will find how far away the new point A is from the Old point, so its a change of (-3,-3). (1,3)+(-3,-3) gets you to the final points of (-2,0)

Another, probably easier, method is to go down from point A until you hit the line, and then go over that many points. In this case, you go down 3 from A to hit the line, and then go 3 to the left which reflects it over the line. Either way you do it, you get (-2,0)

Step-by-step explanation:

3.3% = .033 in decimal

Use the compounding formula

a)  P(t) = 18000 (1 + .033)^t        

b)   for t =2 this computes to 19207.6  bacteria

The volume of a cube is calculated by multiplying the length of one side by itself twice. In this case, the volume of the foam cube is 5 in. x 5 in. x 5 in. = 125 cubic inches.

Density is calculated by dividing the mass of an object by its volume. In this case, the density of the foam cube is 62 g / 125 cubic inches = 0.496 g/cubic inch.

So, the volume of the foam cube is 125 cubic inches and its density is 0.496 g/cubic inch.

Answer:

Step-by-step explanation:

Complementary means angles that add up to 90°

Based on that you can write and equation by adding the 2 angles and making equal to 90

2x+6+1/2x=90          combine like terms on left

5/2x+6=90               subtract both sides by 6

5/2x=84                   multiply by the reciprocal of 5/2 => 2/5

x=168/5 or 33.6

An equation to represent A, the area in square feet, as a function of w, the width in feet is A = 120W -2W²

Here, we have,

According to the question, the school uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides.

Substitute into the perimeter of the rectangle will give:

120 = L + 2W

Area = LW

We know that the area of a rectangle is l × w

When w =10, length = 120 - 20 = 100, area = 100 x 10 = 1000

When w = 20, length = 120 - 40 = 80,  area =  80 x 20  = 1600

When w = 40, length = 120 - 80 = 40.  area = 40 x 40 = 1600.

So, the completed table will be

Width            Length          Area

10                    100              1000

20                    80              1600

40                    40              1600  

w                  120 - 2w        (120 - 2w) w

In order to maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60

On substituting, we have;

A = LW = (120 - 2W) W

L = 120 - 2W,

On simplification, we have

A = 120W -2W²

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m² × m² is equal to m⁴.

w³ × w² is equal to w⁵.

5k³ × 4k⁴ × k is equal to 20k⁸.

The length of each side of the square is 9x.

A simplification of the expression 28x³ ÷ 4x is 7x².

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LB

Where:

By substituting the given parameters into the formula for the area of a rectangle, we have the following;

Area of rectangle = (27x) × (3x)

Area of rectangle = 81x²

Note: Area of square = Area of rectangle

Area of square = (side length)²

81x² = (side length)²

Side length = √(81x²)

Side length = 9x

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Answer:

n = -5

Step-by-step explanation:

We know that when two lines are perpendicular, the slopes of the two lines are negative reciprocals as

[tex]m_{2}=-\frac{1}{m_{1} }[/tex], where m2 is the slope of the line we're usually not given, and m1 is the slope of the line we're given

Thus, we know that m2 must equal -1/2 from the formula since m1 is 2:

[tex]m_{2}=-\frac{1}{2}[/tex]

Of course, -1/2 is already simplified so m2 is the slope of the line passing through (8, n) and (2, -2)

To find n, we must use our knowledge of the slope formula that gives us the slope, m:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where x1 and y1 are one point on the line and x2 and y2 are another point on the line:

If we allow (8, n) to be our x1 and y1 point and allow (2, -2) to be our x1 and y2 point and -1/2 to be our m, we can now solve for m by plugging everything into the slope formula and solving for n (aka y1 in the formula:

[tex]-1/2=\frac{-2-n}{2-8}\\ \\-1/2=\frac{-2-n}{-6}\\ \\3=-2-n\\\\5=-n\\\\-5=n[/tex]

We can even check that we get -1/2 when we plug in -5 into the slope formula:

[tex]-1/2=(-2-(-5))/(2-8)\\-1/2=(-2+5)/(-6)\\-1/2=3/-6\\-1/2=-1/2[/tex]

The formula for p(x) is p(x) = -0.1(x - 5)²(x + 3).

In Mathematics and Geometry, the graph of a polynomial function touches the x-axis at zeros, roots, solutions, x-intercepts, and factors with even multiplicities.

Also, the graph has a zero of multiplicity 2 at x = 5 and zero of multiplicity 1 at x = -3;

x = 5 ⇒ x - 5 = 0.

(x - 5)²

x = -3 ⇒ x + 3 = 0.

(x + 3)

In this context, an equation that represent the polynomial function is given by:

p(x) = a(x - 5)²(x + 3)

By evaluating and solving for the leading coefficient "a" in this polynomial function based on the y-intercept (0, -7.5), we have;

-7.5 = a(0 - 5)²(0 + 3)

-7.5 = a75

a = -7.5/75

a = -0.1.

Therefore, the required polynomial function is given by:

p(x) = -0.1(x - 5)²(x + 3)

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It should be noted that 81.85% of the scores are between 72 and 87.

The probability that a score is greater than 77 is approximately 0.8413.

a) The z-score for 72 is calculated as:

z = (72 - 82) / 5 = -2

The z-score for 87 is calculated as:

z = (87 - 82) / 5 = 1

0.8413 - 0.0228 = 0.8185

So, approximately 81.85% of the scores are between 72 and 87.

b) The z-score for 77 is calculated as:

z = (77 - 82) / 5 = -1

1 - 0.1587 = 0.8413

Therefore, the probability that a score is greater than 77 is approximately 0.8413 (or 84.13%).

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The value of SV, given that point J is the centroid, would be A. 9.

Seeing as we have point J as the centroid for triangle SZU, we can then tell that JV would be:

JV = 1 / 3 x SV

Knowing this, we can make SV the subject of the formula to become:

(JV = 1 / 3 x SV ) / 1 / 3

3 x JV = SV

SV = 3 JV

SV would then be:

SV = 3 x JV

SV = 3 x 3

SV = 9

In conclusion, SV would be 9.

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Answer:

answer is B. 9 :)

Step-by-step explanation: