You deposit $5000 in an account earning 3% interest compounded continuously. How much will you have in the
account in 15 years?

Answer:

To calculate the future value (FV) of an investment with a given return on balance, monthly rate of return, monthly payment, and number of payments, you can use the future value of an ordinary annuity formula:

FV = P * ((1 + r)^n - 1) / r

Where:

FV = Future value

P = Monthly payment

r = Monthly rate of return (expressed as a decimal)

n = Number of payments

In this case, the return on balance and the monthly rate of return are provided separately. To incorporate the return on balance into the monthly rate of return, you can use the following formula:

Effective Monthly Rate of Return = (1 + Monthly Rate of Return) * (1 + Return on Balance) - 1

Let's calculate the effective monthly rate of return using the given values:

Return on Balance = 7.00% (expressed as a decimal) = 0.07

Monthly Rate of Return = 0.583% (expressed as a decimal) = 0.00583

Effective Monthly Rate of Return = (1 + 0.00583) * (1 + 0.07) - 1

= 1.00583 * 1.07 - 1

= 1.0761281 - 1

= 0.0761281

Now that we have the effective monthly rate of return, we can use the future value formula to calculate the future value:

FV = -$200 * ((1 + 0.0761281)^120 - 1) / 0.0761281

Please note that since the monthly payment is negative (-$200), it indicates that it is an outgoing payment or an investment with regular withdrawals.

Calculating the above formula will give you the future value of the investment.

I hope I was helpful

The values of the angles x and y are ∠x = 110 and ∠y = 70

From the question, we have the following parameters that can be used in our computation:

The lines (parallel, transversal and others)

The measure of angle 1 is calculated as

∠1 = 180 - 140 -- angle on a straight line

So, we have

∠1 = 40

Next, we have

∠2 = 180 - 40 - 80 --- corresponding angles

So, we have

∠2 = 60

This means that

∠y = 180 - 60 - 50 -- angle on a straight line

So, we have

∠y = 70

This also means that

∠x = 180 - 60 - 10 -- angle in a triangle

So, we have

∠x = 110

Hence, the values of x and y are ∠x = 110 and ∠y = 70

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Answer: 26.40

Step-by-step explanation:

Sue's total pay for the year based on the values will be £38110

Sue's total pay of year will have three parts

Fixed Salary for 12 months

 one month salary = £1410

 so 12 month salary = £1410 x 12 = £16920

26% of total profit

  Total cost to the company- £473,500

  Total income for the company - £549,000

  Profit =  Total income for the company - Total cost to the company

            =  £549,000 - £473,500 = £75500

   Sues income from profit = 26% of £75500 = (26 × 75500)/100 = £19630

Bonus if Sue sells at least 16 cars

  Given number of months when sue solds atleast 16 cars = 4

  So bonus income = 4 × 390 = £1560

Adding the three above parts

Sue's total pay for the year = £16920 + £19630 + £1560 = £38110

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Complete question

Ace autos sell cars and pay sue each month as follows

-salary of £1410

-26% of the total profit the company makes from her sales

- a £390 bonus if she sells at least 16 cars

The table shows information about the cars she sold last year

Total cost to the company- £473,500

Total income for the company - £549,000

Number of months when she sold at least 16 cars - 4

work out sues total pay for the year

Answer:

Step-by-step explanation:

To estimate the original volume of the pyramid in Figure 15.28, we can use the formula for the volume of a frustum of a pyramid. The frustum is the portion of the pyramid between the top and bottom, created by removing the top section.

The formula for the volume of a frustum of a pyramid is:

V = (1/3) * h * (A + sqrt(A * B) + B)

Where:

V = Volume of the frustum

h = Height of the frustum (vertical distance between the top and bottom)

A = Area of the top base

B = Area of the bottom base

Given the dimensions provided, we can calculate the areas of the bases:

Area of the top base (A) = 4 m * 4 m = 16 m²

Area of the bottom base (B) = 20 m * 20 m = 400 m²

The height of the frustum (h) is given as 12 m.

Now we can plug these values into the formula:

V = (1/3) * 12 m * (16 m² + sqrt(16 m² * 400 m²) + 400 m²)

Calculating the square root and simplifying:

V = (1/3) * 12 m * (16 m² + 20 m² + 400 m²)

V = (1/3) * 12 m * (436 m²)

V = 1744 m³

Therefore, the estimated original volume of the pyramid in Figure 15.28 is approximately 1744 cubic meters.

Correct form of the area of compound shape is:

Given,

Compound shape including triangle and rectangle.

Firstly , calculate the area of rectangle:

Area of rectangle = l* b

l= length of rectangle

b =  breadth of rectangle

Thus,

Area of rectangle = 12*m

Secondly, area of triangle,

Area of triangle = 1/2 *b * h

b = base of triangle

h = height of triangle

Base of triangle = 12 - n

Then,

Area of triangle = 1/2* (12 - n) *m

Area of triangle = 6m - 0.5mn

Now to calculate the total area of the compound shape,

Total area = Area of rectangle  + Area of triangle

Total area = 12m + (6m - 0.5mn)

Total area = 18m - 0.5mn

Hence option 3 satisfies the area of the compound shape .

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The measure of the angle 4, m∠4, obtained from the measure formed by the diagonals of a rhombus is; m∠4 = 38°

The diagonals of a rhombus bisect the angles at the vertices of the rhombus

The diagonals of a rhombus are perpendicular bisectors of each other, therefore;

The measure of the angle m∠2 = 90°

Therefore; m∠1 = 90° - 52° = 38°

The triangle with base angles ∠1, and ∠4, is an isosceles triangle, with the base angles ∠1, and ∠4

The base angles of an isosceles triangle are congruent, therefore;

∠1 ≅ ∠4

m∠1 = m∠4

m∠4 = m∠1 = 38°

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An equation that satisfies all three pairs of a and b values listed in the table include the following: C. 3a - b = 10.

In order to determine an equation that satisfies all three pairs of a and b values listed in the table, we would substitute each of the numerical values corresponding to each variable into the given equations and then evaluate as follows;

a - 3b = 10

0 - 3(-10) = 30 (False).

3a + b = 10

3(0) - 10 = -10 (False).

3a - b = 10

3(0) - (-10)

0 + 10 = 10 (True).

3a - b = 10

3(1) - (-7)

3 + 7 = 10 (True).

3a - b = 10

3(2) - (-4)

6 + 4 = 10 (True)

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Complete Question:

Which equation satisfies all three pairs of a and b values listed in the table?

a b

0 -10

1 -7

2 -4

The equation is?

A.) a-3b=10

B.) 3a+b=10

C.) 3a-b=10

D.) a+3b=10

Without this information, it is not possible to determine if the sample accurately represents the overall distribution of eggs at the farmers' market.

It is impossible to say if the sample of eggs at the farmers' market is likely to be representative based on the information supplied. Jackson appears to have bought 17 eggs from each farmer, which suggests that he did so in an equal amount. It does not, however, provide data on the total number of farmers present at the market or their overall distribution of eggs.

Additional data, such as the total number of farmers present at the market, the average number of eggs each farmer generally has, and the variability in the number of eggs among the farmers, would be required to evaluate the sample's representativeness.

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Answer:

60 cm^3

Step-by-step explanation:

The formula for volume of a pyramid is

V = 1/3Bh, where B is the area of the base and h is the regular height (aka the altitude that connects the top of the pyramid and the base so we can simply ignore the slant height in the problem)

Step 1:  The base of a square pyramid is a square and the formula for area (A) of a square is A = s^2, where s is the side.

Since we're told that the length of the base side length is 6 cm, we can find the area of the base:

A = 6^2 = 36

Step 2:  Now, we can plug in 36 for B and 5 for h in the volume formula to find the volume:

V = 1/3(36)(5)

V = 12 * 5

V = 60 cm^3

A z-score of 0 indicates that the person's score is equal to the mean, so they are right at the Average Performance level.the z-score of a person who scored 300 on the exam is 0.

The z-score of a person who scored 300 on the exam, we can use the formula:

z = (x - μ) / σ

where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.

In this case, the person scored 300 on the exam, which is equal to the mean (μ). Therefore, we can substitute these values into the formula:

z = (300 - 300) / 40

Simplifying the equation, we have:

z = 0 / 40

Since any number divided by zero is undefined, we can conclude that the z-score of a person who scored 300 on the exam is 0.

The z-score measures the number of standard deviations a data point is away from the mean. In this case, a z-score of 0 indicates that the person's score is equal to the mean, so they are right at the average performance level.

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Answer:A

Step-by-step explanation:

The values of P and a such that [tex]f(x) = Pa^x[/tex] is an exponential growth function are given as follows:

C. P = 2; a = 3.

An exponential function has the definition presented according to the equation as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

The conditions for an exponential growth function are given as follows:

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Answer:

Step-by-step explanation:

Make a plan:

Solve the problem:

Draw the conclusion:

Hope this helps!

The coordinates in the solution to the systems of inequalities is (12, 1)

From the question, we have the following parameters that can be used in our computation:

y > -4x + 6

y > 1/3x - 7

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (12, 1)

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Based on the information, we can infer that the correct answer is 90° clockwise (option A).

To identify the correct rotation of this figure we must perform the following procedure:

1. We must identify the reference figure.

2. We must identify the figure that expresses the rotation.

3. We must identify the angle of rotation of the figure.

4. Select the option that correctly expresses the sense of rotation.

Based on the above, we can infer that the correct answer is A. 90° Clockwise because the rotation is to the right.

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The coffee club's assertion that the percentage of bags containing collectible cards is less than 0.2 is unsupported by sufficient data.

To test whether the coffee club's belief that the proportion of bags with collectable cards is less than 0.2 is supported by the sample, conduct a hypothesis test.

Null Hypothesis: The proportion of bags with collectable cards is equal to or greater than 0.2.

Alternative Hypothesis: The proportion of bags with collectable cards is less than 0.2.

Let p be the true proportion of bags with collectable cards in all Joe Coffee bags. Use a one-sample proportion test to test this hypothesis.

The test statistic is calculated as follows:

z = (p - p₀) / √(p₀(1-p₀)/n)

where p = sample proportion (11/65), p₀ = hypothesized proportion (0.2), and n = sample size (65).

Using a significance level of 0.05, the critical z-value for a one-tailed test is -1.645.

Calculating the test statistic:

z = ((11/65) - 0.2) / √(0.2(1-0.2)/65) = -1.469

Since -1.469 is not less than -1.645, we fail to reject the null hypothesis. There is not enough evidence to support the coffee club's belief that the proportion of bags with collectable cards is less than 0.2.

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Answer:

130 degrees

Step-by-step explanation:

DE+DA=130

a. The value of sin θ = 13/18

b. The size of sin θ is 46.2 degrees

First, we need to know the different trigonometric identities.

These trigonometric identities are listed thus;

From trigonometric relations, we have that the ratio for sine identity is represented as;

sin θ = opposite/hypotenuse

Then, we have from the information given that;

Hypotenuse side = 18cm

Opposite side = 13cm

Substitute the values, we have;

sin θ = 13/18

Divide the values

sin θ = 0. 7222

Find the sine inverse value, we have;

so, θ = sin⁻¹(13/18) = 46. 2 degrees

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The exponential function that model this situation is [tex]A(t) = 2500(1 + 0.035)^t.[/tex]

The account will have $5000 in 20 years.

Let A be the amount in the account after t years.

Then, we can model this situation with the function A(t) = 2500(1 + 0.035)^t with the use of compound intererst formula which is [tex]P = A*(1+r)^t[/tex]

To find when the account will have $5000, we can set A(t) = 5000 and solve:

5000 = 2500(1 + 0.035)^t

2 = (1.035)^t

Taking the natural logarithm:

ln(2) = t ln(1.035)

t = ln(2)/ln(1.035)

t = 20.148791684

t = 20 years.

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Answer:

1)  21 years

2) 26 years

Step-by-step explanation:

To model the account balance of Vanessa's account at t years, we can use an exponential function in the form:

[tex]\large\boxed{A(t) = A_0(1 + r)^t}[/tex]

where:

Given Vanessa invested $2500 into the account and it will increase in value by 3.5% each year:

Substitute these values into the formula to create an equation for A in terms of t:

[tex]A(t) = 2500(1 + 0.035)^t[/tex]

[tex]A(t) = 2500(1.035)^t[/tex]

To find when the account balance will be $5000, set A(t) equal to $5000 and solve for t:

[tex]A(t)=5000[/tex]

[tex]2500(1.035)^t=5000[/tex]

[tex](1.035)^t=\dfrac{5000}{2500}[/tex]

[tex](1.035)^t=2[/tex]

[tex]\ln (1.035)^t=\ln 2[/tex]

[tex]t \ln 1.035=\ln 2[/tex]

[tex]t=\dfrac{\ln 2}{ \ln 1.035}[/tex]

[tex]t=20.1487916...[/tex]

[tex]t=20.15\; \sf years\;(2\;d.p.)[/tex]

Therefore, it will take approximately 20.15 years for Vanessa's account to reach a value of $5000.

Since the interest rate is an annual rate of 3.5%, it means that the interest is applied once per year, at the end of the year. Therefore, we need to round up the number of years to the next whole number.

So Vanessa's account will have $5,000 after 21 years.

Note: After 20 years, the account balance will be $4,974.47. After 21 years, the account balance will be $5,148.58.

[tex]\hrulefill[/tex]

To model the increase in movie ticket prices over time, we can use an exponential function in the form:

[tex]\large\boxed{P(t) = P_0(1 + r)^t}[/tex]

where:

Given the initial price of the ticket was $4.22 and the price has increased by 3.1% each year:

Substitute these values into the formula to create an equation for P in terms of t:

[tex]P(t) = 4.22(1 + 0.031)^t[/tex]

[tex]P(t) = 4.22(1.031)^t[/tex]

To find how many years until tickets cost $9.33, we can set P(t) equal to $9.33 and solve for t:

[tex]P(t)=9.33[/tex]

[tex]4.22(1.031)^t=9.33[/tex]

[tex](1.031)^t=\dfrac{9.33}{4.22}[/tex]

[tex]\ln (1.031)^t=\ln \left(\dfrac{9.33}{4.22}\right)[/tex]

[tex]t \ln (1.031)=\ln \left(\dfrac{9.33}{4.22}\right)[/tex]

[tex]t =\dfrac{\ln \left(\dfrac{9.33}{4.22}\right)}{\ln (1.031)}[/tex]

[tex]t=25.9882262...[/tex]

Therefore, it will take approximately 26 years for movie ticket prices to reach $9.33, assuming the annual growth rate remains constant at 3.1%.

The quadratic equation with the given roots is:

y = 0.5x² + 1.5x - 5

For a quadratic equation with a leading coefficient a, and roots:

x = h and x = k, we will get general formula:

y = a*(x - h)*(x - k)

Here we know that the roots are x = 2 and x = -5, replacing that we will get:

y = a*(x - 2)*(x + 5)

And we know that this quadratic passes through (1, -3), replacing these values:

-3 = a*(1 - 2)*(1 + 5)

-3 = a*(-1)*(6)

-3 = -6a

-3/-6 = a

0.5 = a

Replacing that:

y = 0.5*(x - 2)*(x + 5)

Expanding the quadratic we will get:

y = 0.5x² + 1.5x - 5

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Answer:

hey it is

Step-by-step explanation:

22 × 18 or 12 into 18

The probability that a randomly chosen person would score less than 86 is 0.8643, and the probability that a randomly chosen person would score more than 86 is 0.1357.

We consider X to be a random variable that represents the score of a person. So according to the question, X follows the given normal distribution and the given curve represents its distribution.

Now from the curve, we can see that the proportion of observation under the score 86 is 0.8643.

So we have,

P[X < 86] = 0.8643

A) We have to find the probability that a randomly chosen person would score less than 86. i.e, we have to find P[X < 86]

It is clearly given from the curve that, P[X < 86] = 0.8643

B) Now it is required to find the probability that a person chosen at random would score higher than 86 on this test. i.e P[X > 86]

P[X > 86] = 1 - P[X < 86]

= 0.1357

Therefore, the probability that a randomly chosen person would score less than 86 is 0.8643, and the probability that a randomly chosen person would score more than 86 is 0.1357.

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The formula for the area Z (t) (in square meters) of the algae colony after t minutes: Z(t) = 13 * (1.02)² * t²

The area A(r) of a circular algae colony with radius r meters is given by

A(r) = pi * r²

The radius M(t) after t minutes is given by

M(t) = 1.02t

Substituting M(t) into the formula for A(r) gives

A(t) = pi * (1.02t)²

Simplifying gives

Z(t) = 13 * (1.02)² * t²

Therefore, the formula for the area Z (t) (in square meters) of the algae colony after t minutes: Z(t) = 13 * (1.02)² * t²

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The decimal value of point H is then approximately 0.033333.

How to solve:

We must translate the position of the third mark after 2 and 2 tenths into a decimal value in order to determine the decimal value of point H.

We can determine the distance between each tick mark by dividing the distance between the two end points (2.3 - 2.2 = 0.1) by the total number of tick marks (9) because there are nine tick marks between the end points.

To get to point H, we can multiply the distance between each tick mark by the number of ticks: 0.1 / 9 = 0.011111.

The decimal value of point H is then approximately 0.033333.

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Volume of the cylinder =  6838.92 cubic inches

We have to given that;

Sam needs to fill a cylindrical container with punch.

And, The container has a radius of 11 inches and a height of 18 inches.

Since, To determine the amount of cat litter the cylinder can hold, we need to calculate the volume of the cylinder.

Volume of a cylinder = πr²h

Where,

r=radius

h= height

Then,

π=22/7 or 3.14 (constant value)

r=11 inches

h=18 inches

Volume of a cylinder is,

= 3.14 × (11)² × 18

= 6838.92 cubic inches

Hence, Volume of the cylinder =  6838.92 cubic inches

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Answer:

Step-by-step explanation:

The sum of 100,000 + 10,000,000,000,000 is 10,000,100,000,000.

Answer:

x+3x-4=2x+x+5

Step-by-step explanation:

=4x-4= 3x+5

=4x-3x=5+4

= x=9. Done