ƒ(t) = –1∕2t2 + 2t + 6

After 17 months, there will be approximately $970.25 in Fred Flintstone's account.

To calculate the amount in Fred Flintstone's account after 17 months, we can use the formula for the future value of an ordinary annuity. The formula is:

[tex]A = P \times [(1 + r)^n - 1] / r[/tex]

Where:

A stands for the annuity's projected value.

P = the monthly deposit amount

r is the annual percentage rate of interest.

n is the number of compounding periods in total.

In this case, Fred Flintstone deposits $50 every month (P = $50), the interest rate is 12% per year compounded monthly, which means the monthly interest rate is 12% / 12 = 1% or 0.01 (r = 0.01), and the total number of compounding periods is 17 (n = 17).

Now that these numbers have been substituted, we can determine the future value using the formula:

A = $50 × [tex][(1 + 0.01)^{17}- 1] / 0.01[/tex]

A = $50 ×[tex][1.01^{17} - 1] / 0.01[/tex]

Using a calculator or spreadsheet, we can evaluate 1.01^17 to be approximately 1.194051.

A = $50 × [1.194051 - 1] / 0.01

A = $50 × 0.194051 / 0.01

A ≈ $970.25

Therefore, after 17 months, there will be approximately $970.25 in Fred Flintstone's account.

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The exact length of the arc formed by a central angle measuring 120° in a circle with a radius of 12.3 cm is 8.2π cm.

To calculate the exact length of an arc formed by a central angle measuring 120° in a circle with a radius of 12.3 cm, we can use the formula:

Arc Length = (Central Angle / 360°) * Circumference

First, let's calculate the circumference of the circle:

Circumference = 2 * π * radius

Substituting the given radius value into the formula, we get:

Circumference = 2 * π * 12.3 cm

Circumference = 24.6π cm

Now, let's calculate the arc length using the central angle of 120°:

Arc Length = (120° / 360°) * 24.6π cm

Arc Length = (1/3) * 24.6π cm

Arc Length = 8.2π cm

Therefore, the exact length of the arc formed by a central angle measuring 120° in a circle with a radius of 12.3 cm is 8.2π cm.

It's important to note that in this case, since the central angle is given in degrees, the result is expressed in terms of π. If you need a decimal approximation, you can calculate the numerical value using an appropriate approximation for π.

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Answer:

c=6

Step-by-step explanation:

find a common denominator and multiply both sides by 2 to get c-4=2 then add 4 getting c=6

A. The comparison of the periods using the five number summary are

B. The box and whisker plot of the periods is attached

The readings of the periods are given as

The distributions of the periods will be compared using the five-number summaries. This is because the five-number summaries give the following statistical measurements

For the 7th Period, the summaries are

For the 3rd Period, the summaries are

The box and whisker plot of the periods is added as an attachment

From the box and whisker plot attached, we can see the five-number summaries of the periods

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The interval width is 6, while the interval with the most values is 12 -18. There are 30 values in the dataset and the number of values that are 18 or greater is 12. The interval that the number 12 falls into is 12 - 18.

The interval width is gotten by dividing the range of values by the number of intervals.

This gives us: 30 - 0/5  = 6

So, the interval width is 6.

The interval that has the most values is 12 - 18. This is the point where we have the bars with the longest range.

The number of values in the dataset is 30 and this is the maximum number.

The interval where the number 12 will be included is 12 to 18.

The values that are 18 or higher are 12.

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Answer:

First, we arrange the values in ascending order. Given that the data set has 9 values, the median represents the middle value when the values are arranged in order.

In this case, the least value is 8 and the greatest value is 20. To find the median, we need to determine the middle value. Since there are an odd number of values (9), the median will be the value at the (9 + 1) / 2 = 5th position.

Arranging the values in ascending order: 8, x, x, x, 11, x, x, x, 20

From the given information, we know that the median is 11. Therefore, the middle value must be 11.

Arranging the values again: 8, x, x, x, 11, x, x, x, 20

Since the median is the middle value, the remaining values can be any numbers as long as they are greater than or equal to 8 and less than or equal to 20. There is no unique solution for the remaining values in the data set, as long as the conditions are met.
Here are some possible data sets that satisfy the given conditions:

There are many other possible data sets that satisfy the given conditions.

Answer:

the second option

Step-by-step explanation:

Leslie and Colton made in total are Leslie's total earnings: Revenue from sales + Tips = 20s dollars + $15,Colton's total earnings: Revenue from sales + Tips = 30s dollars + $25.

To find out how much Leslie and Colton made in total, we need to determine the revenue from selling cups of strawberry lemonade and the amount they earned in tips separately.

Let's start by calculating the revenue from selling cups of strawberry lemonade:

Leslie sold 20 cups, and Colton sold 30 cups. Since they both sold the same product at the same price, we can assume that the price per cup is s dollars.

Revenue from Leslie's sales: 20 cups * s dollars per cup = 20s dollars

Revenue from Colton's sales: 30 cups * s dollars per cup = 30s dollars

Next, let's calculate the amount they earned in tips:

Leslie made an additional $15 in tips.

Colton made an additional $25 in tips.

Now we can calculate the total earnings for Leslie and Colton:

Leslie's total earnings: Revenue from sales + Tips = 20s dollars + $15

Colton's total earnings: Revenue from sales + Tips = 30s dollars + $25

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The value of x from the venn diagram if P(T | V) = 1/5 is 16

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

The venn diagram

From the venn diagram, we have the following probability values

P(T | V) = (x - 4)/(3x + x - 4)

Evaluate the like terms

So, we have

P(T | V) = (x - 4)/(4x - 4)

From the question, we have

P(T | V) = 1/5

This means that

(x - 4)/(4x - 4) = 1/5

When evaluated, we have

x = 16

Hence, the value of x is 16

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Answer:

105.5mm²

Step-by-step explanation:

There are a rectangle and two triangles.

Rectangle

6x13=78

Big Triangle

1/2x4x10.75=21.5

Small Triangle

1/2x3x4=6

78+21.5+6=105.5

The perimeter of the polygon in this problem is given as follows:

20 units.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure, that is, we must find the length of all the edges of the polygon, and then add these lengths to obtain the perimeter.

The side lengths for the polygon in this problem are given as follows:

Hence the perimeter of the polygon is given as follows:

2 x (3 + 7) = 20 units.

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The x- and y-intercepts of the graph are:

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

-4x + 2y = 28.

For the x-intercepts, we set y to 0

So, we have

-4x = 28

Evaluate

x = -7

For the y-intercepts, we set x to 0

So, we have

2y = 28

Evaluate

y = 14

Hence, the x- and y-intercepts of the graph are -7 and 14, respectively

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A bond will pay income based on an interest rate while stock may give dividends to investors. Both interest income and dividends contribute to the return on an investment.

The return encompasses both interest income and dividends received by the investor. When investing in bonds, the income generated is in the form of interest payments which are typically fixed and predetermined based on the bond's coupon rate. The stocks provide the potential for dividends which are a portion of the company's profits distributed to shareholders.

Both interest income from bonds and dividends from stocks contribute to the overall return on the investment. We must note that the return on an investment can also be influenced by other factors such as capital gains or losses when buying or selling the asset.

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The number of gallons of water that you drink in a year is 240.9 gallons.

We have to find the number of gallons of water that you drink in a year.

For that, first wee need to find the amount of water that you drink in a day.

Each person will drink water in a day in different amounts.

We can take an average of 2.5 liters that a man drink in a day.

Then

Amount of water drink in a year = 2.5 × 365

                                                      = 912.5 liters

Now we need to find the amount of water in gallons.

Convert liters in gallons.

1 liter = 0.264 gallons

So,

912.5 liters = 912.5 × 0.264 gallons

                  = 240.9 gallons

Hence the amount is 240.9 gallons.

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Answer:

B

Step-by-step explanation:

the area (A) of a trapezoid is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)

where h is the perpendicular height between the bases b₁ and b₂

the endpoints of b₁ are (- 2, - 2) and (8, - 2)

since the y- coordinates are equal then b₁ is the difference of the x- coordinates, that is

b₁ = 8 - (- 2) = 8 + 2 = 10

similarly for b₂ with endpoints (2, 3) and (6, 3) , then

b₂ = 6 - 2 = 4

h = 5 ( perpendicular distance between the bases ) , then

A = [tex]\frac{1}{2}[/tex] × 5 × (10 + 4) = 2.5 × 14 = 35 units²

The normal distribution is solved and the retirement ages are normally distributed

P(x ≤ 62) ≈ 22.7%

P(x ≥ 70) ≈ 10.6%

P(55 ≤ x ≤ 60) ≈ 14.5%

P(60 ≤ x ≤ 70) ≈ 78.9%

Given data ,

To solve these probability questions, we can use the properties of the normal distribution. Let's calculate each probability:

a)

P(x ≤ 62):

To find this probability, we need to calculate the z-score corresponding to x = 62 and then find the area under the standard normal distribution curve to the left of that z-score. The formula to calculate the z-score is:

z = (x - mean) / standard deviation

In this case:

z = (62 - 65) / 4 = -0.75

Using a standard normal distribution table or a calculator, we can find that the area to the left of z = -0.75 is approximately 0.2266 or 22.7%

b)

P(x ≥ 70):

To find this probability, we need to calculate the z-score corresponding to x = 70 and then find the area under the standard normal distribution curve to the right of that z-score. Again, we use the z-score formula:

z = (x - mean) / standard deviation

In this case:

z = (70 - 65) / 4 = 1.25

Using a standard normal distribution table or a calculator, we can find that the area to the right of z = 1.25 is approximately 0.1056 or 10.6%

c)

P(55 ≤ x ≤ 60):

To find this probability, we need to calculate the z-scores corresponding to x = 55 and x = 60, and then find the area between those two z-scores under the standard normal distribution curve. Again, we use the z-score formula:

z = (x - mean) / standard deviation

For x = 55:

z1 = (55 - 65) / 4 = -2.5

For x = 60:

z2 = (60 - 65) / 4 = -1.25

Using a standard normal distribution table or a calculator, we can find that the area between z = -2.5 and z = -1.25 is approximately 0.1446 or 14.5%

d)

P(60 ≤ x ≤ 70):

To find this probability, we need to calculate the z-scores corresponding to x = 60 and x = 70, and then find the area between those two z-scores under the standard normal distribution curve.

Using the same z-score formula as above:

For x = 60:

z1 = (60 - 65) / 4 = -1.25

For x = 70:

z2 = (70 - 65) / 4 = 1.25

Using a standard normal distribution table or a calculator, we can find that the area between z = -1.25 and z = 1.25 is approximately 0.7887 or 78.9%

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The values for each probability are:

P(x ≤ 62) is approximately 22.7%.

P(x ≥ 70) is approximately 10.6%.

P(55 ≤ x ≤ 60) is approximately 9.9%.

P(60 ≤ x ≤ 70) is approximately 89.4%.

We have,

To solve these probability problems, we can use the standard normal distribution and Z-scores.

First, we need to convert the given values to Z-scores using the formula: Z = (X - μ) / σ, where X is the given value, μ is the mean, and σ is the standard deviation.

a)

P(x ≤ 62):

Z = (62 - 65) / 4 = -0.75

Using a standard normal distribution table or a calculator, we can find the corresponding area under the curve for a Z-score of -0.75.

This gives us a probability of approximately 0.2266.

To convert this probability to a percentage, we multiply by 100: 0.2266 * 100 ≈ 22.7%

b)

P(x ≥ 70):

To find the probability of x being greater than or equal to 70, we can use the complement rule: P(x ≥ 70) = 1 - P(x < 70)

Z = (70 - 65) / 4 = 1.25

Using a standard normal distribution table or a calculator, we can find the probability of a Z-score being less than 1.25, which is approximately 0.8944.

Now,

We can calculate P(x ≥ 70) = 1 - P(x < 70) = 1 - 0.8944 = 0.1056.

To convert this probability to a percentage, we multiply by 100: 0.1056 * 100 ≈ 10.6%

c)

P(55 ≤ x ≤ 60):

Z1 = (55 - 65) / 4 = -2.5

Z2 = (60 - 65) / 4 = -1.25

Using a standard normal distribution table or a calculator, we can find the probability of a Z-score being less than -1.25, which is approximately 0.1056.

Using the same method, we can find the probability of a Z-score being less than -2.5, which is approximately 0.0062.

Now, we can calculate the probability between -2.5 and -1.25 by subtracting the two probabilities:

P(-2.5 ≤ Z ≤ -1.25) = P(Z ≤ -1.25) - P(Z ≤ -2.5) = 0.1056 - 0.0062 = 0.0994.

To convert this probability to a percentage, we multiply by 100: 0.0994 x 100 ≈ 9.9%

d)

P(60 ≤ x ≤ 70):

Using the same Z-scores as in part c), we can find the probability of a Z-score being less than -1.25, which is approximately 0.1056.

Using the complement rule, we can find P(60 ≤ x ≤ 70) = 1 - P(x < 60) = 1 - 0.1056 = 0.8944.

To convert this probability to a percentage, we multiply by 100: 0.8944 * 100 ≈ 89.4%

Therefore,

P(x ≤ 62) is approximately 22.7%.

P(x ≥ 70) is approximately 10.6%.

P(55 ≤ x ≤ 60) is approximately 9.9%.

P(60 ≤ x ≤ 70) is approximately 89.4%.

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The total surface area for the cylinder in this problem is given as follows:

53π cm².

To obtain the surface area of a figure, we must add the areas of all the parts that compose the figure.

The cylinder in this problem is composed as follows:

The areas of each part are given as follows:

Hence the surface area of the prism is given as follows:

14π + 25π + 14π = 53π cm².

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Answer:

17 + 19i

Step-by-step explanation:

i = √-1

(3 - 2i) (1 + 7i)

= 3(1) + 3(7i) - 1(2i) - (2X7)(i²)

= 3 + 21i - 2i - 14(√-1)²

= 3 + 19i - 14 (-1)

= 3 + 19i + 14

= 17 + 19i

Answer:

16π

Step-by-step explanation:

Circumference = π X D (D = diameter = 2 X radius)

= π (2 X 8)

= 16π

The probability of the normal distribution is  0.8961

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

P(-1.26 < z)

This can be expressed as

P(z > -1.26)

This means that area is to the right of z and is calculated by calculating the probability that the z-score is greater than -1.26

In other words, this is represented as

Probability = P(z > -1.26)

This can then be calculated using a statistical calculator or a table of z-scores,

Using a statistical calculator, we have the area to be

Probability = 0.89617

When this value is approximated, we have

Probability = 0.8961

Hence, the probability is 0.8961

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Question

For a standard normal distribution, find the following.

Express the probability as a decimal rounded to 4 decimal places.

P(-1.26 < z)

The value of x in the equation 1.5(4)²ˣ is equal to 12 is 3/4 after equation the power of same base.

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

We have an equation:

⇒ 1.5(4)²ˣ is equal to 12

Now, We can simplify as;

⇒ 1.5(4)²ˣ is equal to 12

⇒ 1.5(4)²ˣ = 12

⇒ (4)²ˣ = 12/1.5

⇒ (4)²ˣ = 8

⇒ (2²)²ˣ = 2³

⇒ 2⁴ˣ = 2³

By comparing,

⇒ 4x = 3

⇒ x = 3 / 4

Thus, the value of x in the equation 1.5(4)²ˣ is equal to 12 is 3/4 after equation the power of same base.

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Answer:

Eve is 46 and her son is 23

Step-by-step explanation:

let x be the son's age then Eve is 2x. the difference in their ages is 23 , so

2x - x = 23 , that is

x = 23

then

Eve = 2 × 23 = 46 years

son = 23 years

Answer:

D. [tex]-sin^2x[/tex]

The table is completed thus;

1.Volume  = 1/10 ft³

2. Length = 0. 5m

3. Volume  = 1 in³

4.Length = 10km

We need to know that the formula for calculating the volume of a rectangular prism is expressed as;

Volume = Length × width × height

From the information given, we have that;

1. Volume = 1/4 × 2/3 × 3/5

Multiply the values, we get;

Volume = 6/60 = 1/10 ft³

2. Substitute the values, we have;

0. 0005 = 0.1 × 0. 01 × l

Multiply the values

Length = 0. 0005/0. 001 = 0. 5m

3. Substitute the values, we have;

Volume = 4/3 × 3/4 × 1

Multiply the values, we have;

Volume = 12/12 = 1 in³

4. Substitute the values, we have;

9. 9 = 1.1  × L × 0.9

multiply the values

Length = 9.9/0. 99

Divide the values

Length = 10km

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i. The equation shows that dy/dx is -8/x² + 2 and d²y/dx² is -2

ii. The curve has a local maximum at the point (-2, y) and the curve has a local minimum at the point (2, y).

(i) Finding dy/dx:

Given: y = 8/x + 2x

To find dy/dx, we'll differentiate each term with respect to x:

Differentiating 8/x with respect to x:

(d/dx)(8/x) = -8/x²

Differentiating 2x with respect to x:

(d/dx)(2x) = 2

Therefore, dy/dx = -8/x² + 2.

(ii) Finding d²y/dx²:

In order to find the second derivative, we'll differentiate dy/dx with respect to x:

Differentiating -8/x² with respect to x:

(d/dx)(-8/x²) = 16/x³

Differentiating 2 with respect to x:

(d/dx)(2) = 0

Therefore, d²y/dx² = 16/x³.

To find the coordinates of the stationary points, we need to solve the equation dy/dx = 0:

-8/x² + 2 = 0

Rearranging the equation, we have:

-8/x² = -2

-8 = -2x²

Dividing both sides by -2:

4 = x²

Taking the square root of both sides:

x = ±√4

Therefore, the stationary points occur at x = -2 and x = 2.

In order to determine the nature of each stationary point, we'll analyze the second derivative.

When x = -2:

d²y/dx² = 16/(-2)³ = 16/(-8) = -2

Since the second derivative is negative at x = -2, the nature of the stationary point is a local maximum.

When x = 2:

d²y/dx² = 16/(2)³ = 16/8 = 2

Since the second derivative is positive at x = 2, the nature of the stationary point is a local minimum.

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a. The simplified expression is determined as -4

b.  The missing expression is determined as - ¹/₂.

c. The simplified expression is determined as - ⁸³⁷/₁₀₄, and - ⁴⁹/₂₅.

The addition operations, subtraction operations and division operation is simplified as follows;

a. The given expression and its simplification;

- 1 + ( - 2) - (-3) - 4

= - 1 - 2 + 3 - 4

= -4

b. The given expression and its simplification;

-3 - ¹/₂ = - 3 + ?

-3 + 3 - ¹/₂ = ?

- ¹/₂ = ?

c. The given expression and its simplification;

1 ¹/₈ (- 7 ²/₁₃)

= ⁹/₈ x - ⁹³/₁₃

= - ⁸³⁷/₁₀₄

-3 ⁴/₁₅ ÷ (- 1 ²/₃)

= - ⁴⁹/₁₅  ÷  ( - ⁵/₃)

= - ⁴⁹/₁₅  × - ³/₅

= - ⁴⁹/₂₅

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Answer:

tina harner scored 733 points

jessica bradley scored 842 points

Step-by-step explanation:

b + h = 1575

h + 109 = b

plug the second equation into the first

h + 109 + h = 1575

2h + 109 = 1575

subtract 109 from both sides to isolate the variable and its coefficinet

2h = 1466

divide both sides by 2 to get h

h = 733

Farmers, like anyone else, may need to visit a drugstore for various reasons. One reason could be to obtain prescription medications if they fall ill or get injured. Additionally, over-the-counter medicines for minor ailments such as headaches, colds, and stomachaches can be found there. In addition, farmers may need to purchase first aid supplies like bandages, antibiotic ointment, and pain relievers in the event of injuries. Moreover, pharmacists can advise on various health topics, such as medication usage, health care, and injury prevention.

Farmers may visit a drugstore to buy pet medications, vitamins, supplements, baby products, beauty products like shampoo, conditioner, makeup, and personal care items such as deodorant, toothpaste, and soap.