Jack starts to save at age 40 for a vacation home that he wants to buy for his 50th birthday. He will contribute $1000 each quarter to an account, which earns 2. 1% interest, compounded annually. What is the future value of this investment, rounded to the nearest dollar, when Jack is ready to purchase the vacation home?



$11,000



$11,231



$44,000



$44,924

Answer:

[tex]A = 68.75 \text{ square inches}[/tex]

Step-by-step explanation:

First, we need to identify the trapezoid's dimensions:

base 1 = 16

base 2 = 11.5

height = 5

Then, we can plug these values into the trapezoid area formula:

[tex]A = \dfrac{b_1+b_2}{2} \cdot h[/tex]

[tex]A = \dfrac{16 + 11.5}{2} \cdot 5[/tex]

[tex]A = \dfrac{27.5}{2} \cdot 5[/tex]

[tex]A = \dfrac{137.5}{2}[/tex]

[tex]\boxed{A = 68.75 \text{ square inches}}[/tex]

Answer:

Explanation :

We are given with two shapes triangle and a rectangle.

From the above diagram

We can see that Breadth of the rectangle is 5 ft and length of 10 ft.

As we know that area of Rectangle is length × Breadth

Area(rectangle) = l × b

Area (rectangle) = 10 × 5

Area (rectangle) = 50 ft².

Now,

where

Area (triangle) = 4 × 6 ÷ 2

Area (triangle) = 24 ÷ 2

Area (triangle) = 12 ft².

Total area = Area of rectangle + Area of triangle

Total area = 50 + 12

Total area = 62 feet

Therefore, The area of the irregular shape is 62 feet.

A homeowner borrows $65,000 to remodel their home. The loan is financed at a 2.3% interest rate, compounded quarterly.

So we have to find 2.3% of 65,000 which is 1495

Now we have to multiply 1,495 by 8 because it is 8 years which is 11960. Now we add 11,960 to 65,000 and our answer is

Answer : 76960

(Choice 1)

it's not possible to sell at least $675 worth of tickets while also staying within the seating limit of 150 tickets. The theater may need to consider raising ticket prices or finding a larger venue to accommodate more audience members.

Let's denote the number of adult tickets sold as "A" and the number of child tickets sold as "C". Then we can set up the following system of equations to represent the given information:

A + C ≤ 150    (limit on seating)

12A + 7.5C ≥ 675   (minimum revenue required)

We want to find the possible values of A and C that satisfy these equations.

One way to solve this system is to graph the inequalities and find the region of overlap. However, since there are only two variables, we can also use substitution or elimination to solve for one variable in terms of the other.

Let's solve for A in terms of C using the first equation:

A ≤ 150 - C

Substitute this expression for A in the second equation:

12(150 - C) + 7.5C ≥ 675

Expand and simplify:

1800 - 12C + 7.5C ≥ 675

-4.5C ≥ -1125

C ≤ 250

So the number of child tickets sold must be less than or equal to 250.

Now we can substitute this inequality into the first equation to find the maximum number of adult tickets sold:

A + 250 ≤ 150

A ≤ -100

This doesn't make sense, since we can't sell negative tickets. Therefore, there is no solution that satisfies the given conditions.

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Answer:

It's fascinating to observe how the volume of different shapes can vary based on their measurements. For instance, a cylinder with a height of 6 centimeters and radius r1 has a volume of 302 cubic centimeters. Do you require further assistance?

As for the new set of instructions, please consider the following statements:

6. Sometimes true. The period of the function is determined by the formula T= 2π/b, where b is the coefficient of x in the argument of the sine function. In this case, b = π/5, so T= 10.

7. Always true. The maximum height of the object is equal to the amplitude of the function plus the vertical shift, which is 55 centimeters.

8. Sometimes true. The minimum height of the function occurs when the sine function has a value of -1, which happens at x= h-5. So, if h= 0, then x= -5, which means the statement is sometimes true depending on the value of h.

9. Always true. The midline of the function is determined by the vertical shift, which is 55 in this case.

10. Always true. The amplitude of the function is given by A= |b|, where b is the coefficient of x in the argument of the sine function. In this case, A= 42π/5, which simplifies to 84.

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Answer:

9/7

explain:

(36-27) 7

9/7

The logistic function that represents the number of units occupied over time is given by:

[tex]N(t) = (K / (1 + A * e^(-r*t))),[/tex]

where N(t) is the number of units occupied at time t, K is the carrying capacity (maximum number of units that can be occupied),

A is the initial amount of units occupied, r is the growth rate, and e is the base of the natural logarithm.

In this case, the carrying capacity K is 1500 units, and the initial amount of occupied units A is 15 units. The growth rate r can be calculated as follows:

[tex]r = ln((10%)/(100% - 10%)) = ln(0.1/0.9) ≈ -0.101[/tex]

Substituting the given values into the logistic function, we get:

[tex]N(t) = (1500 / (1 + 15 * e^(-0.101*t)))[/tex]

Simplifying further, we get:

[tex]N(t) = (100 / (1 + e^(-0.101*t))) + 15[/tex]

Therefore, the logistic function that represents the number of units occupied over time is:

[tex]N(t) = (100 / (1 + e^(-0.101*t))) + 15[/tex], where t is measured in months.

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The cost of the fabric will be $55.63.

To find the cost of the fabric, you need to first determine the total area of the fabric needed to make the patio umbrella. Since the patio umbrella is in the shape of a regular hexagon, it can be divided into six congruent equilateral triangles. The formula for the area of an equilateral triangle is A = (sqrt(3)/4)*s^2, where s is the length of one side of the hexagon.

Let's assume the length of one side of the hexagon is x. Then the area of one of the equilateral triangles is A = (sqrt(3)/4)x^2. Since there are six of these triangles in the hexagon, the total area of the hexagon is 6A = 6(sqrt(3)/4)*x^2 = (3sqrt(3)/2)*x^2.

To determine the amount of orange fabric needed, you can multiply the area of the hexagon by the number of square yards in one square foot and round up to the nearest whole number of square yards. Similarly, you can do the same for the white fabric.

Let's say the hexagon has a side length of 6 feet, so x=6ft. Then the area of the hexagon is (3sqrt(3)/2)*(6ft)^2 = 93.53 square feet. Converting square feet to square yards gives 10.39 square yards. Therefore, you need to order at least 11 square yards of each fabric.

The cost of the orange fabric is $s. 75 per square yard, so 11 square yards will cost 11 * $s. 75 = $28.13. The cost of the white fabric is $2.50 per square yard, so 11 square yards will cost 11 * $2.50 = $27.50. Therefore, the total cost of the fabric will be $28.13 + $27.50 = $55.63.

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The expansion of (1+root 2)(3-root 2) is 1 +2√2.

What is distributive property?

The distributive Property states that it is necessary to multiply each of the two numbers by the factor before performing the addition operation when a factor is multiplied by the sum or addition of two terms.

Apply the distributive property

1(3-√2) + √2(3-√2)

Apply distributive property

1.4+ 1(-√2) +√2 (3-√2)

Apply the distributive property

1.3 + 1(-√2) + √2. 3+√2 (-√2)

3+1(−√2)+√2⋅3+ √2(-√2)

Multiply − √2 by 1

3−√2+ √2⋅3+√2(−√2)

Move 3 to the left of √2.3−√2+3⋅√2+√2(−√2)

Multiply √2(−√2)

3−√2+3√2−√2²

Rewrite

√2² as 2.

3−√2+3√2− 1⋅2

Multiply − 1 by 2.

3−√2+3√2−2

Subtract 2 from 3.

1−√2+3√2

Add  −√2 and 3√2.

1+2√2

Exact Form:

1 +2√2

Decimal Form:

3.82842712

Therefore, the expansion of (1+root 2)(3-root 2) is 1 +2√2.

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x²y' - 2xy' + (x² + 2)y = 0 is the associated homogeneous equation with non-homogeneous ODE x²yⁿ - 2xy' + (x² +2)y = 3x³.

It should be noted that the equation is same as the variable coefficient linear second order non-homogeneous ODE but just the right side zero.

The complementary solutions or homogeneous solutions to this homogeneous equation serve as the foundation for the space of all solutions to the non-homogeneous equation.

By assuming that y has the form y(x) = xr and substituting this into the homogeneous equation to create a characteristic equation, we can determine the complementary solutions. We may find the values of r that correspond to solutions of the type y(x) = xr by looking at the characteristic equation's roots.

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The rule for the reflection shown above is (x, y) → (x, -y).

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y).

This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate changes from positive to negative or negative to positive.

Conversely, a reflection over or across the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

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Step-by-step explanation:

I had to add some assumed portions to your posted picture. See image.

 The yellow boxed angle is 84 degrees (upper LEFT) due to alternate interior angles of parallel lines transected by another line.

  then, since the triangle is isosceles ....the other (lower LEFT)  angle is 84 degrees also....

      that means that k= 12 degrees    for the triangle interior angles to sum to  180 degrees .

Answer:

a)  3, 2, 1, 4

Step-by-step explanation:

If you have multiple credit cards with different APRs, it is best to pay off the card with the highest APR first.  This is because you will save the most money in interest by paying off the highest-rate debt first.

Therefore, as Michelle has four credit cards, each with different APRs, she should pay them off in order of the highest to lowest interest rate.

Since the highest APR is 23%, credit card #3 should be paid off first.

The next highest APR is 19%, so credit card #2 should be paid off second.

Credit card #1 should be paid off next as it has an APR of 17%.

Finally, credit card #4 should be paid off last, as it has the lowest APR of 15%.

So the order in which Michelle should pay off her credit cards is:

We can use the empirical rule to estimate the percentage of workdays it takes Susan between 38 and 46 minutes to drive to work. According to the empirical rule, for a normal distribution:

- About 68% of the data falls within one standard deviation of the mean

- About 95% of the data falls within two standard deviations of the mean

- About 99.7% of the data falls within three standard deviations of the mean

Since the mean is 42 minutes and the standard deviation is 4 minutes, one standard deviation below the mean is 38 minutes, and one standard deviation above the mean is 46 minutes. So, about 68% of the time it takes Susan between 38 and 46 minutes to drive to work.

Therefore, the answer is (B) 68%.

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Answer: C. 1/24 and that's is your answer to your question

The probability that a student took AP Chemistry given they did not get into their first-choice college is 0.0566.

The probability that a student took AP Chemistry given they did not get into their first-choice college is calculated using the formula below:

P(Not 1st | Chem) =0.1375

P(Chem) = 0.25

P(Not 1st) = P(Chem and Not 1st) + P(Phys and Not 1st) + P(ES and Not 1st) + P(Bio and Not 1st)

P(Not 1st)= 0.1375 + 0.1575 + 0.2400 + 0.0700

P(Not 1st)= 0.6050

Substituting the values in the formula above:

P(Chem | Not 1st) = 0.1375 * 0.25 / 0.6050

P(Chem | Not 1st) = 0.0566

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The correct inequality to describe the problem is A. 10 + x > 15, which means that the total time Farid spends on the level (10 + x) must be greater than 15 minutes in order for him to lose a life.

To solve the inequality, we can start by isolating x on one side of the inequality:

10 + x > 15

Subtracting 10 from both sides, we get:

x > 5

This means that Farid can play for up to 5 more minutes on the level without losing a life, since spending a total of 10 + 5 = 15 minutes on the level would cause him to lose a life.

Therefore, the solution to the inequality is "Farid can play less than 5 more minutes on that level without losing a life."

Overall, the correct option is A. 10 + x > 15.

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Jerome will need approximately 138.72 square meters of grass seed to cover his lawn.

To find the area that the grass seed needs to cover, we first need to find the area of the entire lawn. Let's assume that the lawn is rectangular in shape.

Jerome hasn't given us the dimensions of the lawn, so let's say that it measures 10 meters by 15 meters. Therefore, the area of the entire lawn would be:

10 meters x 15 meters = 150 square meters

Now we need to subtract the area of the pool from the area of the entire lawn.

The pool measures 4 5/6 meters by 2 1/3 meters, which we can convert to improper fractions:

4 5/6 = (4 x 6 + 5) / 6 = 29 / 6
2 1/3 = (2 x 3 + 1) / 3 = 7 / 3

So the area of the pool would be:

29/6 meters x 7/3 meters = 203/18 square meters

To find the area that the grass seed needs to cover, we subtract the area of the pool from the area of the entire lawn:

150 square meters - 203/18 square meters

To subtract these two values, we need to get a common denominator:

150 square meters = (150 x 18) / 18 = 2700/18 square meters
203/18 square meters = 203/18 square meters

So the area that the grass seed needs to cover would be:

2700/18 square meters - 203/18 square meters = 2497/18 square meters

We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 1:

2497/18 square meters ≈ 138.72 square meters

Therefore, Jerome will need approximately 138.72 square meters of grass seed to cover his lawn, excluding the area around the pool.

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Answer:no image

Step-by-step explanation:

The probability that a seal properly fits a valve is approximately 0.9332 or 93.32%.

To determine the probability that a seal properly fits a valve, we need to calculate the probability that the difference in diameter between the seal and valve is less than or equal to 2 mm.

Let X be the diameter of the valve and Y be the diameter of the seal. Then, the difference in diameter between the seal and valve can be expressed as Z = Y - X. We want to find P(Z ≤ 2).

We know that X ~ N(50, 0.3²) and Y ~ N(51, 0.4²), and since Z = Y - X, we have:

Z ~ N(51 - 50,  √(0.3² + 0.4²)²) = N(1, 0.5²)

To find P(Z ≤ 2), we standardize Z by subtracting the mean and dividing by the standard deviation:

(Z - 1)/0.5 ~ N(0, 1)

P(Z ≤ 2) = P((Z - 1)/0.5 ≤ (2 - 1)/0.5) = P(Z ≤ 1.5)

Using a standard normal table or calculator, we find that P(Z ≤ 1.5) ≈ 0.9332.

Therefore, the probability that a seal properly fits a valve is approximately 0.9332 or 93.32%.

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The ounces of filler will the factory need in order to make meatballs out of this shipment of beef is  56.7 oz of filler.

A number of distinct units of mass, weight, or volume are derived from the uncia, an ancient Roman unit of measurement, including the ounce, which remains almost unmodified. The avoirdupois ounce, also known as the US customary and British imperial ounce, is equal to one-sixteenth of an avoirdupois pound.

One factory obtained 90 kg of beef from overseas.

They want to add 1.4oz of filler for each pound of beef.

Given is:

0.45 kg = 1 pound

So,  90 kg = 90 x 0.45 = 40.5 pounds

The company want to add 1.4 oz of filler for each pound of beef.

So for 1 pound we have 1.4 oz of filler

So, for 40.5 pounds they will need = x oz of filler.

x = 1.4 x 40.5 = 56.7

Therefore, the company needs 56.7 oz of filler.

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Complete question;

Factories often add filler when making meatballs sold by the bag. One factory obtained 90kg of beef from overseas. They want to add 1.4oz of filler for each pound of beef. How many ounces of filler will the factory need in order to make meatballs out of this shipment of beef?

Answer:

32

Step-by-step explanation:

There are 28 full shaded squares

There are 8 half squares

2 half squares make up 1 full square

So 28 + 4 = 32

Area is 32 units

The recursive sequence are: 17, 13, 9, 5, 1.

The recursive rule for the sequence  [tex]a_{n}[/tex] = 17 - 4n is

[tex]a_{1[/tex] = 17

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 4 for n ≥ 2

Using this rule, we can find the first few terms of the sequence

[tex]a_{1[/tex] = 17

[tex]a_{2}[/tex] = [tex]a_{1[/tex]  - 4 = 17 - 4 = 13

[tex]a_{3}[/tex] = [tex]a_{2}[/tex] - 4 = 13 - 4 = 9

[tex]a_{4}[/tex] = [tex]a_{3}[/tex] - 4 = 9 - 4 = 5

[tex]a_{5}[/tex] = [tex]a_{4}[/tex]  - 4 = 5 - 4 = 1

and so on.

Therefore, the recursive sequence are: 17, 13, 9, 5, 1.

The question is incorrect and correct question is '' Write a recursive sequence that represents the sequence defined by the following explicit formula  [tex]a_{n}[/tex] = 17 - 4n and find [tex]a_{1[/tex] and   [tex]a_{n}[/tex] ''.

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The length of the hypotenuse of the right triangle is 15 cm.

The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. Using this formula, we can calculate the length of the hypotenuse of a right triangle.

Given that the longer sides of the right triangle are 9 cm and 12 cm long, we can assume that one of these sides is the shorter side and the other is the longer side. Let's assume that the shorter side is 9 cm long and the longer side is 12 cm long.

Using the Pythagorean Theorem, we can calculate the length of the hypotenuse as follows:

Hypotenuse² = Shorter side² + Longer side²

Hypotenuse² = 9² + 12²

Hypotenuse² = 81 + 144

Hypotenuse² = 225

Taking the square root of both sides, we get:

Hypotenuse = √225

Hypotenuse = 15

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The best step when constructing a tangent to the circle is to strike an arc on bq with a center of b that has a length the same as the radius of circle q. The correct answer is option a.

When constructing a tangent to a circle with a center point of Q that passes through point B, and having already connected points Q and B to form line segment BQ, the best next step is to: A) Strike an arc on BQ with a center of B that has a length the same as the radius of circle Q.

This will help you find the point where the tangent line intersects the circle, allowing you to complete the tangent construction. The tangent line will be perpendicular to the radius at the point of tangency.

Therefore option a is correct.

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David's net worth: 86,329.95

To calculate David's new net worth, we need to add the increase in assets and subtract the decrease in liabilities from his current net worth.

New assets value = 62,784.24 + 2,784.89 = 65,569.13

New liabilities value = David's current net worth - his current assets value

New liabilities value = 45,765.78 - 62,784.24 = -17,018.46

Since his liabilities have decreased by 3,742.36, we need to subtract this value from the new liabilities value:

New liabilities value = -17,018.46 - 3,742.36 = -20,760.82

Now we can calculate his new net worth by subtracting his new liabilities value from his new assets value:

New net worth = 65,569.13 - (-20,760.82) = 86,329.95

Therefore, David's new net worth is 86,329.95.

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I must have left home at 4:54 PM in order to arrive at the park at 4:30 PM after 24 minutes of travel time.

Given the parameters in the question: if i went to park at 4:30 and it took me 24 minutes

Arrival time = 4 : 30PM

Travel time = 24 minutes

I can determine when i left home by simply subtracting the travel time from the time I arrived.

Hence,

Add the travel time to the time you arrived at the park.

4:30 PM (arrival time) + 24 minutes (travel time) = 4:54 PM

Therefore, I must have left home at 4:54 PM.

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The value of the simplified expression is -15.

The simplification of the expression is determined by substituting the appropriate values of the variables into the equation.

The given expression; = 54/g - 8h

The value of g = 6 and the value of h = 3,

The value of the expression is calculated as follows;

= 54/g - 8h

= 54/6 - 8(3)

= 9 - 24

= - 15

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The complete question is below:

54/g - 8h, when g = 6 and h=3

If Her pool is 10 m by 5 m and is surrounded by a 1. 5 m border of paving stones. Therefore, Piscine will need a total of 104 square meters of paving stones.

a) The area of the pool plus the surrounding border of paving stones can be calculated as follows:

Total area = (length + 2 x border width) x (width + 2 x border width)

Total area = (10 + 2 x 1.5) x (5 + 2 x 1.5)

Total area = 13 x 8

Total area = 104 square meters

Therefore, Piscine will need a total of 104 square meters of paving stones.

b) We need to convert the dimensions of each paving stone to meters:

25 cm = 0.25 m

40 cm = 0.4 m

The area of each paving stone is:

0.25 m x 0.4 m = 0.1 square metres

The number of paving stones required can be calculated by dividing the total area by the area of each paving stone:

Number of paving stones = Total area / Area of each paving stone

Number of paving stones = 104 / 0.1

Number of paving stones = 1040

In theory, Piscine will need 1040 paving stones.

c) To determine whether the answer in part b) will be enough, we need to see if we can fit the paving stones into the available space without any gaps. We can arrange the paving stones in rows, with each row containing 10 stones (since the width of the pool is 5 m and the width of each paving stone is 0.4 m).

There will be 26 rows of paving stones around the pool (since the length of the pool plus the two borders is 13 m and the length of each paving stone is 0.25 m). Therefore, the total number of paving stones required is: 26 rows x 10 stones per row = 260 stones

Since the number of paving stones required is less than the number calculated in part b), Piscine will have enough paving stones to complete the border around her pool without any waste.

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19.29 cubic feet  is the volume of the composite figure if both the height and the diameter of the cylinder are 2. 5 feet

Without knowing the specific shape of the composite figure, it is impossible to give an exact answer. However, we can provide a general formula for the volume of a cylinder with height h and diameter d, and assume that the composite figure consists of a cylinder and some other shape.

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the cylinder. The diameter of the cylinder is given as 2.5 feet, which means the radius is 1.25 feet.

If the height of the cylinder is also 2.5 feet, then the volume of the cylinder is:

V_cylinder = π(1.25)^2(2.5) = 6.15π cubic feet (exact)

To approximate to two decimal places, we can use the approximation π ≈ 3.14:

V_cylinder ≈ 6.15(3.14) = 19.29 cubic feet (approximate to two decimal places)

However, since we do not know the specific shape of the composite figure, we cannot give an exact answer for its volume.

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