Seth has a bank account which pays 1.01% interest, compounded quarterly. Seth withdraws $4,567 from the account every quarter for 35 years. Assuming that Seth does not make any deposits into this account and that the withdrawals occur at the end of every quarter, find the initial value of the account, rounded to the nearest cent.

3. The amount that should be returned to Meenaski for buying 12 books worth R250.75 each and giving the shopkeeper R4,000, using mathematical operations, is R991.

4. The number of crayon sets that can be bought for R2,750 if one set costs R25, using division operation, is 110.

5. Manu will pay R1,700, exchanging his old bike for a new bike.

The four basic mathematical operations include addition, subtraction, division, and multiplication.

These mathematical operations are performed to solve algebraic problems using the relevant mathematical operands and rules.

The number of books bought = 12

The unit cost of each book = R250.75

The total cost of the 12 books = R3,009 (R250.75 x 12)

The amount advanced to the cashier = R4,000

The balance to be returned = R991 (R4,000 - R3,009)

The cost of a set of crayon = R25

The amount of money for the purchase = R2,750

The number of crayon sets that can be bought with R2,750 = 110 (R2,750/R25).

The price of the new bicycle = R2,500

The value of the old bike for exchange = R800

The amount to be paid = R1,700 (R2,500 - R800)

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The price of the new bicycle is R2,500. The bike on exchange is worth R800.  How much does he pay for his new bike?

The transformations from the function f(x) to g(x) is horizontal shift: Right 4 Units and vertical shift: Up 1 Units.

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.

The given functions are f(x)=x³ and g(x)= -(x-4)³+1.

To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.

Horizontal Shift: Right 4 Units

Vertical Shift: Up 1 Units

Reflection about the x-axis: None

Reflection about the y-axis: Reflected

Vertical Compression or Stretch: None

Therefore, the transformations from the function f(x) to g(x) is horizontal shift: Right 4 Units and vertical shift: Up 1 Units.

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Answer:

1) 16pi square cm

2) 112pi cubed cm

3) 351.68 cubed cm

Step-by-step explanation:

Question 1: The base of a cylinder is a circle. To find the area of a circle, we can use the formula A = pi(r^2). the radius is 4 centimeters. 4^2 = 16.

The answer to the question is 16pi square cm

Question 2: This question is asking for the volume of the cylinder. To find the volume of the cylinder, we must multiply the area of the base by its height. we know the area of the base is 16pi. 16pi x 7(the height) = 112 pi.

The answer to the question is 112 pi cubed cm

Question 3: If pi were to be 3.14, we just need to substitute pi in the equation for question two with 3.14:

16(3.14) x 7 = 351.68

The answer is 351.68 cubed cm

Answer:

69 meters

Step-by-step explanation:

The approximate arc length of one slice of pic is 5.24 inches according to the circle circumference.

Let us assume that the pic is equally cut into 6 pieces. Also given that the diameter of the pie is 10 inches.

Diameter (D)=10.

So the radius will be D/2.

Radius (R)=10/2=5.

The pie's circumference is given by:

C=2πR

C=2π*5

C= 10π (in)

Because the pie is divided into six pieces, the circumference of the pie is divided into six equal-length arcs. So,

Length of Arc (L)= 10π/6

L = 5π/3

L= 5(3.14)/3

L=5.234=5.24

Therefore the approximate arc length of one slice of pie is 5.24 inches.

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Answer:

x=10

Step-by-step explanation:

Answer:

x=10

Step-by-step explanation:

Answer:

Step-by-step explanation:

is this in deltamath or bigideas? lol

(31.19-1.67)/24=x

"/" means divide.

Answer: 825 workers altogether

Step-by-step explanation:

well, if the ratio is 4.5 men to every woman, we just have to multiply 150 by 4.5, which means there will be 675 male workers and 150 female workers.

Natural numbers are sometimes known as counting numbers. Numbers that can be counted but not zero. Whole numbers are a modest extension of natural numbers and include Zero.

A subset of the natural numbers are the positive integers, often known as non-negative integers. Here are a few instances: 1, 2, 3, 4, 5, 6,... In other words, the "natural numbers" are the collection of all whole numbers that do not include 0.

There are just a limited amount of parts to it. Example: A = 1, 2, 3, and 4. An infinite set has unlimited items. All entire numbers are in a set called  whole numbers.

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Answer:

So the polynomial function is

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

Step-by-step explanation:

A polynomial function of lowest degree in standard form with roots x = 1, 3, and 2i can be written as (x - 1), (x - 3), and (x - 2i),

From the above data we can get,

k(x) = (x - 1)(x - 3)(x - 2i)

After expanding the equation ,

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

So the polynomial function is

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

Answer:

x=8 is true for the this condition

Step-by-step explanation:

4x<34

if x=8

4*8<34

32<34

which is true

if x=10

40 is not greater than 34, so it not satisfied the condition

To prove that removing the root of a k-th order binomial tree results in k binomial trees of smaller orders, we will use mathematical induction.

Base case: For k = 1, removing the root of a 1st order binomial tree results in zero smaller binomial trees, which is true.

Inductive hypothesis: Assume that removing the root of a k-th order binomial tree results in k binomial trees of smaller orders, for some positive integer k.

Inductive step: We want to prove that removing the root of a (k+1)-th order binomial tree results in (k+1) binomial trees of smaller orders.

By definition, a (k+1)-th order binomial tree, denoted by B(k+1), is formed by joining two k-th order binomial trees, denoted by Bk, with one of them as the leftmost child of the root of the other. Let us remove the root of B(k+1) to obtain a new binomial tree, denoted by B'.

Since B(k+1) is formed by joining two k-th order binomial trees, we can apply the inductive hypothesis to each of them to obtain that removing their roots results in k smaller binomial trees each. Let these smaller binomial trees be denoted by B1, B2, ..., Bk and C1, C2, ..., Ck,

respectively.

Now, consider B' and observe that it is a k-th order binomial tree, since it has k children, each of which is a smaller binomial tree. Moreover, B' is obtained from B(k+1) by removing the root, which is the parent of the two k-th order binomial trees Bk and Ck. Thus, we have decomposed B' into k smaller binomial trees, namely B1, B2, ..., Bk and C1, C2, ..., Ck.

Therefore, we have shown that removing the root of a (k+1)-th order binomial tree results in (k+1) binomial trees of smaller orders, which completes the induction.

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Answer:

Let's assume that the cost of each box of cookies is "x" dollars.

Based on the given information, Gail sold a total of 3 + 4 + 1 = 8 boxes of cookies this week, and Mr. Millbrook gave a $7 donation. Therefore, the total amount of money collected this week is:

8x + 7

Since we know that Gail sold 10 boxes of cookies last week and collected the same amount of money, we can set up an equation:

10x = 8x + 7

Solving for x, we get:

2x = 7

x = 3.50

Therefore, each box of Girl Scout cookies costs $3.50.

Step-by-step explanation:

The required probability of Mr. Mackinson choosing the names of 2 girls is approximately 0.2273.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
The total number of ways to choose any 2 students from a group of 12 is given by the combination formula:

C(12,2) = 12! / (2! * 10!) = 66

This means there are 66 total ways for Mr. Mackinson to choose any 2 students from the class.

To calculate the probability of choosing 2 girls, we need to count the number of ways to choose 2 girls from the group of 6 girls. We can use the combination formula again:

C(6,2) = 6! / (2! * 4!) = 15

This means there are 15 ways for Mr. Mackinson to choose any 2 girls from the class.

So the probability of Mr. Mackinson choosing 2 girls is:

P(2 girls) = number of ways to choose 2 girls / total number of ways to choose 2 students

= C(6,2) / C(12,2)

= 15 / 66

= 0.2273

Therefore, the probability of Mr. Mackinson choosing the names of 2 girls is approximately 0.2273.

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Answer:

1. The formula for the area of a circle is given by A = πr^2, where r is the radius of the circle. To find the area of the 12" pizza, we first need to find the radius:

r = 12 / 2 = 6 inches

The area of the pizza is then:

A = πr^2 = π * 6^2 = 36π square inches

2. To find the radius of a pizza that is 25% larger, we can first find the amount by which the radius will increase:

increase = 6 * 0.25 = 1.5 inches

The new radius will then be:

new_r = 6 + 1.5 = 7.5 inches.

Step-by-step explanation:

Answer:

113.1, 8

The equation to find the area of a circle is:

Now we can input 12 into the equation:

To find the radius of a pizza that is %25 larger, we can use this equation:

Well, that's a good question! If we were to multiply by 0.25, the radius would get smaller, instead of bigger. We add the 1.0 because we have to add the original radius, not just the added length.

Fitting the radius into the equation:

Therefore, the area of the pizza is 113.1, and the radius of a pizza that is %25 larger is 8.

The required weight of a hippo in pounds is given as 3,000 pounds.

What is a unit of measurement?

Unit of measurement is defined as every entity having its measures in dimensions, weight, and time. Such as for length we have a meter, for liquid we have liters, and so on.

Here,
One ton is equal to 2,000 pounds, so a hippo that weighs 1.5 tons would weigh,

1.5 tons × 2,000 pounds/ton = 3,000 pounds

Therefore, the hippo at the zoo weighs 3,000 pounds.

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Factoring polynomials with a leading coefficient greater than 1 is to use the factoring by grouping technique or quadratic formula.

Factoring a polynomial with a leading coefficient greater than 1 can be more challenging than factoring a polynomial with a leading coefficient of 1. However, there are several methods and techniques that can be used to factor such polynomials.

One common method for factoring polynomials with a leading coefficient greater than 1 is to use the factoring by grouping technique. This involves grouping the terms of the polynomial in pairs and factoring out the greatest common factor of each pair.

The resulting expressions can then be further factored or combined to obtain the final factorization of the polynomial.

Another method for factoring polynomials with a leading coefficient greater than 1 is to use the quadratic formula, which can be used to find the roots of a quadratic polynomial. Once the roots are found, the polynomial can be factored as a product of linear factors.

In some cases, it may also be helpful to use a combination of these techniques, along with other algebraic manipulations, such as completing the square or long division.

Overall, factoring a polynomial with a leading coefficient greater than 1 may require more patience and creativity than factoring a polynomial with a leading coefficient of 1, but with practice and persistence, it is possible to develop the skills and techniques needed to factor such polynomials efficiently and accurately.

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Answer: 0.95m or 3/π

Step-by-step explanation:

Volume of cylinder = 2π[tex]r^{2}[/tex]*h

54 = 2π*9*h

divide 2π*9 on both sides

54/2π*9 = h

54/18π = h

3/π = h

h = 0.95 m

The cost of each order of french Fries is $1.75.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Wendell purchased a hot dog and 3 orders of French fries for $6.00.

If the hot dog cost $2.25.

Then the cost of Hot dog

= 6 - 2.25

= 3.75

and, the cost of each order of French Fries

= 3.75 / 3

= $1.25

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Sarah should blend 80.5 pounds of the high-quality beans and 39.5 pounds of the cheaper beans to make 120 pounds of blended coffee.

In this problem, we are given that Sarah Meeham needs to prepare 120 pounds of blended coffee beans to sell at a rate of $4.17 per pound. She plans to blend two types of coffee beans: a high-quality bean costing $5.25 per pound and a cheaper bean costing $2.00 per pound.

Let x be the number of pounds of the high-quality coffee beans needed and y be the number of pounds of the cheaper coffee beans needed. Since we need 120 pounds of the blended coffee, we have:

x + y = 120

The cost of the blended coffee is $4.17 per pound. This means that the total cost of the blended coffee is:

4.17(120) = 501.6

We can also find the cost of the high-quality and cheaper beans in terms of x and y:

5.25x is the cost of the high-quality beans

2.00y is the cost of the cheaper beans

The total cost of the two types of beans is the sum of their individual costs:

5.25x + 2.00y

Since we need 120 pounds of the blended coffee, we can set up the following equation using the above expressions for total cost:

5.25x + 2.00y = 501.6

Now, we can use the system of equations consisting of x + y = 120 and 5.25x + 2.00y = 501.6 to solve for x and y. One way to do this is by substitution:

x = 120 - y (from the first equation)

5.25(120 - y) + 2.00y = 501.6 (substituting x in the second equation)

Simplifying and solving for y, we get:

630 - 5.25y + 2.00y = 501.6

3.25y = 128.4

y ≈ 39.5

Now we can use this value of y to find x:

x = 120 - y

x = 120 - 39.5

x ≈ 80.5

Therefore, Sarah needs to blend approximately 80.5 pounds of the high-quality coffee beans and 39.5 pounds of the cheaper coffee beans to make 120 pounds of blended coffee that she can sell for $4.17 per pound.

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The addition of two numbers is 410+210 is 620.

From the given numbers,

First number is 410

Second number is 210.

One of the arithmetic operations is addition. The total of the numbers is provided. In other words, addition refers to the operation of adding the numbers together. "+" is the symbol used to denote addition. The outcome of the adding procedure is referred to as the sum. Addends are the numbers that are added together.

The following are the rules of addition operation:

Now,

⇒410+210=620

Therefore, the value is 620.

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The length of B'C' after the translation of the original object is; B'C' = 3 units

Translation in transformation is simply defined as the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system. In translation, only the position of the object changes, its size remains the same.

Now, from the attached image, we see that;

AB = 7 units

BC = 3 units

CD = 4 units

DA = 5 units

Now, by virtue of the definition of translation, it means that the translated object will retain the same dimensions. Thus;

B'C' = 3 units

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If the sales tax rate is 6% and if Sally buy rowboat priced at $842, the amount of tax she will pay,  $50.52

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

To calculate the sales tax on the purchase of a sailboat priced at $842 with a sales tax rate of 6%, you can follow these steps:

1. Convert the sales tax rate from a percentage to a decimal by dividing by:

= 100: 6% ÷ 100

= 0.06.

2. Multiply the price of the sailboat by the sales tax rate to find the amount of tax:

= $842 × 0.06

= $50.52.

Therefore, Sally will pay $50.52 in sales tax for the purchase of the sailboat.

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A heavy rope, 30 ft long, weighs 0.7 lb/ft and hangs over the edge of a building 80 ft high, the work done in pulling the rope to the top of the building is 1785 ft-lb.

To calculate the work done in pulling the rope to the top of the building, we need to use the formula:

W = F x d

where W is the work done, F is the force applied, and d is the distance over which the force is applied.

In this problem, we can calculate the force required to pull the rope as the product of its weight per unit length (0.7 lb/ft) and the length of the rope (30 ft). Thus, the force required is:

F = 0.7 lb/ft x 30 ft = 21 lb

To calculate the distance over which the force is applied, we need to calculate the total length of the rope that needs to be lifted. This can be found using the Pythagorean theorem, as follows:

l = √(30^2 + 80^2) = 85 ft

So the distance over which the force is applied is 85 ft.

Now we can substitute the values for F and d into the formula for work to get:

W = F x d = 21 lb x 85 ft = 1785 ft-lb

This calculation shows how the formula for work can be used to calculate the energy required to lift an object against gravity over a given distance.

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Answer:

Fraction 3/4 percent 75%

Step-by-step explanation:

.75 in simplest form is 3/4

Answer:

heyyyyy

Step-by-step explanation:

whatssss goooddd

The expression is equivalent to 2(a  -3) + 4a will be 6a - 6. Then the correct option is A.

The equivalent is the expression that is in different forms but is equal to the same value.

The expression is given below.

⇒ 2(a  -3) + 4a

Simplify the expression, then we have

⇒ 2(a  -3) + 4a

⇒ 2a - 6 + 4a

⇒ 6a - 6

The expression is equivalent to 2(a  -3) + 4a will be 6a - 6. Then the correct option is A.

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The missing options are given below.

A. 6a - 6

B. 6a - 1

C. a - 6

D. None of the above

The true statements are ∠X and ∠Y are supplementary angles, ∠W and ∠Z are a linear pair and ∠Y and ∠Z are complementary angles. The solution has been obtained by using angles and line.

What are angles and line?

Lines having little depth or width are said to be straight. Lines can be perpendicular, intersecting, transversal, and many more various forms. A figure in which two rays emanate from the same point is referred to be an angle.

We know that angles on a straight line add up to 180° and such angles are called supplementary angles.

Therefore, ∠X and ∠Y are supplementary angles.

Similarly, we know that angles on a straight line form a linear pair.

Therefore, ∠W and ∠Z are a linear pair.

Also, we know that two angles are complementary when their sum is 90°.

We can see from the figure that ∠Z and ∠Y add up to 90°.

Therefore, ∠Y and ∠Z are complementary angles.

Hence, the above provided statements are true about the angles.

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The figure of the question is attached below

Answer:

Step-by-step explanation:

Advantages of Fifth Generatin of Computer:These computers are much faster than other generation computers. Development of true artificial intelligence.

Development of Natural language processing.

Advancement in Parallel Processing. Advancement in Superconductor technology. More user-friendly interfaces with multimedia features. Availability of very powerful and compact computers at cheaper rates.

Disadvantages of Fifth Generatin of Computer: They tend to be sophisticated and complex tools. ...

Example of Third Generation of Computer: Desktop.