Pudge has three times as many apples as Ace, and Ace has twice as many as Christi. How many apples does each
have if Pudge has 12 more than both Ace and Christi together?
Can you work the problem out please? I’m really having a hard time putting it into a formula.

the product of (x + 3/x)² is x² + 6 + 9/x².

Why it is and what is Algebra?

To find the product of (x + 3/x)², we can use the formula for squaring a binomial:

(a + b)² = a² + 2ab + b²

In this case, we have a = x and b = 3/x, so we can substitute these values into the formula and simplify:

(x + 3/x)² = x² + 2(x)(3/x) + (3/x)²

= x² + 6 + 9/x²

Therefore, the product of (x + 3/x)² is x² + 6 + 9/x².

Algebra is a branch of mathematics that deals with the study of mathematical symbols and the rules for manipulating these symbols. It involves the use of letters and symbols to represent numbers and quantities in equations and expressions. The primary goal of algebra is to solve mathematical problems and equations using various operations such as addition, subtraction, multiplication, and division.

Algebraic concepts can be applied to a wide range of mathematical and real-world problems, including geometry, physics, engineering, economics, and statistics.

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Complete question:

Find the product of (x + 3/x)²2.

the organization needs to sell at least 22 tickets to break even.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

Let C be the total production cost and n be the number of tickets sold.

From the problem, we know that the organization had a net loss of $800 after selling 10 tickets, so we have:

10(70) - C = -800

Simplifying, we get:

C = 1500

This means that the total production cost was $1500.

The revenue from selling n tickets at $70 per ticket is given by:

R = 70n

Substituting the values of R and C, we get:

70n = 1500

Solving for n, we get:

n = 1500/70 = 21.43

Since we can't sell a fraction of a ticket, we need to round up to the nearest whole number.

Therefore, the organization needs to sell at least 22 tickets to break even.

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Answer:

Step-by-step explanation:

1. u would do 315/15 bc y/x=k

2. u would do 81/9

3. u would do 56/2

so basically for the next ones just do the money divided by oz to find the unit rate. Note always do y/x y is the dependent variable and x is the independent variable

The values of the side w and the angle x are 2.649 and 26. 206 degrees respectively.

It is important to note that there are different types of trigonometric identities are;

From the image shown, we have;

Using the sine identity

sin θ = opposite/hypotenuse

sin 32 = w/5

find the value

w = 2. 649

To determine the value of angle x , we have;

Using the sine identity

sin x = w/6

sin x = 2. 649/6

sin x= 0. 4416

Take the sine inverse

x = 26. 206 degrees

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if Leo has provided the coordinates of the jungle gym and the four-square courts, we can use the distance formula to calculate the distance between them.  the four-square courts are approximately   [tex]7.2[/tex] grid units, or 36 feet (since the scale is 1 grid = 5 feet).

The distance formula is:

[tex]d = sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]

where  [tex](x1, y1)[/tex] and [tex](x2, y2)[/tex] are the coordinates of two points, and d is the distance between them.

For example, let's say the jungle gym is located at (3, 4) on the grid, and the four-square courts are located at (9, 8). Using the distance formula, we have:

[tex]d = sqrt((9 - 3)^2 + (8 - 4)^2)[/tex]

[tex]= sqrt(6^2 + 4^2)[/tex]

[tex]= sqrt(36 + 16)[/tex]

[tex]= sqrt(52)[/tex]

[tex]\approx 7.2[/tex]

Therefore, the distance from the jungle gym to the four-square courts is approximately   [tex]7.2[/tex] grid units, or 36 feet (since the scale is 1 grid = 5 feet).

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Answer:313:)

Step-by-step explanation:

Answer:

[tex]3^2-5[/tex]

Step-by-step explanation:

    Given equation:

 ( 3 - 2^2) + 5

  3 - 4 + 5   (Simplify exponent)

 -1 + 5  (Solve 3 - 4)

  4 (Simplified)

Evaluation

2^2 + 5

4 + 5

9 (not the answer)

3^2 - 5

9-5

4  (answer)

Answer: 6

Step-by-step explanation:

21 - 1 = 20

20 - 2 = 18

18 - 3 = 15

15 - 4 = 11

11 - 5 = 6

Answer:

  148 cm²

Step-by-step explanation:

You want the surface area of a cuboid with edge lengths 4 cm, 5 cm, and 6 cm.

The formula is shown in your problem statement.

It can be made easier to compute using a little rearranging:

  SA = 2LW +2LH +2WH

  SA = 2(LW +LH +WH)

  SA = 2(LW +H(L +W))

The choice of dimensions for L, W, and H doesn't matter.

  SA = 2(4·6 +5(4+6)) = 2(24 +5(10)) = 2(74) = 148 . . . . cm²

The surface area is 148 cm².

Answer:

Step-by-step explanation:

y = 3x + 9

The flag starts at 0 on the number line and moves 8 feet right to 8.

We can calculate this by adding 8 to 0, which gives us 8. Then the flag moves 12 feet left to -4. We can calculate this by subtracting 12 from 8, which gives us -4. Then the flag moves 13 feet right to 9. We can calculate this by adding 13 to -4, which gives us 9. Nine is less than 10, so the flag ends up on the number line at a value less than 10.We can calculate the total distance moved by adding 8 + (-12) + 13, which gives us 9. This means the flag has moved a total of 9 feet. All of these calculations demonstrate that the flag has moved 8 feet right, 12 feet left, and 13 feet right to end up on the number line at 9, which is less than 10.

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The Converse of the Pythagorean Theorem is proved below.

What is Pythagoras Theorem ?

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

The converse of the Pythagorean theorem states that if a triangle has sides of length a, b, and c, where c is the longest side, and a² + b² = c², then the triangle is a right triangle.

To prove the converse of the Pythagorean theorem, we can use the fact that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. That is, if a triangle has sides of length a, b, and c, where c is the longest side and c² = a² + b², then the triangle is a right triangle.

Proof:

Suppose we have a triangle ABC, with sides of length a, b, and c, where c is the longest side. Assume that a² + b² = c². We want to show that triangle ABC is a right triangle.

We will use the Law of Cosines to show that angle C is a right angle. The Law of Cosines states that for any triangle ABC with sides of length a, b, and c opposite angles A, B, and C, respectively:

c² = a² + b² - 2ab cos(C)

Substituting a² + b² = c² into this equation, we get:

c² = c² - 2ab cos(C)

2ab cos(C) = 0

cos(C) = 0

Since 0 is the cosine of 90 degrees, this implies that angle C is a right angle. Therefore, triangle ABC is a right triangle.

Thus, this completes the proof of the converse of the Pythagorean theorem.

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13

First, we divide to figure out how much Jane makes an hour

143 ÷ 11 = 13

Second, we multiply multiply by 13 until we get 169

13 × 13 = 169

So Jane will make 169 dollars in 13 hours

Answer:

13 Hours

Step-by-step explanation:

$143 ÷ 11hrs = $13/hr that Jane is paid, so to find how many hours she will need to work to make $169

$169 ÷ $13 = 13 hours

Answer:

Step-by-step explanation:

Simplify the expressionApply the logarithm power identityApply the logarithm product identitySimplify the expression2Exponentiate both sides

log10(4x8)=2log10(48)=2

48=102

x=258=258√

Therefore , the solution of the given problem of equation comes out to be  f(x) = sin(/2 x) (when x = 1 or 2).

Variable words are commonly used in complex algorithms to show consistency between two statements that are not compatible. Academic expressions called equations are used to show the equality of various academic numbers. In this case, normalization yields b + 7 as opposed to a single formula the fact that split 12 into two parts, which can be used with data collected from y + 7.

Here,

The goal is to construct a trigonometric equation with only answers at

x = 1 and x = 2.

f(x) = A sin(Bx+C+D)

=> B + C + D + A = 0 (equation 1)

=> Equation 2: A sin(2B + C + D) = 0

=> B + C sin A = 0 (equation 3)

=> Sin(2B+C) = A = 0 (equation 4)

Since sin(x) = 0 when x is a multiple of, formulae 3 and 4 can be rewritten as follows:

=> B + C = nπ (equation 5)

=> 2B + C = mπ (equation 6)

with numbers n and m. When we simultaneously solve equations 5 and 6 for B and C, we obtain:

=> B = (m - n)π/2 (equation 7)

=> C = nπ - B (equation 8)

=> When x = 1, C = /2 - /2 = 0.

=> When x = 2, C =  − /2 = 3/2.

Thus, the result is as follows:

when f(x) = sin(/2 x) (when x = 1 or 2)

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60 adult tickets and 45 children tickets were sold.

Let's use algebra to solve the problem:

Let x be the number of adult tickets sold.

Let y be the number of children tickets sold.

From the problem, we know that:

x + y = 105 (total tickets sold)

10x + 6y = 870 (total amount raised)

We can solve this system of equations by using elimination:

Multiply the first equation by 6: 6x + 6y = 630

Subtract the second equation from the first: 4x = 240

Solve for x: x = 60

Now we can use x to find y:

x + y = 105

60 + y = 105

y = 45

Therefore, 60 adult tickets and 45 children tickets were sold.

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The coordinates of the point P on the directed line segment from A to B such that P is 2/3 the length of the line segment from A to B are (-1, 2).

The coordinates of point P are obtained applying the proportions in the context of the problem.

P is 2/3 the length of the line segment from A to B, hence the equation is given as follows:

P - A = 2/3(B - A)

Then the x-coordinate of P is obtained considering the x-coordinates of A and B as follows:

x - 9 = 2/3(-6 - 9)

x - 9 = -10

x = -1.

The y-coordinate of P is obtained considering the y-coordinates of A and B as follows:

y + 8 = 2/3(7 + 8)

y + 8 = 10

y = 2.

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Answer:

Step-by-step explanation:

To find the total distance traveled in the first second, we need to find the distance traveled during the first half-second and then double it.

The particle starts 2 cm to the right of 0, so its position function is given by:

s(t) = t - t^2 + 2

The distance traveled by the particle during the first half-second (from t = 0 to t = 0.5) is given by:

distance = |s(0.5) - s(0)|

We have:

s(0.5) = 0.5 - (0.5)^2 + 2 = 2.25 cm

s(0) = 0 - 0^2 + 2 = 2 cm

So, the distance traveled during the first half-second is:

|2.25 - 2| = 0.25 cm

To find the total distance traveled in the first second, we double this distance:

total distance = 2 * 0.25 = 0.5 cm

Therefore, the total distance traveled in the first second is 0.5 cm.

Answer:

eflections, rotations, and translations are all transformations that change the position of a figure in the plane. These transformations change the orientation, location, or both of a figure without altering its size or shape. In other words, they change the position or location of the figure in the plane while maintaining the same size and shape.

Answer:

Alright

Step-by-step explanation:

50/1.428

Multiply the numerator by the denominator to get 50000/1428

Set equation up in long division format

Divide 50000 by 1428 to get 3

Divide 7160 by 1428 to get 5

Divide 200 by 1428 to get 0

Divide 2000 by 1428 to get 1

Divide 5720 by 1428 to get 4

Divide 80 by 1428 to get 0

Divide 800 by 1428 to get 0

35.014

Chain discount is a type of discount offered by a seller to a buyer for purchasing a certain amount of goods or services in a series of transactions. The discount is applied incrementally as the buyer meets specific purchasing thresholds.

Chain discounts are often used to encourage larger purchases and build customer loyalty. They can be beneficial for both the buyer and the seller, as the buyer receives a discount and the seller increases their sales volume.

Item: Trotter treadmill

List price: $ [tex]3,000[/tex]

Chain discount:  [tex]9/4[/tex]

To calculate the net price, we first need to determine the amount of the chain discount.

Chain discount = List price x Chain discount rate

Chain discount = $ [tex]3,000 \times 9/4[/tex]

Chain discount = $ [tex]6,750[/tex]

The net price is the list price minus the chain discount:

Net price = List price - Chain discount

Net price = $ [tex]3,000[/tex] - $6,750

Net price = -$3,750

Therefore, The Net price is = -$3,750

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The corresponding point on the graph is (9, 21). This point is within the normal respiratory rate region, which is defined by the system of linear inequalities. Therefore, model breakdown has not occurred.

The given problem involves the normal respiratory rates of children aged 3 to 15 years. The respiratory rate, measured in breaths per minute, is represented as a function of age using a system of linear inequalities. The graph depicts a normal respiratory rate region that models the respiratory rate ranges shown in the table. The problem requires us to identify a specific point on the graph that corresponds to a respiratory rate of 21 breaths per minute for a 9-year-old child. The ordered pair (9, 21) represents the corresponding point on the graph.

Further, we need to determine if this point lies within the normal respiratory rate region or if model breakdown has occurred. The system of linear inequalities defines the normal respiratory rate region, and we can determine if the point (9, 21) satisfies these inequalities. In this case, the point (9, 21) lies within the normal respiratory rate region and satisfies the system of linear inequalities. Therefore, model breakdown has not occurred, and the given model is an appropriate approximation of the normal respiratory rate region for children aged 3 to 15.

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Answer:

To calculate the expected return on the portfolio, we use the following formula:

Expected return = (weight of stock X * expected return of stock X) + (weight of stock Y * expected return of stock Y) + (weight of stock Z * expected return of stock Z)

Expected return = (0.35 * 0.09) + (0.2 * 0.15) + (0.45 * 0.12) = 0.0321 or 3.21%

To calculate the variance of the portfolio, we use the following formula:

Variance = (weight of stock X)^2 * variance of stock X + (weight of stock Y)^2 * variance of stock Y + (weight of stock Z)^2 * variance of stock Z + 2 * weight of stock X * weight of stock Y * covariance of stocks XY + 2 * weight of stock X * weight of stock Z * covariance of stocks XZ + 2 * weight of stock Y * weight of stock Z * covariance of stocks YZ

Assuming that the stocks are uncorrelated, the covariance terms will be zero. Also, we assume that the variances of the stocks are equal to the square of their standard deviations. Therefore, we can simplify the formula to:

Variance = (weight of stock X)^2 * standard deviation of stock X^2 + (weight of stock Y)^2 * standard deviation of stock Y^2 + (weight of stock Z)^2 * standard deviation of stock Z^2

Variance = (0.35)^2 * (0.09)^2 + (0.2)^2 * (0.15)^2 + (0.45)^2 * (0.12)^2 = 0.00060167 or 0.060167%

To calculate the standard deviation of the portfolio, we take the square root of the variance:

Standard deviation = sqrt(0.00060167) = 0.0245 or 2.45%

Therefore, the expected return of the portfolio is 3.21%, the variance is 0.060167% and the standard deviation is 2.45%.

Answer:

Step-by-step explanation:

To calculate the expected return on the portfolio, we need to take the weighted average of the individual stock returns based on their proportions in the portfolio. The expected return on the portfolio can be calculated as follows:

Expected return on portfolio = (weight of stock X × expected return on stock X) + (weight of stock Y × expected return on stock Y) + (weight of stock Z × expected return on stock Z)

Expected return on portfolio = (0.35 × 9%) + (0.20 × 15%) + (0.45 × 12%)

Expected return on portfolio = 3.15% + 3.00% + 5.40%

Expected return on portfolio = 11.55%

To calculate the variance and standard deviation of the portfolio, we need to use the formula that takes into account the individual stock variances, covariances, and the weights of the stocks in the portfolio. Assuming the covariances between the stocks are zero, we can use the following formulas:

Portfolio variance = (wX^2 * σX^2) + (wY^2 * σY^2) + (wZ^2 * σZ^2) + 2(wX * wY * σXY) + 2(wX * wZ * σXZ) + 2(wY * wZ * σYZ)

Portfolio standard deviation = sqrt(portfolio variance)

where wX, wY, and wZ are the weights of stocks X, Y, and Z in the portfolio respectively, σX, σY, and σZ are the standard deviations of returns on stocks X, Y, and Z respectively, and σXY, σXZ, and σYZ are the covariances between the returns on stocks X and Y, X and Z, and Y and Z respectively.

Since we assume the covariances between the stocks are zero, we can simplify the formulas as follows:

Portfolio variance = (wX^2 * σX^2) + (wY^2 * σY^2) + (wZ^2 * σZ^2)

Portfolio standard deviation = sqrt[(wX^2 * σX^2) + (wY^2 * σY^2) + (wZ^2 * σZ^2)]

Substituting the values, we get:

Portfolio variance = (0.35^2 * 0.09) + (0.20^2 * 0.15) + (0.45^2 * 0.12)

Portfolio variance = 0.0036475

Portfolio standard deviation = sqrt[(0.35^2 * 0.09) + (0.20^2 * 0.15) + (0.45^2 * 0.12)]

Portfolio standard deviation = sqrt(0.0036475)

Portfolio standard deviation = 0.06035

Therefore, the expected return on the portfolio is 11.55%, the portfolio variance is 0.0036475, and the portfolio standard deviation is 0.06035.

The mode for the region A is 2.6.

What exactly is mode?

In statistics, the mode is the value that has highest frequency in a data set. It is one of the three measures of central tendency, along with the mean and median.

To find the mode of a data set, you simply identify the value that appears most often. If no value is repeated, the data set has no mode.

The mode is particularly useful when dealing with categorical data or data that can be easily grouped into categories, such as colors, types of fruit, or letter grades. In such cases, the mode can provide insight into which category is most common or prevalent.

Now,

As given Values for Region A are

2.3  2.5  2.6  2.6  2.6  2.7  2.7  2.8

Here 2.6 comes most times or frequency of 2.6 is highest of all.

Hence,

           The mode for the region A is 2.6.

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Answer:

A fraction tells you how many parts of a whole there are. When we find a fraction of an amount, we are working out how much that 'part' is worth within the whole. You can see fractions of amounts all around us

Step-by-step explanation:

i may be wrong but I tried

Answer:

It will be same as angle x because they are on the same line and are alternative angles

So, measurement of angle u will be u=152

Step-by-step explanation:

Hope this helps:)

Good luck

Answer:

B

Step-by-step explanation:

y = x ( 3-x) = 3x - x^2      the ' x^2 ' makes it nonlinear

Answer:

[tex]yeah \: 2 + 2 = 4[/tex]