Manuel bought 9 pounds of apples.
He has eaten 34 of a pound so far and has $15 worth of apples left. Write and solve an equation to find the cost of the apples per pound to the nearest dollar. How much did the apples cost per pound?

Answer:

a = ±6x

b = ±7

Step-by-step explanation:

1.

a² = 36x²

a = ±√(36x²)

a = ±6x

2.

b² = 49

b = ±√(49)

b = ±7

The Cartesian equation for the curve is y = 10, representing a horizontal line 10 units above the x-axis.

To find a Cartesian equation for the curve with the polar equation r = 10 csc(θ) and identify it, follow these steps:

1. Recall the conversion formulas between polar and Cartesian coordinates:
  x = r * cos(θ)
  y = r * sin(θ)

2. Substitute the given polar equation, r = 10 csc(θ), into the formula for y:
  y = (10 csc(θ)) * sin(θ)

3. Simplify the equation by using the property csc(θ) = 1 / sin(θ):
  y = (10 * (1 / sin(θ))) * sin(θ)

4. Cancel out the sin(θ) terms:
  y = 10

The Cartesian equation for the curve is y = 10, which represents a horizontal line 10 units above the x-axis.

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The value of K is 2.

Let's denote the scale factor as K. The surface area of a solid after dilation is directly proportional to the square of the scale factor.

We are given that the initial surface area of the solid is 50 units^2, and after dilation, the surface area becomes 200 units^2.

Using the formula for the surface area, we have:

Initial surface area * (scale factor)^2 = Final surface area

50 * K^2 = 200

Dividing both sides of the equation by 50:

K^2 = 200/50

K^2 = 4

Taking the square root of both sides:

K = √4

K = 2

Therefore, the value of K is 2.

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The side lengths will be 6, since a square's area is just one side length squared.

The probability of the word MATH being found in one of the two piles is approximately 0.0000242, which is a very small probability.

This is a probability question that requires a bit of combinatorics. There are 26 letters in the alphabet, and they are separated into two equal piles, each containing 13 letters.

To calculate the probability of the word MATH being found in one of the piles, we need to first determine the number of ways that the letters can be arranged in each pile.

For the first pile, there are 13 letters to choose from, so we have 13 choices for the first letter, 12 choices for the second letter, 11 choices for the third letter, and 10 choices for the fourth letter.

This gives us a total of 13 x 12 x 11 x 10 = 15,120 possible arrangements.

The same is true for the second pile, so we have a total of 15,120 x 15,120 = 228,614,400 possible arrangements for the two piles combined.

To calculate the probability of the word MATH being found in one of the piles, we need to determine how many of these arrangements contain the letters M, A, T, and H in the same pile.

To do this, we can fix the position of the first letter, which must be one of the letters in MATH.

There are four choices for this letter. We can then fix the position of the second letter, which must be one of the remaining three letters in MATH. There are three choices for this letter.

We can then fix the positions of the remaining two letters, which must be two of the 22 remaining letters in the pile. There are 22 x 21 = 462 possible arrangements for these two letters.

Multiplying these choices together gives us a total of 4 x 3 x 462 = 5,544 possible arrangements that contain the letters M, A, T, and H in the same pile.

Finally, we can calculate the probability of the word MATH being found in one of the piles by dividing the number of arrangements that contain the letters M, A, T, and H in the same pile by the total number of possible arrangements. This gives us:

Probability = 5,544 / 228,614,400 = 0.0000242

So the probability of the word MATH being found in one of the two piles is approximately 0.0000242, which is a very small probability.

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Answer:

d = 3072.2 ft

Step-by-step explanation:

    Circumference of circle = 9687 ft

                                   πd     = 9687

                                      \(\sf \dfrac{22}{7}*d = 9687\\\)

                                              \(d = 9687 * \dfrac{7}{22}\\\\d = 3082.2 \ ft\)

9514 1404 393

Answer:

  y = 14x + 10

Step-by-step explanation:

We are given two points, (x, y) = {(5, 80), (3, 52)}. The 2-point form of the equation for a line can be used to find the equation.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (52 -80)/(3 -5)(x -5) +80 . . . . . fill in the given values

  y = (-28/-2)(x -5) +80 . . . . . simplify a bit

  y = 14x -70 +80 . . . . . eliminate parentheses; next, collect terms

  y = 14x +10

Answer:

x ≤ 4, look for the bold title for the numberline

Step-by-step explanation:

Subtract 7 to both sides

x + 7 ≤ 11

  -7    -7

x ≤ 4

That is the answer.

Can you provide a number line?

sketch of the line 4x + 3y = 11, slope (-4/3),  y-intercept of the line y = 11/3

Step 1: Convert the equation to slope-intercept form (y = mx + b) by solving for y:

3y = -4x + 11

y = (-4/3)x + 11/3

Step 2: Identify the slope and y-intercept:

From the equation in slope-intercept form, we can see that the slope (m) is -4/3 and the y-intercept (b) is 11/3.

Step 3: Plot the y-intercept:

On the y-axis, mark a point at y = 11/3 (approximately 3.67). This is the y-intercept of the line.

Step 4: Use the slope to find additional points:

Using the slope of -4/3, we can find other points on the line. The slope represents the change in y for every 1 unit change in x. So, starting from the y-intercept, we can move down 4 units and to the right 3 units to find the next point, and continue this pattern to find more points.

Step 5: Connect the points:

Once you have a few points on the line, you can connect them with a straight line. Make sure the line extends beyond the plotted points to show that it continues indefinitely.

The resulting line should have a negative slope (-4/3) and be slanting downward from left to right.

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The derivative  of y with respect to x is -2.

To find \(\frac{dy}{dx}\), we first need to express y and x in terms of a common variable, which we choose to be t.

Given x = t^2, we can differentiate both sides with respect to t using the chain rule to obtain:

\(\frac{dx}{dt}\) = 2t

Solving for t, we get:

t = (1/2) \(\frac{dx}{dt}\)

Substituting this value of t into the equation y = 8 - 2t, we get:

y = 8 - 2((1/2) \(\frac{dx}{dt}\))

Simplifying, we get:

y = 8 -\(\frac{dx}{dt}\)

Differentiating both sides with respect to x using the chain rule, we get:

\(\frac{dy}{dx}\) = d/dx(8 - \(\frac{dx}{dt}\))

Using the chain rule again, we have:

\(\frac{dy}{dx}\) = -    \(\frac{d(dx/dx)/dt }\)

Since \(\frac{dx}{dt}\) = 2t, we can substitute this to obtain:

\(\frac{dy}{dx}\) = -\(\frac{d2t}{dt}\)

Taking the derivative of 2t with respect to t, we get:

\(\frac{dy}{dx}\) = -2

Therefore, the derivative of y with respect to x is -2.

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Answer:

choose option 1

Step-by-step explanation:

option one is going to take a longer time to pay off but option 2's annual fees are going to make you spend at least $200 more dollars than option 1

Step 1. Identify the variables.

Step 2. Find the first constraint using the condition for the total number of books in each box.

The problem states "Christina needs to pack the boxes so there are at least 20 books in each box" This means that the sum of x and y must be at least 20, this is represented in the following inequality:

That is the first constraint.

Step 3. Find the second constraint using the condition for the weight of each box.

The problem states: "the boxes cannot weigh more than 30 pounds" and since the paperback books weigh 0.8 pounds and the hardcover books weigh 1.3 pounds each, the sum of their weights is:

This sum cannot be more than 30, which is represented by the following inequality:

Answer:

The set of constraints is

A function f is blank 1 of 1 linear on an interval ii if, for any choice of x1 and x2 in ii, with x1 < x2.

A function f is **question blank 1 of 1** linear on an interval **ii** if, for any choice of **x1** and **x2** in **ii**, with **x1** < **x2**, the function satisfies the properties of a linear function.t

In a linear function, the rate of change (slope) between any two points on the function is constant. This means that the function's value increases or decreases at a constant rate as we move along the interval.

The blank in the question refers to the specific term that should be filled. However, based on the given context, it seems that the most suitable term to fill the blank would be **"is"**. Therefore, the sentence would read as:

"A function f is linear on an interval ii if, for any choice of **x1** and **x2** in **ii**, with **x1** < **x2**, the function satisfies the properties of a linear function."

This statement highlights the key characteristic of a linear function, where the function's behavior between any two points on the interval is consistent and can be represented by a straight line.

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An area of mathematics that studies how competing parties interact is known as "game theory."

Game theory analyzes strategic decision-making in situations where multiple participants, known as players, make choices that affect each other's outcomes. It examines the interactions, strategies, and outcomes of these competitive or cooperative situations.

Game theory provides mathematical models and frameworks to analyze various scenarios, such as conflicts, negotiations, auctions, voting systems, and economic markets. It studies the behavior of rational players, their objectives, and the choices they make to maximize their own outcomes, considering the actions and reactions of other players.

The field of game theory explores concepts such as strategies, payoffs, Nash equilibrium, dominant strategies, and cooperative or non-cooperative games. It aims to predict and understand the behavior and outcomes of competitive situations and provides insights into decision-making, resource allocation, and the dynamics of interactions between individuals, organizations, or even nations.

Overall, game theory serves as a valuable tool in various disciplines, including economics, political science, psychology, and computer science, to analyze and model situations where competing parties interact.

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The expected number of coins that are heads at the end after Jennifer has tossed 64 fair coins and those that landed on tails were tossed again is 32. the expected number of coins that are heads at the end is 48.

Here is a detailed explanation:Jennifer tosses 64 coins, and each coin has an equal chance of landing on either heads or tails. Thus, the probability that any one coin lands on heads is 0.5, and the probability that it lands on tails is also 0.5.When Jennifer tosses the 64 coins, some of them will land on tails.

Those coins will be tossed again. However, the probability of getting heads or tails for these coins is still 0.5 since the coins are fair.Therefore, the probability that a coin that has already been tossed and landed on tails to land on heads the second time is also 0.5.

The same applies to the third toss. The probability that a coin will land on heads or tails is 0.5.The total number of coins that land on tails during the first toss is given by

64*0.5 = 32.

Since these coins are tossed again, the expected number of coins that land on tails for the second toss is given by

32*0.5 = 16.

The remaining coins that landed on heads during the first toss are not affected. Thus, the expected number of coins that landed on heads during the first toss is

64 - 32 = 32.

The total number of coins that landed on heads during the first toss is given by 32.

Adding the expected number of coins that land on heads during the second toss (16),

the expected number of coins that land on heads is

32 + 16 = 48.

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Answer:

The number of pennies owned is 7 pennies

Step-by-step explanation:

The given parameters are;

The number of pennies left over when we break the pennies into groups of 2s = 1 penny

The number of pennies left over when we break the pennies into groups of 3s = 1 penny

Let the number of pennies owned = c

What we are given are as follows;

2 × a = c - 1

3 × b = c - 1

2 × a = 3 × b

a/b = 3/2

Therefore, if we multiply 2 by 3, and 3 by 2 we get 6

2 × 3 = 6, similarly 3 × 2 = 6

If we put 6 = c - 1, we get;

c = 6 + 1 = 7

c = 7

The number of pennies owned = 7 pennies.

Answer:

31781715561888155919761999

Answer:

10h+6b=£48

5h+2b=£19

12h+9b=£60

Step-by-step explanation:

10h+6b=(3h+1b)+(7h+5b)

5h+2b=(7h+5b)-(2h+3b)

12h+9b=(10h+6b)+(2h+3b)

h=handles

b=bolts

The value of the expression as in the task content is; 1/4.

It follows from the task content that the value of the expression is to be determined.

Hence, since the expression whose value is required to be determined is ; (1 + (1/2))² - 2.

It follows from PEMDAS guidelines that the parentheses be solved first so that we have;

(3/2)² - 2........After solving the parentheses.

Next, the exponent should be solved as follows;

= (9/4) - 2.

And finally, by solving the subtraction; we have;

= 1/4 = 0.25.

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The test value to test linear correlation between the number of absences and the final grades is -0.729, which indicates a moderately strong negative correlation between the two variables.

Using the formula for the correlation coefficient, we can calculate the test value to test linear correlation as follows

First, we need to calculate the mean of x and y

mean(x) = (0+3+6+4+9+2+15+8+5)/9 = 6.22

mean(y) = (98+86+80+82+71+92+55+76+82)/9 = 79.67

Next, we need to calculate the deviations from the means:

deviations from mean of x: -6.22, -3.22, -0.22, -2.22, 2.78, -4.22, 8.78, 1.78, -1.22

deviations from mean of y: 18.33, 6.33, 0.33, 2.33, -8.67, 12.33, -24.67, -3.67, 2.33

Then, we need to calculate the product of deviations

product of deviations: (-6.22)(18.33), (-3.22)(6.33), (-0.22)(0.33), (-2.22)(2.33), (2.78)(-8.67), (-4.22)(12.33), (8.78)(-24.67), (1.78)(-3.67), (-1.22)(2.33)

Summing the products of deviations gives

Σ(xy) = -221.04

Next, we need to calculate the sum of squares of deviations

Σ(x²) = 325.56

Σ(y²) = 20334.67

Then, we can plug these values into the formula for the correlation coefficient

r = Σ(xy) / √(Σ(x²) Σ(y²)) = -221.04 / √(325.56 * 20334.67) ≈ -0.729

Therefore, the test value to test linear correlation is -0.729.

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--The given question is incomplete, the complete question is given below "the data below are the number of absences and the final grades of 9 randomly selected students from a statistics class. find the test value to test linear correlation.

Number of absences, x 0 3 6 4 9 2 15 8 5

Final grade, y 98 86 80 82 71 92 55 76 82 "--

The angle that is complementary to angle X is 90 degrees minus angle X.

1. Complementary angles are two angles whose sum is 90 degrees.

2. Let's assume that angle X is given.

3. To find the angle that is complementary to angle X, we need to subtract angle X from 90 degrees.

4. The formula to find the complementary angle is: Complementary Angle = 90 degrees - angle X.

5. Substitute the value of angle X into the formula to calculate the complementary angle.

6. For example, if angle X is 45 degrees, the complementary angle would be: 90 degrees - 45 degrees = 45 degrees.

7. Similarly, if angle X is 60 degrees, the complementary angle would be: 90 degrees - 60 degrees = 30 degrees.

8. Therefore, to find the complementary angle to any given angle X, subtract that angle from 90 degrees.

9. The result will be the measure of the angle that is complementary to angle X.

10. Remember that complementary angles always add up to 90 degrees.

11. By using this approach, you can find the complementary angle for any given angle X.

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Answer:

1

Step-by-step explanation:

The rate of change in this table of values is also the slope. Solve for the slope using any two points in the table. In this instance we will be using (1,5) and (2,6)

Therefore, the rate of change is 1.

Answer:

X = 6y-2 is the easier substitution for another equation because all you have to do is just plug in the equation into the value of x.

Answer:

I think the answer is b the answer is b

Answer:

The answer is really and surely B

Answer:

89%

Step-by-step explanation:

Answer: range is 10 hope it helps

Step-by-step explanation: