Harrison paid $36.50 for 5 cans of yellow tennis balls and 3 cans of white ones. Beverly paid $50.25 for 7 cans of yellow tennis balls and 4 cans of white ones. Assume they both paid the same prices, and then answer the questions below.

a how much did each can of yellow tennis balls cost
b how much did each can of white tennis balls cost

in the Golden Balls game, there is only one pure strategy Nash equilibrium, which is (Split, Split).

In the Golden Balls game, there are two players, Player 1 and Player 2. Each player can choose to either "Split" or "Steal." The payoffs for each possible combination of actions are as follows:

If both players choose Split, they both receive a payoff of 50.

If Player 1 chooses Steal and Player 2 chooses Split, Player 1 receives 100, and Player 2 receives 0.

If Player 1 chooses Split and Player 2 chooses Steal, Player 1 receives 0, and Player 2 receives 100.

If both players choose Steal, they both receive a payoff of 0.

To find all the pure strategy Nash equilibria, we need to identify any strategies where neither player has an incentive to deviate unilaterally.

Pure Strategy Nash Equilibria:

(Split, Split): This is a pure strategy Nash equilibrium because if both players choose Split, neither player can improve their payoff by unilaterally changing their strategy to Steal.

Now let's consider mixed strategy Nash equilibria, where players randomize between their available strategies.

Mixed Strategy Nash Equilibrium:

To find the mixed strategy Nash equilibrium, we need to examine whether there exists a probability distribution over strategies that maximizes the expected payoff for each player, given the other player's strategy.

In this case, there is no mixed strategy Nash equilibrium since Player 2's expected payoff from choosing Split is always lower than the expected payoff from choosing Steal, regardless of the probabilities assigned to each strategy by Player 1. Similarly, Player 1's expected payoff from choosing Split is always lower than the expected payoff from choosing Steal, regardless of the probabilities assigned to each strategy by Player 2.

Therefore, in the Golden Balls game, there is only one pure strategy Nash equilibrium, which is (Split, Split).

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To find the values of z that make the product with the complex number 5-6i a real number, we need to consider the imaginary part of the product.

The product of z and 5-6i can be written as:

z * (5 - 6i)

Expanding this expression, we get:

5z - 6zi

For the product to be a real number, the imaginary part (-6zi) must be equal to zero. This means that the coefficient of the imaginary unit i, which is -6z, must be zero.

Setting -6z = 0, we find:

z = 0

So, one possible nonzero value of z is 0.

However, since we are looking for nonzero values of z, we need to find another value that satisfies the condition.

Let's consider the equation for the imaginary part:

-6z = 0

Dividing both sides of the equation by -6, we have:

z = 0/(-6)

z = 0

Again, we find z = 0, which is not a nonzero value.

Therefore, there are no other nonzero values of z that make the product with the complex number 5-6i a real number. The only value that satisfies the condition is z = 0.

The point-slope form is y - 4 = -1(x - 8).

Find the equation for the line that passes through the points (8, 4) and (9, 3) in point-slope form.

Find the slope (m) of the line using the slope formula,

m = (y2 - y1) / (x2 - x1).

Using the given points (8, 4) as (x1, y1) and (9, 3) as (x2, y2):

m = (3 - 4) / (9 - 8) = (-1) / (1) = -1

Use the point-slope form equation, y - y1 = m(x - x1), and one of the given points (e.g., (8, 4)).

y - 4 = -1(x - 8)

The equation for the line that passes through the points (8, 4) and (9, 3) in point-slope form is y - 4 = -1(x - 8).

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The Laplace transform table contains properties and formulas for common transforms, as well as the inverse Laplace transform and the shift theorem. It also includes properties such as linearity, scaling, and time shifting.

The Laplace transform table is an important tool for solving linear differential equations. It contains information about common transformations and their associated formulas, as well as the inverse Laplace transform and the shift theorem. The table also includes properties such as linearity, scaling, and time shifting. Linearity states that if a function f(t) is a linear combination of two functions f1(t) and f2(t), then its Laplace transform F(s) is the sum of the Laplace transforms of f1(t) and f2(t). Scaling states that if a function f(t) is multiplied by constant k, then its Laplace transform F(s) is divided by k. Time shifting states that if a function f(t) is shifted by x units in time, then its Laplace transform F(s) is multiplied by \(e^(-sx)\). These properties can be used to simplify Laplace transforms and to solve linear differential equations. The Laplace transform table is a useful tool for engineers and physicists who use linear differential equations in their work.

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Answer:

-8,-6

Step-by-step explanation:

Answer:

The mean is 11

Step-by-step explanation:

To find the mean, add up all the scores and divide by the number of scores

( 5+9+11+16+18+7)/6 =

66/6

11

Answer:

11

Step-by-step explanation:

5 + 9 + 11 + 16 + 18 + 7 = 66

66 / 6 = 11

Answer:

Fractional Expression for how much each person pays = (64.04/4)

Each person pays $16.01.

Step-by-step explanation:

Complete Question

Write an expression using fractions to show how to determine the amount that each person will pay. Then calculate each person's contributions showing all steps in long division.

The total of the bill is $64.04 and there are 4 people splitting the bill.

Solution

Total amount to be shared equally by 4 persons = $64.04

Fractional Expression for how much each person pays = (64.04/4)

Long division method to do this division.

     16.01  

4 | 64.04

      4  

    24

    24

      00

    0

    04

      4

    0

Each person pays $16.01.

Hope this Helps!!!

Answer:

\(\boxed {x = \frac{8}{3}}\)

Step-by-step explanation:

Solve for the value of \(x\):

\(x - \frac{17}{3} = -3\)

-Add both sides by \(\frac{17}{3}\) and convert \(-3\) to a fraction \(-\frac{9}{3}\):

\(x - \frac{17}{3} + \frac{17}{3} = -3 + \frac{17}{3}\)

\(x = -\frac{9}{3} + \frac{17}{3}\)

-Since both \(-\frac{9}{3}\) and \(\frac{17}{3}\) have the same denominator, then you would add the numerators:

\(x = \frac{-9 + 17}{3}\)

\(\boxed {x = \frac{8}{3}}\)

Therefore, the value of \(x\) is \(\frac{8}{3}\).

The average rate of change per hour in the temperature is 0.83 degrees.

To find the average rate of change per hour, we need to divide the total change in temperature by the number of hours over which the temperature changed.

The temperature rose by 5 degrees from 6:00 am to 12:00 pm, which is a period of 6 hours.

Therefore, the average rate of change per hour can be calculated as follows:

average rate of change per hour = total change in temperature / number of hours

So, we have

average rate of change per hour = 5 degrees / 6 hours

average rate of change per hour = 0.83 degrees/hour (rounded to two decimal places)

So, the average rate of change per hour is 0.83 degrees.

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Answer:

\(\displaystyle f'(x) = -12x^2 + 4x\)

General Formulas and Concepts:

Algebra I

Terms/Coefficients

Calculus

Limits

Differentiation

The definition of a derivative is the slope of the tangent line:                       \(\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}\)

Step-by-step explanation:

Step 1: Define

Identify.

\(\displaystyle f(x) = -4x^3 + 2x^2\)

Step 2: Differentiate

∴ the derivative of the given function will be equal to -12x² + 4x.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

$13,400

Step-by-step explanation:

Simple Interest = principal × rate × time

principal= $9000

Rate= 12/100=0•12

Time=5years

Simple interest =PRT

= 9000× 0•12 × 5

= 5400

Total amount to be paid = 9000 + 5400

= $13400

Answer:

y = -2x + 16

Step-by-step explanation:

the way to solve this is to use the formula to find the slope

m = (y2 - y1) / (x2 - x1)

(-2,20) (5,6)

(20-6) / (-2 - 5)

14/ -7

-2 = m

then you can substitute m and one of the given points into the y = mx + b to find b

y = mx + b

20 = (-2)-2 + b

20 = 4 + b

16 = b

putting it all together, you get y = -2x + 16

To determine an orthonormal basis for the subspace of p2 spanned by the polynomials f(x), g(x), and h(x), we can use the Gram-Schmidt process. This process allows us to transform a set of linearly independent vectors into an orthonormal set.

Let's go through the steps of the Gram-Schmidt process for this specific problem Start with the first polynomial, f(x), as our first vector. Normalize f(x) by dividing it by its magnitude (or norm). This will give us our first orthonormal vector, let's call it u1. Next, we move on to g(x), the second polynomial. Subtract the projection of g(x) onto u1 from g(x) itself. The projection of g(x) onto u1 is found by taking the dot product of g(x) and u1, and then multiplying u1 by this dot product. Subtracting this projection from g(x) gives us a new vector, which we'll call v2.

Normalize v2 by dividing it by its magnitude. This will give us our second orthonormal vector, u2. Finally, we move on to h(x), the third polynomial. Again, we subtract the projections of h(x) onto u1 and u2 from h(x) itself. The projection of h(x) onto u1 and u2 is found by taking the dot product of h(x) and each u vector, and then multiplying the respective u vector by these dot products. Subtracting these projections from h(x) gives us a new vector, which we'll call v3. It's important to note that the Gram-Schmidt process can be applied to any set of linearly independent vectors to obtain an orthonormal basis. The resulting orthonormal basis is useful in various areas of mathematics, such as solving systems of linear equations and diagonalizing matrices.

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Answer: 3/52

Step-by-step explanation:

You want to pick a diamond jack, diamond queen or diamond king

There are only 3 of those so

P(DJ or DQ or DK) = 3/52        There are 3 of those out of 52 total

Answer:

Step-by-step explanation:

B

Answer:

Its would be A

Step-by-step explanation:

4 X 64=256

Hope this helped. If you check its simple math really! :))

For the 5.5% coupon corporate bond, the coupon payment would be $55 per year. For the 6.45% coupon treasury note, the coupon payment would be $64.50 per year.

Calculations using percentages show how much a given number contributes to the total. It is computed by dividing the number by the sum and multiplying by 100. It is denoted by the sign "%." For example, if a basket contains ten apples, three of which are red, the proportion of red apples in the basket is 30% (3/10 x 100). In a wide range of disciplines, including business, statistics, and education, percentage is often utilized. Calculating interest rates, taxes, and other financial activities in the finance industry annually frequently uses percentages. The frequency of events or the likelihood of a certain outcome are both measured using this method in statistics. Calculating grades and evaluating a student's overall performance are both done using this in education.

How to solve?

For the 5.5% coupon corporate bond, the coupon payment would be 5.5% of $1,000 = $55 per year.

For the 6.45% coupon treasury note, the coupon payment would be 6.45% of $1,000 = $64.50 per year.

For the corporate zero-coupon bond maturing in 10 years, there are no coupon payments. The bond will only make a payment of $1,000 at maturity.

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The number of pints of water in the bucket is given by the formula P(t) = t + 5, where P(t) is the number of pints of water in the bucket, and t is the number of seconds Christopher ran the hose into the bucket. The slope of the formula P(t) = t + 5 represents the rate of change of water level in the bucket with respect to time.

The formula P(t) = t + 5, where P(t) is the number of pints of water in the bucket, and t is the number of seconds Christopher ran the hose into the bucket. The formula shows that the number of pints of water in the bucket is increasing linearly with respect to time. That is, for every one-second increment in time, Christopher puts one more pint of water in the bucket.

The formula, therefore, describes a linear relationship between the volume of water in the bucket and the time Christopher spends running the hose. It means that the slope of the formula represents the rate at which the water level in the bucket changes with respect to time.

The slope is 1 or 1/1, which means that the water level in the bucket increases at the rate of one pint per second. Therefore, the slope of the formula represents the rate of change of water level in the bucket with respect to time (or the speed of filling of the bucket with water).

Conclusively, the slope of the formula P(t) = t + 5 represents the rate of change of water level in the bucket with respect to time.

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i) The probability of drawing exactly 3 aces is 0.24.

ii) The expected number of aces drawn is approximately 4.62

i) The probability of drawing exactly 3 aces out of 60 cards, with replacement, from a standard deck is given by the binomial probability formula:

(n choose k) * (p^k) * (1-p)^(n-k)

where n is the total number of trials (60), k is the number of successful trials (3), p is the probability of success on a single trial (4/52 or 1/13) and 1-p is the probability of failure on a single trial (48/52 or 12/13).

So the probability of drawing exactly 3 aces is:

(60 choose 3) * (1/13)³ * (12/13)⁵⁷ = 0.24.

ii) The expected number of aces is given by:

n * p = 60 * (1/13) = 4.62.

So the expected number of aces drawn is approximately 4.62.

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Answer:

Loading,please wait...

Step-by-step explanation:

Answer:

4500 miles

Step-by-step explanation:

750 rounded to the nearest hundred is 800. 2,488 rounded to the nearest hundred is 2,500. 155 rounded to the nearest hundred is 200. 1,015 rounded to the nearest hundred is 1,000. So 800+2,500+200+1,000= 4,500

In summary: Sequence 1 has no term out of increasing order. Sequence 2 has the first term out of increasing order at position 2. Sequence 3 has the first term out of increasing order at position 7. Sequence 4 has the first term out of increasing order at position 4. Sequence 5 has the first term out of increasing order at position 3.

1 5 78 99 101 202 400: This sequence is in increasing order throughout, so there is no term that breaks the increasing pattern.

5 2 7 90 85 80 72: The sequence starts with 5, then decreases to 2 (out of increasing order) at position 2.

5 6 9 10 14 21 20: The sequence is increasing until position 6, where it reaches 21. However, the next term, 20, is lower than the previous term, 21 (out of increasing order) at position 7.

3 7 10 9 8 14 17: The sequence starts with 3 and increases until position 3 (10). However, at position 4, the next term, 9, is lower than the previous term, 10 (out of increasing order).

5 77 25 45 22 94 58 99: The sequence is increasing until position 2, where it reaches 77. However, at position 3, the next term, 25, is lower than the previous term, 77 (out of increasing order).

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Answer:

A 5 cups blended peaches for every 3 cups vanilla yogurt

B 8 cups blended peaches for every 5 cups vanilla yogurt

Step-by-step explanation:

Adsila’s recipe for peach frozen yogurt says to mix 3 cups blended peaches for every 2 cups vanilla yogurt. Which of these frozen yogurt recipes has a stronger

peach taste than Adsila’s? Select all that apply.

A 5 cups blended peaches for every 3 cups vanilla yogurt

= 5 : 3

= 5/3

= 1.67

Stronger peach taste

B 8 cups blended peaches for every 5 cups vanilla yogurt

= 8 : 5

= 8/5

= 1.6

Stronger peach taste

C 9 cups blended peaches for every 6 cups vanilla yogurt

= 9 : 6

= 9/6

= 1.5

Equal peach taste

D 10 cups blended peaches for every 8 cups vanilla yogurt

= 10:8

= 10/8

= 1.25

Lesser peace taste

E 14 cups blended peaches for every 10 cups vanilla yogurt

= 14 : 10

= 14/10

= 1.4

Lesser peach taste

Cups of Blended peaches : cups of vanilla yogurt = 3 : 2

= 3/2

= 1.5

All that applies includes:

A 5 cups blended peaches for every 3 cups vanilla yogurt

B 8 cups blended peaches for every 5 cups vanilla yogurt

A/B

Step-by-step explanation:

The formula for the general term of  sequence {1, 0, -1, 0, 1, 0, -1, 0,...} is given by

\(a_{n} = cos\frac{(n-1)\pi }{2}\).

According to the given question.

We have a sequence {1, 0, -1, 0, 1, 0, ...}

Since, we have to find the formula for the general term of the given sequence.

Here, the first term is 1.

Second term is 0.

And the third term is -1.

From the given sequence we can say that all the even term is 0 and other terms are followed by 1 and -1.

Therefore, the formula for the general term of  sequence {1, 0, -1, 0, 1, 0, -1, 0,...} is given by

\(a_{n} = cos\frac{(n-1)\pi }{2}\).

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The time, Lynn worked on her Science project is 1 8/15 hours.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split.

In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

In this situation, she spent 1 1/6 hours writing her English composition and 3/10 hours on her Maths homework.

The time used for science will be the addition of 1 1/6 and 3/10 which will then be subtracted from 3. This will be calculated thus:

= 3 - ( 1 1/6 + 3/10)

= 3 - (1 5/30 + 9/30)

= 3 - 1 14/30

= 1 8/15

Therefore, Lyn used 1 8/15 hours for the science homework.

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Answer:

0 < x ≤ 10 and 0 < y ≤ 20.

Step-by-step explanation:

I did the test and got it right ma bois.

Answer: Its A

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer: 518

Step-by-step explanation: 28(5) + 28(16)

Answer:

It looks like you want the point slope form of a line

y-4 = -2 (x +3)

Step-by-step explanation:

y -\(y_{1}\) = m(x- \(x_{1}\))  You plug in 4 for \(y_{1}\), -2 for m and -3 for\(x_{1}\)

y - 4 =(2(x - -3)  x - -3 is the same at x + 3

y-4 + -2(x + 3)