Two friends, rachel and joey, enjoy baking bread and making apple pies. rachel takes two hours to bake 1 loaf of bread and one hour to make 1 pie. joey takes four hours to bake 1 loaf of bread and four hours to make 1 pie. what is rachel's opportunity cost of baking 1 loaf of bread?
a. 1 loaf of bread
b. 2 pies
c. 1/2 loaf of bread
d. 1 pie
e. 4 pies

The amount that the woman should pay to play the game is $1.23. Computed using the expected return and the probability of an event.

The probability of an event is the ratio of the number of favorable outcomes to the event, to the total number of possible outcomes in the experiment.

In the question, we are given that in a gambling game, a woman is paid $3 if she draws a jack or a queen and $5 if she draws a king or an ace from an ordinary deck of 52 playing cards. If she draws any other card, she loses.

We are asked the amount the woman should pay to play the game if it is fair.

The amount that the woman should pay to play the game is her expected return from the game.

Her expected return can be shown as E(X), where X represents all possible returns, which is calculated as:

E(X) = ∑ x.P(x), where P(x) is the probability of x.

The values of x can be:

3 when she draws a jack or a queen,

5 when she draws a king or an ace, and

0 when she draws any other card.

The probabilities of drawing a:-

The total number of possible outcomes remains constant throughout as 52.

Jack or a queen:

Number of favorable outcomes = 8 {4 jacks + 4 queens}.

Thus, the probability = 8/52 = 2/13.

King or an ace:

Number of favorable outcomes = 8 {4 kings + 4 ace}.

Thus, the probability = 8/52 = 2/13.

Any other card:

Number of favorable outcomes = 36 {All remaining cards, that is, 52 - 8 - 8 = 36}.

Thus, the probability = 36/52 = 9/13.

Thus, the expected return:

E(X) = ∑ x.P(x),

or, E(X) = 0.(9/13) + 3.(2/13) + 5(2/13),

or, E(X) = 0 + 6/13 + 10/13,

or, E(X) = 16/13 = 1.23.

Thus, the amount that the woman should pay to play the game is $1.23. Computed using the expected return and the probability of an event.

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The car speed in miles per minute is 0.8 miles per minute and the car will travel 1.6 miles in 2 minutes.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

The speed of the car = 48 miles per hour

Speed in miles per minute = 48/60 = 0.8 miles per minute

Time = 2 minutes

Speed = 0.8 miles per minute

Distance = 0.8×2 = 1.6 miles

Thus, the car speed in miles per minute is 0.8 miles per minute and the car will travel 1.6 miles in 2 minutes.

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divide 322 by 2 and then subtract the width

322 /2 = 161

161-72 = 89

 length is 89 feet

57 / 3 =19

18 + 19 +20 = 57

 largest number is 20

Answer:

20

Step-by-step explanation:

Final answer:

To meet the client's investment goals with an investment return of $1,620 on a total of $26,000, the client should invest $8,000 in AAA bonds, $14,000 in A bonds, and $4,000 in B bonds. This is derived from setting up and solving a system of linear equations based on the conditions provided.

Explanation:

Part A: Investment Calculations

To solve for the amount to invest in each type of bond, we can set up a system of equations based on the given conditions. Let x be the amount invested in AAA bonds, y be the amount invested in A bonds, and z be the amount invested in B bonds. We are told that the client wants to invest twice as much in AAA bonds as in B bonds, which gives us the equation x = 2z. The total investment is $26,000, so we have x + y + z = $26,000. The desired annual return is $1,620, and this gives us another equation based on the yields: 0.04x + 0.06y + 0.11z = $1,620.

By solving this system of equations, we can find the amounts to invest in each bond.

From x = 2z, we can substitute for x in the other equations.

The total investment equation becomes 2z + y + z = $26,000, simplifying to 3z + y = $26,000.

The return equation becomes 0.08z + 0.06y + 0.11z = $1,620, simplifying to 0.19z + 0.06y = $1,620.

We can now solve these two new equations for y and z, and then find x using x = 2z.

After solving, we get:

z (B bonds) = $4,000

x (AAA bonds) = 2z = $8,000

y (A bonds) = $26,000 - x - z = $14,000

Part B: Investment Calculations with Updated Values

The process for part B is similar, but with the updated total investment of $38,000 and a desired return of $2,360. The equations are adjusted accordingly, and after solving, we would get the new investment amounts for AAA, A, and B bonds.

The client should invest $8,000 in AAA bonds, $14,000 in A bonds, and $4,000 in B bonds for the conditions in part A.

LaToya originally had 300 basketball cards. She gave away 3/4 of her collection, keeping 1/4 which is 75 cards. By solving the equation 1/4 x = 75, we find that x equals 300.

LaToya originally had a certain number of basketball cards. She gave half of them to Aaron and a fourth of them to her brother, leaving her with 75 cards. To find out how many cards she started with, let's define the total number of cards as x. Given that half and a fourth were given away, this means that 3/4 of x has been given to others, leaving her with 1/4 of her original number of cards.

Now, we can set up the equation: 1/4 x = 75. To solve for x, multiply both sides of the equation by 4, giving us x = 75 * 4, which equals 300. Therefore, LaToya originally had 300 basketball cards.

To find the number of cards LaToya started with, we can set up an equation based on the information given and solve for the unknown value.

To find the number of cards LaToya started with, we need to work backwards from the information given. We know that she has 75 cards left after giving half to her friends and a fourth to her brother. Let's assume that the number of cards she started with is 'x'.

If she gave half to her friends, that means she gave x/2 cards to her friends. Then, if she gave a fourth to her brother, she gave x/4 cards to her brother. So the total number of cards given away is x/2 + x/4 = 3x/4.

Since she has 75 cards left, we can set up the equation: x - 3x/4 = 75. Solving this equation will give us the value of x, which represents the number of cards LaToya started with.

Answer:

Equation is [tex]-8x+4y-12=0[/tex]

Step-by-step explanation:

An equation is a mathematical statement that two things are equal .

A system of equations is a set of two or more equations consisting of same unknowns.

Two equations [tex]a_1x+b_1y+c_1=0\,,\,a_2x+b_2y+c_2=0[/tex] have unique solution if [tex]\frac{a_1}{a_2}\neq \frac{b_1}{b_2}[/tex]

infinite solution if [tex]\frac{a_1}{a_2}= \frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]

no solution if [tex]\frac{a_1}{a_2}= \frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex]

Here, given: [tex]-4x+2y=6[/tex]

We can write this equation as [tex]-4x+2y-6=0[/tex]

Take another equation as [tex]-8x+4y-12=0[/tex]

Here, [tex]a_1=-4\,,\,a_2=-8\,,\,b_1=2\,,\,b_2=4\,,\,c_1=-6\,,\,c_2=-12[/tex]

[tex]\frac{a_1}{a_2}=\frac{-4}{-8}=\frac{1}{2}\\\frac{b_1}{b_2}=\frac{2}{4}=\frac{1}{2}\\\frac{c_1}{c_2}=\frac{-6}{-12}=\frac{1}{2}[/tex]

such that [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}[/tex]

Reggie Jackson hit 5 home runs in 6 games sos he hit 5/6 = 0.833 home runs per game

lou gehrig hit 4 home runs in 4 games so he hit 4/4 = 1 home run per game

0.833 is less than 1 so Reggie Jackson hit fewer home runs per game

The current population of rabbits in the forest can be found by substituting t = 0 into the given formula P = 12,000 + 1000(t+1).

To find the number of rabbits currently in the forest, we can substitute the value of t = 0 into the given formula. The formula P = 12,000 + 1000(t+1) represents the population of rabbits in the forest at any given year, where t is the number of years from the present. Since we want to find the current population, we substitute t = 0:

P = 12,000 + 1000(0+1)

P = 12,000 + 1000(1)

P = 12,000 + 1000

P = 13,000

Therefore, there are currently 13,000 rabbits in the forest.

Answer:

There are so many little things that go into organic farming and each of them adds additional costs.

Some of these additional costs are listed in the article located here.

Use the data table at the end of the document to answer the questions.

Which cost category in the table shows an example of direct variation?  

Weed-Hand

The total cost for office expenses to run the organic strawberry farm varies directly with the number of months it is used. Which equation represents this scenario?

y = 63x

What would be the total cost for office expenses for 24 months?

$1,512.00

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54-36 =18

 they can make 18 bouquets

54/18 =3

36/18 =2

18 bouquets with 3 red and 2 white roses each

Answer:

3

GCF of 54 and 36 = 18

so, 18 bouquets

then,

54 red roses ÷ 18 = 3 red roses in each bouquet

The two numbers are 7 and 9, which are determined by setting up an algebraic equation based on the information that one number is 2 more than the other and the difference between their squares is 32.

The question involves finding two numbers where one number is 2 more than another and the difference between their squares is 32. To solve this problem, we denote the first number as ‘x’. Therefore, the second number will be '‘x+2’, as it is given to be 2 more than the first number. Next, we set up an equation based on the provided information that the difference between their squares is 32: ‘(x+2)² - x² = 32’.

Expanding the squared terms, we get ‘x² + 4x + 4 - x² = 32’. After simplifying the equation by canceling out ‘x²’ from both sides and subtracting 4 from both sides, we get ‘4x = 28’. Dividing both sides by 4 gives us ‘x = 7’. Thus, the first number is 7, and the second number is 7 + 2, which is 9.

The two numbers in question are 7 and 9, and they meet the criteria given in the problem statement.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{5x^3 + 2}\\\mathsf{= 5(-1)^3+2}\\\\\mathsf{(-1)^3}\\\mathsf{= -1\times-1\times-1}\\\mathsf{=1\times-1}\\\mathsf{= \bf -1}\\\\\mathsf{= 5(-1) + 2}\\\\\mathsf{5(-1)}\\\mathsf{= \bf -5}\\\\\mathsf{= -5 + 2}\\\mathsf{=\bf -3}\\\\\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \bf -3}}}\huge\checkmark\\\\\\\\\huge\text{Good luck on your assignment \& enjoy your day!}\\\\\\\frak{Amphitrite1040:)}[/tex]

The limit of the given expression is undefined.

To find the limit of lim  θ→0  cos(4θ) - 1 / sin(7θ), we can simplify the expression first. Using the identity cos(2θ) = 2cos²θ - 1, we can rewrite the numerator as 2(cos²(2θ) - 1). The denominator, sin(7θ), can be rewritten as sin(2θ + 5θ). By applying the sum-to-product identities, we get sin(2θ)cos(5θ) + cos(2θ)sin(5θ), or cos(5θ)sin(2θ) + cos(2θ)sin(5θ).

Now, if we multiply both numerator and denominator by 1/sin(2θ)cos(5θ), we can simplify the expression further:

lim  θ→0 (2cos²(2θ) - 1) / (cos(5θ)sin(2θ) + cos(2θ)sin(5θ)) = lim  θ→0 (2cos(2θ) - 1/sin(2θ)) / (cos(5θ) + cos(2θ)tan(5θ)).

Now, we can substitute θ = 0 into the expression. Since cos(0) = 1 and sin(0) = 0, the denominator becomes cos(5(0)) + cos(2(0))tan(5(0)) = cos(0) + cos(0)tan(0) = 1 + 1(0) = 1. Thus, the limit is:

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