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2 months ago

Guest #163

2 months ago

P(ace card) = 4/52 = 1/13

Expected number of aces in a single hand of cards = 1/13 x 13 = 1

**Answer: 1 ace card**

Expected number of aces in a single hand of cards = 1/13 x 13 = 1

Guest #164

2 months ago

One ace card is the answer

Question

Jacob drove from town a to town b at an average rate of x miles per hour, then returned along the same route at y miles per hour. if he then drove back to town b at z miles per hour along the same route, what was jacob's average rate of speed for the entire trip, in miles per hour?

Solution 1

The answer is 1,000 miles

Question

1. Discuss the differences between the measurement of the surface area and the measurement of the volume of a right rectangular prism. Include the following topics in your discussion. (a) Description of regions that are measured (b) Units for each type of measure and why the units are different (c) Examples of when you would want to measure for each type of measure

Solution 1

Surface area=area needed to wrap a box

volume=amount of space in the box

surface area=2hl+2hw+2wl=2(hl+hw+wl)

volume=hlw

h=height

l=legnth

w=width

a. surface area is the outside area. lets say you have a cardboard cube and cut it on all the corners and edges so you ended up with 6 squares, the total areas of those squares is the surface area of the cube

volume is how much stuff can be put into the cube, we measure how many 1 by 1 by 1 cubes can fit into the object or how much water can fit in the cube

b. surface area is 2 dimentional since it is area and can be folded flat so the units would be square feet or square inches (ft^2, in^2)

volume is 3 dimentional since it is legnth width and height so it would be cubic foot, cubic inch (in^3, ft^3)

c. surface area=wrapping paper, wrapping stuff, painting an object

volume=how much water can fit in pool, how much punch to put in the jar to fill it up,Â which water bottle to bring so you have enough water

volume=amount of space in the box

surface area=2hl+2hw+2wl=2(hl+hw+wl)

volume=hlw

h=height

l=legnth

w=width

a. surface area is the outside area. lets say you have a cardboard cube and cut it on all the corners and edges so you ended up with 6 squares, the total areas of those squares is the surface area of the cube

volume is how much stuff can be put into the cube, we measure how many 1 by 1 by 1 cubes can fit into the object or how much water can fit in the cube

b. surface area is 2 dimentional since it is area and can be folded flat so the units would be square feet or square inches (ft^2, in^2)

volume is 3 dimentional since it is legnth width and height so it would be cubic foot, cubic inch (in^3, ft^3)

c. surface area=wrapping paper, wrapping stuff, painting an object

volume=how much water can fit in pool, how much punch to put in the jar to fill it up,Â which water bottle to bring so you have enough water

Solution 2

surface area=area needed to wrap a box

volume=amount of space in the box

surface area=2hl+2hw+2wl=2(hl+hw+wl)

volume=hlw

h=height

l=legnth

w=width

a. surface area is the outside area. lets say you have a cardboard cube and cut it on all the corners and edges so you ended up with 6 squares, the total areas of those squares is the surface area of the cube

volume is how much stuff can be put into the cube, we measure how many 1 by 1 by 1 cubes can fit into the object or how much water can fit in the cube

b. surface area is 2 dimentional since it is area and can be folded flat so the units would be square feet or square inches (ft^2, in^2)

volume is 3 dimentional since it is legnth width and height so it would be cubic foot, cubic inch (in^3, ft^3)

c. surface area=wrapping paper, wrapping stuff, painting an object

volume=how much water can fit in pool, how much punch to put in the jar to fill it up, Â which water bottle to bring so you have enough water

Question

Part A: Factor 5x2b2 + 14xb2 âˆ’ 3b2. Show your work. Part B: Factor x2 âˆ’ 18x + 81. Show your work.
Part C: Factor x2 âˆ’ 121. Show your work.

Solution 1

Â

Â 5x2b2 + 14xb2 - 3b2

Â Rewriting we have:

Â b2 (5x2 + 14x - 3)

Â

Â x2 - 18x + 81

Â Rewriting we have:

Â (x-9) (x-9)

Â

Â

Â

Â x2 - 121

Â Rewriting we have:

Â

Question

He probability of choosing a vowel (a, e, i, o, or u) from a deck of cards containing the 26 letters of the alphabet is shown below. what is the probability of choosing the letters a and e one after the other without replacement?

Solution 1

The probability is 1/650.

There is 1 a out of 26 letters; P(a) = 1/26

There is 1 e out of 26 letters; however, since it comes after drawing the a and is done without replacement, it is out of 25: 1/25

Together, their probabilities are 1/26(1/25) = 1/650

There is 1 a out of 26 letters; P(a) = 1/26

There is 1 e out of 26 letters; however, since it comes after drawing the a and is done without replacement, it is out of 25: 1/25

Together, their probabilities are 1/26(1/25) = 1/650

Question

A pair of fair dice is rolled once. suppose that you lose â€‹$ 8 if the dice sum to 3 and win â€‹$ 13 if the dice sum to 10 or 12. how much should you win or lose if any other number turns up in order for the game to beâ€‹ fair?

Solution 1

You should lose $1.20 for any other outcome to make it a fair game.

There are 2 ways to get a sum of 3 out of 36 outcomes; this probability is 2/36.

There are 4 ways to get a sum of 10 or 12 out of 36 outcomes; this probability is 4/36.

There are 36-(2+4) = 36-6 = 30 other outcomes out of 36; this probability is 30/36.

We lose $8 if we get a sum of 3; this expected value is -8(2/36) = -16/36.

We win $13 if we get a sum of 10 or 12; this expected value is 13(4/36) = 52/36.

Using x as the amount we win or lose for the other outcomes, the expected value is 30x/36.

In order to be a fair game, the amount we win and/or lose should come outto( $0 total.

Together we have the equation

-16/36+52/36+30x/36 = 0

Adding the fractions, we have

(-16+52+30x)/36 = 0

(30x+36)/36 = 0

Multiplying both sides by 36,

30x+36=0*36

30x+36=0

Subtracting 36 from both sides,

30x+36-36=0-36

30x=-36

Dividing both sides by 30,

30x/30 = -36/30

x=-36/30 = -1.2

Thus we should lose $1.20 for any other roll.

There are 2 ways to get a sum of 3 out of 36 outcomes; this probability is 2/36.

There are 4 ways to get a sum of 10 or 12 out of 36 outcomes; this probability is 4/36.

There are 36-(2+4) = 36-6 = 30 other outcomes out of 36; this probability is 30/36.

We lose $8 if we get a sum of 3; this expected value is -8(2/36) = -16/36.

We win $13 if we get a sum of 10 or 12; this expected value is 13(4/36) = 52/36.

Using x as the amount we win or lose for the other outcomes, the expected value is 30x/36.

In order to be a fair game, the amount we win and/or lose should come outto( $0 total.

Together we have the equation

-16/36+52/36+30x/36 = 0

Adding the fractions, we have

(-16+52+30x)/36 = 0

(30x+36)/36 = 0

Multiplying both sides by 36,

30x+36=0*36

30x+36=0

Subtracting 36 from both sides,

30x+36-36=0-36

30x=-36

Dividing both sides by 30,

30x/30 = -36/30

x=-36/30 = -1.2

Thus we should lose $1.20 for any other roll.

Question

A quality control expert randomly samples 60 pairs of sunglasses and finds 5 defective pairs. predict how many defective pairs will be in a shipment of 420 sunglasses.

Solution 1

For this case the first thing you should do is find the percentage of sunglasses that are defective.

For this, we make the following rule of three:

60 pairs -------------------> 100%

5 pairs ---------------------> x

From here, we clear the value of x.

We have then:

We now look for the amount of sunglasses that may come with defects.

We have then:

Rounding to the nearest whole number:

**Answer: **

**About 35 defective pairs will be in a shipment of 420 sunglasses**

Solution 2

420/60=7

7*5=35 sunglasses

7*5=35 sunglasses

Question

If a storage tank that measures 12 feet by 9 feet by 8 feet is designed to store gas that costs $1.82 per cubic foot, what does it cost to fill the tank to one-half of its capacity?

Solution 1

For this case, the first thing to do is find the volume of the tank.

Â We have then:

Â V = (12) * (9) * (8)

Â V = 864 feet ^ 3

Â Then, the cost of filling half the tank is given by:

Â C = (1/2) * (1.82) * (864)

Â C = 786.24 $

Â**Answer:**

Â**It costs to fill the tank to one-half of its capacity about:**

Â**C = 786.24 $**

Â We have then:

Â V = (12) * (9) * (8)

Â V = 864 feet ^ 3

Â Then, the cost of filling half the tank is given by:

Â C = (1/2) * (1.82) * (864)

Â C = 786.24 $

Â

Â

Â

Question

I have milk that contains 1 percent fat and milk that contains 4 percent fat. a customer wants a double latte made with 1/3 of a pint of 2 percent milk. how much of each type of milk should i use ?

Solution 1

The **double lathe milk **with 2 percent fat **concentration**, is made by

considering the concentration and amount of each **constituent**.

The **amount** of each type of **milk **to be used in the pint of **double lathe**

are;

- pint of the 1 percent fat milk and Â pint of the 4 percent
**fat milk**.

**Reasons**:

Let *x* **represent the amount **of the milk that contains 1 percent fat in the

volume of the 2 percent fat milk.

Therefore, we have;

The amount of the **4 percent fat milk** to be used =

Therefore;

4 - 9Â·x = 2

4 - 2 = 9Â·x

The amount of the **1 percent fat milk** to be used for the double lathe, x =

of a pint.

The amount of the 4 percent fat milk to be used for the double lathe =

Therefore;

The mount of the **4 percent fat milk** =

The amount of the 4 percent **fat milk** to be used for the double **lathe **=

pint.

Learn more here:

Solution 2

You should use 2/9 of a pint of the 1% milk and 1/9 of a pint of the 4% milk.

Let x be the amount of 1% milk used.Â 1% = 1/100 = 0.01; this gives us 0.01x to represent this.

We know that we will use the 4% milk to make up the rest of the 1/3 pint; this gives us 0.04(1/3-x).

Together, they will make 1/3 pint of 2% milk, or 0.02(1/3)

This gives us the equationÂ

0.01x+0.04(1/3-x) = 0.02(1/3)

Multiplying, we have

0.01x+0.04/3-0.04x = 0.02/3

We can multiply everything by 3 to eliminate the fractions:

0.01x*3 + 0.04 - 0.04x*3 = 0.02

0.03x + 0.04 - 0.12x = 0.02

Combining like terms, we have

-0.09x + 0.04 = 0.02

Subtract 0.04 from both sides:

-0.09x + 0.04 - 0.04 = 0.02 - 0.04

-0.09x = -0.02

Divide both sides by -0.09:

-0.09x/-0.09 = -0.02/-0.09

This gives us x = 2/9, so we will use 2/9 of a pint of the 1% milk.

1/3 - 2/9 = 3/9 - 2/9 = 1/9; we will use 1/9 of a pint of the 4% milk.

Let x be the amount of 1% milk used.Â 1% = 1/100 = 0.01; this gives us 0.01x to represent this.

We know that we will use the 4% milk to make up the rest of the 1/3 pint; this gives us 0.04(1/3-x).

Together, they will make 1/3 pint of 2% milk, or 0.02(1/3)

This gives us the equationÂ

0.01x+0.04(1/3-x) = 0.02(1/3)

Multiplying, we have

0.01x+0.04/3-0.04x = 0.02/3

We can multiply everything by 3 to eliminate the fractions:

0.01x*3 + 0.04 - 0.04x*3 = 0.02

0.03x + 0.04 - 0.12x = 0.02

Combining like terms, we have

-0.09x + 0.04 = 0.02

Subtract 0.04 from both sides:

-0.09x + 0.04 - 0.04 = 0.02 - 0.04

-0.09x = -0.02

Divide both sides by -0.09:

-0.09x/-0.09 = -0.02/-0.09

This gives us x = 2/9, so we will use 2/9 of a pint of the 1% milk.

1/3 - 2/9 = 3/9 - 2/9 = 1/9; we will use 1/9 of a pint of the 4% milk.

Question

An electrician can wire a house in 20 hours. if she works with an apprentice, the same job can be completed in 12 hours. how long would it take the apprentice, working alone, to wire the house?

Solution 1

We know that

An electrician can wire a house in ------------> 20 hours

so

100%----------------> 20 hours

Â X-------------------> 12 hour

x=12*100/20----> x=60%

that meansÂ

the apprentice in 12 hours complete the (100-60)----> 40%

the apprentice in 12 hours complete -------> 40%

x hours------------------------------------> 100%

x=100*12/40-----> x=30 hours

**the answer is**

**30 hours**

An electrician can wire a house in ------------> 20 hours

so

100%----------------> 20 hours

Â X-------------------> 12 hour

x=12*100/20----> x=60%

that meansÂ

the apprentice in 12 hours complete the (100-60)----> 40%

the apprentice in 12 hours complete -------> 40%

x hours------------------------------------> 100%

x=100*12/40-----> x=30 hours

Question

A man has 25 25 coins in his pocket, all of which are dimes and quarters. if the total value of his change is $ 4.45 $4.45, how many dimes and how many quarters does he have?

Solution 1

If all were dimes, the value would be $2.50. The man has $1.95 more than that amount. Trading a dime for a quarter increases the value by $0.15, so there must be

Â $1.95/$0.15 = 13

quarters.

The man has 12 dimes and 13 quarters.

_____

Check:

Â 12*$0.10 +13*$0.25 = $1.20 +3.25 = $4.45 . . . (answer checks OK)

Â $1.95/$0.15 = 13

quarters.

The man has 12 dimes and 13 quarters.

_____

Check:

Â 12*$0.10 +13*$0.25 = $1.20 +3.25 = $4.45 . . . (answer checks OK)

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