Answer:
Part a) Alyssa's expectation is equal to $0.33
Part b) Gabriel's expectation is equal to -$0.33
Step-by-step explanation:
we know that
The expected value is the probability of winning multiplied by the value you get when you win, plus the probability of losing multiplied by the value you get when you lose (which is negative as it is a loss).
Part a) Determine Alyssa's expectation
we know that
1) If Alyssa rolls a 1, 2, or 3, Gabriel gives Alyssa $4
The probability is 3/6
so
we have
[tex]\frac{3}{6}(4)=\$2[/tex]
2) If Alyssa rolls a 4, or 5, Gabriel gives Alyssa $1
The probability is 2/6
so
we have
[tex]\frac{2}{6}(1)=\$0.33[/tex]
3) if Alyssa rolls a 6, she gives Gabriel $12
The probability is 1/6
so
we have
[tex]-\frac{1}{6}(12)=-\$2[/tex] ---> is negative because is a loss
therefore
Alyssa's expectation is equal to
[tex]\$2+\$0.33-\$2=\$0.33[/tex]
Part b) Determine Gabriel's expectation
we know that
1) If Alyssa rolls a 1, 2, or 3, Gabriel gives Alyssa $4
Is a loss for Gabriel
The probability is 3/6
so
we have
[tex]-\frac{3}{6}(4)=-\$2[/tex] ---> is negative because is a loss
2) If Alyssa rolls a 4, or 5, Gabriel gives Alyssa $1
Is a loss for Gabriel
The probability is 2/6
so
we have
[tex]-\frac{2}{6}(1)=-\$0.33[/tex] ---> is negative because is a loss
3) if Alyssa rolls a 6, she gives Gabriel $12
Is a win for Gabriel
The probability is 1/6
so
we have
[tex]\frac{1}{6}(12)=\$2[/tex]
therefore
Gabriel's expectation is equal to
[tex]-\$2-\$0.33+\$2=-\$0.33[/tex]
The expected outcomes for both Alyssa and Gabriel from the game are $0. This is calculated using the probabilities of each outcome and their respective gains or losses.
Explanation:In the game between Alyssa and Gabriel, we are to calculate the expected outcomes for both players. To calculate the expectation, we will weigh the possible outcomes ($4, $1, -$12 for Alyssa and -$4, -$1, $12 for Gabriel) by their probabilities.
The dice has six faces, so the probability for each outcome is determined by the number of corresponding faces divided by six. Let's calculate the expectation for both:
Alyssa's expectation: (1/2 * $4) + (1/3 * $1) - (1/6 * $12) = $2 - $2 = $0. Gabriel's expectation: -(1/2 * $4) - (1/3 * $1) + (1/6 * $12) = -$2 + $2 = $0.
So, both Alyssa and Gabriel have an expected gain of $0 from this game.
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In the xy-plane, line h passes through the points
(0,5) and (4,0). Which of the following is an
equation of line h?
A) 4x + 5y = 20
B) 5x + 4y = 20
C) 4x - 5y = 20
D) 5x – 4y = 20
Answer:
5x + 4y = 20
Step-by-step explanation:
(x1,y1) and (x2, y2)
(0, 5) and (4 ,0).
From equation of a line
y2 - y1/x2 - x1 = y - y1/ x - x1
Where x1 = 0, y1 =5 , x2 = 4 , y2 = 0
Imputing values,
0- 5/4-0 = y - 5 / x - 0
-5/4 = y -5/x
Multiply both sides by 4x I. E lcm of 4 and x
4x × -5/4 = y-5/x × 4x
-5x = 4(y - 5)
-5x = 4y - 20
Add 5x to both sides
-5x + 5x = 5x + 4y - 20
5x + 4y - 20 = 0
Add 20 to both sides
5x + 4y - 20 +20 = 0+20
5x + 4y = 20
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Quadrilateral ABCD is an isosceles trapezoid with median EF. Which of the following statements is true?
Select the best answer from the choices provided.
A. EF is parallel to the bases.
B. EF = 2(AB + DC)
C. 1/2EF = AB + DC
D. EF =1/2(AD + CB)
Answer:
The answer is A
Step-by-step explanation:
There is no way to prove any of the others to be true
Final answer:
The median EF in an isosceles trapezoid is parallel to its bases, making option A the correct answer.
Explanation:
The student asked a question related to properties of an isosceles trapezoid and its median. In an isosceles trapezoid, the median is a line segment that connects the midpoints of the non-parallel sides. The properties of a trapezoid's median include that it is parallel to the two bases and that its length is equal to the average of the lengths of the two bases. Therefore, the correct statement from the list provided is that the median EF is parallel to the bases.
For more clarity:
EF is indeed parallel to the bases AB and CD; this corresponds to option A.EF is not twice the sum of the lengths of AB and DC, so option B is incorrect.EF is also not half the sum of the lengths of AB and DC, which means option C is incorrect.The length of EF is not half the sum of the lengths of the non-parallel sides AD and CB, so option D is incorrect.points [50] Amelie's bird cage is shaped like a rectangular prism. The cage has a height of 26 inches and a volume of 7,280 cubic inches. Amelie puts a piece of newspaper on the bottom of the cage. The newspaper fits the bottom of the cage perfectly.
What is the area of the newspaper on the bottom of the cage?
Enter your answer in the box.
Two times the difference of -10 and 4 amounts to -28
Answer:
True
Step-by-step explanation:
We want to determine whether the given statement is true or false.
The difference of -10 and 4 is
[tex] - 10 - 4 = - 14[/tex]
We multiply the result by 2 to obtain;
[tex]2( - 14) = - 28[/tex]
Therefore two times the difference of -10 and 4 amounts to -28 is a true statement.
Everly needs to order stock for her store and wants to order the items that have the greatest probability of having repeat customers. She has to decide between the national brand and the store brand for both cereal and crackers. She has recorded the sale of each type and the probability that a customer bought the same item again. Which should she stock?
Answer:
B) National Brand Cereal and Store Brand Crackers
Step-by-step explanation:
Since she wants to order the items that have the greatest probability of repeat customers she needs to order the items with the larger probability. That is National Brand Cereal and Store Brand Crackers
Answer:
b
Step-by-step explanation:
Find the area of the shape shown below.
Answer:
240 square units
Step-by-step explanation:
Area of shape =area of rectangle + area of triangle
[tex] = 20 \times 10 + \frac{1}{2} \times 20 \times 4 \\ = 200 + 40 \\ = 240 \: {units}^{2} [/tex]
A line with a slope of 3 passes through the points (-3, 4) and (a, -8). What is the value of a?
using the slope formula:
m = y2-y1/x2-x1
3 = -8 - 4/a- -3
3 = -12/a+3
multiply each side by a +3
3a + 9 = -12
move the 9 over by subtraction
3a = -21
divide by 3
a = -7
check it:
3 = -8 - 4/-7 - -3
3 = -12/-4
3 = 3
How do you find an equal ratio for example is 63:27 14:6 a equivalent ratio?
Answer:
Step-by-step explanation:
Find a common denominator or greatest common factor. 63 and 27 are both multiples of 9. When you divide each by 9 you get 7:3. 14 and 6 are both multiples of 2. When you divide each by 2 you get 7:3 again. So these ratios are equivalent.
Start with any set of numbers. Multiply them each by the same factor and the new set will be an equivalent ratio.
Use the ratio table to solve the percent problem.
What percent is 12 out of 20?
Answer:
It would be 60%.
Step-by-step explanation:
To find the answer, you would have to do x/100 = 12/20. You would cross multiply leaving you with 20x=1200 you would then divide by 20. This would leave you with the answer of 60. Therefore, your answer is 60%.
Answer: 60%.
Step-by-step explanation:
From the question, 12 : 20 = x
Let the missing value be x.
12/ 20 x 100/1 = 60%
Therefore 12 out of 20 is 60%.
A taxi cab driver charges a $2.00 initial fee and $1.75 for each mile.
1) Shannon wants to keep her fare under $35. How many miles can she travel in the taxi?
2) Samantha has $70 for her taxi fare. If she plans on traveling 20 miles in the taxi, does she have enough money to cover the fare? Explain your answer.
1. She can travel 18 miles. Subtract 35 - 2 (initial fee) to have 33. divide 33 by 1.75 to get 18.85. To check how much her total would be, use inverse operations. 18.85 * 1.75 = 32.9875. 32.9875 + 2 = 34.9875. It is barely under $35 but still in her budget.
2. 20m * $1.75 = $35. $70 - $35 = $35. Yes, she can cover the fare. Samantha has more than needed. She can afford the taxi fare and still have money left for future use.
Answer:
Step-by-step explanation:
1) Shannon can travel exactly 18 miles.
2) Yes, Samantha has enough money for her taxi. The ride would cost her $37. She would have $33 left over.
Which expressions are equivalent to 7 (negative three-fourths x minus 3)? Select two options
Answer:
The answers are A and E
what is the solution to the equation 5a^2-44=81
Answer:
5
Step-by-step explanation:
[tex]5a^{2} -44=81\\5a^{2} -44+44=81+44\\5a^{2} =125\\\frac{5a^{2} }{5} =\frac{125}{5}\\a^2=25\\\sqrt{25} =x=5[/tex]
The sum of k and 5 is 11
Answer:
j
Step-by-step explanation:
j
Answer:
K=6
Step-by-step explanation:
Subtract 5 from 11
value Rent-A-Car rents a luxury car at a daily rate of $37.25 plus 20 cents per mile. A business person is allotted $110 for car rental each day. How many miles can the business person travel on the $110
Answer:
110- 37.25=72.25
72.25 divided by .20 =361.25
but since you can not drive part of a mile it would be 361 miles in one day.
Step-by-step explanation:
Final answer:
After subtracting the fixed daily rental rate from the daily budget and dividing the remainder by the cost per mile, it is calculated that the business person can travel 363.75 miles with the $110 budget.
Explanation:
To calculate how many miles the business person can travel on the $110 budget using the daily car rental rate provided, we can set up an equation based on the cost structure of Value Rent-A-Car. The rental cost consists of a fixed daily rate plus a variable cost per mile.
The fixed daily rate is $37.25, and the cost per mile is $0.20 (20 cents). With a daily budget of $110, we first subtract the fixed rate from the daily budget to find out how much money is left for the variable cost per mile:
Daily budget for miles = Total daily budget - Fixed daily rate
Daily budget for miles = $110 - $37.25
Daily budget for miles = $72.75
Now, we divide the money left for miles by the cost per mile to find the number of miles the business person can travel:
Number of miles = Daily budget for miles / Cost per mile
Number of miles = $72.75 / $0.20
Number of miles = 363.75 miles
The business person can travel 363.75 miles on the daily budget of $110, given the cost structure of the car rental.
Which statement is FALSE for this situation?
A) A linear function represents Company A's payments.
B) An exponential function represents Company B's payments.
C) Company A's payments grow by a factor of 2.
D) Company B's payments grow by a factor of 2.
Option C: Company A's payments grow by a factor of 2
Explanation:
We need to determine the statement which is false.
Option A: A linear function represents Company A's payments.
From the table, it is obvious that the y - value increases by adding 5000.
Thus, the payments of company A can be written in linear function.
Hence, the statement a linear function represents Company A's payments is true.
Therefore, Option A is not the correct answer.
Option B: An exponential function represents Company B's payments.
From the table, it is obvious that the y - value increases by a factor of 2.
Thus, the payments of company B can be written in exponential function.
Hence, the statement an exponential function represents Company B's payments is true.
Therefore, Option B is not the correct answer.
Option C: Company A's payments grow by a factor of 2.
From the table, it is obvious that the y - value increases by adding the 5000.
Hence, the statement Company A's payments grow by a factor of 2 is false.
Therefore, Option C is the correct answer.
Option D: Company B's payments grow by a factor of 2.
From the table, the y - value increases by a factor of 2.
Hence, the statement Company B's payments grow by a factor of 2 is true.
Therefore, Option D is not the correct answer.
6 yd
11 yd
16 yd
5 yd
13 yd
Answer: We find out what these numbers have in common for example:
11yd+5yd=16yd so what is 13yd+6yd it is 19yd. This is your answer.
Step-by-step explanation: I hope this helps!
Allowance $10
Earn $18
Spend $3.28, $7.15, and $9.54
Save?
Answer:
8.03
Step-by-step explanation:
10+18 = 28
28 - 3.28 - 7.15 - 9.54 = 8.03
What is the solution to 3/4(x+8)>1/2(2x+10)
Answer:
x < 4
Since you have to simplify on both sides and then divide or multiply the coefficient on both sides to get the answer.
1.)
What is the solution to the system of equations below?
y = 2x + 8
3(-2x + y) = 19
Answer:
y = 2x + 8
6x + 3y = 19
6x + 3(2x + 8) = 19
6x + 6x + 24 = 19
12x = -5
x = -5/12
y = 2(-5/12) + 8
y = -5/6 + 48/6
y = 43/6
Marge has 4 more than 2 times as many books as Susan. If Marge has 22 books and x is the number of books that Susan has, the relationship can be written as 4 + 2x = 22. How many books does Susan have?
Susan have 9 books.
Explanation:
Given that Marge has 4 more than 2 times as many books as Susan.
Let x represents the number of books that Susan has.
The relationship is written as
[tex]4+2x=22[/tex]
To find: Number of books that Susan have.
The number of books that Susan have can be determined by solving the expression for x.
Thus, we have,
[tex]4+2x=22[/tex]
Subtracting 4 from both sides of the equation, we get,
[tex]2x=18[/tex]
Dividing both sides by 2, we get,
[tex]x=9[/tex]
Therefore, Susan has 9 books.
What are the slope and y intercept of the relationship shown in the table? X 10000 y 2500; x 20000 y 3000; x 30000 y 3500
Answer: slope ; increasing by 10000, y - intercept ; increasing by 500.
Step-by-step explanation:
y = mx+b
x is increasing by 10000
y is increasing by 500
The slope of the table is 1/200 and the y-intercept is 2550.
What is a slope?The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
The table is given below;
x y
10000 2500
20000 3000
30000 3500
To find the slope:
m = (3500 - 2500)/(30000 - 10000)
m = 1000/20000
m = 1/200
Now, the equation of the line that passes through points (10000, 2500) and has a slope of 1/200 is,
y - 2500 = 1/200(x - 10000)
To find the y-intercept:
Put x = 0,
we get,
y - 2500 = 50
y = 2550
Therefore, 2550 is the y-intercept.
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A hotel charges $90 per day for a double room $80 per day for a single room. If a total of 80 single and double rooms are occupied and a total revenue of $6930 is taken in, how many of each type of room are there?
Answer:
the number of single room is 27 and the number of double room is 53
Step-by-step explanation:
Let x is the number of single room
Let y is the number of double room
We know that:
x + y = 80 <=> x = 80 -y (1)
80x +90y= 6930 (2)
Substitute (1) in (2) we have:
80 (80 - y) + 90y = 6930
<=> 6400 - 80y +90y = 6930
<=> y = 53
> x = 80 - 53 = 27
the number of single room is 27 and the number of double room is 53
At the end of a baseball game, the players were given the choice of having a bottle of
water or a box of juice. Of all of the players, 12 chose a bottle of water, which was three-fourths of the total number of players. Write and solve an equation to determine p,
the total number of players at the baseball game.
Answer:
16 players
12(3/4) = p
Step-by-step explanation:
12/[tex]\frac{3}{4}[/tex] = 16
or 12/3 = 4 x 4 = 16
Answer:16 players
Step-by-step explanation:
Radius=6 in.
Height=3 in.
Answer:
[tex]V = 108π {units}^{2} [/tex]
Step-by-step explanation:
Assuming you are looking for the volume of a cylinder with radius=6in and height =3 in.
First , write the formula for the volume of a cylinder.
[tex]V = \pi {r}^{2} h[/tex]
Next, substitute the radius , r=6 and the height , h=3 .
[tex]V = \pi \times {6}^{2} \times 3[/tex]
[tex]V = \pi \times 36 \times 3[/tex]
[tex]V = 108\pi {units}^{2} [/tex]
Jack has a summer job caddying at a golf course. Jack earns $120
a week. By rounding his weekly income to the nearest hundred
dollars, find a reasonable estimate for his total income during the
12 week summer.
OA) $700
O B) $800
OC) $1200
OD) $1700
Answer:
His total income during the summer is $1200 ⇒ C
Step-by-step explanation:
To round a number to a nearest given digit
Look to the number right to this digitIf the digit is 1, 2, 3, 4 keep the given digit as it and put all the digits right to it 0If the digit is 5, 6, 7, 8, 9 add the given digit by 1 and put all the digits right to it 0Examples:
1. Round 1235 to the nearest hundred, the hundred digit is 2 and the digit right to it is 3, then keep the hundred digit 2 and put all the digit right to it 0, so the answer is 1200
2. Round 1265 to the nearest hundred, the hundred digit is 2 and the digit right to it is 6, then add the hundred digit 2 by 1 and put all the digit right to it 0, so the answer is 1300
Now let us solve the problem
∵ Jack earns $120 a week
- By rounding his weekly income to the nearest hundred dollars
∵ The hundred digit is 1
∵ The digit right to it is 2
- Keep the hundred digit 1 and put the digits right to it 0
∴ The rounded number is 100
∴ Jack earns $100 per week
- To estimate his total income during the 12 week summer
multiply 100 by 12
∴ His total income during the summer = 100 × 12
∴ His total income during the summer = $1200
Answer:
1200
Step-by-step explanation:
what is the opposite of-5.5
Answer:
5.5
Step-by-step explanation:
think of a numberline that might help
hope this helps!
3
4
x +
1
4
(x + 12) − 12 = 4x − 21
Answer:
x = -4.02
Step-by-step explanation:
3 4 x + 1 4 (x + 12) − 12 = 4x − 21
Open bracket
34x + 14x + 168 - 12 = 4x - 21
Collect like terms
34x + 14x - 4x = -21+12-168
44x = -177
Divide both sides by 44
x = -177/44
x = -4.02
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To solve for z, you divide each side of the equation by what number?
3/4z = 15
a. 4/3
b. 3/4
c. 15
d. 4
Answer:
B
Step-by-step explanation:
PLEASE GIVE BRAINLYEST
1. Find n.
2 ft
Area = 28 sq ft
Answer:
n=14
Step-by-step explanation:
do 28/2=14
The value of n is 14 when area is 28 square feet.
What is Area of Rectangle?The area of Rectangle is length times of width.
The formula for the area of a rectangle is
Area = length × width
The width = 2ft and
the area = 28 sq ft.
So, we can write the above equation as
28 = n×2
2n = 28
Divide both sides by 2.
n=14
Hence, the value of n is 14 when area is 28 square feet.
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The ratio of the number of boys to the number of girls at school is 4:5. a. What fraction of the students are boys? b. If there are 120 boys, how many students are there altogether? *
Answer: a. 4/9
b. 270 students
Step-by-step explanation:
Answer:
270
Step-by-step explanation:
120÷4= 30
30×5=150
150+120=270