A red die and a blue die are rolled. You win or lose money depending on the sum of the values of the two dice. If the sum is 6 or 10, you win $4. If the sum is 5, 9, or 12, you win $1. If the sum is any other value (2, 3, 4, 7, 8, or 11), you lose $2. Let X be a random variable that corresponds to your net winnings in dollars. What is the expected value of X
Answer:
The expected value of X is $0.0833.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
For each dice, there are 6 possible outcomes(values from 1 to 6). So for 2 dices, there are [tex]6^2 = 36[/tex] desired outcomes.
Desired outcomes:
Sum 5: (1,4), (2,3), (3,2), (4,1).
Sum 6: (1,5),(2,4),(3,3),(4,2),(5,1)
Sum of 9: (3,6), (4,5), (5,4), (6,3)
Sum of 10: (4,6), (5,5), (6,4)
Sum of 12: (6,6)
Probabilities:
5 + 3 = 8 outcomes in which the sum is 6 or 10, that is, 8/36 probability of winning $4.
4 + 4 + 1 = 9 outcomes in which the 5, 9, or 12, that is, 9/36 probability of winning $1.
36 - (8 + 9) = 36 - 17 = 19 remaining outcomes, that is, 19/36 probability of losing $2.
What is the expected value of X?
Multiplication of each outcome by its probability. So
[tex]E(X) = \frac{8}{36}*4 + \frac{9}{36}*1 - \frac{19}{36}*2 = \frac{8*4 + 9*1 - 19*2}{36} = \frac{32 + 9 - 38}{36} = \frac{3}{36} = 0.0833[/tex]
The expected value of X is $0.0833.
What is the value of x
[tex]x {}^{2} \times 5x = 625[/tex]
Answer:
x = 5
Step-by-step explanation:
x^2 * 5x = 5x^3
5x^3 = 625 Divide by 5
x^3 = 625/5
x^3 = 125 Take the cube root of 125
x = 5
2/6 = 1/2 1/3
which one is the answer
Answer:
1/3
Step-by-step explanation:
2+2+2=6
There are three 3's
A bag contains 6 red and 10 black marbles. If you pick a marble, record its color, and return it to the bag 200 times, how many times can you expect to pick a black marble?
Answer:
12.5
Step-by-step explanation:
6+10= 16 200/16=12.5
plssssssssssssssssss helpppppppppppppppppppppppppppppppppppppppppppppppppp
The diagram shows the dimensions of a triangular prism what is the volume. Click on photo to see
Answer:
36 in^3
Step-by-step explanation:
1) find the area of the triangle
A = (leg 1 x leg2)/2 = (3 x 4)/2 = 6 in^2
2) find the volume
V = base area x height = 6 x 6 = 36 in^3
A farmer sells 6.5 kilograms of apples and pears at the farmer's market.
3
4
of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?
Answer:
1.625 kg
Step-by-step explanation:
For each equality decide whether the solution is represented by X less than 2 .5 or X greater than 2.5 -4x+5>-5 -25>-5(x+2.5)
Answer:
[tex]x<2.5[/tex] and [tex]x > 2.5[/tex] are the solutions
Step-by-step explanation:
Given
[tex]-4x + 5 > -5[/tex]
[tex]-25 > -5(x + 2.5)[/tex]
Required
Determine if their solution is x < 2.5 or x > 2.5
[tex]-4x + 5 > -5[/tex]
Collect like terms
[tex]-4x>-5-5[/tex]
[tex]-4x>-10[/tex]
Divide by -4
[tex]x<\frac{-10}{-4}[/tex]
[tex]x<2.5[/tex]
[tex]-25 > -5(x + 2.5)[/tex]
Open bracket
[tex]-25 > -5x - 12.5[/tex]
Collect like terms
[tex]5x > 25- 12.5[/tex]
[tex]5x > 12.5[/tex]
Divide by 5
[tex]x > \frac{12.5}{5}[/tex]
[tex]x > 2.5[/tex]
Review later
A spinner with 3 equally likely sections is spun. If you were to spin the
spinner 150 times, how many times would you expect to land in each
section?
What is the unit rate for the ratio 4/7: 8/21?
Answer:
The unit rate is 1.5
Step-by-step explanation:
Given
[tex]Ratio = 4/7 : 8/21[/tex]
Required
Determine the unit rate
To do this, we need to express the ratio as:
[tex]Ratio = m : 1[/tex]
Where m is the unit rate
[tex]Ratio = 4/7 : 8/21[/tex]
Express as fraction
[tex]Ratio = \frac{4/7 }{ 8/21}[/tex]
Solve
[tex]Ratio = \frac{4}{7} * \frac{21}{8}[/tex]
[tex]Ratio = 1.5[/tex]
Express as ratio
[tex]Ratio = 1.5 : 1[/tex]
Hence, the unit rate is 1.5
During a flu epidemic, 35% of the school's students have the flu. Of those with the flu, 90% have high
temperatures. However, high temperatures are possible for people who do not have the flu. It is estimated that
12% of those without the flu have high temperatures.
If a student has a high temperature, what is the probability that the student has the flu?
Answer: 0.8015
Step-by-step explanation:
Let F= event that a person has flu
H= event that person has a high temperature.
As per given,
P(F) =0.35
Then P(F')= 1- 0.35= 0.65 [Total probability= 1]
P(H | F) = 0.90
P(H|F') = 0.12
By Bayes theorem, we have
[tex]P(F|H)=\dfrac{P(F)\timesP(H|F)}{P(F)\timesP(H|F)+P(F')\timesP(H|F')}\\\\=\dfrac{0.35\times0.90}{0.35\times0.90+0.65\times0.12}\\\\=\dfrac{0.315}{0.315+0.078}\approx0.8015[/tex]
Required probability = 0.8015
A culture of bacteria has an initial population of 470 bacteria and doubles every 8 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P t =P 0 ⋅2 d t , where P_tP t is the population after t hours, P_0P 0 is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 7 hours, to the nearest whole number?
Answer:
Step-by-step explanation:
The population of bacteria in the culture after 7 hours is approximately 883.
What is an exponential function?Several real-world phenomena, including population expansion, radioactive decay, compound interest, and the spread of diseases, are modeled using exponential functions. In calculus, where they are used to define the exponential and logarithmic functions—essential ideas in calculus and other fields of mathematics—they also play a significant role.
Using the formula [tex]P_t = P_0 \times 2^{\frac{t}{d}}[/tex], where P_t is the population after t hours, P₀ is the initial population, t is the time in hours and d is the doubling time, we can find the population of bacteria in the culture after 7 hours as follows:
Since the initial population is 470, we have P₀ = 470.
The doubling time is 8 hours, so we have d = 8.
Substituting these values into the formula, we get:
[tex]P_7 = 470 \times 2^{\frac{7}{8}}[/tex]
P₇≈ 882.77
To know more about an exponential function follow
https://brainly.com/question/22967542
#SPJ2
I need help soo yah cna you help ne?
Which is the best type of graph to show the kilograms of food consumed and kilograms of food wasted in the
school cafeteria each day?
A. stem and leaf plot
B. line graph
C. dot plot
D. double bar graph
Answer:
Double Bar Graph
Step-by-step explanation:
Ive been asking too many questions but Im really dmb so heres another one
Answer:
12(6)/2
B: 36
Step-by-step explanation:
Timmy and Sarah head out to dinner and Garfinkels in Vaile. Timmy brings $40 with him. If buy two French Dips costing $10.95 a piece and two sodas costs $1.95 each, how much does Timmy have left if there is a 6% sales tax and they tip 20% on the food including the sales tax
Answer:
$3.80
Step-by-step explanation: :)
Naomi has a bag that contains pineapple chews, cherry chews, and peach chews. She performs an experiment. Naomi randomly removes a chew from the bag, records the result, and returns the chew to the bag. Naomi performs the experiment 72 times. The results are shown below: A pineapple chew was selected 31 times. A cherry chew was selected 3 times. A peach chew was selected 38 times. Based on these results, express the probability that the next chew Naomi removes from the bag will be pineapple chew as a decimal to the nearest hundredth.
Answer:
0.43
Step-by-step explanation:
Answer:
0.43
Step-by-step explanation:
The experiment occurred 72 times , pineapple was selected 31 times
Probability the next chew will be pineapple:
31/72 = 0.430555
Round to the nearest hundredth: 0.43
find the value of x
plssss help me
Answer:
x = 20
Step-by-step explanation:
The angles are supplementary so:
7x + x + 20 = 180
8x + 20 = 180
8x = 160
x = 20
Rachel had a loan for $4,000 loan for 4 years.
She paid a total of $608 in simple interest over the 4 years.
What was the annual interest rate for the loan?
9514 1404 393
Answer:
3.8%
Step-by-step explanation:
The interest on a simple-interest loan is ...
I = Prt
where P is the principal value, r is the annual rate, and t is the number of years.
Solving for r, we get ...
r = I/(Pt) = 608/(4000×4) = 0.038 = 3.8%
The annual interest rate for the loan was 3.8%.
The area of a square is 54 cm. What
is the length of each side of the
square?
A. between 8cm and 9cm
B. between 5cm and 6cm
C. between 6cm and 7cm
D. between 7cm and 8 cm
Victor buys 4 sleeves of golf balls. He has coupons for $0.75 off the regular price of each sleeve. After using the coupons, the total cost of the golf balls is $11. What is the regular price of each sleeve of golf balls?
Which statements are true about triangle ABC and its translated image, A'B'C'? Select two options
look at pic 10 points
Answer:
120
Step-by-step explanation: 10 x 12 = 120 m. Hope this helps
Factorise the following expression:
[tex] {a}^{2} + 10a + 24[/tex]
Step-by-step explanation:
[tex]a^{2} + 10a + 24[/tex]
= [tex]a^{2}[/tex] + 6a + 4a + 24
= a(a + 6) + 4(a + 6)
= (a + 6)(a + 4)
Answer:
solution:
[tex] {a}^{2} + 10a + 24[/tex]
a²+6a+4a+24
a(a+6)+4(a+6)
(a+6)(a+4) is your answer
) Find the area of the shape.
Answer:
1/2Bh
Step-by-step explanation:
u never said we had to answer
What type of correlation is shown in the graph?
A. Positive
B. Negative
C. No Correlation
D. Linear
Answer:
This graph shows a negative correlation
Hope this helps!
There are 7 apples and 15 oranges in a fruit basket at the grocery store. What is the ratio of oranges to all fruit
Answer:
15:22
Step-by-step explanation:
15 oranges and 22 fruits in total
Find the product of
How do I solve this problem below!
Answer:
$5.44
Step-by-step explanation:
$1.75 + $1.26 + $1.08 + $0.52 = $4.56
$10.00 - $4.56 = $5.44
What is the surface area of the composite figure shown?
Answer:
531 m²
Step-by-step explanation:
9x9x5=405 (5 sides that are 9x9, including the bottom)
1/2x9x7x4=126 (4 triangles on top)
405+126=531
