Answer:
a)
The possible values are 0, 1, 2 and 3.
The probability mass function of X is:
P(X = 0) = 0.125
P(X = 1) = 0.375
P(X = 2) = 0.375
P(X = 3) = 0.125
b)
[tex]P(X \geq 1) = 0.875[/tex], [tex]P(X > 1) = 0.5[/tex]
c) E(X) = 1.5, Var(X) = 0.75
Step-by-step explanation:
For it time the coin is flipped, there are only two possible outcomes. Either it comes up heads, or it comes up tails. Each toss is independent of other tosses. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The variance of the binomial distribution is:
[tex]V(X) = np(1-p)[/tex]
A fair coin is flipped three times.
This means that [tex]n = 3[/tex]
Fair coin means that it is equally as likely to be heads or tails, so [tex]p = \frac{1}{2} = 0.5[/tex]
a) Give both the possible values and probability mass function of X.
The possible values are from 0 to n, so 0, 1, 2 and 3.
The probability mass function is the probability of each outcome. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.5)^{0}.(0.5)^{3} = 0.125[/tex]
[tex]P(X = 1) = C_{3,1}.(0.5)^{1}.(0.5)^{2} = 0.375[/tex]
[tex]P(X = 2) = C_{3,2}.(0.5)^{2}.(0.5)^{1} = 0.375[/tex]
[tex]P(X = 3) = C_{3,0}.(0.5)^{3}.(0.5)^{0} = 0.125[/tex]
(b) Find P(X ≥ 1) and P(X > 1).
[tex]P(X \geq 1) = P(X = 1) + P(X = 2) + P(X = 3) = 0.375 + 0.375 + 0.125 = 0.875[/tex]
[tex]P(X > 1) = P(X = 2) + P(X = 3) = 0.375 + 0.125 = 0.5[/tex]
(c) Compute E[X] and Var(X).
[tex]E(X) = np = 3*0.5 = 1.5[/tex]
[tex]Var(X) = np(1-p) = 3*0.5*0.5 = 0.75[/tex]
(-2+6y+3x)(-3) distributive property to remove the parentheses
Answer:
6-18y-9x
Step-by-step explanation:
A supermarket has found that the relationship between a day's high temperature and the amount of money taken in on that day from frozen yogurt sales can be modeled by the equation y = 4x + 164, where x is the high temperature in degrees Fahrenheit and y is the amount taken in from frozen yogurt sales in dollars. Which of these statements is true according to the model?
Answer:
On a day when the high temperature is 79° F, the supermarket can expect to take in $380 in frozen yogurt sales.
Step-by-step explanation:
a train travels 16 miles in 20 minutes how many minutes would 12 miles be
Answer:Then 16x = 240, and x = 240/16 = 15. It will take 15 minutes to travel 12 miles.
Step-by-step explanation:
16 miles = 12 miles
20 mins. how many mins?
16 = 12 cross multiply 16? = 240 divide by 16 240 divided by 16 = 15 miles
20 ? because 15 x 16 = 240
Answer:
It will take 15 minutes to travel 12 miles.
Step-by-step explanation:
Write and solve an equation of ratios:
16 miles 20 min
----------- = -----------
12 miles x
Then 16x = 240, and x = 240/16 = 15.
Which is the value of the expression? (-2) to the fourth power
A. -16
B. -8
C. 8
D. 16
Answer:
Variant D
Step-by-step explanation:
-2*(-2)*(-2)*(-2)=16
I NEED TO KNOW KNOW PLEASEEE
Answer:
2624
Step-by-step explanation:
30 * 64 = 1920
64 * 22 (1/2) = 704
1920 + 704 = 2624
i hope this helps, good luck :)
Evaluate the expression
Answer:
32
Step-by-step explanation:
4 to the third power is 64
(7-3) = 4
*2
64/4*2 = 32
Hope this helps
Please answer question for my friend, Will mark brainliest.
A bottle of orange juice says it contains 200 milligrams of vitamin C, which is 200% of the daily recommended allowance of vitamin C for adults. What is 100% of the daily recommended allowance of vitamin C for adults?
Answer:
im guessing 100 milligrams of vitamin c
Step-by-step explanation:
Answer:
100 mg
Step-by-step explanation:
you could think of it like this: if you divide 200mg and 200% both by two you get 100mg for 100%
What two numbers have a sum of 142 and a difference of 16?
Answer:
x=79,y=63 I have solve it in above picture
Explain 5 different ways you use Math in your everyday life.
Answer:
Buying Groceries, paying for a house, maybe in your job, doing schoolwork of course, and counting money.
Step-by-step explanation:
Answer:
1. you use it to calculate time (managing your day)
2. you use it while driving (use in angles and degrees)
3. you use it while drawing (again, use in angles and degrees)
4. you use it while cooking
5. you use it while banking (financial help)
Step-by-step explanation:
hope this helps:) please mark brainliest
A population of 2000 fish increases at an annual rate of 7.5%. Write the model, then predict how
many fish will there be in 10 years?
Answer:
The model is [tex]P(t) = 2000(1.075)^{t}[/tex].
There will be 4122 fish in 10 years.
Step-by-step explanation:
Exponentially increasing population:
An exponentially increasing population can be represented by the following model:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(t) is the population after t years, P(0) is the initial population, and r is the growth rate, as a decimal.
A population of 2000 fish increases at an annual rate of 7.5%.
This means that [tex]P(0) = 2000, r = 0.075[/tex]
So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 2000(1+0.075)^t[/tex]
[tex]P(t) = 2000(1.075)^{t}[/tex]
This is the model.
How many fish will there be in 10 years?
This is P(10).
[tex]P(t) = 2000(1.075)^{t}[/tex]
[tex]P(10) = 2000(1.075)^{10} = 4122[/tex]
There will be 4122 fish in 10 years.
Given the equation 14 - 4x = 26
Answer:
-3
Step-by-step explanation:
can you mark me brainliest
Answer:
x=-3
Step-by-step explanation:
14-4x=26
-14 -14
-4x=12
/-4 /-4
x=-3
A penguin starts at 15 meters above sea level and ends at 7 meters below sea level. What is the change in elevation?
Answer:
22 meters
Step-by-step explanation:
If the penguin goes from 15 meters above sea level to sea level (0 meters), they traveled 15 meters in elevation.
Then they traveled another 7 meters when going 7 meters below sea level.
15 + 7 = 22
Hope this helps :)
Estimate the sum or difference.
7/8-1/5
Answer:27/40
Step-by-step explanation:
7/8-1/5
35/40-8/40=27/40
how do I solve -6(4 – t) = 121
Total world consumption of iron was approximately 900 million tons in 1993. If consumption had increased by 2.5% each year and the resources available for mining in 1993 were 450 billion tons, how much longer would the world’s iron resources have lasted?
Step-by-step explanation:
We can model the annual consumption of iron by the equation
c = 900 million tons x [tex]1.025^n[/tex], where
n is the number of years after 1993 and
c is the consumption for that year.
An estimate for the total consumption of iron can now be obtained by integrating this equation with respect to a dummy variable, x from 0 to n.
[tex]C = 900*10^6* \int\limits^n_0 {1.025^x} \, dx[/tex]
This equation simplifies to
C = 900 million tons x (1.025^n - 1) / ln(1.025), where
x is a dummy variable and
C is the total consumption of iron n years after 1993.
Let R be the amount of iron remaining at n years after 1993, so
R = 480 billion tons - C
R = 480 billion tons - 900 million tons x (1.025^n - 1) / ln(1.025)
We need to find the value of n when R is 0, so
0 = 480 billion tons - 900 million tons x (1.025^n - 1) / ln(1.025)
Simplify this equation to obtain
n = 107.4
So the iron will run out in the year 1993 + 107 = 2100
Collectively, what are the interest costs and other fees for using a credit card called? A. balance B. credit line C. finance charge Reset Next
The correct answer is C. Finance charge
Explanation:
A credit card is a service offered by financial entities such as banks that allows customers to buy goods and pay them later. This implies the customer does not immediately for goods but pays for these after a specific time. The use of this benefit implies related costs such as fees for the use of the credit card, and interest costs (money charged for borrowing the money from the bank), which are known as finance charge or the money charged for the benefit of using credit. According to this, the correct answer is C.
Evaluate f(x)=6x2 – 12 when x =-3.
Mr. Gardener invested $500.000. His annual interest was $40.000. What was the annual interest rate?
Answer:
8% per year
Step-by-step explanation:
............
Ms. Ortiz borrows $2.50 every day for a school week (5 days) to buy a bacon egg and cheese. How much does
she owe by the end of the week? (Use negative numbers to show how much she owes
It’s multiplying signed numbers
Answer: She will owe $12.50 at the end of the week, and her account balance will be -12.50 dollars.
Step-by-step explanation:
A school week is 5 days. If Ms. Ortiz borrows $2.50 every day, then we will have to multiply 2.50 by 5 to find how much Ms. Ortiz owes at the end of the week.
2.50 x 5 = 12.5, or $12.50.
Therefore, Ms. Ortiz owes $12.50 at the end of the week, and her account balance will be -12.50.
17 > 4x
• A) X= 4
- B) x = 5
• C) x = 6
• D)x=7
Answer:
La D
Step-by-step explanation:
porque la variable de divide
Please help I will give Brainliest
Daisy is making lemonade with water and lemons. Based on the table below, how many lemons are needed for 24 oz. of water?
ANSWER NOW PLEASE
is 15.09 less than 12.63
Answer: No
15.09 is greater than 12.63
find the x (please help lol)
Answer:
x = 23.5
Step-by-step explanation:
x is the midsegment theorem of the trapezoid given.
Based on the midsegment theorem of a trapezoid, thus:
x = (7 + 40)/2
x = 47/2
x = 23.5
find the slope of the line
Answer:
The slope of the line is: 1
Step-by-step explanation:
Use the equation
[tex] \frac{y2 - y1}{x2 - x1} [/tex]
Use the two sets of points given to you to slve the equation.
Assign the points their variables:
x1 y1 x2 y2
(4, 4) (8, 8)
Insert the numbers into the equation:
[tex] \frac{8 - 4}{8 - 4} [/tex]
Simplify:
[tex] \frac{4}{4} = 1[/tex]
Guys I need help what is 6 divided by 398
Self-select sampling is a sample in which members choose to be in the survey.
True
False
Answer:
true
Step-by-step explanation:
awser the circled question
Answer:
7.5
Step-by-step explanation:
if one square is unit then use area formula for a right triangle which is 1/2bh
since height is 5 and base is 3, 5*3= 15 and 15/2= 7.5
hope this helps
Find each angle measure to the nearest degree please help
9514 1404 393
Answer:
4°48°Step-by-step explanation:
The inverse cosine function of your calculator is used to find the angle from the cosine value. (Be sure your calculator is set to 'degrees' mode.)
1) A = arccos(0.9976) ≈ 4°
2) U = arccos(0.6691) ≈ 48°
Help for brainliest !!
Answer:
I think the option b
But not sure about it
Answer:
A. 5/9 square meters
Step-by-step explanation:
Given
Length (L) = 5/6 meter
Breadth (b) = 2/3 meter
Now
Area of the garden
= L * b
= 5/ 6 * 2 / 3
= 5 / 9 square meters.
Hope it will help :)
