Answer:
Suppose that in a given event, there are N outcomes:
{x₁, x₂, ..., xₙ}
Such that the probabilities are:
{p₁, p₂, ..., pₙ}
The expected value is:
EV = x₁*p₁ + x₂*p₂ + ... + xₙ*pₙ
In this case, we know that each ticket costs $3.
There is 1 winning ticket out of 300 tickets, where the prize is $62.
Then we have two events, the one where you win.
x₁ = $62 - $3 = $59
With a probability:
p₁ = 1/300
The one where you don't win (and still pay for the ticket):
x₂ = -$3
p₂ = 299/300
a) Then the expected value is:
EV = ( 1/300)*$59 + (299/300)*(-$3) = -$2.79
b) The expected value is additive, this means that if you buy 6 tickets, the expected value will be equal to 6 times the expected value of a single ticket.
EV = 6*(-$2.79) = -$16.74
c) For the PTO the events are:
Winner ticket, so you lose $62 and win $3 for selling the ticket.
x₁ = $3 - $62 = -$59
p₁ = 1/300
Normal ticket, you win $3.
x₂ = $3
p₂ = 299/300
In this case the expected value is:
EV = (1/300)*(-$59) + (299/300)*$3 = $2.79
d) If the PTO sells the 300 tickets, then the expected value is 300 times the expected value for a single ticket:
EV = 300*$2.79 = $837
We should have the exact same than selling the 300 tickets:
300*$3 = $900
minus the $62 for the price:
$900 - $62 = $838
There is a difference of $1, that happens because we rounded the value of the expected value (the actual one was $2.792...)
Imagine you wish to determine whether the mean number of hours worked per week by men in a sample differs from the 40-hour standard. Use the information below to calculate the value of the single-sample t statistic.
Range = 60
Min Value = 5
Max value = 65
Mean = 42.31
Variance =100.00
Standard deviation = 10.00
Sum = 1,227
Answer:
[tex]t = 7.359[/tex]
Step-by-step explanation:
Given
[tex]Range = 60[/tex]
[tex]Min = 5[/tex]
[tex]Max = 65[/tex]
[tex]\bar x = 42.31[/tex]
[tex]\sigma^2 =100.00[/tex]
[tex]\sigma = 10.00[/tex]
[tex]\sum = 1227[/tex]
[tex]n=40[/tex]
Required
The t statistic
This is calculated using:
[tex]t = \frac{\bar x - \mu}{\sigma/\sqrt n}[/tex]
Where
[tex]\mu \to[/tex] Population mean
[tex]\mu = \frac{\sum }{n}[/tex]
[tex]\sum = 1227[/tex] and [tex]n=40[/tex]
[tex]\mu = \frac{1227}{40}[/tex]
[tex]\mu = 30.675[/tex]
So, we have:
[tex]t = \frac{\bar x - \mu}{\sigma/\sqrt n}[/tex]
[tex]t = \frac{42.31 - 30.675}{10/\sqrt{40}}[/tex]
[tex]t = \frac{42.31 - 30.675}{10/6.325}[/tex]
[tex]t = \frac{11.635}{1.581}[/tex]
[tex]t = 7.359[/tex]
Harry received a package for his birthday. The package weighed 350,000 centigrams. Select the conversions that are equivalent to 350,000 centigrams. Select all that apply.
35 kilograms
3,500 decigrams
350 dekagrams
3,500 grams
PLEASE ANSWER PLEASE
Given:
The package weighed 350,000 centigrams.
To find:
The conversions that are equivalent to 350,000 centigrams
Solution:
We know that,
1 centigrams (cg) = 0.000001 kilograms (kg)
1 cg = 0.1 decigrams (dg)
1 cg = 0.001 dekagrams (dag)
1 cg = 0.01 grams (g)
Using these conversions, we get
350,000 centigrams = 3.5 kilograms
350,000 centigrams = 35,000 decigrams
350,000 centigrams = 350 dekagrams
350,000 centigrams = 3,500 grams
Therefore the correct options are C and D.
A different pack has 72 cards.
5/9 are yellow
Work out the number of yellow cards.
Leon wants to know whether the students at his middle school use e-mail, telephone, or text messaging to communicate most often.
Which group should Leon survey to get the most accurate results?
O A. the students in his math class
O B. every 5th student entering the school
O c. the boys he hangs out with at lunchtime
D. every 8th student who uses the computer center
Since Leon wants to know whether the students at his middle school use e-mail, telephone, or text messaging to communicate most often, the appropriate group will be D. every 8th student who uses the computer center.
What is communication?It should be noted that communication simply had to do with the exchange of information.
In this case, Leon wants to know whether the students at his middle school use e-mail, telephone, or text messaging to communicate most often.
In this case, the people who enter the computer center will his him the necessary information that he needs.
Therefore, the correct option is D.
Learn more about communication on:
brainly.com/question/26152499
#SPJ1
A vertex of square is at(1,1) and its two parallel sides are y=x and y=x+1. find the equation of the remaining sides.Show your work;
note:
[ans:x+y=2,x+y=1 or x+y=2 ,x+y=3]
Be away from links,random answers:
Answer:
[tex] \displaystyle y = - x + 2[/tex]
[tex]y = - x +1[/tex]
Step-by-step explanation:
we are given a vertex of a square i.e (1,1)
and the equations of the two parallel sides
notice that, the given vertex coordinates satisfy one of the parallel side i.e y=x which means that (1,1) points lie on one of Parallel sides
remember that,
every angles of a square is 90°
therefore,
we need to figure out the remaining Perpendicular line of the given Parallel sides so
let's figure out the perpendicular line of y=x line
recall that,
Parallel lines have the same slope thus
[tex] \displaystyle m_{ \rm perpedicular} = - 1[/tex]
since we are given a vertex the equation of the perpendicular line should be
[tex] \displaystyle y - 1 = - 1(x - 1)[/tex]
distribute:
[tex] \displaystyle y - 1 = - x + 1[/tex]
add 1 to both sides:
[tex] \displaystyle y = - x + 2[/tex]
to figure out the second perpendicular line we can consider the coordinates (0.5,0.5) of y=x equation
so the slope of the perpendicular line is -1
and the equation:
[tex]y - 0.5 = - 1(x - 0.5)[/tex]
distribute:
[tex]y - 0.5 = - x +0 .5[/tex]
add 0.5 to both sides:
[tex]y = - x +1[/tex]
and we are done!
select all the expressions that have a value greater than 19 X 12
Answer:
123
Step-by-step explanation:
Home pregnancy tests, like all medical tests, are not perfectly accurate. Suppose one such test has an accuracy level such that if a woman is pregnant there is a 12% chance that the test will fail to show it. On the other hand, if the woman is not pregnant there is still a 3% chance that the test will incorrectly say that she is. Show all the steps including identification of what formulas/properties you used. Points will be deducted from answers if only the final answer is provided.
a) If Joan is pregnant what is the chance that the test will detect it?
b) Based on other factors, Joan estimates there is an 80% chance that she is pregnant.
Therefore, Joan takes a pregnancy test. What is the probability that the test will indicate that she is pregnant?
c) Joan looks at the test result and it does indicate that she is pregnant. Given this test result, what is the probability that she is pregnant?
d) Pamela has also taken this particular home pregnancy test. Before taking the test, she estimated there was a 75% chance that she
Answer:just go to the doctor
Step-by-step explanation:
Please help me with this answer
9514 1404 393
Answer:
x = 12∠H = 94°Step-by-step explanation:
The marked angles are supplementary, so ...
(5x +26)° +(8x -2)° = 180°
13x = 156 . . . . . . . . . . . . . . divide by °, subtract 24
x = 12 . . . . . . . . . . . divide by 13
∠H = (8x -2)° = (8·12 -2)°
∠H = 94°
Tell if each shape is a polygon or is not a polygon. Explain how you know. What makes that shape a polygon or not a polygon?
hope it helps :-) good morning ☀️.
Help please!!! Don't come and steal my points please, I really need this answered.
Answer: 4x [tex]\leq[/tex] 36
Step-by-step explanation: Four times the number is no more than ("less than or equal to") 36: 4x ≤ 36 (by dividing both sides by 4, this is equivalent to x ≤ 9 )
Hope this helped!!!!!!!!!! And ps why are there so many people stealing points on here now
Consider the points plotted on the number line shown below
the original price of a book is $15 the book is selling for 25% less because of the slight damage .what is the cost of the damaged book
Answer:
the cost of the damaged book is 11.25
Step-by-step explanation:
since it is 25% off the 100% cost it is dicounted to 75% of the price
multiply full price by 75% (.75) to get 11.25
The probability that the patient recovers from a rare deadly disease is 40% and failure to recover is 60%.If 15 people contracted this disease what is the probability that a. 5 will survive? b. 8 will survive? c.12 will survive?(complete solution)
Answer:
a) 0.1859 = 18.59% probability that 5 will survive.
b) 0.1181 = 11.81% probability that 8 will survive.
c) 0.0016 = 0.16% probability that 12 will survive.
Step-by-step explanation:
For each patient, there are only two possible outcomes. Either they survive, or they do not. The probability of a patient surviving is independent of any other patient. This means that the binomial probability distribution is used 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 probability that the patient recovers from a rare deadly disease is 40%
This means that [tex]p = 0.4[/tex]
15 individuals
This means that [tex]n = 15[/tex]
a. 5 will survive
This is P(X = 5). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{15,5}.(0.4)^{5}.(0.6)^{10} = 0.1859[/tex]
0.1859 = 18.59% probability that 5 will survive.
b. 8 will survive
This is P(X = 8). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 8) = C_{15,8}.(0.4)^{8}.(0.6)^{7} = 0.1181[/tex]
0.1181 = 11.81% probability that 8 will survive.
c.12 will survive
This is P(X = 12). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 12) = C_{15,12}.(0.4)^{12}.(0.6)^{3} = 0.0016[/tex]
0.0016 = 0.16% probability that 12 will survive.
find height of the density curve
Answer:
0.2 on khan academy
Step-by-step explanation:
Which expression is equivalent to (see the picture)
A. 20x-21y +14
B. 20x + 11y + 14
C. 20x - 11y + 6
D. 20x + 21y +6
-4x-10=2x+14
solve for x
Step-by-step explanation:
[tex]x = - 4 \\ [/tex]
hope am right
please help, the answer below is a option but i need a answer for the question
Answer:
12 units^2
Step-by-step explanation:
This is the floor of isaac's kitchen. Isaac needs to determine the area of the floor so he can order new tile. Enter the area, in square feet, of Isaac’s kitchen floor.
Answer:
134
Step-by-step explanation:
first, separate the floor into 3 different rectagles to calculate the area and then add them together.
area of rec=L*B
rec 1: 9.5*7=66.5
rec 2: (10.5-4.5)*(14.5-5-7)=15
rec 3:5*10.5=52.5
Then:
66.5+52.5+15=134
In 2002, the manufacturers of M&M's surveyed people from around the world and asked them to vote for a new color: purple, aqua, or pink. In the United States, 42% of those who voted said purple, 37% said aqua, and 19% said pink. What's the probability that a randomly picked survey respondent from the United States preferred purple or pink?
Answer:
don't know
Step-by-step explanation:
dont know...........
We know that the length of time required for a student to complete a particular aptitude test has a normal distribution with a mean of 41.0 minutes and a variance of 3.4 minutes. What is the probability, rounded to four decimal places, that a given student will complete the test in more than 35 minutes but less than 43 minutes?
Answer:
0.6832 = 68.32% probability that a given student will complete the test in more than 35 minutes but less than 43 minutes
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 41.0 minutes and a variance of 3.4 minutes.
This means that [tex]\mu = 41, \sigma = 3.4[/tex]
What is the probability, rounded to four decimal places, that a given student will complete the test in more than 35 minutes but less than 43 minutes?
This is the p-value of Z when X = 43 subtracted by the p-value of Z when X = 35.
X = 43
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{43 - 41}{3.4}[/tex]
[tex]Z = 0.59[/tex]
[tex]Z = 0.59[/tex] has a p-value of 0.7224
X = 35
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 41}{3.4}[/tex]
[tex]Z = -1.76[/tex]
[tex]Z = -1.76[/tex] has a p-value of 0.0392
0.7224 - 0.0392 = 0.6832
0.6832 = 68.32% probability that a given student will complete the test in more than 35 minutes but less than 43 minutes
Use the Pythagorean theorem to solve for the missing side
Answer:
13
Step-by-step explanation:
a2+b2=c2
12^2+5^2=c^2
144+25=169
square root of 169
13
Find the volume of the rectangular prism
Answer:
210cm
Step-by-step explanation:
Hope this helps
A spinner with 6 equally sized slices has 2 red slices, 1 blue slice, and 3 yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a red slice?
Answer:
The probability is 2/6, or 1/3 (about 33%)
Step-by-step explanation:
A box holds 12 markers. Nan takes out 6. Then she puts 2 back. Are there enough markers in the box for Fen to take out 10?
Answer:
Nope
Step-by-step explanation:
No because you can (12 + 6) +2 and get 8. so yea
Consider this data set.
13, 17, 21, 3, 14, 34, 22, 20, 16, 19, 15
Which data values are outliers?
Select each correct answer
3
13
15
34
Answer:
3 and 34
Step-by-step explanation:
they are the extremes in this, you want to look for out of place numbers when dealing with outliers
What Expression is equivalent to 4 square root of 6 over 3square root of two
Answer:
4√6/3√2 = 4.62
Step-by-step explanation:
JK and LM are straight lines. Find /NOK.
( help me pls)
Answer:
[tex]NOK = 58[/tex]
Step-by-step explanation:
Given
[tex]JOM = 108[/tex]
[tex]LON = 50[/tex]
Required
Find NOK
From the attached triangle, we have:
[tex]LOK = JOM =108[/tex] --- Corresponding angles
And
[tex]LOK = LON + NOK[/tex]
Substitute for LOK and LON
[tex]108= 50+ NOK[/tex]
Make NOK the subject
[tex]NOK = 108 - 50[/tex]
[tex]NOK = 58[/tex]
If OB = 6 and AB = 8, then EA
Answer:
what is that means i think it's better to ask by take a picture
Without using the formula, work out the gradient of the graph shown.
Give your answer in its simplest form.
9514 1404 393
Answer:
3/4
Step-by-step explanation:
The x- and y-intercepts are -4 and +3, respectively. These indicate a rise of 3 units for a run of 4 units. The gradient is the ratio of rise to run (sorry, that is the formula), so is ...
gradient = 3/4
The Quadratio Formula gives which roots for the equation 3x² + 3x = 2 ?
Step-by-step explanation:
the correct answer is option B