Answer:
The joint probability of the two events is one.
Step-by-step explanation:
Complementary events:
If two events are complimentary, these three following things are true:
They are dependent.
The intersection of them is zero.
The joint probability of the two events is one.
The last one is the correct choice.
You are paid $25 per hour.
You work 7 hours a day.
You work 5 days a week.
How much is your total pay each week? $=
Answer:
The total pay would be $50, But there would also be tax to consider in this situation.
A person takes a multiple-choice exam in which each question has five possible answers. Suppose that the person has no idea about the answers to three of the questions and simply chooses randomly for each one.
Required:
a. What is the probability that the person will answer all three questions correctly?
b. What is the probability that the person will answer exactly two questions correctly?
c. What is the probability that the person will answer exactly one question correctly?
d. What is the probability that the person will answer no questions correctly?
e. Suppose that the person gets one point of credit for each correct answer and that 1/3 point is deducted for each incorrect answer. What is the expected value of the person’s score for the three questions?
Answer:
a. 0.008 = 0.8% probability that the person will answer all three questions correctly.
b. 0.096 = 9.6% probability that the person will answer exactly two questions correctly.
c. 0.384 = 38.4% probability that the person will answer exactly one question correctly.
d. 0.512 = 51.2% probability that the person will answer no questions correctly.
e. The expected value of the person’s score for the three questions is -0.2.
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the person answers it correctly, or they do not. The probability of a person answering a question correctly is independent of any other question. 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.
Each question has five possible answers.
Person has no idea which option is correct, so the probability of answering correctly is:
[tex]p = \frac{1}{5} = 0.2[/tex]
Three questions:
This means that [tex]n = 3[/tex]
a. What is the probability that the person will answer all three questions correctly?
This is [tex]P(X = 3)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.2)^{3}.(0.8)^{0} = 0.008[/tex]
0.008 = 0.8% probability that the person will answer all three questions correctly.
b. What is the probability that the person will answer exactly two questions correctly?
This is [tex]P(X = 2)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{3,2}.(0.2)^{2}.(0.8)^{1} = 0.096[/tex]
0.096 = 9.6% probability that the person will answer exactly two questions correctly.
c. What is the probability that the person will answer exactly one question correctly?
This is [tex]P(X = 1)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{3,1}.(0.2)^{1}.(0.8)^{2} = 0.384[/tex]
0.384 = 38.4% probability that the person will answer exactly one question correctly.
d. What is the probability that the person will answer no questions correctly?
This is [tex]P(X = 0)[/tex]. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{3,0}.(0.2)^{0}.(0.8)^{3} = 0.512[/tex]
0.512 = 51.2% probability that the person will answer no questions correctly.
e. Suppose that the person gets one point of credit for each correct answer and that 1/3 point is deducted for each incorrect answer. What is the expected value of the person’s score for the three questions?
The expected number of correct answer is:
[tex]E(X) = np = 3*0.2 = 0.6[/tex]
And the expected number of wrong answers is 3 - 0.6 = 2.4. So, the expected score is:
[tex]S(x) = 0.6 - \frac{2.4}{3} = 0.6 - 0.8 = -0.2[/tex]
The expected value of the person’s score for the three questions is -0.2.
Suppose you wanted to find a critical test statistic for a confidence interval for the slope of the regression line. How many degrees of freedom would you need to use?
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the regression line is not given.
However, I will give a general explanation of how to calculate the degree of freedom of a slope of regression line
The degree of freedom is calculated using:
[tex]df = n - k[/tex]
Where
[tex]k \to number\ of\ parameters[/tex]
[tex]n \to sample\ size.[/tex]
For a regression line; there are two parameters that are being estimates;
The intercept and the slope. So:
[tex]k = 2[/tex]
Hence, the degree of freedom of a slope of regression line is:
[tex]df = n -2[/tex]
So; if for example
[tex]n =101[/tex]
the degree of freedom will be:
[tex]df =101 - 2[/tex]
[tex]df =99[/tex]
Find the area of the polygon shown. Enter the number into the box.
m 2
2 mi
10 mi
4 mi
12 mi
1
2
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the image of the polygon is not given.
I will answer this question with the attached image (similar to your question)
The attached polygon is a trapezoid of the following dimensions.
[tex]Height = 4ft[/tex]
Parallel sides
[tex]Side\ 1 = 4ft[/tex]
[tex]Side\ 2 = 4ft+1ft = 5ft[/tex]
So, the area is:
[tex]Area = \frac{1}{2} * (Side\ 1 + Side\ 2) * Height[/tex]
[tex]Area = \frac{1}{2} * (4ft + 5ft) * 4ft[/tex]
[tex]Area = \frac{1}{2} * 9ft * 4ft[/tex]
[tex]Area = 18ft^2[/tex]
Grace examines two different size bottles of the same laundry detergent. The price for the 100100100-ounce bottle is \$9.99$9.99dollar sign, 9, point, 99 and the price for the 150150150-ounce bottle is \$12.99$12.99dollar sign, 12, point, 99. How much money will Grace save per 100100100 ounces if she purchases the larger bottle
Answer:
$1.33
Step-by-step explanation:
Determine the cost per ounce of the larger bottle
cost per ounce = cost of larger bottle / total ounces
$12.99 / 150 = $0.0866
Multiply cost per ounce by 100
$0.0866 x 100 = $8.66
Subtract the above figure from 9.99
9.99 - $8.66 = $1.33
Please help me, and can you do it by a table math
Answer:
Yeah
Step-by-step explanation:
A large auditorium has stadium with stadium seating. There are 8 seats in the first row, 10 seats in the second row, 12 seats in the third row and 300 seats in the last row. How many rows of seats are in the auditorium
What is 10 percent in 66
There are 3 liters of orange juice at a school party. 10 students want to drink all of the orange juice, and they all want to get exactly the same amount. How much orange juice can each get? (enter your answer as a fraction or mixed number)
Answer:
3 1/3 each
Step-by-step explanation:
10/3=3 1/3
an international company has 16,600 employees in one country. if this represents 28.8% of the company's employees, how many employees does it have in total? round your answer to the nearest whole number
Answer:
57639 employees in total.
Step-by-step explanation:
28.8% of X = 16600
X = 16600 / 28.8%
= 16600 / 0.288
= 57638.89
=57639
find the probability of spinning an A 3 times
If it takes 1074 digits to number the pages of a book starting with page 1. how many pages are in the book? The book has a total of pages.
Answer:
394 pagesStep-by-step explanation:
1- digit numbers:
1 to 9, number of digits = 92- digit numbers:
10 to 99, number of digits = 2(99 - 9) = 1803- digit numbers:
100 to 999, number of digits = 3(999 - 99) = 2700This is more than we have, but we know the number of pages is 3-digit.
Let it be x, then we have:
9 + 180 + 3(x - 99) = 10743(x - 99) = 1074 - 1893(x - 99) = 885x - 99 = 885/3x - 99 = 295x = 295 + 99x = 394what is the value of 9 (n + 2) - 5n when n =1/4
9514 1404 393
Answer:
19
Step-by-step explanation:
The evaluation is easier if we simplify the expression first.
9(n +2) -5n = 9n +18 -5n = 4n +18
For n = 1/4, this is ...
= 4(1/4) +18 = 1 +18
= 19
The value of the expression for n = 1/4 is 19.
What percent of 0.2 gram of 32 mg
Answer:
625
Step-by-step explanation:
First, you have to convert 0.2 grams to mg. To do this, multiply 0.2 by 1000. This yield 200. Now 200 is what percent of 32.
200 * 100 / 32
= 625
11. If Kaleb has 26 candy bars and sells them for $2.50 each, how much money will he
make if he sells half of the candy bars.
Answer:
$32.50
Step-by-step explanation:
The total amount of candy bars is 26. Half of that is 13. 13 times the $2.50 for each is $32.50.
Hello if you're able to answer this question help me and provide work as well, Thank you.
Answer:
Option A. Only Khaled
Step-by-step explanation:
To know which option is correct, we shall use the formula suggested by both Khaled and Wilma to see which will give the sequence given in the question.
For Khaled:
F(n) = 1 • 3ⁿ¯¹
n = 1
F(n) = 1 • 3ⁿ¯¹
F(1) = 1 • 3¹¯¹
F(1) = 1 • 3⁰
F(1) = 1 × 1
F(1) = 1
n = 2
F(n) = 1 • 3ⁿ¯¹
F(2) = 1 • 3²¯¹
F(2) = 1 • 3¹
F(2) = 1 × 3
F(2) = 3
n = 3
F(n) = 1 • 3ⁿ¯¹
F(3) = 1 • 3³¯¹
F(3) = 1 • 3²
F(3) = 1 × 9
F(3) = 9
For Wilma
F(n) = 1 • 3ⁿ
n = 1
F(n) = 1 • 3ⁿ
F(n) = 1 • 3¹
F(1) = 1 × 3
F(1) = 3
n = 2
F(n) = 1 • 3ⁿ
F(2) = 1 • 3²
F(2) = 1 × 9
F(2) = 9
n = 3
F(n) = 1 • 3ⁿ
F(3) = 1 • 3³
F(3) = 1 × 27
F(3) = 27
SUMMARY
Using Khaled's formula i.e F(n) = 1 • 3ⁿ¯¹ we obtained 1, 3, 9,..
Using Wilma's formula i.e F(n) = 1 • 3ⁿ
We obtained 3, 9, 27,..
Now, comparing the sequence obtained using the formula of both Khaled and Wilma, we can see that only the sequence of Khaled is the same with the one given in the question. Therefore, only Khaled's formula is correct.
X^2-10x = −16 solution??
Mason randomly chooses a card from a standard deck of playing cards. What is the probability that it is not an ace, given it is a red card
Answer:
there are 52 cards in a deck so the chance is a red card (or not a red card) is 26 out of 52.
Step-by-step explanation:
The solution is 12/13
The probability that the selected card is not an ace but a red card is 12/13
What is Probability?
The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
The value of probability lies between 0 and 1
Given data ,
Let the probability of the selected card is not an ace but a red card be P
Now , the equation will be
Mason randomly chooses a card from a standard deck of playing cards
So , the probability that the card is a red card is
There are 26 red cards in the deck of 52 cards
So , the probability of selecting a red card = 26/52
Now , from the 26 red cards , the probability that the card is not an ace would be = 26 - ( Ace of hearts + Ace of diamonds )
And ,
The probability of the selected card is not an ace but a red card P = 24/26
The probability of the selected card is not an ace but a red card P = 12/13
Therefore , the value of P is 12/13
Hence , the probability is 12/13
To learn more about probability click :
https://brainly.com/question/17089724
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Please can somebody help I am not very good at maths
Answer:
z = 3a + 4
Step-by-step explanation:
Add 4 to both sides
please answer both questions thanks
Answer:
1. tan(65) = x/3
x = 3tan(65)
= 6.434
≈ 6.4
(nearest 10th)
2. cos(43) = AB/17
AB = 17cos(43)
= 12.433
≈ 12.43
(nearest 100th)
A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 30 cm, and the bicycle wheel
makes 3 full rotations before stopping.
How long is the trace of water left on the floor?
Round your answer to the nearest cm.
Answer:
The trace of the water left on the floor is 566 cm.
Step-by-step explanation:
The bicycle wheel has a circular shape, therefore;
1 revolution is the same as the circumference of the wheel. So that 3 revolutions is the same as multiplying the circumference of the wheel by 3.
circumference = 2[tex]\pi[/tex]r
where r is the radius of the wheel (r = 30 cm).
Thus,
circumference = 2 x [tex]\frac{22}{7}[/tex] x 30
= [tex]\frac{1320}{7}[/tex]
circumference = 188.57 cm
3 revolutions = 3 x 188.57
= 565.71 cm
Therefore, the trace of the water left on the floor is 566 cm.
NEED HELP ON THIS ASAP PLZ!! (Marking BRAINLIST)
Answer:
brainllest if right
2
Step-by-step explanation:
Answer:
I don't know sorry
Step-by-step explanation:
The sum of two numbers is 69. One number is 15 less than the other. Find the numbers.
Answer:
58+-43=15
Step-by-step explanation:
The height of a rocket a given number of seconds after it is released is modeled by h(t)=-16t+32t+10 what does t represent?
I forgot a long time ago, What is the slope of the line?
See the image as the line doesn't go through -2 on the x nor -1 on the y
Answer:
[tex] - \frac{4}{5}[/tex]
Step-by-step explanation:
Line is passing through the points (-3, 1) & (2, - 3)
Therefore,
Slope of line
[tex] = \frac{ - 3 - 1}{2 - ( - 3)} \\ \\ = \frac{ - 4}{2 + 3} \\ \\ = - \frac{4}{5} [/tex]
33. What does equal in the solution of the system of equations below? 33 – 4y - z= 14 2r + 3y - 32 = 17 x + 2y + x = 20 10 04 -10 O-4
9514 1404 393
Answer:
(a) 10
Step-by-step explanation:
Attached is a graphical solution using "substitution." An expression was written for z using the first equation, and it was substituted into the remaining two equations. This gave two equations in x and y, easily solved graphically.
We found x = 10, y = 3, so ...
z = 3(10) -4(3) -14 = 30 -12 -14 = 4
The whole solution is (x, y, z) = (10, 3, 4).
Find the domain and range of the function y = √x-3 + 6
Answer:
Domain: [tex][3,\infty)[/tex]
Range: [tex][6,\infty)[/tex]
Step-by-step explanation:
I assume you mean [tex]y=\sqrt{x-3} +6[/tex]?
Take note of how x cannot be less than 3 because it would result in a negative number under the radical, which isn't real. However, x CAN be 3 because [tex]\sqrt{3-3}+6=\sqrt{0}+6=0+6=6[/tex] which is real.
Therefore, the domain of the function is [tex][3,\infty)[/tex]
As for the range of the function, we saw previously that the minimum of the domain resulted in the minimum of the range, which was 6.
Therefore, the range of the function is [tex][6,\infty)[/tex]
See attached graph below for a visual.
in a function hall chairs were arranged in 20 rows and 15 columns on day 1 the next day same chairs were arranged in different numbers of rows and colums
Answer:
What exactly is the question?? u only gave the statement -_-
Step-by-step explanation:
5th grade math. correct answer will be marked brainliest
Answer: How are we going to point it?
Step-by-step explanation:
In Triangle QRS, Angle R is a right angle, m angle Q = 57° and QS = 35. Which of the following expressions correctly
calculates the length of line QR ?
9514 1404 393
Answer:
(3) 35·cos(57°)
Step-by-step explanation:
The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
For the given triangle, this is ...
cos(57°) = QR/QS
Multiplying by QS gives ...
QS·cos(57°) = QR
Filling in the value of QS, we have ...
QR = 35·cos(57°)