Probabilities are used to determine the chances of an event.
Let P represents the event that a student passes the course, and C represents the event that a student completes the assignment
(a) The probability a student passed the course given that they completed their homework?
From the table, we have:
[tex]\mathbf{n(P\ n\ C) = 25}[/tex]
[tex]\mathbf{n(C) = 30}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P\ n\ C)}{n(C)}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{25}{30}}[/tex]
[tex]\mathbf{Pr = 0.8333}[/tex]
Express as percentage
[tex]\mathbf{Pr = 83.33\%}[/tex]
Hence, the probability a student passed the course given that they completed their homework is 83.33%
(b) The probability a student passed the course given that they didn't complete their homework
From the table, we have:
[tex]\mathbf{n(P\ n\ C'= 7}[/tex]
[tex]\mathbf{n(C') = 25}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P\ n\ C')}{n(C')}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{7}{25}}[/tex]
[tex]\mathbf{Pr = 0.28}[/tex]
Express as percentage
[tex]\mathbf{Pr = 28\%}[/tex]
Hence, the probability a student passed the course given that they didn't complete their homework is 28%
(c) The probability a student completed their homework given that passed the course?
From the table, we have:
[tex]\mathbf{n(P\ n\ C) = 25}[/tex]
[tex]\mathbf{n(P) = 32}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P\ n\ C)}{n(P)}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{25}{32}}[/tex]
[tex]\mathbf{Pr = 0.78125}[/tex]
Express as percentage
[tex]\mathbf{Pr = 78.125\%}[/tex]
Approximate
[tex]\mathbf{Pr = 78.13\%}[/tex]
Hence, the probability a student completed their homework given that they passed the course is 78.13%
(d) The probability a student didn't complete their homework given that they didn't pass the course
From the table, we have:
[tex]\mathbf{n(P'\ n\ C'= 18}[/tex]
[tex]\mathbf{n(P) = 23}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P'\ n\ C')}{n(P')}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{18}{23}}[/tex]
[tex]\mathbf{Pr = 0.7826}[/tex]
Express as percentage
[tex]\mathbf{Pr = 78.26\%}[/tex]
Hence, the probability a student didn't complete their homework given that they didn't pass the course is 78.26%
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Find the point on the line y=x that is closest to the point (-4,8)
Answer:
(2,2)
Step-by-step explanation:
What is 2x-3 when x=6
Answer:
0
Step-by-step explanation:
The graphs show information about the different journeys of 4 people.
a)
Which graph shows a person running then walking?
b)
Which graph shows a person who forgot something
and had to return home?
Answer:
A) b
B) c
Step-by-step explanation:
A) a large distance is covered in a short period of time but then the speed decreases
B) the person travels some distance but then returns to their starting point for a while(their home) and then starts on their journey again
What is 3 x 320 x 5 x 10245?
Answer:
49176000
I hope this helps.
How many equal parts are there in this image
Answer:
6
It's kind of blury, so I can't really see it.
Answer:
4
Step-by-step explanation:
In which quadrant does the angle t lie if tan(t)>0 and cos(t)<0?
A) II
B) IV
C) Cannot be determined
D) III
E) I
Quadrant is a quarter of a coordinate plane
The location of angle t is in quadrant 3
The trigonometry equations are given as:
tan(t)>0 and cos(t)<0
The cosine of an angle is negative in the following quadrants
Quadrant 2Quadrant 3The cosine of an angle is positive in the following quadrants
Quadrant 3The intersection of the above points is quadrant 3
This means that the angle is in quadrant 3
Hence, the true option is (D) III
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Solve
-x + 4 = x + 6
Answer:
-1
Step-by-step explanation:
1. subtract 4 from both sides
-x = x+2
2. subtract x from both sides
-2x = 2
3. divide both sides by 2
simplify
x= -1
Hope this helps :)
PLEASE HELP! Economics
Answer:
C is the answer.
Step-by-step explanation:
the US capital account was in surplus and Japanese current account
The ratio of ronnys tern, dougs rent and ronalds rent is 4:5:8. Their total rent if $3723. What is the cost of each persons rent
Answer:
The cost of Ronny is $876, Dough is $1095 and Ronald is $1752.
Step-by-step explanation:
Firstly, make all ratios into units:
Let Ronny = 4 units, Doug = 5 units,
Ronald = 8 units, Total = $3723
4 units + 5 units + 8 units = 17 units
17 units = $3723
1 unit = $3723 ÷ 17
1 unit = $219
Given that 1 unit is equals to $219. Let find the amounts:
Ronny = 4 × 219 = $876
Doug = 5 × 219 = $1095
Ronald = 8 × 219 = $1752
Find the argument of the complex number 2 = 4+ 3i to the nearest whole degree.
Using it's formula, it is found that the argument of the complex number z = 4+ 3i is of 37º.
The standard format of a complex number is:
[tex]z = a + bi[/tex]
In which:
a is the real part.b is the imaginary part.The argument is given by:
[tex]\theta = \tan^{-1}\left(\frac{b}{a}\right)[/tex]
In this problem, the number is:
[tex]z = 4 + 3i[/tex]
Hence, [tex]a = 4, b = 3[/tex], and:
[tex]\theta = \tan^{-1}\left(\frac{3}{4}\right) = 37[/tex]
For more on the argument of a complex number, you can take a look at https://brainly.com/question/4569130
If you are conducting an experiment where the probability of a success is 0.06 and you are interested in the probability of two successes in 15 trials, the correct probability function to use is the _____.
In the question, the probability of getting the given number of success
from a specified number of trials is required.
The correct probability function to use is the binomial probability function.
Reasons:
The given parameters are;
The probability of success = 0.06
The number of trials = 15 trials
The probability of interest = The probability of two successes in 15 trials
Solution;
The required probability is given by the following binomial probability
distribution formula;
[tex]P(x) = \dbinom{n}{x}\cdot p^x \cdot q^x = \mathbf{\dfrac{n!}{(n - x)! \cdot x!} \cdot p^x \cdot q^x}[/tex]
Where:
n = Number of trials
x = Number of required success
p = Probability of a success
q = Probability of one failure = 1 - p
For the question, we get;
[tex]P(x) = \dfrac{15!}{(15 - 2)! \times 2!} \times 0.06^2 \times (1 - 0.06)^{15 - 2} \approx \mathbf{0.169}[/tex]
Therefore, the correct option is, a binomial probability function
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The question options are;
Binomial probability function
Normal probability density function
Standard normal probability density function
Poisson probability function
What is the decimal multiplier to decrease by
15%?
Answer:
0.85
Step-by-step explanation:
Answer:
first calculate the percenatge of the ammount and then either add this answer on to increase the qauntity
The graph of y=⅔ x - 12 intersects the y-axis at Q (0, -12) and is perpendicular to a line joining Q to the point P ( x , 0). Find x
The ratio of the number of cupcakes to the number of pastries in a box is 7:2. Which table shows the possible amounts of cupcakes and pastries in a box, given the ratio? (2 points)
Question 1 options:
1)
Cupcakes Pastries
7 2
21 6
42 8
84 10
2)
Cupcakes Pastries
7 2
21 6
28 12
35 24
3)
Cupcakes Pastries
7 2
21 17
42 38
84 80
4)
Cupcakes Pastries
7 2
14 4
28 8
56 16
Answer:
I wish I could help but I don't know
Answer:
D is correct
Step-by-step explanation:
A new hotel was built with r rooms. The first weekend it was open, 3/5 of them were reserved. Which of the following expressions represents the number of rooms which were reserved?
A r-3/5
B r x 3/5
C r+3/5
D ÷3/5
PLEASE HELP ITS STUDY ISLAND
Answer:
c r/ 3/5
Step-by-step explanation:
i think
Write a function in any form that would match the graph shown below
Answers:
Vertex form: y = -2(x-1)^2 + 8Standard form: y = -2x^2 + 4x + 6Pick whichever form you prefer.
=============================================================
Explanation:
The vertex is the highest point in this case, which is located at (1,8).
In general, the vertex is (h,k). So we have h = 1 and k = 8.
One root of this parabola is (-1,0). So we'll plug x = -1 and y = 0 in as well. As an alternative, you can go for (x,y) = (3,0) instead.
Plug those four values mentioned into the equation below. Solve for 'a'.
y = a(x-h)^2 + k
0 = a(-1-1)^2+8
0 = a(-2)^2+8
0 = 4a+8
4a+8 = 0
4a = -8
a = -8/4
a = -2
The vertex form of this parabola is y = -2(x-1)^2+8
Expanding that out gets us the following
y = -2(x-1)^2+8
y = -2(x^2-2x+1)+8
y = -2x^2+4x-2+8
y = -2x^2+4x+6 .... equation in standard form
HELPPP LAST ATTEMPT!!
Answer:
B' (-1,-5)
Step-by-step explanation:
When it is reflected over the y-axis, the y coordinate stays the same but the x coordinate inverses. In this situation since the x in point B is a positive, the x in point B' will be a negative.
can someone heelp me plz
Answer:
1052 is MLII, 450 is CDL, 952 is CMLII, and 942 is CMXLII.
Step-by-step explanation:
For 1052, M=1000 L=50 and II= 2 and if you add all those you get 1052. For 450, CD=400 and L=50 and if you add all those up then you get 450. For 952, CM=900 L=50 and II=2 and if you add all those up then you get 952. For 942, CM=900 XL=40 and II=2, and if you add all those up then you get 942.
POSSIBLE POINTS: 33.33
homeowner collects data about the amount of oil A, in gallons, used to heat the house per month for 5 months and the
verage monthly temperature t, in degrees Fahrenheit, for those months. The scatter plot shows the data. The function
(t) = -1.4t + 96 best fits these data.
=============================================================
Explanation:
Check out the diagram below. I've plotted the regression line A(t) = -1.4t+96 on the same xy grid as the given scatterplot. This line tries to get as close as possible to all of the points.
From here, we plug in each of the temperatures mentioned in the five answer choices (10, 15, 68.5, 55, 0). The outputs form the second column of the table in that same diagram.
For example, if we plugged in t = 10, then,
A(t) = -1.4t+96
A(10) = -1.4(10)+96
A(10) = -14 + 96
A(10) = 82
Telling us that a temperature of 10 degrees F would have a predicted or estimated usage of roughly 82 gallons of oil. This points to choice A being one of the answers.
The other temperature values are handled the same way. Choice B is false because t = 15 does not lead to A(t) = 85. Instead, it's A(15) = 75 meaning it's 10 degrees off the mark.
Choice C is true though. Plugging t = 68.5 into A(t) leads to A(t) = 0.1 which rounds to 0 assuming we're only worried about whole numbers. If your teacher is considering decimal values, then choice C is unfortunately false. For now I'll assume your teacher wants you to round.
If we tried t = 55, then we'd get A(15) = -1.4*55+96 = 19 which is not 5 as we'd want. This rules out choice D.
Lastly, plug in t = 0 to find that A(t) = 96. This leads to choice E being one of the answers.
For the graph attached statements A, C and E are true.
Function that fits the given data in the graph,
A(t) = -1.4t + 96Here, t = temperature in Fahrenheit
A(t) = Oil used in gallons
By substituting the value of 't' in the equation we can get the amount of oil used A(t) to heat the house.
Option A
By substituting t = 10°F,
A(10) = -1.4(10) + 96
= 82 gallons
Therefore, statement is true.
Option B
For t = 15°F,
A(15) = -2.4(15) + 96
= 60 gallons
Statement is False.
Option C
For t = 68.5°F
A(5) = -1.4(68.5) + 96
= 0.1 gallons
≈ 0 gallons
Statement is True.
Option D
For t = 55°F,
A(55) = -1.4(55) + 96
= 19 gallons
Statement is False.
Option E
For t = 0°F
A(0) = -1.4(0) + 96
= 96 gallons
Statement is true.
Therefore, statements given in options A, C and E are True.
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If right you get brainiest!
A little mermaid can swim 12 miles downstream in the same amount
of time she can swim 8 miles upstream. What is the little mermaid's
speed in still water if the speed of the current is 4 mph?
Answer:
20 mph
Step-by-step explanation:
time = distance / speed
speed up stream = s - 4
speed down stream = s + 4
time up = time down
8 / (s - 4) = 12 / (s + 4)
cross multiply
8s + 32 = 12s - 48
subtract 8v from both sides
32 = 4s - 48
add 48 to both sides
80 = 4s
Divide both sides by 4
20 = s
20mph
Need help please
Will give Brainliest
Answer:
Step-by-step explanation:
1) Inequality Form: a < 2.9 Interval Notation: ( 2.9 )
2) graph
same as 3, 4, 5
6) Inequality Form: 2 < y < 5 Interval Notation: ( 2 , 5 )
7)
a) 110+92=202+x=c
b) 110+92=202
202+98=300
helppppppp pleaseeee again im sorry but i dont know any of itttttt.
Step-by-step explanation:
sqrt(5x)×(sqrt(8x²) - 2×sqrt(x)) =
sqrt(5x × 8x²) - 2×sqrt(5x × x) =
sqrt(40x) × x - 2x × sqrt(5) =
2x×sqrt(10x) - 2x×sqrt(5)
therefore, the last option is correct.
Through how many radians does the minute hand of a clock turn in three hours?
3 pi
9 pi
6 pi
Ashley received a $24 discount on a radio she bought for $98.00. What is the percent of discount she saved?
Answer:
24.49
Step-by-step explanation:
Answer:
24.489%, but most of the time they only go to 2 decimal places so 24.49%
Step-by-step explanation:
Silvia is planning to use a 4-year loan to purchase a car.
• The price of the car is $8,575.
• The amount of interest she will have to pay on the loan is $1,036
Silvia will combine the price of the car and the amount of interest to determine how much she must repay. She will make 48 equal monthly
payments.
Which of the following is the best estimate of each monthly payment Silvia will make?
A. $175
B. $200
C. $225
D. $250
Answer:
B
Step-by-step explanation:
8575 + 1036 = 9611
9611 is the full payment
9611 / 48 months = 200.229
About $200 every month
The best estimate of each monthly payment that Silvia will make is given by: Option B: $200
What to calculate net payable amount after interest is applied?The net payable amount is the sum of main amount to be paid + the amount of interest.
For this case, it is specified that:
The price of the car is $8,575.The amount of interest she will have to pay on the loan is $1,036Thus, we get:
Total payable amount by Silvia for car purchasing = $8575 + $1036 = $9,611
This payable amount is divided in 48 equal parts. The value of each part (the monthly payment amount by Silvia) is:
[tex]\dfrac{9611}{48} \approx 200 \: \rm dollars[/tex]
Thus, the best estimate of each monthly payment that Silvia will make is given by: Option B: $200
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Please help me find my gpa I don’t know how
I have a C, A, B the rest are f
Answer:
Your GPA would be 1.5 If you have 6 periods.
Step-by-step explanation:
A = 4 GPA Points
B = 3 GPA points
C = 2 GPA Points
D = 1 GPA Points
F = 0 GPA Points
With that knowledge you calculate 2 (C) + 4 (A) + 3 (B) + 0 (F) + 0 (F) + 0 (F) assuming you have 6 periods which adds up to 9. You divide by the number of periods (6) totaling to 1.5 GPA Points.
Write a function in any form that would match the graph shown below
9514 1404 393
Answer:
f(x) = 2(x +2)^2(x -5)
Step-by-step explanation:
The root at x=-2 has even multiplicity. The curve is not flat there, so the multiplicity is 2, not higher. The root at x=5 has multiplicity 1. Then the factored form of this cubic is ...
f(x) = a(x +2)^2·(x -5)
The local minimum when a=1 is about -50, so we judge the leading coefficient to be 2. The desired function is ...
f(x) = 2(x +2)^2(x -5)
Interest and fees
the total cost of a credit purchase.
A. maintain
O B. decrease
C. do not affect
D. increase
Answer:
D. increase
Step-by-step explanation
Intrest and fees are used to make process, and It increases the cost. You have to pay it back in the end.
Answer:
B
Step-by-step explanation:
Normally a normal card purchase won't affect the credit but since your using your credit's to purchase I think it will decrease it, it also depends how many times you use your card, cuz banks sure do be checking. So I hope I helped!
The numbers and letters on a license plate are determined by the state that issues the license
plate. Suppose a state had a system that used 5 letters and 2 digits for a total of 7 characters on
a license plate. How many different license plates can this system produce?
297, 034, 400
594, 068, 800
1, 188, 137, 600
O 2, 376, 275, 200
Which set of side lengths will form a triangle
A: 16ft, 4ft, 21ft
B: 30ft, 30ft, 60ft
C: 12ft, 12ft, 20ft
D: 3ft, 5ft, 10ft
PLS HELP
Answer:
the set of side lengths will be d