Answer:
a) 0.0031 = 0.31% probability of marking exactly 3 incorrect answers.
b) 0.0035 = 0.35% probability of passing.
Step-by-step explanation:
For each question, there are only two possible outcomes. Either the student chooses the correct answer, or he does not. Questions are independent of each other. 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.
10 multiple choice questions
This means that [tex]n = 10[/tex]
4 answers that are equally likely to be the correct one. The quiz taker selects the answers randomly.
This means that [tex]p = \frac{1}{4} = 0.25[/tex]
a) Probability of marking exactly 3 incorrect answers.
3 incorrectly = 7 correctly, so this is P(X = 7).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{10,7}.(0.25)^{7}.(0.75)^{3} = 0.0031[/tex]
0.0031 = 0.31% probability of marking exactly 3 incorrect answers.
b) Probability of passing
At least 7 correct, so
[tex]P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{10,7}.(0.25)^{7}.(0.75)^{3} = 0.0031[/tex]
[tex]P(X = 8) = C_{10,8}.(0.25)^{8}.(0.75)^{2} = 0.0004[/tex]
[tex]P(X = 9) = C_{10,9}.(0.25)^{9}.(0.75)^{1} \approx 0[/tex]
[tex]P(X = 10) = C_{10,10}.(0.25)^{10}.(0.75)^{0} \approx 0[/tex]
[tex]P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0031 + 0.0004 + 0 + 0 = 0.0035[/tex]
0.0035 = 0.35% probability of passing.
5th grade math. Correct answer will be marked brainliest.
Answer:
part a is 3500
Step-by-step explanation:
WILL GIVE BRAINLIEST, 100 POINTS
The diagram shows a 6 ft student standing near a tree. The shadow of the student and the shadow of the tree end at point A. What is the height of the tree?
Question 1 options:
90 ft^2
90 ft
18 ft
18 ft^2
Answer:
18ft
Step-by-step explanation:
:p
The height of the tree is 14 feet.
What is Proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
Height of Man= 6 feet
Shadow height= 5 feet
and, Height of tree shadow= 15 feet
So, using Proportion
FE/ BC = FA/ AC
6 / x = 5 / 15
5x= 90
x= 14 feet
Hence, the tree is 14 feet tall.
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Last month, when Joe took his puppy to the veterinarian, the puppy weighed 4.8 pounds. This month, the puppy weighed 7.2 pounds. What is the percentage increase of the weight of the puppy?
Cheese Or Pickles? WILL GIVE BRAINLIEST
Answer:
Pickles. My friends are allergic to cheese.
A soda company conducted a taste test for three different kinds of soda that it makes.
It surveyed 200 people in each age group about their favorite flavor and the results are shown in
the table below.
Age
Soda A Soda B Soda C
Under 20
30
44
126
20 to 39
67
75
58
40 to 59
88
78
34
60 and over
141
49
10
10.
What is the probability that a participant chose Soda C or was under 20 years old?
Rounded to the nearest tenth
35.2%
37.8%
52.5%
50%
Answer:
Step-by-step explanation:
35percent was yonger
10.Suppose that you have bought 3 large glass-fronted cabinets. You have three workers, A, B and C, to help you with transporting the cabinets from the furniture store to your home, and you want them to finish it in (at most) one trip each. From past experience, it is known that the probability that A breaks something in a given trip is 10%, the probability that B breaks something in a given trip is 15%, and the probability that C breaks something in a given trip is 20%. The events that A, B, or C breaks something in a given trip are independent of each other. You come up with three strategies: (a) A transports all the furniture, (b) A transports two cabinets and B transports one cabinet, or (c)
Answer:
Step-by-step explanation:
To find the expected no of broken cabinets for each strategy.
If A transport all the furniture
Suppose X₁ = number of furniture A broken
X₁ follows a binomial with n = 3, p = 0.10
E(X₁) = np
E(X₁) = 3 × 0.1
E(X₁) = 0.3
If A transport two (2) cabinets & B transport one (1) cabinet
expected no. of the broken cabinet by A out of 2 is
= 2 × 0.1
= 0.2
Suppose X₂ denotes the no of broken furniture by B
E(X₂) = np
where n= 1 and p = 0.15
E(X₂) = np
E(X₂) = 1 × 0.15
E(X₂) = 0.15
Thus. the expected number of broken cabinets = 0.2 + 0.15 = 0.35
5) The diagram below shows a ramp connecting the ground
to a loading platform 4.5 feet above the ground. The ramp
measures 11.75 feet from the ground to the loading
platform. What is the angle of elevation formed by the
ramp and the ground to the nearest degree?
Step-by-step explanation:
///////hope it helps:)
The trigonometric function gives the ratio of different sides of a right-angle triangle. The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse.
What is Sine (Sinθ)?The Sine or Sinθ in a right angle triangle is the ratio of its perpendicular to its Hypotenuse. it is given as,
Sin(θ) = Perpendicular/Hypotenuse
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The hypotenuse is the longest side of the triangle.
The angle of elevation is equal to,
The angle of elevation = Sin⁻¹ (4.5/11.75)
= 22.5183° ≈ 23°
Hence, the angle of elevation formed by the ramp by the ground to the nearest degree is 23°.
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i need helppp could you help please pl,s pls pls pls pls pls plks pls pls pls pls pls pls
Answer:(-4,6)
Step-by-step explanation:
you go down four then over six and you find the letter F
Answer:
(6, -4)
Step-by-step explanation:
x axis is before the y axis
16 .Write an equation that represents the statement
below.
"Twelve less than a number, x, is 18."
Answer:
x-12=18
Step-by-step explanation:
Answer: if X = 30, then the equation is 30 - 12 = 18
A recipe requires one quarter cup of milk as a base and then, In addition, 1 cup of milk for every 4 cups of flour. Choose a linear equation that describes the relations.
Answer:
Step-by-step explanation:
Where are the choices?
m and f are the cups of milk and flour, respectively.
m = ¼f + 1
Can I please get the answer ?
Answer:
The sign depends on the sign of the larger number.
Determine which is the better buy
1 kilogram of bananas for $2.06 or 4 kilogram of bananas for $7.48
PLZ EXPLAIN PLZ
Answer: 4 kilograms of bananas for $7.48
Step-by-step explanation:
Unit price for 1 kilo= $2.06
2.06 x 4 = 8.24
Unit price for 4 kilo= $1.87
2.06 > 1.87
So, 4 kilograms of bananas is the better buy.
Simple form:
Answer 1: 2.06
Answer 2: 1.87
Answer 3: greater than
Answer 4: 4 kilograms of bananas for $7.48
A stereo store is offering a special price on a complete set of components (receiver, compact disc player, speakers, turntable). A purchaser is offered a choice of manufacturer for each component.
Receiver: Kenwood, Sony, Sherwood
Compact disc player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity, Polk
Turntable: Onkyo, Sony, Teac, Technics
A switchboard display in the store allows a customer to hook together any selection of components (consisting of one of each type). Use the product rules:
A. In how many ways can one component of each type beselected?
B. In how many ways can components be selected if boththe receiver and the cd player are to be sony?
C. In how many ways can components be selected if noneis to be sony?
D. In how many ways can a selection be made if at leastone sony component is to be included?
E. If someone flips the switches on the selection in acompletely random fashion, what is the probability that the systemselected contains at least one sony component?
Answer:
Step-by-step explanation:
A stereo store is offering a special price on a complete set of components (receiver, compact disc player, speakers, turntable). A purchaser is offered a choice of manufacturer for each component.
Receiver: Kenwood, Sony, Sherwood
Compact disc player: Onkyo, Pioneer, Sony, Technics
Speakers: Boston, Infinity, Polk
Turntable: Onkyo, Sony, Teac, Technics
A switchboard display in the store allows a customer to hook together any selection of components (consisting of one of each type). Use the product rules:
A. In how many ways can one component of each type beselected?
B. In how many ways can components be selected if boththe receiver and the cd player are to be sony?
C. In how many ways can components be selected if noneis to be sony?
D. In how many ways can a selection be made if at leastone sony component is to be included?
E. If someone flips the switches on the selection in acompletely random fashion, what is the probability that the systemselected contains at least one sony component?
Suppose Raj receives a raise for his hard work and now earns $6.25 per hour how many hours would he need to work to earn $132?
Answer:
22
Step-by-step explanation:
Answer & Step-by-step explanation:
Divide how much he wants to earn by how much he earns per hour:
132/6.25 = 21.12
He needs to work 21.12 hours to earn $132.
Guys can u help me please
Answer:
the first one is 5 times 5 times 5
the second is 7 times 7
the third is 2 times 2 times 2
Step-by-step explanation:
5x5x57x72x2x2PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLS SHOW THE WORK!!!!!!!!
Answer:
1. x = - 1 -y over 2
2. x = -4(2+y) over 3
Step-by-step explanation:
Answer:
1. x = - 1 -y over 2
2. x = -4(2+y) over 3
:)
what is 3/5 + 3/2 ?
I’ll mark as BRAINLIEST
Answer:
2 1/10
Step-by-step explanation:
What are the slope and Y intercept of Y≥-2x+3
Some one please help me on this I am very much dum
I don’t get this Need help asap
Answer:
Step-by-step explanation:
x - 2y =8
-2y = -x + 8
[tex]y = \frac{-1}{-2}x+ \frac{8}{-2}\\\\y =\frac{1}{2}x - 4[/tex]
When x = 4,
[tex]y = \frac{1}{2}*4-4\\\\ = 2-4\\\\y = -2[/tex]
(4, - 2)
When x = -4,
[tex]y =\frac{1}{2}*(-4) - 4\\\\ = -2 - 4\\\\= - 6[/tex]
(-4, -6)
Plot the points (4, -2) and (-4 , -6) in the graph and Join the points
find x and round to the nearest tenth
Answer and Step-by-step explanation:
22ft = x (c)
20ft = y (b)
18ft = z (a)
Plug into equation.
[tex]22^{2} = 20^{2} + 18^{2} - 2(20)(18)cosC (X)\\\\484 = 724 - 720cosC\\\\-240 = -720cosC\\\\\frac{1}{3} = cosC\\\\cosx^{1} (\frac{1}{3} ) = C\\\\C = 70.5288\\\\[/tex]
C ≈ 70.5 is the answer.
Please answer the question and explain your answer. I will be marking brainiest with the correct answer and best explanation.
Answer:
28.26
Step-by-step explanation:
A = r^2
So the equation is. Area of circle = pi(3.14) * radius(3) to the power of 2 (^2)
A = 3.14(3)^2
A = 3.14(9)
A = 28.26
SOMEONE PLSS HELP ASAP
Chloe has $15 to spend on pencils. Each box of pencils costs $2. How many
boxes of pencils can Chloe have buy? How much money will she have left
after she buys the pencils?
Please help I need by Tomorrow!
Answer:
[tex]f(a) = 5a + 1[/tex]
[tex]f(a + h) = 5a + 5h +1[/tex]
[tex]\frac{f(a + h) - f(a)}{h} =5[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5x + 1[/tex]
Solving (a): f(a)
Substitute a for x in [tex]f(x) = 5x + 1[/tex]
[tex]f(a) = 5a + 1[/tex]
Solving (b): f(a + h)
Substitute a + h for x in [tex]f(x) = 5x + 1[/tex]
[tex]f(a + h) = 5(a + h) +1[/tex]
Open bracket
[tex]f(a + h) = 5a + 5h +1[/tex]
Solving (c): [tex]\frac{f(a + h) - f(a)}{h}[/tex]
In (a):
[tex]f(a) = 5a + 1[/tex]
In (b):
[tex]f(a + h) = 5a + 5h +1[/tex]
So:
[tex]\frac{f(a + h) - f(a)}{h} =\frac{5a+5h+1 - (5a+1)}{h}[/tex]
Open bracket
[tex]\frac{f(a + h) - f(a)}{h} =\frac{5a+5h+1 - 5a-1}{h}[/tex]
Collect Like Terms
[tex]\frac{f(a + h) - f(a)}{h} =\frac{5a- 5a+5h+1 -1}{h}[/tex]
[tex]\frac{f(a + h) - f(a)}{h} =\frac{5h}{h}[/tex]
[tex]\frac{f(a + h) - f(a)}{h} =5[/tex]
0.7k − 1.6 ÷ 2 − 5.2 = 1.7 − 0.7
your answer is k=10 the step by step is kn the picture
Ben flew his small airplane 660 km in 6 hours flying with the wind. He flew 350 km against the
wind in 7 hours. Find the rate at which he flew in still air and the rate of the wind.
Answer:
r = 80 KM/HR
w= 30 CM/HR
Step-by-step explanation:
Chicken costs $3.20 per pound, and beef costs $4.59 per pound. What is the exact cost of 3 pounds of chicken?
Answer:
$9.60
Step-by-step explanation:
3.20x3=9.60
Jamie can paint a wall in 54 minutes Together Connie and Jamie can paint the same wall in 36 minutes How long would it take Connie to paint the same wall by herself
Answer:
The answer is 108
Step-by-step explanation:
I did this for my exam got 100
Together they can paint 5/108 of a wall in 1 minute. So they can paint the entire wall in 108 minutes.
We have given that,
John can paint 1/54 of a wall in 1 minute.
James can paint 1/36 of a wall in 1 minute.
What is the formula for total wall paint in one minute?Total wall paint of both in one minute is calculated by adding the both the paint in one minute it gives us the total paint in one minute
Therefore ,total wall paint in one minute =1/54 + 1/36
So if they work together, they can both paint 1/54 + 1/36 of a wall in 1 minute.
1/54 + 1/36 = 2/108 + 3/108 = 5/108 = 0.04629.
Therefore,together they can paint 5/108 of a wall in 1 minute. So they can paint the entire wall in 108 minutes.
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i need help.........
Answer:
17
Step-by-step explanation:
