Answer:
a) 0.0000001024 probability that he will answer all questions correctly.
b) 0.1074 = 10.74% probability that he will answer all questions incorrectly
c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.
d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly
Step-by-step explanation:
For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that 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.
Each question has five answers, of which only one is correct
This means that the probability of correctly answering a question guessing is [tex]p = \frac{1}{5} = 0.2[/tex]
10 questions.
This means that [tex]n = 10[/tex]
A) What is the probability that he will answer all questions correctly?
This is [tex]P(X = 10)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024[/tex]
0.0000001024 probability that he will answer all questions correctly.
B) What is the probability that he will answer all questions incorrectly?
None correctly, so [tex]P(X = 0)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]
0.1074 = 10.74% probability that he will answer all questions incorrectly
C) What is the probability that he will answer at least one of the questions correctly?
This is
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
Since [tex]P(X = 0) = 0.1074[/tex], from item b.
[tex]P(X \geq 1) = 1 - 0.1074 = 0.8926[/tex]
0.8926 = 89.26% probability that he will answer at least one of the questions correctly.
D) What is the probability that Richard will answer at least half the questions correctly?
This is
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264[/tex]
[tex]P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055[/tex]
[tex]P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008[/tex]
[tex]P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001[/tex]
[tex]P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0[/tex]
[tex]P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0[/tex]
So
[tex]P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328[/tex]
0.0328 = 3.28% probability that Richard will answer at least half the questions correctly
2. Which are not the measures of the sides of a right triangle?
A. O 1, 3,3
B.O 2,2,3,4
cks 1, 3,2
D.O
Answer:
B. because there are too many side lengths to be a triangle
The ratio of the vertical change to the horizontal change to any two points on a line is called _______ of the line
Answer:
The ratio of the vertical change to the horizontal change to any two points on a line is called ___slope___ of the line
Step-by-step explanation:
Slope will be your answer, hope this helps!
work out the circumference of this circle
give your answer in terms of pi
Answer:
37.68
Step-by-step explanation:
Well, the first thing first is to know the outline of the question. So I made sure I knew the diameter. In this case we didn't, so I multipilied 6 by 2 and got 12. Then I multipyed 12 by 3.14 to get 37.68
Explicit formula for
1,5,3,6,12
If 78% of the total is 156 marks, find the total marks in the test
200
206
176
210
Please help What’s the answer?
Answer:
A. x=54 And
B. x= 89
these numbers are less then hundred.
< this sign prove that what is the less number of given question.
A net of a three-dimensional figure is shown.
5 ft
4.ft
10 ft
6 ft
SED
What is the surface area of the three-dimensional figure?
Answer:
184 ft²
Step-by-step explanation:
16x10=160
2x1/2x4x6=24
160+24=184
As a punishment for something naughty that we did, my little brother and I have to whitewash both sides of a fence. We start at the same time, and we each work at a constant rate.
If we each whitewash one side, I'll finish in $2$ hours and my brother will finish in $3$ hours. But I'm a nice kid, so after I finish my side, I go around to the other side and help my brother finish his side. From the time I start helping him, how many minutes does it take us to finish the job?
Answer:
60 minutes which grade
are you in I did it I think
Step-by-step explanation:
I Finish Work in 2 hrs
Work done in 1 Hr = 1/2
Brother Finish work in 3 Hrs Work done in 1 hr = 1/3
Let Say both Complete Work in T hrs as it has to be painted on both sides
Then T (1/2+1/3) = 2
=> T × 5/6 = 2
=> T = 2 Hr 24 Mins
=> T = 12/5 I will Take 2 Hrs to finish my work & 24 Mins to finish after start Helping
Learn more here:
Ajay along with Vijay do a work in 10 days. If Ajay do a work in 1/2...
https://brainly.in/question/10694066Atul, Bhaskar and Chetan can complete a work in 10, 20 and 25..
https://brainly.in/question/920470610 men can complete a job in 200 days. They started the work. After...
https://brainly.in/question/13973456Please tell me how much it would be for 1
Answer: tall is 12 dollars
Step-by-step explanation:
The chart shows the temperatures at noon during a week in January. HELP
Day
Monday
Tuesday
Wednesday
Thursday
Friday
Temperature
-6°F
0°F
5°F
-3°F
3°F
Which day was the coldest?
A. Monday
B. Tuesday
C. Thursday
D. Friday
Monday was the coldest day of the week, at -6 degrees Fahrenheit.
7 divided by 8 in long division
Answer: 0.875
Step-by-step explanation:
Write an emergency that could happen that would have a financial cost
Answer:
Your house burning down.
Step-by-step explanation:
You would have to pay to repair it.
Answer:
Earthquake will make the building crash and people will lost their things and money. And the building need to rebuild.
The building fire will make people lost their things and the building need to rebuild.
Tsunami will make the things near beach all destroy, all the things will lost and more people will die in disaster. All the building need to rebuild in this disaster.
Bank robbery will lost money, sometimes people will kill by the gun of the thief, and the building do not need to rebuild, maybe the window need to rebuild.
Rob the shop will make the boss of the shop lose all the money in the store, the door or window might need to rebuild.
Blasting vehicle will make the things in the car lose. the car need to put the windows on again.
Terrorist attacks will lost lives more than lost money or other things.
Volcanic eruptions will make the building near burn, and so plant and many other things. The building might need to rebuild.
That is all I can think of.
Please Help Now i will give brainest
Answer:
7.14 and 7.15
Step-by-step explanation:
The true square root of 51 to three decimal places is 7.141.
x < 7.141 < y.
If you insert the numbers above, you get a true inequality of
7.14 < 7.141 < 7.15.
Therefore, 7.14 and 7.15 will be your answer.
Hope this helps. Have a nice day. Oh, and one more thing. Surprised I'm not stealing points?
HELP PLEASE DUE IN 3 MINUTES
Answer:
1/5
Step-by-step explanation:
3/5 * 1/3 == 3/15 or 1/5
Answer:
1/3 I believe I could be wrong
Step-by-step explanation:
The length of a piece of ribbon is 250 millimeters.
Which is the equivalent length in meters?
Answer:
250 mm = 0.25 m
Step-by-step explanation:
Answer:
0.25m
Step-by-step explanation:
choose the correct equation
Answer:
y = -3x - 10
Step-by-step explanation:
Equation to represent the given table can be written in the slope-intercept form, y = mx + b.
m = slope = ∆y/∆x
Using the coordinates of any two pairs of values from the table, (0, -10) and (1, -13):
Slope (m) = [(-13 - (-10)]/[1 - 0] = -3/1
Slope (m) = -3
b = y-intercept = the value of y when x is 0 = -10
To write the equation, substitute m = -3 and b = -10 into y = mx + b.
Thus:
y = -3x + (-10)
y = -3x - 10
what is 4x + 8 = 10
The three angles of triangle are in
the ratio 2:3:5. Calculate the size of
the smallest angle.
A. 90°
B.549
C.36
D. 30°
E. 20°
AN
D
♡
Answer:
E I think
..........hope this helps
may kapangyarihan bilang pinakamataas na hukuman sa kolonya
Answer:
which language is this .
Sale 10 % off During the sale, Susan pays $603 for a wedding cake. What was the original price?
Answer:
$670
Step-by-step explanation:
1/10x + 603 = x
x -10x = -6030
-9x = -6030
x = 670
Algebra 2
Help me pls
Answer:
log (150)=2.176091259
Answer:
log104=2.107
log150=2.176
log1025=3.011
log10570=4.024
log7=0.845
Step-by-step explanation:
To solve these questions, you can just plug them into your calculator:
log104=2.107033339≈2.107
log150=2.176091259≈2.176
log1025=3.010723865≈3.011
log10570=4.024074987≈4.024
log7=0.84509804≈0.845
plzzz need help for this question
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The teacher wants to group 87 students into teams which have the same number of students. There must be more than one team. At least how many teams are there and how many students are there in each team?
Answer:
3 teams and 29students in each team.
let, the team be x,y,&z
given all the team r equal so, x=y=z
x+y+z=87
3x=87
x=87/3
x=29
we get, x=y=z=29
hope it helps.
If 9% of a number equals 10, find 90% of that number.
Answer:
100
Step-by-step explanation:
In this problem 10 represents 9% of a number. So, to find 90% you must multiply 10 by 10. You do this because 9% times 10 equals 90%; therefore, 100 must be 90%.
This can also be proven through cross multiplication. To set up a proportion put the percent over the number like, [tex]\frac{9}{10}=\frac{90}{x}[/tex]. Then cross multiply to get the equation, [tex]9x=900[/tex]. Finally, divide both sides to get x=100.
what is the slope of the line passing through po bye A and B?
Factor completely
486+108x+6x^2
Thank you!
Answer:
6(x + 9) (x + 9)
or
[tex]6 (x+9)^{2}[/tex]
Step-by-step explanation:
[tex]468 + 108x + 6x^{2} \\6x^{2} +108x + 468[/tex]
Greatest common factor of 6, 108, and 486:
6 x 1 = 6
6 x 18 = 108
6 x 81 = 486
GCF: 6
so:
[tex]6(x^{2} +18x +81)[/tex]
[tex]x^{2} +18x + 81[/tex]
factors to:
(x + 9) (x + 9)
because:
9 x 9 = 81
9 + 9 = 18
So:
It factors completely too:
6(x + 9) (x + 9)
or
[tex]6 (x+9)^{2}[/tex]
Mike wants to find the volume of 4 basketballs. If each basketball has a radius of 4.5
in, what would the volume of 4 basketballs be?
Emma is training for a 10-kilometer race. She wants to beat her last 10-kilometer time, which was 1 hour 10 minutes. Emma has already run for 55 minutes. Which inequality can be used to find how much longer she can run and still beat her previous time? (1 hr = 60 min)
let x be how much longer she can run the race and still beat her previous time
55(min) + x(min) < 1(hr) + 10(min)
55(min) + x(min) < 60(min) + 10(min)
55 + x < 60 + 10
x < 60 + 10 - 55
x < 15(min)
Answer:
Answer is A
Step-by-step explanation: Taking the test so the answer is A
please help me to understand. Thanks.
Answer:
B. {(x, y): y = x²}
Step-by-step explanation:
A function is a graph where every input (x-value) has one and only one output (y-value). In other words if the value for x=2, there will only be one corresponding point for y. For the function in B, that y-value would be 4. Both A and D, solve for y, means taking the square root which leaves a +/- x-value. C is absolute value of y, which means the positive and negative values for y would have the same point. Only choice B has x-values corresponding to a singular y-value. If you can remember what these graphs look like you can test if they are functions based on the vertical line test.
Question 8 of 10 A decrease in the amount of principal owed on a loan is called what? A. Note reduction B. Payment number C. Amortization O D. Unpaid balance
Answer:
A (Note Reduction)
Step-by-step explanation:
A p e x of course
Answer: note reduction
Step-by-step explanation:
A PE C
