A student is about to take a true-false, 5-question quiz, with absolutely no knowledge of the subject. So, the student flips a coin to determine their response to each question. If you let the random variable X = "a number of correct answers on the quiz," what is the correct histogram?
Answers are from 1-4, and they are all in order.
Answers
Using the binomial distribution, considering the probability of each event, the correct histogram is the fourth one.
For each question, there are only two possible outcomes, either the student guesses the correct answer, or not. The probability of guessing the correct answer on a question is independent of any other question, hence the binomial distribution is used to solve this question.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
There are questions, hence n = 5.They are true-false questions, that is, they have one correct option out of 2, hence p = 0.5.Then, the probabilities are as follows:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.5)^{0}.(0.5)^{5} = 0.03125[/tex]
[tex]P(X = 1) = C_{5,1}.(0.5)^{1}.(0.5)^{4} = 0.15625[/tex]
[tex]P(X = 2) = C_{5,2}.(0.5)^{2}.(0.5)^{3} = 0.3125[/tex]
[tex]P(X = 3) = C_{5,3}.(0.5)^{3}.(0.5)^{2} = 0.3125[/tex]
[tex]P(X = 4) = C_{5,4}.(0.5)^{4}.(0.5)^{1} = 0.15625[/tex]
[tex]P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]
Hence the fourth histogram is correct.
More can be learned about the binomial distribution at https://brainly.com/question/14424710
Related Questions
( PLEASE HURRY, WILL GIVE BRAINLIEST IF CORRECT )
LMNP is rotated 180° clockwise about the origin
What are the coordinates of M’?
o A. M’(4, -3)
o B. M’(3, -4)
o C. M’(-3, -4)
o D. M’(-4, 3)
Answers
Answer:
the answer is c, (-3,-4)
Step-by-step explanation:
the rule for a 180 degree rotation is: (x,y) ---> (-x,-y)
Hope this helps! :)
please help me im stuck all the info is in the screenshot
Answers
Answer:
ok so the sale ticket cost 54 so we want to find what the regurler one cost so lets just make a algreva equation
0.9x=54
divide by 0.9
54 divide by 0.9=60
so a regurer ticket cost 60
54=0.9r
Hope This Helps!!!
Find the distance between the two points
(4, 2) and (8,8)
Answers
Answer:
Exact Form:
2[tex]\sqrt[/tex]13
Decimal Form:
7.21
-----------------
Have a great day! :D
What is the volume of the shape
Answers
Answer:
942m^2
Step-by-step explanation:
to find the answer you do pi * r^2 *h
pi is 3.14 r is 5 and h is 12= 3.14* 5^2 * 12
now you have 78.5*12
now you're left with your answer 942m^2
To celebrate the first day of school, Emma brought in a tray of caramel brownies and walnut brownies. The tray had a total of 30 brownies, of which 90% were caramel. How many caramel brownies did Emma bring?
Answers
Answer:
90/100×30=27
27 caramel brownies
Value of expression a (a2 + a +1) + 5 for a = 0 is ___________
Answers
Answer:
5
Step-by-step explanation:
0(0×2 + 0 + 1) + 5
0(0+0+1)+5
0 + 0 + 0 +5
= 5
Yesterday, Grace drove 35 1/2
miles. She used 1 1/4
gallons of gasoline. What is the unit rate for miles per gallon?
Answers
Answer:
35 1/2 Miles divied by 1 1/4=28.4 gallons
Step-by-step explanation:
what is the measure of ∠C?
Answers
Answer:
Measure C, the Sacramento Community Stabilization and Fair Rent Charter Amendment is on the November ballot for the city of Sacramento after a lengthy court battle. The measure is written to supersede the Sacramento Tenant Protection Act, which was passed in 2019. Here are the results for Measure C as they come in:
Step-by-step explanation:
i will give 100 points
Answers
Answer:
y-intercept = (0, 8)
x-intercepts = (4, 0) and (-2, 0)
vertex = (1, 9)
5th point = (2, 8)
Step-by-step explanation:
As the coefficient of x² is negative, the curve will be "n" shaped.
y-intercept
crosses the y-axis when x = 0
substitute x = 0 into the function and solve for y:
[tex]\implies y=-(0)^2+(2 \times 0)+8=8[/tex]
Therefore, y-intercept = (0, 8)
x-intercept
crosses the x-axis when y = 0
set the function to zero and solve for x:
[tex]\implies -x^2+2x+8=0[/tex]
[tex]\implies x^2-2x-8=0[/tex]
[tex]\implies (x-4)(x+2)=0[/tex]
[tex]\implies x=4, x=-2[/tex]
Therefore, x-intercepts = (4, 0) and (-2, 0)
vertex
vertex form: [tex]y=a(x-h)^2 +k[/tex], where (h, k) is the vertex
expand vertex equation: [tex]y=ax^2 -2ahx+ah^2 +k[/tex]
compare coefficients with original function: [tex]y=-x^2+2x+8[/tex]
[tex]\implies a=-1, h=1, k=9[/tex]
So vertex = (1, 9)
5th plot point
You can choose any value of x and input it into the equation for y, but for symmetry, I have chosen to find the other value of x (aside x = 0) when y = 8
[tex]\implies -x^2+2x+8=8[/tex]
[tex]\implies -x^2+2x=0[/tex]
[tex]\implies x^2-2x=0[/tex]
[tex]\implies x(x-2)=0[/tex]
[tex]\implies x=0, x=2[/tex]
5th point = (2, 8)
Kathy saves $1 on the first day, $2 on the second day, $3 on the third day and so
on, saving an extra $1 on each subsequent day. On which day will she have over
$100 in total?
Answers
Answer:
3 moths and 10 days
Step-by-step explanation:
on each day she gets 1$ that means
1 month = 30 days
e.g. 3 6 9 30 60 90
means 90 days if we add also 1 month it will be 120 days
so 90 + 10 = 100
thats why 3 months and 10 day :)
Which statement is sufficient evidence that DEF is congruent to ABC?
Answers
please help me solve the problem
Answers
Answer:
x = 130°
y = 50°
Step-by-step explanation:
x = 130° (Exterior alternate angles)
x + y = 180° (Angles in linear pair)
y = 180° - x
y = 180°- 130°
y = 50°
The solution to the problem in the figure attached in the question is: x = 130°, y = 50°
What are alternate angles?Alternate angles are angles that are formed in a situation whereby a line intersects two other lines, which lie on opposite sides of a transverse line and on contrasting proximate sides of the other lines.
From the given figure:
Angle x is an alternate angle to angle 130°.
Thus, x = 130°
Using the sum of angles on a straight line:
x + y = 180°
130° + y = 180°
y = 180° - 130°
y = 50°
Learn more about alternate angles here:
https://brainly.com/question/26167358
Need help with trigonometry, due in two days
Will mark as brainliest if helpful
Answers
[tex]\boxed{\sf tan\theta=\dfrac{Perpendicular}{Base}}[/tex]
Perpendicular=27.8ftBase=19.6ftNow
[tex]\\ \tt\hookrightarrow tanx=\dfrac{27.8}{19.6}[/tex]
[tex]\\ \tt\hookrightarrow tanx=\dfrac{13.9}{9.8}[/tex]
[tex]\\ \tt\hookrightarrow tanx=1.418[/tex]
[tex]\\ \tt\hookrightarrow \underline{\boxed{\bf tanx=1.42}}[/tex]
Value of x
[tex]\\ \tt\hookrightarrow x=tan^{-1}(1.42)[/tex]
[tex]\\ \tt\hookrightarrow x=54.8°[/tex]
Hope It helps
A cupcake stand has 64 cupcakes the available flavors are lemon carrot and caramel if five eights of them are caramel and lemon how many carrot cupcakes are there pls help
Answers
Answer:
24
Step-by-step explanation:
64 * (5/8) = 40 lemon and caramel
64- 40 = 24 carrot cupcakes
The initial cost to rent a bike is $5. Each hour the bike is rented costs $1.75. is going to rent a bike and can spend at most $10.25. Write and solve an inequality to find how long she can rent the bike.
Answers
Answer:
1.75h + 5 ≤ 10.25
number of hours she can rent is a maximum of 3
Step-by-step explanation:
h = hours bike is rented
1.75h + 5 ≤ 10.25
subtract 5 from each side:
1.75h ≤ 5.25
divide each side by 1.75:
h ≤ 3
PLEASE HELP ME: the ratio of cars to trucks on a highway at any given time is 12 to 8. If there are always more than 105 cars on the highway, what is the minimum number of cars that can be on the highway?
Answers
Answer:
70
Step-by-step explanation:
First, set up the ratio of c:t, which is 12:8. Then set up your new ratio of c:t, which is 105:?. The way I find the easiest is to divide 105 by 12, which is 8.75, then multiply that by 8, which is 70. To check if it's right, just divide 12 by 8, and 105 by 70, and if they're the same number, you've got it right.
Ps. I'm guessing you meant to ask the minimum number of trucks, not cars.
Karen fills an aquarium to a depth of 25 meters in 4 minutes. What is the unit rate in minutes per meter? Write your answer in simplest form.
PLEASE HELLP NOW!!! no links plz
Answers
Answer: 0.16min/m
Step-by-step explanation:
The depth of the aquarium is 25 meters
Time is take for water to reach the bottom = 4 minutes per 25 meters
= 4/25 min/m
= 0.16 min/m
Graph the first six terms of a sequence where aj = 4 and r = 2.
Answers
Answer:
trangle?
Step-by-step explanation:
The answer is in the image
Graph: y – 3 = } (x + 2)
Answers
Answer:x2 355b. Hhgguyuy
Step-by-step explanation:
Find the distance of A(p,a) B(a,-p). Pls answer ASAP!!!
Answers
Answer:The solution is in the file below
Step-by-step explanation:
a man brought 10 bags for Rs 5000. He sold 7 bags at Rs 550 wash and remaining at the rate of cost price.Find his profit percent
Answers
Answer:
7%
Explanation:
cost of 10 bag is rs 5000.
then cost of one bag is 500.
he sold 7 bag for rs550 each then total =550×7
= 3850
again, he sold rest 3bag at cost price =500 ×3
=1500
then ,. profit percentage; s.p- c.p/5000×100
350/5000×100
= 7%
Jaime has $2. 60 in dimes and nickels. The number of dimes is 14 more than the number of nickels. How many of each coin does he have?.
Answers
Dime is one-tenth of a dollar, while nickle is one-twentieth part of a dollar. Jaime has got 22 dimes and 4 nickle coin in this case.
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For the given case, since number of dimes is given in terms of number of nickels, so lets assume that:
Number of nickle Jaime got = [tex]x[/tex]Number of dime Jaime got = 14 more than the number of nickle = [tex]14 +x[/tex]Since 1 nickle's cost = $0.05,
thus, x nickles' cost = [tex]x \times 0.05[/tex] (in dollars)
And as 1 dime's cost = $0.10,
thus, 14 + x dimes' cost = [tex]0.10 \times (14 + x)[/tex] (in dollars)
Total amount Jamie have = Amount by nickles + Amount by dimes
Total amount Jamie have = [tex]0.10(14+x) + 0.05x[/tex] (in dollars) = $2.60 (as given in the problem)
Thus, we get:
[tex]0.10 (14+x) + 0.05x = 2.60\\1.4 + 0.10x + 0.05x = 2.60\\\\\text{Subtracting 1.4 from both the sides}\\\\0.15x = 1.2\\\text{Dividing both the sides by 0.15}\\\\\dfrac{0.15x}{0.15} = \dfrac{1.2}{0.15}\\\\x = 8\\[/tex]
Thus, Jamie got x = 8 nickles.
And number of dimes he got = x + 14 = 8 + 14 = 22
Thus, Jaime has got 22 dimes and 4 nickle coin in this case.
Learn more about forming equations here:
https://brainly.com/question/11938672
Please help! I would appreciate it!
-10x-1=-51
PLEASE show your steps!
Answers
Answer:
x = 5
Step-by-step explanation:
-10x - 1 = -51
add 1 to each side
-10x = -50
divide each side by -10
x = 5
a bicycle shop is offering a 15% discount on a bike that has an original price of 275. there is an additional 5% discount off the sale price. what is the final price of the bike, including both discounts?
Answers
Step-by-step explanation:
• the original price= 275,
275 → 100 %
i) find the price with the 15 % discount
100% - 15% = 85 %
if, 275 → 100 %
100 % → 275
1% → 275 / 100
85 % → (275/100) * 85
= 233. 75
ii) find the add. 5% of the :
sale price = 233. 75
add. discount = 5%
= 5/ 100 * 233.75
= 11.6875
iii) subract the 5% discount from the sale price.
final price = 233. 75 - 11.6875
= 222. 0625
hope this helps you!
-s.
HELP ME PLZZ what is the y intercept in the equation y= 4x-3
Answers
Answer:
-3
Step-by-step explanation:
4x is the slope and the + or - always is the y intercept. also this would be a linear equation :)
Craig has a resçe ta zguires 3 cups of mik if i cup = 8 ounces, nou mary ounces of mik does Craig need?
A
34 ounces
B
28 ounces
c
24 ounces
D
12 ounces
C2022
Answers
Maggie is buying 2 shirts that cost $8. 50 each. There is a 6. 5% sales tax. What is the total Maggie will pay for the shirts? Enter your answer in the box.
Answers
The total cost of the two shirt Maggie will pay after including the sales tax is $18.105.
What is cost price per ounce?The cost price per unit is the amount of money required to buy one unit of a brand or goods.
To find the cost price per unit, divide the total amount of cost of the goods to the total number of goods.
The cost of one shirt bought by the Maggie is $8. 50 each. Thus, the cost of the 2 shirts is,
[tex]C=2\times8.50\\C=17[/tex]
Thus, the total cost of the two shirts is $17.
Now, there is a 6. 5% sales tax on the selling price. Thus, the cost of the 2 shirts after the sales tax is,
[tex]C=17+17\dfrac{6.5}{100}\\C=17+1.105\\C=18.105[/tex]
Hence, the total cost of the two shirt Maggie will pay after including the sales tax is $18.105.
Learn more about the cost price per unit here;
https://brainly.com/question/18628158
Answer:
$18.11
Step-by-step explanation:
I took the test on k-12
WILL GIVE BRAINLIEST FOR HELP
(5x3−2x2+3x−8)-(3x2−4x−1) and then the result of that minus 4x − x2 + 5
Answers
Answer:
-15x^5 + 26x^4 - 12x^3 + 35x^2 - 33x - 3
Step-by-step explanation:
(5x^3 - 2x^2 + 3x - 8) + (-3x^2 + 4x + 1)
do foil but with extra terms
-15x^5 + 20x^4 + 5x^3
+6x^4 - 8x^3 - 2x^2
-9x^3 + 12x^2 + 3x
+ 24x^2 - 32x - 8
combine like terms
(-15x^5 + 26x^4 - 12x^3 + 34x^2 - 29x - 8) - (4x - x^2 + 5) or -4x + x^2 - 5
-15x^5 + 26x^4 - 12x^3 + 35x^2 - 33x - 3
Answer:
[tex]x^3-4x^2+3x-12[/tex]
Step-by-step explanation:
[tex](5x^3-2x^2+3x-8)-(3x^2-4x-1)\\\implies 5x^3-2x^2+3x-8-3x^2+4x+1\\\implies 5x^3-5x^2+7x-7[/tex]
[tex](x^3-5x^2+7x-7)-(4x-x^2+5)\\\implies x^3-5x^2+7x-7-4x+x^2-5\\\implies x^3-4x^2+3x-12[/tex]
Charlie bought a $670 computer, but his total was $720. What percent slales tax did he pay?
Answers
Answer:
7%
Step-by-step explanation:
[tex]Formula: \frac{Value2-Value1}{Original.Amt(Value1)}*100[/tex]
[tex]\frac{720-670}{670} *100[/tex]
[tex]\frac{50}{670} *100[/tex]
[tex]7.46268656716[/tex] Round to nearest whole 7%
[RevyBreeze]
Answer:
7.463%
Step-by-step explanation:
$720 - $670 = $50
the sales tax price = $50
sale tax in percentage =
[tex] \frac{tax}{computer \: price} \times 100 =[/tex]
[tex] \frac{50}{670} \times 100 = 7.462[/tex]
Need help with this question ASAP!
What is the length of CE?
Answers
Answer:
its 8
Step-by-step explanation: