Answer:
The answer is B, I know this because I just took a test with this question lol
If 12 correct answers constitute a passing grade on a 20-item true-false exam, the probability that someone will pass is 1/2 if they are guessing.
What is meant by probability?Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of events occurring. Probability = the number of possible paths to success. The total number of possibilities For example, the probability of flipping a coin and getting heads is 12, because there is only one way to get a head and there are two possible outcomes.Therefore,
Let X denote the number of correctly answered questions out of a total of 20.
Bernoulli trails are formed by repeated coin tosses. Because the "head" on a coin represents the correct answer and the "tail" represents the incorrect answer, the questions that are correctly answered are Bernoulli trials.
[tex]$&\therefore \mathrm{p}=\frac{1}{2} \\[/tex]
[tex]&\therefore \mathrm{q}=1-\mathrm{p}=1-\frac{1}{2}=\frac{1}{2}[/tex]
X follows a binomial distribution with n = 20 and p = 1/2
[tex]&\therefore P(X=x)={ }^n C_x q^{n-x} p^x \\[/tex]
[tex]&={ }^{20} C_x\left(\frac{1}{2}\right)^{20-x} \cdot\left(\frac{1}{2}\right)^x \\[/tex]
[tex]&={ }^{20} C_x\left(\frac{1}{2}\right)^{20}[/tex]
P ( at least 12 questions answered correctly )= P (X ≥ 12)
[tex]&=\mathrm{P}(\mathrm{X}=12)+\mathrm{P}[/tex][tex](\mathrm{X}=13)+\ldots+\mathrm{P}(\mathrm{X}=20) \\[/tex]
[tex]&={ }^{20} \mathrm{C}_{12}\left(\frac{1}{2}\right)^{20}+{ }^{20}[/tex][tex]\mathrm{C}_{13}\left(\frac{1}{2}\right)^{20}+\ldots+{ }^{20}[/tex][tex]\mathrm{C}_{20}\left(\frac{1}{2}\right)^{20} \\[/tex]
[tex]&=\left(\frac{1}{2}\right)^{20} \cdot\left[{ }^{20} \mathrm{C}_{12}+{ }^{20} \mathrm{C}_{13}+\ldots+{ }^{20} \mathrm{C}_{20}\right][/tex]
Hence, If 12 correct answers constitute a passing grade on a 20-item true-false exam, the probability that someone will pass is 1/2 if they are guessing.
The complete question is:
In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers 'true', if it falls tails, he answers 'false'. Find the probability that he answers at least 12 questions correctly.
To learn more about probability, refer to:
https://brainly.com/question/24756209
#SPJ2
Can someone please help, ty!! (Will mark brainliest)
Answer:
x - y = 4
Step-by-step explanation:
Hope this helped! :)
Find 8% of $40 answers with the nearest penny
Answer:
3.20
Step-by-step explanation:
Sorry i had the same question and i asked the teacher if he could help and he did but he sorta juts gave me the answer so cant really give an explanation so sorry.
Simpty to create an ealent expression
8k-5(-5k+3)
Answer:
Tge answer:8k+25k-15
1. You are eating on a Tootsie Roll Lollipop that is in the shape of a sphere. It is giving up volume at a steady rate of 0.25 in3 /min. How fast will the radius be decreasing when the Tootsie Roll Pop is .75 inches across?
Answer:
Step-by-step explanation:
Since the Tootsie Roll lollipop is a sphere
volume of sphere= [tex]\frac{4}{3}piR^3[/tex] = -0.25 [tex]in^3/min[/tex]
the negative sign indicates that the volume is decreasing
upon differentiating
as the diameter given is =0.75 so radius will be = 0.375
[tex]dV/dt = 4piR^2*dR/dt[/tex]
so [tex]dR/dt = 0.25/4*3.14 *(0.375)^2[/tex]
So the radius is decreasing at the rate of dR/dt= 0.142in/min
help bro I give you brailess no cheating
Tina recorded the number of calories she burned during a bike ride. The graph shows Tina’s calories burned, y, after x hours.If Tina rode her bike at a constant rate for the first three hours, what was Tina’s average calories burned, in calories per hour, between hour 0 and hour 3?
Answer:
400 calories per hour in the first 3 hours
Step-by-step explanation:
The c.o.p for the first 3 hours is 400
5. Paul is x years old.
Rebecca is four times older than Paul.
Gemma is 10 years older than Paul.
the sum of their ages is 82 Years.
(a) Form a simplified equation in terms of x
(b) Solve the equation and work out each persons age.
Answer: A) The equation will be x + 4x + x + 10 = 82 B) Paul's age is 12, Rebecca's age is 48 and Gemma's age is 22.
Step-by-step explanation:
We will represent Paul's age by the equation p= x where p is Paul
We will represent Rebecca's age by the equation r = 4x Where r is Rebecca
We will represent Gemma's age by the equation g = x + 10 where g is also Gemma's age.
We given that the sum of their ages is 82 years so meaning that x + 4x + x + 10 has to equal 82.
A) The equation will be x + 4x + x + 10 = 82
Solve for the x equation to find Paul age because his age is x.
B) (x) + (4x) + (x+10) = 82 combine like terms on the left side
6x + 10 = 82
-10 -10
6x = 72
x= 12
Paul age is 12.
r= 4(12)
r = 48
Rebecca's age is 48.
g= 12 +10
g= 22
Gemma's age is 22.
A scuba diver swam 96 ft.
below the surface of the
lake. He then swims up 49
ft. What is his depth now?
Answer:
96-49=47
Step-by-step explanation:
he goes down then up so 47
Answer:
-47
Step-by-step explanation:
-96 + 49
-47
Who thinks ree kid,Joshdub Juicy and mully are super funny!
Answer:
me
Step-by-step explanation:
Answer:
I do! Juicy do be kinda cute too tho. EddieVR though is probably the most funny. Especially his Horror VR videos.
Step-by-step explanation:
What about Narrator? He seems like he'd be really nice and he's funn-
when Mully cuts him off, it's golden lolololol
A and B are complementary angles. If mA = (2x + 30)° and mB = (7x – 3), then find the measure of B.
Answer:
mB=46
Step-by-step explanation:
2x+30+7x-3=90
Combine like terms
9x+27=90
Subtract by 27 on both sides
9x=63
Divide by 9 on both sides
x=7
mB=(7x-3)
Substitute 7 for x
mB= 7(7)-3
mB= 49-3
mB=46
Answer:
The measure of B is 46°
Step-by-step explanation:
To solve this equation, you need to add the two equations, and set them equal to 90° since they are complementary angles
2x+30+7x-3=90
You also need to add like terms, so 2x+7x and 30+-3, or 30-3
9x+27=90
Then you need to isolate the variable by subtracting 27 from both sides
9x+27-27=90-27
=
9x=63
Then you need to divide both sides by 9 to get x=7
Since we know what x is, we plug x into the equation (7x-3) and we will now have 7(7)-3.
To solve this, we multiply 7 and 7, and subtract 3 to get 46.
So the answer is mB=46
I hope this helps!!
The slope of a line is ¾. A different line passes through the points (6, 3) & (-1, 5). Are the lines parallel? Why or why not?
Answer:
B. They are not parallel because their slopes are not equal.
Step-by-step explanation:
Find the slope of the line that runs through points (6, 3) and (-1, 5):
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 3}{-1 - 6} [/tex]
[tex] slope (m) = \frac{2}{-7} = -\frac{2}{7} [/tex]
Since the slope of the line that passes through points (6, 3) and (-1, 5) is not the same with line that has a slope of ¾, therefore, both lines cannot be parallel.
The answer is "B. They are not parallel because their slopes are not equal."
What is 5/8 divided by 1/4?
Answer: 2.5
Step-by-step explanation: If you do 5/8 divided by 1/4 in the calculator it is 2.5.
What is the value of p?
Identify the holes, vertical asymptotes, and horizontal asymptotes of the following.
[tex]f (x) = \frac{2}{x-3}[/tex]
Answer:
Horizontal asymptote: y = 0
Vertical asymptote: x = 3
Step-by-step explanation:
The vertical asymptote in this graph would be when x = 3 because it would make the denominator 0, which would make the equation undefined.
There will not be any holes in the graph, because there won't be any point undefined in the function except for when x = 3, but that's a vertical asymptote.
Now, for the horizontal asymptote, we see what value y approaches as x approaches plus and minus infinity. Since x is in the denominator, y will approach 0 when it's plus or minus infinity.
Horizontal asymptote: y = 0
Vertical asymptote: x = 3
Find the limit
(calculus)
Answer:
I believe [tex]\lim_{x \to a} f(x)[/tex] also equals 0.
Step-by-step explanation:
We know that g(x) has to be greater than or equal to 0. That means f(x) has to be smaller than g(x) or equal to 0.
If we plug in any value of x, f(x) will be positive because of the absolute value. The only way we are going to get f(x) smaller than g(x) or equal to g(x) is to have very small fractions.
Therefore, if [tex]\lim_{x \to a} g(x)=0[/tex], then [tex]\lim_{x \to a} f(x)=0[/tex] because f(x) must be smaller or equal to 0 as well.
Answer:
[tex]\displaystyle{ \lim_{x\to a}f(x)=0[/tex]
Step-by-step explanation:
The other user posted a great answer, but I would like to show you a more mathematical way!
We have [tex]|f(x)|\leq g(x)[/tex].
By the definition of absolute value, this is the same as saying:
[tex]f(x)\leq g(x)\text{ and } -f(x)\leq g(x)[/tex]
For the right, we can divide both sides by -1 to acquire:
[tex]f(x)\leq g(x)\text{ and } f(x)\geq- g(x)[/tex]
We can now combine them. This yields:
[tex]-g(x)\leq f(x)\leq g(x)[/tex]
Now, we can use the Squeeze Theorem (a.k.a. Pinch or Sandwich Theorem). The Squeeze Theorem posits that if we have:
[tex]g(x)\leq f(x)\leq h(x)[/tex]
And:
[tex]\displaystyle{ \lim_{x \to c} g(x)= \lim_{x \to c} h(x)=L}[/tex]
Then the following must be true:
[tex]\displaystyle{ \lim_{x \to c} f(x)=L[/tex]
We have:
[tex]-g(x)\leq f(x)\leq g(x)[/tex]
And we know that:
[tex]\displaystyle{ \lim_{x \to a} g(x)=0[/tex]
Then it follows that:
[tex]\displaystyle{ \lim_{x \to a} -g(x)=- \lim_{x \to a} g(x)=0[/tex]
Therefore, by using the Squeeze Theorem, we can conclude that:
[tex]\displaystyle{ \lim_{x\to a}f(x)=0[/tex]
And we're done!
What is the value of 4(x - 2)(x + 3) + 7(x - 2)(x - 5) - 6(x - 3)(x - 5) when x = 5?
Answer:
96
Step-by-step explanation
4(x - 2)(x + 3) + 7(x - 2)(x - 5) - 6(x - 3)(x - 5)
4(5 - 2)(5 + 3) = 12(8) = 96
7(5 - 2)(5 - 5) = 0
- 6(5 - 3)(5 - 5)= 0
96+0-0 = 96
Find both the greatest common factor and the least common multiple of 24 and 30.
Answer:
24 = 2, 3 , 4, 6, 8, 12, 24
30 = 2, 3, 5, 6, 10, 15, 30
Step-by-step explanation:
Least common for both is 2
Greatest common factor for both is 6
34(8x – 6) – 2 = 12 – x
Answer:
sorry for my handwriting
i think this is the correct answer
Elena’s bedroom door is 1.2 m wide. How wide should the door be on the scale drawing? Explain how you know.
Answer:
0.016cm
Step-by-step explanation:
I would convert 2cm in terms of meters
2cm/1 = 1m/100cm
since there are cm on top and bottom it cancels out
2•1 /1m• 100 = 2m/100 = .02 m
now you solve using proportions
x/.8 = .02/1
x= (.8)(.02) cross multiples)
x= 0.016
Solve for u.
3u = 4.8
I don’t know how to find what u equals can someone help me
Answer:
U = 1.6
Step-by-step explanation:
Divide 4.8 by 3.
the 80th term of an arithmetic sequence is 110.75 and the common difference is 1.25. What is the first term of the sequence?
Answer:
12
Just plug it in [the equation] to try it to
Pick three numbers to make a fact family when write each fact family
5 7
2 4
Answer: Maybe it is 2,4
Step-by-step explanation:
A fact family is a group of math facts using the same numbers. In the case of addition and subtraction, you use three numbers and get four facts.
For example, you can form a fact family using the three numbers 3, 10, and 13: 10 + 3 = 13, 3 + 10 = 13, 13 − 10 = 3, and 13 − 3 = 10.
Addition facts − Here the sum of two of the three given numbers is the remaining third number. This sum is expressed in two possible orders. Thus, there are two addition facts for any three given numbers
For 3, 10 and 13, the two addition facts are:
3 + 10 = 13;
10 + 3 = 13
Subtraction facts − Here the difference of two of the three given numbers is the remaining third number. There are two such differences. Thus, there are two subtraction facts for any three given numbers.
For 3, 10 and 13, the two subtraction facts are:
13 − 10 = 3;
13 − 3 = 10
We use fact families to reinforce the connection between addition and subtraction, and to help students learn and memorize the basic addition & subtraction facts.
Problem 1:
Make four related number sentences using each set of 3 numbers.
10, 7, 3:
There should be two additions and two subtractions.
Solution
10, 7, 3:
Step 1:
The addition facts using above three numbers are:
7 + 3 = 10;
3 + 7 = 10;
Step 2:
The subtraction facts using above three numbers are:
10 – 7 = 3;
10 – 3 = 7
Problem 2:
Make four related number sentences using each set of 3 numbers.
13, 8, 5
There should be two additions and two subtractions.
Solution
13, 8, 5
Step 1:
The addition facts using above three numbers are:
5 + 8 = 13;
8 + 5 = 13;
Step 2:
The subtraction facts using above three numbers are:
13 – 5 = 8;
13 − 8 = 5
Mackenzie has one candy bar to share equally with her best friend. What portion of the candy bar does Mackenzie give to her best friend.
Answer:1/2
Step-by-step explanation:
Answer: 1/2
Step-by-step explanation: if each of you get part of the candy bar and you need to share it equally, both of you get 1/2 of it.
Which of the following options have the same value as
5% of 352
Choose 2 answers:
which integer represents 19°F bellow
Draw out a vertical number line. Positive values are above 0, and negative values are below zero.
Q13. A stone is dropped from a height of 5 km. The distance it falls through varies directly with the
square of the time taken to fall through that distance. If it falls 64 min 4 seconds. find the distance the
stone covers in the 5th second?
A. 36 m
B. 58 m
C. 72 m
D. 100 m
Answer:
The stone covers 36 m in the 5th second. Correct choice: A.
Step-by-step explanation:
Proportions
Two variables are said to be proportional if one of them can be calculated by multiplying the other by a constant of proportionality. If y and x are those variables, then:
y=k.x
There are other similar proportions where the relation is not linear. For example, if y is proportional to the square of x, then:
[tex]y=k.x^2[/tex]
According to the conditions of the question, the distance traveled by a stone dropped from a height of 5 Km varies directly with the square of the time taken to fall through that distance. If d is the distance and t is the time, then;
[tex]d=k.t^2[/tex]
To find the value of k, we use the given condition: The stone falls d=66 meters in t=4 seconds. Substituting:
[tex]64=k.4^2=16k[/tex]
Solving:
[tex]k=64/16=4[/tex]
Substitute the value of k into the equation to get the complete model.
[tex]d=4.t^2[/tex]
Now we calculate the distance when t=5 seconds:
[tex]d=4\cdot 5^2=4\cdot 25=100[/tex]
The stone has covered 100 m in 5 seconds. But we need to find the distance covered in the 5th second, that specific interval between 4 sec and 5 sec.
Since we already know the distance for t=4 sec (64 m), and the distance for t=5 sec (100 m), then:
distance in the 5th second = 100 m - 64 m = 36 m
The stone covers 36 m in the 5th second. Option A.
A set of history exam scores are normally distributed with a mean of 83.2 points and a standard deviation
of 8 points.
What proportion of exam scores are between 82 and 89.2 points?
You may round your answer to four decimal places.
Answer: .3330
Step-by-step explanation:
The proportion of exam scores are between 82 and 89.2 points is 0.3330.
What is standard deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
When comparing data sets that may have the same mean but a different range, it is helpful.
The mean of the two numbers 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30 for instance, is the same. The second, though, is obviously more dispersed.
Given:
mean = 83.2 points and
standard deviation = 8 points.
So, the proportion is
P(82 ≤ x ≤ 89.2)
=P( 82- 83.2 / 8 ≤ z ≤ 89.2 - 83.2/8)
=P (0.75) - P(-0.15)
=0.7734 -(0.4404)
= 0.3330
Learn more about standard deviation here:
https://brainly.com/question/13905583
#SPJ2
Hillary needs to know if the triangle shown is a right triangle. Which equation should she use to help?
Answer:
a2+b2=c2
Step-by-step explanation:
A right triangle is a triangle in which one of the angles is a 90∘ angle. A triangle can be determined to be a right triangle if the side lengths are known. If the lengths satisfy the Pythagorean Theorem (a2+b2=c2) then it is a right triangle.
A river has a current of 2km per hour. Find the rate of Fred’s boat in still water if it travels 30 km downstream and the same time it takes to travel 14 km upstream.
Answer:
32km
Step-by-step explanation:
Solve each proportion for x. Round to the nearest tenth.
117/45=x/95
Answer: x=247
Step-by-step explanation:
1. Set up the equation
117/45=x/95
2. Cross multiply
117(95) = 11115
45(x)= 45x
3. Set both equal to each other
11115=45x
4. Divide 45 on each side
11115/45 = 45x/45
5. Solve for x
x=247
Hope this helps :)
-Morgan
a chef has 5 5/8 pound beef filet. she slices the fillet into 8 ounce steaks A. how many pounds is each steak. write your answer as a fraction in simplest form. B. how many 8 ounce steaks can the chef create from the fillet? How many ounces of beef are left over
Answer:
1/2 pound
90 ounces
11
Remaining 2 ounces
Step-by-step explanation:
Beef filet = 5 5/8 pounds
Slices of fillet = 8 ounces
A. how many pounds is each steak. write your answer as a fraction in simplest form.
1 pound = 16 ounces
Pounds of each steak = ounces per steak / ounces per pound
= 8 ounces / 16 ounces
= 1/2 pound
B. how many 8 ounce steaks can the chef create from the fillet? How many ounces of beef are left over
Beef filet = 5 5/8 pounds
= 45 / 8 pounds
Convert to ounces
= 90 ounces
Number of 8 ounces the chef can create = 90 ounces / 8 ounces
= 11.25
= 11
Remaining 2 ounces of beef