In a 20 item true-false examination, if 12 correct answers constitute a passing grade,
what is the probability that someone will pass, if they are guessing?
A. .8398
B. .2517
C. .1201
D. .1317

Answers

Answer 1

Answer:

The answer is B, I know this because I just took a test with this question lol

Answer 2

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.

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Related Questions

pleas help me ill give brainleyest

Answers

Answer:

11.8% Decrease

Step-by-step explanation:

I googles it i am sorry if it's not right

A and B are complementary angles. If mA = (2x + 30)° and mB = (7x – 3), then find the measure of B.

Answers

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!!

   

Find the general solution of y''' + 9y'' + y' − 111y = 0 if it is known that y1 = e−6x cos(x) is one solution.

Answers

Answer:

[tex]\mathbf{y(x) = \dfrac{(c_1 + c_2) \ cos (x)}{e^{6x} }+ \dfrac{i(c_1 -c_2) \ sin (x)}{e^{6x}}+ c_3e^{3\ x}}[/tex]

Step-by-step explanation:

The objective of this question is to solve:

[tex]\dfrac{dy(x)}{dx}+ 9\dfrac{d^2y(dx)}{dx^2}+\dfrac{d^3y(x)}{dx^3}-111y(x) = 0 :[/tex]

Suppose the general solution is proportional to [tex]e^{\lambda x}[/tex] for [tex]\lambda[/tex] is constant; Then:

Let's replace [tex]y(x) = e^{\lambda\ x}[/tex] into the above equation:

i.e.

[tex]\dfrac{d^3}{dx^3}(e ^{\lambda x} )+ 9 \dfrac{d^2}{dx^2}(e ^{\lambda x} ) + \dfrac{d}{dx}(e ^{\lambda x} )- 111 \ e ^{\lambda x} = 0[/tex]

To Replace:

[tex]\dfrac{d^3}{dx^3}(e ^{\lambda x} )[/tex] with [tex]\lambda^3 e ^{\lambda x }[/tex]

[tex]\dfrac{d^2}{dx^2}(e ^{\lambda x} ) \ with \ \lambda^2 e^{\lambda\ x}[/tex]

[tex]\dfrac{d}{dx}(e ^{\lambda x} ) \ with \ \lambda e ^{\lambda \ x}[/tex]

Thus;

[tex]\lambda^3 e ^{\lambda x }[/tex] + [tex]9 \lambda^2 e^{\lambda\ x}[/tex] + [tex]\lambda e ^{\lambda \ x}[/tex] - 111 [tex]e ^{\lambda \ x}[/tex] = 0

[tex]e ^{\lambda \ x} (\lambda ^3 + 9 \lambda ^2 + \lambda - 111 )= 0[/tex]

In as much as [tex]e^{ \lambda x}\neq 0[/tex] for any finite [tex]\lambda[/tex]; Then:

[tex]\lambda ^3 + 9 \lambda ^2 + 111 = 0[/tex]

By Factorization:

[tex](\lambda - 3) ( \lambda ^2 + 12 \lambda + 37) = 0[/tex]

[tex]\lambda = -6 + i \ or\ \lambda = -6 - i \ or \ \lambda = 3[/tex]

However;

The root [tex]\lambda = -6 \pm i[/tex] yield;

[tex]y_1 = (x) = c_1 e ^ {(-6+i)x}[/tex]

[tex]y_2 (x) = c_2e^{(-6-i)x}[/tex]

The root [tex]\lambda = 3[/tex] yield;

[tex]y_3(x) = c_3 e^{3x}[/tex]

The general solution is:

[tex]y(x) = y_1(x) + y_2(x) + y_3(x) = \dfrac{c_1}{c^{(6-i)}x}+\dfrac{c_2}{c^{(6+i)}x}+ c_3e^{3x}[/tex]

Using Euler's Identity ;

[tex]e^{\alpha+i \beta} = e^\alpha \ cos (\beta ) + i \ e^\alpha \ sin ( \beta)[/tex]

[tex]y(x) = c_1 ( \dfrac{cos (x) }{e^{6x}}+ \dfrac{i \ sin x }{e^{6x} }) + c_2 ( \dfrac{cos (x)}{e^{6x}}- \dfrac{-i \ sin (x)}{e^{6x}})+c_3 e^{3x}[/tex]

[tex]\mathbf{y(x) = \dfrac{(c_1 + c_2) \ cos (x)}{e^{6x} }+ \dfrac{i(c_1 -c_2) \ sin (x)}{e^{6x}}+ c_3e^{3\ x}}[/tex]

Is anyone willing to answer this question I can’t do it

Answers

Answer:

Not 100% sure on this make sure you double check

Step-by-step explanation:

X- 10          

Y- 10

Slope- (-1)

like I said this could be wrong  

Bart drives 45 miles in 30 minutes. If he drove 3 hours in total at the same rate how far did he go! How many minutes did Bart drive in total!

Answers

Answer:

270 miles and 180 minutes

Step-by-step explanation:

Please Solve Brainliest and 10 points!

Answers

Answer:

x=20°

Step-by-step explanation:

statements:                                        

1.) m<DOB = m<DOE + m<BOE (or m<EOB)    

2.) m<DOB = 90°+x

3.) m<AOC = m<DOB

4.) 110° = 90° + x

5.) x = 20°

reasons:

1.) given

2.) substitution

3.) vertical/reflexive

4.) substitution

5.) algebra

A cookbook originally cost $13.00. Yesterday, Marta bought it at 40% off.
Horn
40%
OFF
How much was deducted from the original price? (4 pt.)
А
$0.40
B
$5.20
$7.80

Answers

The answer is A, just so you know this was the best math class I’ve ever been in

A percentage is a way to describe a part of a whole. The amount paid by Marta for the cookbook is $7.80.

What are Percentages?

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

As it is given that the original price of the cookbook was $13, Marta bought it for 40% off. Therefore, Marta only paid 60% of the original cost,

[tex]\text{Amount paid by Marta} = \text{60\% of the original cost}\\\\\text{Amount paid by Marta} = \dfrac{60}{100} \times \$13\\\\\text{Amount paid by Marta} = \$7.8[/tex]

Thus, the amount paid by Marta for the cookbook is $7.80.

Learn more about Percentages:

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A one dimensional object with no endpoint is a?
A.ray
B.line segment
C.line
D.point

Answers

Answer:

its line fjfjfjjejjdjdj

As per the given condition, the required one dimensional object with no end point is a line.

What is a ray?

"In geometry, a ray can be defined as a part of a line that has a fixed starting point but no end point. It can extend infinitely in one direction.

On its way to infinity, a ray may pass through more than one point. When naming a ray, it is denoted by drawing a small ray on top of the name of the ray. "

What is a line segment?

"A line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints."

What is a line?

"A line is a one-dimensional object, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely. It is determined by two points in a two-dimensional plane. "

What is a point?

"A point is a primitive notion that models an exact location in the space, and has no length, width, or thickness. In modern mathematics, a point refers more generally to an element of some set called a space."

Given, a one dimensional object with no endpoint.

Therefore, the require object is a line.

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An angle measures 50° less than the measure of its supplementary angle. What is the measure of each angle?

Answers

Answer:

115, 65

Step-by-step explanation:

Let x be an angle measurement

x-50 is the supplement

They add to 180

x + x-50 = 180

2x-50 = 180

Add 50 to each side

2x-50 + 50 =180+50

2x = 230

Divide by 2

2x/2 =230/2

x = 115

The measure are 115 and 115-50=65

-3(x + 2) = 16 - x
I need helpppp ASAP

Answers

Answer:

x = -11

Step-by-step explanation:

-3(x + 2) = 16 - x

-3x - 6 = 16 - x

-22 = 2x

Divide

-22/2 = x

-11 = x

3252614683754629158741032465x93756356872264881+432757232878247-3243566=

Answers

Answer:

bout 7

Step-by-step explanation:

Answer:3.049533e+44 to be exact

Step-by-step explanation:

Given parallelogram ABCD, the measure of angle C

Answers

Answer:

70 is the answer to the question

Answer:

[tex]70^{o}[/tex]

Step-by-step explanation:

Opposite angles in a parallelogram are equal. The opposite angle to A is C and we are trying to find angle C. Therefore, <C = <A, therefore, <c= 70 degrees

Mari claims that 2(to the fifth power) × 3² x 5 is a multiple of a number. Is she correct? Explain. ASAP

Answers

Answer:

Hello!!! Princess Sakura here ^^

Step-by-step explanation:

The answer to [tex]2^{5} *3^{2} *5[/tex] is 1440.

I believe she is correct because 1440 can be divided by another number without any remainders.

Kyle invested $ 500 and received $ 650 after three years. What had been the interest rate?

Answers

Answer:
216 2/3 : 1
1= one year

Since Kyle invested $500 and received $650 after three years, the value of Kyles's interest rate is 43.3%.

Given the following data:

Principal = $500Simple interest = $650Time = 3 years

To calculate the value of Kyles's interest rate:

Mathematically, simple interest is given by the formula:

[tex]S.I = \frac{PRT}{100}[/tex]

Where:

S.I is the simple interest.P is the principal amount.R is the interest rate.T is the time measured in years.

Making R the subject of formula, we have:

[tex]R = \frac{100S.I}{PT}[/tex]

Substituting the given parameters into the formula, we have;

[tex]R = \frac{100 \times 650}{500 \times 3}\\\\R = \frac{65000}{1500}[/tex]

Interest rate, R = 43.3%

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Please answer this correctly without making mistakes

Answers

Answer:

This is what internet says. Maybe this helps.

Graph the system of linear inequalities on the coordinate plane.
y [tex]\geq[/tex] 1/2x + 2 1/2
y< 1/5 x + 6
a. Shade the solution to the system of inequalities.
b. Pick a point and show your solution is correct.

Answers

what’s the second inequality symbol?

Answer: Images of Graphs are listed below. I am unsure on how to conduct the second part. but there is the first part

Step-by-step explanation:

Which order pairs are solutions to the equation 4x+2y=4

Answers

Answer:

Slope=2.000/4.000

​ −2.000x−intercept= 22

​  =1y−intercept= 12

=2.00000

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    4*x+2*y-(4)=0

 Pull out like factors :

  4x + 2y - 4  =   2 • (2x + y - 2)

Solve :    2   =  0

This equation has no solution.

A non-zero constant never equals zero.

 Solve   2x+y-2  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  2x+y-2  = 0 and calculate its properties

Notice that when x = 0 the value of y is 2/1 so this line "cuts" the y axis at y= 2.00000

 y-intercept = 2/1  =  2.00000

When y = 0 the value of x is 1/1 Our line therefore "cuts" the x axis at x= 1.00000

 x-intercept = 2/2  =  1

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 2.000 and for x=2.000, the value of y is -2.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.000 - 2.000 = -4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = -4.000/2.000 = -2.000

4x = 7y + 5 what is the slope

Answers

Step-by-step explanation:

7y=4x-5

y=(4/7)x-5/7

slope is equal to m where m is

y=mx+b

in this case m is 4/7

so slope =4/7

Slope=4/7
Hoped I can help!

324 soldiers queued up such that the number of queues is equal to the number of soldiers in each queue. find the number of queues

Answers

I think so answer will be 164.

3/4x-4=5/6
Rewrite so it doesn’t have any fraction

Answers

The correct answer is X=58/9

A taxi company charges $3 per ride plus $1.50 for each mile traveled. Andrea wants to spend no more than $24 on a taxi ride. How many miles can Andrea travel? Select all that apply.

Answers

Answer:

x=14

Step-by-step explanation:

3+1.50x=24

24-3=21

21/1.50=14

Answer is C which is 14

Drag the operator to the correct location on the image. Which operation results in a trinomial?

Answers

Answer:

-

Step-by-step explanation:

I took the test

The correct operator that enters a circle is a subtraction sign.

Given the expressions

[tex](4x^5-8x) ()(3x^2-8x+9)[/tex]

We need to know which sign goes into the bracket that will give a trinomial when simplified.

A trinomial is a function containing 3-terms.

Using the subtraction sign.

[tex](4x^5-8x) - (3x^2-8x+9)[/tex]

Expand

[tex]= 4x^5-8x - 3x^2+8x-9\\= 4x^5-3x^2-8x+8x-9\\=4x^5-3x^2+0-9\\=4x^5-3x^2-9[/tex]

Since the resulting term is a trinomial (3 terms), hence the correct operator that enters a circle is a subtraction sign.

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PLEASE HELP!!! ILL GIVE BRANLIEST *EXTRA POINTS* dont skip :((

Answers

Answer:

-3.21

Step-by-step explanation:

If you pay close attention the numbers are 5 points away from each other, so after -3.2 is -3.21! Hope that helped love :)

The Jackson family went to eat at Applebees. Their bill came to $32.89. They gave the waiter a 15% tip. What was the total amount they paid for their bill?

Answers

$32.89

15% tip

Is $4.94

Making the total of the bill

$37.83

How do you Subtract 9x^2 + 22x - 46 from 12x^2 - 8x + 12.

Answers

Subtract the [tex]x^2[/tex] terms from each other, then the [tex]x[/tex] terms, then the ones without any [tex]x[/tex] whatsoever.

[tex](12x^2 - 8x + 12) - (9x^2 +22x-46)[/tex]

First, we'll subtract [tex]9x^2[/tex] from [tex]12x^2[/tex]

[tex]12x^2-9x^2- = 3x^2[/tex]

Result: [tex]3x^2[/tex]

Next, we'll subtract [tex]22x[/tex] from [tex]-8x[/tex]

[tex]-8x - 22x = -30x[/tex]

Result: [tex]-30x[/tex]

Finally, we'll subtract [tex]-46[/tex] from [tex]12[/tex]

[tex]12-(-46) = 12+46 = 58[/tex]

Result: [tex]58[/tex]

Now, we can add these 3 results together.

First, we had [tex]3x^2[/tex], then [tex]-30x[/tex], and finally [tex]58[/tex].

Thus, our subtraction of

[tex](12x^2 - 8x + 12) - (9x^2 +22x-46)[/tex]

equals

[tex]3x^2-30x+58[/tex]

Christina's ice cream parlor sold 60 vanilla cones on the first day of summer. If the goal is to increase the number of vanilla cones sold each day by 4, how many will be sold 20 days later?

Answers

1280 cones because you would add 60 +4 and multiply by 20, and would get 1280 cones.

PLEASE HELP ME!



I would really appreciate it.

Answers

Answer:

Step-by-step explanation:

It's D the reasoning here is just look at the points at the graph and their x y coordinate

The answer is d - (-2,1), (0,-1) and (2,-3).

3/7 times 13 as a mixed number

Answers

Answer:

[tex]5\frac{4}{7}[/tex]

Step-by-step explanation:

Answer is 39/7 or 5 and 4/7

find the value of x
I have to show the work

Answers

Answer:

x = 39

Step-by-step explanation:

A circle is made up of 360 degrees

235+ 54+ x+32 = 360

Combine like terms

x+321=360

Subtract 321 from each side

x+321-321 = 360-321

x = 39

The mapping diagram shows a functional relationship.

A mapping diagram shows a relation, using arrows, between domain and range for the following ordered pairs: (8, 4), (negative two-thirds, 3), (11, negative 1), (4, one-half).

Complete the statements.

Answers

Answer:

do you have the diagram

Step-by-step explanation:

Answer:

yes ido

Step-by-step explanation:

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