A multiple-choice standard test contains total of 25 questions, each with four answers. Assume that a student just guesses on each question and all questions are answered independently. (a) What is the probability that the student answers more than 20 questions correctly

Answers

Answer 1

Answer:

[tex]P(x>20)=9.67*10^{-10}[/tex]

Step-by-step explanation:

If we call x the number of correct answers, we can said that P(x) follows a Binomial distribution, because we have 25 questions that are identical and independent events with a probability of 1/4 to success and a probability of 3/4 to fail.

So, the probability can be calculated as:

[tex]P(x)=nCx*p^{x}*q^{n-x}=25Cx*0.25^{x}*0.75^{25-x}[/tex]

Where n is 25 questions, p is the probability to success or 0.25 and q is the probability to fail or 0.75.

Additionally, [tex]25Cx=\frac{25!}{x!(25-x)!}[/tex]

So, the probability that the student answers more than 20 questions correctly is equal to:

[tex]P(x>20)=P(21)+P(22)+P(23)+P(24)+P(25)[/tex]

Where, for example, P(21) is equal to:

[tex]P(21)=25C21*0.25^{21}*0.75^{25-21}=9.1*10^{-10}[/tex]

Finally, P(x>20) is equal to:

[tex]P(x>20)=9.67*10^{-10}[/tex]


Related Questions

Which number best represents the location of the point on the line?
X
-4.44
-T
11
3
_V17
RETRY

Answers

Answer:

- 11 over 3 Just did it on edg 2021

Please help thank you

Answers

Answer:

8000

Step-by-step explanation:

It's the only number missing from the answer to arrive at the answer itself :)

Answer:

8,000

Step-by-step explanation:

70 + x + 8 + 800,000,000 = 800,008,078    Add on the left side

800,000,078 + x = 800,008,078

-800,000,078        - 800,000,078     Subtract 800,000,078 from both sides

x = 8,000

Oliver had $43 on the day before his birthday. After he received some money for his birthday, he had $68. Write an equation to find how much money Oliver received for his birthday.

Answers

Answer:

$25

Step-by-step explanation

If oliver had $43 before his birthday he was given (+) an amount of money, in order to find out  how much money was given you need to reverse the equation (-) $68-$43= $25

What is the MEDIAN of this data?

Answers

Answer:

I think the median is 7

if it is not im so sorry

The median of the data is 7.

please see the attached picture for full solution

Hope it helps

Good luck on your assignment

A company that manufactures video cameras produces a basic model and a deluxe model. Over the past year, 41% of the cameras sold have been of the basic model. Of those buying the basic model, 31% purchase an extended warranty, whereas 48% of all deluxe purchasers do so. If you learn that a randomly selected purchaser has an extended warranty, how likely is it that he or she has a basic model

Answers

Answer:

[tex]75.6\%[/tex]

Step-by-step explanation:

Let B be the event of buying a basic model.

Given that P(B) = 41%

Let D be the event of buying a basic model.

Given that P(D) = 1 - 41% = 59%

Let E be the event of extended warranty.

Given that:

P(E [tex]\cap[/tex] B) = 31% and

P(E [tex]\cap[/tex] D) = 48%

P(E) = P(E [tex]\cap[/tex] B) [tex]\times[/tex] P(B) + P(E [tex]\cap[/tex] D) [tex]\times[/tex] P(D)

P(E) = 31% [tex]\times[/tex] 41% + 48% [tex]\times[/tex] 59% = 0.4103

To find: P(B/E)

Formula:

[tex]P(B/E) = \dfrac{P(E \cap B)}{P(E)}[/tex]

[tex]\Rightarrow \dfrac{0.31}{0.41}\\\Rightarrow 0.756\\\Rightarrow 75.6\%[/tex]

So, the correct answer is [tex]75.6\%[/tex].

Triangle JKL was dilated using the rule D Subscript M, one-third. The image, triangle J'K'L', is the result of the dilation. Point M is the center of dilation. Triangle J K L is dilated to form smaller triangle J prime K prime L prime. The length of M L prime is 2.5. What is L'L? 5 units 7.5 units 10 units 12.5 units

Answers

Answer: the answer is A 5 units

The length of L'L in the dilated figure is 5 units.

What is transformation?

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

Dilation is the increase or decrease in size of a figure.

Triangle JKL was dilated by 1/3 with M as the center of dilation to form J'K'L'.

Given that ML' = 2.5 units, hence:

L'L = (2.5 * 3) - 2.5 = 5 units

The length of L'L in the dilated figure is 5 units.

Find out more on transformation at: https://brainly.com/question/1620969

Leila runs each lap in 6 minutes. She will run less than 9 laps today. What are the possible numbers of minutes she will run today? Use t for the number of minutes she will run today. Write your answer as an inequality solved for t.​

Answers

Answer:

I'm not sure if Leila is allowed to run 0 laps.

6 ≤ t ≤ 48

Step-by-step explanation:

To find the number of possible laps, you just find the smallest possible number and the largest.

1 = smallest

8 = largest

But, you have to multiply by 6 to find the time.

6 ≤ t ≤ 48

Help me please and thanks

Answers

Hey there! :)

Answer:

B.

Step-by-step explanation:

To find the solution to the inequality, we can begin by solving for 'x':

2x + 1 ≥ 3

Subtract 1 from both sides:

2x ≥ 2

Divide both sides by 2:

x ≥ 1.

This means that the graph must contain all values of x greater or equal to one. The only number line that shows solutions greater than 1 is B.

The area of a circle is 497 squared meters.
What is the radius, in meters?

Answers

Answer: r= 12.58m

Step-by-step explanation:

100% SURE

Simplify (1+√3) (2-√3).

Answers

Answer:

[tex] \sqrt{3} - 1[/tex]

Step-by-step explanation:

[tex](1 + \sqrt{3} )(2 - \sqrt{3} ) \\ 2 - \sqrt{3} + 2 \sqrt{3} - 3 \\ = \sqrt{3} - 1[/tex]

Please answer this correctly without making mistakes

Answers

Answer:

746 mi^2

Step-by-step explanation:

The top rectangle has an area of

A = 22*23 =506

The bottom rectangle has an area of

A =10 *24 = 240

Add the areas together

506+ 240 =746

Answer:

746

Step-by-step explanation:

22*23= 506

24*10= 240

506+240= 746

plz mark brainliest

p(x) is a polynomial with integer coefficients and p(-3) = 0. Which statements must be true? Choose all that apply. x - 3 is a factor of the polynomial. -3 is the constant term of the polynomial. p( x) can have at most 3 linear factors. x + 3 is a factor of the polynomial.

Answers

Answer:

yes all that apply to this q9

If f(x) = 4 – x2 and g(x) = 6x, which expression is equivalent to (9-1(3)?

Answers

Answer:

( g − f ) ( 3 ) = 23

Step-by-step explanation:

(g-f)(x)=g(x)-f(x)

=6x-(4-X(2))

=x(2)+6x-4

to evaluate (g-f) (#) substitute x=3 into (g-f)(x)

(g-f)=(9)+(6 x 3) -4=23

What is the area of the circle?

Answers

Answer:

A =50.24 in ^2

Step-by-step explanation:

The diameter is 8 inches

The radius is 1/2 diameter

r = d/2 = 8/2 = 4

The area of the circle is given by

A = pi r^2

A = 3.14 (4)^2

A =50.24 in ^2

Answer:

C. 50.24 in²

Step-by-step explanation:

d= 8 in

r= 8/2= 4 in

Area= πr²= 3.14×4²= 50.24 in²

Lindsay needs to make some house repairs in four years that will cost $8,000. She has some money in an account earning 8% annual interest. How much money needs to be in the account today so she will have enough to pay for the repairs

Answers

Answer:

$5,882

Step-by-step explanation:

To calculate the money Lindsay needs today, you can use the following formula to calculate the present value:

PV=FV/(1+i)^n

PV= present value

FV= future value= $8,000

i= interest rate= 8%

n= number of periods= 4

PV= 8,000/(1+0.08)^4

PV=8,000/1.08^4

PV=8,000/1.36

PV= 5,882

According to this, Lindsay will need to have $5,882 in the account today so she will have enough to pay for the repairs in four years.

PLEASE HELP !!

Problem:
Find P(3).

Answers:
1/6
1/8
3/6
1

Answers

Answer:

The probability of spinning a 3 out of the 6 options is 1/6.

Answer: 1/6

Step-by-step explanation:

Im assuming the p stands for probability. There is a total of 6 slices, the 3rd slice takes up 1/6th of the circle

The list of ordered pairs below represents a relation. {(−6,10),(−5,4),(−1,−9),(9,−4)} Find the range of the relation.

Answers

Answer:

The range is simply all the y values of the ordered pairs in the relation so the answer (in increasing order) is -9, -4, 4, 10.

Please answer this correctly

Answers

Answer:

Set the height of the bar to 5

Step-by-step explanation:

Since there are 5 quantities between 20-29, So set the height up to 5

The vertex of this parabola is at (-2,-3). When the x-value is -1, the y-value is -5. What is the coefficient of the squared expression in the parabola’s equation? A. 8 B. -8 C. -2 D. 2

Answers

Answer:

Option C is correct

Step-by-step explanation:

Given: vertex of this parabola is at (-2,-3)

To find: coefficient of the squared expression in the parabola’s equation if the x-value is -1, the y-value is -5

Solution:

The equation of parabola is of the form [tex]y=a(x-h)^2+k[/tex]

Here, a is the coefficient of the squared expression in the parabola’s equation.

Put [tex](h,k)=(-2,-3)\,,\,(x,y)=(-1,-5)[/tex]

[tex]-5=a(-1+2)^2-3\\-5+3=a(1)^2\\-2=a\\a=-2[/tex]

So, the coefficient of the squared expression in the parabola’s equation is [tex]-2[/tex]

The price of a visit to the dentist is $50. If the dentist fills any cavities, an additional charge of $100 per cavity
gets added to the bill.

Answers

Answer:

Cost of visit = 50 + 100n

Step-by-step explanation:

$50 is the set price of the visit.

$100 is the cost per cavity.

N is the number of cavities.

Since we don't know the number of cavities, 'n' will fill that spot.

100 x n will be the total cavity cost.

Cavity cost + set price of visit will equal the total cost of the visit.

The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 38 hours and the median is 34.2 hours. Twenty-four of the families in the sample turned on the television for 23 hours or less for the week. The 14th percentile of the data is 23 hours. Step 2 of 5 : Approximately how many families are in the sample? Round your answer to the nearest integer.

Answers

Answer:

There are approximately 171 families in the sample.

Step-by-step explanation:

Percentile meaning:

When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x)% of the values in the set are higher than V.

Twenty-four of the families in the sample turned on the television for 23 hours or less for the week. The 14th percentile of the data is 23 hours.

This means that 24 is 14% of the total number of families.

Approximately how many families are in the sample?

Using a rule of three.

24 - 0.14

x - 1

0.14x = 24

x = 24/0.14

x = 171.4

Rounding to the nearest integer

There are approximately 171 families in the sample.

Use the following to answer questions

Employment statistics in the US are often based on two nationwide monthly surveys: the Current Population Survey (CPS) and the Current Employment Statistics (CES) survey. The CPS samples approximately 60,000 US households and collects the employment status, job type, and demographic information of each resident in the household. The CES survey samples 140,000 non-farm businesses and government agencies and collects the number of payrolls jobs, pay rates, and related information for each firm.

a. What is the population in the CPS survey?

b. What is the population in the CES survey?

Answers

Answer:

A. The population in the CPS survey are all US households.

B. The population in the CES survey are all the non-farm businesses and government agencies.

Step-by-step explanation:

A sample is the number of people from a whole population who actually participated in a survey. The population is the entire group of people whom the survey is meant to study. The sample is an off shoot of the population.

In the given question, the Current Population Survey is a study on the entire US households. Since every household cannot be interviewed because of the large population, a sample of 60,000 households is used.  The whole households in the United States thus form the population under study.

For the Current Employment Statistics survey, the goal is to understand employment statistics in all the non-farm businesses and government agencies. This is the population. Since the entire population cannot be studied, a sample of 140,000 is used.

What is the value of p ?????

Answers

Answer:

d) 50

Step-by-step explanation:

40 + 90 + p = 180

p = 50

Distribute and simplify these radicals. square root of 60

Answers

Answer:

2 sqrt(15)

Step-by-step explanation:

sqrt(60) = sqrt(4*15) = 2 sqrt(15)

The square of a number is 12 less than 7 times the number.what is the number?

Answers

Answer:

n = 3 or n = 4

Step-by-step explanation:

Let the unknown number be n.  

Then:

n² = 7n - 12

In standard quadratic form, we have:

n² - 7n + 12 = 0

In factored form, we have:

(n - 3)(n - 4) = 0, and so

n = 3 and n = 4

Factor the following expression using the GCF. Type your factored expression below.



4xy+12w+12z

Answers

Answer:

4(xy + 3w + 3z)

Step-by-step explanation:

The GCF is 4, so you can take that out and put it in front of the parentheses. Then you just divide all of the terms by 4 (4xy / 4 = xy; 12w / 4 = 3w; 12z / 4 = 3z), etc.

Help plzzzzzzzssssss

Answers

Answer:

16

Step-by-step explanation:

There are three possible equations: the first is used for inputs (x-values) in between negative infinity and -7, the second for inputs in between -7 and 2, and the third for inputs in between 2 and infinity. 7 is in between 2 and infinity so the third equation is applicable.

[tex]g(x)=(x+1)(x-5)[/tex]

[tex]g(7)=(7+1)(7-5)[/tex] Plug in the values

[tex]g(7)=(8)(2)[/tex] Simplify

[tex]g(7)=16[/tex]

your answer is 16

hope this helped

Let f(x)=−9x+1. Match the function with the description.

The graph of g is a reflection in the y-axis of the graph of f.
The graph of g is a reflection in the x-axis of the graph of f.
The graph of g is a horizontal translation 16 units right of the graph of f.
The graph of g is a vertical translation 16 units down of the graph of f.

Answers

Answer:

I guess that we want to find the function g(x) for the 4 cases.

first, f(x) = -9*x + 1.

a) The graph of g is a reflection in the y-axis of the graph of f.

First remember: if we have the point (x,y) and we reflect it over the y-axis, we get (-x,y)

then g(x) = f(-x) = -9*-x + 1 = 9*x + 1.

b) The graph of g is a reflection in the x-axis of the graph of f.

if we have a point (x, y) and we reflect it over the x-axis, the point transforms into (x, -y)

then we have: g(x) = -f(x) = 9*x - 1

c) The graph of g is a horizontal translation 16 units right of the graph of f.

When we want to have a translation in the x-axis, we must change x by x - A.

If A is positive, this transformation moves the graph by A units to the right, in this case, A = 16.

g(x) = f(x - 16) = -9*(x - 16) + 1

d) The graph of g is a vertical translation 16 units down of the graph of f.

For vertical translations, if we want to move the graph by A units down (A positive) we should do y = f(x) - A

In this case, A = 16.

then: g(x) = f(x) - 16 = -9*x + 1 - 16 = -9*x - 15.

please help!! Select the two reasons which fit best in lines 1 and 2 of the proof (given and details in photo)

A: 1.) Vertical Angles are congruent
2.) SSS Congruence Postulate
B: 1.) Definition of Angle Bisectors
2.) SAS Congruence Postulate
C: 1.) Vertical Angles are congruent
2.) AAS Congruence Postulate
D. 1.) Vertical Angles are congruent
2.) SAS Congruence Postulate

Answers

Answer:

D

Step-by-step explanation:

Line 1: Since these angles are vertical, they are congruent

Line 2: We have 2 sides and an angle in between them so it is SAS

This means the answer is D.

Answer: The correct answer is this set:

1.) Vertical Angles are congruent

2.) SAS Congruence Postulate

PLEASE ANSWER THIS , I WILL MAKE U BRAINLIEST IF RIGHT

Answers

Answer:

hope this helps you

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