If a multiple choice test consists of ​questions, each of which with of which only 1 is​ correct, ​(a) in how many different ways can a student check off one answer to each​ question? ​(b) in how many ways can a student check off one answer to each question and get all the answers​ wrong? ​(a) The test can be answered in 25 ways.

Answers

Answer 1

Answer:

Step-by-step explanation:

From the given information.

suppose a multiple choice test consists of 5 questions, each with 4 possible answers of which 1 is correct.:

So, we can now suggest that a person can answer each question in 4 different ways given that there are 5 different questions.

Thus, the  students can check off one answer to each question in [tex]4^5 \ different \ ways[/tex]

= 4 × 34 × 4 × 4 × 4

= 1024 different ways.

From the 4 possible answers, since 1 will be correct, definitely 3 other answers will be incorrect.

Thus, the number of ways a student can check off one answer to each question and get all the answers wrong is = 3⁵

= 3 × 3 × 3 × 3 × 3

= 243 ways


Related Questions

x-2 =3 (x-4) two column proof but i can figure out the reasons on my own.

Answers

Answer:

5

Step-by-step explanation:

Step 1:

x - 2 = 3x - 12

Step 2:

- 2 = 2x - 12

Step 3:

10 = 2x

Step 4:

5 = x

Hope This Helps :)

y varies directly with x Part 1

19. If y = 4 when x = -2, find x when y = 6
20. If y = 6 when x = 2, find x when y = 12
21. If y = 7 when x = 2, find x when y =3

Answers

Answer:

  19. -3

  20. 4

  21. 6/7

Step-by-step explanation:

Since the variables are proportional, you can multiply the given x value by the new/old ratio of y-values.

  19. x = 6/4(-2) = -3

  20. x = (12/6)(2) = 4

  21. x = (3/7)(2) = 6/7

In June 2012, Twitter was reporting 400 million tweets per day. Each tweet can consist of up to 140 characters (letter, numbers, etc.). Create a comparison to help understand the amount of tweets in a year by imagining each character was a drop of water and comparing to filling something up

Answers

Assuming each tweet reaches the max of 140, there would be 56 billion drops of water daily. This would equate to 738,681.7 gallons of water or 98,870.4 cubic feet. This amount of drops of water could fill up almost half of the Goodyear blimp

In comparing different job opportunities, you found that firm A will start your salary at
RM25000 per year and guarantee you a raise of RM1200 each year while firm B will start
your salary at RM28000 per year but will guarantee you a raise of RM900 each year.
(a) In what year of service the yearly salary from both firm will be the same?
(b) In what year of service the total salary from both firm will be the same?
(c) Hence, state the firm for which you should choose if you plan to work for 25 years.

Answers

Answer: the answer i think is c

what is 3/5 times 9/7

Answers

Answer:

[tex] \frac{27}{35} \\ [/tex]

Step-by-step explanation:

If you are going to multiply fractions, you just going to multiply their numerators and denominators and simplify when needed.

[tex] \frac{3}{5} \times \frac{9}{7} \\ \frac{3 \times 9}{5 \times 7} \\ \frac{27}{35} [/tex]

The exact form 27/35
Decimal form 0.7714285

what is square root of 64?

Answers

Answer:

8

Step-by-step explanation:

8*8=64

Find the slope intercept form of the equation of the line through the points(2,-4) parallel to the line 8x+2y+2=0

Answers

Answer:

y = -4x + 4

Step-by-step explanation:

8x+2y+2=0

turn that into slope intercept form:

y = -4x - 1

a parallel line has the same slope, but different y-intercept

y = -4x + b

put (2,-4) into the equation

-4 = -4(2) + b

you get b=4

final product:

y = -4x + 4

plz help i need to rase my grade

Answers

The average of anything is calculated by adding up all the terms in the data set and dividing by the amount of terms in the data set.

In this problem,

The average = $1000

the amount of terms = 3

x = the amount earned Sunday

($1073 + $1108 + x) / 3 = $1000

First, multiply both sides by 3

$1073 + $1108 + x = $3000

Add together like terms

$2181 + x = $3000

Subtract $2181 from both sides.

x = $819

The restaurant needs to earn $819 on Sunday to have an average of $1000

Find the dimensions of a rectangle whose width is 8 miles less than its length and whose area is 105 square miles

Answers

Area of a rectangle = w*l

w = width

l = length

In our problem,

Area = 105mi^2

l = x

w = x - 8

Let's plug our values into the formula above.

105mi^2 = x(x - 8)

Distribute the x

105mi^2 = x^2 - 8x

Subtract 105mi^2 from both sides.

0 = x^2 - 8x - 105

Let's factor the right side.

0 = (x - 15)(x + 7)

Set both terms equal to 0

x - 15 = 0

Add 15 to both sides.

x = 15

x + 7 = 0

Subtract 7 from both sides.

x = -7

Since the length cant be a negative number, 15 is the correct answer.

Length = x = 15 mi

Width = x - 8 = 15 - 8 = 7 mi

The length of the rectangle is 15 miles while the width is 7 miles.

What is a rectangle?

A rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

The perimeter of rectangle = 2( length + width).

Suppose the length is L while the width is W.

Area of rectangle = length × width.

L x W = 105

W = L - 8

By substitution,

L x (L - 8) = 105

L² - 8L - 105 = 0

L² - 15L + 7L - 105 = 0

L(L - 15) + 7(L - 15) = 0

(L + 7)(L - 15) = 0

L = -7, L = 15

Since length will not be negative thus L = 15 miles.

W = 15 - 8 = 7 miles

Hence "The length of the rectangle is 15 miles while the width is 7 miles."

For more about rectangles,

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10 decreased by twice a is 23

Answers

I think the answer your looking for is A= 16.5, because a doubled is 33 then if you subtract 10 you get 23

THERE YOU GO I HAVE TO TYPE WORDS

Savannah's balance in her checking account was –$638.57. She deposited two checks, each in the amount of $298.40. What is Savannah’s new checking account balance after the deposits?

Answers

$-41.77 you’re welcome

Round $537.307 to the nearest cent

Answers

Answer:

$531.31

round to the nearest cent is round to 2 decimal places

Answer:

537.31 hope this helps you out

Which statement best explains whether these ordered pairs represent a function? (-4, 2) (6, 7) (-8, 3) (9, 10) (12, 14) (6, 9)

Answers

Answer:

These ordered pairs does NOT represent a function.

Step-by-step explanation:

One of the x-values repeast (6), which is not a characteristic of a function. Because so, it also does not pass the vertical line test because it would pass through the points twice.

y = 4x - 5.
Graph the math problem

Answers

Answer:

so first put a dot on -5 on the y axis then go up 4 and to the right 1 and put a second dot and connect them

Please help. Look at the picture

Answers

Answer:

QR = 16

Step-by-step explanation:

Because PML ~ TRQ

So PM / TR = ML / RQ

35 / 14 = (7x-9) / (2x+2) = 5/2

2(7x-9) = 5(2x+2)

14x-18 = 10x + 10

4x = 28

x= 7

=> QR = 2(7) + 2=16

Margo baked 120 cookies for the school big sale 84 of the cookies were chocolate chip what portion of the cookies were chocolate chip select the three correct answers a 42/60 B 84% C7/10 D 0.70 E 0.84

Answers

D

Explanation:
120*0.70
84

So, 70 percent of 120 is 84. Which means the chocolate chip cookies are 70% (0.70) of the cookies in all.

S1. Three numbers are in the ratio of 2:3:4. The sum of their cubes is 3,34,125. Find the numbers.​

Answers

Answer:

Step-by-step explanation:

sum of their cubes=0.334125

The ratio of three numbers is 2:3:4.

Let the numbers be 2x, 3x and 4x.

Cubes of numbers = (2x)^3, (3x)^3, (4x)^3 = 8x^3, 27x^3, 64x^3

(8x^3) + (27x^3) + (64x^3) = 99x^3

99x^3 = 0.334125

x^3 = (0.334125) / 99

x^3 = 0.003375

x^3 = (0.15)^3

x = 0.15

Therefore, the numbers are (2 x 0.15), (3 x 0.15) and (4 x 0.15) i.e. 0.3, 0.45 and 0.6

Porsches mom told her to choose 3 crayons out of a box

Answers

Pink, yellow, and lime green.

I think this what your looking for ও

Hope this helped ♡

A tourist information center is between a bus station and a train station. When mapped on a grid, the tourist information center is located at (1,4) and the bus is located at (-3,7) The train station is located at point

Answers

Answer: The train station is located at point (5,1).

Step-by-step explanation:

Given: On a grid, information center is located at (1,4) and the bus is located at (-3,7).

A tourist information center is between bus station and train station.

i.e.  tourist information center is a mid point  of line joining bus station and  train station.

Midpoint between (a,b) and (c,d) is given by :-

[tex](x,y)=(\dfrac{a+c}{2},\dfrac{b+d}{2})[/tex]

Let (a,b) be the coordinates of train station , then

[tex](1,4)=(\dfrac{-3+a}{2},\dfrac{7+b}{2})\\\\\Rightarrow\ 1=\dfrac{-3+a}{2}\ \ \ , 4=\dfrac{7+b}{2}\\\\\Rightarrow\ 2=-3+a\ \ \ , 8=7+b\\\\\Rightarrow\ 2+3=a\ \ \ , 8-7=b\\\\\Rightarrow a= 5,\ \ b=1[/tex]

Hence, the train station is located at point (5,1).

kx-fy=cx+p for x ????????????

Answers

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

x=[tex]\frac{p + fy}{K - c}[/tex]

Think of a number. Double the number. Substract 6 from the result and divide the answer by 2. The quotien will be 20. What is the number?

Answers

Answer:

23 is your answer hope this helps

Answer:

The number is 23

Step-by-step explanation:

23*2=46

46-6=40

40/2=20

The answer is 23

Hope that helps!

Crude oil imports to one country from another for 2009–2013 could be approximated by the following model where t is time in years since the start of 2000. I(t) = −33t2 + 800t − 3,000 thousand barrels per day (9 ≤ t ≤ 13) According to the model, approximately when were oil imports to the country greatest?

Answers

Answer:

Import in 2012 was the greatest

Step-by-step explanation:

Given

l(t) = -33t² + 800t - 3000

9 ≤ t ≤ 13

Required

Determine the year with highest import.

To do this we simply substitute the values of t from 9 to 13 in the given function.

When t = 9

l(t) = -33t² + 800t - 3000

l(9) = -33 * 9² + 800 * 9 - 3000

l(9) = -33 * 81 + 800 * 9 - 3000

l(9) = -2673 + 7200 -3000

l(9) = 1527

When t = 10

l(10) = -33 * 10² + 800 * 10 - 3000

l(10) = -33 * 100 + 800 * 10 - 3000

l(10) = -3300 + 8000 - 3000

l(10) = 1700

When t = 11

l(11) = -33 * 11² + 800 * 11 - 3000

l(11) = -33 * 121 + 800 * 11 - 3000

l(11) = -3993 + 8800 - 3000

l(11) = 1807

When t = 12

l(12) = -33 * 12² + 800 * 12 - 3000

l(12) = -33 * 144 + 800 * 12 - 3000

l(12) = -4752 + 9600 - 3000

l(12) = 1848

When t = 13

l(13) = -33 * 13² + 800 * 13 - 3000

l(13) = -33 * 169 + 800 * 13 - 3000

l(13) = -5577 + 10400 - 3000

l(13) = 1823

Comparing the values of l(t) for the range of t = 9 to 13,

The highest value of l(t) is:

l(12) = 1848

Hence, the year with the highest import is 2012

The oil imports to the country are greatest during the year 2012

Given the model where t is time in years since the start of 2000 expressed as I(t) = −33t² + 800t − 3,000

The oil imports more oil during the year 2012, is t = 12

I(12) = −33(12)² + 800(12) − 3,000

I(12) = -33(144) + 9600 - 3000

I(12) = -4752 + 6600

I(12) = 1848

Hence the oil imports to the country are greatest during the year 2012

Learn more on functions here: https://brainly.com/question/17192405

I need to know this I don’t understand and it is last one

Answers

Answer:

The answer is 4x

Step-by-step explanation:

Hope this helped

Evaluate the difference quotient for the given function. Simplify your answer.
f(x) = 5 + 4x – x2,
f(3 + h) – f(3)
h
1-1-2h-h² x
Enhanced Feedback
Please try again. To evaluate f(a + h), replace x by (a + h) in the expression for f(x). Substitute this
Need Help?
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What steps or reasoning did you use? Your work counts towards your score.
substituting (3+h) into the equation by replacing (3+h) where there is a x value we can get the quotient. Then repla

Answers

Answer:

  -2-h

Step-by-step explanation:

It doesn't hurt to follow directions.

  [tex]q=\dfrac{f(3+h)-f(3)}{h}=\dfrac{(5 +4(3+h)-(3+h)^2)-(5 +4(3)-(3)^2)}{h}\\\\=\dfrac{5-5+4(3+h-3)-((3+h)^2-3^2)}{h}=\dfrac{4h-(6h+h^2)}{h}\\\\=\dfrac{-2h-h^2}{h}=\boxed{-2-h}[/tex]

__

Steps: substitute 3+h and 3 for x in the definition of f(x) and simplify the result.

Chin researched the body weight, in pounds, of professional football players. He created a table of different sample means from his data. Sample Sample Mean (pounds) 1 240 2 236 3 245 4 243 5 238 6 242 Which statements are true? Select three choices. The variation in the sample means makes it possible to make predictions about the population mean. The actual population mean is greater than 236. The actual population mean is less than 245. The actual population mean is greater than 245. The population mean is the average of the sample means.

Answers

Answer:

The variation in the sample means makes it possible to make predictions about the population mean. The actual population mean is greater than 236. The actual population mean is less than 245.

Step-by-step explanation:

Sample data

1 2 3 4 5 6240 236 245 243 238 242

Mean = sum of sample data/sample frequency

(240+236+245+243+238+242)/6 = 240.67

Answer choices:

The variation in the sample means makes it possible to make predictions about the population mean.

Correct.  

The actual population mean is greater than 236.

Correct. 240.67 > 236

The actual population mean is less than 245.

Correct. 240.67 < 245

The actual population mean is greater than 245

Incorrect.

The population mean is the average of the sample means.

Incorrect.  

Answer:

It is numbers 1, 2, and 3!

Step-by-step explanation:

Can someone tell me the solutions to this please its urgent​

Answers

The first line is 20
The second line is 18
The 3rd line is 4

Answer:

The first one is 20

The second one is 18

And the last one is 4

Point S is on line segment RT. Given ST = 2x – 10, RS = 2x - 5, and
RT = 3x + 1, determine the numerical length of RT.

Answers

Answer: 49

Step-by-step explanation:

The numerical length of RT is 49 units if point S is on the line segment RT. Given ST = 2x – 10, RS = 2x - 5, and RT = 3x + 1.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Point S is on line segment RT.  

ST = 2x – 10,

RS = 2x - 5, and

RT = 3x + 1,

RT = RS + ST

3x + 1 = 2x - 5 + 2x - 10

The above equation is representing a linear equation in one variable.

After simplifying:

3x + 1 = 4x - 15

4x - 3x = 15 + 1

x = 16

RT = 3x + 1

Plug x = -14

RT = 3(16) + 1

RT = 48 + 1

RT = 49

The numerical value of RT = 49

Thus, the numerical length of RT is 49 units if point S is on line segment RT. Given ST = 2x – 10, RS = 2x - 5, and RT = 3x + 1.

Learn more about the linear equation here:

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-3x - 9y = 18

Solve for y

Answers

Steps to solve:

-3x - 9y = 18

~Add 3x to both sides

-9y = 18 + 3x

~Divide -9 to everything

y = -1/3x - 2

Best of Luck!

What is equal to 15.9 divided by 3

Answers

Answer:

5.3

Step-by-step explanation:

The answer is 5.3. Hope this could help

what is88226 X 9991?

Answers

881465966 is ur answer, i think you could just use google calculator if u don’t have one

Answer:

881465966

Step-by-step explanation:

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