A TEACHER IS CONSTRUCTING A MATHEMATICS TEST
CONSISTING OF 10 QUESTIONS. SHE HAS A POOL OF 28 QUESTIONS, WHICH ARE
CLASSIFIED BY LEVEL OF DIFFICULTY AS FOLLOWS: 6 DIFFICULT QUESTIONS, 10
AVERAGE QUESTIONS, AND 12 EASY QUESTIONS. HOW MANY DIFFERENT 10
QUESTION TESTS CAN SHE CONSTRUCT FROM THE POOL OF 28 QUESTIONS IF
HER TEST IS TO HAVE 3 DIFFICULT, 4 AVERAGE, AND 3 EASY QUESTIONS?

Answers

Answer 1

The number of ways of constructing questions from the pool of 28 questions if her test is to have 3 difficult, 4 average and 3 easy questions is  924, 000 ways

How to determine the combination

Note that the formula for combination is given as;

Combination = [tex]\frac{n!}{r!(n-r)!}[/tex]

From the information we have that;

There are 28 questions in the pool

The test should have a total of 10 questions;

6 difficult , 10 average and 12 easy questions

We are asked to determine the combination of;

3 difficult questions

4 average questions

3 easy questions

6C3 = [tex]\frac{6!}{3!(6-3)!}[/tex]

6C3 = [tex]\frac{720}{36}[/tex]

6C3 = 20

10C4 = [tex]\frac{10!}{4!(10-4)!}[/tex]

10C4 = [tex]\frac{3628800}{17280}[/tex]

10C4 = 210

12C4 = [tex]\frac{12!}{4!(12-4)!}[/tex]

12C4 = 220

The number of ways of constructing the questions is

= 20 × 210 × 220

= 924, 000 ways

Thus, the number of ways of constructing questions from the pool of 28 questions if her test is to have 3 difficult, 4 average and 3 easy questions is  924, 000 ways

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Related Questions

Question 1 Which number has the greatest value? O 0.095 O 1.24 1.215 O 0.365 Confident​

Answers

Answer:

1.24

Step-by-step explanation:

because 1.24>1.215>0.365>0.095

Find the point at which the line with parametric equations x = 2 3t, y =-4t, z =5 t intersects the plane 4x 5y -2z=18

Answers

It looks like you have

[tex]\begin{cases}x=2+3t\\y=-4t\\z=5+t\end{cases}[/tex]

Substituting these in to the plane equation, we have

[tex]4x+5y-2z = 4(2+3t) + 5(-4t) - 2(5+t) = -2-10t = 18 \\\\ \implies-10t = 20 \implies t = -2[/tex]

When [tex]t=-2[/tex], we get the point

[tex]\begin{cases}x=2+3(-2)\\y=-4(-2)\\z=5+(-2)\end{cases} \implies (x,y,z) = \boxed{(-4,8,3)}[/tex]

Two sides of a triangle are 12cm and 8cm. Complete the inequality to show the possible lengths for the third side.

Answers

The inequalities that represents the third side of the triangle is  c ≥ 4 or c ≤ 20

How to find the third side of a triangle?

The triangle inequality theorem states that that the sum of any two sides of a triangle is greater than or equal to the third side.

Therefore, the two sides of the triangle are 12 cm and 8 cm.

A triangle with sides a, b and c follows the principle below;

a + b ≥ c.

Therefore,

let

c = third sides

12 + 8 ≥ c

20 ≥ c

c + 8 ≥ 12

c ≥ 4

c + 12 ≥ 8

Therefore, the third third should be greater than or equals to 4 or less than or equals to 20

c ≥ 4 or c ≤ 20

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Someone please help me with this question thank youuu

Answers

Answer: 148 degrees

Step-by-step explanation:

The total measure of all exterior angles of a convex pentagon is 360 degrees.

If four of them equal 53 degrees then all those together is 212 degrees

53 times 4 = 212

Then you would just subtract 212 from 360 to see the measure of the last exterior angle. Which is 148 degrees!

Hope this helps :)

Please Help!!!
Type the correct answer in the box. Use numerals instead of words.
The surface area of a cone is square units. The height of the cone is times greater than the radius.

What is the length of the radius of the cone to the nearest foot?

The radius is about
feet.

Answers

Answer:

Step-by-step explanation:

9.05737

The length of the radius of the cone to the nearest foot is 5 feet.

What is a cone?

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

Given, The surface area of a cone is 216π sq units and the height of the cone is  (5/3) times of the radius.

∴ h = (5/3)r and we know l = √(h² + r²) ⇒ l = √{(25/9)r² + r²} ⇒ l = √{(34/9)r²}.

πrl = 216π.

√{(34/9)r³ = 216.

1.9r³ = 216.

r³ = 113.7.

r = 4.8 feet Or 5 feet.

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how is the e - lambda figured out as 0.00248?

Answers

Answer:

Step-by-step explanation:

e^-6 = 1/e^6 = about 0.00248

Question 5
Find the interest rate for a principal of $6570 and charged $30105 in interest for 12 years.

The Formula is
I
PT
x 100
Take the interest divide by the principal
then divide by the years
then times by 100
Round your answer to 1 decimal place.

Answers

Answer:

R=i

Step-by-step explanation:

R=i×100÷p×t

r=30105×100÷6570×12

r=3010500÷78840

r=38.18

WHEN LOIS MARTIN WAS BORN, HER FATHER DEPOSITED $2000 IN A SAVINGS
ACCOUNT IN HER NAME AT A SAVINGS AND LOAN ASSOCIATION (S&L). AT THE TIME,
THE S&L PAID 6% INTEREST COMPOUNDED SEMI-ANNUALLY. AFTER 10 YEARS, THE
S&L CHANGED TO A RATE OF 6% COMPOUNDED QUARTERLY. WHAT WAS THE
VALUE OF THE ACCOUNT AFTER 18 YEARS WHEN THE MONEY WAS WITHDRAWN TO
HELP PAY FOR HER COLLEGE EXPENSES

Answers

The future value of the savings account, after 18 years when it was withdrawn to help pay for Lois Martin's college expenses, would be $5,816.85.

How are the future values determined?

The future values of the savings account are calculated in two installments.

The first installment is for 10 years when the account earns 6% compounded semiannually.

Using the future value after 10 years, the second installment is for 8 years when the account earns 6% compounded quarterly.

Future values can be determined using the future value formula or an online finance calculator, as follows:

Data and Calculations:Investment of $2,000 for 10 years:

N (# of periods) = 20 (10 years x 2)

I/Y (Interest per year) = 6%

PV (Present Value) = $2,000

PMT (Periodic Payment) = $0

Results:

FV = $3,612.22

Total Interest $1,612.22

Investment of $3,612.22 for 8 years:

N (# of periods) = 32 (8 years x 4)

I/Y (Interest per year) = 6%

PV (Present Value) = $3,612.22 ($2,000 + $1,612.22)

PMT (Periodic Payment) = $0

Results:

FV = $5,816.85

Total Interest $2,204.63

Thus, the value of the account after 18 years was $5,816.85.

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Please I need the answer this is due in on monday!!

Answers

The number sets that each number belong too are given as follows:

1. Rational.

2. Irrational.

3. Rational.

4. Whole.

5. Whole.

6. Integer.

What is the classification of the number -4.2?

It is a terminating decimal, hence it is a rational number.

What is the classification of the number 3 times square root of 5?

The square root of 5 is not exact, hence it is a non-terminating decimal, meaning that is an irrational number.

What is the classification of the number 5/3?

It is a fraction, hence it is a rational number.

What is the classification of the number 9?

It is a positive non-decimal number, hence it is a whole number.

What is the classification of the square root of 16?

The square root of 16 is of 4, which is a positive non-decimal number, hence it is a whole number.

What is the classification of the square root of -8/2?

The result of the division is of -4, which is a negative non-decimal number, hence it is an integer number.

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Tyson uploaded 500 videos to the Internet. Sarita uploaded fewer videos than Tyson. Write an inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded.


→WILL MARK BRAINLIEST←

Answers

The inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded is v - 500 < y

Inequality

number of videos Sarita uploaded = v

number of videos Tyson uploaded = 500

Total videos updated = y

Inequality for number of videos Sarita uploaded:

v - 500 < y

Therefore, the inequality that compares the number of videos Sarita uploaded, v, to the number of videos Tyson uploaded is v - 500 < y

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Answer:

- v < 500

Step-by-step explanation:

Question 8 of 10
Factor the polynomial: -5x³ - 10x² - 15x
OA. 5x(x²+2x-3)
OB. -5x(-x2 - 2x - 3)
C. -5x(x2 + 2x - 15)
OD. -5x(x2+2x+3)

Answers

Letter D

All terms are negative, so A won’t work
-5x^3/-5x = x^2, so B won’t work
-15x/-5x = 3, so C won’t work

What is the value of 2 + (- 2/3)^2 ÷ 1/3 ?

16
3
-2
0

Answers

Answer:

3

Step-by-step explanation:

2+ (-2/3)^2 ÷ 1/3

make -2/3 postive because its being raised by an even exponent

you never divide by fractors so make 1/3 into 3 and make it multiplication

2+ (2/3)^2 × 3

raise the fraction to the power of 2

2+ (4/9)× 3

cancel out the GCF

2+ 4/3

add

10/3

simplify

3.3 ≅ 3

Five interlocked, colored rings make up the Olympic symbol. The rings are
blue, black, red, yellow, and green and represent Africa, the Americas, Asia,
Australia, and Europe. The symbol looks like this:
1. In how many ways could the five colors of the Olympic symbol have been
arranged among the rings?

Answers

Answer:

120

Step-by-step explanation:

5 rings 5 colors

for the first ring there are 5 colors to choose from

4 colors for the second

3 for the third

2 for the fourth

1 for the last one

so 5! = 120

Show all work to write the expression in simplified rational exponent form:
[tex]\sqrt[4]{17x^{2}}[/tex]
(Fourth root of 17 x squared)

Answers

Answer:

[tex](17x)^{\frac{2}{4}}[/tex]

Step-by-step explanation:

There's not much work to show for this problem, but I'll explain it for you

Use the exponent rule for roots to combine the 4 and the 2 like a fraction

2 on the top and 4 on the bottom

[tex](17x)^{\frac{2}{4} }[/tex]

That's it!  Pretty easy

Good Luck!

pls mark brainliest

Assume the graph is derivative f(x). Answer for f(x)

Answers

The intervals which the original function f(x) concave down are (-5, -2) and (3, 5)

How to determine the intervals which the original function f(x) concave down?

The information that completes the question are added as an attachment

The question requires that we determine the intervals which the original function f(x) concave down

From the attached graph, we have the following turning points

(-2, -4) and (3, 2)

From the domain of the graph, the curve starts at (-5, 0), turns at (-2, -4), also turns at (3, 2) and then stops at (5, 0)

So, we have:

(-5, 0), (-2, -4), (3, 2) and (5, 0)

Remove the y coordinates

x = -5, -2, 3 and 5

Express as intervals

(-5, -2) and (3, 5)

Hence, the intervals which the original function f(x) concave down are (-5, -2) and (3, 5)

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Find the number if 11% of it is 55

Answers

Answer:

Step-by-step explanation:

.11x = 55

11x = 5500

x = 500

There are 96 football players at all levels at Davenport High School. If two-thirds of the players make the honor roll for their grades how many olayers are on the list?
64 players
48 players
72 players
54 players

Answers

64 players
Reason- 2/3 of 96 = (32 x 2 = 64) telling us how many got on the list

Which statement best reflects the solution(s) of the equation? ASAP

Answers

The solutions to the equation 1 / (x - 1) + 2/x = x / (x - 1) are two solution which are x = 2; and x = 1

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

Given the equation:

1 / (x - 1) + 2/x = x / (x - 1)

Multiplying through the equation by x(x - 1):

x + 2(x - 1) = x(x)

x² - 3x + 2 = 0

x² - 2x - x + 2 = 0

(x - 2)(x - 1) = 0

x = 2; and x = 1

The solutions to the equation 1 / (x - 1) + 2/x = x / (x - 1) are two solution which are x = 2; and x = 1

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question:

|x-2|, if x > 5
simplify without the absolute value sign

Answers

Answer:

x - 2, if x > 5

Step-by-step explanation:

The vertical lines either side of the expression mean absolute value.

The absolute value of a number is its positive numerical value.

if x > 5 then as 5 > 2, the values inside the vertical lines will always be positive.  Therefore, we can disregard the absolute value.

Therefore:  

x - 2,  if x > 5

To find the range (output values) of the expression, substitute x = 5 into the expression:

⇒ 5 - 2 = 3

Therefore, |x - 2| > 3,  if x > 5

A chemical company makes two brands of antifreeze. The first brand is 30% pure antifreeze and the second brand is 55% pure antifreeze. In order to obtain 160 gallons of a mixture that contains 45% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answers

Answer:

64 gallons 30%96 gallons 55%

Step-by-step explanation:

The amount of each brand can be found by writing and solving an equation that makes use of the given relations.

Setup

Let x represent the quantity of 55% pure antifreeze needed in the mixture. Then the quantity of the 30% brand is (160-x). The amount of pure antifreeze in the mixture is ...

  0.55x +0.30(160 -x) = 0.45(160)

Solution

Subtracting 0.30(160), we have ...

  x(0.55 -0.30) = 160(0.45 -0.30)

  x = 24/0.25 = 96 . . . . . simplify, divide by the coefficient of x

96 gallons of the 55% brand, and 64 gallons of the 30% brand must be used.

__

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Solve the differential equation. (x^2 + 11)y' = xy

Answers

Separate the variables.

[tex](x^2+1) \dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x^2+11} \, dx[/tex]

Integrate both sides. On the right, substitute [tex]u=x^2+11[/tex] and [tex]du=2x\,dx[/tex].

[tex]\displaystyle \int \frac{dy}y = \int \frac x{x^2+11}\,dx = \frac12 \int \frac{du}u[/tex]

[tex]\ln|y| = \frac12 \ln|u| + C[/tex]

[tex]\ln|y| = \ln\left(\sqrt{x^2+11}\right) + C[/tex]

[tex]e^{\ln|y|} = e^{\ln\left(\sqrt{x^2+11}\right)+C}[/tex]

[tex]\boxed{y = C\sqrt{x^2+11}}[/tex]

Using separation of variables, the solution to the differential equation is:

y = ksqrt(x² + 11)

What is separation of variables?

In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.

In this problem, the differential equation is:

(x² + 11)y' = xy

Applying separation of variables, we have that:

y'/y = x/(x² + 11)

[tex]\int \frac{y^{\prime}}{y} = \int \frac{x}{x^2 + 11}[/tex]

[tex]\ln{y} = \frac{\ln{x^2 + 11}}{2} + K[/tex]

[tex]\ln{y} = \ln{(x^2 + 11}^{\frac{1}{2}}) + K[/tex]

[tex]\ln{y} = \ln{\sqrt{x^2 + 11}} + K[/tex]

Hence the solution is:

y = ksqrt(x² + 11)

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Compute the probability of event E if the odds in favor of E are 28 to 29.

Answers

Answer:

28/57

Step-by-step explanation:

odds in favor of event occurring = (probability event occurs)/(probability event does not occur)

Let p = probability event occurs.

Then the probability the event does not occur is 1 - p.

Let the odds = a/b.

a/b = p/(1 - p)

a(1 - p) = bp

a - ap = bp

bp + ap = a

p(a + b) = a

p = a/(a + b)

p = 28/(28 + 29)

p = 28/57

As per the given scenario, the probability of event E is 28/57 or approximately 0.4912.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is usually expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to occur.

If the odds in favor of an event E are "a to b," then the probability of E is given by:

P(E) = a / (a + b)

In this case, the odds in favor of E are 28 to 29, which means that there are 28 favorable outcomes for E and 29 unfavorable outcomes against E.

So, using the formula above, we can compute the probability of E as:

P(E) = 28 / (28 + 29)

P(E) = 28 / 57

Therefore, the probability of event E is 28/57 or approximately 0.4912.

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Find the cube root of Z =1+i the power of 5​

Answers

Answer:

Cube Root Calculator

Use this calculator to find the cube root of positive or negative numbers. Given a number x, the cube root of x is a number a such that a3 = x. If x positive a will be positive, if x is negative a will be negative. Cube roots is a specialized form of our common radicals calculator.

It will help you alot.

Step-by-step explanation:

100 000 , 10 000 , 1000 , 100 , A , B

The two missing numbers in the pattern are:

A=___?

B=___?

Answers

The two missing numbers in the pattern are 10 and 1

How to determine the missing numbers?

The sequence is given as:

100 000 , 10 000 , 1000 , 100 , A , B

From the above sequence, the next term is the quotient of the current term and 10.

So, we have:

A = 100/10 = 10

B = A/10 = 10/10 = 1

Hence, the two missing numbers in the pattern are 10 and 1

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Juan and Ari went to the farmers market to buy fruit. Juan’s bag of apples that he bought weighed StartFraction 31 over 7 EndFraction pounds. Ari’s bag of oranges that he bought weighed StartFraction 19 over 3 EndFraction pounds. Using compatible fractions, estimate how much heavier Ari’s bag is compared to Juan’s bag.

Answers

Answer:

approximately 2 lb

Step-by-step explanation:

Juan: 31/7

Ari: 19/3

Juan's fraction is close to 32/8 = 4

Ari's fraction is close to 18/3 = 6

6 - 4 = 2

Answer: approximately 2 lb

Ronaldo specializes in creating sewing patterns for dresses, and wants to set up his own website to sell electronic copies. He pays $120 for a domain name and web hosting services for the first year. Ronaldo makes $14.25 for each electronic pattern that he sells. How many patterns must he sell to cover the cost of the website for the first year? Round your answer to a whole number.

Answers

Answer:

8

Step-by-step explanation:

120/14.25=8.4 rounded off to a whole number is 8

List the angles in order from the largest to the smallest for ΔABC. AB⎯⎯⎯⎯⎯⎯⎯=14, AC⎯⎯⎯⎯⎯⎯⎯⎯=15, BC⎯⎯⎯⎯⎯⎯⎯⎯=16

Answers

Answer:

BC 1

AC 2

AABC 3

Step-by-step explanation:

BC=16

AC = 15

AABC= 15

Answer: C, B, A

Step-by-step explanation: It just is

Graph on the number line all values of x that satisfy 2x+2/x+7 >= 0

Please help, if you help me I will give you a brainlist.

Answers

All values of x that satisfy 2x+2/x+7 >= 0 are represented as x >= -1

How to graph the inequality on a number line?

The inequality expression is given as:

2x+2/x+7 >= 0

Multiply both sides by x + y

2x+2 >= 0

Subtract 2 from both sides

2x > -2

Divide both sides by 2

x >= -1

Hence, all values of x that satisfy 2x+2/x+7 >= 0 are represented as x >= -1

See attachment for the number line of x >= -1

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According to a recent poll at a​ university,70.7 ​% of high school seniors in a certain region had a​ driver's license. A sociologist thinks this rate has declined. The sociologist surveys randomly selected high school seniors and finds that have a​ driver's license. a. Pick the correct null hypothesis. b. Pick the correct alternative hypothesis. c. In this​ context, what does the symbol p​ represent?

Answers

your mother i swear

Step-by-step explanation:

ask yo mom

Hi,

Could anyone help with this please?

Many thanks,

Answers

Length: 2.6 meters

Width: 1.8 meters

Area: 4.68 meters

Since the scale is 1/40, we can multiply the centimeter measurements by 40 thus making it our scale factor.

Length

2.6 x 40 = 260

260 cm = 2.6 m

Width

4.5 x 40 = 180

180 cm= 1.8 m

Area

1.8 x 2.6 = 4.68 m

Length: 2.6 meters

Width: 1.8 meters

Area: 4.68 meters

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