1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
beks73 [17]
3 years ago
15

RSM wants to send four of its 18 Math Challenge teachers to a conference. How many combinations of four teachers include exactly

one of either Mrs. Vera or Mr. Jan?
Mathematics
1 answer:
tatiyna3 years ago
4 0

Answer:

1120 combinations of four teachers include exactly one of either Mrs. Vera or Mr. Jan.

Step-by-step explanation:

The order in which the teachers are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

In this question:

1 from a set of 2(Either Mrs. Vera or Mr. Jan).

3 from a set of 18 - 2 = 16. So

C_{2,1}C_{16,3} = \frac{2!}{1!1!} \times \frac{16!}{3!13!} = 1120

1120 combinations of four teachers include exactly one of either Mrs. Vera or Mr. Jan.

You might be interested in
Please simplify this please it’s due really soon!
iren2701 [21]

Step-by-step explanation:

\frac{ {13}^{6}  \div  {13}^{8}  \times  {13}^{ - 4} }{ {13}^{ - 2} }

You need to remember the properties of exponents: multiplication adds the exponents, division subtracts the exponents.

If you multiply two powers with the same base, the result will be the base to the sum of the powers.

If you divide two powers with the same base, the result will be the base to the difference of the powers.

In your case you will this:

{13}^{6 - 8 + ( - 4) - ( - 2)}

That is:

{13}^{ - 4}

Or:

\frac{1}{ {13}^{4} }

7 0
3 years ago
Solve the right triangle, ΔABC, for all the missing side and angles to the nearest tenth given sides a = 10.6 and b = 19.2.
Aliun [14]

Answer:

Part 1) c=21.9\ units

Part 2) B=61.1\°

Part 3) A=28.9\°

Part 4) C=90\°

Step-by-step explanation:

step 1

Find the length side c

Applying the Pythagoras Theorem

c^{2}=a^{2}+b^{2}

substitute the given values

c^{2}=10.6^{2}+19.2^{2}

c^{2}=481

c=21.9\ units

step 2

Fin the measure of angle B

we know that

In the right triangle

tan(B)=b/a

substitute the given values

tan(B)=19.2/10.6

B=arctan(19.2/10.6)=61.1\°

step 3

Find the measure of angle A

we know that

The measure of interior angles in a triangle must be equal to 180 degrees

so

∠A+∠B+∠C=180°

Remember that in a right triangle the measure of angle C is 90 degrees

we have

B=61.1\°

C=90\°

substitute

A+61.1\°+90\°=180\°

A=28.9\°

4 0
3 years ago
BRAINLIST BRAINLIST BRAINLIST
musickatia [10]

Answer:

0.5 onces

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
What is the volume, in cubic centimeters, of a right rectangular prism that has a lenght of 4 centimeters, a width of 9 centimet
Temka [501]

Answer:

The volume of the prism is 360 cm^3.

Step-by-step explanation:

The rectangular prism is a three dimensional figure formed by six rectangular faces. It's volume is given by the product of it's three dimensions. The calculation for the volume of this prism is shown bellow:

volume = width*height*length

volume = 9*10*4

volume = 360 cm^3

The volume of the prism is 360 cm^3.

7 0
3 years ago
Read 2 more answers
Julie uses 12 oz of cheese in her potato soup recipe.her recipe yields 8 servings.if julie needs enough for 20 servings,how many
Makovka662 [10]
I think the answer is 240oz
4 0
3 years ago
Other questions:
  • What is the area of this figure?
    5·1 answer
  • What is the value of 4x-7 when x=4
    5·2 answers
  • What is the coordinate for the image of point H(2, –6) under a 90° clockwise rotation about the origin?
    12·1 answer
  • A researcher has participants choose between three advertisements. She finds that 54 prefer Ad A, 86 prefer Ad B, and 60 prefer
    12·1 answer
  • Combine the like terms to create an equivalent expression: \large{-k-(-8k)}−k−(−8k)minus, k, minus, (, minus, 8, k, )
    9·1 answer
  • 2x+9−5x=12 i dont under stand how to get the answer
    13·1 answer
  • If three-fifths of seventh-grade class has missed at least one day of school, what percentage of 7th grade has missed at least a
    11·1 answer
  • 2/5 × [ -3/7] - 1/6 × 3/2 + 1/14 × 2/5
    5·2 answers
  • U A cube is a rectangular prism whose edge lengths are all the same.
    14·1 answer
  • Find the surface area of the prism
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!