The library is to be given 5 books as a gift. the books will be selected from a list of 21 titles. if each book selected must have a different title, how many possible selections are there?

Answers

Answer 1
Answer:

This is a combination problem. Order does not matter and the books are all different. You would write this as 21C5 or \tbinom{21}{5}. Combinations are not fractions.

The answer is (21 * 20 * 19 * 18 * 17)/(1 * 2 * 3 * 4 * 5)

which = 20349 different ways these books can be chosen.


Answer 2
Answer:

Answer:

20,349.

Step-by-step explanation:

We have been that a library is to be given 5 books as a gift. the books will be selected from a list of 21 titles.

We will combinations to solve our given problem.

_(r)^(n)\textrm{C}=(n!)/(r!(n-r)!)

Different ways to choose 5 books from 21 tiles:

_(5)^(21)\textrm{C}=(21!)/(5!(21-5)!)

_(5)^(21)\textrm{C}=(21!)/(5!(16)!)

_(5)^(21)\textrm{C}=(21*20*19*18*17*16!)/(5*4*3*2*1*(16)!)

_(5)^(21)\textrm{C}=(21*19*18*17)/(3*2)

_(5)^(21)\textrm{C}=(21*19*3*17)/(1)

_(5)^(21)\textrm{C}=20,349

Therefore, there are 20349 possible selections.


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Geometry question

No explanation necessary, I need an answer in two words or less

Answers

Answer: circle

Step-by-step explanation:

All cross sections of a sphere are circles.

Ali and Kiana buried a treasure together on their school's field. The actual field is 400 feet wide. Ali made an 8-inch-wide map to record its location. Kiana made her map using a scale of 1 in. To 20 ft. On Kiana's map, the treasure is 2 inches from the south edge of the field. How far is the treasure from the south edge on Ali's map?

Answers

Answer:

The treasure is 0.8 inches from the south edge on Ali's map.

Step-by-step explanation:

Scaling factor, f = (Original length)/(Scalet length)...(i)

Let f_1 and f_2 be the scaling factors used by Ali and Kiana respectively.

Given that the field is 400 feet= 400x12 inches wide and Ali made an 8-inch-wide map to record its location.

So, f_1 = (400*12)/8=600...(ii)

Kiana made her map using a scale of 1-inch to 20 feet=20x12 inches.

So, f_2=(20*12)/1=240...(iii)

As on Kiana's map, the treasure is 2 inches from the south edge of the field,

so, from equations (i), and (ii), the original length of the treasure for the south edge of the field

=2* f_2

=2x240

=480 inches

Now, again from the equation (i) and (ii), the scaled length of the treasure on Ali's map

= 480/f_1

=480/600

=0.8 inches

Hence, the treasure is 0.8 inches from the south edge on Ali's map.

$25;300%increse percent change

Answers


well and 300% increase means you multiply by 3 and then add the original number


in this case 300% of 25 is 75 and its an increase so 25+75=100

the answer is 100

It takes omar four minutes to eat eight carrots sticks. how long does it take him to eat one ?

Answers

It takes Omar 30 seconds to eat one considering he ate 8 in 4 minutes ...

If we really wanted to we could turn this into the fraction 8/4
8 being the amount of carrot sticks he ate and 4 being the time it took
now all u have to do is simplify that turns into 2/1 and since the 1 is one minute and her can eat 2 in one minute we can safely say he eats 1 carrot stick every 30 seconds 

:) hope this helps!!

Given that the measure of ∠x is 60°, and the measure of ∠y is 90°, find the measure of ∠z.

Answers

The measure of ∠x is 60°, and the measure of ∠y is 90°, the measure of ∠z is 30°

What is an angle ?

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

Given that,

In right angle triangle, Δxyz

Angle ∠x is 60°

Angle ∠y is 90°

It is already known that sum of all the interior angles of any  triangle is equal to 180°

So,

∠x + ∠y + ∠z = 180°

60° + 90° + ∠z = 180°

∠z = 30°

Therefore, the third angle is  30°

To know more about angle check:

brainly.com/question/28451077

#SPJ2

This is a right triangle. And every traingle should have total 180°. 180-150 = 30° is the answer

One side of a triangular garden is x feet long. The other two sides of the garden are both 5 feet less than twice the length of the first side of the garden.Part A: Write a simpiflied expression for perimeter, in feet, of the garden.

A fence is placed along the entire perimeter of the triangular garden. The roll of fencing is 40 ft long.

Part B: Write a simplified expression to show the amount of fencing, in feet, which is left from the roll of fencing.

Answers

I think Part A is (X x 2)-5 and Part B is 40 x 3. I'm not so sure because I'm in 5th grade and I haven't learned this yet. I hope it helps a little bit and I hope it is right.