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3 years ago

What is the area of this parallelogram? Please help me

Mathematics

1 answer:

stich3 [128]3 years ago

8 0

The answer is 60cm2

Arectangle=L×W

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Suppose that 5 out of 13 people are to be chosen to go on a mission trip. In how many ways can these 5 be chosen if the order in

algol [13]

5 People can be chosen in 1287 ways if the order in which they are chosen is not important.

Step-by-step explanation:

Given:

Total number of students= 13

Number of Students to be selected= 5

To Find :

The number of ways in which the 5 people can be selected=?

Solution:

Let us use the permutation and combination to solve this problem

$nCr=\frac{(n)!}{(n-r)!(r)!}$

So here , n =13 and r=5 ,

So after putting the value of n and r , the equation will be

$13C_5=\frac{(13)!}{(13-5)!(5)!}$

$13C_5=\frac{(13 \times12 \times11 \times10 \times9 \times8\times7 \times6 \times5 \times4 \times3 \times2 \times1)}{(8 \times7 \times6 \times5 \times4 \times3 \times2 \times1)(5 \times4 \times3 \times2 \times1)}$

$13C_5=\frac{(13 \times12 \times11 \times10 \times9 )}{((5 \times4 \times3 \times2 \times1)}$

$13C_5=\frac{154440}{120}$

$13C_5= 1287$

8 0

4 years ago

which property does the example shows. 23.1+42.6=42.6+23.1. A. associative property of addition or B.Distributive property

konstantin123 [22]

A) distributive is where it distributes a number through a set of parenthesis.

4 0

4 years ago

Read 2 more answers

A pyramid has a square base of length 8cm and a total surface area of 144cm². Find the volume of the pyramid. (Please use Pythag

Sveta_85 [38]

Answer:

$\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

Step-by-step explanation:

we are given surface area and the length of the square base

we want to figure out the Volume

to do so

we need to figure out slant length first

recall the formula of surface area

$\displaystyle A_{\text{surface}}=B+\dfrac{1}{2}\times P \times s$

where B stands for Base area

and P for Base Parimeter

$\sf\displaystyle \: 144=(8 \times 8)+\dfrac{1}{2}\times (8 \times 4) \times s$

now we need our algebraic skills to figure out s

simplify parentheses:

$\sf\displaystyle \: 64+\dfrac{1}{2}\times32\times s = 144$

reduce fraction:

$\sf\displaystyle \: 64+\dfrac{1}{ \cancel{ \: 2}}\times \cancel{32} \: ^{16} \times s = 144 \\ 64 + 16 \times s = 144$

simplify multiplication:

$\displaystyle \: 16s + 64 = 144$

cancel 64 from both sides;

$\displaystyle \: 16s = 80$

divide both sides by 16:

$\displaystyle \: \therefore \: s = 5$

now we'll use Pythagoras theorem to figure out height

according to the theorem

$\displaystyle \: {h}^{2} + (\frac{l}{2} {)}^{2} = {s}^{2}$

substitute the value of l and s:

$\displaystyle \: {h}^{2} + (\frac{8}{2} {)}^{2} = {5}^{2}$

simplify parentheses:

$\displaystyle \: {h}^{2} + (4 {)}^{2} = {5}^{2}$

simplify squares:

$\displaystyle \: {h}^{2} + 16 = 25$

cancel 16 from both sides:

$\displaystyle \: {h}^{2} = 9$

square root both sides:

$\displaystyle \: \therefore \: {h}^{} = 3$

recall the formula of a square pyramid

$\displaystyle V_{pyramid}=\dfrac{1}{3}\times A\times h$

where A stands for Base area (l²)

substitute the value of h and l:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times \{8 \times 8 \}\times 3$

simplify multiplication:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times 64\times 3$

reduce fraction:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{ \cancel{ 3 \: }}\times 64\times \cancel{ \: 3}$

hence,

$\sf\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

8 0

3 years ago

Find the area of a room that is 28 feet long and 46 feet wide?

Oxana [17]

Answer:

A =1288 ft^2

Step-by-step explanation:

A = l*w

A = 28*46

A =1288 ft^2

8 0

4 years ago

Read 2 more answers

125 divided by 32 equals what

andreyandreev [35.5K]

32 × 2 = 68
32 × 3 = 96
32 × 4 = 128

So far we can conclude that the answer to your question lies somewhere between the numbers 3 and 4. To narrow down the answer some more, multiply 32 by 3.5 (a midway point between 3 and 4).

32 × 3.5 = 112
The number 112 tells us that the decimal we are looking for is higher than 3.5. (Because we need to get to 125, not 112.) Let's try some decimals between 3.5 and 4.

32 × 3.7 = 118.4
32 × 3.8 = 121.6
32 × 3.9 = 124.8
32 × 4 = 128

As we narrow down our answer, we can see that the number we are looking for lies between 3.9 and 4 on the number line. Now we need to start testing some decimals between 3.9 and 4.

32 × 3.905 = 124.96
Again, use the number five as a "midway" point to decide if you should use numbers that are higher or lower than 3.905. In this case, we need to use numbers higher than 3.905.

32 × 3.906 = 124.992
32 × 3.907 = 125.024

We are getting even closer to our number now that we know the decimal is somewhere between 3.906 and 3.907.

32 × 3.9065 = 125.008
With our midway point we can see that our number lies between 3.906 and 3.9065. Let's try a quarter point to see where our number lies from there.

32 × 3.90625 = 125
And BINGO! We have found the answer to the question. To be rephrased, our answer can be put like this:

$\frac{125}{32}$ = 3.90625

6 0

4 years ago