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3 years ago

1.Point E is the midpoint. Find EF. *

Mathematics

1 answer:

Soloha48 [4]3 years ago

5 0

Step-by-step explanation:

Since, Point E is the midpoint of DF

Therefore,

DE = EF

10x = 4x + 12

10x - 4x = 12

6x = 12

x = 12/6

x = 2

EF = 4x + 12 = 4*2+12 = 8 * 12 = 20

EF = 20

AB = BC

6x + 2 = 9x - 10

10 + 2 = 9x - 6x

12 = 3x

12/3 = x

x = 4

BC = 9x - 10 = 9*4 - 10 = 36 - 10 = 26

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tim and his brother are building towers out of blocks. Tim is using blue blocks that are 6 cm tall and his brother is using gree

sergiy2304 [10]

The shortest possible height of the tower is 24 cm

They used 4 blue blocks and 3 green blocks

Step-by-step explanation:

Tim and his brother are building towers out of blocks

Tim is using blue blocks that are 6 cm tall
His brother is using green blocks that are 8 cm tall
They both made towers the same height

We need to find the shortest possible height of the tower and how many of each color block they used

∵ Tim is using blue blocks that are 6 cm tall

∴ The height of his tower is a number divisible by 6

∵ His brother is using green blocks that are 8 cm tall

∴ The height of his tower is a number divisible by 8

∵ The heights of their towers are equal

∴ The height of the towers must be a number divisible by 6 and 8

Let us write some multiples of 6 and 8 to find the first common multiple of them

∵ The multiples of 6 are 6 , 12 , 18 , 24 , 30 , 36 , .........

∵ The multiples of 8 are 8 , 16 , 24 , 32 , 40 , .............

∵ The first common multiple of them is 24

∴ The shortest possible height of the tower is 24 cm

∵ The height of each blue block is 6 cm

- Divide the height of the tower by the height of the block to

find the number of blue blocks

∵ 24 ÷ 6 = 4

∴ Time is using 4 blue blocks

∵ The height of each green block is 8 cm

- Divide the height of the tower by the height of the block to

find the number of green blocks

∵ 24 ÷ 8 = 3

∴ His brother is using 3 green blocks

The shortest possible height of the tower is 24 cm

They used 4 blue blocks and 3 green blocks

Learn more:

You can learn more about the word problems in brainly.com/question/6569012

#LearnwithBrainly

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3 years ago

during a particular period a university's information technology office received 20 service orders for problems with printers, o

stira [4]

Answer:

0.2384 = 23.84% probability that 3 were laser printers.

Step-by-step explanation:

The printers will be chosen without replacement, which means that the hypergeometric distribution is used to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

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:

20 orders means that $N = 8$

8 were laser printers, which means that $k = 8$

Sample of 5 means that $n = 5$

What is the probability that 3 were laser printers?

This is P(X = 3).

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}$

$P(X = 3) = h(3,20,5,8) = \frac{C_{8,3}*C_{12,2}}{C_{20,5}} = 0.2384$

0.2384 = 23.84% probability that 3 were laser printers.

4 0

3 years ago