Pick three numbers and make a fact family. <br><br> 4, 5 <br><br> 2, 1

Ten times the sum of half a number x and 8 is 12.

Diano4ka-milaya [45]

BREAKDOWN

10 times: 10 ×

The sum of: ( ) + ( )

which would be : 10 × ( ) + ( )

half a number: 10 × ( X/2 ) + ( )

and 8: 10 × ( X/2 ) + ( 8 )

is 12 : 10 × ( X/2 + 8 ) = 12

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SIMPLIFICATION

Multiply ten: 10 X (X/2 + 8) = 12

which equals to: 5x + 80 = 12

bring the like terms together: 5x = 80 - 12

Equals: 5x = 78

Find out X:. x = 78/5

FINAL ANSWER:. X = 15.9

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6 0

3 years ago

Each number in the sequence is 8 less than the previous number which list of number can be described by the following rule

Ganezh [65]

Answer: a

Step-by-step explanation:

4 0

3 years ago

In Illinois, 9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders; that is, they have been arre

Veseljchak [2.6K]

Answer:

a) 21.58% probability that exactly 3 people are repeat offenders

b) 97.91% probability that at least one person is a repeat offender

c) 3.69

d) 1.83

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

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

And p is the probability of X happening.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

9% of all drivers arrested for DUI (Driving Under the Influence) are repeat offenders

This means that $p = 0.09$

41 people arrested for DUI in Illinois are selected at random.

This means that $n = 41$

a. What is the probability that exactly 3 people are repeat offenders?

This is P(X = 3).

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 3) = C_{41,3}.(0.09)^{3}.(0.91)^{38} = 0.2158$

21.58% probability that exactly 3 people are repeat offenders

b. What is the probability that at least one person is a repeat offender?

Either none are repeat offenders, or at least one is. The sum of the probabilities of these outcomes is 1. So

$P(X = 0) + P(X \geq 1) = 1$

We want $P(X \geq 1)$ .

Then

$P(X \geq 1) = 1 - P(X = 0)$

In which

$P(X = 0) = C_{41,0}.(0.09)^{0}.(0.91)^{41} = 0.0209$

$P(X \geq 1) = 1 - P(X = 0) = 1 - 0.0209 = 0.9791$

97.91% probability that at least one person is a repeat offender

c. What is the mean number of repeat offenders?

$E(X) = np = 41*0.09 = 3.69$

d. What is the standard deviation of the number of repeat offenders?

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{41*0.09*0.91} = 1.83$

4 0

3 years ago

ILL GIVE MORE BRAINLY IF YOU GIT IT RIGHT PLS END OF 1/4 IS TODAY

aivan3 [116]

Answer:

60

Step-by-step explanation:

Just use similar triangles.

12/10 = 72/x

Now solve for x.

x = 72 * 10 / 12 = 60

4 0

3 years ago

Suppose that a butterfly can fly 82 feet in 4 seconds. A dragonfly can fly 50 feet in 2 seconds. Which can fly faster and by how

Lady bird [3.3K]

A butterfly can fly 82 feet in 4 seconds.

Distance traveled by butterfly = 82 feet.

Time taken by butterfly =4 seconds

Speed = distance /time

Speed of butterfly = 82/4 = 20.5 feet/second

A dragonfly can fly 50 feet in 2 seconds.

Distance traveled by dragonfly =50 feet.

Time taken by dragonfly =2 seconds.

Speed of dragonfly = 50/2 = 25 feet/second

So dragonfly can fly faster than the butterfly.

Difference in speed = speed of dragonfly - speed of butterfly = 25-20.5 = 4.5

So The dragonfly is 4.5 feet per second faster than butterfly.

Answer: B) The dragonfly is 4.5 feet per second faster.

5 0

3 years ago

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Pick three numbers and make a fact family. 4, 5 2, 1