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valina [46]
3 years ago
9

What is one half as a decimal

Mathematics
2 answers:
iVinArrow [24]3 years ago
7 0
One half as a decimal is .5
vovikov84 [41]3 years ago
3 0
One half as a decimal is 0.5. All you need to do is do 1 divided by 2.
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A company is in the business of finding addresses of long-lost friends. The company claims to have a 70% success rate. Suppose t
Galina-37 [17]

Answer:

a) Figure attached

b) E(X) =\mu= np = 9*0.7=6.3

Sd(X) =\sigma= \sqrt{np(1-p)}= \sqrt{9*0.7*(1-0.7)}=1.375

c) For the case n= 6

P(X \leq 2) = 0.9891

For the case n= 5

P(X \leq 2) = 0.9692

So then we need at least  n=5 or n=6 to satisfy the condition required.

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=9, p=0.7)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Part a

For this case we can use the following R code:

> x <- seq(0,9,by = 1)

> y <- dbinom(x,9,0.7)

> plot(x,y,main="Histogram",type = "h")

And we can see on the figure attached the solution.

We see that the higher probabilities are from 4 to 9

Part b

The expected value is given by:

E(X) =\mu= np = 9*0.7=6.3

The variance is given by:

Var (X) =\sigma^2= np(1-p) = 9*0.7*(1-0.7)= 1.89

And the standard deviation is:

Sd(X) =\sigma= \sqrt{np(1-p)}= \sqrt{9*0.7*(1-0.7)}=1.375

Part c

First we can find the probability that at least two addresses will be found in the list of 9 that we have like this:

P(X \geq 2)

We can use the complement rule and we have:

P(X \geq 2) = 1-P(X

We find the indicidual probabilities:

P(X=0)=(9C0)(0.7)^0 (1-0.7)^{9-0}=0.00001968

P(X=1)=(9C1)(0.7)^1 (1-0.7)^{9-1}=0.000413

P(X \geq 2) = 1-[0.00001968+0.000413]=0.9996

If we use the case of n=8 and we find P(X\leq 2), we got:

P(X \leq 2) = 0.9987

For the case n= 7

P(X \leq 2) = 0.9962

For the case n= 6

P(X \leq 2) = 0.9891

For the case n= 5

P(X \leq 2) = 0.9692

So then we need at least  n=5 or n=6 to satisfy the condition required.

5 0
3 years ago
What 89,659 rounded to the nearest hundred thousand
lisov135 [29]
100,000

Since 8 rounds up to 10, it will go up to 100,000.
5 0
3 years ago
Mary makes trail mix with bulk nuts and dried fruit. She spends $4.50 on the dried fruit. Mixed nuts cost $2.50 per pound. She h
AnnyKZ [126]

Answer: 3 pounds

Step-by-step explanation: 12 - 4.50 = 7.50 7.50/2.50=3

4 0
3 years ago
Solve each proportion 3/39= y/13
Sphinxa [80]

Answer:

y = 1

Step-by-step explanation:

\frac{3}{39}  =  \frac{y}{13}

Cross multiply

39 = 39y

Divide by 39

y = 1

6 0
2 years ago
Read 2 more answers
The length of a board is 2 5/8 feet long. If 5/6 of a foot is trimmed off, find the new length
nalin [4]

Answer:

New length is 3 3/20 ft.

Step-by-step explanation:

The total board is 2 5/8 feet long. And since 5/6 of a foot is trimmed off, that means each piece of wood is 5/6 feet.

We can now set up an equation like this ---> 5/6 ⋅ x = 2 5/8

Now we're going to simplify --->  5/6 ⋅ x = 2 5/8

                                                      5/6 ⋅ x = 21/8              

                                                      (multiply both sides by 6)

                                                      5x = 63/4

                                                      (divide both sides by 5)

                                                      x = 63/20

                                                      x= 3.15

So, the new length is 3.15 feet long, or 3 3/20 in mixed fraction.

6 0
2 years ago
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