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3 years ago

What is f(x) = 3log(x+5)=2

Mathematics

1 answer:

trasher [3.6K]3 years ago

3 0

Answer:

x=10^{\frac{2}{3}}-5

Step-by-step explanation:

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USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counse

pychu [463]

Answer:

a) $P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

b) $E(X) = np = 4*0.75=3$

c) $Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

d) $P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

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".

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

$X \sim Binom(n=4, p=1-0.25=0.75)$

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

$P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

Part b

The expected value is givn by:

$E(X) = np = 4*0.75=3$

Part c

For the standard deviation we have this:

$Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

Part d

For this case the sample size needs to be higher or equal to 9. Since we need a value such that:

$P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

We can verify this using the following code:

"=1-BINOM.DIST(3,9,0.75,TRUE)" and we got 0.99 and the condition is satisfied.

4 0

3 years ago

HELP!! Which truck pulled 2,000 pounds at the average<br> speed of 2 yards per minute?

Advocard [28]

The correct answer it would be B

Ford

8 0

3 years ago

A railway car is shaped like a rectangular prism with a length of 18 meters, a width of 3 meters, and a height of 4 meters.

nekit [7.7K]

Answer:

216 cubic meters

Step-by-step explanation:

4 0

2 years ago

How long will it take an emperor penguin to swim 14 miles if it is swimming 7 mph

xz_007 [3.2K]

It will take the penguin 2 hours i think
14 miles
7 miles per hour
1 hour- 7 miles
2 hours- 14 miles

7 0

3 years ago

The Daily News offers a 15% discount on a Saturday ad that also runs on Tuesday. Skyler Sporting Company contracts for half-page

mart [117]

The ad cost for half page Saturday after discount is

15% of 380 = 0.15×380 = 57
380 - 57 = 323

The ad cost for half page Tuesday after discount is

15% of 330 = 0.15×330 = 49.5
330 - 49.5 = 280.5

Cost of the ads for 10 Saturdays and 10 Tuesdays

(10×323)+(10×280.5) = 3230+2805 = 6035

6 0

3 years ago

Read 2 more answers