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3 years ago

Triple a number, x, increased by 1 is between -20 and 10. What are the solutions for x?

1 answer:

3 0

Hello,
$-20 \leq 3x+1 \leq 10\\
\Rightarrow\ -21 \leq 3x \leq 9\\
\Rightarrow\ -7 \leq x \leq 3\\

Sol=[-7\ 3]\ if\ x\ is\ a\ real.
$

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A researcher collected data from a sample of correctional officers and found that on average they made 47,173 dollars a year wit

ollegr [7]

Answer:

a) $z = \frac{40000- 47173}{6364} = -1.127$

b) $z = \frac{50000- 47173}{6364} = 0.444$

c) $P(X>40000)=P(\frac{X-\mu}{\sigma}>\frac{40000-\mu}{\sigma})=P(Z>\frac{40000-47173}{6364})=P(z>-1.127)$

And we can find this probability using the complement rule and the normal standard distribution or excel and we got:

$P(z>-1.127)=1-P(z$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the amount of money of a population of interet, and we know the following info:

Where $\bar X=47173$ and $s=6364$

We can assume that the sample size is large and the estimators can be used as a good description for the parameters $\mu \sigma$

The z score for 40000 would be:

$z = \frac{40000- 47173}{6364} = -1.127$

Part b

The z score for 50000 would be:

$z = \frac{50000- 47173}{6364} = 0.444$

Part c

We are interested on this probability

$P(X>40000)$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X>40000)=P(\frac{X-\mu}{\sigma}>\frac{40000-\mu}{\sigma})=P(Z>\frac{40000-47173}{6364})=P(z>-1.127)$

And we can find this probability using the complement rule and the normal standard distribution or excel and we got:

$P(z>-1.127)=1-P(z$

8 0

3 years ago

Find the discounted price.<br> Light:$18:00 Discount:25%

lbvjy [14]

The discounted price is $13.5. You do $18 and times it by 0.25. You will get 4.5. You then subtract the 4.5 from the $18 and you get $13.5

4 0

3 years ago

How do i factor 2x^2+11x+5

ira [324]

For simple integer factors as this one has, you want to find two values for the quadratic in the form ax^2+bx+c. Let the two values be j and k. These two values must satisfy two conditions.

jk=ac=10 and j+k=b=11, so j and k must be 1 and 10.

Now replace bx with jx and kx...

2x^2+x+10x+5 now factor 1st and 2nd pair of terms.

x(2x+1)+5(2x+1)

(x+5)(2x+1)

7 0

3 years ago

Read 2 more answers

A scale on a map shows that 2 inches equals 25 miles how many inches on the map represents 60 miles?? I NEED HELP ASAP

irakobra [83]

Answer:

60 miles is equal to 4.8 inches.

Step-by-step explanation:

To find the answer to this question, we need divide 60 by 25 to find out how much to multiply 2 by so its equal.

60/25=2.4

2*2.4=4.8

60 miles is equal to 4.8 inches.