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11Alexandr11 [23.1K]
3 years ago
11

If f(x) = 2x + 1 and g(x) = x2 - 2, find f(g(3)).

Mathematics
2 answers:
pentagon [3]3 years ago
8 0

Answer:

9?

Step-by-step explanation:

f(3*2-2)

=4

then

2*4+1

=9 is the answer

padilas [110]3 years ago
7 0

Answer:

15

Step-by-step explanation:

g(3)=(3)^2-2=7

f(g(3))=f(7)=2*7+1=15

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xeze [42]

Answer:

LM =  2.82 ft

MN =  2.39 ft

Step-by-step explanation:

We suppose ΔGNF is isosceles and GF bisect ∠NGF, so that GK ⊥ NF

LH // MJ // NK

GL / GH = LM / HJ = MN / JK

11.3 / 10.4 = LM / 2.6 = MN / 2.2

LM = 11.3 / 10.4 x 2.6 = 2.82

MN = 11.3 / 10.4 x 2.2 = 2.39

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3 years ago
write the slope intercept form of the equation of each line given the slope and y intercept. // slope= 1/3 y-intercept= 4 // slo
professor190 [17]

Answer:

Slope: 1/3; Y-iintercept: 4     y=1/3x+4

Slope: -2;  Y-intercept: 4      y=-2x

Step-by-step explanation:

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3 years ago
Why is it necessary to apply inverse operations on both sides of the equals l sign when solving an equations
liraira [26]
Take this example (cause it's easy to explain)

10+5x=15x

To solve it we have to minus five on both side. We have to do this because we need to isolate the variable (in this case x) on the one side so we can divide and solve.

You would -5x (inverse from positive 5) from both sides on this because whatever you do to one side you have to do to the others to make it equal. In this case the answer would be x=1 (again cause it's easy lol.)

I hope this helps you!
8 0
3 years ago
With a height of 68 ​in, Nelson was the shortest president of a particular club in the past century. The club presidents of the
Ivahew [28]

Answer:

a. The positive difference between Nelson's height and the population mean is: \\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in.

b. The difference found in part (a) is 1.174 standard deviations from the mean (without taking into account if the height is above or below the mean).

c. Nelson's z-score: \\ z = -1.1739 \approx -1.174 (Nelson's height is <em>below</em> the population's mean 1.174 standard deviations units).

d. Nelson's height is <em>usual</em> since \\ -2 < -1.174 < 2.

Step-by-step explanation:

The key concept to answer this question is the z-score. A <em>z-score</em> "tells us" the distance from the population's mean of a raw score in <em>standard deviation</em> units. A <em>positive value</em> for a z-score indicates that the raw score is <em>above</em> the population mean, whereas a <em>negative value</em> tells us that the raw score is <em>below</em> the population mean. The formula to obtain this <em>z-score</em> is as follows:

\\ z = \frac{x - \mu}{\sigma} [1]

Where

\\ z is the <em>z-score</em>.

\\ \mu is the <em>population mean</em>.

\\ \sigma is the <em>population standard deviation</em>.

From the question, we have that:

  • Nelson's height is 68 in. In this case, the raw score is 68 in \\ x = 68 in.
  • \\ \mu = 70.7in.
  • \\ \sigma = 2.3in.

With all this information, we are ready to answer the next questions:

a. What is the positive difference between Nelson​'s height and the​ mean?

The positive difference between Nelson's height and the population mean is (taking the absolute value for this difference):

\\ \lvert 68-70.7 \rvert = \lvert 70.7-68 \rvert\;in = 2.7\;in.

That is, <em>the positive difference is 2.7 in</em>.

b. How many standard deviations is that​ [the difference found in part​ (a)]?

To find how many <em>standard deviations</em> is that, we need to divide that difference by the <em>population standard deviation</em>. That is:

\\ \frac{2.7\;in}{2.3\;in} \approx 1.1739 \approx 1.174

In words, the difference found in part (a) is 1.174 <em>standard deviations</em> from the mean. Notice that we are not taking into account here if the raw score, <em>x,</em> is <em>below</em> or <em>above</em> the mean.

c. Convert Nelson​'s height to a z score.

Using formula [1], we have

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

\\ z = \frac{68\;in - 70.7\;in}{2.3\;in}

\\ z = \frac{-2.7\;in}{2.3\;in}

\\ z = -1.1739 \approx -1.174

This z-score "tells us" that Nelson's height is <em>1.174 standard deviations</em> <em>below</em> the population mean (notice the negative symbol in the above result), i.e., Nelson's height is <em>below</em> the mean for heights in the club presidents of the past century 1.174 standard deviations units.

d. If we consider​ "usual" heights to be those that convert to z scores between minus2 and​ 2, is Nelson​'s height usual or​ unusual?

Carefully looking at Nelson's height, we notice that it is between those z-scores, because:

\\ -2 < z_{Nelson} < 2

\\ -2 < -1.174 < 2

Then, Nelson's height is <em>usual</em> according to that statement.  

7 0
3 years ago
What is the probability of rolling a number less than or equal to 2 on a six sided die?
Kruka [31]
The dice only has 6 sides so if you need to roll a 2 or less that only leaves the number one. So it would be 2/6
7 0
3 years ago
Read 2 more answers
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