solve for the solution of each linear equation.

1. 3x+1=4

2. 7x-6=0

3. 4x-5=19

4. 9x+6=8

5. 8x-7=15

Answers

Answer 1

Answer:

no.1 answer 0

Step-by-step explanation:

3x + 1= 4

or; 3x = 4 - 1

or; x = 3 ÷ 3

x = 0


Related Questions

What is the solution set for |z+4|> 15

Answers

Answer:

I think that answer would be B.

Step-by-step explanation:

Tammy makes 8 dollars for each hour of work. Write an equation to represent her total pay p after working h hours.

Answers

Answer:

P=8(h)

Step-by-step explanation:

P is her total pay. You find that by multiplying what she makes an hour (8) by the total number of hours she has worked (h).

Answer:

p=8h

Step-by-step explanation:

Pay equals $8 per the number of hours

Help pls ty!
Adios!
Bye

Answers

wouldnt angle rsq be 90 degrees

Questions 23 and 29: Use the following information to answer each question. A recent book noted that only 20% of all investment managers outperform the Dow Jones Industrial Average over a five-year period. A random sample of 200 investment managers that had graduated from one of the top ten business programs in the country were followed over a five-year period. Fifty of these outperformed the Dow Jones Industrial Average. Let p be the true proportion of investment managers who graduated from one of the top ten business programs who outperformed the Dow Jones over a five-year period.
23. Based on the results of the sample, a 95% confidence interval for p is:
a. (1.95, 3.15)
b. (0.0195, 0 .0315)
c. (0.190, 0.310)
d. (0.028, 0.031)
e. (0.195, 0.315)
f. We can assert that p = 0.20 with 100% confidence, because only 20% of investment managers outperform the standard indexes.
24. Suppose you had been in charge of designing the study. What sample size would be needed to construct a margin of error of 2% with 95% confidence? Use the prior estimate of pâ=0.2 for this estimate.
a. n=2401
b. n=1537
c. n=16
d. n=1801
e. n>30
Suppose you wish to see if there is evidence that graduates of one of the top ten business programs performs better than other investment managers. Conduct a hypothesis test. Use a level of significance of α=0.05
25. Which of the following pairs of hypotheses is the most appropriate for addressing this question?
a. H0: p=0.2
Ha: p<0.2
b. H0: p=0.2
Ha: pâ 0.2
c. H0: p=0.2
Ha: p>0.2
d. H0: p<0.2
Ha: p=0.2
e. H0: pâ 0.2
Ha: p=0.2
f. H0: p>0.2
Ha: p=0.2
26. How many measurements must you have in order to assure that p^ is normally distributed?
a. nâ¥30
b. nâ¥5
c. npâ¥10 and n(1âp)â¥10
d. npâ¥5 and n(1âp)â¥5
27. The value of your test statistic is:
a. 1.768
b. 0.039
c. 1.923
d. 0.077
28. The P-value of your test is:
a. 1.768
b. 0.039
c. 1.923
d. 0.077
29. Is there sufficient evidence to conclude that graduates from the top ten business programs perform better than other investment managers?
a. Yes. I rejected H0
b. Yes. I failed to reject H0
c. Yes. I accepted Ha
d. No. I rejected H0
e. No. I failed to reject H0
f. No. I failed to accept Ha

Answers

Answer:

https://www.chegg.com/homework-help/questions-and-answers/questions-23-29-use-following-information-answer-question-recent-book-noted-20-investment--q13619465

Step-by-step explanation:

this might help you

An exterior angle of a regular convex polygon is 40°. What is the number of sides of the polygon?

A. 8

B. 9

C. 10

D.11

Answers

Answer:

option B

Step-by-step explanation:

Sum of interior angles of a polygon with n sides:

                                                                          [tex]= (n - 2 )\times 180[/tex]

[tex]Therefore, Each \ interior \ angle = (\frac{n - 2}{n} )\times 180[/tex]

[tex]Sum \ of \ one \ of \ the \ interior \ angle \ with \ its \ exterior \ angle \ is \ 180^\circ[/tex]

                      [tex][ \ because \ straight \ line \ angle = 180^\circ \ ][/tex]

That is ,

[tex]Exterior \ angle + Interior \ angle = 180^\circ\\\\40^ \circ + (\frac{n-2}{n}) \times 180 = 180^\circ\\\\40 n + 180n - 360 = 180n\\\\40n = 180n - 180n + 360 \\\\40n = 360 \\\\n = 9[/tex]

OR

Sum of exterior angles of a regular polygon = 360

Given 1 exterior angle of the regular polygon is  40

Therefore ,

               [tex]n \times 40 = 360\\\\n = \frac{360}{40} \\\\n = 9[/tex]

Answer:

9

Step-by-step explanation:

Sofia bought a clothes iron that was discounted 15% off of the original price of $35. What was the sale price of the clothes iron?

Answers

Answer:

35 - 0.15 * 35 so it is $29.75

Step-by-step explanation:

I got u

Answer:

$29.75

Step-by-step explanation:

15% = .15

.15 x 35 = 5.25

35 - 5.25 = 29.75

A box contains 10 balls, of which 3 are red, 2 are yellow, and 5 are blue. Five balls are randomly selected with replacement. Calculate the probability that fewer than 2 of the selected balls are red.

Answers

Answer:

The required probability is 0.1.

Step-by-step explanation:

red balls = 3

yellow balls =  2

blue balls = 5

Selected balls = 5

Number of elemnets in sample space = 10 C 5 = 1260

Ways to choose 1 red ball and 4 other colours =  (3 C 1 ) x (7 C 4) = 105

Ways to choose 5 balls of other colours = 7 C 5 = 21

So, the probability is

[tex]\frac{105}{1260} + \frac {21}{1260}\\\\\frac{126}{1260}=0.1[/tex]  

currently, the US interest rate is at 2% annually. how long it will take an investor to make 10% of money from an investment if the bank pays simple interest

Answers

Answer:

5 years

Step-by-step explanation:

Brian made $198 for 11 hours of work.
At the same rate, how many hours would he have to work to make $324 ?

Answers

Answer:

18 hours

Step-by-step explanation:

Forst u must find out how much u get for 1 hour which is 198/11=18 so every hour u get 18 dollars.

Next, Ypu must divide 324/18 to see how many hours he worked which we get 18

Finally 18 is the answer!

Step-by-step explanation:

If he made $198 in 11hrs

how many hours will he take to make $324

Let hours be x

$198=11hours

$324= x hours

= $324 *11hours / $198

= 18 hours

I hope this helps.

Find x so that B = 3x i +5j is perpendicular to is perpendicular to A=2i - 6j​

Answers

Answer:

5

Step-by-step explanation:

I'm going to call x, x1 because I want to use x as a variable.

So we have a ray with points (0,0) and (3x1,5) on it. This equation for this ray would be y=5/(3x1)×x.

We have another ray with points (0,0) and (2,-6). This equation for this ray would be y=-6/2×x or y=-3x.

We want these two lines' slopes to be opposite reciprocals. The opposite reciprocal of -3 is 1/3.

So we want to find x1 such that 5/(3x1)=1/3.

Cross multiply: 15=3x1

Divide both sides by 3: 5=x1

We want x1 to be 5 so that 5/(3×5) and -3 are opposite reciprocals which they are.

Another way:

If two vectors are perpendicular, then their dot product is 0.

The dot product of <3x,5> and <2,-6> is 3x(2)+5(-6).

Let's simplify:

6x-30.

We want this to be 0.

6x-30=0

Add 30 on both sides:

6x=30

Divide both sides by 6:

x=5

In this triangle, D is the midpoint of AB and E is the midpoint of BCIf AC = 36 what is the length of DE?

Answers

Answer:

A. 18

Step-by-step explanation:

Recall: the Mid-segment Theorem states that the length of the mid-segment theorem of a triangle is half the length of its third side.

DE = ½(AC) (Triangle Mid-segment Theorem)

AC = 36 (given)

Plug in the value

DE = ½(36)

DE = 18

5.11.
A manufacturing process produces 500 parts per hour. A sample part is selected about every half hour, and after five parts are obtained, the average of these five measurements is plotted on an x control chart.
(a) Is this an appropriate sampling scheme if the assignable cause in the process results in an instantaneous upward shift in the mean that is of very short duration?
(b) If your answer is no, propose an alternative procedure. If your answer is yes, justify.
5.12.
Consider the sampling scheme proposed in Exercise 5.11. Is this scheme appropriate if the assignable cause results in a slow, prolonged upward drift in the mean? If your answer is no, propose an alternative procedure.

Answers

Answer:

Following are the response to the given points:

Step-by-step explanation:

For question 5.11:

For point a:

For all the particular circumstances, it was not an appropriate sampling strategy as each normal distribution acquired is at a minimum of 30(5) = 150 or 2.5 hours for a time. Its point is not absolutely fair if it exhibits any spike change for roughly 10 minutes.

For point b:

The problem would be that the process can transition to an in the state in less than half an hour and return to in the state. Thus, each subgroup is a biased selection of the whole element created over the last [tex]2 \frac{1}{2}[/tex] hours. Another sampling approach is a group.

For question 5.12:

This production method creates 500 pieces each day. A sampling section is selected every half an hour, and the average of five dimensions can be seen in a [tex]\bar{x}[/tex]line graph when 5 parts were achieved.

This is not an appropriate sampling method if the assigned reason leads to a sluggish, prolonged uplift. The difficulty would be that gradual or longer upward drift in the procedure takes or less half an hour then returns to a controlled state. Suppose that a shift of both the detectable size will last hours [tex]2 \frac{1}{2}[/tex] . An alternative type of analysis should be a random sample of five consecutive pieces created every [tex]2 \frac{1}{2}[/tex] hour.

exponential function in the form y=ab^xy=ab
x
that goes through points (0, 13)(0,13) and (5, 416)(5,416).

Answers

Hello!

[tex]\large\boxed{y = 13(2)^x}}[/tex]

y = abˣ

We know that at x = 0, b = 1 because any number to the power of 0 = 1.

Therefore:

13 = a(1)

13 = a

Now, plug in this value to solve for b:

y = 13bˣ

Substitute in the next point:

416 = 13(b)⁵

Divide both sides by 13:

32 = b⁵

Take the 5th root of both sides:

2 = b

Rewrite:

y = 13(2)ˣ

Graph the line that represents this equation:
y = -5.1 +2

Answers

That's for the equation I got from the picture

Ed decided to build a storage box. At first, he was planning to build a cubical box with edges of length n inches. To increase the amount of storage, he decided to make the box 1 inch taller and 2 inches longer while keeping its depth at n inches. The volume of the box Ed built has a volume how many cubic inches greater than the box he originally planned to build?

Answers

Answer:

The new volume is 3n^2+2n inches greater.

Step-by-step explanation:

Volume of a cube = s^3 where s is side of cube

Original volume = n^3

Volume of a Rectangular Prism = LBH

New Volume = (n+1)(n+2)(n)= n^3+3n^2+2n

DIfference = New- original = 3n^2+2n

PLEASE HELP!!! WILL GIVE BRAINLIEST!!!!

Answers

Finding the line of best fit is something a Machine Learning Model would do.

This particular ML model is called "Linear Regressor" or "Linear Regression Model". Look it up and there are definitely calculators for it, as it is relatively simple.

You can also, if you know how to use ML libraries and code, use Python to determine the value of [tex]b[/tex].

Hope this helps.

How to answer this question

Answers

Answer:

(0.3049 ; 0.3751)

Step-by-step explanation:

The confidence interval for proportion can be obtained using the relation :

Phat ± Zcritical * [√phat(1-phat) / n]

phat = x / n

Sample size, n = 700

x = 238

phat = 238/700 = 0.34

Zcritical at 95% = 1.96

C.I = 0.34 ± 1.96 * [√0.34(1-0.34) / 700]

C.I = 0.34 ± 1.96 * 0.0179045

C. I = 0.34 ± 0.0350928

Lower boundary = 0.34 - 0.0350928 = 0.3049

Upper boundary = 0.34 + 0.0350928 = 0.37509

(0.3049 ; 0.3751)

when a force of 400N is applied on a body at angle of 60 degree to the horizontal displacement,the body covers a distance of 8m.what is the work done?

Answers

Answer:

1600N

Step-by-step explanation:

Force = 400 N

Angle with horizontal = 60°

Displacement in horizontal direction = 8 m

work done formula when angle is included: Force * distance * cos(angle)

400 * 8 * cos(60)

= 400 * 8 * 1/2

= 1600N

Keith used the following steps to find the inverse of f, but he thinks he made an error.

Answers

the answer is C
i hope this helps <3

The graphs below have the same shape. Complete the equation of the blue
graph. Enter exponents using the caret (-1); for example, enter xas x^3. Do
not include "G(x) =" in your answer.

Answers

Step-by-step explanation:

The graphs below have the same shape. What is the equation of the blue graph? A. G(x) = (x + 3)^3 B. G(x) = x^3 + 3 C. G(x) = x^3 - 3 D.

G(x) = (x - 3)^3

The function of the blue curve in the graph is g(x)=(x+3)²+1.

What is the function?

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is f(x)=x².

In the image, we have two functions, the red one is a parent function, which is the most basic version of it. The blue function is a transformation of the red one, that is, it was only moved to the left and upwards.

From the graph, we can see that the blue function was moved to the left and upwards, that means we have to sum units to x and f(x).

So, g(x)=(x+3)²+1

Therefore, the function of the blue curve in the graph is g(x)=(x+3)²+1.

To learn more about the function visit:

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Help!! Picture included

Answers

Answer:

The answer is the last option- the fourth root of 16x^4.

Step-by-step explanation:

(16x^4)^(1/4) = 2*abs(x).

Whenever you are dealing with a square root of a variable, if you have an even root and get out an odd power, you're going to need to always include an absolute value.

g ) If it is raining, a home security system detects an intruder with probability 0.70. If it is NOT raining, the probability becomes 0.92. The probability of rain on any 2 given day is 0.25. To test the system on a randomly chosen day, the system technician pretends to be an intruder. Given that the technician will NOT be detected, what is the probability that it is NOT raining

Answers

Answer:

0.4444 = 44.44% probability that it is NOT raining

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Technician not detected.

Event B: Not raining.

Probability the technician is not detected:

0.3 of 0.25(raining).

0.08 of 0.75(not raining). So

[tex]P(A) = 0.3*0.25 + 0.08*0.75 = 0.135[/tex]

Probability the technician is not detected and it is not raining:

0.08 of 0.75. So

[tex]P(A \cap B) = 0.08*0.75 = 0.06[/tex]

Given that the technician will NOT be detected, what is the probability that it is NOT raining?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.06}{0.135} = 0.4444[/tex]

0.4444 = 44.44% probability that it is NOT raining

To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equation of the tangent line at the point (36, 6), we know that (36, 6) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x

Answers

Answer:

[tex]m = \frac{1}{12}[/tex]

Step-by-step explanation:

Given

[tex](x,y) = (36,6)[/tex]

[tex]f(x) = \sqrt x[/tex] ----- the equation of the curve

Required

The slope of f(x)

The slope (m) is calculated using:

[tex]m = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}[/tex]

[tex](x,y) = (36,6)[/tex] implies that:

[tex]a = 36; f(a) = 6[/tex]

So, we have:

[tex]m = \lim_{h \to 0} \frac{f(a + h) - f(a)}{h}[/tex]

[tex]m = \lim_{h \to 0} \frac{f(36 + h) - 6}{h}[/tex]

If [tex]f(x) = \sqrt x[/tex]; then:

[tex]f(36 + h) = \sqrt{36 + h}[/tex]

So, we have:

[tex]m = \lim_{h \to 0} \frac{\sqrt{36 + h} - 6}{h}[/tex]

Multiply by: [tex]\sqrt{36 + h} + 6[/tex]

[tex]m = \lim_{h \to 0} \frac{(\sqrt{36 + h} - 6)(\sqrt{36 + h} + 6)}{h(\sqrt{36 + h} + 6)}[/tex]

Expand the numerator

[tex]m = \lim_{h \to 0} \frac{36 + h - 36}{h(\sqrt{36 + h} + 6)}[/tex]

Collect like terms

[tex]m = \lim_{h \to 0} \frac{36 - 36+ h }{h(\sqrt{36 + h} + 6)}[/tex]

[tex]m = \lim_{h \to 0} \frac{h }{h(\sqrt{36 + h} + 6)}[/tex]

Cancel out h

[tex]m = \lim_{h \to 0} \frac{1}{\sqrt{36 + h} + 6}[/tex]

[tex]h \to 0[/tex] implies that we substitute 0 for h;

So, we have:

[tex]m = \frac{1}{\sqrt{36 + 0} + 6}[/tex]

[tex]m = \frac{1}{\sqrt{36} + 6}[/tex]

[tex]m = \frac{1}{6 + 6}[/tex]

[tex]m = \frac{1}{12}[/tex]

Hence, the slope is 1/12

Find m∠GHIm∠GHI if m∠GHI=14x+6m∠GHI=14x+6, m∠QHI=130∘m∠QHI=130∘, and m∠GHQ=3x−3m∠GHQ=3x−3.

Answers

Answer:

m∠GHI = 160

Step-by-step explanation:

From the question given above, the following data were obtained:

m∠GHI = 14x + 6

m∠QHI = 130°

m∠GHQ = 3x – 3

m∠GHI =?

Next, we shall determine the value of x. This can be obtained as follow:

m∠GHI = m∠QHI + m∠GHQ

14x + 6 = 130 + (3x – 3)

14x + 6 = 130 + 3x – 3

Collect like terms

14x – 3x = 130 – 3 – 6

11x = 121

Divide both side by 11

x = 121 / 11

x = 11

Finally, we shall determine the value m∠GHI. This can be obtained as follow:

m∠GHI = 14x + 6

x = 11

m∠GHI = 14(11) + 6

m∠GHI = 154 + 6

m∠GHI = 160

A sprinkler releases water st a rate of 150 liters per hour. If the sprinkler operated for 80 minutes how many liters of water will be released

Answers

200 liters for 80 minutes of run time

The amount of water released from the sprinkler for 80 minutes is 200 L

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount of water from the sprinkler for 80 minutes be = A

Now , the value of A is given by the equation

A sprinkler releases water st a rate of 150 liters per hour

So , 60 minutes = 150 Liters of water

80 minutes = 1/60 hours

80 minutes = 1.333 hours

The amount of water released for 1.333 hours A = 150 x 1.333

On simplifying the equation , we get

The amount of water released for 1.333 hours A = 200 L

Therefore , the value of A is 200 L

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The x intercepts of the function f(x) = 2x(x-5)^2(x+4)^3
are…

Answers

Answer:

[tex]\boxed{\sf x- intercepts = 0 , 5 \ and \ -4}[/tex]

Step-by-step explanation:

A function is given to us and we need to find the x Intercepts of the graph of the given function . The function is ,

[tex]\sf \implies f(x) = 2x( x - 5 ) ^2(x+4)^3 [/tex]

For finding the x intercept , equate the given function with 0, we have ;

[tex]\sf \implies 2x ( x - 5 )^2(x+4)^3= 0 [/tex]

Equate each factor with 0 ,

[tex]\sf \implies 2x = 0[/tex]

Divide both sides by 2 ,

[tex]\sf \implies\bf x = 0[/tex]

Again ,

[tex]\sf \implies ( x - 5)^2=0 [/tex]

Taking squareroot on both sides,

[tex]\sf \implies x - 5 = 0 [/tex]

Add 5 to both sides,

[tex]\sf \implies \bf x = 5[/tex]

Similarly ,

[tex]\sf \implies \bf x = -4 [/tex]

Hence the x Intercepts are -4 , 0 and 5 .

{ See attachment also for graph } .

The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with mean of 1262 and a standard deviation of 118. Determine the 26th percentile for the number of chocolate chips in a bag. ​(b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags. ​(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip​ cookies?

Answers

Answer:

a) 1186

b) Between 1031 and 1493.

c) 160

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Normally distributed with mean of 1262 and a standard deviation of 118.

This means that [tex]\mu = 1262, \sigma = 118[/tex]

a) Determine the 26th percentile for the number of chocolate chips in a bag. ​

This is X when Z has a p-value of 0.26, so X when Z = -0.643.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.643 = \frac{X - 1262}{118}[/tex]

[tex]X - 1262 = -0.643*118[/tex]

[tex]X = 1186[/tex]

(b) Determine the number of chocolate chips in a bag that make up the middle 95% of bags.

Between the 50 - (95/2) = 2.5th percentile and the 50 + (95/2) = 97.5th percentile.

2.5th percentile:

X when Z has a p-value of 0.025, so X when Z = -1.96.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-1.96 = \frac{X - 1262}{118}[/tex]

[tex]X - 1262 = -1.96*118[/tex]

[tex]X = 1031[/tex]

97.5th percentile:

X when Z has a p-value of 0.975, so X when Z = 1.96.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.96 = \frac{X - 1262}{118}[/tex]

[tex]X - 1262 = 1.96*118[/tex]

[tex]X = 1493[/tex]

Between 1031 and 1493.

​(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip​ cookies?

Difference between the 75th percentile and the 25th percentile.

25th percentile:

X when Z has a p-value of 0.25, so X when Z = -0.675.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.675 = \frac{X - 1262}{118}[/tex]

[tex]X - 1262 = -0.675*118[/tex]

[tex]X = 1182[/tex]

75th percentile:

X when Z has a p-value of 0.75, so X when Z = 0.675.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]0.675 = \frac{X - 1262}{118}[/tex]

[tex]X - 1262 = 0.675*118[/tex]

[tex]X = 1342[/tex]

IQR:

1342 - 1182 = 160

To make a salad dressing you mix vinegar and olive oil in the ratio 2:5 how much olive oil is needed with 20 ml of vinegar

Answers

Answer:

Step-by-step explanation:

Set this up as a proportion with the ratios being

[tex]\frac{vinegar}{oil}[/tex]  If there is a 2:5 ratio of vinegar to oil, that ratio looks like this:

[tex]\frac{v}{o}:\frac{2}{5}[/tex] and if we are looking for how much oil, x, is needed for 20 ml of vinegar, then that ratio completes the proportion:

[tex]\frac{v}{o}:\frac{2}{5}=\frac{20}{x}[/tex] and cross multiply.

2x = 100 so

x = 50 ml of oil

the graph function f(x) is illustrated in figure below (-2,1) ,(-1,2) ,(1,2) ,(2,3) .Use the transformation techniques to graph the following functions

a) y=f(x)-2
b) y=f(-x)

Answers

Answer:

a) y = f(x) - 2 (x, y) ⇒ (x, y - 2)b) y = f(-x) (x, y) ⇒ (-x, y)

a) y=f(x)-2

(-2, 1) → (-2, 1 - 2) = (-2, -1)(-1, 2) → (-1, 2 - 2) = (-1, 0)(1, 2) → (1, 2 - 2) = (1, 0)(2, 3) → (2, 3 - 2) = (2, 1)

b) y=f(-x)

(-2, 1) → (-(-2), 1) = (2, 1)(-1, 2) → (-(-1), 2) = (1, 2)(1, 2) → (-1, 2)(2, 3) → (-2, 3)

Find the median: 16.12.7.9.10.16

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