Answer:
27
Step-by-step explanation:
Any positive integer to 3rd power will have positive answer.
Odd functions with number next to x^3 that is positive are increasing from left to right and thay also have a rotational symmetry with respect to the origin.Whe you put this together it's clear that the answer is 27
The price of a dress is reduced by 50%. When the dress still does not sell, it is reduced by 50% of the reduced price. If the price of the dress after both reductions is $100, what was the original price?
Answer:
the answer is 400$
Step-by-step explanation:
A 10-sided fair die, a 20-sided fair die, and a 12-sided fair dice are rolled. What is the probability of all three happening: Showing 8 on the first die Showing either 19 or 20 on the second die Showing an odd number on the third die
Answer:
0.5%
Step-by-step explanation:
The number of faces of each die what it indicates is the total number of events.
On the first die, it has 10 sides and an 8 must come out, that is, 1 event out of 10 possible, therefore the probability is:
1/10
On the second die, which has 20 sides, 19 or 20 can come out, that is 2 events out of 20 possible, so the probability is:
2/20
And on the third die, which is 12 sides, they tell us that an odd number can come out, the odd numbers would be 1, 3, 5, 7, 9, 11; that is, 6 events out of 12 possible, the probability would be:
6/12
Now the final probability would be the product of all:
(1/10) * (2/20) * (6/12) = 0.005
In other words, the probability of this happening is 0.5%
Out of 25 students taking a midterm psychology exam, 15 answered the first of two bonus questions, 11 answered the second bonus question, and 1 didn't bother with either one. Round your answer to the nearest percent. What percentage of students tried both questions? What percentage tried at least one question?
Answer:
Percentage of students who tried both questions = [tex]8\%[/tex]
Percentage of students who tried at least one question = [tex]96\%[/tex]
Step-by-step explanation:
Given: 25 students take a midterm psychology exam, 15 answered the first of two bonus questions, 11 answered the second bonus question, and 1 didn't bother with either one.
To find: percentage of students who tried both questions and percentage of students who tried at least one question
Solution:
Let A denotes students who answered the first of two bonus questions and B denotes students who answered the second bonus question.
Let U denotes the universal set denoting students who take a midterm psychology exam.
[tex]n(A)=15\,,\,n(B)=11\,,\,n(U)=25[/tex]
[tex]n\left ( A'\cap B' \right )=1[/tex]
[tex]n\left ( A'\cap B' \right )=n\left ( A\cup B \right )'\\=n(U)-n\left ( A\cup B \right )\\\Rightarrow 1=25-n\left ( A\cup B \right )\\n\left ( A\cup B \right )=25-1=24[/tex]
[tex]n\left ( A\cup B \right )=n(A)+n(B)-n\left ( A\cap B \right )\\24=15+11-n\left ( A\cap B \right )\\n\left ( A\cap B \right )=15+11-24=2[/tex]
Percentage of students who tried both questions = [tex]\frac{2}{25}\times 100=8\%[/tex]
Percentage of students who tried at least one question = [tex]\frac{24}{25}\times 100=96\%[/tex]
Which of the x-values are solutions to both of the following inequalities? 60 > X and x > 57. Also, Please hurry I will give brainliest to whoever answers 1st.
Answer:
B
Step-by-step explanation:
x must be a number between 60 and 57 and those numbers are 58 or 59
60 is greater than 59, and 59 is greater than 57
Answer:
x = 59
Step-by-step explanation:
The number must be less than 60 from the first inequality and greater than 57 from the second inequality
so the integers allowed are 58,59
A researcher wanted to see if giving a selective serotonin reuptake inhibitor (anti-depressant) would decrease the number of self-injurious behaviors (SIB’s) found in adolescents. They gave the anti-depressant to a group of 8 participants and counted the numbers of SIBs a person performed for a month after taking the drug for 6 months. Here are the number of SIB’S performed by the 8 people, 27, 25, 32, 40, 43, 37, 35, 38.
a. Find the mean variance, and standard deviation of this group.
b. Suppose the u=45, what is the z score?
c. What is the SEM for this particular group?
Answer:
a. The mean of the sample is M=35.
The variance of the sample is s^2=39.125.
The standard deviation of the sample is s=6.255.
b. z=-1.6
c. SEM = 2.212
Step-by-step explanation:
The mean of the sample is M=35.
The variance of the sample is s^2=39.125.
The standard deviation of the sample is s=6.255.
Sample mean
[tex]M=\dfrac{1}{8}\sum_{i=1}^{8}(27+25+32+40+43+37+35+38)\\\\\\ M=\dfrac{277}{8}=35[/tex]
Sample variance and standard deviation
[tex]s^2=\dfrac{1}{(n-1)}\sum_{i=1}^{8}(x_i-M)^2\\\\\\s^2=\dfrac{1}{7}\cdot [(27-(35))^2+(25-(35))^2+(32-(35))^2+(40-(35))^2+(43-(35))^2+(37-(35))^2+(35-(35))^2+(38-(35))^2]\\\\\\[/tex]
[tex]s^2=\dfrac{1}{7}\cdot [(58.141)+(92.641)+(6.891)+(28.891)+(70.141)+(5.64)+(0.14)+(11.39)]\\\\\ s^2=\dfrac{273.875}{7}=39.125\\\\\\s=\sqrt{39.125}=6.255[/tex]
b. If the population mean is 45, the z-score for M=35 would be:
[tex]z=\dfrac{M-\mu}{\sigma}=\dfrac{35-45}{6.255}=\dfrac{-10}{6.255}=-1.6[/tex]
c. The standard error of the mean (SEM) of this group is calculated as:
[tex]SEM=\dfrac{s}{\sqrt{n}}=\dfrac{6.255}{\sqrt{8}}=\dfrac{6.255}{2.828}=2.212[/tex]
The chef at a school cafeteria asked 100 male and 100 female students
whether they like peas. 42 of the males said they like peas. 64 of the females
said they dislike peas. Which two-way table correctly shows these results?
Answer:
A
Step-by-step explanation:
The best way to do is this by cancellation. Cancel out the answers that are incorrect.
D is incorrect. There are 100 male students and 100 female students. This table shows that there 94 male students and 106 female students.
C and B are both incorrect because they say that there are 42 male students that dislike peas. Really, there are 42 male students that like peas.
This leaves you with letter A. The table matches the data given, so this is the answer.
The table shows the result of the statement given below.
Given that, the chef at a school cafeteria asked 100 male and 100 female students whether they like peas.
42 of the males said they like peas. 64 of the females said they dislike peas.
The number of males who like peas=42 and the number of males who dislikes peas=58.
The number of females who like peas=36 and the number of females who dislikes peas=64.
The table shows the result of the statement given below.
To learn more about the data table visit:
https://brainly.com/question/17084863.
#SPJ2
please help asap! will mark as brainliest! and please no guessing! thank you :)
A circle has a circumference of q and an area of p. Define p in terms of q. Which one is the correct answer?
a. 4q^2π
b. q/2π
c.q^2/π
d. q^2/4π
Answer:
d. q^2/(4π)
Step-by-step explanation:
The circumference in terms of r is ...
q = 2πr
So, the radius in terms of q is ...
r = q/(2π)
The area in terms of radius is ...
p = πr^2
so, in terms of q, it is ...
p = π(q/(2π))^2 = (π/π^2)(q^2/4)
p = q^2/(4π)
_____
Comment on answer
It is unfortunate that your answer choice doesn't have parentheses on the denominator. They are required by the Order of Operations. As written, none of the choices is correct, as the last one must be interpreted as ...
(q^2/4)π
which is quite different from the correct answer of q^2/(4π).
The area of a hall is 806 sq. ft. Its length is 5 ft greater than its width. Find the dimensions of the hall. Enter the results in the answer box. Show work that leads to the final answer and clearly state the final answer.
Answer:
width is = 26ft
length is = 31ft
Step-by-step explanation:
The area of hall is 806 sq. ft.
length is 5 ft greater than its width.
L = 5+b
L*b = 806
(5+b)*b= 806
5b +b² = 806
B²+5B-806= 0
Solving quadratically
B² +31B -26B -806= 0
B(B+31)-26(B+31)= 0
(B-26)(B+31)= 0
B= 26 or -31
So the value of the width must be positive so the width is = 26ft
If width is 26, length is 26+5 = 31ft
A local hamburger shop sold a combination total of 565 hamburgers and cheeseburgers on Monday there were 65 more cheeseburgers sold than hamburgers how many hamburgers were sold on Monday
Answer:
250
Step-by-step explanation:
I have an easy way of doing this that works for me. Since there are 65 more cheeseburgers, you can subtract 65 from the total number, which leaves you with 500. Then, you just divide that number by 2 and your quotient (250) is the number of hamburgers.
Answer:
250 hamburgers and 315 cheeseburgers
Step-by-step explanation:
565-65=500
then u divide 500 by 2 which =250 hamburgers sold then you add 65 to get the cheeseburgers
Base of building 180 meters
Step-by-step explanation:
please give me full question
A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Suppose state regulators double-check a random sample of cars that a suspect repair shop has certified as okay. They will revoke the shop's license if they find significant evidence that the shop is certifying vehicles that do not meet standards.
a. In this context, what is a Type I error?
b. In this context, what is a Type II error?
c. Which type of error would the shop's owner consider more serious? d. Which type of error might environmentalists consider more serious?
Answer:
Step-by-step explanation:
The null hypothesis in this case is: There is significant evidence that the shop is certifying vehicles that do not meet standards so their license gets revoked
a. A type I error in this context occurs if the null is rejected when in actuality, it is true. This means, the shop is certifying vehicles that do not meet standards but their license does not get revoked
b. A type II error in this context occurs if they fail to reject the null when in actuality, it is no true. This means, the shop is not certifying vehicles that do not meet standards but their license does get revoked.
c. Which type of error would the shop's owner consider more serious?
The type II error because it affects the shop owner despite their credibiity
d. Which type of error might environmentalists consider more serious?
The type I error.
Using π = 3.14, find the area of a circle with a radius of 9. Round your answer to the nearest hundredth.
Answer:
A =254.34 unit^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2
A = 3.14 ( 9)^2
A =254.34
Answer:
254.34
Step-by-step explanation:
The formula for the area of a circle is πr² or in this case, 3.14r²
3.14×9²=
3.14×81=
254.34
Sorry if it looks like I'm copying Wegnerkolmp2741o but I didn't mean to make my answer like theirs.
This diagram to the right represents a small stage in the shape of a SEMIcircle (half of a circle). Find the area of the stage. ***Diameter of the semi circle is 10 yards
Answer:
above is the answer
Step-by-step explanation:
Area of a circle=
[tex]\pi {r}^{2} [/tex]
but this Is a semicircle so you divide it by 2 as in
[tex] a = \frac{\pi {r}^{2} }{2} [/tex]
so d=2r so r=5yd
A=5×5 pie/2
=25 pie/2=12.5 yards
Select the equivalent expression.
A, B or C?
Answer:
A
Step-by-step explanation:
The relevant rules of exponents are ...
(a^b)^c = a^(bc)
a^-b = 1/a^b
__
[tex]\left(\dfrac{2^{-10}}{4^2}\right)^7=\dfrac{2^{(-10)(7)}}{4^{(2)(7)}}=\dfrac{2^{-70}}{4^{14}}\\\\=\boxed{\dfrac{1}{2^{70}\cdot 4^{14}}}[/tex]
1 describe how the figures are alike 2Describe how the figures are different.
Answer:
they are all polyhedrons and 3 dimensional shapes but they all have different volumes and surface areas
Solve the equation.
43.6 = n + 17.5
Answer:
26.1 = n
Step-by-step explanation:
43.6 = n + 17.5
Subtract 17.5 from each side
43.6-17.5 = n + 17.5-17.5
26.1 = n
Answer:
[tex]n = 26.1[/tex]
Step-by-step explanation:
[tex]43.6 = n + 17.5 \\ 43.6 - 17.5 = n \\n = 26.1 \\ [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
The best interpretation of the coefficient of Q2 (-0.054) in the regression equation is:_________.
a) the revenues in the second quarter of a year is approximately 5.4% lower than the average over all 4 quarters.
b) the revenues in the second quarter of a year is approximately 5.4% lower than it would be during the fourth quarter.
c) the revenues in the second quarter of a year is approximately 11.69% lower than it would be during the fourth quarter.
d) the revenues in the second quarter of a year is approximately 11.69% lower than the average over all 4 quarters.
Answer:
The correct answer is (b) the revenues in the second quarter of a year is approximately 5.4% lower than it would be during the fourth quarter
Explanation:
Solution:
Given that
Log₁₀ Y = 6.012 + 0.012 X - 0.129 Q₁
= -0.054 Q₂ + 0.098 Q₃
Now,
Given that X =0
We substitute for Q₁ = 1
Thus,
Y = 6.012 + 0.012 (0) - 0.129 (1)
= -0.054 (0) + 0.098 (0)
= 6.012 - 0.129
=5.973
So
Q₂ = 1
Y = 6.102 - 0.054 (1) + 0.012 (0)
= - 0.129 (0) + 0.098 (0)
= 6.012 - 0.054
= 6.048
For Q₃=1
Y = 6.012 + 0.012 (0) - 0.129 (0)
= -0.054 (0) + 0.098 (1)
= 6.102 + 0.098
=6.2
From the given question, the option b is correct.
Note: Kindly find an attached copy of the complete question below.
What values of x and y satisfy the system of equations {10x+3y=−5−5x−4y=10? (0,−53) (25,−3) (−2,0) (12,−103)
Answer:
The solution of the equation
( 0.4 ,-3)
Step-by-step explanation:
Explanation:-
Step(i):-
Given system of equations
10 x+3 y = −5 ...(i)
- 5 x - 4 y = 10 ...(ii)
Multiply (i) with '5'
10 × 5 x + 3×5 y = - 25
50 x + 15 y = 25 ...(iii)
Multiply (ii) with '10'
-5 × 10 x - 4×1 0 y = 100
- 50 x - 40 y =100 ...(iv)
Step(ii):-
Solving (iii) and (iv)
50 x + 15 y =- 25
- 50 x - 40 y =100
- 25 y = 75
Dividing ' - 25' on both sides, we get
y = -3
substitute y = -3 in equation (i) , we get
10 x+3 y = −5
10 x - 9 = - 5
10 x = -5 + 9
[tex]x = \frac{4}{10}[/tex]
x = 0.4
Final answer:-
The solution of the equation ( 0.4 ,-3)
The Grand canyon national park has a new parking lot.the perimeter is 84feet the shape of the parking lot is a square what is the length of each sides
Answer:
21 feet
Step-by-step Explanation:
Given that the new parking lot of the Grand Canyon National park has a square shape, which means all the lengths of the 4 sides of the parking lot are equal and the same, the perimeter of the parking lot = 4(L) = 84feet.
L = length of 1 side of the parking lot; perimeter = 84feet,
Therefore, solving for L (length of each side) would be:
84 = 4(L)
84/4 = L
L = 21ft
The length of each sides are all equal and each would be 21 feet long.
Suppose that in a certain sinkhole the ground dropped 76.8 ft in 24 hour. Find the unit rate representing the change in altitude per hour
Answer:i dont know
Step-by-step explanation:
Types of bonds are divided into three categories: good risk, medium risk, and poor risk. Assume that of a total of 11, 332 bonds, 7,311 are good risk, 1,182 are medium risk, and the rest are poor risk. One bond is chosen at random. What is the probability that the bond is not a poor ? Write only a number as your answer. Round to two decimal places (for example : 0.43). Do not write as a percentage .
Answer:
Probabilty of not poor= 0.75
Step-by-step explanation:
total of 11332 bonds.
7311 are good risk.
1182 are medium risk.
Poor risk
= total risk-(good risk+ medium risk)
= 11332-(7311+1182)
= 11332-8493
= 2839.
Poor risk = 2839
Probabilty that the ball choosen at random is not poor= 1 - probability that the ball is poor
Probability of poor = 2839/11332
Probabilty of poor= 0.2505
Probabilty that the ball choosen at random is not poor= 1- 0.2505
= 0.7495
To two decimal place= 0.75
It is known that the highest weekly average price for gasoline in California during 2005 was $3.15 per gallon and the lowest weekly average price for gasoline in California during 2005 was $2.56. Use this information to estimate the standard deviation of the weekly average price for gasoline in California during 2005. The standard deviation is ($3.15-2.56) / 6. I was wondering why you divide by 6?
Answer:
$0.15
Step-by-step explanation:
To solve this problem, we apply the Range rule for estimating Standard deviation.
By the Range Rule:
Standard Deviation
Highest weekly average price for gasoline= $3.15 per gallon.
Lowest weekly average price for gasoline =$2.56 per gallon.
Therefore:
[tex]\text{Standard Deviation}\approx \dfrac{3.15-2.56}{4} \\=\dfrac{0.59}{4} \\\\=\$0.15 $(correct to the nearest cent).[/tex]
The standard deviation of the weekly average price for gasoline is approximately $0.15.
NOTE: You divide by 4 not 6.
Write an algebraic expression for the phrase.
the sum of f and 6
Answer:
f+6
f+6 =(f+6)
The bottom of a deposit, of 300l of capacity, is cover by a layer of salt. Assuming that the velocity at which the salt is disolved is proportional to the difference between the concentration at this time and the concentration of the saturated solution ( 1 kg of salt for 3 liters of water), and also take into account that the amount of pure water disolve 1/3 de Kg of salt per minute. Find the ODE giving the amount of salt x(t), as a function of time, integrate it, and determine the amount of salt in the solution after one hour.Find the solutions of the ODE that satisfy the indicated conditions when x → ±[infinity]
Answer:
Step-by-step explanation:
Assuming x(t) to be the number of salt
The maximum bottom of deposits =300 Litre
Initial Concentration of the saturated salt solution = 1 kg of salt for 3 liters of water
[tex]x_ic_i= \dfrac{1}3[/tex]
⇒x = 0
The differential equation is :
[tex]\dfrac{dx(t)}{dt}[/tex] [tex]={x_ic_i}-{x_oc_o}[/tex]
[tex]= \dfrac{1}{3} - \dfrac{x(t)}{300}[/tex]
[tex]\dfrac{dx(t)}{dt} + \dfrac{x(t)}{300} = \dfrac{1}{3}[/tex]
Using the first order differential equation of the form :
x' + p(t) x = q(t)
where
[tex]p(t) = \dfrac{1}{300}[/tex] ; [tex]q(t) = \dfrac{1}{3}[/tex]
By integrating the factor:
[tex]\mu = e^{\int\limitsP(t)dt } \\ \\ =e^{\int\limits \dfrac{1}{300}dt } \\ \\ = e^{\frac{t}{300} }[/tex]
[tex]x(t) = \dfrac{1}{\mu(t) }\int\limits \mu (t) * q(t) dt \\ \\ = e ^{- t/300} \ \ [\int\limits e ^{+ t/300} * \dfrac{1}{3}dt ][/tex]
[tex]= e ^{- t/300} \ \ [\dfrac{1}{3} * \dfrac{e^{t/300}}{1/300} + C ][/tex]
[tex]x(t) = 100 + Ce ^{-t/300[/tex]
Thus the differential equation solution is : [tex]x(t) = 100 + Ce ^{-t/300[/tex]
However; we have initial concentration x(0) = 0
SO;
[tex]0 = 100 + Ce^{-0/300}[/tex]
C = -100
[tex]x(t) = 100 -100e ^{-t/300[/tex]
when x → ±[infinity]
[tex]\infty = 100 + Ce^{- \infty /300}[/tex]
[tex]x(t) = 100 -100e ^{-t/300[/tex]
Now; the amount of salt after an hour is as follows:
1 hour = 60 minutes
t = 60 min
[tex]x(60) = 100 -100e ^{-60/300[/tex]
= 100 -100 (0.818)
= 100 - 81.8
= 18.2
x(60) = 18.2 kg
Five cards are drawn from a standard 52-card playing deck. A gambler has been dealt five cards—two aces, one king, one 3, and one 6. He discards the 3 and the 6 and is dealt two more cards. What is the probability that he ends up with a full house (3 cards of one kind, 2 cards of another kind)? (Round your answer to four decimal places.)
Answer:
The probability that he ends up with a full house is 0.0083.
Step-by-step explanation:
We are given that a gambler has been dealt five cards—two aces, one king, one 3, and one 6. He discards the 3 and the 6 and is dealt two more cards.
We have to find the probability that he ends up with a full house (3 cards of one kind, 2 cards of another kind).
We know that gambler will end up with a full house in two different ways (knowing that he has given two more cards);
If he is given with two kings.If he is given one king and one ace.Only in these two situations, he will end up with a full house.
Now, there are three kings and two aces left which means at the time of drawing cards from the deck, the available cards will be 47.
So, the ways in which we can draw two kings from available three kings is given by = [tex]\frac{^{3}C_2 }{^{47}C_2}[/tex] {∵ one king is already there}
= [tex]\frac{3!}{2! \times 1!}\times \frac{2! \times 45!}{47!}[/tex] {∵ [tex]^{n}C_r = \frac{n!}{r! \times (n-r)!}[/tex] }
= [tex]\frac{3}{1081}[/tex] = 0.0028
Similarly, the ways in which one king and one ace can be drawn from available 3 kings and 2 aces is given by = [tex]\frac{^{3}C_1 \times ^{2}C_1 }{^{47}C_2}[/tex]
= [tex]\frac{3!}{1! \times 2!}\times \frac{2!}{1! \times 1!} \times \frac{2! \times 45!}{47!}[/tex]
= [tex]\frac{6}{1081}[/tex] = 0.0055
Now, probability that he ends up with a full house = [tex]\frac{3}{1081} + \frac{6}{1081}[/tex]
= [tex]\frac{9}{1081}[/tex] = 0.0083.
Answer:
0.0083
Step-by-step explanation:
The gambler will have full house if he is dealt two kings or ace and a king.Now, there are 47 cards left in the deck and two which are aces and three are king.
The probability of these event are [tex]\frac{3C_2}{47C_2}[/tex]
and [tex]\frac{3C_1\times 2C_1}{47C_2}[/tex] respectively. So, the probability of a full house is given as:
[tex]\frac{3C_2}{47C_2}+\frac{3C_1\times 2C_1}{47C_2}[/tex]
=0.0083
Use the GCF and the distributive property to find the expression that is
equivalent to 36 + 60.
18 (2+4)
3(12 + 20)
6(6+10)
12 (3+5)
Answer:
[tex]D[/tex]
Step-by-step explanation:
[tex]36 + 60[/tex]
[tex]12(3)+12(5)[/tex]
[tex]12(3+5)[/tex]
Answer:
12( 3+5)
Step-by-step explanation:
how much does 757 go into 68
Answer:
Divide 757 by 68 so:
Step-by-step explanation:
757 / 68 = 11.9 so 757 can go into 68 11.9 times.
Hope this helps, have a good day! :)
(Brainliest would be appreciated?)
find the arc length of a partial circle
Answer:
23.55 or [tex]\frac{15}{2}[/tex]π
Step-by-step explanation:
The arc is 75% of the full circumference, as the cut away angle is 90º.
To find the arc length, you multiply the ratio of the whole circle that remains by the circumference: [tex]\frac{270}{360}[/tex]×π×2(5)=[tex]\frac{15}{2}[/tex]π, or 23.55 if you round pi to 3.14.
Answer:
7.85
Step-by-step explanation:
Solve this by using the formula for arc length with central angle in degrees.
Do this by identifying the formula and plugging in the given values. The formula for arc length is [tex]arc length = 2\pi r (\frac{theta}{360} )[/tex] , where the theta is represented by the central angle and r is the radius
The radius is shown on the circle is 5 and the theta (angle in degrees) is 90, represented by the tiny square in the middle.
Plug it all into the formula. Your equation should now look like this: arc length = 2 (3.14 or [tex]\pi[/tex]) (5) ([tex]\frac{90}{360}[/tex])
Solve for arc length and enter your answer as a decimal or in terms of pi
What’s the correct answer for this?
Answer:
MN = 48
Step-by-step explanation:
Since AB is a diameter , so it divides MN into 2 equal parts i.e. MO = NO
7x-4 = 6x
7x-6x = 4
x = 4
Now
MN = MO + NO
MN = 7x-4+6x
MN = 7(4)-4+6(4)
MN = 28-4+24
MN = 48
Answer:
48
Step-by-step explanation:
Since AB is a diameter, MO = NO
7x - 4 = 6x
7x - 6x = 4
= 4
MN = MO + NO
= 7x - 4 + 6x
= 7 * 4 - 4 + (6 * 4)
= 28 - 4 + 24
= 48
Hope this helps!
9. What is the scale factor of the dilation?
Answer:
D
Step-by-step explanation:
The scale factor is the ratio of the corresponding sides, image to original, that is
scale factor = [tex]\frac{P'S'}{PS}[/tex] = [tex]\frac{6}{3}[/tex] = 2 → D
