How is the graph of log x + 6 translated from the graph of log x

Answers

Answer 1

Translated 6 units vertically upwards.

Answer 2

THE CORRECT ANSWER IS Translated 6 units vertically upwards

Related Questions

how many times greater is the value of the 2 in 204,936 than the value of the 2 in 124,936

A. 1/100

B. 1/10

C. 10

D. 100

E. 1,000

Answers

I believe it would be C.10

The value of the 2 in 204,936 is 10 times greater than the value of the 2 in 124,936. So the answer is C

evaluate a = log(0.1) and b = ln(e^3)

Answers

[tex]log0.1=log\dfrac{1}{10}=log10^{-1}=-log10=-1\to a=-1\\\\lne^3=3lne=3\to b=3\\\\Used:\\\\a^{-1}=\dfrac{1}{a}\\\ loga^b=b\cdot loga\\\\log_aa=1[/tex]

please help. there is a picture below

Answers

Two triangles are similar if and only if all corresponding angles are equal (congruence), even if the corresponding sides are equal or not, therefore the answer is true because ΔJKL and ΔRST are similar and the statement above demands that "it must be", namely, this is a sufficient condition.

is it always true that trapezoids height is the distance between the 2 bases?

Answers

No. One side can be higher than the other side, therefore, a trapezoids height isn't always the distance between the 2 bases.

Find the probability of drawing a heart or a black card from a standard deck of cards

Answers

75%

Hearts and black cards make up 3 of the 4 suits of cards. You could count the amount of them and then divide by 52 cards, or you can divide 3 by 4 since there are the same amount in every suit.

Final answer:

The probability of drawing a heart or a black card from a standard deck of cards is 3/4.

Explanation:

In a standard deck of cards, there are 52 cards in total. However, since we are interested in finding the probability of drawing a heart or a black card, we need to determine how many cards satisfy this condition.

There are 13 hearts in a deck, so the probability of drawing a heart is 13/52 or 1/4. Additionally, there are 26 black cards (13 spades and 13 clubs) in a deck, so the probability of drawing a black card is 26/52 or 1/2.

To find the probability of drawing a heart or a black card, we can add the probabilities together: 1/4 + 1/2 = 3/4.

Learn more about Probability here:

https://brainly.com/question/22962752

#SPJ2

PLS HELP ME ASAP WITH 1 AND 2, THANK YOU!! SM!!

(Brainliest will be given hopefully!)

(Random answers gets moderated.)

Answers

I can't really help with 2) because I don't have my calculator on me, but I hope this helps :)

See the attachment for a table (1) and graph (2).

(3) The graph represents a function. The table has a domain of [0, 7] and a range of [170, 240].

The function might reasonably be used over a domain of [0, 24] and a range of [0, 240].

Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. x - 2; 4x2 - 3x + 22

Answers

Answer:

[tex]x-2[/tex] is not a factor of [tex]p(x)=4x^2-3x+22[/tex].

Step-by-step explanation:

According to the factor theorem, if [tex]x-a[/tex] is a factor of [tex]p(x)[/tex], then [tex]p(a)=0[/tex].

Let [tex]p(x)=4x^2-3x+22[/tex]. If [tex]x-2[/tex] is a factor of [tex]p(x)=4x^2-3x+22[/tex], then [tex]p(2)=0[/tex].

Let us plug in [tex]x=2[/tex] in to the function to see if it will give us zero.

[tex]p(2)=4(2)^2-3(2)+22[/tex]

We simplify to obtain,

[tex]p(2)=4(4)-3(2)+22[/tex]

[tex]p(2)=16-6+22[/tex]

[tex]p(2)=10+22[/tex]

[tex]p(2)=32[/tex]

Since [tex]p(2)\ne0[/tex], [tex]x-2[/tex] is not a factor of [tex]p(x)=4x^2-3x+22[/tex].

Final answer:

According to the Factor Theorem, 'x - 2' is not a factor of the polynomial '4x^2 - 3x + 22'. This determination was made by plugging '2' into the second polynomial and finding that it does not result in zero.

Explanation:

For a polynomial P(x), the Factor Theorem states that if you plug a value 'a' into the polynomial and get zero (P(a) = 0), then x-a is a factor of that polynomial. In this case, you are asked to determine whether 'x - 2' is a factor of the quadratic function '4x^2 - 3x + 22'.

To do so, according to the Factor Theorem, plug the value '2' into the second polynomial function, so we have 4*(2)^2 - 3*(2) + 22 = 16 - 6 + 22 = 32. Because this does not equal zero, we can conclude that 'x - 2' is not a factor of the second polynomial '4x^2 - 3x + 22' based on the Factor Theorem.

Learn more about Factor Theorem here:

https://brainly.com/question/35460223

#SPJ3

Write an equation in intercept form of the parabola that Passes through (-1,40) and x=-5, 4

Answers

At first I didn't understand what you meant by "x = -5, 4. What I think you meant was "the horizontal intercepts of the graph of this parabola are (-5,0) and (4,0)."

If this is the case, then the equation of the parabola is found as follows:

y=ax^2 + bx + c for the point (-5, 0) is 0=a(-5)^2 + b(-5) + c
for the point (4,0) is 0 = a(4)^2 +b(4) + c
for the point (-1,40) is 40 = a(-1)^2 + b(-1) + c

Here we have 3 equations in 3 unknowns, which is enough to solve for {a,b,c}. Using matrix algebra, I found that a= -2, b= -2, c= 40.

Then one equation for this parabola would be:

y = -2x^2 - 2x + 40

Check this by substitution. Does the point (-5,0) satisfy y = -2x^2 - 2x + 40?
Yes. So y = -2x^2 - 2x + 40 is the general form of the equation of this parabola. To express it in intercept form, factor y = -2x^2 - 2x + 40.

What is the minimum value of the graph of y=sin x assumes

Answers

Short answer: - 1
The first thing you should do is draw this or get a program to do it. I use desmos. It is included. The graph shows one complete cycle every 2*pi intervals (or 360 degrees.)

You will find no lower value that y = - 1 (nor any value greater than y = 1)

Answer:

the answer is

negative one

- 1

Step-by-step explanation:

Maria needs to mail 3 letters. Each letter costs $0.41 to mail. How much change will she get back if she gives the clerk $2.00?

Answers

If Maria gives the clerk $2.00 then she will get $0.77 back in change.

I found this by using the expression x = 2.00 - 3(0.41) and solving for x.

Final answer:

Maria has to mail 3 letters, each costing $0.41, totaling to $1.23. She gives the clerk $2.00, so the change she will get back is $2.00 - $1.23 = $0.77.

Explanation:

This problem is about simple arithmetic and money management. Maria has to mail 3 letters, each costing $0.41. This means that the total expense that Maria has to pay is $0.41 * 3, which equals $1.23. Maria gives the clerk $2.00, so to find out the change, subtract the total cost of the letters ($1.23) from the amount she gave to the clerk ($2.00). So, the change Maria will get back is $2.00 - $1.23 = $0.77.

Learn more about Change Calculation here:

https://brainly.com/question/32819635

What are the minimum, first quartile, median, third quartile, and maximum of the data set?
12, 6, 8, 3, 10, 15, 18, 7

Answers

If we rearrange the given data set from lowest to highest, we have
[tex]3,\:6,\:7,\:8,\:10,\:12,\:15,\:18[/tex]

The minimum is 3.

The first quartile is the average of 6 and 7, which is 6.5

The median is the average of 8 and 10 which is 9.

The third quartile is the average of 12 and 15 which is 13.5.

The maximum is 18.

Select all that are undefined. sec (45°) csc (0°) sec (90°)

Answers

sec(45°) = 1/cos(45°) = 1/(rt(2)/2) = rt(2)

csc(0°) = 1/sin(0°) = 1/0 /undefined/

sec(90°) = 1/cos(90°) = 1/0 /undefined/

Final answer:

The sec(45°) and sec(90°) are defined, but csc(0°) is undefined.

Explanation:

To determine which of the given trigonometric functions are undefined, we need to understand the domains of these functions. In trigonometry, the secant and cosecant functions are undefined for angles where the cosine and sine functions are equal to zero, respectively.

For sec(45°), the cosine of 45° is equal to √2/2, which is not zero. Therefore, sec(45°) is defined.For csc(0°), the sine of 0° is equal to 0, which results in division by zero. Hence, csc(0°) is undefined.For sec(90°), the cosine of 90° is equal to 0, which again leads to division by zero. Thus, sec(90°) is undefined.

Identify the pattern for the following sequence. Find the next three terms in the sequence. 5, 2, -1, -4, ____, ____, ____,... a. Subtract 3; -7, -10, -13 b. Add 3; -7, -10, -13 c. Subtract -3; 7, 10, 13 d. Add 3; 1, 4, 7 Please select the best answer from the choices provided

Answers

The correct answer for the completion exercise shown above is the first option (Option a), which is:

a. Subtract 3; -7, -10, -13

The explanation is shown below:

1. You have the following sequence 5, 2, -1, -4

2. The first second number is the result of a substraction:

5-3=2

3. Then you have:

2-3=-1
-1-3=-4
-4-3=-7
-7-3=-10
-10-3=-13

Therefore, the answer is the optiones mentioned before.

Answer:

A.Subtract 3:-7,-10,-13

Step-by-step explanation:

We are given that a sequence

5,2,-1,-4,...

We have to identify the pattern of the givens sequence and next three terms.

[tex]a_1=5,a_2=2,a_3=-1,a_4=-4[/tex]

[tex]a_2-a_1=2-5=-3[/tex]

[tex]a_3-a_2=-1-2=-3[/tex]

[tex]a_4-a_3=-4-(-1)=-3[/tex]

The difference between two consecutive terms are equal.When the difference between two consecutive terms are equal then the sequence is called arithmetic sequence.Hence, the sequence is arithmetic sequence.

[tex]a_5=a_4-3=-4-3=-7[/tex]

[tex]a_6=a_5-3=-7-3=-10[/tex]

[tex]a_7=a_6-3=-10-3=-13[/tex]

Answer:A.Subtract 3:-7,-10,-13

PLEASEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE HELP!! WILL GET BRAINIEST IF YOU SHOW WORK

1. Simplify the radical

2. Simplify the radical

3. Simplify the radical

4. Simplify the radical

Answers

the root of 27 is 3root3.

The simplification of the radical is c/3

What are radicals in math?

Radicals in math refer to expressions containing square roots or higher-order roots.

Represented by the radical symbol (√), they involve finding the root of a number. For example, √9 equals 3, as 3 * 3 equals 9.

Simplifying the surd;

√3c²)/√27

= √3 × √c²)/√9 × √3

= √3c/3√3

= c/3

Therefore the simplification of √3c²)/√27 is c/3.

learn more about radicals from

https://brainly.com/question/738531

#SPJ3

A set of n = 15 pairs of scores (X and Y values) has SSX = 4, SSY = 25, and SP = 6. What is the Pearson correlation for these data

Answers

The Pearson correlation can be calculated by the formula:
[tex]r = \frac{SP}{ \sqrt{SS_{x}SS_{y} } } [/tex]

Therefore:

r = 6 / √(4·25)
= 6 / √100
= 6 / 10
= 0.60

Hence, the Pearson correlation for this set is 0.60

How many Liters of a liquid can be held in a barrel

Answers

a lot of water because it has to fill a barrel!!

If (-3)^-5=1/x, what is the value x?

Answers

[tex](-3)^{-5} = \frac{1}{x}, \frac{1}{(-3)^{5}} = \frac{1}{x} , (-3)^{5}=x, x= - 243[/tex]

The solution is, x = -243 is the value of (-3)^-5=1/x.

What is algebraic identities?

The algebraic equations are those which are valid for all values of variables in them are called algebraic identities.

Here we have:

Given that,

(-3)^-5=1/x

now, we have to simplify this expression, to get the value o x .

so, we get,

1/(-3)^5=1/x

or, (-3)^5=x

or, x = -243

Hence the value of the expression (-3)^-5=1/x , is x= -243.

(Note the expression asked is different by minus sign, but generally these questions solved as above. It would be a printing mistake)

To learn more about algebraic identities, refer to the link:

brainly.com/question/953809

#SPJ3

Help
A survey was taken of 36 people to see if they owned a car and/or a truck. The results are shown in the Venn diagram.

Enter your answers in the boxes to complete the two-way table based on the given data.

Answers

Answer: The table should look like this

4 9 13

15 8 23

19 17 36

Step-by-step explanation:Happy to help

Based on the complete table, 19 people own a car, 13 people own a truck while 8 people neither own a car nor a truck.

How to complete the table

A survey was taken of 36 people to see if they owned a car and/or a truck. The results are shown in the Venn diagram.

own a car Dont own a car Total

Own a trcuk 4 9 13

Dont own a trcuk 15 8 23

Total 19 17 36

Those that own car 15 + 4 =19

those that own truck 9 + 4 = 13

Those that own car and truck 4 (Given)

Those that owns none = 36-15-9 - 4 = 8

Read on Venn diagram on https://brainly.com/question/30599101

#SPJ3

JK, KL, and LJ are all tangent to circle O. The diagram is not drawn to scale. If JA = 10, AL = 23, and CK = 9, what is the perimeter of ∆JKL
A.84
B.66
C.42
D.38

Answers

Answer: the perimeter of JKL is 84

ik this is rlly late but to help anyone else who gets this question:

This is an equilateral triangle, so the adjacent length is gonna be the same value as its corresponding length that was listed

JA = 10

JB = JA, JB is also 10

JA + JB (10+10) = 20

AL = 23

LC = AL, LC is also 23

AL + LC (23+23) = 46

CK = 9

KB = CK, KB is also 9

CK + KB (9+9) = 18

add all those up:

20 + 46 + 18 = 84

Which function represents a reflection of f(x) = 5(0.8)x across the x-axis? A. g(x) = 5(0.8)–x B. g(x) = –5(0.8)x C. g(x) = 1/5(0.8)x D. g(x) = 5(–0.8)x

Answers

If g(x) is a reflection of f(x) over the x axis, then g(x) = -1*f(x), which can be shortened to g(x) = -f(x). We stick a negative outside the entire f(x) function to flip the signs of each y coordinate. For example, if the point (1,2) was on f(x), then (1,-2) is on g(x).

So f(x) = 5(0.8)^x turns into g(x) = -5(0.8)^x

Answer: Choice B

Answer:

2nd option

Step-by-step explanation:

A two digit number with two different digits has a special property when th sum of its digits is added to the product of its digits the result is the number itself

Answers

When th sum you forgot the e on the

The sum of two numbers is 25, and the difference of their squares is 75. what are the two numbers?

Answers

x+y=25
14*14=196
11*11=121

196-121=75
the answer is x=14 and y=11

find the point slope equation for (-2,-20) and (9,79)

Answers

Start by identifying your x1, x2, y1, and y2 values
x1: -2
x2: 9
y1: -20
y2: 79

The general form for writing a point slope equation is y-y1 = m(x-x1)
M is your slope.
To find the slope, plug the values you just identified into the equation y2-y1/x2-x1
This leaves you with 79+20/9+2
Which equals 9, so your slope (m) equals nine.
you can now plug everything into the general form which gives you:
y+20 = 9(x+2)

Final answer:

The point-slope equation for the points (-2,-20) and (9,79) is y + 20 = 9(x + 2).

Explanation:

To find the point-slope equation, we can use the formula: y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Firstly, we calculate the slope using the formula: m = (y2 - y1)/(x2 - x1). Given the points (-2, -20) and (9, 79), the slope is (79 - (-20))/(9 - (-2)). Simplifying the expression, we get m = 99/11 = 9.

Next, we substitute one of the points and the calculated slope into the point-slope formula. Let's choose (-2, -20). So the equation becomes: y - (-20) = 9(x - (-2)). Simplifying further, we have: y + 20 = 9(x + 2).

This is the point-slope equation for the given points: y + 20 = 9(x + 2).

Learn more about Point-slope equation here:

https://brainly.com/question/33918645

#SPJ11

A. 0
B. 4
C. 2
D. -2

Answers

The way to find the midpoint of a segment is to add the coordinates of the points you're trying to do the midpoint for and then divide by two (so it's the midpoint). Sine we're trying to find the midpoint of WQ, we need to add the coordinate of W and the coordinate of Q and then divide by 2. The coordinate of W is -8, and the coordinate of Q is 4. -8 + 4 = -4, divided by 2 is -2. That means that our answer is D, or -2.

A quiz consists of two multiple-choice questions. the first question has a total of 7 possible answers followed by the second question which has a total of 3 possible answers. if both questions are answered with random guesses,

Answers

the probability to answer both correctly is 1/7(1/3)=1/21, if that was the question.

Using sin^2x+ cos^2 x=1 and other trig properties, simplify the following: (cos^2Ø*tan^2Ø)/(1-cos^2 Ø.

Answers

[tex]\dfrac{\cos^2\O\cdot\tan^2\O}{1-\cos^2\O}=\dfrac{\cos^2\O\cdot\tan^2\O}{\sin^2\O}=\dfrac{\cos^2\O}{\sin^2\O}\cdot\tan^2\O\\\\=\dfrac{1}{\dfrac{\sin^2\O}{\cos^2\O}}\cdot\tan^2\O=\dfrac{1}{\left(\dfrac{\sin\O}{\cos\O}\right)^2}\cdot\tan^2\O=\dfrac{1}{\tan^2\O}\cdot\tan^2\O\\\\=\dfrac{\tan^2\O}{\tan^2\O}=1[/tex]

[tex]Used:\\\\\sin^2\O+\cos^2\O=1\to1-\cos^2\O=\sin^2\O\\\\\tan\O=\dfrac{\sin\O}{\cos\O}[/tex]

cos^2 x is the right answer.

The area of a rectangular garden is given by the trinomial x2 + x – 42. What are the possible dimensions of the rectangle? Use factoring.

Answers

x^2 + x - 42 =

= x^2 + 1x - 42
             ^      ^
             |       |
             |      you need two numbers that multiply to -42
             |
           and add to 1

Find two numbers whose product is -42 and whose sum is 1.
The numbers are -6 and 7.

x^2 + x - 42 = (x - 6)(x + 7)

Final answer:

The dimensions of the rectangle given by the trinomial (x² + x – 42) are 7 and 6, which are derived by factoring the trinomial and applying the quadratic formula.

Explanation:

To find the possible dimensions of the rectangle, we start by factoring the trinomial that represents the area of the rectangle, namely x² + x – 42.

This can be factored as (x + 7)(x - 6), which are the roots of the quadratic equation when set to equal zero.

The roots, or solutions to this equation, can be calculated using the quadratic formula, -b ± √b² - 4ac 2a, which includes squaring the coefficient of the x-term, subtracting four times the product of the remaining coefficients, and dividing the result by twice the leading coefficient.

In this case, the dimensions that correspond to these roots, namely length and width, are 7 and -6. However, since dimensions cannot be negative, we disregard -6. Therefore, the possible dimensions of the rectangle are 7 and 6.

Learn more about Factoring Trinomial here:

https://brainly.com/question/9702142

#SPJ3

David wants to rent a movie. He wants to watch either a comedy or a drama. The movie rental store has 18 comedies and dramas available for rent. Seven of the movies are comedies, and eleven of the movies are dramas. David has not seen two of the comedies, and he has not seen four of the dramas. If David selects a movie randomly, what is the probability the movie will be a comedy or a movie that he has not seen?

Answers

Let
A = number of ways to pick a movie David wants (either a comedy or a movie he hasn't seen)

B = number of movies total

There are 7 comedies and 4 dramas that David hasn't seen (note: the comedy movies that he hasn't seen are part of the "comedy movie" count, so there's no need to double count these). So there are 7+4 = 11 movies that David would want to rent. Therefore, A = 11.

There are 18 movies total for rent, so B = 18

Dividing the two values
A/B = 11/18 = 0.6111 approximately

The answer as a fraction is exactly 11/18
The answer in decimal form is roughly 0.6111
The answer in percent form is approximately 61.11%

[tex] |\Omega|=18\\
|A|=7+4=11\\\\
P(A)=\dfrac{11}{18}\approx61\% [/tex]

your mom is looking at he amount of sugar in two different drinks the apple juice has 216 grams sugar for every 8 serving the sprite 234 grams of sugar for every 9 serving which drink has more sugar

Answers

The apple juice has 27 grams per serving and the sprite has 26 grams per serving. So the apple juice has more. You just divide the total amount by the number of servings.

A family of four (two kids and two parents) spend the day at an amusement park. At the end of the day, the family adds up all of the receipts from their meals: $16.25, $17.96, $3.58, $4.61, $5.23. What is the mean and median cost spent? What does the mean cost represent? Why is the mean cost significantly different from the median cost? Which measurement of central tendency is a better representation of the amount of money that the family spent at the amusement park?

Answers

A family of four spent the following for their meals $16.25, $17.96, $3.58, $4.61, $5.23.

Mean cost spent is calculated by:

Total Cost/Number of Meals

(16.25+17.96+3.58+4.61+5.23)/5

47.63/5

$9.53

Mean Cost represents the average amount per meal the family has spent.

Median cost is the cost that in the middle of the five costs which is $5.23.

The mean cost is significantly different from the median cost because it is higher.

Median cost is a better representation of the amount of money that the family spent because, with regard to meal costs, this means that exactly half of the meals in the amusement park are above this price ($5.23) and exactly half are below.

Other Questions

True or False: A rectangular equation that is not a function may be a function in the polar coordinate system . . . I was so determined not to try, not to be anybody different that I learned to play only the most ear-splitting preludes, the most discordant hymns. . . . For the talent show, I was to play a piece called "Pleading Child" from Schumann's Scenes from Childhood. It was a simple, moody piece that sounded more difficult than it was. I was supposed to memorize the whole thing, playing the repeat parts twice to make the piece sound longer. But I dawdled over it, playing a few bars and then cheating, looking up to see what notes followed. I never really listened to what I was playing. I daydreamed about being somewhere else, about being someone else. What does the narration in the excerpts reveal about Jing-mei's character? The song is much too difficult for Jing-mei, so she cannot concentrate no matter what she does. She thinks the talent show is a big joke and is not willing to work for it. She is trying her best, but she keeps getting distracted by her own imagination. She believes she cannot succeed even if she tries, so she doesn't bother to try. Which two chemicals, found in the sting gland, produce a synergistic response when combined? What building is pictured below? a. Elizabeth Hall, the home of Elizabeth Shewsbury b. Hardwick Hall, the home of Elizabeth Shrewsbury c. Smythson Hall, the home of Elizabeth Shrewsbury d. Hardwick Hall, the home of Elizabeth Smythson A recipe for cake calls for 5.25 deciliters of milk. How many liters of milk are needed for the cake? I WILL MARK BRAINLIESTJesus is playing soccer and his coach was pointing out different areas of the goal box. The offensive strategy his coach was suggesting Jesus shoot the ball was: From the right corner kick area From the left corner kick area When the defender is directly in front of him When the goalie is out of position According to article ii of the united states constitution all federal impeachment must start in what The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y)^6 are _____. Which of these immigration policies no longer exists in the United States? national ethnic quotas visa requirements annual maximums How does the resistance change as you add bulbs to a series circuit? The resistance does not change. The resistance decreases. The resistance increases. under normal conditions describe how increasing the temperature affects the solubility of a typical salt When ultraviolet light with a wavelength of 400 nm falls on a certain metal surface, the maximum kinetic energy of the emitted photoelectrons is measured to be 1.10 ev . part a what is the maximum kinetic energy of the photoelectrons when light of wavelength 295 nm falls on the same surface? emax =? Which famous world war ii unit, made up entirely of japanese-americans, bears the distinction of being the most highly decorated military unit in american history? what are the ways in which fashion is a serious business Rewrite with only sin x and cos x. sin 2x - cos 2x Select one: a. 2 sin2x - 2 sin x cos x + 1 b. 2 sin x c. 2 sin2x + 2 sin x cos x - 1 PLZ HURRRY!!Of the 12,000 votes cast in an election, 42% of the votes were for Mr.Jones. How many votes were cast for all the other candidates? In The Man to Send Rain Clouds, which statement best explains how the clanspeople feel about Father Pauls funeral customs? They allow him to practice his own customs. They are willing to adapt his custom to theirs. They only practice their own customs.They lack respect for his customs. The phenomenon in which rna molecules in a cell are destroyed if they have a sequence complementary to an introduced double-stranded rna is calleda. rna interference.b. rna obstruction.c. rna blocking.d. rna targeting.e. rna disposal. Which is the best way to help earths water supply last for future generations? A. Make factories recycle water B. Increase neighborhood lawn sprinkling C. Build thermal power plants D. Avoid drop irrigation system on farms exactly 2/5 of the unversity students live off campus. Of those students, 3/10 of them live at home. what fraction of the univesity's students live at home? Reduce your answer to lowest terms