Final answer:
To find the exponential function that passes through (-3, 80) and (-1, 20), we use the general form y = abˣ. By solving a system of equations using these points, we find that the exponential function is y = 40*2ˣ.
Explanation:
To write an exponential function that passes through the points (-3, 80) and (-1, 20), we can use the general form of an exponential function, which is y = abˣ. Here, a and b are constants we need to find. Given two points, we can set up a system of equations to solve for a and b.
Using the first point (-3, 80):
80 = a*b⁻³
Using the second point (-1, 20):
20 = a*b⁻¹
Dividing the second equation by the first gives us:
b2 = 4 which simplifies to b = 2 or b = -2. However, in exponential functions, b is positive, so we choose b = 2.
Substituting b = 2 into the second equation gives a = 40. Thus, the exponential function is y = 40*2ˣ.
How is this one solved?
Answer:
see below
Step-by-step explanation:
This is solved by simplifying each expression and identifying the column heading it matches.
1. (6 x^2/(x^2 - 7 x + 10)) / (2 x)/(x - 5))
= (6 x^2/(x^2 - 7 x + 10)) · (x -5)/(2 x) . . . . invert and multiply
= (6x^2)/(2x) · (x -5)/((x -2)(x -5)) . . . . . . . factor so common factors can cancel
= 3x/(x -2) . . . . matches column 1
__
2. (x - 4) (x + 2)/(x^2 + 5 x + 6) + (-3 x^2 + 24 x - 20)/((x + 3) (4 x - 5))
= (x -4)(x +2)/((x +3)(x +2)) + (-3x^2 +24x -20)/((x +3)(4x -5)) . . . factor
= (x -4)/(x +3) + (-3x^2 +24x -20)/((x +3)(4x -5)) . . . . cancel common factor
= ((x -4)(4x -5) +(-3x^2 +24x -20))/((x +3)(4x -5)) . . . . use common denominator
= (4x^2 -21x +20 -3x^2 +24x -20)/((x +3)(4x -5)) . . . expand product
= (x^2 +3x)/((x +3)(4x -5)) . . . . . . collect terms
= (x)(x +3)/((x +3)(4x -5)) . . . . . . factor numerator
= x/(4x -5) . . . . . . . . . . . . . . . . . . cancel common factor ... matches column 2
__
3. 3 x^2/(x + 3) · (2 x + 6)/(2 x^2 - 4 x)
= 3·2·x·(x +3)/((x +3)(2·x)(x -2)) = 3/(x -2) . . . . matches column 1
__
4. 3 x/(4 x - 5) - 4 x^2/(8 x^2 - 10 x)
= 3x/(4x -5) - 4x^2/(2x(4x -5)) = (3x -2x)/(4x -5) = x/(4x -5) ... matches col 2
__
5. 5 x^2/(x - 2) · (2 x + 6)/(8 x^2 - 4 x) . . . . no match (has a denominator factor of 2x-1 that doesn't cancel any numerator factors)
__
6. -x/(4 x - 5) - 4 x^2/(16 x^2 - 22 x)
In order to match one of the columns, the term on the right must reduce to 2x/(4x-5), which it does not, or must have a denominator factor of x-2, which it also does not. no match.
I need some help plz
Answer:
one solution is (0, -2)
Step-by-step explanation:
The line y = -x is the boundary of the solution space of the first inequality. The less-than symbol (<) tells you that the line will be dashed and the shading will be below it. The line has a slope of -1 and goes through the y-intercept point (0, 0).
The line y = x - 2 is the boundary of the solution space for the second inequality. The less-than-or-equal-to symbol (≤) tells you the line will be solid (or equal to) and the shading will be below it (less than). The line has a slope of +1 and goes through the y-intercept point (0, -2).
The area of the graph where the shadings overlap is the solution space for the system of inequalities. Any point in that area will do, including points on the solid line where y < -x. (0, -2) is one such point.
A doctor measured a patient’s resting pulse rate at 80 beats per minute. Draw a graph to show the relationship between time and the number of times the patient’s heart beats. Use it to estimate how many times the patient’s heart will beat in 18 minutes. Write an equation in Y = mx + b form.
Answer:
i also need the answer to this question
Step-by-step explanation:
Answer:
y= 8x +18
Step-by-step explanation:
(There is a picture but I can't put it in the question)
Sides of the triangle: 2x, 4x-2, 3x-1
Find a single expression that represents the perimeter of the triangle.
A) x + 1
B) 5x − 3
C) 3x − 1
D) 9x − 3
The perimeter of a triangle is just adding all the sides.
So, (2x)+(4x-2)+(3x-1)= 9x-3
So, the answer is D, 9x-3
Answer:
D.
Step-by-step explanation:
The perimeter = the sum of the 3 sides.
Perimeter = 2x + 4x - 2+ 3x - 1
= 9x - 3.
solve the equation. a/6 - 11 = 25
Answer:
a=216.
Step-by-step explanation:
What you do is you need to get a by itself.
a/6-11=25. You first add 11 to both sides.
a/6=36. Next you will times 6 on both sides to get
a=216 as your answer.
At the beginning of year 1, Mike invests $800 at an annual compound interest rate of 3%. He makes no deposits to or withdrawals from the account. Which example explicit formula can be used to find the account's balance at the beginning of year 7.
Answer:
C. A(7) = 800·(1 +0.03)^(7-1)
Step-by-step explanation:
Note that the times are described as "the beginning of year 1" and "the beginning of year 7." If you consider the formula to be the one marked (choice D), you find the general case is ...
A(n) = 800·1.03^n
When you put in 1 for n, you see it gives you ...
A(1) = 800·1.03^1 = 824 . . . . . . . incorrect value for "the beginning of year 1"
The exponent of 1.03 needs to be the difference in year numbers: 7-1, as in choice C.
The appropriate formula is ...
A(7) = 800·(1 +0.03)^(7-1)
5t ≤-15 is....????? i need help and if u guys could maybe explain it to me plz?
Answer:
t ≤ -3
Step-by-step explanation:
5t ≤ -15
You are solving for t. That means you want t alone on the left side. t is being multiplied by 5. To get rid of a multiplication by 5, you do the opposite operation, and you divide by 5. You must do the same operation to both sides of an inequality, so you must divide both sides by 5.
5t/5 ≤ -15/5
t ≤ -3
Sets L, M, and N are shown. Which of the sets represents L ∪ (M ∩ N) (the union of L with the intersection of sets M and N)? L = {0, 20, 40, 80, 100} M = {5, 10, 15, 20, 25} N = {10, 20, 30, 40, 50} A) {0, 5, 10, 15, 20, 25, 30, 40, 50, 80, 100} B) {0, 10, 20, 40, 80, 100} C) {20, 40} D) {20}
Answer:
B) L ∪ (M ∩ N)={0,10,20,40,80,100}
Step-by-step explanation:
The given sets are;
L = {0, 20, 40, 80, 100}
M = {5, 10, 15, 20, 25}
and
N = {10, 20, 30, 40, 50}
(M ∩ N) are elements in set M and set N
(M ∩ N) ={10,20}
The elements in L ∪ (M ∩ N) are elements in L or M ∩ N or both
L ∪ (M ∩ N)={0,10,20,40,80,100}
The correct choice is B.
Answer:
B
Step-by-step explanation:
L ∪ (M ∩ N) means take "common" between M and N and take "sum of that and L".
Let's find (M ∩ N) (common between M and N):
We know
M = {5, 10, 15, 20, 25} , and
N = {10, 20, 30, 40, 50}
Thus, the common elements are 10 & 20, thus (M ∩ N) = {10,20}
Now we have:
L = {0, 20, 40, 80, 100}
(M ∩ N) = {10,20}
So sum of L and (M ∩ N) are all the unique elements of both the sets. They are 0, 10, 20, 40, 80, 100, or Option B
Given: Circumscribed △ELT, EL=14, LT=17, ET=15.
Find: EI, LJ, and ST
Answer:
EI=6 units
LJ=8 units
ST=9 units
Step-by-step explanation:
step 1
we know that
The triangle ELT is a circumscribed triangle
so
EI=ES
LI=LJ
TS=TJ
EL=EI+LI ------> 14=EI+LI -----> 14=EI+LJ -----> equation A
LT=LJ+TJ----> 17=LJ+TJ ----> 17=LJ+TS ----> equation B
ET=ES+TS ---> 15=ES+TS----> 15=EI+TS ----> equation C
Subtract equation A from equation C
15=EI+TS
14=EI+LJ
--------------
15-14=TS-LJ
TS=1+LJ ------> equation D
substitute equation D in equation B and solve for LJ
17=LJ+(1+LJ)
17=2LJ+1
2LJ=17-1
LJ=8
Find the value of TS
TS=1+LJ -----> TS=1+8=9
Find the value of EI
14=EI+LJ ------> 14=EI+8 ----> EI=14-8=6
therefore
EI=6 units
LJ=8 units
ST=9 units
in an isosceles triangle ABC, AB=AC and the altitude from A to BC is 20. If the perimeter of the triangle is 80, find the area of the triangle.
Answer:
300 square units
Step-by-step explanation:
Let M be the midpoint of BC. Then AM =20 is the altitude. Let x represent the length BM=MC, and let y represent the length AB=AC. Then the perimeter is ...
2x +2y = 80
x +y = 40 . . . . divide by 2 . . . . . [eq A]
The Pythagorean theorem tells us ...
x^2 + 20^2 = y^2 . . . . . . . y is the hypotenuse of right triangle AMC
Rearranging, we have ...
y^2 -x^2 = 400
(y -x)(y +x) = 400
(y -x)·40 = 400
y -x = 10. . . . . . . . . [eq B]
Subtracting [eq B] from [eq A], we find ...
(x +y) -(y -x) = (40) -(10)
2x = 30
x = 15
The area of interest is 20x, so is ...
A = 20·x = 20·15 = 300 . . . . square units
object weighs 8,000 grams, how many kilograms does it weigh? A) 8 kilograms B) 80 kilograms C) 800 kilograms D) 80,000 kilograms
Answer:
A) 8 kilograms
Step-by-step explanation:
"kilo-" is a prefix meaning 1000. So, 8 kilo-grams = 8 thousand grams = 8,000 grams.
To convert 8,000 grams to kilograms, divide by 1,000, resulting in 8 kilograms. Therefore, an object that weighs 8,000 grams would indeed weigh 8 kilograms, which is option A.
If an object weighs 8,000 grams and you want to convert it to kilograms, you need to know the conversion between grams and kilograms. In the metric system, one kilogram is equal to 1,000 grams. So, to convert grams to kilograms, you divide the number of grams by 1,000.
To calculate the weight of the object in kilograms from grams:
Take the weight of the object in grams, which is 8,000 grams.Divide the weight in grams (8,000) by the number of grams in one kilogram (1,000).The calculation will be 8,000 \/ 1,000 = 8 kilograms.Therefore, an object that weighs 8,000 grams would weigh 8 kilograms, which corresponds to option A.
help please ........
Example:
a) mutually exclusive
b) not mutually exclusive
c) not mutually exclusive
Your Turn:
a) not mutually exclusive
b) not mutually exclusive
c) not mutually exclusive
d) mutually exclusive
Step-by-step explanation:Events are mutually exclusive if they cannot both occur together. Otherwise, they are not mutually exclusive.
Example
a) the winner cannot be both a junior and a senior — mutually exclusive
b) the winner could be a female sophomore — not mutually exclusive
c) the winner could be a male freshman — not mutually exclusive
___
Your Turn
a) the card could be the ace of clubs — not mutually exclusive
b) the number could be divisible by both 5 and 10 — not mutually exclusive
c) the card could be the 5 of hearts — not mutually exclusive
d) the result cannot be both 6 and 7 — mutually exclusive
Which expression is equivalent to (x2 − 8) − (−2x2 + 4)?
Answer: 6(x-2)
Step-by-step explanation:
(x·2-8)-(2x·2+4)
(2(x-4))+2x·2-4
2(x-4)+2x·2-4
2(x-4)+4x-4
2(x-4+2x-2)
2(3x-4-2)
2(3x-6)
2·3(x-2)
6(x-2)
Answer:
3x^2-12
Step-by-step explanation:
Just took it on USATestPrep, if that's where the question came from! ;)
What is the equation of the circle in standard form see attachment
Center (-1,1), radius 5 so
[tex](x - -1)^2 + (y - 1)^2 = 5^2[/tex]
[tex](x+1)^2 + (y-1)^2 = 25[/tex]
Third choice
Answer:
○ (x + 1)² + (y - 1)² = 25
Step-by-step explanation:
According to one of the Circle Equations, (X - H)² + (Y - K)² = R², all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY careful inserting the center into the formula with their CORRECT signs. Then in the end, square the radius.
The radius is five, so squaring this will give you twenty-five.
I am joyous to assist you anytime.
The container that holds the water for the football team is 3/4
full. After pouring out 7 gallons of water, it is 1/2 full. How many gallons can the container hold?
Answer:
28 Gallons
Step-by-step explanation:
This one is really easy, so i want you to look at my steps:
1. Gather all given information, container is 3/4, 7 gallons are poured out to make it 1/2 full.
2. Find a common denominator for the fractions 1/2 and 3/4, this would be 4.
3. Make them both the same denominator, 2/4 and 3/4.
4. Subtract the remaining amount from the original amount to see how much 7 gallons made up, 3/4 - 2/4 = 1/4
5. Now that you know that 7 gallons made up 1/4 of the container, you can just multiply 7 by 4 to get the total amount of gallons that can fit in the container.
7 * 4 = 28 gallons is the max that the container can hold.
Answer:
28 gallons
Step-by-step explanation:
Got it right on test
Given the function f(x) = 4|x – 5| + 3, for what values of x is f(x) = 15?
Start with the definition of absolute value |x|:
|x| = x for x>=0
|x| = -x for x<0
We are given a function f(x) and are asking when is that function = 15.
This means we are asking:
4|x-5| + 3 = 15, or simplified:
|x-5| = 3
but at this point further simplification seems stuck on the absolute value. Time to use the above definition, and we split this into two cases:
|x-5| = 3 -->
Case 1: (x-5) = 3 for (x-5)>=0
Case 2: -(x-5) = 3 for (x-5)<0
and now we can proceed and solve each case separately:
Case 1: x = 8 for x >= 5
Case 2: x = 2 for x < 5
Give it sharp look and realize that both cases are valid because each case has a solution of an x that is "allowed" by the inequality condition (meaning it is not contradicting it), therefore both solutions
x1 = 2 and x2 = 8
are valid solutions to the equation 4|x-5|+3=15. For both the function f(x) will have the value 15 (and please do verify for yourself!)
WILL MARK BRAINLIEST!!!NEED HELP ASAP!! Carrie will spin the arrow on the spinner four times. What is the probability that the arrow will stop on A, then B, then C, then D? 3/256 1/64 1/256 3/4
The probability that the arrow will land on any of them once is 1/4.
The probability that the arrow will land on any of them twice is 1/4 * 1/4. This is because the probability of Event A and Event B is P(B) * P(A).
Based on this:
[tex]P(a\cap b\cap c\cap d) = \frac{1}{4}\times \frac{1}{4}\times\frac{1}{4}\times\frac{1}{4}\\\\=\frac{1}{4\times4\times4\times 4}\\=\frac{1}{256}[/tex]
1/256
Hope this helps, let me know if I missed anything!
Answer:
1/256 or 2/512
Step-by-step explanation:
How do you simplify 2(3y - 4) without parenthesis
Answer:
6y -8
Step-by-step explanation:
Use the distributive property. It tells you the product can be simplified to the product of the outside factor and each of the individual terms in parentheses:
2(3y - 4) = 2·3y + 2·(-4) = 6y -8
I NEED HELP NOW!!!
Monelle started an arithmetic sequence. The first four terms of her sequence are shown below.
13,9,5,1,...
1.) What is the common difference for Monelle's sequence? Show or explain how you got the answer
2.) What is the sixth term of Monelle's sequence? Show or explain how you got the answer.
Fin started a geometric sequence. The first four terms of his sequence are show below.
162,54,18,6,...
3.) What is the sixth therm of Fins sequence? Show or explain how you got the answer.
4.) Write an expression that represents the ᵗʰ term of Fins sequence.
Answer: 1. Common difference= 4 . 2.The sixth term would be -7.
Step-by-step explanation: 1. 13-9=4 and 9-5=4 and 5-1=4. 2. Sixth term: 1-4=-3 And -3-4=-7.
The common difference in Monelle's arithmetic sequence is -4, and the sixth term is -7. For Fin's geometric sequence, the ratio is 1/3, with the sixth term being 2. The formula for the nth term of Fin's sequence is 162 * (1/3)^(n-1).
Explanation:In mathematical terms, an arithmetic sequence is a number sequence in which the difference between every two successive members is a constant. From the first part of your question, in Monelle's arithmetic sequence: 13, 9, 5, 1,... the common difference can be calculated by subtracting any term from the one that comes after it. In this case, 9 - 13 or 5 - 9 will give us the common difference, which is -4.
Once you've found the common difference, you can calculate the sixth term by taking the first term (13) and adding the common difference (-4) times the number of terms minus 1 (for the sixth term, this would be 5 times). This gives us 13 - 4 * 5 = -7 for the sixth term of Monelle's sequence.
Conversely, a geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the 'ratio'. Looking at Fin's sequence: 162, 54, 18, 6, ..., we can find the ratio by dividing any term by the one before it. So 54 divided by 162, or 18 divided by 54, gives us the common ratio of 1/3. To find the sixth term, we multiply the first term by the ratio raised to the power of (the term's position number minus 1). The sixth term then is 162 * (1/3)^5 = 2.
The expression that represents the ᵗʰ term of Fin's sequence can be written general form as a * r^(n-1), where 'a' is the first term, 'r' is the ratio, and 'n' is the term's position number. In this case, the formula for the nth term of Fin's sequence would be 162 * (1/3)^(n-1).
Learn more about Sequences here:https://brainly.com/question/36944481
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write the point intercept form and the slope-intercept form.
(-5,1) and (2,-5)
write as a product 27a^3−(a−b)^3
Answer:
(2a +b)·(13a^2 -5ab +b^2)
Step-by-step explanation:
The factorization of the difference of cubes is a standard form:
(p -q)^3 = (p -q)(p^2 +pq +q^2)
Here, you have ...
p = 3aq = (a-b)so the factorization is ...
(3a -(a -b))·((3a)^2 +(3a)(a -b) +(a -b)^2) . . . . substitute for p and q
= (2a +b)·(9a^2 +3a^2 -3ab +a^2 -2ab +b^2) . . . . simplify a bit
= (2a +b)·(13a^2 -5ab +b^2) . . . . . . collect terms
can someone help me with 2.5
Answer:
A
Step-by-step explanation:
Givens
The board has been placed 1/2 the length of the 10 foot ladder across to 1/2 the length of the 15 foot ladder. That means that the rung holding the board on the 10 foot ladder is 1/2 up the length of the 10 foot ladder. That makes the hypotenuse of the small triangle = 5The distance from where the ladders meet to the paint = xFind x
x^2 + 3^2 = 5^2
x^2 + 9 = 25 Subtract 9 from both sides
x^2 = 25 - 9 Combine
x^2 = 16 Take the sqrt of both sides
x = 4
Find the height
The ratio of all dimensions involving the 2 ladders and the board is 1 to 2.
So the total height from where the ladders meet to the ground is 2*4 = 8
Answer: The distance from the bucket to the ground is 1/2 * 8 = 4
Answer: A
6 is 30% of, please answer
Answer:
20
Step-by-step explanation:
30% × ? = 6
? =
6 ÷ 30% =
6 ÷ (30 ÷ 100) =
(100 × 6) ÷ 30 =
600 ÷ 30 =
20
The ratio of the number of skiers who bought season passes to the number of snowboarders is 9:6. If a total of 225 people bought season passes, how many snowboarders bought season passes?
Answer:
90
Step-by-step explanation:
The total number of "ratio units" is 9+6 = 15, so each one must stand for 225/15 = 15 people. Then 6·15 = 90 people were snowboarders who bought season passes.
find the zero of y=4x^2-12x-16
HELPP
Answer:
-1, 4
Step-by-step explanation:
factor out common term 4
4(x^2 - 3x - 4) find factors of -4 1 (-4)= -4 (c term) also 1 - 4 = -3 (b term)
4(x+1)(x-4) = 0
zeros are -1, 4
Answer:
[tex]\large\boxed{x=-1\ or\ x=4}[/tex]
Step-by-step explanation:
[tex]y=4x^2-12x-16\\\\\text{the zeros are for}\ y=0:\\\\4x^2-12x-16=0\qquad\text{divide both sides by 4}\\\\x^2-3x-4=0\\\\x^2+x-4x-4=0\\\\x(x+1)-4(x+1)=0\\\\(x+1)(x-4)=0\iff x+1=0\ \vee\ x-4=0\\\\x+1=0\qquad\text{subtract 1 from both sides}\\\boxed{x=-1}\\\\x-4=0\qquad\text{add 4 to both sides}\\\boxed{x=4}[/tex]
What linear function represents the line given by the point slope equation y+7= 2/3(x+6)?
Answer:
the correct answer is the 3rd one
Answer:
the third option is correct
Step-by-step explanation:
The area of the circular base of a cylinder is 36 square units. The height of the cylinder is 2 units. What is the lateral area of the cylinder? Express the answer in terms of n.
Answer:
The lateral area of the cylinder is [tex]24 \pi\ units^{2}[/tex]
Step-by-step explanation:
we know that
The lateral area of the cylinder is equal to
[tex]LA=2\pi rh[/tex]
step 1
Find the radius of the base of the cylinder
The area of the base is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]A=36 \pi\ units^{2}[/tex]
so
substitute and solve for r
[tex]36 \pi=\pi r^{2}[/tex]
Simplify
[tex]r=6\ units[/tex]
step 2
Find the lateral area
we have
[tex]r=6\ units[/tex]
[tex]h=2\ units[/tex]
substitute the values
[tex]LA=2\pi (6)(2)=24 \pi\ units^{2}[/tex]
Use the information in the table to find the constant of proportionality and write the equation.
Thanks
Answer:
y = (5/2)x
Step-by-step explanation:
A proportional relation can be written as ...
y = kx
Solving for k, you divide by x to get ...
y/x = k
The contant of proportionality is the ratio of y to x. Any pair of x and y will do for computing k. The first pair requires no reduction in the fraction that results:
5/2 = k
So, your equation is ...
y = (5/2)x
Answer:
The constant of proportionality is
✔ 2.5
The equation that represents this proportional relationship is
✔ y = 2.5x
Step-by-step explanation:
hope this helps:)
1) Given: circle k(O), ED= diameter ,m∠OEF=32°, m(arc)EF=(2x+10)° Find: x
2)Given: circle k(O), m(arc) FE=56°, FD=ED Find: m∠EFO, m∠EFD
The value of x in Problem 1 is 11 degrees. The measures of angles EFO and EFD in Problem 2 are 28 degrees and 84 degrees respectively.
Explanation:In both problems, we're dealing with geometric principles related to circles and angles.
Problem 1: Given that OEF is a central angle standing on the arc EF, we know from circle geometry that the measure of the central angle is equal to the measure of the arc it intercepts. Therefore, 32° = 2x + 10°. Solving this equation, we get x = 11°.Problem 2: Since the angles are located at the circumference and standing on the same arc FE, the angle subtended by an arc at the center is double the angle subtended at the circumference. Therefore, m∠EFO= 56°/2 = 28°. Seeing as ∠EFD is an exterior angle of triangle EFO, its measure is equal to the sum of the two non-adjacent interior angles (angle sum property of a triangle). Therefore, m∠EFD = ∠EFO + ∠FEO = 28° + 56° = 84°.Learn more about Circle Geometry here:https://brainly.com/question/27802544
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1. The value of x is 11
2. angle EFO = 28°
3. angle EFD = 90°
In geometry, the central angle of a circle's arc is equal to the subtended arc's measure.
The relationship is given by
Central Angle = Arc Measure
Central Angle=Arc Measure in degrees. This property is fundamental in circular geometry.
1. Since arc EF = 2x + 10
2x + 10 = 32( angle at the centre equal measure of arc it intercept)
2x = 32 - 10
2x = 22
x = 11
Since FE = 56
EFO = 1/2 × 56 ( angle at the center is 2× angle at the circumference)
EFO = 28°
angle EFD = 90° ( angle substended from the diameter of a circle to the circumference is 90°)
please help I will give brainless.
15% answered swimming.
39 people said swimming, so 39 people is 15% of the total people surveyed.
To find the total number of people, divide 39 by 15%:
39 / 0.15 = 260
There were 260 total people surveyed.