Answer:
Step-by-step explanation:
B. Vertically stretch by a factor of 3, and
D. Shift down 1 unit.
To determine which transformations were applied to the linear parent function f(x) = x to obtain the given function g(x) = 3x - 1, we need to examine the changes made to the function. Let's analyze each choice:
A. Horizontally stretch by a factor of 3.
A horizontal stretch would mean that the x-values are being multiplied by a constant factor. However, in g(x) = 3x - 1, it's the output values (y-values) that have been multiplied by 3 when compared to f(x) = x. Thus choice A is not correct.
B. Vertically stretch by a factor of 3.
In g(x) = 3x - 1, each output value has been multiplied by 3 relative to the parent function f(x) = x. In other words, y has been replaced by 3y, which causes a vertical stretch or scaling by a factor of 3. So choice B is correct.
C. Shift left 1 unit.
A horizontal shift of the graph would involve an addition or subtraction inside the function's argument (x). For instance, f(x - 1) would indicate a shift to the right by 1 unit, and f(x + 1) would be a shift to the left by 1 unit. Since there is no such term in g(x) = 3x - 1, no horizontal shift has occurred. Choice C is not correct.
D. Shift down 1 unit.
A downward shift is indicated by a subtraction outside the function. In g(x) = 3x - 1, there is indeed a "-1" applied to the entire function, which results in every point on the graph being shifted down 1 unit. Therefore, choice D is correct.
In summary, the transformations applied to f(x) = x to get g(x) = 3x - 1 are:
B. Vertically stretch by a factor of 3.
D. Shift down 1 unit.
Find an equation in standard form for the ellipse with the vertical major axis of length 18 and minor axis of length 6.
a)x squared divided by 81 plus y squared divided by 9 = 1
b)x squared divided by 9 plus y squared divided by 3 = 1
c)x squared divided by 9 plus y squared divided by 81 = 1
d)x squared divided by 3 plus y squared divided by 9 = 1
C seem reasonable to me
The following function represents the production cost f(x), in dollars, for x number of units produced by company 1:
f(x) = 0.15x2 − 6x + 400
The following table represents the production cost g(x), in dollars, for x number of units produced by company 2:
x g(x)
50 75
60 60
70 55
80 60
90 75
Based on the given information, the minimum production cost for company _____ is greater.
[Put 1 or 2 in the blank space]
Answer:
The answer is confirmed 1. Just took it.
Step-by-step explanation:
Answer:
Company 1 is greater.
Step-by-step explanation:
Given,
The function that shows the production cost of company 1,
[tex]f(x)=0.15x^2-6x+400[/tex]
Differentiating with respect to x,
We get,
[tex]f'(x)=0.30x-6[/tex]
Again differentiating,
[tex]f''(x)=0.30[/tex]
For minimum or maximum,
f'(x) = 0,
[tex]\implies 0.3x-6=0[/tex]
[tex]\implies x = 20[/tex]
Since, at x = 20, f''(x) = Positive,
So, f(x) is minimum at x = 20,
⇒ Minimum cost in company 1 is,
[tex]f(20)=0.15(20)^2-6(20)+400[/tex]
[tex]=340[/tex]
Also, by the given table,
The minimum cost of company 2 is at x = 70,
g(70) = 55,
Since, 340 > 55,
Hence, Based on the given information, the minimum production cost for company 1 is greater.
Identify the volume of a cube with edge length 13 ft. HELP PLEASE!!
Answer:
V=2197
Step-by-step explanation:
Equation for volume of a cube:
V= side length cubed
V=(13)(13)(13)
V=2197
Answer:
V = 2,197 ft3
Step-by-step explanation:
Your welcome ;)
A catch and release fisherman catches a fish and then releases the fish back into the river so as to not to harm the fish.
At a local river, 50% of the fish are white sturgeon, 35% brook trout, and 15% Chinook salmon.
If a fisherman catches then releases a fish and then catches and releases a second fish, then what is the probability that both fish he caught were white sturgeon?
Answer:
25%
Step-by-step explanation:
Assuming the catching of a fish is a random process and that the probability of catching any of the listed kinds of fish is proportional to their population, then the probability of catching a sturgeon is 50%. The probability of catching another one is also 50% (assuming the events are independent). So, the joint probability is the product of these:
0.50 × 0.50 = 0.25 = 25% . . . . . probability of catching 2 sturgeon in a row.
The probability of both fish being white sturgeon is 0.25.
To calculate the probability, we need to multiply the probabilities of catching a white sturgeon each time. Since 50% of the fish are white sturgeon, the probability of catching one is 0.5. Therefore, 0.5 multiplied by 0.5 equals 0.25.
If the walls are 9' high, how much paint would I need to buy to paint the walls of all three bedrooms?
Answer:
The required paint for a total of [tex]1.404\ ft^{2}[/tex] is approximate 6 gallons
Step-by-step explanation:
we know that
To find how much paint would I need to buy to paint the walls of all three bedrooms, calculate the area of all three bedrooms
Master Bedroom
The area is equal to
[tex]A1=(16+16+12+2+18)*9=576\ ft^{2}[/tex]
2 Bedroom
The area is equal to
[tex]A2=(12+14+10+10)*9=414\ ft^{2}[/tex]
3 Bedroom
The area is equal to
[tex]A3=(10+10+14+10+2)*9=414\ ft^{2}[/tex]
The total area is equal to
A=A1+A2+A3
[tex]A=576+414+414=1.404\ ft^{2}[/tex]
Approximate one gallon of paint covers 250 square feet
so
[tex]1.404/250=5.6\ gal[/tex]
Evaluate.
9!/7!
A.) 63
B.) 72
C.) 81
ANSWER
B.) 72
EXPLANATION
Recall the expansion for the factorial notation:
[tex]n! = n \times (n - 1) \times (n - 2) \times ...3 \times 2 \times 1[/tex]
We want to simplify
[tex] \frac{9!}{7!} [/tex]
Let us expand the numerator up to 7! while maintaining the denominator.
[tex] \implies \: \frac{9 \times 8 \times 7!}{7!} [/tex]
When we cancel out the common factors,we obtain:
[tex]\implies \: \frac{9 \times 8 \times 1}{1} [/tex]
This simplifies to
[tex]\implies \: \frac{72}{1} = 72[/tex]
The correct answer is B.
If a jelly bean machine contains 16 pink jelly beans, 34 blue jelly beans, 24 black jelly beans and 26 purple jelly beans, what is the probability that a jelly bean chosen at random will be blue?
A. 13/50
B. 6/25
C. 4/25
D. 17/50
Answer:
The correct answer option is D. 17/50.
Step-by-step explanation:
We are given that a jelly bean machine has 16 pink jelly beans, 34 blue jelly beans, 24 black jelly beans and 26 purple jelly beans.
We are to find the probability of getting a blue jelly bean chosen at random.
Total number of jelly beans = 16 + 34 + 24 + 26 = 100
Number of blue jelly beans = 34
P (getting a blue jelly bean) = 34/100 = 17/50
Find the maximum and minimum values of the function.
y=7cosx
Answer:
B
Step-by-step explanation:
If a sinusoidal function is given in the form y = B Sin x or y = B Cos x, then,
B is called the amplitude of the function. It will define minimum and maximum.
The minimum & maximum of this form of a cos function is B and -B.
The function given is y = 7 Cos x, so the Maximum is 7 and Minimum is -7
Correct answer is B.
-2 is a solution of 5x + 3 = 13
True OR False
False.
Replace x with -2 and simplify. 5(-2) + 3 = 13
Multiply. -10 + 3 = 13
Add. -7 = 13
This is not true, so -2 is not a solution, therefore the answer to the question is false.
The equation that models the current water temperature t of the swimming pool is t -6=78 which best describes the error made when solving for the current temperature
Answer:
The same number was not added to both sides.
Step-by-step explanation:
The same number was not added to both sides.
In line 2, 6 was added to the left side and 78 was added to the right side.
The best that describes the error made when solving for the current temperature is that the same number was not added to both sides of the equation.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The given equation can be solved as shown below.
t - 6 = 78
t - 6 + 6 = 78 + 6
t = 84
Now, if we compare it with the given equation, we can find that the error made when solving for the current temperature is that the same number was not added to both sides of the equation.
Hence, the best that describes the error made when solving for the current temperature is that the same number was not added to both sides of the equation.
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A cooler at a picnic contains 100 cans of soda covered by ice. There are 34 cans of cola, 50 cans of orange soda, 12 cans of ginger ale, and 4 cans of root beer. The cans are all the same size and shape. If one can is selected at random from the cooler, determine the probability that the soda selected is root beer, cola comma or ginger ale.
The probability that the can selected is a root beer, cola comma or ginger ale is nothing .
(Type an integer or a simplified fraction.)
Answer:
P = 1/2 = 0.5
Step-by-step explanation:
Total amount of cans = 100
Cans of cola = 34
Cans of orange soda = 50
Cans of ginger ale = 12
Cans of root beer = 4
Probability of selecting
- a can of cola = 34/100 = 0.34
- a can of orange soda = 50/100 = 0.5
- a can of ginger ale = 12/100 = 0.12
- a can of root beer = 4/100 = 0.04
Since we are asked the probability that the can selected is a root beer, cola, or ginger ale, we need to add together the probabilities of each.
P = 0.04 + 0.34 + 0.12 = 0.5 = 1/2
A medium sized apple has 70 calories. This is 10 calories less than 1\4 of the calories in an old westie chocolate bar.How many calories are in the chocolate bar?
Answer:
[tex]\boxed{320}[/tex]
Step-by-step explanation:
Let x = calories in chocolate bar
¼x = ¼ of the calories
¼x – 10 = 10 calories less than half the calories
¼x – 10 = 70
¼x = 80
x = 320
There are [tex]\boxed{320}[/tex] calories in the chocolate bar.
A room contains three urns: u1, u2, u3. u1 contains 3 red and 2 yellow marbles. u2 contains 3 red and 7 yellow marbles. u3 contains 1 red and 4 yellow marbles. 66) referring to urns we enter the room and select an urn, but we are not sure which, and then we randomly remove a marble from the urn. find the probability that the marble is red.
Answer:
[tex]\dfrac{11}{30}[/tex]
Step-by-step explanation:
Urn U1: 3 red and 2 yellow marbles, in total 5 marbles.
The probability to select red marble is [tex]\dfrac{3}{5}=0.6.[/tex]
Urn U2: 3 red and 7 yellow marbles, in total 10 marbles.
The probability to select red marble is [tex]\dfrac{3}{10}=0.3.[/tex]
Urn U1: 1 red and 4 yellow marbles, in total 5 marbles.
The probability to select red marble is [tex]\dfrac{1}{5}=0.2.[/tex]
The probability to choose each urn is the same and is equal to [tex]\frac{1}{3}.[/tex]
Thus, the probability that the marble is red is
[tex]\dfrac{1}{3}\cdot 0.6+\dfrac{1}{3}\cdot 0.3+\dfrac{1}{3}\cdot 0.2=\dfrac{1.1}{3}=\dfrac{11}{30}.[/tex]
the equation of a line is given below.
4x + 3y = -24
find the x-intercept and the y-intercept.
then use them to graph the line.
x-intercept: ?
y-intercept: ?
Answer:
See below.
Step-by-step explanation:
4x + 3y = -24
We convert to slope/intercept form ( y = mx + b):
3y = - 4x - 24
Divide through by 3:
y = (-4/3)x - 8
Comparing this with y = mx + b:
we see that b ( the y-intercept) is -8.
To find the x -intercept solve (-4/3)x - 8 = 0
(-4/3)x = 8
Multiplying through by -3/4:
x = 8 * -3/4 = -6 = x-intercept.
To draw the graph draw a line through the points (-6,0) and (0, -8).
Answer:
-3/4 y-6
Step-by-step explanation:
Given: circle k(O), m RK =70° Find: m∠ERK
Check the picture below.
Answer:
Step-by-step explanation:
55
Rearrange the formula a2 + b2 = c2 for a. A) a = (c2 − b2)2 B) a = (c2 + b2)2 C) a = c2 − b2 D) a = c2 + b2
Answer:
C2 + a2 +2 = b
Would be the new formula
Answer:
the correct answer is:
a = √ c^2 − b^2
Step-by-step explanation:
a^2 + b^2 = c^2
Explanation:
a^2 + b^2 = c^2
a^2 = c^2 − b^2
a = √ c^2 − b^2
Kesha rode her bike 12 miles from home to the store. She rode her bike back towards home from the store for 8 miles then walked another 4 miles. How many more miles does Kesha needs to go before she is home?
Answer:
0 Kesha is already home 8+4 is 12 and it's 12 miles from the store to her house .-.
Step-by-step explanation:
Answer:
0 more miles.
Step-by-step explanation:
If 12 miles is the total distance from her house to the store the answer should be 0. She should be at home because 8 miles on the bike + the 4 walked = 12 miles, which is how many she rode to the store in the first place.
The depth of a lake is 100 centimeters less than 1401 meters what is the depth in kilometers
The depth of the lake is 1.4 kilometers after converting the result to kilometers.
To find the depth of the lake in kilometers when it is 100 centimeters less than 1401 meters, first convert the depth difference to meters.
Since 100 centimeters is equivalent to 1 meter, the actual depth of the lake in meters is 1400 meters (which is 1401 meters - 1 meter).
To convert this depth into kilometers, we divide by 1000, since there are 1000 meters in one kilometer.
Hence, the depth is 1.4 kilometers.
The longest side in a right triangle is 24 cm, and the second longest side is 20 cm. Find the length of the shortest side
Answer:
13.3 cm
Step-by-step explanation:
Apply the Pythagorean Theorem:
hyp² = (2nd longest side)² + (shortest side)². Here the numbers are:
(24 cm)² = (20 cm)² + (shortest side)², or
576 - 400 = 176 = hyp²
Taking the square root of both sides, we get (shortest side) = 13.3 cm
Answer: the answer is 13.3
In the system shown below, what are the coordinates of the solution that lies in quadrant IV?
Write your answer in the form (a,b) without using spaces
[tex]2x^2+y^2=33\\x^2+y^2+2y=19[/tex]
Answer:
The coordinates of the solution that lies in quadrant IV are (2, -5)
Step-by-step explanation:
We have 2 equations, the first of an ellipse and the second of a circumference.
[tex]2x^2+y^2=33\\x^2+y^2+2y=19[/tex]
To solve the system solve the second equation for x and then substitute in the first equation
[tex]x^2+y^2+2y=19\\\\x^2 = 19 -y^2 -2y[/tex]
So Substituting in the first equation we have
[tex]x^2 = 19 -y^2 -2y\\\\2(19 -y^2 -2y)+y^2=33\\\\38 -2y^2-4y +y^2 = 33\\\\-y^2-4y+5=0\\\\y^2 +4y-5 = 0[/tex]
Now we must factor the quadratic expression.
We look for two numbers that multiply as a result -5 and add them as result 4.
These numbers are -1 and 5.
Then the factors are
[tex]y^2 +4y-5 = 0\\\\(y-1)(y+5) = 0[/tex]
Therefore the system solutions are:
[tex]y = 1[/tex]; [tex]y = -5[/tex]
In the 4th quadrant the values of x are positive and the values of y are negative.
So we take the negative value of y and substitute it into the system equation to find x
[tex]y=-5\\\\2x^2+(-5)^2=33\\\\2x^2 = 33-25\\\\2x^2 = 8\\\\x^2 = 4[/tex]
[tex]x = 2[/tex], and [tex]x= -2[/tex]
In the 4th quadrant the values of x are positive
So we take the positive value of x
the coordinates of the solution that lies in quadrant IV are (2, -5)
If g=27 and F=54° find h. Round to the nearest tenth
(picture provided)
For this case we have to:
[tex]cos (F) = \frac {h} {27}[/tex]
That is, the cosine of the angle F, will be equal to the adjacent leg on the hypotenuse.
So, by clearing h we have:
[tex]h = 27 * cos (54)\\h = 27 * 0.58778525\\h = 15.87020175[/tex]
Rounding out the value of h we have:
[tex]h = 15.9[/tex]
Answer:
Option B
Answer:
The correct answer is option b. 15.9
Step-by-step explanation:
Points to remember:-
Trigonometric ratio
Cos θ = adjacent side/Hypotenuse
From the figure we can see a right triangle triangle FGH.
To find the value of h
It is given that, g=27 and F=54°
Cos F = adjacent side/Hypotenuse
Cos 54 = adjacent side/Hypotenuse
= FG/FH = h/g
h = g * Cos F = 27 * Cos 54 = 27 * 0.5878 = 15.87 ≈ 15.9
Therefore the correct answer is option b. 15.9
2) If events A and B are DEPENDENT, then A) A and B must occur together. B) A and B cannot occur together. C) A's occurrence can affect the probability of B's occurrence. D) A's occurrence cannot affect the probability of B's occurrence.
Answer:
by 5
Step-by-step explanation: because tgey wou;d nred help
Answer:
C.) If events A and B are DEPENDENT, then A's occurrence can affect the probability of B's occurrence. For example, when two cards are chosen from a deck without replacement, the possibilities change for the second card.
IXL question
I don't understand this one and I need more than 0 points :/
[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\[2em] \begin{array}{ccccllll} &\stackrel{ratio~of~the}{Sides}&\stackrel{ratio~of~the}{Areas}&\stackrel{ratio~of~the}{Volumes}\\ \cline{2-4}&\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}\\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \cfrac{\textit{small cylinder}}{\textit{large cylinder}}\qquad \stackrel{\stackrel{\textit{ratio of the }}{\textit{sides}}}{\cfrac{3}{6}}= \stackrel{\stackrel{\textit{ratio of the }}{\textit{volumes}}}{\cfrac{\sqrt[3]{V}}{\sqrt[3]{V}}}\implies \cfrac{3}{6}=\sqrt[3]{\cfrac{1000}{V}}\implies \left( \cfrac{3}{6} \right)^3=\cfrac{1000}{V} \\\\\\ \left( \cfrac{1}{2} \right)^3=\cfrac{1000}{V}\implies \cfrac{1^3}{2^3}=\cfrac{1000}{V}\implies \cfrac{1}{8}=\cfrac{1000}{V}\implies V=8000[/tex]
Which of the following is true?
A. Sine is negative in Quadrant I.
B. Tangent is positive in Quadrant III.
C. Cosine is positive in Quadrant III.
D. Sine is negative in Quadrant II.
Please help!
Answer:
Tangent is positive in Quadrant III.
Step-by-step explanation:
All trigonometric functions are positive in QUADRANT I
The Sine function is positive in QUADRANT II
The Tangent function is positive in QUADRANT III
The Cosine function is positive IN QUADRANT IV
*ASTC JUST REMEMBER THAT :)*
There are four quadrants in a plane, and the true statement is (b) Tangent is positive in Quadrant III.
How to determine the true statement?There are four quadrants in a coordinate plane, and they have the following properties
Quadrant I
All positiveQuadrant II
Sine positiveOther negativeQuadrant III
Tangent positiveOther negativeQuadrant IV
Cosine positiveOther negativeThe above means that the true statement is (b) Tangent is positive in Quadrant III.
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Which of the following steps were applied to ABCD to obtain A'B'C'D?
A. shifted 3 units left and 3 units up
B. shifted 4 units left and 4 units up
C. shifted 4 units left and 3 units up
D. shifted 3 units left and 4 units up
C. shifted 4 units left and 3 units up
If you compare the graphs (ABCD=Blue; A’B’C’D’=Red), you see that ABCD was moved left 4 and up 3 to become A’B’C’D’.
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position. The correct option is A.
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
To know the steps that were applied to ABCD to obtain A'B'C'D, we need to observe the coordinates of any one point of the polygon given.
Now, if we look at the coordinates of the points D and D', then it can be observed that point D is shifted 3 units left and 3 units up to form A'B'C'D.
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The value of ∛x^10, when x = -2, can be written in simplest form as a∛b, where a = ___ and b = ___.
Answer:
a = -8
b = -2
Step-by-step explanation:
We have been given the following radical expression;
[tex]\sqrt[3]{x^{10} }[/tex]
The radical can be expressed using the law of exponents;
[tex]\sqrt[n]{x}=x^{\frac{1}{n} }[/tex]
The radical can thus be re-written as;
[tex]\sqrt[3]{x^{10} }=(x^{10})^{\frac{1}{3} }[/tex]
Using the law of exponents;
[tex](a^{b})^{c}=a^{bc}[/tex]
The last expression becomes;
[tex](x^{10})^{\frac{1}{3} }=x^{\frac{10}{3} }=x^{3}*x^{\frac{1}{3} }\\\\=x^{3}\sqrt[3]{x}[/tex]
substituting x with -2 yields;
[tex]-2^{3}\sqrt[3]{-2}=-8\sqrt[3]{-2}[/tex]
Identify the surface area of the composite figure in terms of π. HELP PLEASE!!
Answer:
S = 264π m²
Step-by-step explanation:
Left cone
= π(6)(8)
= 48π m²
Central cylinder
= 2π(6)(14)
= 168π m²
Right cone
π(6)(8)
= 48π m²
Surface area = 48π + 168π + 48π = 264π m²
The surface area of the composite figure is 264π [tex]m^{2}[/tex]
How to find the surface area of a composite figure?r = 6m
h = 14m
l = 8m
The curved surface area of the cylinder = 2πrh
= 2*[tex]\pi[/tex]*6*14
=168π [tex]m^{2}[/tex]
The curved surface area of the cone = πrl
=π*6*8
=48π [tex]m^{2}[/tex]
The total surface area of the composite figure
= CSA of cylinder + 2( CSA of cone )
= 168π + 2*48π
=168π + 96π
= 264π [tex]m^{2}[/tex]
Therefore, option S = 264π [tex]m^{2}[/tex] is the correct answer
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Help please! (See image.)
FED is 5/4 times bigger than CBA. So, 44×1.25 is 55. 40×1.25 is 50. The perimeter is 125
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
The number generator is fair. it picked the approximate percentage of red most of the time.
Answer:
The number generator is fair, It picked the approximate percentage of red s*ckers most of the time.
Step-by-step explanation:
7*3+9*3+8*4 = 80
80 divided by 10 gives you an average of 8 red s*ckers each time which is exactly 80% of the amount of s*ckers picked
(s*ckers is banned for some reason)
Chose a prize and explain your reasoning:
1st prize: $250000 in cash
2nd prize: free gas for life
Answer:
1st prize
Step-by-step explanation:
Not all people use a car. Some people walk, take a bike, etc. So, if you won free gas for life, you might not be able to use it.
1st prize. To decide between $250,000 in cash or free gas for life, one must analyze projected gas consumption, inflation, and investment opportunities. The cash offers immediate value and investment potential, whereas the value of free gas depends on driving habits and future fuel prices.
When presented with the options of receiving a 1st prize of $250,000 in cash or a 2nd prize of free gas for life, a comparative analysis based on present value, inflation, personal consumption, and lifestyle must be conducted. The choice primarily depends on one's driving habits, projected longevity of vehicle use, and the current and forecasted price of gas.Concretely, one could estimate the amount of gas consumed annually and project this over an expected driving lifetime, accounting for inflation and potential changes in fuel costs. Then one would compare the total estimated value of free gas to the lump sum of $250,000, determining if it could be invested to yield a greater return than the estimated value of the free gas.Using a net present value calculation, if the $250,000 is invested at an assumed interest rate, you could assess which option has a higher present value, factoring in that the value of the money may also depreciate due to inflation over time. If an individual expects to drive significantly and fuel prices are expected to rise, the free gas for life could potentially be of greater value.However, the flexibility of cash and potential returns on investment typically make the cash prize more appealing for most people. So, 1st prize.