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You have a 52 standard deck.
There are 4 suites on the deck: diamonds, hearts, spades, and clubs.
Each suite has 13 ranks: Ace, 2, 3, 4, 5, 6, 7, 8, 9, Jack, Queen, and King → This means that there are 4 cards with each rank on the deck.
The "9 of clubs is missing on your deck"
This means that:
1) Your deck has one less card, the total number of cards is 51.
2) Your deck has one less club, instead of 13 club cards, you have 12.
3) Your deck has one 9 less, which means that there are 3 nines on your deck.
a) You have to select one event, whose probability decreased due to the missing 9 of clubs.
For example, the event "you draw a card at random and it's a 9"
The expected probability of drawing a 9 of the deck can be determined as the number of nines divided by the number of cards on the deck:
[tex]\begin{gathered} P(9)=\frac{4}{52} \\ P(9)=\frac{1}{13} \\ P(9)=0.076\approx7.6\% \end{gathered}[/tex]But in reality, there is one 9 is missing from the deck, so you have 3 nines and 51 cards on the deck, its probability is:
[tex]\begin{gathered} P(9)=\frac{3}{51} \\ P(9)=\frac{1}{17} \\ P(9)=0.059\approx5.9\% \end{gathered}[/tex]The expected probability of drawing a card at random and the card being a 9 is 7.6%, but due to the missing card, the probability dropped to 5.9%.
This means that drawing a card at random and selecting a 9 is less likely than expected.
b) You have to select one event whose probability increased due to the missing card.
For example, the probability of drawing an Ace, knowing that the card is a club:
On a normal deck there are 13 clubs and "one Ace of clubs", the expected probability of drawing the ace, given that the card is a club can be determined as follows:
[tex]\begin{gathered} P(\text{Ace}|\text{Club)}=\frac{1}{13} \\ P(\text{Ace}|\text{Club)}=0.076\approx7.6\% \end{gathered}[/tex]But we are missing one club, which means that the total number of clubs is missing, so instead of having 13 clubs, we have twelve. The probability can be determined as follows:
[tex]\begin{gathered} P(\text{Ace}|\text{Club)}=\frac{1}{12} \\ P(\text{Ace}|\text{Club)}=0.083\approx8.3\% \end{gathered}[/tex]The expected probability of drawing the Ace, given that the card is a club, on a normal deck is 7.6%, but due to the missing 9 of clubs, this probability has increased to 8.3%.
So this event is more likely due to the missing card.
c) You have to select an event whose probability hasn't changed due to the missing card.
For example, the event "draw a card at random and is a Heart"
The expected probability of drawing a heart from the deck is equal to the quotient between the number of hearts and the total number of cards on the deck:
[tex]\begin{gathered} P(H)=\frac{13}{52} \\ P(H)=\frac{1}{4} \\ P(H)=0.25\approx25\% \end{gathered}[/tex]Your deck is missing one card, so there are 13 Hearts and a total of 51 cards, the probability can be determined as follows:
[tex]\begin{gathered} P(H)=\frac{13}{51} \\ P(H)\approx0.254\approx25.4\% \end{gathered}[/tex]The probability of drawing a heart is around 25% when the deck is complete or missing one card.
Related Questions
Jessica and her father are comparing their ages. At the current time, Jessica's father is 24 years older than her l. Three years from now, Jessica father will be five times her age at the pointQUICK PLEASE
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Current ages
Jessica's age = x
Jessica's father = x + 24
In 3 years time, there ages will be:
Jessica's age = x+ 3
Jessica's father = x + 24 + 3 = x + 27
But Jessica's father will be 5 times her age
Hence;
x + 27 = 5(x+3)
Open the parenthesis
x + 27 = 5x + 15
collect like term
5x - x = 27 - 15
4x = 12
Divide both-side of the equation by 4
x = 3
In the current time;
Jessica is 3 years old
Jessica's father is x + 24 = 3 + 24 = 27 years old
Julie is buying chocolate chip and oatmeal cookies from the bakery. Chocolate chip cookies cost 25¢ each and oatmeal cookies cost 20c each. She wants to buy a mixture of at least 50 cookies. Julie is planning to spend less than $10. Let: C = number of chocolate chip cookies she can buy. M = number of oatmeal cookies she can buy. Select the system of inequalities that represents this situation.
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You are to show how to correctly graph y = -x - 5
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Answer and Explanation:
The slope-intercept form of the equation of a line is generally given as;
[tex]y=mx+b[/tex]where m = the slope of the line
b = the y-intercept of the line
So given the equation;
[tex]y=-x-5[/tex]Comparing the two equations, we can deduce the following;
* m = -1
This means that the line will have a negative slope
* b = -5
This means that the line will cut the y-axis at -5.
We can now choose values for x and determine the corresponding values of y and then proceed to plot the graph.
When x = 1;
[tex]\begin{gathered} y=-1-5 \\ y=-6 \end{gathered}[/tex]When x = 0,
[tex]\begin{gathered} y=-0-5 \\ y=-5 \end{gathered}[/tex]When x = -2,
[tex]\begin{gathered} y=-(-2)-5 \\ y=2-5 \\ y=-3 \end{gathered}[/tex]When x = -4,
[tex]\begin{gathered} y=-(-4)-5 \\ y=4-5 \\ y=-1 \end{gathered}[/tex]When x = -6;
[tex]\begin{gathered} y=-(-6)-5 \\ y=6-5 \\ y=1 \end{gathered}[/tex]With the above values and information, we can then go ahead and plot our graph as shown below;
In a dog race of 9 equally talented runners, what is the probability that Dasher, Dancer, and Prancer will finish first,second, and third, respectively?21/907201/3628801/5041/3
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Combinations and Variations of Elements
Let's suppose we have two dogs only, A and B. They can only finish in two possible orders: AB or BA.
If we add a third dog, let's say C, the combinations (better-called variations here) are now ABC, ACB, BAC, BCA, CAB, and CBA, a total of 6 variations.
Note that we added a 3rd element and the variations changed from 2 to 6, that is, the number was multiplied by 3.
If we add a fourth dog, the total number of possible variations is 6*4 = 24
Following this very same pattern, for 9 dogs, there will be a total of
9*8*7*6*5*4*3*2 = 362880 variations.
Out of these possibilities, we are trying to find the probability that the first three places are occupied by three specific dogs, and the other 6 positions can be filled up with a random variation that will give us
6*5*4*3*2 = 720 variations.
Thus the required probability is:
[tex]\begin{gathered} p=\frac{720}{362880} \\ \text{Simplifying the result, we get:} \\ p=\frac{1}{504} \end{gathered}[/tex]Question 6 of 21Which of the following best describes the graph of the polynomial functiibelow?5Х-55-5-
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Solution:
The zeros of a polynomial function are the points at which the graph of the function cuts the x-axis.
Given the graph of the polynomial function as shown below:
[tex]\begin{gathered} When\text{ the curve cuts the x-axis twice, this implies that the graph has 2 zeros.} \\ When\text{ the curve cuts the x-axis once, this implies that the graph has only 1 zero.} \\ \end{gathered}[/tex]Since the curve on the graph cuts the x-axis once, it implies that the graph has one zero.
The correct option is D.
Question 41: Find the product and express it in rectangular form.
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ANSWER:
[tex]-18-18\sqrt[]{3}i[/tex]SOLUTION:
In the relationship shown by the data linear ? If so , model the data with an equation A. The relationship is not linear B. The relationship is linear; y+2=4/5 (x+9) C . The relationship is linear; y + 9 = - 4/5 (x+2) D. The relationship is linear; y+ 2 = -5/4 (x+9)
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Let's take two points so that we can get the equation of the line which goes through those points. P1 (-9, -2), P2 (3, -17):
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-17-(-2)}{3-(-9)}=\frac{-17+2}{3+9}=-\frac{15}{12}=-\frac{5}{4}[/tex][tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-2)=-\frac{5}{4}\cdot(x-(-9)) \\ y+2=-\frac{5}{4}\cdot(x+9)_{} \\ y=-\frac{5}{4}x-\frac{45}{9}-2 \\ y=-\frac{5}{4}x-7 \\ f(x)=-\frac{5}{4}x-7 \end{gathered}[/tex]So, y is the line which goes through the first and last points of the chart.
To proof that the rest of points go through the line as well, we will evalute each point
[tex]\begin{gathered} f(-5)=-\frac{5}{4}\cdot(-5)-7=\frac{25}{4}-7=-\frac{3}{4}\ne-7 \\ f(-1)=-\frac{5}{4}(-1)-7=\frac{5}{4}-7=-\frac{23}{4}\ne-12 \end{gathered}[/tex]Since the evaluation of these points don't correspond to the values of the chart we can assure that the relationship is not linear
Erika is working on solving the exponential equation 50^x = 17; however, she is not quite sure where to start. Using complete sentences, describe to Erika how to solve this equation.
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
50^x = 17
Step 02:
exponential equation:
1. Apply logarithms to both sides of the equality.
[tex]log\text{ 50}^x=\text{ log 17}[/tex]2. Apply properties of logarithms.
[tex]x\text{ log 50 = log 17}[/tex]3. Apply the algebraic rules to find the value of x.
[tex]x\text{ = }\frac{log\text{ 17}}{log\text{ 50}}\text{ }[/tex]The answer is:
x = (log 17) / (log 50)
HELPPPP MEEEEEE PLEASEEEEhey tutor how you doing doing I struggle with math so much.
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Answer:
[tex]m\measuredangle8=110^o[/tex]Explanation:
The angles 4 and 8 are equal; therefore,
[tex]m\measuredangle8=m\measuredangle4[/tex][tex]3x+20=x+80[/tex]Subtracting x from both sides gives
[tex]2x+20=80[/tex]Subtracting 20 from both sides gives
[tex]2x=80-20[/tex][tex]2x=60[/tex]Finally, dividing both sides by 2 gives
[tex]\boxed{x=30.}[/tex]With the value of x in hand, we now find the measure of angle 8.
[tex]m\measuredangle8=x+80[/tex][tex]m\measuredangle8=30+80[/tex][tex]\boxed{m\measuredangle8=110^o\text{.}}[/tex]Hence, the measure of angle 8 is 110.
complete the table using y=5x+9 (x)-1,0,1,2,3(y)
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To complete the table, plug each given x value into the equation. Then,
[tex]\begin{gathered} \text{ If x = -1} \\ y=5x+9 \\ y=5(-1)+9 \\ y=-5+9 \\ y=4 \\ \text{ So, you have the point} \\ (-1,4) \end{gathered}[/tex][tex]\begin{gathered} \text{ If x = 0} \\ y=5x+9 \\ y=5(0)+9 \\ y=0+9 \\ y=9 \\ \text{ So, you have the point} \\ (0,9) \end{gathered}[/tex][tex]\begin{gathered} \text{ If x = 1} \\ y=5x+9 \\ y=5(1)+9 \\ y=5+9 \\ y=14 \\ \text{ So, you have the point} \\ (1,14) \end{gathered}[/tex][tex]\begin{gathered} \text{ If x = 2} \\ y=5x+9 \\ y=5(2)+9 \\ y=10+9 \\ y=19 \\ \text{ So, you have the point} \\ (2,19) \end{gathered}[/tex][tex]\begin{gathered} \text{ If x = 3} \\ y=5x+9 \\ y=5(3)+9 \\ y=15+9 \\ y=24 \\ \text{ So, you have the point} \\ (3,24) \end{gathered}[/tex]Therefore, you would get the table
If y varies directly with x, and y = 12 when x = 8, write the direct linear variationequation.O y=8xO y = 12xO y=2/3xO y= 3/2 x
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A direct linear variation of y with x has the general form:
[tex]y=mx[/tex]Where m is the ratio of y to x, which is a y divided by x.
Since we know that when x equals 8, y equals 12, we can calculate m, like this:
[tex]m=\frac{y}{x}=\frac{12}{8}=\frac{6}{4}=\frac{3}{2}[/tex]Now that we know that m=3/2, the linear variation equation would be:
[tex]y=\frac{3}{2}x[/tex]
A skating rink attendant monitored the number of injuries at the rink over the past year. He tracked the ages of those injured and the kinds of skates worn during injury. In-line skates Roller skates Age 8 11 10 Age 10 4 9 Age 12 3 16 What is the probability that a randomly selected injured skater was not age 12 and was not wearing roller skates? Simplify any fractions.
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Given data:
The given table is shown.
The expression for the probability of that a randomly selected injured skater was not age 12 and was not wearing roller skates is,
[tex]undefined[/tex]15 Points and branliest for all three!
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According to SAS Congruence Theorem and the reflexive property of congruence, it can be proved that ΔSPQ ≅ ΔTPQ.
It is given to us that -
PQ bisects ∠SPT
SP ≅ TP
We have to prove that ΔSPQ ≅ ΔTPQ
Now, as PQ bisects ∠SPT,
∠SPQ = ∠TPQ
Also, according to the Reflexive Property of Congruence, PQ is a common side of both triangles - ΔSPQ and ΔTPQ.
Thus, according to SAS Congruence Theorem,
"If two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are congruent."
Therefore, according to SAS Congruence Theorem, we have proved that ΔSPQ ≅ ΔTPQ.
To learn more about SAS Congruence Theorem visit https://brainly.com/question/11804042
#SPJ1
The graph of y= 2x^2 - kx + 6 touches the x-axis. What are the possible value(s) of k?
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Given:
The graph of
[tex]y=2x^2-kx+6[/tex]Required:
What are the possible value(s) of k?
Explanation:
[tex]Set\text{ y = 0, evaluate the quadratic at }h=-\frac{b}{2a}and\text{ solve for k}[/tex]You want to find the value the value of k such that the y coordinate of the vertex is 0.
[tex]\begin{gathered} y=2x^2-kx+6 \\ 0=2x^2-kx+6 \end{gathered}[/tex]The x coordinate, h , of the vertex is found, using the following equation:
[tex]\begin{gathered} D=b^2-4ac \\ b^2-4ac=0 \\ k^2-4\times2\times6=0 \\ k^2-48=0 \\ k^2=48 \\ k=\pm4\sqrt{3} \end{gathered}[/tex]Answer:
So, values of k are above.
what is the simplified form of the expression x^2+4x-21 over 4(x+7)
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Answer:
x-3 over 4
Let me know if you need elaboration
Jennifer uses a coupon that gives you20% off your order. If the total was$18, how much money did she save?
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let M be the money, hence, she saved
[tex]\begin{gathered} (0.2)\cdot18=3.6\text{ dollars} \\ \\ \end{gathered}[/tex]What is the reason these triangles are congruent? M N Р o Not Congruent
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Since the line in red is common to both triangles and segments PM and ON are parallel, then the angles in purple are congruent and so are the angles in green. So they are congruent by ASA
how do i find out if a table is a linear function? i know the formula i just dont know how to figure out if its linear, thanks!
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Answer:
Table 3
Explanation:
A linear function has a constant slope.
To determine if the table represents a linear function, find the slope for two different pairs of points.
Table 1
Using the points (1,-2), (2,-6)
[tex]\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-6-(-2)}{2-1}=-6+2=-4[/tex]Using the points (2,-6), (3,-2)
[tex]\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-2-(-6)}{3-2}=-2+6=4[/tex]The slopes are not the same, thus, the function is not linear.
Table 3
Using the points (1,-2), (2,-10)
[tex]\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-10-(-2)}{2-1}=-10+2=-8[/tex]Using the points (2,-10), (3,-18)
[tex]\text{Slope},m=\frac{Change\text{ in y-axis}}{Change\text{ in x-axis}}=\frac{-18-(-10)}{3-2}=-18+10=-8[/tex]The slopes are the same, thus, the function is linear.
Table 3 is the correct option.
T-Mobile charges a flat fee of $20 plus $10 per Gig of data used per month. AT&T charges $60 for an unlimiteddata use. How many Gigs of data would you have to use so that the cost will be the same for both companies?
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For this case we can set uo an equation given by:
[tex]y=10x+20[/tex]Where y represent the final cost. x the number of Gig used and for this case we can set up the following equation:
[tex]60=10x+20[/tex]And solving for x we got:
[tex]x=\frac{60-20}{10}=\frac{40}{10}=4[/tex]And the final answer for this case woudl be 4 Gig of data used
of the 800 participants in a marathon, 120 are running to raise money for a cause. How many participants out of 100 are running for a cause?a.8 b. 20c. 15d. 12OMG i hate iready please heeeelp
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To find how many participants out of 100 are running for a cause we can use the next proportion:
[tex]\frac{800\text{ total participants}}{100\text{ total participants}}=\frac{120\text{ running for a cause}}{x\text{ running for a cause}}[/tex]Solving for x:
[tex]undefined[/tex]The salesperson earned a commission of $1110.20 for selling $7930 worth of paper products. Find the commission rate
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Commision = $1110.20
Selling= $7930
x is the commission rate
[tex]7930\cdot\frac{x}{100}=1110.20[/tex]Then we isolate the x
[tex]x=\frac{1110.20\cdot100}{7930}=14\text{ \%}[/tex]ANSWER
The commission rate is 14%
diana and her classmates are reading the same book.on Monday, diana started to write down the number of pages she has left to read at the end of each day from Monday through Thursday, which person is reading the same number of pages per day as diana.
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From the diana table we can conclude:
[tex]\begin{gathered} x1=187 \\ x2=181 \\ x3=175 \\ x4=169 \\ x2-x1=x4-x3=6 \end{gathered}[/tex]She's reading 6 pages per day.
Since:
[tex]\begin{gathered} y1=180 \\ y2=174 \\ y3=168 \\ y4=162 \\ y2-y1=y4-y3=6 \end{gathered}[/tex]Keith is also reading 6 pages per day.
A homeowner has decided to fill in his pool. The pool is rectangular and measures 20ft wide, 40ft long, and 5.5ft deep throughout. Each cubic yard of fill dirt cost $12. How much will it cost to fill the pool?
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The volume of the pool is
[tex]20ft\text{ }\times40ft\text{ }\times5.5ft=4400ft^3[/tex]a cubic foot is 0.037 cubic yards.
thus
[tex]4400ft^{3^{}}^{}=4400\times0.037=162.8yd^3[/tex]but a cubic yard of dirt costs $12, and we need 162.8 cubic yards.
that would cost
[tex]12\times162.8=\text{ \$1953.6}[/tex]The Dover Symphony categorizes its donors as gold, silver, or bronze depending on the amount donated.
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Explanation
Given the donors as
[tex]\begin{gathered} Gold=4 \\ silver=7 \\ Bronze=9 \end{gathered}[/tex]The total number of donors are
[tex]9+7+4=20[/tex]Therefore, the percent of donors at the bronze or silver level is
[tex]\frac{sum\text{ }of\text{ }bronze\text{ }and\text{ }silver\text{ donors}}{number\text{ of donors}}=\frac{9+7}{20}\times100=16\times5=80\text{\%}[/tex]Answer:
How do I find the area of different shapes? Is it the same exact as finding the area of a square?Please help! e.g. Trapezoid, Triangle, Octagon
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Then area of each shape can be find ina different form. Each figure have a formula to find the area.
For example
Trapezoid:
[tex]A=\frac{1}{2}(B_1+B_2)\cdot h[/tex]Where B1 is one of the bases and B2 the other base. h is the vertical height.
Triangle:
[tex]A=\frac{1}{2}(b\cdot h)[/tex]b is the base and h is the vertical height.
Regular polygon:
[tex]A=\frac{P\cdot a}{2}[/tex]P is the perimeter of the regular polygon and a is the apothem (the distance for the center of the polygon to the mind-point of a side.
Find the volume of a rectangular prism with the following dimensions.length: 4.2 cmwidth: 7 cmheight: 15 cmvolume = ____ cm3
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Given:
length: 4.2 cm
width: 7 cm
height: 15 cm
Required:
volume = ____ cm3
Explanation:
volume of prism=
[tex]\begin{gathered} l\times w\times h \\ 4.2\times7\times15 \\ =441cm^3 \end{gathered}[/tex]Required answer:
[tex]441cm^3[/tex]
Select the correct answer. What is the difference of the values of the two variables in this system of equations? y= 2x + 1 x + 3y = 10 O A. 0 B. 1 KD C. 2 KD D. 3
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According to the given data we have the following equation:
2x + 1 x + 3y = 10
There are two types of variables in the equation above.
The variable x and the variable y
In order to calculate the difference of the values of the two variables we would make the following:
First we would sum elements of variable x
variable x=2x + 1x=3x
variable y=3y
Therefore, the difference of the values=3x-3y=0
So, The right answer would be A, the value is 0.
Solve each systems of the equations by elimination. 1* x-y=-13 x+y=-52* 2x-9y=17 2x+3y=-19
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Let us solve the given system of equations by using the elimination method.
Question 1:
[tex]\begin{gathered} x-y=-13\quad eq.1 \\ x+y=-5\quad eq.2 \end{gathered}[/tex]Add these two equations so that the y variable cancels out
So, the value of x can be found now
[tex]\begin{gathered} 2x=-18 \\ x=-\frac{18}{2} \\ x=-9 \end{gathered}[/tex]Substitute the value x into any of the two equations to find the value of y.
[tex]\begin{gathered} x-y=-13 \\ -9-y=-13 \\ y=-9+13 \\ y=4 \end{gathered}[/tex]Therefore, the solution of this system is x = -9 and y = 4
can you help me solve this
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just need help with this one real quick. What do I put for B.I know the maximum value is (3,24)
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We were given:
[tex]\begin{gathered} f(x)=-3x^2+18x-3 \\ f(x)=y \\ \Rightarrow y=-3x^2+18x-3 \\ y=-3x^2+18x-3 \\ a=-3,b=18,c=-3 \end{gathered}[/tex]We will calculate the minimum point as shown below:
[tex]\begin{gathered} min=c-\frac{b^2}{4a} \\ min=-3-\frac{18^2}{4(-3)} \\ min=-3-\frac{324}{-12} \\ min=-3-(-27) \\ min=-3+27 \\ min=24 \\ \text{This is the maximum value (not minimum)} \\ x=-\frac{b}{2a} \\ x=-\frac{18}{2(-3)} \\ x=\frac{-18}{-6} \\ x=3 \\ \\ \therefore Maximum\text{ point is (3, 24)} \end{gathered}[/tex]This quadratic equation opens downward because the value of ''a'' is negative. Hence, the function only has a maximum point, it does not have a minimum point
The maximum value of the function is 24 and it occurs at x equals 3