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In a board game, a certain number of points is awarded to a player upon rolling a six
sided die (labeled 1 to 6) according to the function f(x) = 2x − 1, where x is the
value rolled on the die. Find and interpret the given function values and determine an
appropriate domain for the function.
Answers
The function values are: 1, 3, 5, 7, 9, and 11. The interpretation of these function values means the number of points awarded to the player for rolling each of the possible values on the die.
The appropriate domain for the function is all possible values that can be rolled on a six-sided die.
How do you determine the function values and it's interpretation?The function f(x) = 2x - 1 assigns a certain number of points to a player based on the value rolled on a six-sided die. The possible values of x are 1, 2, 3, 4, 5, and 6. When we plug each of these values into the function, we get the following function values:
f(1) = 2 * 1 - 1 = 1
f(2) = 2 * 2 - 1 = 3
f(3) = 2 * 3 - 1 = 5
f(4) = 2 * 4 - 1 = 7
f(5) = 2 * 5 - 1 = 9
f(6) = 2 * 6 - 1 = 11
Therefore, the function values for this function are 1, 3, 5, 7, 9, and 11. These values represent the number of points awarded to the player for rolling each of the possible values on the die.
The appropriate domain for this function is all values of x between 1 and 6, inclusive. This includes all possible values that can be rolled on a six-sided die.
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Related Questions
A square room has a floor area of 81 square feet. the height of the room is 5 what is the area of one wall
Answers
Answer:
45 square feet
Step-by-step explanation:
Area of square and area of rectangle:
Area of square = 81 square feet
\(\sf \boxed{Side \ of \ square = \sqrt{area}}\)
\(\sf = \sqrt{81}\\\\ = \sqrt{9*9}\\\\ = 9 \ feet\)
height = 5 ft
length of wall = 9 ft
Area of one wall = length * height
= 9 * 5
= 45 square feet
Simita has 25 coins, consisting of 10c and 5c, which total $2.25. how many of each does she have?
Answers
Answer:
10c = 20
5c = 5
Step-by-step explanation:
Let x be the number of 10c coins; let y be the number of 5c coins. The total is $2.25, so the amount of 10c and 5c coins will add to that. Simita has 25 coins, so x and y, the number of coins, will have to add to 25. Hence, solve the simultaneous equation.
10x + 5y = 225 (1) - times by 0
x + y = 25 (2) - times by 5
10x + 5y = 225 (1)
5x + 5y = 125 (2)
Then, take equation 2 away from equation 1.
5x = 100
x = 20
Substitute x back into the original equation.
x + y = 25
20 + y = 25
y = 5
Evaluate the function, f(x) = 3x²-8
f(5x)
Answers
Answer:
\(f(x)=3x^{2} -40fx\) i think
Step-by-step explanation:
Find matrix M such that M × [3 -2 , 6 -8 ] = [-2 16]
Answers
The matrix M is: M = [2/9 -8/27 , 4/9 -8/27 ]
Let's say that M is a 2 x 2 matrix that satisfies M × [3 -2 , 6 -8 ] = [-2 16]. This means that the product of matrix M and matrix [3 -2 , 6 -8 ] will give us the result matrix [-2 16]. We know that the product of two matrices is equal to the sum of the products of their corresponding elements. We can use this knowledge to solve for the unknown elements in matrix M. Let us assume that M = [a b , c d] so that we can solve for its elements.
a(3) + b(6) = -2 ... (1) c(3) + d(6) = 16 ... (2) a(-2) + b(-8) = -2 ... (3) c(-2) + d(-8) = 16 ...
(4)Simplifying equations (1) to (4), we get:
3a + 6b = -2 ... (5) 3c + 6d = 16 ... (6) -2a - 8b = -2 ... (7) -2c - 8d = 16 ... (8)
Solving for a, b, c, and d, we get:a = 2/9 b = -8/27 c = 4/9 d = -8/27.
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Problem 7Letq=a/b and r=c/d be two rational numbers written in lowest terms. Let s=q+r and s=e/f be written in lowest terms. Assume that s is not 0.Prove or disprove the following two statements.a. If b and d are odd, then f is odd.b. If b and d are even, then f is evenPlease write neatly. NOCURSIVE OR SCRIBBLES
Answers
We have proved that if b and d are odd, then f is odd, but the statement that if b and d are even, then f is even is false.
a. If b and d are odd, then f is odd.
Proof:
Since q and r are written in lowest terms, a and b are coprime, and c and d are coprime. Therefore, we have:
ad - bc = 1 (by the definition of lowest terms)
Multiplying both sides by bf, we get:
adf - bcf = f
Similarly, we have:
bf = bd (since b and d are coprime)
df = bd (since s=q+r=a/b+c/d=(ad+bc)/(bd))
Substituting these values in the previous equation, we get:
adf - (s-b)bd = f
adf - sbd + b^2d = f
Since b and d are odd, b²d is odd as well. Therefore, f is odd if and only if adf - sbd is odd. But adf - sbd is the product of three odd numbers (since a, b, c, and d are all odd), which is odd. Therefore, f is odd.
b. If b and d are even, then f is even.
Counterexample:
Let q = 1/2 and r = 1/2. Then s = 1, which can be written as e/f for any odd f. For example, if f = 3, then e = 3 and s = 1/2 + 1/2 = 3/6, which is written in lowest terms as 1/2. Therefore, the statement is false.
Thus, we have proved that if b and d are odd, then f is odd, but the statement that if b and d are even, then f is even is false.
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PLEASE HELP ILL GIVE BRAINLIEST
Answers
Answer:
Um I'm just guessing
Step-by-step explanation:
2)congruent
3)noncongruent
4)noncongruent
5)noncongruent
6)congruent
7)noncongruent
8)noncongruent
9)noncongruent
10)congruent
my answers might have a high chance it is incorrect but maybe this might still help give a hint or small step on solving the problem?
a binding less than or equal to (≤) constraint in a maximization problem meansa. the variable is up against an upper limit. b. the minimum requirement for the constraint has just been met. c. another constraint is limiting the solution. d. the shadow price for the constraint will be positive.
Answers
The variable is up against an upper limit. in a maximization problem, a binding less than or equal to (≤)
constraint indicates that the variable associated with the constraint has reached or is at its upper limit. It implies that the variable cannot increase further without violating the constraint.
This constraint acts as a restriction that limits the potential values the variable can take in the optimization problem.
When a constraint is binding, it means that the optimal solution to the problem is achieved when the constraint is satisfied with equality. In the context of a maximization problem,
if a variable is up against an upper limit and the constraint is binding, it suggests that the variable is already maximizing its value within the given constraint.
In contrast, if the constraint is not binding, it means that the variable has not reached its upper limit and has the potential to increase further while still satisfying the constraint. In such cases, the variable can be increased to improve the objective function value and optimize the problem further.
It's important to note that the shadow price, also known as the dual value or marginal value, represents the rate of change of the objective function with respect to a constraint. It indicates the sensitivity of the objective function to changes in the constraint.
The sign of the shadow price is not determined by the direction of the constraint (≤ or ≥), but rather by the problem formulation and the specific constraints and variables involved.
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Please help me on this
Answers
Answer:
4
Step-by-step explanation:
16/4
You have 3 door of equal size to case, it take 2 pieces at 84" and 1 piece at 36" to case a door how many feet of casing do you need to complete the job?
Answers
Given data: The size of the door = 3 (equal size).The amount of casing needed to case a single door is given as 2 pieces at 84" and 1 piece at 36".calculate the amount of casing needed to complete the job,
first, we need to find out the length of casing required for a single door. Therefore, Length of casing required for a single door = 2 pieces at 84" + 1 piece at 36"= (2 x 84) + 36= 168 + 36= 204 inches Now, we need to convert inches to feet.1 inch = 1/12 feet So, 204 inches = 204/12 feet= 17 feet (approx.)Therefore, the amount of casing needed to case three doors = 3 doors x 17 feet per door= 51 feet Hence, 51 feet of casing is needed to complete the job.
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solve the system of equations algebraically -5x+2y=4 2x+3y=6
Answers
(2x+3y=6).5
-10x+4y=8
10x+15y=30
[10x+(-10x)]+[15y+4y]=[30+8]
19y=38
y=38/19
y=2
2x+3y=6
2x+3(2)=6
2x=6-6=0
x=0
Step-by-step explanation:
-5x+2y= 4 <==== Multiply entire equation by -3 to get:
15x-6y = -12
2x+3y= 6 <==== Multiply entire equation by 2 to get :
4x+6y = 12 Add the two underlined equations to eliminate 'y'
19x = 0 so x = 0
sub in x = 0 into any of the equations to find: y = 2
(0,2)
5
math geniuses help please!!
math
Answers
Answer:
A
Step-by-step explanation:
5pi/4 is in Q III so BOTH rectangular coordinates will be NEGATIVE
x = 4 cos (5pi/4) y = 4sin (5pi/4)
x = -4 sqrt (2)/2 y = - 4 sqrt (2) /2
x = - 2 sqrt 2 y = -2 sqrt 2
A big school bus was 2/7 full when it left Area A. When it arrived at Area B, 9 children alighted the bus and there were 31 children on the bus after that. How many children can fit into the big school bus?
Answers
The total capacity of the big school bus is 140 children.
To find out how many children can fit into the big school bus, let's work through the given information step by step.
When the bus left Area A, it was 2/7 full. This means that 2/7 of the bus's capacity was occupied by children. Let's represent the total capacity of the bus as 'x'. Therefore, 2/7 of 'x' corresponds to the number of children on the bus when it left Area A.
After the bus arrived at Area B, 9 children alighted, which means the number of children decreased by 9. We are then told that there were 31 children remaining on the bus. So, the number of children on the bus before any alighted was 31 + 9 = 40.
Since 2/7 of the bus's capacity was occupied by children when it left Area A, we can set up the following equation:
(2/7) * x = 40
To solve for 'x', we can multiply both sides of the equation by (7/2):
x = 40 * (7/2)
x = 140
Therefore, the total capacity of the big school bus is 140 children.
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What is the measure of each interior angle of the regular polygon pictured below? If
necessary, round to the nearest tenth.
Answers
Answer:
Step-by-step explanation:
it has 14 sides
360/14= 25.714
rounding to the nearest tenth we get:
25.7
who has a better chance of winning the super bowl 2023
Answers
The Kansas City Chiefs has a better chance of winning the super bowl 2023.
In 1967's Super Bowl I, Las Vegas sportsbooks gave the Green Bay Packers a 14-point advantage against the Kansas City Chiefs. Nevada was the only state up until 2018 to allow legal Super Bowl sports betting.
The reigning champion Kansas City Chiefs are the early favorited in the Super Bowl 58 odds, according to the top NFL betting companies. At BetMGM, the Super Bowl 58 odds for the Kansas City Chiefs are +600. You can evaluate the odds on a team you prefer to discover the best price because competing sportsbooks provide different odds for each team to win the Super Bowl.
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what is 5.589 x 10^6 writen in standard form
Answers
Answer:
5,589,000
Step-by-step explanation:
D A B Which expression can be used to calculate 15% of 3500? 2 A. B. C. D. 31 2 15 2 x 35 ×3500 31 100 2 16 7000 7000
Answers
The correct expression can be used to calculate 15% of 3500 is,
⇒ 15/100 × 3500
Given that;
The expression is,
⇒ 15% of 3500
Now, We can simplify as;
⇒ 15% of 3500
⇒ 15/100 × 3500
⇒ 15 × 35
⇒ 525
Thus, The correct expression can be used to calculate 15% of 3500 is,
⇒ 15/100 × 3500
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Please help
**IMAGE BELOW**
Answers
Answer:
B
Step-by-step explanation:
the plus 8 is the y intercept because its a whole number and its not attached to a variable
Kate places greeting cards from two different companies on a display rack that can hold up to 90 cards. She
has agreed to display at least 40 of company a's cards on the rack and at least 25 of company b's cards.
kate makes a profit of $0. 30 on each card she sells from company a and $0. 32 on each card she sells from
company b.
Answers
To get the maximum profit, Kate should display as many cards from company B as possible, since she makes a higher profit from those cards.
Let x be the number of cards from company A and y be the number of cards from company B.
The constraints are:
x + y ≤ 90 (the display rack can hold up to 90 cards) x ≥ 40 (at least 40 of company A's cards must be displayed) y ≥ 25 (at least 25 of company B's cards must be displayed)The objective function is:
P = 0.30x + 0.32y (the profit from selling the cards)
To maximize the profit, we need to maximize the value of y. Since the display rack can hold up to 90 cards, we can set y = 90 - x.
Substituting this into the objective function:
P = 0.30x + 0.32(90 - x)
P = 0.30x + 28.8 - 0.32x
P = -0.02x + 28.8
To maximize P, we need to minimize x. Since x must be at least 40, we can set x = 40.
Substituting this back into the objective function:
P = -0.02(40) + 28.8
P = 28
So the maximum profit Kate can make is $28, by displaying 40 cards from company A and 50 cards from company B.
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A square and a triangle have equal perimeters. The lengths of the three sides of the triangle are 6.1 cm, 8.2 cm and 9.7 cm. What is the area of the square in square centimeters?
Answers
Answer:
Area of the square: 36
Step-by-step explanation:
6.1+8.2+9.7=24. Squares have 4 sides so 24/4=6. Area= base times highet, Base=6 Highet=6. 6 times 6=36!
Answer:
A=36 cm²
Step-by-step explanation:
the perimeter of triangle=a+b+c
P=6.1+8.2+9.7
P= 24 cm
P of triangle = P of square ( square has 4 equal sides):
24=4a
a=24/4=6
Area of square : a²
A=6² = 36 cm²
h(x) = 2x + 5
g(x) = 3x + 2
Find h(x) · g(x)
A) 6x² - 19x + 10
C) 5x + 3x³ + 15x² + 15x
B) 6x² + 19x + 10
D) -6x³x² + 6x
Answers
Answer:
B
Step-by-step explanation:
(hx)(gx)
(2x+5)(3x+2)
6\(x^{2}\)+4x+15x+10
6\(x^{2}\)+19x+10
Answer B
408 x 291 show work pls
Answers
Answer: 118728
Step-by-step explanation:
You can just simply find this answer using a calculator.
work shown in picture
What happens when a triangle is dilated using one of the vertices as the center of the dilation? Complete
the explanation.
The sides of the triangles adjacent to the center of dilation will be collinear. The third sides of the pre-
image and image will be ?
The vertex used as the center of dilation will be in
Answers
Answer:
The sides of the triangles adjacent to the center of dilation will be collinear. The third sides of the pre-
image and image will be “parallel”
The vertex used as the center of dilation will be in “the same location in both triangles”
I need help!!! Thank you
Answers
Answer:
i think 32. because have 5 slot and 40 division 5 equal 8. us have 4 slot no réd color
A store has been selling a certain TV for $210. If the store raised the price by 5% (of the original
price), what would be the new price?
Answers
Answer:
Step-by-step explanation:
Selling price = $210
percentage increase = 5 %
Increased amount = 5% of 210
= 0.05 * 210
= $ 10.5
New selling price = 210 + 10.5 = $ 220.50
If the area of a circle is 144pi square meters, what is the area of the sector for 80 degrees of the circle, rounded to the nearest hundredth?
Answers
Answer:
32pi
Step-by-step explanation:
help please!! where do the points go?
Answers
Answer:
See below.
Step-by-step explanation:
You can graph by finding ordered pairs for each function.
Which expression represents the greatest common factor (GCF) of 48 and 136?A.2 x 2B.2 x 2 x 2C.2 x 2 x 2 x 3D.2 x 2 x 2 x 3 x 17
can someone pls help me
Answers
Find the greatest common factor of both 48 and 136:
GCF is 8.
The expression that equals 8 is
B. 2x2x2
Answer:
B. 2 x 2 x 2
Step-by-step explanation:
I took a quiz and got this right!!
helppp plss i don’t understand this at all
Answers
Answer:
Look at explanation
Step-by-step explanation:
Well according to the picture (it doesn't have the full problem so this is what I can explain):
To make 1 dozen cupcakes (x), you need 1 cup of butter (y). (Or you can see in the question on the picture: y = 0.5x)
So let's say, he wants to make half a dozen cupcakes, he would need 0.5 cups of butter. How many cups of butter he uses is how many dozens he can make.
Hopefully this helps :3 sorry if wrong :( plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3
-Bee~
what is the approximate side length of a square game board with and area of 188 in. squared.
Answers
Answer:
Side length of a square game board is
11.916
inches.
Explanation:
If the area is
142
∈
2
, as area is square of side length of a square,
Side length is
√
142
=
11.916
inches.
Step-by-step explanation:
Answer:
13.7 inches
Step-by-step explanation
Area = base*height
(since it's a square, the lengths of all four sides of the board are equal. therefore, we can write the equation above like the following)
Area of square = side length^2
(square root both sides of the equation, and you get the following)
\(\sqrt{Area\\}\) = side length
(now, substitute the info)
\(\sqrt{188\\}\) = x
(solve)
x = 13.7 inches
What is the value of X
Answers
Answer:
The Value of X in 2nd one can be 14√3.
The Value of X in 1st one can be 6√3.
Step-by-step explanation:
2.)here we used tan 60° formula with P/B as x/14 respectively.
as the value of tan 60° is √3, we got,
√3= x/14
x= 14√3.
1.) Here we used sin 30° formula with 1/√2 as P/H
so we got,
6/x= 1/√2
hence the answer comes:-
x= 6√2..
Hope so it helped you........
Something and 14√3.
Steps
The person above me has calculated something.
The way to get 14√3 can be seen in the image above.
