Find the value of x.
The 7x side is half the length of the 28 side.
7x = 14
x = 2
Consider a weighted voting system with three players. If n one has veto power, and no one is a dummy., find the Banzhof power distribution.
Player 1 ____
Player 2 ____
Player 3 ____
Give each value as a fraction or decimal.
The Banzhaf power distribution value in the fraction is,
Player 1: = 0.6
Player 2: = 0.2
Player 3: = 0.2.
What is the distribution?
The mathematical expression known as a distribution function expresses the likelihood that a system would adopt a certain value or range of values. The traditional examples include games of chance.
List of winning coalitions:
1. P1, P2, P3
2. P1, P2
3. P1, P3
No. of times P1 is critical = 3 (P1 is critical all 3 times as it has veto power)
No. of times P2 is critical = 1 (in the second coalition)
No. of times P3 is critical = 1 (in the third coalition)
Total no. of critical times = 3 + 1 + 1 = 5
Banzhof Power Distribution:
Player 1: No. of times P1 is critical/Total no. of critical times
= 3/5 = 0.6
Player 2: No. of times P2 is critical/Total no. of critical times
= 1/5 = 0.2
Player 3: No. of times P3 is critical/Total no. of critical times
= 1/5 = 0.2
Hence, the Banzhaf power distribution value in the fraction is,
Player 1: = 0.6
Player 2: = 0.2
Player 3: = 0.2
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How can the logarithmic expression be written?
Select True or False for each statement.
Answer:
False, True, False-------------------------------------------
Simplify the left side and compare if the answer matches the right side.
[tex]log_3\ v-4log_3\ w=log_3\ v-log_3\ w^4 \implies False[/tex][tex]log_4\ (n\sqrt{m})= log_4\ (nm^{1/2})=log_4\ n+log_4\ m^{1/2}=log_4 n+\frac{1}{2} \ log_4 \ m\implies True[/tex][tex]log_2\ (\cfrac{cd^3}{e^4} )=log_2\ c+log_2\ d^3-log_2\ e^4=log_2\ c+3log_2\ d-4log_2\ e\implies False[/tex]
Solve each of the following equations using the Principle of Zero Products and match it to its correct pair of solutions on the
right. Each pair on the right will be used once.
(x-9)(3x + 4) = 0
(x-4) (9x + 1) = 0
(x+9)(3x-4)= 0
(x+4)(9x-1)=0
x = -4 or x =
x = -9 or x =
x = 9 or x = -
x = 4 or x=-1
Each correct pair using Principle of Zero Products are-
Part a: (x-9)(3x + 4) = 0: x = 9 or x = -4/3
Part b: (x-4) (9x + 1) = 0: x = 4 or x= -1/9
Part c: (x+9)(3x-4)= 0: x = -9 or x = 4/3
Part d: (x+4)(9x-1)=0; x = -4 or x = 1/9
Explain the term zeros of the equation?The values of x that fulfill the formula f(x) = 0 are the zeros of a polynomial. The polynomial's zeros are the x values for which the function's value, f(x), equals zero in this case.The degree of a equation f(x) = 0 determines how many zeros a polynomial has.For the stated equation-
Part a: (x-9)(3x + 4) = 0
Equating each term to zero;
(x-9) = 0
x = -9
And, (3x + 4) = 0
x = -4/3
Option: x = 9 or x = -4/3
Part b: (x-4) (9x + 1) = 0
Equating each term to zero;
(x-4) = 0
x = 4
And, (9x + 1) = 0
x = -1/9
Option; x = 4 or x= -1/9
Part c: (x+9)(3x-4)= 0
Equating each term to zero;
(x+9) = 0
x = -9
And, (3x-4) = 0
x = 4/3
Option: x = -9 or x = 4/3
Part d: (x+4)(9x-1)=0
Equating each term to zero;
(x+4) = 0
x = -4
(9x-1)
x = 1/9
Option: x = -4 or x = 1/9
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The complete question is-
Solve each of the following equations using the Principle of Zero Products and match it to its correct pair of solutions on the
right.
Each pair on the right will be used once.
(x-9)(3x + 4) = 0
(x-4) (9x + 1) = 0
(x+9)(3x-4)= 0
(x+4)(9x-1)=0
x = -4 or x = 1/9
x = -9 or x = 4/3
x = 9 or x = -4/3
x = 4 or x= -1/9
The line x - y = 5 passes through
O (0,5)
O (-5, 0)
O (0,-5)
Answer:
(0,-5)
Step-by-step explanation:
A $300 suit is marked down by 20%. Find the sales price to the nearest dollar.
Fill in the blanks
markdown = _% x $_
markdown = $_
$_ - $_
sale price = $_
markdown = 20% x $300
markdown = $60
$300 - $60
sale price = $240
Function A is represented by the equation y=2 x+5
Function B is a linear function that goes through the points shown in the table.
Which statement correctly compares the rates of change of the two functions?
Answer:
The rate of change is the same for both A and B (2)
Step-by-step explanation:
In the equation, the rate of change is shown as the coefficient of the variable x. That is the number before the x which is 2.
In the table you find the rate of change as the change in y over the change in x. In the table the y's are increasing by 4 (3- -1), 2 (5-3) and 4 (9-5). The x's are increasing by 2 (3-1), 1 (4-3) and 2 (6-4).
If I take the change in y over the change in x, I will get 4/2 = 2, 2/1 = 2 or 4/2 = 2
From the table the rate of change is also 2.
Find the greatest common factor of 10b³ and 4b.
Solution:
2b would be the greatest common factor (GCF) between both 10b^3 and 4b.
Hope this helps!
Given m || n, find the value of x.
Answer:
x = 11
Step-by-step explanation:
Since it's given n || m, we can write the following equation to find the value of x:
9x - 3 = 7x + 19 because these two are alternate exterior angles and have equal angle measurement.
transfer like terms to the same side of the equation9x - 7x = 19 + 3
add/subtract terms2x = 22
Divide both sides by 2x = 11
PLEASE ANSWER
Carter and his children went into a movie theater and he bought $33 worth of drinks and candies. Each drink costs $4.50 and each candy costs $3. He bought 3 times as many drinks as candies. Determine the number of drinks and the number of candies that Carter bought.
The number of drinks and the number of candies that Carter bought are 6 and 2 respectively.
How to determine the number of drinks and candies?In order to determine the number of drinks and the number of candies that Carter bought, we would have to write a system of linear equation and assign variables to the number of drinks and number of candies respectively, and then translate the word problem into algebraic equation as follows:
Let the x indicate the number of drinks.Let the y indicate the number of candies.Since each drink costs $4.50 and each candy costs $3 and Carter bought 3 times as many drinks as candies;
x = 3y .......equation 1.
4.50x + 3y = 33 .......equation 2.
Substituting equation 1 into equation 2, we have:
4.50(3y) + 3y = 33
13.50y + 3y = 33
16.50y = 33
y = 33/16.50
y = 2 candies.
For the value of x, we have:
x = 3(2)
x = 6 drinks.
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If V is the incenter of APQR, QT = 5, VO = 7, and PV = 29, find each measure.
Answer:
each measure 120
Step-by-step explanation:
A recipe calls for 2 cups of flour for every 1/4 cup of raisins. If 1 1/2 cups of raisins were used, how many cups of flour would be added?
The quantity of the cups of flour that would be added would be = 12 cups.
What is flour?Flour is the product of wheat grains that is commonly used for baking of dough and it measured with measuring cups or weighting scales.
According to the recipe from the given question above;
2 cups of flour = 1/4 of raisin
X cups of flour = 1½ of raisin
Make X cups of flour the subject of formula:
X cups = 2×1½ /¼
X cups = 3/¼
X cups = 3×4 = 12 cups.
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Solve for X.
(Please I need help on this problem.)
Answer:
sum of angles in a triangle is 180
it is an equilateral triangle so each angle gets 60 degrees.
6x +6 is 60
6x is 60 - 6
6x is 54
divide both sides by 2
6x/6 is 54/2
x is 9
6. A chemist needs to create 100mL of 38% acid solution. On hand she has a 20% acid solution and
a 50% acid solution. How many mL of each solution should she use?
Answer:
Step-by-step explanation:
:On hand she has a 20% acid solution and a 50% acid solution. How many ml of each solution should sheStep-by-step explanation:this is the answer
A chemist needs 40mL of 20% acidic solution and 60mL of 50% acidic solution.
What is percentage?The percentage is the ratio of number expressed as a fraction of 100.
Assume chemist needs x mL of 20% of acidic solution and y mL of 50% acidic solution.
A total of 100mL solution is to be created.
x+y=100
x=100-y
The concentration of 20% acidic solution will be 0.2x, concentration of 50% acidic solution will be 0.5x and the sum of their concentrations should be 0.38(100).
0.2x+0.5y=0.38(100)
0.2x+0.5y=38
Substitute x=100-y into the obtained equation.
0.2(100-y)+0.5y=38
20-0.2y+0.5y=38
20+0.3y=38
0.3y=18
y=18/0.3
y=60
Substitute y=60 into x=100-y.
x=100-60
=40
So, the chemist needs 40mL of 20% acidic solution and 60mL of 50% acidic solution.
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Simplify.
(-√7) (-√7)
O A. √7
B. -7
OC.
C. 7
о
O
D. 49
E. -49
K
The population of a town has been decreasing since 1991. The population of the town was 26,700 people in the year 1995. In the year 2003, the population of the town had decreased to 20,300 people.
i. Find the linear function P=m- t+b that models the town's population P as a function of the number of years, t, since 1991
ii. Find a reasonable domain for the function P
Domain:
iii. Find a reasonable range for the function P
Range:
iv. Interpret the slope of the function P
The population is Select an answer at a rate of
v. In what year will the population of the town be 14,700?
Year:
Answer:
i. P = -800t + 29900
ii. as an inequality: 0≤t≤37.375; interval notation: [0,37.375]
iii. as an inequality: 0≥P≥29900; interval notation: [0,29900]
iv. the population decreases at a rate of 1600 people every 3 years
v. 2010
Step-by-step explanation:
i. a) use the points *(4,26700) and **(12,20300) to find the slope (m)
*: the year 1995(4 years after 1991) and the population that year
**: the year 2003(12 years after 1991) and the population that year
m = (20300-26700)/(12-4) = -6400/8 = -800
b) use one of the points and m in (a) to find b
26700 = -800(4) + b
26700 = -3200 + b
29900 = b
ii. starting value for domain will be 0 since 1991 is year 0. Find the ending domain value by using P=0 and solving the equation for t:
0 = -800t + 29900
800t = 29900
t = 37.375
iii. population starts at a high of 29900 people and can't go lower than 0 people.
iv. the slope is given in (population change) / (number of years)
v. make P=14700 and solve the equation for t
14700 = -800t + 29900
800t = 15200
t = 19 (19 years after 1991)
resolve 75 = 15r. how do i resolve this
The value of r in the given expression is 5.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
We are given that the expression as;
75 = 15r
Now we need to find the value of r.
Therefore, we wil divide the 15 both side;
r = 75/ 15
r = 5
Hence, the value of r in the given expression is 5.
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15(2 x+3)+100=110-5x
30 x+45+100=110-5x
30 x+145=110-5x
35 x+145=110
35 x=-35
x=-1
Step-by-step explanation:
Reasons for each step
1. Distribute: 15(2x + 3) = 30x + 45
2. Combine Like Terms: 45+100 = 145
3. Addition Property of Equality: 30x+5x+145 = 110-5x+5x => 35x+145 = 110
4. Subtraction Property of Equality: 35x+145-145 = 110-145 => 35x = -35
5. Division Property of Equality: 35x/35 = -35/35 => x = -1
The woods behind Wendy’s house were 8 miles wide and have an area of 24 mi.² what is the length of the woods 
Answer:
48 miles
Step-by-step explanation:
i think thats it.
Answer: 4.
Step-by-step explanation: 8+8=16. count how many more until you get to 24, that is 8. Split 8 in half. We get 4.
Hope this helps!
If CB is the diamater...Find x:
Assuming [tex]\overline{BC}[/tex] is a diameter, minor arc [tex]AB[/tex] has a measure of [tex]180^{\circ}-108^{\circ}=72^{\circ}[/tex].
Using the inscribed angle theorem, [tex]36=x+3 \implies x=\boxed{33}[/tex].
The area of the smaller regular pentagon is about 27.5 cm².
What is the best approximation for the area of the larger regular pentagon?
11cm²
172 cm²
70 cm²
275 cm²
Answer:172 cm²
when we put this in the pentagon formula, and it will get 172.03, and we round it and will be 172
formula of pentagon is 1/2 × p × a
The graph shows the speed of a car while it is
slowing down to a stop.
a) Using an appropriate triangle with two of its
vertices on the curve, estimate the distance
travelled by the car during this time.
b) Is your answer an underestimate or an
overestimate?
Linear Algebra question.
Answer:
ax + y = (21, -16, 29)
Step-by-step explanation:
ax + y = [(-6a + 3), (3a - 7), (-8a + 5)]
now,
-8a + 5 = 29
a = (29 - 5)/-8
a = -3
ax + y = [(-6)(-3)+3, 3(-3)-7, 29]
ax + y = (21, -16, 29)
drew checks his pulse while exercising. he counts 25 beats in 10 seconds. at this rate how many times will his heart beat in one minute?
Answer:
Step-by-step explanation:
There are 60 Seconds in a Minute.
60/10 = 6
25 x 6 = 150 beats in one minute
Answer: 150
kara divided 560.9 by 1000 and got a quotient of 0.5609. Kevin thinks the quotient of 0.5609. Who is correct
Answer:
both are correct
Step-by-step explanation:
theyre the same answer I think the questions wrong
The diagram shows the graphs of y=x²-3x - 2 and
y = x + 3.
Use the diagram to solve the equation x² – 3x − 2 = x + 3
=
graphically.
Y
11+
10
9
8-
7-
6543
6-
5-
4-
2-
1
-8-7-6-5-4-3-2-1, 1-2-3/4-5_6_7_8
23456
-2-
-3-
-4-
-5-
-6-
-7-
-8-
-9-
--10-
-11+
x
The solution of the expression is,
⇒ x = - 1 and x = 5
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Solve the expression,
x² – 3x − 2 = x + 3
Now, We can simplify as;
x² – 3x − 2 = x + 3
x² – 3x − 2 - x - 3 = 0
x² - 4x - 5 = 0
x² - 5x + x - 5 = 0
x (x - 5) + 1(x - 5) = 0
(x + 1) (x - 5) = 0
x = - 1
x = 5
Thus, The solution of the expression is,
⇒ x = - 1 and x = 5
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Brody and Qasim are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Brody is 272 miles away from the stadium and Qasim is 320 miles away from the stadium. Brody is driving along the highway at a speed of 43 miles per hour and Qasim is driving at speed of 59 miles per hour. Let BB represent Brody's distance, in miles, away from the stadium tt hours after noon. Let QQ represent Qasim's distance, in miles, away from the stadium tt hours after noon. Write an equation for each situation, in terms of t,t, and determine the number hours after noon, t,t, when Brody and Qasim are the same distance from the stadium.
B= -43t +272 and Q=-59t+320 equations for each situation, in terms of t, and at 3 hours Brody and Qasim are the same distance from the stadium.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
At noon, Brody is 272 miles away from the stadium
B represent Brody's distance, in miles, away from the stadium tt hours after noon.
Brody is driving along the highway at a speed of 43 miles per hour
Qasim is 320 miles away from the stadium
Qasim is driving at speed of 59 miles per hour.
Q represent Qasim's distance, in miles, away from the stadium t hours after noon
B= -43t +272
Q=-59t+320
-43t+272=-59t+320
-43t+59t=320-272
16t=48
t=3
Hence, B= -43t +272 and Q=-59t+320 equations for each situation, in terms of t, and at 3 hours Brody and Qasim are the same distance from the stadium.
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PLS HURRY DUE TOMMOROW!!!
1) Farmer John has cows and chickens on his farm. His farm animals have 120 legs and 48 heads total. How many cows and how many chickens are on the farm?
a. Setup a system, of two equations, to help you solve this riddle.
b. Solve this system using either Elimination or Substitution, show your work, and state your answer as a complete sentence.
The number of cows is 12 and number of chickens are 36.
What is a system of linear equation?A "system" of equations is a set or collection of equations that you deal with all together at once.
Given that, Farmer John has cows and chickens on his farm. His farm animals have 120 legs and 48 heads total.
Let the number of chickens be x and that of cows be y,
A cow has 4 legs and that of chickens have 2,
Setting the equations, we get,
2x+4y = 120
x+2y = 60
x+y = 48
Solving the equation by elimination, we get,
2y - y = 60 - 48
y = 12
Therefore, x = 36
Hence, The number of cows is 12 and number of chickens are 36.
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Simplify the expression: -3(2x+4)-8x
Answer:
- 14x - 12
Step-by-step explanation:
- 3(2x + 4) - 8x ← distribute terms in parenthesis by - 3
= - 6x - 12 - 8x ← collect like terms
= - 14x - 12
Answer:
-14x-12
Step-by-step explanation:
1) Expand by distributing terms.
-(6x+12)-8x
2) Remove parentheses.
-6x-12-8x
3) Collect like terms.
(-6x-8x)-12
4 Simplify.
−14x−12
13/7 + 3 2/3 solve the expression