The board in shape of rectangle must be at least 6.4 feet.
What is a rectangle?
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees. The two sides at each corner or vertex, meet at right angles. The opposite sides of the rectangle are equal in length which makes it different from a square.
For example, if one side of a rectangle is 20 cm, then the side opposite to it is also 20 cm.
A rectangle has two diagonals, that bisects each other. Both the diagonals are equal in length.
Perimeter, P = 2 (Length + Width)
Area of Rectangle=Length*Breadth
Now,
Given length of board they want to cut=1 3/5 feet=8/5 feet.
No. of board they want to cut=4
so, length of rectangular board must be at least=4*8/5 feet
=32/5=6.4 feet
Hence,
The board in shape of rectangle must be at least 6.4 feet.
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In Exercises 1-4, determine if the system has a nontrivial solution. Try to use as few row operations as possible. (1). 2 x1 - 5 x2 + 8 x3 = 0 -2 x1 - 7 x2 + x3 = 0 4 x1 - 2 x2 + 7 x3 = 0 (2). x1- 3 x2 + 7 x3 = 0 -2 x1 - x2 + 4 x3 = 0 x1 - 2 x2 + 9 x3 = 0 (3). -3 x1 - 5 x2 + 7 x3 = 0 -6 x1 - 7 x2 + x3 = 0 (4). -5 x1 - 7 x2 + 9 x3 = 0 x1 - 2 x2 + 6 x3 = 0
(1). 2 x1 - 5 x2 + 8 x3 = 0
-2 x1 - 7 x2 + x3 = 0
4 x1 - 2 x2 + 7 x3 = 0
Add the first and second equation:
0 x1 - 12 x2 + 9 x3 = 0
Add the third equation:
4 x1 - 2 x2 + 7 x3 = 0
So, the system has a nontrivial solution because the last equation is not the trivial solution.
(2). x1- 3 x2 + 7 x3 = 0
-2 x1 - x2 + 4 x3 = 0
x1 - 2 x2 + 9 x3 = 0
Add the first and second equation:
-x1 - 4 x2 + 11 x3 = 0
Add the third equation:
0 x1 - 6 x2 + 16 x3 = 0
So, the system has a nontrivial solution because the last equation is not the trivial solution.
(3). -3 x1 - 5 x2 + 7 x3 = 0
-6 x1 - 7 x2 + x3 = 0
Add the first and second equation:
-9 x1 - 12 x2 + 8 x3 = 0
So, the system has a nontrivial solution because the last equation is not the trivial solution.
(4). -5 x1 - 7 x2 + 9 x3 = 0
x1 - 2 x2 + 6 x3 = 0
Add the two equations:
-4 x1 - 5 x2 + 15 x3 = 0
So, the system has a nontrivial solution because the last equation is not the trivial solution.
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{100 points} Shown is the graph of a force function (in newtons) that increases to its maximum value and then remains constant. How much work W is done by the force in moving an object a distance of 8 m?
W = _______ J
The work done by the force in moving an object a distance of 8 m is; 144 J
How to solve a Force Distance Graph?A force-displacement graph will have force (in N) on the vertical axis and displacement (in m) on the horizontal axis. The area of the graph is = Fs. This quantity represents the work done on the object.
The area of the given graph is gotten by using the area of a trapezium which is;
Area = ¹/₂(sum of parallel sides) * height
Plugging in the relevant values gives;
Area = ¹/₂(8 + 4) * 24
Area = 144 J
This area represents the work done
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jill wants to make a blend of mango and papaya juices and store it in a container that can hold no more than a total of 32 ounces. if m represents the number of ounces of mango juice in the blend and p represents the number of ounces of papaya juice in the blend, which of the following inequalities represents this scenario? A m - p< 32 m - p2 32 C m+p<32 D m+p2 32
jill wants to make a blend of mango and papaya juices and store it in a container that can hold no more than a total of 32 ounces. So, m + p ≤ 32 inequalities represents this scenario.
What is an inequality?A relationship that compares two numbers or even other mathematical expressions in an unequal way is known as an inequality in mathematics. The majority of the time, size comparisons between two numbers on the number line are made. Less than, larger than, less than or equal to, and more than or equal to are the four fundamental inequalities. A mathematical connection between two expressions is known as an inequality, and it is shown using one of the following: "≤" , "≥" , "<" and ">".
Given that,
Number of mango = m
Number of papaya = p
The limit of juices should be less than or equal to 32 ounces
Thus, the sum of mass of mangoes and papaya should be less than or equal to 32 ounces.
So, m + p ≤ 32
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The complete question is as follows:
PLEASE ANSWER
The perimeter of the rectangle below is 120 units. Find the length of side VY .
Write your answer without variables.
The length of side VY is 25.
What is a regular figure and its perimeter?A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).
Suppose that length of each side of that figure be of u units, then we have the perimeter as:
P=u+u+...+u (n times) = n xu
units.
Given;
The perimeter of the rectangle below is 120 units
The two sides of rectangle are 2y+3 and3y+2
Now,
2l+2b=120
2(2y+3)+2(3y+2)=120
4y+6+6y+4=120
10y+10=120
y+1=12
y=11
VY=2y+3
VY=2*11+3
VY=25
Therefore, the length according to given perimeter will be 25units.
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Calculate the average speed of a cyclist who travels 30 km in 3 hr
Given:-
[tex] \rm{Distance= \bold{ 30km}}[/tex][tex] \: [/tex]
[tex] \rm{Time = \bold{3hr}}[/tex][tex] \: [/tex]
To Find:-
[tex] \rm{Speed \: of \: a \: cyclist = ?}[/tex][tex] \: [/tex]
By using formula:-
[tex] \boxed{ \bold{ \rm{ \color{skyblue}Speed = \frac{Distance}{Time} }}}[/tex][tex] \: [/tex]
Solution:-
[tex] \rm{Speed = \frac{Distance}{time} }\\ = \rm{\cancel\frac{30}{3}} \\ \: \:\: \: \: \: \: \: \: \underline {\boxed{\rm \red{= 10km/hr}}}[/tex]
[tex] \: [/tex]
hope it helps!:)
The average speed of the cyclist is 10 km/hr.
What is Average speed?Average speed is defined as the ratio of the total distance traveled by a body to the total time taken for the body to reach its destination.
As per the question,
Given that the distance is 30 km and the time is 3 hours.
To calculate the average speed of a cyclist, we can use the formula:
average speed = distance/time
Substitute the given values in the above formula,
average speed = 30 km / 3 hr
average speed = 10 km/hr
Therefore, the average speed of the cyclist is 10 km/hr.
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Question content area top
Part 1
A car moving at a constant speed passed a timing device at tequals
0.
After 9
seconds, the car has traveled 828
ft. Write a linear function rule to model the distance in feet d the car has traveled any number of seconds t after passing the timing device.
Then the linear function rule to model the distance the car has traveled in any number of seconds will be d = 92t.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.
We know that the speed formula
Speed = Distance/Times
s = d/t
d = st
The value of 's' is given as,
s = 828 / 9
s = 92 feet per second
Then the linear function rule to model the distance the car has traveled in any number of seconds will be d = 92t.
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The perimeter of a rectangle window is 352 cm. If the length of the window is 95 cm, what is its width? ADD WORK/STEPS!!
The width of the rectangle is 81 cm.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Perimeter = 352 cm
Length = 95 cm
Width = W
Now,
Perimeter = 2 (Length + Width)
352 = 2 (95 + W)
176 = 95 + W
W = 176 - 95
W = 81 cm
Thus,
The width is 81 cm.
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qualitive or quantitive .tHE NUMBER OF CARS SOLD by a car dealer last month
A video game system and several games are sold for $668. The cost of the games is 3 times as much as the cost of the system. Find the cost of the
system and the cost of the games.
Cost of the video game system:
URGENT
the cost of the system and the cost of the games is: $501. This can be solved using the concept of equation.
What is an equation?The connection between the two expressions on each side of the sign is represented by a mathematical equation. One variable and an equal sign are often present.
The total cost of the video game system and the several game = $668
Let, the cost of several game = x and
The cost of video game system = 3x
To find the cost of the system and the games
According to the problem,
or, x + 3x = 668
or, 4x = 668
or, x = $167
Hence, the cost of several game = $167 and
The cost of video game system = $3 × 167 = $501
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Question 3 Mutiple Choice Worth 4 points)
(05.02 MC)
Two families went to a baseball game. The first family bought 3 pretzels and 5 sodas, which totaled $23. The second family bought 4 pretzels and 6 sodas, which totaled $28. How much did one soda cost?
O $3
O$4
O $5
O $6
Answer:
B) $4--------------------------------
Let the cost of a pretzel be p and cost of a soda be s.
The first family bought 3 pretzels and 5 sodas, which totaled $23:
3p + 5s = 23The second family bought 4 pretzels and 6 sodas, which totaled $28:
4p + 6s = 28Divide the second equation by 4 to get:
p + 1.5s = 7p = 7 - 1.5sSubstitute this into first equation and solve for s:
3(7 - 1.5s) + 5s = 2321 - 4.5s + 5s = 230.5s = 23 - 210.5s = 2s = 2/0.5s = 4Cost of a soda is $4, this is option B.
Answer:
B is the answer
Step-by-step explanation:
I took the test and I got 100 percent.
Solve the given initial-value problem. dy + 2(t + 1)y2 = 0, y(0) dt 1 15 1 y(t) = 2 + 2t + 15 x Give the largest interval I on which the solution is defined. (Enter your answer using interval notation.)
The Largest interval in which the solution of the differential equation is defined is (-5, 3).
dy/dt + 2(t + 1)y² = 0 and y(0) = -1/15
Now, dy/dt + 2(t + 1)y² = 0
dy/dt = -2(t + 1)y²
By separating variables
dy/y² = -2(t + 1) dt
Integrating both sides
∫dy/y² = -∫(t + 1) dt
-1/y = -(t²+2t) + c
y(t) = /(t²+2t - c)
We know, y(0) = -1/15
So, -1/15 = 1/(0+0-c)
c = 15
∴ y(t) = 1/(t² + 2t - 15)
Now, y(t) is defined if t² + 2t - 15 ≠ 0
Let t² + 5t - 3t - 15 = 0
(t + 5)(t - 3) = 0
t = -5, 3
So, the intervals are (-∞ , -5), (-5, 3) and (3, ∞)
As t = 0 lies in between (-5, 3) hence the interval in which the solution is defined is (-5, 3)
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What is the solution to the square root equation?
x+3 = √2x−1 +5
Answer: x - √2x = 1
Step-by-step explanation:
Simple Question what is 100 plus 100
Answer: 200 because 100 plus 100 equal 200
In radiation protection, which of the following is a measure of the probabilistic health effect on an individual as a result of an intake of radioactive material into the body?
A. TEDE
B. Gyt
C. Gya
D. CEDE
The correct answer is A. TEDE, which stands for Total Effective Dose Equivalent.
This is a measure of the effective dose equivalent to an individual resulting from an intake of radioactive material. It takes into account the type of material ingested and the radiation dose received.
It takes into account the type of material ingested and the radiation dose received. TEDE is generally used in radiation protection to estimate the probabilistic health effect on an individual as a result of an intake of radioactive material.
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when drawn on a coordinate plane with the x-axis as the baseline, a wave with a crest that is closer to the baseline has a smaller .(1 point) responses. true or false
When drawn on a coordinate plane with the x-axis as the baseline, a wave with a crest that is closer to the baseline has a smaller
The above statement is false.
The origin, or the point where the x- and y-axes connect, is where both the x and y coordinates are zero (0, 0).
The point is located on the 2D coordinate plane in one of its four quadrants if both the x and y values are non-zero.
The intersection of two number lines creates a two-dimensional plane known as a coordinate plane. The x-axis, a horizontal number line, and the y-axis, a vertical number line, are two examples of these number lines.
A graph having one x-axis and one y-axis is referred to as a cartesian plane (also known as an X-Y graph). The orientation of these two axes is perpendicular. The graph's exact centre is marked by the origin (O).
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Can someone help me please
I have to do this maze for Geometry and it’s due tomorrow.
X has to equal 11 and all I have to work with is “the measure of angle 2 = 3x+5” and a random 64.
These are isosceles triangles. I don’t understand.
Help :’)
The measure of angle 2 is 38° and the value of x is 11
How to find the measure of angle 2?Geometry is a branch of mathematics concerned with the study of space, shapes, sizes, and positions of objects. It covers topics such as points, lines, angles, surfaces, and solids.
Check the attached image for labelling. From the figure:
u = 64° (base angles of an isosceles triangle are equal)
t = 180 - 64 - 64 = 52° (Sum of angles in a triangle)
y = 90 - t
y = 90 -52 = 38°
y = m∠2 (base angles of an isosceles triangle are equal)
m∠2 = 38°
m∠2 = 3x + 5
3x + 5 = 38°
3x = 38 - 5
3x = 33
x = 33/3
x = 11
Therefore, the value of x is 11
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Draw a rough sketch of the function (x-1)(x+2)(x+5)
Answer:
Step-by-step explanation:
Zeroes of a Function:The main idea you need to understand here is multiplicity, zeroes, and end behavior.
If a function has an odd degree that means that the end behaviors will be opposite so if on the right side the polynomial is going up, then on then on the left side it's going down and vice versa.
As for multiplicity, if the multiplicity or exponent of a zero is odd then it crosses the x-axis otherwise it has a turning point meaning it touches the x-axis and just turns around.
The last thing to understand is if the polynomial has a positive leading coefficient then the graph will be going up on the right side otherwise it will be going down.
We're given the function: f(x) = (x-1)(x+2)(x+5) and if you set each factor equal to zero, you can solve for the zeroes getting: x = 1, --2, and -5 as zeroes. Since the coefficients inside the factors are all positive when we multiply this out, we would get a positive leading coefficient and since the exponent of them is all one, the degree would be 3 when multiplying out the 3 binomials.
So on the right side it's going up, the left side it's going down (since odd degree) and at each zero it crosses the x-axis since they all have an odd multiplicity. This allows us to draw a rough sketch which I have provided using paint.,
7. A system of linear equations with fewer equations than unknowns is sometimes called an underdetermined system. Can such a system have a unique solution? Explain. Choices: a. No, it cannot have a unique solution. Because there are more variables than equations, there must be at least one free variable. If there is a free variable, the solution set contains a unique solution. b. No, it cannot have a unique solution. Because there are more variables than equations, there must be at least one free variable. If the linear system is consistent and there is at least one free variable, the solution set contains infinitely many solutions. If the linear system is inconsistent, there is no solution. c. Yes, it can have a unique solution. Because there are more equations than variables, there are no free variables. If the system is consistent and there are no free variables, the solution set contains a unique solution. If the system is inconsistent, there is no solution. d. Yes, it can have a unique solution. Because there are more variables than equations, there must be at least one free variable. If the linear system is consistent and there is at least one free variable, the solution set contains either a unique solution or infinitely many solutions. If the linear system is inconsistent, there is no solution.
The correct answer is b. No, it cannot have a unique solution. Because there are more variables than equations, there must be at least one free variable. If the linear system is consistent and there is at least one free variable, the solution set contains infinitely many solutions. If the linear system is inconsistent, there is no solution.
A linear system is a set of linear equations that can be expressed in the form Ax = b, where A is a matrix of coefficients, x is a vector of unknowns, and b is a vector of constants. Linear systems can be solved using a variety of methods, such as matrix inversion, Gaussian elimination, or the LU decomposition. In addition, linear systems can be used to model a variety of real-world problems, such as linear programming, optimization problems, and electrical networks.
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PLEASE ANSWER
Value Rent-A-Car rents a luxury car at a daily rate of $37.33 plus 25 cents per mile. A business person is allotted $110 for car rental each day. How many miles can the business person travel on the $110?
Answer:
290.68 miles
Step-by-step explanation:
fixed rate 37.33 per day
mileage 0.25 per miles
allowance 110 per day
how many miles = x
110 = 37.33+0.25x
0.25x =110-37.33 = 290.68 miles
Help Please I have 7 of these to do within 30 minutes and i dont get them
Answer:
angle JKL is 22°
Step-by-step explanation:
You want the measure of exterior angle JKL represented by (5x-3)°, given that the remote interior angles of ∆IJK are I = (2x +8)° and J = (x -1)°.
Exterior angleThe exterior angle is equal to the sum of the remote interior angles:
angle JKL = angle I + angle J
5x -3 = (2x +8) +(x -1)
5x -3 = 3x +7 . . . . . . . . . simplify
2x = 10 . . . . . . . . . . . add 3-3x
x = 5 . . . . . . . divide by 2
5x -3 = 5(5) -3 = 22 . . . . . degrees
Angle JKL is 22 degrees.
__
Additional comment
It is helpful to draw a figure. The attached figure is not to scale, but the angle measures are appropriately labeled.
The unlabeled interior angle at K is supplementary to the labeled exterior angle there. That same interior angle is also supplementary to the sum of the other two interior angles, since the sum of all the angles is 180°. Two angles supplementary to the same angle are congruent. This means the exterior angle JKL is congruent to the sum of the two marked interior angles. It's a simple relation, easy to derive, and useful to remember.
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A party planner organized a dinner party. The party planner recorded the height of the candlesticks over time and graphed the relationship.
graph with the x axis labeled time in hours and the y axis labeled height of candlestick in inches and a line going from the point 0 comma 9 through the point 3 comma 7
Find and interpret the slope and y-intercept in this real-world situation.
The slope is negative two thirds, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases two thirds of an inch every hour.
The slope is negative three halves, and the y-intercept is 9. The candle starts at a height of 9 inches and decreases three halves of an inch every hour.
The slope is 9, and the y-intercept is negative two thirds. The candle starts at a height of two thirds of an inch and decreases 9 inches every hour.
The slope is 9, and the y-intercept is negative three halves. The candle starts at a height of three halves of an inch and decreases 9 inches every hour.
The y-intercept is at (27/2 ,9) in the Slope Intercept Form .
What is a line's Slope Intercept Form?
A line with m as its slope, m as its y-intercept, and c as its coefficient makes up the graph of the linear equation y = mx + c. The values of m and c in this version of the linear equation known as the slope-intercept form are real numbers.
The graph of the line passes through (0,9) and (3,7) .
Slope of the line = (7 - 9)÷(3 - 0) = -2/3
Hence the line will have the equation:
y - 9 = -2/3 ( x - 0 )
or, y - 9 = -2x/3
or, 3y - 27 = -2x
2x + 3y = 27
Now from the real world situation at y = 0, x = 27/2
and at x = 0, y = 9
Hence the y-intercept is at (27/2 ,9)
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8. Teuscher is one of the best chocolates in the world with a cost of $8 per gram. Saffron is a spice
used for flavoring and coloring foods and costs $14 per gram. A party planner for a celebrity event
wants to include no more than 8 grams (g) of Teuscher Chocolate and Saffron in a gift bag. She has
to keep the cost to less than $42.
The cost of 8 grams of Teuscher Chocolate is 8 x $8 = $64. The cost of 8 grams of Saffron is 8 x $14 = $112. Therefore, the total cost of the two items combined is $64 + $112 = $176.
What is the cost ?The cost of a 100-word answer depends on what type of service or product you are requesting. If you need a professional writing service, the cost will vary depending on the complexity of the answer and the quality of the writing. If you are looking for a plagiarism-free answer, the cost will also depend on the source of the answer, as well as the complexity, length, and research involved.
Since this exceeds the $42 budget, the party planner cannot include more than 8 grams of Teuscher Chocolate and Saffron in the gift bag.
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need halp with 6 & 7
The value of x is 26 and TanΘ is equals to 10 / 24
What is triangle ?
Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.
From the given triangle,
We can say that ,
Hypothenuse ^2 = base^2 + opposite^2
let the hypothenuse of given triangle be x
so,
x^2 = 10 ^2 + ^2
x ^2 = 100 + 576
x^2 = 676
x = 26
SO,
TanΘ = 10 / 24
TanΘ = 5/12
TanΘ = 0.4169
Therefore, The value of x is 26 and TanΘ = 10 / 24
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What is the value of the expression below when w = 6?
Answer:
7w+6
Submit Answer
the value of expression is 48 at w = 6.
What is an expression?Expression in math's is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given, an expression 7w + 6,
Since the value of w is given 6
Thus,
The value of Expression = 7 * 6 + 6
The value of Expression = 48
Therefore, the value of expression is 48 at w = 6.
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Which of the following is a factor of 9x^2+21+10
Answer: 3x+5
Step-by-step explanation:
trust me i had that question for home work
There are only 7 days left until the launch of our new product and we only have $668.00 left in our promotion budget. We need to spend $85.00 o the last day. Can you calculate how many dollars a day we can spend on the remaining days.
The number of dollars each day we can spend in the remaining days is, $97
What is division?Division is a mathematical operation, in which we distribute the number in equal parts, the number on the upper side is the total quantity and the number on the bottom side is equal parts of numbers which have to be distributed.
We denote division by '÷' this symbol.
Given that,
Amount left in promotion budget = $668.00
Amount we need to spend on the last day = $85.00
The number of dollars in can spend each day = ?
Total amount can spend in remaining days = $668.00 - $85.00
= $583
Each day can spend = 583/6
= 97
Hence, the number of dollars can spend each day, $97
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A store surveyed their customers to find out their ages. The bar graph below shows the number of customers in each age group
What percent of customers surveyed were 18-24? Round your answer to one decimal place
The percentage of customers who were surveyed and were 18 - 24, would be 24 %
How to find the percentage ?To find the percentage of customers who were surveyed and were between the ages of 18 and 24, find the total number of people surveyed :
= 25 + 30 + 35 + 25 + 10
= 125 people
The percentage of surveyed customers aged 18 - 24 is therefore:
= Number of customers between 18 - 24 / Total number of customers
= 30 / 125 x 100 %
= 24 %
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You are a marketing manager and need to summarize recent spending on advertisements. You have placed 2 small advertisements that cost $325 each, 5 WILL FAST!! MARK BRAINLYIST IF RIGHT ANSWER
medium-sized advertisements that cost $750 each, and 12 large advertisements that cost $1,300 each. Which expression shows how to calculate the mean cost per advertisement?
A: 325 + 750 + 1,300 / 3
B: 325 + 750 + 1,300 / 19
C: 2 X 325 + 5 X 750 + 12 X 1,300 / 3
D: 2 X 325 + 5 X 750 + 12 X 1.300 / 120
The required expression used to calculate the mean cost per advertisement is 325 + 750 + 1,300 / 3. Option A is correct.
What is mean?The mean of the values is the ratio of the total sum of values to the number of values.
Here,
Mean cost of each type of advertisement
= the sum of the cost of small. medium and large advertisement / 3
= 325 + 750 + 1,300 / 3
Thus, the required expression used to calculate the mean cost per advertisement is 325 + 750 + 1,300 / 3. Option A is correct.
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Determine whether the solution of each equation is positive or negative. Select Positive or Negative for each solution. -9x=36 -36 - 12 = -7b -8.2d 28.1 = 3.6d 2 (4t-5) = 6t - 18 Positive Positive Positive Positive O Negative ONegative O Negative O Negative
The solutions of the given equations are grouped into negative or positive as follows:
-9x=36= negative
-3b-12=-7b = positive
-8.2d+28.1=3.6d = positive
How to calculate the positive and negative equations?For -9x=36;The final result is a negative result because of the following;
-9x= 36
X= -36/9
X= -4
For -3b-12=-7b;The final result is a positive result because of the following;
-3b-12=-7b
-3b+7b =12
4b=12
b= 12/4= 3
-8.2d+28.1=3.6d;The final result is a positive result because of the following;
-8.2d+28.1=3.6d
28.1= 3.6d+8.2d
28.1 = 11.8d
28.1/11.8 = d
d= 2.4
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Blake flips a fair coin and stops flipping once he gets a head. He gets the minimum of $16 and $2 n, where n is the total number of Blake's flips. For example, if Blake flips a head on the first try, then n=1. What is the fair value of this game?
If Blake flips a fair coin , and stops flipping once he get head , then the fair value of the game is 7 .
The Fair Value /Expected value is a mathematical definition that refers to the average outcome of a random process, such as a game or an investment. It is calculated by taking into account all the possible outcomes of the process, weighting each outcome by its probability of occurrence, and summing up the results.
We know that every coin flip has a equal chance of being heads or tails.
So, the probability of getting a head on each flip = 0.5 ;
The expected value is calculated as :
⇒ P(n=1)×(2¹) + P(n=2)×(2²) + P(n=3)×(2³) + P(n=4)×(2⁴) + P(n=5)×(2⁵) + P(n≥6)×(2⁶) ;
⇒ (0.5¹)×2 + (0.5²)×4 + (0.5³)×8 + (0.5⁴)×16 + (0.5⁵)×32 + (1-0.5-0.25-0.125-0.0625 - 0.03125)×64 ;
⇒ 5 + 0.03125 × 64 ;
⇒ 5 + 2
⇒ 7
Therefore , The Fair Value of this game is 7 .
The given question is incomplete , the complete question is
Blake flips a fair coin and stops flipping once he gets a head. He gets the minimum of $16 and $2ⁿ , where n is the total number of Blake's flips. For example, if Blake flips a head on the first try, then n=1. What is the fair value of this game?
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