a board has a red space, a blue space, and a yellow space. a checker is situated on the red space. on each move the checker is transferred to one of the other two spaces. in how many ways can one make a series of 11 moves which result in the checker returning to the red space?

The logarithmic equation gives the value of n; n = 11/ 6.

This is a form of equation which requires the application of one of the laws of logarithm to solve or determine the value of a variable.

To solve the given logarithmic equation, we have the following steps to follow;

64^(2n - 3) = 4^2

4^3(2n - 3) = 4^2

divide the common terms on both sides to have;

3(2n - 3) = 2

6n - 9 = 2

6n = 2 + 9

6n = 11

n = 11/ 6

Therefore on solving the logarithmic equation, the value of n is 11/ 6.

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Answer:

18

Step-by-step explanation:

see attached

60 students chose chocolate ice cream If 84 students chose vanilla ice cream.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, Elmhurst School organized an ice cream social for the incoming sixth graders. At the social, 7 students chose vanilla ice cream for every 5 that chose chocolate ice cream.

Since,

The ratio of students who choose vanilla ice cream to chocolate ice cream is: 7/5

Thus,

for every students choose chocolate ice cream = 5/7 student who chooses vanilla ice cream

If 84 students chose vanilla ice cream

Thus, students choose chocolate ice cream = 5/7 * 84

students choose chocolate ice cream = 12* 5

students choose chocolate ice cream = 60

Therefore, If 84 students chose vanilla ice cream, 60 students chose chocolate ice cream.

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Answer:6/5 or 1 1/5

Step-by-step explanation:

1. Add 2 on each side

2. Then divide 1/5 and 6

Answer:

X = 30

Step-by-step explanation:

Add 2 on both sides, cancelling the -2. Divide 1/5 by 6 (4+2) and you'll get 30

Answer:

The answer is side side side (SSS)

Answer:

SSS Similarity

Step-by-step explanation:

121/9 = 8/6 = 16/12

Similar by SSS Similarity

A population is the entire group of items of interest in a particular study, and it is not necessarily the same size as the sample. It is not the same as a sample, which is a subset of the population chosen for the study.

A population is the complete set of items of interest in a study. It could be people, animals, plants, objects, or anything else being studied. A population can be large or small, and it is not always the same size as the sample. A sample is a subset of the population that is chosen to represent the entire population. It is important to choose a sample that accurately reflects the population. Sampling techniques, such as random sampling, are used to ensure that the sample is representative of the population. Once the sample is chosen, data is collected from the sample to infer information about the population. This data can then be used to draw conclusions about the population as a whole.

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The number of the arrangement for the five sequences will be 6.

Combination and permutation are two different ways in mathematics to divide up a set of elements into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a particular order.

Given that a sequence is a sequence of positive integers whose terms add up to $5.$ For example, 2, 2, 1 and 2, 1, 2.

The number of the ways will be calculated as:-

3! = 3 x 2

3! = 6

Hence, the number of the different arrangements for the sum of 5 will be 6.

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The y-intercept of a line is the point at which the line crosses the y-axis. This means that the x-coordinate of the point is 0.

To find the equation of a line passing through two points, we use the slope-intercept form of the equation of a line: y = mx + b, where m is the slope of the line and b is the y-intercept.

To find the y-intercept of a line passing through two points, we can use the slope-intercept form of the equation of a line and the coordinates of the two points:

(y1, y2) = m(x1, x2) + b

m = (y2-y1)/(x2-x1)

In this case, the two points are (-1,-5) and (6,0)

m = (0-(-5))/(6-(-1)) = 5/7

We can substitute the slope in the slope-intercept form of the equation of a line:

y = mx + b

so we can substitute point (-1,-5) in the equation and solve for b

-5 = (5/7)*(-1) + b

b= -5 + (5/7) = -5 + 0.7142857142857143

So, the y-intercept of the line passing through the two points (-1,-5) and (6,0) is -4.2857142857142865

Answer: To check if Jose has enough string for his project, we need to add the lengths of the strings he has and compare it to the amount of string he needs for the project.

The length of the first string is 9 1/2 feet, the second string is 3 1/4 feet and the third string is 4.5 feet.

To add these lengths we need to convert them all to the same unit of measurement.

3 1/4 feet can be converted to 3.25 feet

So the total length of the strings Jose has is 9 1/2 + 3.25 + 4.5 = 17.25 feet

Jose needs 20 1/3 feet of string for his project, and he has 17.25 feet of string.

So he doesn't have enough string for his project.

Step-by-step explanation:

If Alex has an 80% chance of passing a test and Brad has a 60% chance of passing the test ,then the probability that Alex and Broad both fail the test is 0.8 or 8%   .

The percent chance that Alex passes the test is = 80% = 0.8  ;

So , probability that Alex fails the test is = 1 - 0.8 = 0.2 ;

the percent chance that Brad passes the test is = 60% = 0.6 ;

So , the probability that Brad fails the test is - 1 - 0.6 = 0.4 ;

we have to find the probability that Alex and Broad both fail the test ,

the required probability of both failing can be found by using formula :

= (probability Alex fails the test) × (probability Brad fails the test)

= 0.2 × 0.4

= 0.8 .

Therefore , the probability that both fail  the test is 0.8 or 8% .

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Answer:

Kinda Hard to explain hope this helps

Step-by-step explanation:

Lets say molly is 6 and parker bought 4 times as many then he bought 24 marbles.Then cole bought 5 fewer then parker so 24-5=19

the equation is 4(6)m=p(24) Cole p(24)-5=Cole

M=6

The line segment AB has point B(x, y) = (11, - 4) as its other endpoint.

Herein we find the case of a line segment, of which the coordinates of its midpoint and one of its endpoints are known. Midpoint and endpoints are related by following expression:

0.5 · A(x, y) + 0.5 · B(x, y) = M(x, y)

Where:

If we know that A(x, y) = (- 1, 8) and M(x, y) = (5, 2), then the coordinates of the other midpoint are:

0.5 · (- 1, 8) + 0.5 · B(x, y) = (5, 2)

(- 1, 8) + B(x, y) = 2 · (5, 2)

(- 1, 8) + B(x, y) = (10, 4)

B(x, y) = (11, - 4)

The point B(x, y) = (11, - 4) is an endpoint of line segment AB.

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The dimensions of the rectangle are 8 inches as width and 13 inches as length.

An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

The equation is given as:

x² + 5x - 104.

x² + 13x - 8x - 104

x(x + 13) - 8 (x + 13).

x - 8 = 0

x = 0 + 8

Width = 8

Length = x + 5

= 8 + 5.

= 13

The width is 8 inches and length is 13 inches.

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Determine the solutions of the equation. What solution

makes sense for the situation?

A rectangle has a length that is 5 inches greater than its

width, and its area is 104 square inches. The equation (x

+5)x = 104 represents the situation, where x represents

the width of the rectangle.

(x + 5)x = 104

x2 + 5x - 104 = 0

What are the dimensions of the rectangle?

Answer:

Step-by-step explanation:

x=4
x=-3/2

hope this helps !! :)

Answer:

89

Step-by-step explanation:

The angles are congruent since they are alternate interior angles of parallel lines cut by a transversal.

30x - 1 = 29x + 2

x = 3

30x - 1 = 30 × 3 - 1 = 89

The solution to the simultaneous equation is x = 38 and y = 8

From the information given, we have the equations;

From equation (1), make 'x' the subject of formula;

4x = 48 - 5y

Divide both sides by 4

x = 48 - 5y/4

Substitute the value x in equation (2)

7(48 - 5y/4) - 3y = -10

expand the bracket

336 - 35y/4 - 3y = -10

Find the lowest common multiple

336 - 35y - 12y/4 = -10

336 - 47y/4 = -10

cross multiply

336 - 47y = -40

collect like terms

-47y = 376

y = 8

Substitute the value into equation 3

x = 48 - 5(8)/4

x = 48 - 10

x = 38

Hence, the values are 38 and 8

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A solution for the given system of linear inequalities is the shaded area below the solid line.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the cost of vegetarian meal and cost of meat meal, and then translate the word problem into algebraic equation as follows:

Since each vegetarian meal cost $2.25 to make while each meat meal cost $2.75 and Chef Malik can spend no more than $800, a linear inequality which represents this situation is given by;

2.25x + 2.75y ≤ 800

Additionally, Chef Malik wants to serve at least 400 meals;

x + y ≥ 400

Next, we would use an online graphing calculator to graphically solve the system of linear inequalities.

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Complete Question:

Chef Malik decided to spend the grant money to package and deliver his meals to reach more community members. Each vegetarian meal now costs $2.25 to make and each meat meal now costs $2.75. Chef Malik wants to serve at least 400 meals and spend no more than $800.

Write and solve the system of inequalities graphically.

If in the party there are 5 different appetizers and 6 different desserts , then the number of different ways the 3 appetizers and 2 desserts can be selected is 150  ways .

the number of different appetizers in dinner party is = 5 ;

the number of different desserts in dinner party is = 6 ;

the number of ways of selecting 3 appetizers from 5 is = ⁵C₃ = 10 ;

number of ways of selecting 2 desserts from 6 is = ⁶C₂ = 15 ;

the number of ways of selecting 3 appetizers and 2 desserts is

= 15 × 10

= 150 ways .

Therefore , 3 appetizers and 2 desserts can be selected in 150 ways .

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The sum of the numbers on the three chosen slips of paper is either 21 or 23 in both the given cases.

We are given that one of the slips chosen is numbered 7, so the only possible sums of the remaining two slips are:

16 = 7 + 9

14 = 7 + 7

In the statement (1), the sum of two of the numbers chosen is 16, which means that the remaining two slips are 7 and 9. So the sum of the numbers on the three chosen slips of paper is 7 + 9 + 7 = 23.

In the statement (2), the sum of two of the numbers chosen is 14, which means that the remaining two slips are 7 and 7. So the sum of the numbers on the three chosen slips of paper is 7 + 7 + 7 = 21.

Hence, we get that in both cases, the sum of the numbers on the three chosen slips of paper is either 21 or 23.

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The correct answer is done by Curran,the equation is an example for Inequality Equations. X = -1\2

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols.

Examples,

Symbol Name               Symbol                          Example

Not equal                            ≠                                     x ≠ 3

Less than                            (<)                           x + 7 < √2

Greater than                       (>)                        1 + 10x > 2 + 16x

Less than or equal to         (≤)                            y ≤ 4

Greater than or equal to     (≥)                             -3 - √3x ≥ 10

Let's solve your inequality step-by-step.

−4(x−6)<22

Step 1: Simplify both sides of the inequality.

−4x+24<22

Step 2: Subtract 24 from both sides.

−4x+24−24<22−24

−4x<−2

Step 3: Divide both sides by -4.

−4x/4<= -2/-4x

x-1/2

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In the parallelogram, the coordinates form of the vectors WX, XY, WZ, OZ are (18,3), (24, 21), (2x, y)  and (0,0).

The term coordinate in math is known as the set of values that represents the exact position on the coordinate plane

Here we know that WXYZ is a parallelogram and the position vectors of W, X and Y are (2,1), (6,3) and (4,7) respectively.

Then the value of the coordinate vectors are calculated as,

=> WX = (2,1) x (6,3) = (18, 3)

And the value of XY is calculated as,

=> XY = (6,3) x (4,7) = (24, 21)

And we know that the value of Z is (x, y), then the vector is calculated as,

=> WZ = (2,1) x (x, y) = (2x, y)

Finally the value of OZ is calculated as,

=> OZ =(0,0)  x (x , y) = (0, 0)

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Step-by-step explanation:

the surface area of a half-cylinder is, surprise, surprise, half of the surface area of a whole cylinder ...

the surface area of a cylinder is

A=2×pi×r×h + 2×pi×r²

r being the radius, h being the height of the cylinder.

the formula simply adds

the sidewall area (which is a rectangle of

circle circumference × height)

+

the top and base circle areas

half of this area calculation for a half-cylinder is

A/2 = pi×r×h + pi×r²

Assume the resting position is at y=0, so the function is y = 10sin(π/4 x + π/4).

First one the first point will not be on the midline and will be at the maximum height.

In physics, amplitude refers to the greatest displacement or distance that a point on a vibrating body or wave can move relative to its equilibrium location.

amplitude = 10 = A and y = Asin(Bx - C) + D

Time = 8 seconds

B = 2π/time

B = 2π/8

B = π/4

The sine graph is pushed back by π/2 units since the weight is at its maximum position at x = 0; as a result, C = π/2, D = 0 (the midline is y = 0).

y = 10sin(π/4 x + π/4) is the function.

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The complete question is:

A researcher observes and records the height of a weight moving up and down on the end of a spring. At the beginning of the observation the weight was at its highest point. From its resting position, it takes 12 seconds for the weight to reach its highest position, fall to its lowest position, and return to its resting position. The difference between the lowest and the highest points is 10 in. Assume the resting position is at y = 0. Use the sine tool to graph the function. The first point must be on the midline and the second point must be a maximum or minimum value on the graph closest to the first point.

[tex]\textit{midsegment of a trapezoid}\\\\ m=\cfrac{a+b}{2} ~~ \begin{cases} a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ a=11.5\\ m=18.7 \end{cases}\implies 18.7=\cfrac{11.5+b}{2} \\\\\\ 37.4=11.5+b\implies 25.9=b=AB[/tex]

1). To eliminate variable x,

we subtract the equation 2 to equation 1

And 2). The solution of the system is x = 16 and y = 20.

One or many equations having the same number of unknowns that can be solved simultaneously called as simultaneous equation. And simultaneous equation is the system of equation.

Given:

Each of 36 students at a school play bought either a cup of orange juice or a sandwich.

A cup of orange juice costs $1 and a sandwich costs $3.

The total amount collected was $76.

Let x represent the number of students who bought a cup of orange juice and y represents the number of students who bought a sandwich.

Then the problem can be represented by this system of equations:

x + 3y = 76   {equation 1}

x + y = 36     {equation 2}

1). To eliminate variable x,

we subtract the equation 2 to equation 1,

2y = 40

y = 20.

And x = 16.

2). The solution of the system is x = 16 and y = 20.

To check the solution, substituting the values to the equation 2,

16 + 20 = 36

36 = 36

Therefore, all the required values are given above.

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Answer: 2.294524311274043, 4.294524311274043, 6.294524311274043 and 8.294524311274043 radians.

Step-by-step explanation: We can start by isolating the sin function on one side of the equation:

sin (2x-4) = 2/3

Next, we can use the inverse sine function (sin^-1) to find the value of 2x-4:

2x-4 = sin^-1(2/3)

We know that the domain of the inverse sine function is [-1,1], so the value of 2/3 falls in that range. To find the value of x, we can add 4 to both sides and divide both sides by 2:

x = (sin^-1(2/3) + 4) / 2

The value of sin^-1(2/3) is approximately 0.5890486225480862 radians and that's the first solution in the range [0, pi], and we can add multiples of pi to get the other solutions.

x = (0.5890486225480862 + 4) / 2 = 2.294524311274043 radians (in the range [0, pi])

x = (0.5890486225480862 + 4 + pi) / 2 = 4.294524311274043 radians (in the range [pi, 2pi])

x = (0.5890486225480862 + 4 + 2pi) / 2 = 6.294524311274043 radians (in the range [2pi, 3pi])

x = (0.5890486225480862 + 4 + 3pi) / 2 = 8.294524311274043 radians (in the range [3pi, 4*pi])

So there are four solutions to this equation: 2.294524311274043, 4.294524311274043, 6.294524311274043 and 8.294524311274043 radians.

[tex]3\sin(2x-4)=2\implies \sin(2x-4)=\cfrac{2}{3}\implies 2x-4=\sin^{-1}\left( \cfrac{2}{3} \right) \\\\\\ 2x=\sin^{-1}\left( \cfrac{2}{3} \right)+4\implies x=\cfrac{\sin^{-1}\left( \frac{2}{3} \right)+4}{2} \\\\\\ x=\cfrac{\sin^{-1}\left( \frac{2}{3} \right)}{2}+2\implies x\approx\cfrac{0.73}{2}+2\implies \stackrel{II~Quadrant}{x\approx 2.365}\hspace{5em}\stackrel{III~Quadrant}{\stackrel{\frac{\pi -0.73}{2}+2}{x\approx 3.206}}[/tex]

Answer:

The Rate of Interest is 6%.

Step-by-step explanation:

S.I= Amount - Principle

S.I=885-750=135.

Rate= S.I*100/(P*T)

Rate=(135*100)/(750*3)

Rate=6%

Simple interest is a quick and easy method of calculating the interest charge on a loan.

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9.43 inches is the measure of the longest segment

We are aware that the diagonal connecting the two opposing corners at the top and bottom will be the longest segment.

We know how to find the diagonal of a right triangular prism using the following formula:

d = [tex]\sqrt{w^2 + l^2+h^2} \\\\[/tex]

where w = width = 1.4

l = length = 4.8

h = height = 8

We would put these values in the formula above

[tex]d = \sqrt{1.4^2 + 4.8^2+8^2} \\\\[/tex]

d = [tex]\sqrt{1.96+23.04+64}[/tex]

d = 9.43

The measure of the longest line segment is given as 9.43 inches

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The child has 14 quarters and 28 dimes if child's bank contains $6.30 in dimes and quarters.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

With coin problems you need to keep track of the count of the coins and the value.

d = number of dimes

10d = value of the dimes in cents

q = number of quarters

25q = value of the quarters in cents

10d + 25q = 630 cents

d = 2q

substitute

10(2q) + 25q = 630

20q + 25q = 630

45q = 630

q = 14

d = 2q

d = 2*14 = 28

Check the values to be sure this answer is right.

25(14) = 350 cents

10(28) = 280 cents

total = 630 cents

Therefore,  The child has 14 quarters and 28 dimes.

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