Abdoulaye is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if he rolls a fair die in the shape of a cube that has six sides labeled 1 to 6 and spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange?​

Answer:

True

Step-by-step explanation:

THIS is because if you sum them that's 42/6 you divide them by two each you get 21/3

Answer:

C (0,3)

Step-by-step explanation:

Plot the two equations and the points.  See the attached graph.  The blue area reflects the inequality of y+3x<=8:  many points satisfy this equation and they are all blue.

The red line is equation y-3=x.  There is only one point on this line that is also in the blue area:  (0.3).  The other three points (A, B, and D) do not satisfy either equation.  The metric term for them is losers.

Answer:

picking my brain I see.... I might be wrong..... I havent done much of these yet

Step-by-step explanation:

I thinks its B) if im correct?

Answer:

Step-by-step explanation:

The worth of the card =$75

The value of the card decreases after each music purchase forming a sequence:

75,74.11,73.22,72.33...

Now,

We see that the sequence forms an arithmetic sequence:

Where the first term, a is 75

Common difference, d=-0.89

We want to write an equation to define A(n), the amount of money on the gift card after n song purchases.

For an arithmetic sequence,the nth term A(n)=a+(n-1)d

Therefore:

The amount of money on the gift card after n song purchases.

A(n)=75-0.89(n-1)

A(n)=75+0.89-0.89n

A(n)=75.89-0.89n

To find out how many songs can Josh purchase with this card only, we take our nth term A(n) of the sequence to be 0 and solve for n.

A(n)=75.89-0.89n

0=75.89-0.89n

0.89n=75.89

Divide both sides by 0.89

n=85.3

n=85

Therefore, Josh can purchase 85 songs with this card only

Answer: The length of each tile is 3 1/8 inches and the width is 2 3/4 inches. To find the area of one tile, we need to multiply the length and width:

Area of one tile = (3 1/8) x (2 3/4)

= (25/8) x (11/4)

= 275/32

Therefore, the area of 9 tiles is:

Area of 9 tiles = 9 x (275/32)

= 2475/32

= 77.34 (rounded to two decimal places)

Since Chris cannot use a fraction of a tile, he can cover the greatest area by arranging the tiles in a rectangle with as close to equal length and width as possible. Let x be the length of the rectangle and y be the width. Then:

x = (number of tiles in length) x (length of one tile)

= 3 x 3 1/8

= 9 3/8

y = (number of tiles in width) x (width of one tile)

= 3 x 2 3/4

= 8 1/4

The area of the rectangle is:

Area of rectangle = x * y

= (9 3/8) * (8 1/4)

= 77.34 (rounded to two decimal places)

Therefore, the greatest area Chris can cover with these tiles is 77.34 square inches, using all 9 tiles arranged in a rectangle.

Step-by-step explanation:

Answer:

1) 48

2)44

Step-by-step explanation:

Answer:  48 44 Are The Correct Answers

Step-by-step explanation:Hope This Helps

By Solving the system of equations using substitution method we get value  of x=3  , y = -2  .

In the question

it is given that

3x + 2y = 5     ...(i)

x = 2y + 7       ...(ii)

Substituting the value of x given in equation (ii) in equation (i) we get ,

3x + 2y = 5

3(2y + 7) + 2y = 5

6y + 21 + 2y = 5

Adding the like terms

8y+21=5

8y = 5-21

8y = -16

y = -16/8

y = -2

We substitute the value of "y" in equation (ii) we get

x = 2(-2) + 7

x = -4 + 7

x = 3

Therefore , the value of x=3 and y=-2 on solving the system of equations using substitution.

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The triple integral for the volume of D in spherical coordinates is:

∫[0,π/4]∫[0,2π]∫[0,2cos(φ)]ρ^2 sin(φ) dρ dθ dφ + ∫[π/4,π/2]∫[0,2π]∫[0,6cos(φ)]ρ^2 sin(φ) dρ dθ dφ

To set up the triple integral for the volume of D in spherical coordinates, we need to express the bounds of integration in terms of spherical coordinates.

First, we note that the base of the cylinder lies in the xy-plane and has a radius of 2 cos(theta), which means that in spherical coordinates, the cylinder is defined by:

0 ≤ ρ ≤ 2cos(φ)

0 ≤ θ ≤ 2π

0 ≤ z ≤ 5 - ρ cos(φ) sin(θ) - ρ sin(φ) cos(θ)

Next, we consider the region bounded below by the cone phi = pi/4 and above by the sphere Q = 6. In spherical coordinates, the cone is defined by:

0 ≤ ρ ≤ 6 cos(φ)

0 ≤ θ ≤ 2π

0 ≤ φ ≤ π/4

The sphere is defined by:

0 ≤ ρ ≤ 6

0 ≤ θ ≤ 2π

0 ≤ φ ≤ π/2

To find the volume of D, we need to integrate over the region that is common to both the cylinder and the region bounded by the cone and sphere.

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Answer:

A

Step-by-step explanation:

A. 8(3+8x)

8 times 3 is 24. 8 times 8 is 64 making it 24+64x

We can solve for x and y in two equations by using the Elimination method for the simultaneous linear equations.

The Elimination approach results in the reduction of one problem to a single-variable equation when two simultaneous linear equations are solved. Following this, the answer is the same as when one line was vertical or parallel. The Gaussian elimination method is the name given to this approach.

We can understand the above method through an example:

Equation 1:     4x + 6y = 8

Equation 2:     3x + 4y = 5

Step 1: In order to ensure that the two equations have the same leading coefficient, multiply each equation by a reasonable value. Equation 1 may be easily solved by multiplying it by 3, the x coefficient from Equation 2, and Equation 2 by 4, the x coefficient from Equation 1.

Therefore the equations become,

12x + 18y = 24

12x + 16y = 10

Step 2: Subtract equation 2 from equation 1

We get 2y = 14

From the above equation, we get the value of y as 7

Step 3: We will substitute the value of y in one of the initial equations

Substituting the value of y in equation (1) 4x + 6y = 8

4x + 6(7) = 8

4x + 42 = 8

4x = 34

x = \(\frac{34}{4}\)

x = \(\frac{17}{2}\)

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After solving an equation as per given relation of Lan, Lisa and Jim height ,now Lan's height is 174centimeters.

As given ,

Let h be Lan's height today in centimeters.

As per the relation between  Lan, Lisa and Jim height we have,

Lan=h cm

Lisa=h + 4

Jim=h -8

After 4 months, every month their heights increase by 2 cm

Lan=h + 8

Lisa=h + 4 +8

Jim=h -8 +8

Required equation for given condition:

Lan + Jim=170 +Lisa

⇒h +8 + h -8 + 8=170 + h + 4+8

⇒2h+8=h+182

⇒h=174cm

Therefore, after solving an equation as per given relation of Lan, Lisa and Jim height ,now Lan's height is 174centimeters.

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The dimensions that would guarantee that the garden has the greatest possible area is 190 feet on the shorter side and 380 feet on the longer side to produce an area of 72,200 square feet.

A dimensions of a rectangle is the length of each side.

Let x = length of the shorter side

y = length of the longer side

If one side of the garden is bordered by a river and so it does not need any fencing, and assume that the longer side is this side, then the perimeter that only needs to be fenced by 760 feet of fencing materials is

2x + y = 760

y = 760 - 2x

The area of the rectangular garden is the product of the shorter side and the longer side of the garden. Hence,

A = xy

A = x(760 - 2x)

A = 760x - 2x²

To obtain the largest area possible, the first derivative of the area should be equal to zero.

A(x) = 760x - 2x²

A'(x) = 0

760 - 4x = 0

Solve for x.

760 - 4x = 0

4x = 760

x = 190

length of the shorter side = 190 feet

y = 760 - 2x

y = 760 - 2(190)

y = 380

length of the longer side = 380 feet

Solve for the greatest possible area.

A = xy

A = 190 feet(380 feet)

A = 72,200 square feet

" A gardener has 760 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing. What dimensions would guarantee that the garden has the greatest possible area? "

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The Gantt Chart for the given jobs using FCFS (First-Come-First-Served) scheduling algorithm is as follows:

Job Start Time End Time

P1 0 8

P2 8 10

P3 10 15

P4 15 17

P5 17 20

The average waiting time and average response time can be calculated as follows:

To calculate the average waiting time, we need to find the difference between the start time of each job and its arrival time, and then take the average.

Average Waiting Time = (0 + 8 + 10 + 15 + 17) / 5 = 10 ms

To calculate the average response time, we consider the time from when a job arrives to when it first starts executing (which is the same as waiting time in FCFS).

Average Response Time = Average Waiting Time = 10 ms

In FCFS scheduling, jobs are executed in the order of their arrival, without any preemption. Therefore, the waiting time for a job is the sum of the lengths of all previous CPU bursts. In this case, since the jobs arrive in sequential order, the waiting time for each job is simply the sum of the CPU burst lengths of the preceding jobs.

The average waiting time represents the average amount of time each job has to wait before starting its execution. The average response time, in the case of FCFS, is the same as the average waiting time since the response time is defined as the time from arrival to the start of execution.

In this example, both the average waiting time and average response time for FCFS are 10 ms.

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(a) Regular expression for natural numbers:^[1-9]\d*$

This regular expression specifies the syntax for natural numbers. It starts with a digit from 1 to 9 (excluding zero) and is followed by zero or more digits from 0 to 9. It ensures that the number does not have any leading zeros.

(b) Regular expression for strings starting with capital letters: ^[A-Z][a-zA-Z]*

This regular expression represents strings over the alphabet {a, b, A, B} that start with capital letters. It starts with a capital letter (A-Z) and is followed by zero or more letters (a-z, A-Z) from the given alphabet.

(c) Regular expression for numeric constants: ^(0[0-7]*|0x[0-9a-fA-F]+|[1-9]\d*)$

This regular expression specifies the syntax for numeric constants in language X. It includes three alternatives separated by the vertical bar (|) symbol. The first alternative matches octal integers starting with 0 and containing digits from 0 to 7. The second alternative matches hexadecimal integers starting with 0x or 0X, followed by one or more digits from 0 to 9 and letters from a/A to f/F. The third alternative matches decimal integers, which are any non-zero digit followed by zero or more digits. The ^ and $ symbols indicate the start and end of the string, respectively.

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If x = 5cos(t), then y = 8sin(t) is the corresponding parametric equation for the ellipse x^2/5^2 + y^2/8^2 = 1.

To obtain the parametric equation for y when x = 5cos(t), we can use the equation of the ellipse x^2/5^2 + y^2/8^2 = 1. Rearranging the equation, we have y^2/8^2 = 1 - x^2/5^2. Taking the square root of both sides, we get y/8 = ±√(1 - x^2/5^2). Multiplying both sides by 8, we have y = ±8√(1 - x^2/5^2).

Since the curve is traced clockwise as the parameter increases, we choose the negative sign in the equation to ensure clockwise motion. Therefore, the parametric equation for the ellipse is:

x = 5cos(t)

y = -8√(1 - x^2/5^2)

These equations describe the motion of a point on the ellipse as the parameter t varies. As t increases, the point moves clockwise along the ellipse. By substituting different values of t, we can obtain corresponding points on the ellipse and plot them to visualize the shape of the curve.

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Answer: d (A,B) = 9

Step-by-step explanation: d(A,B) = √(xB - xA)^2 + (yB - yA)^2

                                              d(A,B) = √(8-(-1))^2 + (-3 - (-3))^2

                                              d(A,B) = √81 + 0    

                                              d(A,B) = 9                                        

Answer:

$47

Step-by-step explanation:

Create a system of equations where s is the cost of a shirt and t is the cost of a tie:

s + t = 64

s = t + 30

Solve by substitution by substituting (t + 30) into the first equation as s:

s + t = 64

(t + 30) + t = 64

Add like terms and solve for t:

2t + 30 = 64

2t = 34

t = 17

Then, plug in 17 as t into one of the equations to find s:

s = t  + 30

s = 17 + 30

s = 47

So, the cost of the shirt is $47

3/8 in a decimal, divide the denominator by the numerator to get 3/8 as a decimal 3/8 is 0.375.

We divide the numerator by the denominator to convert a fraction to a decimal number. This results in a decimal value because, when dividing, we add the decimal place and then add the necessary number of zeros to finish the division.

3/8

3[1/2 x 1/2 x 1/2]

3[0.5 x 0.5 x 0.5]

3 x 0.125

0.375

To convert a fraction to a decimal, all you have to do is divide the numerator by the denominator. We position the number over its place value when converting a decimal to a fraction.

Just dividing the numerator by the denominator is all that is required to convert a fraction to a decimal.

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Answer:

2[(1 + 5x) (1 - 5x)]

Step-by-step explanation:

Given:

Expression

2 - 50x²

Find:

Factorization of the given expression

Computation:

2 - 50x²

By taking 2 as common

⇒ 2[1 - 25x²]

⇒ 2[(1)² - (5x)²]

We know that;

⇒ a² - b² = (a + b)(a - b)

In given expression;

⇒ a = 1

⇒ b = 5x

⇒ 2[(1)² - (5x)²]

2[(1 + 5x) (1 - 5x)]

Factorization of the given expression

2[(1 + 5x) (1 - 5x)]

Answer:

1.1666... recurring

Step-by-step explanation:

Answer:

1/2 + 2/3 = 7/6

Step-by-step explanation:

Answer:

3x-6/2\(\sqrt{x-1\)

Step-by-step explanation:

1. first we have to get the denominator the same, so we multiply by \(\sqrt{x-1\) to the first fraction top and bottom which leaves as with

3(x-1)/2\(\sqrt{x-1\)   -  3/2\(\sqrt{x-1\)

- we can expand the numerator of the first fraction which becomes

3x-3/ 2\(\sqrt{x-1\)  -  3/2\(\sqrt{x-1\)

2. we can now subtract te fraction as we have the same denominator this gives us

3x-6/2\(\sqrt{x-1\)

3. your final answer would be  

3x-6/2\(\sqrt{x-1\)

{If the question asked to simplify your answer you would rationalize your answer by multiplying top and bottom by \(\sqrt{x-1\) to give you the answer of

(3x-6)\(\sqrt{x-1\)/2x-2}

Answer:

2/5

hope it helps

Thank you

The solution of (1/3x) -6 = -7 will be -1 / 3.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is (1/3x) -6 = -7. The expression will be solved as below:-

(1/3x) -6 = -7

1 / 3x = -7 + 6

1 / 3x = -1

x = -1 / 3

Hence, the solution of the expression for the value of x will be -1 / 3.

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Applying the root test to the series ∑n=1[infinity]an, where an=(5n−8)2n(3n 4)2n, reveals that the series converges.

To determine the convergence of the series using the root test, we need to consider the limit of the absolute value of the nth root of the general term, as n approaches infinity. In this case, the general term is an=(5n−8)2n(3n 4)2n. Taking the nth root and absolute value, we have:

lim┬(n→∞)⁡〖|an|^(1/n) 〗= lim┬(n→∞)⁡〖|(5n−8)^(2n(3n 4)2n) 〗^(1/n) 〗

Simplifying the expression inside the limit:

|(5n−8)^(2n(3n 4)2n) 〗^(1/n) = |5n−8|^(2(3n 4)) = (5n−8)^(6n-8)

Now, as n approaches infinity, the base (5n−8) grows infinitely large, and since the exponent (6n-8) is also positive, the limit of the expression becomes infinity.

Therefore, lim┬(n→∞)⁡〖|an|^(1/n) 〗= ∞.

Since the limit is greater than 1, according to the root test, the series ∑n=1[infinity]an diverges.

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⇒To get the slope it requires us to have two points \((x_{1} ,y_{1} ) \\(x_{2} ,y_{2} )\)

⇒you can take any two points of your choice

I will take (1,5) and (2,10)

⇒To calculate the slope of the line we use the formula

\(m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\)

where m is the variable that represent the slope of the line.

Let us substitute the points and simplify to get the slope.

⇒\(m=\frac{10-5}{2-1} \\m=\frac{5}{1} \\m=5\)

⇒The gradient of the line is equal to 5

⇒ the general equation of finding the equation of a straight line is y=mx+c

where y is the y coordinate,

x is the x coordinate

and c is the y-intercept that you want in this case.

⇒To get it in the place of x and y in the general equation choose any point of your choice and plug it in.

⇒You already have the known variable m which is the slope in this case equal to 5.

⇒You can plug in any point of your choice in the picture as you would still get the same value of the y-intercept represented by letter c in the equation.

⇒I will use the point (2,10) in the place of (x,y)

\(y=mx+c\\10=5(2)+c\\10=10+c\\c=10-10\\c=0\)

⇒As indicated in the calculation the y intercept is 0 as c=0

⇒Now for the equation according to the values we find previously m=5

c=0

∴ the equation of this straight line is y=5x+0

simply because 0 has no effect ∴ y=5x

Answer: All of the above

Step-by-step explanation:

The formula for the standard error of the mean is:

σM =σ/√N

where,

σM = standard error of the mean

σ = standard deviation of sample

√N = square of sample size

As the sample size of a population rises, it should be noted that the standard error of the mean will decrease. This is due to the fact that when there's an increase in sample size, there'll be cluster of the sample mean around the population mean.

Also, the the standard error of the mean measures the variability of the sample mean from sample to sample and is never larger than the standard deviation of the population.

Therefore, the answer will be "all or the above".

the correlation coefficient between x and y is -0.8. The correct answer is C. -0.8.

The correlation coefficient between x and y can be calculated using the formula:
correlation coefficient = covariance / (sample standard deviation of x * sample standard deviation of y)
Substituting the given values, we get:
correlation coefficient = -120 / (10 * 15) = -0.8
Therefore, the correct answer is C. -0.8.
The correlation coefficient between x and y can be calculated using the formula:
Correlation coefficient (r) = Covariance(x, y) / (Standard deviation(x) * Standard deviation(y))
Given the values:
Standard deviation(x) = 10
Standard deviation(y) = 15
Covariance(x, y) = -120
Plugging in the values into the formula:
r = (-120) / (10 * 15)
r = -120 / 150
r = -0.8
So, the correlation coefficient between x and y is -0.8. The correct answer is C. -0.8.

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Answer:

multiply the population each year by 4% or 0.04

year 1 increase by 9600, population 249,600

year 2 increase by 9984, population 259,584

year 3 increase by 10,383, 269,967

year 4 increase by 10,799, 280,766

year 5 increase by 11,231, 291,997

year 6 increase by 11,680, 303, 677

Step-by-step explanation:

I rounded the totals.

this the answer of . Factorise : 625y ^ 2 + 400y - 36 + 20z - z ^ 2