If Colin tosses a normal die from a board game, what is the probability that the result will be prime?
A. 2/3
B. 5/6
C. 1/2
D. 1/6

The complete sentence that describes the expression (5) (x+3) (y + 2) is the expression contains 3 factors and 2 variables.

The expression is given as:

(5) (x+3) (y + 2)

Each of the expression in the bracket are the factors of the expression.

So, we have

Factors = 3

Also, the alphabets are the variables of the expression

So, we have

Variable = 2

Hence, the complete sentence that describes the expression (5) (x+3) (y + 2) is the expression contains 3 factors and 2 variables.

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Answer:

y = mx + c

since m = 0

c = 9

Answer: 60

suppose: the width of a rectangle is x (x > 0)

⇒ The length of a rectangle is 4x

because  the area of the rectangle is 144 ft

=> 4x.x = 144

⇔ x² = 144/4 = 36

⇒ x = 6

with x = 6 ⇒ The length of a rectangle is 4.6 = 24

the perimeter of the rectangle is (6 + 24).2 = 60

Step-by-step explanation:

Answer:

The 3rd one

Step-by-step explanation:

I took the Quiz

Answer:

Answer = 37

Step-by-step explanation:

= (5)² + (2)³ + (4)¹

= 25 + 8 + 4

= 37 Answer

Answer: The answer is 37

Step-by-step explanation:

Step 1: Use Negative Power Rule: x^-a=1/x^a. So 1/(1/5)^2+(1/2)^-3+(1/4)^-1

Step 2: Use Division Distributive Property: (x/y)^a=x^a/y^a. So 1/1/5^2+(1/2)^-3+(1/4)^-1

Step 3: Simplify 5^2 to 25. So 1/1/25+(1/2)^-3+(1/4)^-1

Step 4: Use Negative Power Rule: x^-a=1/x^a. So 1/1/25+1/(1/2)^3+(1/4)^-1

Step 5: Use Division Distributive Property: (x/y)^a=x^a/y^a. So 1/1/25+1/1/2^3+(1/4)^-1

Step 6: Simplify 2^3 to 8. So 1/1/25+1/1/8+(1/4)^-1

Step 7: Use Negative Power Rule: x^-a=1/x^a. So 1/1/25+1/1/8+1/1/4

Step 8: Invert and multiply. 25+1/1/8+1/1/4

Step 9: Invert and multiply. 25+8+1/1/4

Step 10: Invert and multiply. 25+8+4

Step 11: Simplify 25+8 to 33. So 33+4

Step 12: Simplify. So the answer is 37

Answer:

155

Step-by-step explanation:

There are many more people awaiting such a transplant than there are available organs, leading to a large backlog of patients who are not able to receive an organ transplant.

In 2008, the United States Department of Health and Human Services reported that there were approximately 113,000 patients in the United States awaiting organ transplants. Of those, only 28,535 received an organ transplant that year. This is a ratio of approximately 1 in 4. This can be expressed mathematically as 28,535/113,000 = 0.25, or one fourth. This means that for every 4 people awaiting an organ transplant in the United States in 2008, only 1 actually received one. While organ transplants are a life-saving procedure for many, the reality is that there are many more people awaiting such a transplant than there are available organs, leading to a large backlog of patients who are not able to receive an organ transplant.

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Complete question:What were the numbers of patients waiting for and receiving an organ transplant/donation in the United States in 2008, according to Mark Cherry?

Answer:

8 people

Step-by-step explanation:

120x=750+25x

120x-25x=750

95x=750

x=7.89

round up to 8 and check answer

(25×8)+750=950

950÷8 people =$118.75 per person

Answer:

Step-by-step explanation:

average=(sum of numbers)/number of numbers

15=(sum of numbers)/3

sum of numbers=15×3=45

To complete the table, we want to choose any value on the given intervals and test its sign on each columns, (t - 2) and (t - 1). If both have + signs, the las column will also have + sign. If both have - sign, the last column will have + sign. If one has + sign and the other has - sign, the last column will have - sign.

The first internal is "less than 1 hour".

One easi pick here is t = 0:

Since both are negative, we have:

So, the first row is:

less than 1 hour - - +

The second is not an interval it is "1 hour", so:

Since any number multiplied by 0 is also 0, the result on the third column will also be 0:

So, the second row is:

1 hour - 0 0

The third interval is "between 1 and 2 hours", so we can pick 1.5, for example. We have:

Since one is - and the other is +, the third column will be negative:

So, the third row is:

between 1 and 2 hours - + -

In the fourth, we have a value of 2 hours, so:

Since one of them is 0, the third column will also be 0, so:

So, the fourth row is:

2 hours 0 + 0

The last interval is "more than 2 hours", so we can pick 3, for example:

Since both are +, the third column will also be +:

So, the fifth row is:

more than 2 hours + + +

So, we have:

interval of time (t-2) (t-1) 4(t-2)(t-1)

less than 1 hour - - +

1 hour - 0 0

between 1 and 2 hours - + -

2 hours 0 + 0

more than 2 hours + + +

Answer: It's good to think about things before doing them because it is more thought out and you have a better chance of getting things correct whereas without thinking your most likely going to get it wrong. Without thinking through your options you are basically guessing the answer. I hope this helped you have a great day and god bless you :D

It should be noted that a polygon that's inscribed in a circle has each vertex on the outer figure.

It should be noted that a polygon simply means a plane figure that has a finite number of straight line segments.

In this case, a polygon that's inscribed in a circle has each vertex on the outer figure. Also regular polygons can be inscribed in a circle.

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The street dance group performed a total of 4.5 hours for 8 days during the summer.

From the given image, on the first two days which are Day-1 and Day-2 they performed for 1/4 hour which is  0.25 hours on each day. The next 3 days which are day-3, day-4, and day-5 they performed for 2/4 hour which is 0.5 hour on each day. For the next 2 days which is day-6 and day-7, they performed for 3/4 hours which is 0.75 hours for each day. On the final day which is day-8, they performed for 1 hour.

To find mathematically, the total hours they performed in 8 days is

Total hours = (2 x 0.25) + (3 x 0.5) + (2 x 0.75) + 1 (1)

                   = 0.5 + 1.5 + 1.5 + 1

                   = 4.5 hours

From the above analysis, we can conclude that the dance group performed for a total of 4.5 hours for 8 days.  

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The function that represents the volume is as follows:

V(x) = x³ - 4x

The length, width, and height of the ottoman if the volume is 5,760 in³ are as follows:

length = 18 inches

width = 18 - 2 = 16 inches

height = 18 + 2 = 20 inches

where

l = length

w = width

h = height

Therefore,

The length is as follows:

The width two inches shorter than the length:

The height two inches taller than the length:

Therefore,

volume = x (x - 2)(x + 2)

volume = x(x² + 2x - 2x - 4)

volume = x(x² - 4)

volume = x³ - 4x

If the volume is 5760 in³, the length, height and width can be found as follows:

5760 = x³ - 4x

x³ - 4x - 5760 = 0

By trying a few value of x, x = 18.

Therefore,

length = 18 inches

width = 18 - 2 = 16 inches

height = 18 + 2 = 20 inches

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The maximum value of the objective function Z = 40x₁ + 5x₂, subject to the constraints x₁ + x₂ ≤ 5 and 6x₁ + x₂ ≤ 20, where x₁, x₂ are integers between 0 and 25, can be found using the branch and bound method.

To solve this problem, we start with an initial solution by considering the constraints and finding the feasible region. Then, we compute the objective function for this initial solution. Next, we branch the problem into subproblems by considering different combinations of x₁ and x₂. We calculate the lower bounds for each subproblem to determine the potential for improvement. We continue branching and bounding until we find the optimal solution with the maximum value of Z.

The branch and bound method systematically explores the solution space, optimizing the objective function by considering different feasible regions. It provides a structured approach to find the optimal solution for linear programming problems.

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Answer:

A and D choices (Plato)

Step-by-step explanation:

The upper boundary of the first equation is at x = 12, y = 0. With these values, this is the second equation:

100(12) − 200(0) = 1,200.

The lower boundary of the first equation is at x = 0, y = 12. With these values, this is the second equation:

100(0) − 200(12) = -2,400.

Both of these scores are possible in the game, so they are both viable.

Because the upper boundary is greater than 600, it suggests that you can still score 600 points and win the game even if you get one or two of the questions incorrect.

In fact, you could give 10 correct and 2 incorrect answers to score 600 points and still beat the champion, Kimberly, assuming she answers 15 correct and 5 incorrect to score 500 points.

Step-by-step explanation:

The five true phyla of fungi are the Chytridiomycota (Chytrids), the Zygomycota (conjugated fungi), the Ascomycota (sac fungi), the Basidiomycota (club fungi) and the recently described Phylum Glomeromycota.

The matricial equation of the degenerate parabola is \(\left[\begin{array}{c}x'\\y'\end{array}\right] = \left[\begin{array}{c}\frac{ \sqrt{2} }{2}\cdot x + \frac{1}{8}\cdot x^{2}+1 \\\-\frac{\sqrt{2}}{2}\cdot x + \frac{1}{8}\cdot x^{2} + 1 \end{array}\right]\).

A parabola is degenerated when its axis of symmetry is not parallel to any orthogonal axis (i.e. x, y). First, we have to find an "equivalent" parabola whose axis of symmetry is parallel to the y-axis and whose vertex is along that axis.

Direction of the degenerate parabola

\(\tan \theta = \frac{2 - 1}{2 - 1}\)

tan θ = 1

θ = 45°

This means that the degenerate parabola must be rotated 45° clockwise (- 45°) around the origin with respect to the "equivalent" parabola.

Distance from the vertex to the focus

\(p = \sqrt{(2 - 1)^{2}+(2 - 1)^{2}}\)

\(p = \sqrt{2}\)

Vertex of the "equivalent" parabola

\((h', k') = (0, \sqrt{2})\)

Equation of the "equivalent" parabola

\(y = \frac{1}{4\cdot p}\cdot x^{2} + k'\)

\(y = \frac{1}{4\sqrt{2}}\cdot x^{2}+\sqrt{2}\)

Now we apply following rotation formula:

\(\left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{cc}\cos (-45^{\circ})&-\sin (-45^{\circ})\\\sin (-45^{\circ})&\cos (-45^{\circ})\end{array}\right] \cdot \left[\begin{array}{c}x\\\frac{1}{4\sqrt{2}}\cdot x^{2}+\sqrt{2}} \end{array}\right]\)

\(\left[\begin{array}{c}x'\\y'\end{array}\right] = \left[\begin{array}{c}\frac{ \sqrt{2} }{2}\cdot x + \frac{1}{8}\cdot x^{2}+1 \\\-\frac{\sqrt{2}}{2}\cdot x + \frac{1}{8}\cdot x^{2} + 1 \end{array}\right]\)

A representation of the degenerate parabola is shown in the figure attached below.

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The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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811-354

you are taking away 354 from 811

answer: 547

please consider giving be brainliest, i need it to level up

Answer:

slope = - \(\frac{3}{2}\)

Step-by-step explanation:

calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (2, 1 ) and (x₂, y₂ ) = (8, - 8 ) ← 2 ordered pairs from the table

note that any 2 ordered pairs may be used to calculate m

m = \(\frac{-8-1}{8-2}\) = \(\frac{-9}{6}\) = - \(\frac{3}{2}\)

The inverse Z-transform (IZT) is a mathematical tool used to transform discrete-time signals into the time-domain.

It is the inverse of the Z-transform and is used to find the time-domain representation of a given discrete-time signal represented in the frequency domain. The Z-transform is a powerful tool for the analysis and design of linear, time-invariant, discrete-time systems.

The operator of the inverse Z-transform for X(z) is represented as x[n], where x[n] is the discrete-time signal in the time-domain and X(z) is its corresponding representation in the frequency domain.

The inverse Z-transform is computed by performing a partial fraction expansion and finding the residue of each term in the expansion. The result of the inverse Z-transform is a function of the time index, n.

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1. The 95% confidence interval is between 567.07 and 739.93 vehicles per hour
2. The 98% confidence interval is between 547.47 and 759.53 vehicles per hour
3. The sample size needed for a 95% confidence interval to specify the mean to within ±55 vehicles per hour is 121
4. The sample size needed for a 98% confidence interval to specify the mean to within ±55 vehicles per hour is 187

1. To find the 95% confidence interval, we use the formula:

Mean improvement +/- (t-value * standard error)

where t-value for 49 degrees of freedom at 95% confidence level is 2.009.

The standard error can be found by dividing the standard deviation by the square root of the sample size:

Standard error = 311.7 / sqrt(50) = 44.06

So the 95% confidence interval is:

653.5 +/- (2.009 * 44.06) = (567.07, 739.93)

Therefore, we can say with 95% confidence that the true mean improvement in traffic flow is between 567.07 and 739.93 vehicles per hour.

2. To find the 98% confidence interval, we use the same formula but with a different t-value. For 49 degrees of freedom at 98% confidence level, the t-value is 2.678.

The 98% confidence interval is:

653.5 +/- (2.678 * 44.06) = (547.47, 759.53)

Therefore, we can say with 98% confidence that the true mean improvement in traffic flow is between 547.47 and 759.53 vehicles per hour.

3. To find the sample size needed for a 95% confidence interval to specify the mean to within ±55 vehicles per hour, we use the formula:

n = \((z * s / E)^2\)

where z is the z-value for 95% confidence level (1.96), s is the standard deviation (311.7), and E is the margin of error (55).

Plugging in the values, we get:

n = \((1.96 * 311.7 / 55)^2\) = 120.25

Rounding up, we need a sample size of 121 to achieve a 95% confidence interval with a margin of error of ±55 vehicles per hour.

4. To find the sample size needed for a 98% confidence interval to specify the mean to within ±55 vehicles per hour, we use the same formula but with a different z-value. For 98% confidence level, the z-value is 2.33.

Plugging in the values, we get:

n = \((2.33 * 311.7 / 55)^2\) = 186.34

Rounding up, we need a sample size of 187 to achieve a 98% confidence interval with a margin of error of ±55 vehicles per hour.

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The equation of a line perpendicular to y = 3x - 8 which contains the point (3, -2) is y=-1/3 x-1.

The given line equation is y = 3x - 8 and the coordinate point is (3, -2).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope of a line y = 3x - 8 is m=3.

The slope of a line perpendicular to given line is m1=-1/m2 = -1/3

Now, put m=-1/3 and (3, -2) in y=mx+c, we get

-2=-1/3(3)+c

⇒ -2 = -1+c

⇒ c=-1

Substitute, m=-1/3 and c=-1 in y=mx+c, we get

y=-1/3 x-1

Therefore, the equation of a line perpendicular to y = 3x - 8 which contains the point (3, -2) is y=-1/3 x-1.

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Answer:

can you translate in english,would be better...

answer maybe wrong because of the language but stil....

9x(2+6x+1)

=9x(9x)

81x..

Answer:

wrong

Step-by-step explanation:

The division property states that when we have an equation in the form \(ax=b\), then \(x=b/a\)(i.e. we "divide" by \(a\) on both sides).

So, Mark was supposed to get \(x=9/23\), which is not equal to \(6\).

So, Mark solved it \(\boxed{wrong}\)

No, Mark solve the equation correctly.

because, Mark was supposed to get x = 27/2 , which is not equal to x= 6.

The division property of equality applicable.

The division property of equality is a property that tells us if we divide one side of an equation by a number, we must also divide the other side by the same number so that our equation stays the same. The formula for this property is if a = b, then a / c = b / c.

We have the following information available from the question is:

The equation is:

\(\frac{2}{3}x=9\)

It solved by using the Division Property of Equality and get x = 6

If we solved for x: then,

x = 27/2

No, Mark solve the equation correctly.

So, Mark was supposed to get x = 27/2 , which is not equal to x= 6.

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Answer:

1590 minutes

Step-by-step explanation:

November 17 ends on 12:00, which is 8 hours after 4:00 pm. The time from the beginning of November 18 to noon is 12 hours, and the distance from noon to 6:30 is 6 hours and 30 minutes, so the total time in hours is 8+12+6 +1/2=26 1/2.

Because we know that one hour is 60 minutes, 26 hours is going to be 60*26, which is equal to 60*20+60*6=1560.

1/2 * 60 = 30. 1560+30=1590, so the value of minutes is 1590 minutes.

Answer:

72 games in total

Step-by-step explanation:

hope this helps :)

Using it's concept, it is found that Brandon's net yardage for the game was of 26.

The total net yardage is the sum of all the yardage they gain, that is, the positive gains are added with a plus signal, while the negative gains are added with a negative signal.

Hence, his net yardage, considering that he gained 20 yards on his last 7 carries, is given by:

6 + 20 = 26.

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