A wheel has 5 equally sized slices numbered from 1 to 5.
Some are grey and some are white.
The slice numbered 1 is grey.
The slices numbered 2, 3, 4, and 5 are white.
The wheel is spun and stops on a slice at random.
Let X' be the event that the wheel stops on a white slice, and let P(X) be the
probability of X
Let not X' be the event that the wheel stops on a slice that is not white, and let
P (not X) be the probability of not X.
Event
X
not X
(a) For each event in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter
the probability of the event.
(b) Subtract.
Outcomes
12345
0
0
O
1- P(not X) -
0
O
O
Probability
00000 P(not X) -
P(X) -
010
8
X
(c) Select the answer that makes the sentence true.
1-P (not X) is the same as (Choose one)
8
X
5 1
X
4
3
2

The value of coordinates of fourth vertex of rectangle is, (0, 3)

We have to given that;

A rectangle is made up from points (-2,-1), (4,-1), (4,3),

Since, Midpoints of the points are same both diagonal.

Hence, Let the fourth vertex = \(x, y)

Midpoint of point (- 2, - 1) and (4, 3) is,

(- 2 + 4) / 2,. (- 1 + 3) / 2

(2, 1)

Midpoint of (x, y) and (4, - 1) is,

(x + 4)/2, (y - 1)/2

Which is same as (2, 1).

Hence, We can compare as;

(x + 4) / 2 = 2

x + 4 = 4

x = 0

y - 1 / 2 = 1

y - 1 = 2

y = 3

Thus, The value of coordinates of fourth vertex of rectangle is, (0, 3)

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Complete question is,

If a rectangle is made up from points (-2,-1), (4,-1), (4,3),

Then, The value of fourth coordinate is?

Hello! Here are the recursive definitions of the given sequence:

A) The sequence is increasing by 7 for each term, so the recursive definition can be written as:

a1 = 3

an = an-1 + 7

So, the recursive definition of the sequence is: 3, 3+7=10, 10+7=17, 17+7=24, ...

B) The second option given, "anan-1 + 10 a1 = 3" is not a recursive definition of the sequence.

C) The third option given, "San = 10an-1" is also not a recursive definition of the sequence because it uses a different variable 'S' instead of 'a'.

The scale factor of the given drawing is expressed as: 1:5

We are given the dimensions of the scale drawing of the blanket as:

Length = 10 inches

Width = 6 inches

We are given that the actual dimensions of the baby blanket are:

Length = 50 inches

Width = 30 inches

The size by which a shape is enlarged or reduced is called as its scale factor. It is used when we need to increase the size of a 2D shape, such as circle, triangle, square, rectangle, etc. If y = Kx is an equation, then K is the scale factor for x.

The scale factor is:

50/10 = 30/6 = 5

Thus, we have 1:5

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Answer: 97

Step-by-step explanation:

Average: All the numbers added divided by the number of numbers

Start adding the smallest grade in her notes: 87+96+81+89+81= 434/5= 86.8

Keep adding 1 to the last grade until you find a number that gives us an average of 90.

87+96+81+89+97+ 450

Then divide it by the amount of grades

450/5= 90

The second data set best shows asymmetric distribution.

To identify the weekend whose data best shows asymmetric distribution, we need to look for the data set that is skewed, or "lopsided", meaning it has a longer tail on one side than on the other.

We can begin by creating a histogram for each of the data sets to visualize their distributions

The second data set, however, shows a clear skew to the left, with a longer tail of observations on the left side of the center than on the right side.

This makes the second data set the one that best shows asymmetric distribution.

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1) Using the Law of Syllogism, we can combine statement 1 and statement 3 to conclude that Sally weighs more than Jill's car:

If something weighs more than 2000 pounds, then it weighs more than Jill’s car.

Sally weighs more than 2000 pounds.

Therefore, Sally weighs more than Jill's car.

2) Using the Law of Detachment, we can apply statement 2 to our conclusion from the Law of Syllogism to conclude that Sally is too heavy for the bridge:

If something weighs more than Jill’s car, then it is too heavy for the bridge.

Sally weighs more than Jill's car.

Therefore, Sally is too heavy for the bridge.

The Law of Syllogism opines that if two conditional statements have the same terms, then we can combine them to form a conclusion.

The Law of Detachment states that if a conditional statement is true and its hypothesis is true, then its conclusion is also true.

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The probability of drawing two green marbles in a row is 4/9.

Given that, a box has 1 red marble, 1 blue marble, and 4 green marbles.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Number of favorable outcomes = 4

Total number of outcomes = 6

Probability of drawing 1st green marble = 4/6

= 2/3

Probability of drawing 2nd green marble = 4/6

= 2/3

Probability of drawing two marbles = 2/3 × 2/3

= 4/9

Therefore, the probability of drawing two green marbles in a row is 4/9.

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The standard error of the mean δ  for a sample of size n is calculated as:

δ = σ / √(n)

where σ is the population standard deviation and n is the sample size.

For a sample of size 8 taken from a normally-distributed population with a mean of 32 and a standard deviation of 7, the δ is:

δ  = 7 / √(8) ≈ 2.475

The 99.7% confidence interval for the sample mean is given by:

x ± 3 Substituting the values, we get:

32 ± 3(2.475)

where x is the sample mean.

Substituting the values, we get:

32 ± 3(2.475)

which simplifies to:

[24.575, 39.425]

Therefore, about 99.7% of the sample means taken from this population will fall within the interval [24.575, 39.425].

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Tom's ploy to get other boys to do his work:  through Tom's use of persuasion and trickery to get the work done. Option B

The reader is left wondering if Tom will be caught and punished for his conduct because he uses persuasion and deceit to persuade other lads to perform his work for him.

The reader is also left wondering whether the other lads will finally grasp what Tom is up to and cease assisting him, or whether they will continue to be duped by him. The use of persuasion and cunning adds a sense of danger and risk-taking to the situation, heightening the story's tension.

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The percent of data within the following interval from 28 to 82 is 99.73%

From the question, we have the following parameters that can be used in our computation:

Mean = 55

Standard deviation = 9

Scores = from 28 to 82

So, we have

z = (28 - 55)/9 = -3

z = (82 - 55)/9 = 4

This means that it is between a z-score of -3 and a z-score of 3

This is represented as

Probability = (-3 < z < 3)

Using a graphing calculator, we have

Probability =  0.9973

Express as percentage

Probability =  99.73%

Hence, the probability is 99.73%

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The volume of the hemisphere as given in the task content to the nearest tenth is; 718.4 mm³.

It follows from the task content that the volume of the hemisphere as represented in the attached image is to be determined.

Since the volume of the hemisphere is given by;

V = 2/3πr³

where radius = diameter/2 = 14/2 = 7.

Consequently, the volume, V is;

V = 2/3 × π × 7³

V = 718.4 mm³.

Ultimately, the volume is; 718.4 mm³.

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-1 is the value of the slope.

To find the slope of a line that is perpendicular to the line x - y = 0, we need to find the slope of the given line first.

To do this, we can rearrange the equation x - y = 0 to solve for y:

x - y = 0

y = x

So the given line has a slope of 1 since the coefficient of x is 1.

Since a line perpendicular to this line will have a slope that is the negative reciprocal of the slope of the given line, we can find the slope of the perpendicular line by taking the negative reciprocal of 1:

the slope of the perpendicular line = -1/1

the slope of the perpendicular line = -1

Therefore, the slope of a line that is perpendicular to the line x - y = 0 is -1.

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Answer:

(1/2)(4)(3)(2) = 12 cubic yards

The correct answer is A.

Answer: 9.66666667

Step-by-step explanation:

To find the number of days it would take to build a similar house, we would need to create a proportion.

Workers: 27:9

Days: 29:?

Let's simplify.

Workers: 3:1

Days: 29:?

Now, we divide 29 by 3 to see how many days it would take to build a similar house.

29/3=9.666666667 (9.6 repeating)

So, your answer would be 9.6

Hope this helps!

The requreid smallest whole number that rounds to 2,560 to the nearest ten is 2,565. When we round 2,565 to the nearest ten, we get 2,570, which is the desired result.

When rounding a number to the nearest ten, look at the digit in the tens place. If that digit is 5 or greater, we round up by adding 1 to the digit in the hundreds place. If that digit is less than 5, round down by keeping the digit in the hundreds place the same.

In the given question, 2,560 rounded to the nearest ten would be,

2,560 rounded up to 2,560 + 10 = 2,570.

Therefore, the smallest whole number that rounds to 2,560 to the nearest ten is 2,565. When we round 2,565 to the nearest ten, we get 2,570, which is the desired result.

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The solution of the inequality is y > 32.

We have the inequality,

1/4 y > 8

Now, solving the inequality for y

Multiply both side by 4 we get

1/4 y(4) > 8 (4)

y > 32

Thus, the solution of the inequality is y > 32.

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Answer:

the missing value is y = 48.

Step-by-step explanation:

In a direct variation, the ratio of the two variables remains constant. We can use this fact to find the missing value y:

y / 18 = 8 / 3

To solve for y, we can cross-multiply:

y = 18 * 8 / 3

y = 48

Therefore, the missing value is y = 48.

The length x in the similar triangle is 7.06 units.

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.

Therefore, let's use the similarity of the triangle to find the value of x in the triangle.

Hence, using the proportion,

y / 8 = 8 / 17

cross multiply

17y = 64

y = 64 / 17

y = 3.76470588235

y = 3.76

Therefore,

17 - 3.76 = 13.24

Hence,

13.24 / x = x / 3.76

cross multiply

x² = 49.7824

x = √49.7824

x = 7.05566439111

Hence,

x = 7.06 units

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The number name of 97600305 in international system of numeration Ninety-Seven Million, Six Hundred Thousand, Three Hundred and Five.

The number 97600305 can be written with commas as,

Place the commas after hundred.

That is after 305.

Read as three hundred five.

then place the commas after thousands.

Place the comma after 600.

Read as six hundred thousands.

and place the comma after million.

that is after 97.

Read as Ninety-Seven Million.

Combine all and write in the international system of numeration,

The number 97600305 is read as,

Ninety-Seven Million, Six Hundred Thousand, Three Hundred and Five.

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The given question is incomplete, I answer the question in general according to my knowledge:

Write the number name for the numeral 97600305 by inserting commas and write the number name in international system of numeration.

The requried amount of fencing needed t cover the pond in this backyard is 319.36 meters.

A figure of Robert's backyard has been shown, we have to determine the perimeter of his backyard,

The perimeter of backyard = 2L + 2[πw/2]
The perimeter of backyard = 2*78 + 2[π*52/2]
The perimeter of the backyard = 319.36 meters

Thus, the requried amount of fencing needed t cover the pond in this backyard is 319.36 meters.

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The mean number of ice chests in a section is 46.75.

The mean is the average or the most common value in a collection of numbers. In statistics, it is a measure of central tendency along median and mode..

To find the mean number of ice chests in a section, we need to calculate the sum of the ice chests and then divide total number of sections sampled.

Sum of ice chests = 48 + 51 + 26 + 73 + 51 + 48 + 26 + 51

Sum of ice chests = 374

Mean number of ice chests will be:

= (Sum of ice chests) / (Total number of sections sampled)

= 374 / 8

= 46.75

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The Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.

For the Average Order's Gross Profit for the clothing eCommerce company in this scenario, we need to subtract the cost of production and shipping from the Average Order Value as;

⇒ Gross Profit = Average Order Value - Cost of production - Cost of shipping Gross Profit

⇒ Gross Profit = USD 65 - USD 35 - USD 15

⇒ Gross Profit = USD 15

Therefore, the Average Order's Gross Profit for the clothing eCommerce company in this scenario is USD 15.

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The correct sentences in the passage are option A, option B, and option E.

Let's check all the options, then we have

Any two squares are either similar or congruent. The statement is true.

If two lines are parallel, they never intersect. The statement is true.

If all the angles of a polygon are congruent, then it is a square. The statement is false because a regular polygon has an equal angle but it may be a pentagon, hexagon, etc.

The intersection of two lines always forms 4 congruent angles. The statement is false because opposite angles are the same. But if adjacent angles become the same, then the statement will be true.

A line can be drawn through any two distinct points. The statement is true.

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The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

We have,

The volume of the can = The volume of the cylinder - The volume of the three tennis balls.

The volume of the cylinder.

V(cylinder) = πr²h

where r is the radius and h is the height of the cylinder.

Since the can holds three tennis balls snugly, the height of the cylinder is equal to three times the diameter of a tennis ball.

= 3 × 2(3.5 cm)

= 21 cm.

V(cylinder)

= π (3.5 cm)² (21 cm)

= 2709.38 cm³

The volume of one tennis ball.

V (ball) = (4/3)πr³

where r is the radius of the tennis ball. Thus,

V(ball) = (4/3)π(3.5 cm)³ = 179.594 cm³

The total volume of the three tennis balls is:

V(3balls) = 3 V(ball)

= 3(4/3) π (3.5 cm)³

= 538.782 cm³

The volume of the can not be occupied by tennis balls.

V(not occupied) = V(cylinder) - V(3 balls)

= 2709.38 - 538.782

= 2170.598 cm³

The percentage of the can that is not occupied by tennis balls.

percentage = (V(not occupied / V(cylinder)) × 100%

= (2170.598 cm^3/2709.38 cm^3) × 100%

= 80.14%

Therefore,

The percentage of the can that is not occupied by tennis balls is approximately 80.14%.

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On Solving the equations "6x + 3y = 45"  and "2x - 2y = 6", we get that the solution is x = 6 and y = 3.

An "Equation" is defined as a mathematical statement which shows the equality of "two-expressions", which are separated by equal sign.

To solve the simultaneous equations:

6x + 3y = 45      ...equation(1)

2x - 2y = 6         ...equation(2)

We Multiplying the equation(2) by 3, we get:

⇒ 6x - 6y = 18,

Subtracting this equation to the first equation, we get:

⇒ 6x + 3y - 6x + 6y = 45 - 18,

⇒ 9y = 27,

⇒ y = 3,

Now, we can substitute this value of "y" into any of the original equations to find "y". Let's use the first equation:

⇒ 6x + 3y = 45,

Substituting y = 3, we get:

⇒ 6x + 3(3) = 45,

⇒ 6x + 9 = 45,

⇒ 6x = 45 - 9,

⇒ x = 6,

Therefore, the solution to the simultaneous equations is x = 6 and y = 3.

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The given question is incomplete, the complete question is

Solve the following simultaneous equation

6x + 3y = 45  and 2x - 2y = 6.

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{-8})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{5}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{- \cfrac{5}{4}}(x-\stackrel{x_1}{(-4)}) \implies y +8 = - \cfrac{5}{4} ( x +4)[/tex]

The total interest that the credit card holder paid at 11.99% APR for $6,299.59 is D. $559.56.

The total interest is a function of the APR, the principal, and the period involved.

The total interest can be determined using an online finance calculator with some adjustments.

N (# of periods) = 11 months

I/Y (Interest per year) = 11.99%

PV (Present Value) = $6,299.59

PMT (Periodic Payment) = $-350

Results:

FV = $-2,979.39

Sum of all periodic payments = $-3,850.00

Total Interest = $529.80

12th Month Interest = $29.76 ($2,979.39 x 11.99% x 1/12)

Total interest up to the 12th month = $559.56 ($529.80 + $29.76)

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The solution of the equation 1/(x-3) + 1/(x+5) = 1/3 is x=-3, x=7, option D is correct

The given equation is 1/(x-3) + 1/(x+5) = 1/3

Take LCM on left hand side

(x+5)+(x-3)/(x-3)(x+5)= 1/3

2x+2/(x-3)(x+5) = 1/3

2(x+1)/(x-3)(x+5) = 1/3

6(x+1)=(x-3)(x+5)

6x+6 = x²+5x-3x-15

6x+6 = x²+2x-15

x²+2x-6x-15-6=0

x²-4x-21=0

x² -7x+3x-21=0

x(x-7)+3(x-7)

(x+3)(x-7)

The solutions are x=-3, x=7

Hence, the solution of the equation 1/(x-3) + 1/(x+5) = 1/3 is x=-3, x=7, option D is correct

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Answer:7.02

Step-by-step explanation: cause im right