What is the value of x?

5/6 is the probability that the number landed on an odd or is greater than 4

Probability is defined as the likelihood or chance that an event will occur.

If a number cube is rolled, the sample space will be:

(S) = {1, 2, 3, 4, 5, 6}

n(S) = 67

If it lands on a odd number, the number of events will be:

(E) = {1, 3, 5}

n(E) = 3

If it lands on a number greater than 4 the number of events will be:

(E) = {5, 6}

n(E) = 2

Pr(even or greater then 4) = 3/6 + 2/6

Pr(even or greater then 4) = 5/6

The probability that the number landed on an odd or is greater than 4 is 5/6

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Answer: 4/6 or 2/3

Step-by-step explanation:

Even number=3/6 or 1/2 chance

Greater than 4=2/6 chance or 1/3 chance

Union basically means either or

So: 1/2+1/3 or 3/6+2/6 or 5/6

This doesn't always work though, so we use trial and error

1 2 3 4 5 6

1 3 5 are the ones not even

13 are the ones not greater than 4

The scale factor k is 2.

Given that 2 quadrilateral that KLMJ and K'L'M'J'.

To find the scale factor by inspection method.

Consider the given data and  inspection method gives,

In quadrilateral KLMN, KL = 2 units, LM = 6 units, MJ = 5 units,

KJ =  6 units.

In quadrilateral K'L'M'J', K'L' = 4 units, L'M' = 12 units, M'J'= 10 units,

K'J '=  12 units.

That implies,

Quadrilateral K'L'M'J' is twice the quadrilateral KLMN.

Thus, k =  2.

Therefore, the scale factor k is 2.

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The value of x and y from the given triangle are 52.3 feet and 42.84 feet respectively.

Given that, an engineer sketches a right triangle to show that the screen in a movie theater is 30 ft high and that the vertical viewing angle from the from row is 35 degree.

We know that, sinθ = Opposite/Hypotenuse

sin35° = 30/x

0.5736 = 30/x

x = 30/0.5736

x = 52.3 feet

We know that, tanθ = Opposite/Adjacent

tan35°=30/y

0.7002=30/y

y = 30/0.7002

y = 42.84 feet

Therefore, the value of x and y from the given triangle are 52.3 feet and 42.84 feet respectively.

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The circumference of a circle is calculated using the formula:

[tex]\sf\:C = 2 \pi r \\[/tex]

where C represents the circumference and r represents the radius of the circle.

Given that the radius of the circle is one meter (r = 1), we can substitute this value into the formula to find the circumference:

[tex]\sf\:C = 2 \pi (1) \\[/tex]

[tex]\sf\:C = 2 \pi \\[/tex]

Therefore, the circumference of a circle with a radius of one meter is [tex]\sf\:2 \pi \\[/tex] meters.

Rounding to the nearest tenth of a centimeter, the slant height is approximately 43.1 centimeters.

The lateral area of a cone is given by the formula L = πrs, where L is the lateral area, r is the radius, and s is the slant height.

We are given that the lateral area L is equal to 612π m², and the radius r is 14.2 cm (0.142 m).

We can rearrange the formula to solve for the slant height s:

L = πrs

612π = π × 14.2 × s

Dividing both sides by π and 14.2:

612 = s × 14.2

Now, solve for s:

s = 612 / 14.2

s ≈ 43.0986

L = rs, where L is the lateral area, r is the radius, and s is the slant height, gives the lateral area of a cone.

We are informed that the radius r is 14.2 cm (0.142 m), and the lateral area L is equivalent to 612 m2.

To solve for the slant height s, we may rewrite the formula as follows:

L = πrs 612π = π × 14.2 × s

612 = s 14.2 after dividing both sides by and 14.2

Next, find the value of s: s = 612 / 14.2 s 43.0986

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[tex] \sqrt[5]{ {2}^{13} \times {3}^{5} } [/tex]

[tex] \sqrt[5]{ {2}^{13} } [/tex]

James is eligible for a refund of £47.19 for one month's subscription.

To calculate the refund for James's subscription, we need to determine the cost of one month's subscription and subtract it from the total amount he has paid for four quarters.

James pays £12.87 per quarter, which means he pays £12.87 x 4 = £51.48 for a full year in advance.

To find the cost of one month's subscription, we divide the annual cost by 12 (number of months in a year):

£51.48 / 12 = £4.29

The cost of one month's subscription is £4.29.

To calculate the refund, we subtract the cost of one month's subscription from the total amount James has paid:

£51.48 - £4.29 = £47.19

We must figure out the price of a month's membership and deduct it from the total amount James has paid for four quarters in order to compute the refund for his subscription.

James pays £12.87 every quarter, or £12.87 x 4 = $51.48 for the entire year up front.

We divide the yearly cost by 12 (the number of months in a year) to get the price for a month's subscription:

£51.48 / 12 = £4.29

Therefore, a membership for one month costs £4.29 in total.

We deduct the price of a single month's membership from James' overall payment to determine the refund:

£51.48 - £4.29 = £47.19

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Answer:

let the percentage be x.

32 = x% of 80

32 = x/100 *80

32 = 80x/100

32*100 = 80x

0.32 = 80x

0.32/80 = x

x = 0.004

x = 40/100

x = 40%

Answer:

Jane spent on coffee.

She started with $80 on her gift card and ended with $49.76, so she spent:

80 - 49.76 = $30.24

We know that she bought coffee that cost $7.56 per pound, so we can set up an equation to find how many pounds of coffee she bought:

7.56x = 30.24

where x is the number of pounds of coffee she bought.

Solving for x, we get:

x = 30.24 / 7.56 = 4

So Jane bought 4 pounds of coffee with her gift card.

It is not a statistical question to ask "How much did Adventure Rapids water park make on opening day this year?"

The process of obtaining information and using it to infer or derive conclusions about a population or phenomenon is known as statistical question-solving. It usually concentrates on trends, patterns, or connections between various variables.

Instead of attempting to analyse or comprehend facts, the inquiry in question asks for a single numerical value (the amount of money made on opening day).

Making statistical inferences or generalising from a sample to the population are not involved. As a result, it does not satisfy the requirements for a statistical question.

Thus, the answer is no.

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Answer:

Mr Jones: $399.69
Mr Williams: $290.31

Step-by-step explanation:

Calculate the total investment: $2000 + $1450 = $3450.

Calculate Mr Jones' share: ($2000 / $3450) * $690 ≈ $399.69.

Calculate Mr Williams' share: ($1450 / $3450) * $690 ≈ $290.31.

Hence, Mr Jones will receive approximately $399.69 in profit, while Mr Williams will receive approximately $290.31 in profit.

Answer:

1:72

Step-by-step explanation:

The scale of a drawing is the ratio of the length in the drawing to the real length.

Drawing length: 7 inches

Real length: 42 ft × 12 in. / ft = 504 in.

Scale:

7 in. to 504 in.

Divide both numbers by 7:

1 in. to 72 in.

Scale: 1:72

It is noticed that the factors then the x-intercepts are the same value as that of factors.

Given that, the quadratic equation represented on the graph in factored form is y=(x-3)(x+2).

From the graph, x-intercepts are x=-2 and x=3.

The vertex of the given quadratic graph is (0.5, -6)

Therefore, it is noticed that the factors then the x-intercepts are the same value as that of factors.

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We can say that 120 is 80% of 150.The percentage that 120 is of 150 will be the length of this line divided by the length of the entire double number line (which is 100%).

To use the double number line diagram to find what percent 120 is of 150, we first need to plot the two numbers on the double number line. We can do this by drawing a horizontal line and labeling it with the two numbers, 120 and 150, and then dividing the line into equal segments.

Next, we can find the difference between the two numbers (150-120=30) and use this to label the corresponding points on the double number line. The point representing 120 should be 3/4 of the way between the two numbers (since 120 is 3/4 of 150).

Finally, we can use the double number line to find the percentage that 120 is of 150. To do this, we can draw a vertical line from the point representing 120 up to the top of the double number line.

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The average weight of the 50 students is 37 kilograms.

In mathematics, a continuous series is a sequence of numbers that has no gaps between any of its values. In order to find the average weight of a continuous series of 50 students, we can divide the sum of their weights by the total number of students.

Let us assume that the weight of each student is measured in kilograms. If the sum of the weights of 50 students is 1,850 kilograms, then the average weight can be calculated as follows:

Average weight = Total weight / Number of studentsIn this case, the total weight is 1,850 kilograms and the number of students is 50. Therefore, we can substitute these values into the formula and simplify as follows:

Average weight = 1,850 / 50Average weight = 37 kilograms It is important to note that this calculation assumes that all of the weights are evenly distributed among the students and that there are no outliers or extreme values that would skew the average.

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These symbolic representations use the symbols ∧ (and) to indicate that all conditions must be true, ∨ (or) to indicate that at least one condition must be true, and ¬ (not) to negate a statement.

Using the given symbols ∧ (and), ∨ (or), and ¬ (not), we can represent the statements as follows:

Let h = "John is healthy," w = "John is wealthy," and s = "John is wise."

John is healthy and wealthy but not wise.

Symbolic form:

h ∧ w ∧ ¬s

John is not wealthy but he is healthy and wise.

Symbolic form:

¬w ∧ h ∧ s

John is neither healthy, wealthy, nor wise.

Symbolic form:

¬h ∧ ¬w ∧ ¬s

John is neither wealthy nor wise, but he is healthy.

Symbolic form:

¬w ∧ ¬s ∧ h

John is wealthy, but he is not both healthy and wise.

Symbolic form:

w ∧ (¬h ∨ ¬s)

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Answer: D

Step-by-step explanation:

you can just note the points where the 2 lines meet and note down the x values

The greatest distance that can be filmed by the drone is 6374.5 km. Rounded to the nearest kilometer, 6375 km.

Now, For the greatest distance that can be filmed by a drone with a maximum altitude of 0.12 km, we can use the Pythagorean theorem.

Let's a right triangle with one leg being the radius of the Earth 6378 km and the other leg being the maximum altitude of the drone 0.12 km.

Hence, The hypotenuse of this triangle represents the line of sight from the drone's camera to the horizon.

Hence, By Using the Pythagorean theorem, we can solve for the length of the hypotenuse:

h² = 6378² + 0.12²

h = √40684000.145

h = 6374.5 km

Therefore, The greatest distance that can be filmed by the drone is 6374.5 km. Rounded to the nearest kilometer, 6375 km.

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Hello!

(3x⁶y⁴)(-4x²y³)

= -12x⁶y⁴x²y³

= -12x⁸y⁷

The speed that a tsunami can travel is modeled by the equation s = 356 StartRoot d EndRoot , where S is the speed in kilometers per hour and d is the average depth of the water in kilometers.

This is written mathematically as:

S = 356√d

S = 200km/hr

Hence:

200km/hr = 356√d

Divide both sides by 356

200/356 = 356√d/356

√d = 200/356

Square both sides

(√d)² = (200/356)²

d =(0.5617977528)²

d = 0.3156167151km

Approximately = 0.32km

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1)

Given:

cos^2x = sin^2x + 1/2

Now,

Further simplify the trigonometric equation to get the value of x .

cos²x - sin²x = 1/2

∴cos² - sin²x = cos2x

cos2x = 1/2

2x = cos^-1(1/2)

2x = 60

x = 30° .

Hence the value of x is 30° .

2)

Given:

2cos( π/2 - x) * sin (π/2 + x) - 1 = 0

∴cos(90-x) = sinx

∴sin(90 +x) = cosx

2sinxcosx = 1

sin2x = 1

2x = sin^-1(1)

2x = 90

x = 45° .

Hence the value of x is 45° .

3)

Given:

1 + cosx = cos x/2

Further simplifying,

1 = cosx/2  - cosx

Put x = 180

1 = cos90 - cos180

1 = 0 - (-1)

1 =1

Hence LHS = RHS and x = 180°

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The optimal solution for the linear programming problem is X1 = 5, X2 = 10, S1 = 0, and S2 = 0.

Based on the given table, the linear programming model can be represented as follows:

Objective function:

Maximize Z = 50X1 + 40X2

Constraints:

Subject to:

X1 + 5X2 + S1 = 20

X1 + 5X2 + S2 = 30

X1, X2, S1, S2 ≥ 0

Solution Group of the Primary Program:

The solution group represents the values of the decision variables (X1, X2) and the slack variables (S1, S2) that satisfy the constraints and optimize the objective function.

From the given table, the solution group is as follows:

X1 = 5

X2 = 10

S1 = 0

S2 = 0

This means that the optimal solution for the linear programming problem is X1 = 5, X2 = 10, S1 = 0, and S2 = 0, which maximizes the objective function Z = 50X1 + 40X2.

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The interest for Part 1 is approximately $385.10.

The interest for Part 2 is approximately $709.31.

The formula is as follows:

Interest is calculated as follows: Principal * Rate * Time

Where

Part 1:

$132,000 is the principal.

(Decimal) Rate = 12% = 0.12

Time = 8 days/365 days.

How much interest is there in Part 1?

Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10

Therefore, the interest for Part 1 is approximately $385.10.

Part 2:

$106,750 as the principal

(Decimal) Rate = 12% = 0.12

Time = 20 days / 365 days.

How much interest will there be in Part 2

Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31

Therefore, the interest for Part 2 is approximately $709.31.

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A pair of corresponding angles, alternate interior angles, and alternate exterior angles include the following:

Corresponding angles: ∠1 ≅ ∠5.

Alternate interior angles: ∠4 ≅ ∠6.

Alternate exterior angles: ∠2 ≅ ∠8

In Mathematics, corresponding angles can be defined as a postulate (theorem) which states that corresponding angles are always congruent when the transversal intersects two (2) parallel lines:

∠1 ≅ ∠5

By applying the alternate interior angles theorem to parallel lines m and n, we have the following congruent angles:

∠4 ≅ ∠6

By applying the alternate exterior angles theorem to parallel lines m and n, we have the following congruent angles:

∠2 ≅ ∠8

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The height of the pyramid is of about 88.5 in.

The Pythagorean Theorem states that in the case of a right triangle, the square of the length of the hypotenuse, which is the longest side,  is equals to the sum of the squares of the lengths of the other two sides.

Hence the equation for the theorem is given as follows:

c² = a² + b².

In which:

The parameters for this problem are given as follows:

Hence the height h is obtained as follows:

h² + 19.6² = 90.6²

[tex]h = \sqrt{90.6^2 - 19.6^2}[/tex]

h = 88.5 in.

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a) To find the number of students getting more than 45 marks, we count the students whose marks are greater than 45 in the given list.

In the given list, the students with marks greater than 45 are: 50, 49, 47, 48, 49, 48, 47, 49, 48, 50, 47, 49, 48, 46, 47, 48, 47.

Counting these numbers, we find that there are 17 students who obtained more than 45 marks.

b) To find the number of students getting less than 45 marks, we count the students whose marks are less than 45 in the given list.

In the given list, the students with marks less than 45 are: 44, 44, 42, 41, 41, 42, 41, 44, 44, 42, 45, 45, 45, 44, 45.

Counting these numbers, we find that there are 15 students who obtained less than 45 marks.

c) To find the maximum number of students getting the same marks, we look for the mark that appears most frequently in the given list.

In the given list, the marks obtained by the students are: 44, 50, 44, 49, 42, 47, 45, 42, 44, 48, 49, 48, 47, 49, 47, 41, 45, 48, 41, 48, 41, 42, 47, 49, 49, 48, 50, 47, 49, 48, 46, 44, 45, 45, 46, 44, 42, 47, 48, 45.

Counting the frequency of each mark, we find that the marks 47 and 48 appear most frequently, with a count of 6 each. Therefore, the maximum number of students getting the same marks is 6.

d) To find the average marks obtained by the students in the class, we sum up all the marks and divide by the total number of students.

Total marks = 44 + 50 + 44 + 49 + 42 + 47 + 45 + 42 + 44 + 48 + 49 + 48 + 47 + 49 + 47 + 41 + 45 + 48 + 41 + 48 + 41 + 42 + 47 + 49 + 49 + 48 + 50 + 47 + 49 + 48 + 46 + 44 + 45 + 45 + 46 + 44 + 42 + 47 + 48 + 45

           = 1912

Total number of students = 40

Average marks = Total marks / Total number of students

                 = 1912 / 40

                 = 47.8

Therefore, the average marks obtained by the students in the class is 47.8.

e) To find the number of students getting more than the average marks, we count the students whose marks are greater than 47.8.

In the given list, the students with marks greater than 47.8 are: 50, 50, 49, 48, 49, 48, 49, 48, 50, 49, 49, 48, 48, 50, 49, 49, 48, 48, 47, 49, 49, 48, 50, 47,

49, 49, 48, 50, 47, 49, 49, 48, 48, 49, 48, 47, 48, 49, 49, 48, 50, 49.

Counting these numbers, we find that there are 40 students who obtained more than the average marks.

The equation matches the graph is -2cosx.

The graph of the function y = -2cos(x) represents a cosine function that has been reflected vertically and stretched by a factor of 2.

The cosine function is a periodic function that oscillates between -1 and 1. The negative sign in front of the function (-2cos(x)) reflects the graph across the x-axis. This means that all the positive values of the cosine function become negative, and vice versa.

So, the coefficient of -2 stretches the graph vertically by a factor of 2. This means that the amplitude of the graph doubles, and the oscillations are more spread out vertically.

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Answer: 65,82,101,122

Step-by-step explanation:

Its adding odd numbers because first it was +1 then +3, +5 +7, +9 +11, +13 and so on :)))