Ian is taking a true/false quiz that has four questions on it. The correct sequence of answers
is T, T, F, T. Ian has not studied and yet guesses all answers correctly- He decides he wants
to determine how likely this is to happen using a simulation. He decides to use a fair coin to
do the simulation.
Describe the design of a simulation that would allow Ian to determine how likely it would
be to guess all answers correctly on this quiz.

The equilateral triangle ABC have a side length of 2 units of the radius length of the circle tangent to the line AB.

An equilateral triangle have all its side lengths equal so;

line AB = line BC = line AC

At points B and C where the lines AB and AC are tangent to the circle is the a side length BC of the equilateral triangle

Line BC form the diameter of the circle which is 2 radius of the circle so;

line BC = 2 × radius of the circle

line BC = 2 × 1

line BC = 2

Therefore, the side length of the equilateral triangle is 2 units of the radius of the circle tangent at point B and C.

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The equation of the line passing through the points (-2,9) and (1,3) is

y = -2x + 11 where the slope is -2 and the y-intercept is +11

The equation of a line can be formed with the help of the slope of the line and a point on the line. The slope of the line is the inclination of the line with the positive x-axis and is expressed as a numeric integer, fraction, or the tangent of the angle it makes with the positive x-axis. The point refers to a point in the coordinate system with the x coordinate and the y coordinate.

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

y1 = 9

y2 = 3

x1 = -2

x2 = 1

m = (3 - 9) / (1 - (-2))

m = - 6 / 3

m = - 2

The equation of the line;

m = (y - y1) / (x - x1)

-2 = y - 9 / x - 1

y - 9 = -2(x - 1)

y - 9 = -2x + 2

y = -2x + 11

Therefore the y-intercept is +11.

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Answer: There is no picture

Step-by-step explanation:

The given parametric equation represents the graph mentioned in Option A.

A parametric equation is defined as a kind of equation that inherit an independent variable called a parameter, and where dependent variables are defined as continuous functions of the parameter.

here,
For equation, x = t cos (t), y = t, z = t sin(t), t ≥ 0.
Since,

x² + y² = t²cos²(t) + t² sin²t
x² + y² = t²
x² + y² = z²

Here, the x-z cross-section of the curve is a circle. But as t accumulates, the radius of the circle also advances in the y direction, and those circular cross-sections extend as the value of the parameter t increase.
The curve will draft as circles in x-z planes while moving towards y direction and also the radius of those circular cross sections increases at the same rate as its advancement towards y direction.

Thus, the given parametric equation represents the graph mentioned in Option A.

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Answer:

Step-by-step explanation:

Given L is the line through A(1, 2, -1) and B(5, -3, 4), you want its direction vector, a parameterization of L, 2 points on L that are 2 units from A, and a unit speed parametrization of L.

A direction vector for L will be the vector AB.

  [tex]\overrightarrow{AB}=B-A=(5,-3,4)-(1,2,-1)\\\\\boxed{\overrightarrow{AB}=(4, -5,5)}[/tex]

The parameterized equation will be ...

  [tex]L=A+t\cdot\overrightarrow{AB}\\\\\boxed{L=(1+4t,2-5t,-1+5t)}[/tex]

The direction vector has length √66, so we can find two points on L that are 2 units from A by using t = ±2/√66 in the parameterized equation.

Here, they are:

  P1 = L(2/√66) = (1 +8/√66, 2 -10/√66, -1 +10/√66)

  P2 = L(-2/√66) = (1 -8/√66, 2 +10/√66, -1 -10/√66)

In the Answer section above, these are written with rationalized denominators.

The unit speed parametrization uses the unit direction vector instead of the unnormalized direction vector in the parameterized equation. Effectively, t is scaled by a factor of 1/√66.

  L = (1 +4t/√66, 2 -5t/√66, -1 +5t/√66)

In the Answer section above, this is written with rationalized denominators.

You might notice here that it is easier to answer part 3 if you have this equation. You need only substitute t=±2 to get the points 2 units from A.

The solution to the given quadratic equation is x = -1 + 3i OR x = -1 - 3i

From the question, we are to solve the given quadratic equation

From the given information,

The quadratic equation is

x² + 2x + 10 = 0

Using the Quadratic formula,

x = [-b ± √(b² - 4ac)] / 2a

From the equation,

a = 1, b = 2, and c = 10

Then,

x = [-b ± √(b² - 4ac)] / 2a

x = [-(2) ± √((2)² - 4(1)(10))] / 2(1)

x = [-2 ± √(4 - 40)] / 2

x = [-2 ± √(-36)] / 2

x = [-2 ± -6i] / 2

x = -1 ± 3i

x = -1 + 3i OR x = -1 - 3i

Hence, the solution is x = -1 + 3i OR x = -1 - 3i

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6% of the salary is $366

The total amount that would in the retirement account in the account each month is $732.

The amount that would be in the retirement account when you retire is $345,418.50.

The amount of money that you put in the account is $162,504.

The amount of money that the employer put in the account is $162,504.

The interest that was gained over the years is $20,410.50.

3% of the salary is $183.

The total amount that would in the retirement account in the account each month is $366.

The amount that would be in the retirement account when you retire is $172,709.25.

The amount of money that you put in the account is $81,252

The amount of money that the employer put in the account is $81,252

The interest that was gained over the years is $10,205.25.

6% of the salary = salary x percentage

6% of the salary = 6% x $6,100

6% of the salary = 0.06 x $6,100 = $366

The amount in your account at the end of the month = amount the company puts + amount you deposit

= $366 + $366 = $732

Amount that would be in your retirement account = (1 + interest rate) x amount in the account

Amount that would have been deposited in the account at retirement = number of years until retirement x number of months in a year x amount deposited each year

Amount in the account at retirement = $732 x 12 x (62 -25)

$732 x 12 x 37 = $325,008

Amount in the account at retirement = (1 + 0.0628) x $325,008 = $345,418.50

Amount the employer put in the account =  $325,008 \ 2 = $162,504

Interest earned = $345,418.50 - $325,008 = $20,410.50

3% of the salary = salary x percentage

3% of the salary = 3% x $6,100

3% of the salary = 0.03 x $6,100 = $183

The amount in your account at the end of the month = amount the company puts + amount you deposit

= $183 + $183 = $366

Amount that would be in your retirement account = (1 + interest rate) x amount in the account

Amount that would have been deposited in the account at retirement = number of years until retirement x number of months in a year x amount deposited each year

Amount in the account at retirement = $366 x 12 x (62 -25)

$366 x 12 x 37 = $162,504

Amount in the account at retirement = (1 + 0.0628) x $325,008 = $172,709.25

Amount the employer put in the account =  $162,504 \ 2 = $81,252

Interest earned = $172,709.25 - $162,504 = $10,205.25

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The correct solutions for this question are as:

(A) Bearing of B from A = 72°

(B) Bearing of B from C = 342°

(C) Bearing of A from B = 252°

(D) Bearing of A from C = 293°

Step by step solution:

(A) Bearing of B from A:

= 72° (Given in question)

(B) Bearing of B from C: = 342°

Solution:

As sum of co-interior angles is 180° , i.e.  ∠NBC +∠NCB =180°

so, 162° + ∠NCB = 180°

     ∠NCB = 180°-162°

     ∠NCB = 18°

reflexive angle NCB =360° - ∠NCB

reflexive angle NCB = 360° - 18°

reflexive angle NCB = 342°

So, bearing of B from C: = 342°

(C) Bearing of A from B: = 252°

Solution:

First extend the line AB to any point (let's say "X")

So, ∠NBX = 72°   [BY USING CORRESPONDING ANGLES]

Bearing of A from B = ∠NBX + 180°

Bearing of A from B =72° + 180°

Bearing of A from B =252°

(D) Bearing of A from C: = 293°

Solution:

Bearing of A from C= 360° - (∠BCA + ∠BCN)

Bearing of A from C= 360° - (49° + 18°)

Bearing of A from C= 360° - (67°)

Bearing of A from C= 293°

Important Points for "Bearing of Angles":

A bearing is an angle that is calculated clockwise from the north. A traverse should be regarded as anticlockwise unless differently stated or obvious from the bearings.

The angle between two lines cannot be directly read using a regular compass. By tracking the two lines bearings away from their point of confluence, the angles can be found.

Two angles—an inner angle and an exterior angle—are created when the two lines converge at a place. These two angles add up to a 360° angle.

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The total length needed in inches will be 490.5 inches.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

Since the machinist must cut 12 strips of metal that are each 3 ft 4 7/8 in. long  The total length needed in inches will be:

= (3 ft 4 7/8 inch × 12)

Note that 1 feet = 12 inches

= (12 × 3) + (4 7/8) × 12

= (36 + 4.875) × 12

= 490.5 inches

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Answer:

y = 1/3x - 7

Step-by-step explanation:

start with the point-slope form:

(y-y1) = m(x-x1)

substitute the values of (x,y) into the formula:

(y-(-5)) = 1/3(x-6)

y+5 = 1/3x - 2

now write in slope-intercept form:

y = 1/3x - 2 - 5

y = 1/3x - 7

Answer:

= 18√2

decimal =25.45584412

The first equation in the second system is a multiple of  second equation

is the first equation and the second equation  in the second system is a multiple of both equation in the first system

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The ratio 81:108 can be simplified to 9:13. To find the simplest form of the ratio, you can divide both numbers by the greatest common factor. The greatest common factor of 81 and 108 is 9, so you can divide both numbers by 9 to get the simplified ratio of 9:13.

Answer:

it is not always true that 75% of a number will be greater than 50% of any other number

Step-by-step explanation:

Leila's statement is not true. It is possible for 50% of a number to be greater than 75% of another number.

For example, consider the numbers 10 and 100. 50% of 10 is 5, and 75% of 100 is 75. In this case, 50% of 10 (5) is greater than 75% of 100 (75).

Here's another example: 50% of 20 is 10, and 75% of 30 is 22.5. In this case, 50% of 20 (10) is again greater than 75% of 30 (22.5).

Therefore, it is not always true that 75% of a number will be greater than 50% of any other number.

Answer:

p = 20

Step-by-step explanation:

120 divided by 6 would = 20

Answer: p = 20

Step-by-step explanation:

120/6=20

6x20=120

Alright I got it.

So first what I did was I made an equation that match did the word problem.

The equation was 15x=250+10x

When I solved it the answer was 50.

so they would need to sell 50 Tshirts (x=50)

For, n = 0, 1 we proved that 7⁽ⁿ⁺⁴⁾ - 7ⁿ hence by induction it is divisible by 30 for all n ∈ N.

An inductive proof requires two cases. The first, or base case, establishes the proposition that n = 0 without requiring any prior knowledge of other situations. The second example, the induction step, demonstrates that if the assertion is true for any particular case where n = k, then it must also be true for the subsequent case when n = k + 1. These two actions prove that the statement is true for all n = 1 natural numbers. The base case establishes the truth of the statement for all natural numbers n N, but it does not always start with n = 0. Instead, it frequently starts with n = 1, and it may also start with any fixed natural number n = N.

Given, We have to prove 7⁽ⁿ⁺⁴⁾ - 7ⁿ is divisible by 30 for all n ∈ N.

Let, n = 0.

Therefore,

7⁴ - 7⁰.

= 2401 - 1.

= 2400.

= 30×80, Divisible by 30.

Similarly for n = 1 we have,

7⁵ - 7¹.

= 16807 - 7.

= 16800.

= 30×560.

Hence by induction, the cycle will continue.

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If you are dealt one card from a​ 52-card deck. The probability that you are not dealt a jack or a ten is 12/13.

Since there are 4 aces in a deck of card 52 first step is to find the number of cards  not aces in a deck of 52

Number of cards  not aces in a deck = 52 -4

Number of cards  not aces in a deck = 48

Now let find the probability that you won't draw an ace.

Probability = 48/52

Probability = 24/26

Probability = 12/13

Therefore we can conclude that the probability is 12/13.

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The figure with equal opposite sides and all the interior angles being right angles is a rectangle.

A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.

A rectangle is a special type of quadrilateral in which opposite sides are of equal length(not all sides are the same) and all the interior angles are right angles.

From the given diagram the opposite sides are equal and all the interior angles are right angles hence the figure is a rectangle.

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Answer:

x = 32

Step-by-step explanation:

• any lower base angle is supplementary to any upper base angle.

here base angle = 2(x - 10) and upper base angle = 4x + 8

supplementary angles sum to 180°

sum the base and upper base angles and equate to 180

2(x - 10) + 4x + 8 = 180

2x - 20 + 4x + 8 = 180

6x - 12 = 180 ( add 12 to both sides )

6x = 192 ( divide both sides by 6 )

x = 32

I'm sorry but I didn't get that

The slope-intercept form of the equations presented on the graph are;

y = 4

y = 3

The slope-intercept form of the equation of a line is; y = m·x + c, where;

m = The slope of the graph

c = The y-intercept of the graph

The equation of the lines in the graphs (blue line, and red line) are found as follows;

The slope of the blue line is found using the points on the graph as follows;

The coordinates of points on the blue line graph are; (0, 4), (2, 4), (4, 4)

The slope is therefore; m = (4 - 4)/(4 - 2) = 0

The y-intercept, obtained from the graph is; c = 4

The value of the slope, m = 0, indicates that the graph is an horizontal line with an equation y = c

c = 4

The equation of the blue line graph in slope-intercept form is therefore;

The coordinates of points on the red line graph are; (0, 3), (2, 3), (4, 3)

The slope of the red line graph is therefore;

m = (3 - 3)/(4 - 2) = 0

The y-intercept of the red line graph is; c = 3

The value of the slope, m = 0, and the y-intercept, c = 3, indicates that the equation of the red line graph is therefore;

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Answer:

$2

Step-by-step explanation:

Amount of pounds that Ben get back is £75.

Exchange rate is defined as the value of a currency with respect to another currency in order to convert the currency.

Ben changes £800 to Euros before he goes on holiday.

Before holiday, exchange rate is, £1 = 1.25 Euro

£800 = 800 × 1.25 Euros = 1000 Euros

He spends 895 Euros.

Euros left = 1000 - 895 = 105 Euros

Now, the exchange rate is £1 = 1.40 Euro.

or 1.40 Euro = £1

⇒ 1 Euro = £ 1/1.40

⇒ 105 Euros = £ (1/1.40) × 105 = £75

Hence Ben got £75 of pounds back.

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Part A

g(x) = 9.25x

g(8) = 9.25*8

g(8) = 74

He would make $74 before taxes if he worked 8 hours.

------------------------------------------------------

Part B

g(x) = 9.25x

g(14) = 9.25*14

g(14) = 129.50

He would make $129.50 before taxes if he worked 14 hours.

------------------------------------------------------

Part C

g(x) = 9.25x

g(27.5) = 9.25*27.5

g(27.5) = 254.375

g(27.5) = 254.38

He would make $254.38 before taxes if he worked 27.5 hours.

Answer:

Solution below.

Step-by-step explanation:

This question is basically asking you to substitute corresponding x values to find g(x).

Given the function from the question:

g(x) = 9.25x where x is the work hours and g(x) is the wages.

Given x = 8,

g(8) = 9.25 * 8 = $74.00

Given x = 14,

g(14) = 9.25 * 14 = $129.50

Given x = 27.5,

g(27.5) = 9.25 * 27.5 = $254.38 (rounded off to nearest cent)

The perimeter of the isosceles triangle with altitude 30 inches and base 10 inches is calculated to be 70.82 inches

Perimeter of a triangle refers to the surface dimensions, this is calculated by the formula

Perimeter, P = a + b + c

where

a, b, c are sides of the triangle

The third side of the triangle will be calculated using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

The right triangle consist 1/2 the isosceles triangle base = 5 inches and the altitude = 30 inches

plugging the values as in the problem

let x be the required distance

x² = 30² + 5²

x² = 900 + 25

x² =  925

x = √925

x = 30.41 inches

Perimeter of the isosceles triangle

= 30.41 + 30.41 + 10

= 70.82 inches

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