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The number of angles that are alternate interior angles with angle 9 are 2 angles.

In Mathematics and Geometry, the Alternate Interior Angles Theorem states that when two (2) parallel lines are cut through by a transversal, the pairs of alternate interior angles that are formed are congruent:

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

∠7 ≅ ∠9 (The transversal is line s while the parallel lines are t and u).

∠9 ≅ ∠15 (The transversal is line u while the parallel lines are s and r).

In conclusion, we can logically deduce that there are only 2 angles that are alternate interior angles with angle 9.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer: 0.0493 Chance of Probability

Answer:11

Step-by-step explanation:

Answer:

x = 155° , y = 25° , z = 155°

Step-by-step explanation:

in a parallelogram

• opposite angles are congruent

• consecutive angles sum to 180°

then

x + 25° = 180° ( subtract 25° from both sides )

x = 155°

y = 25°

z = 155°

(a) The algebraic expression, -5x - 2 + 5x + 2 is simplified as 0.

(b) The algebraic expression, 5x -2  - (5x + 2) is simplified as -4.

The given algebraic expression is simplified by adding similar terms together, as it will make the expression to be in simplest form.

The given algebraic expressions are;

-5x - 2 + 5x + 2

5x -2  - (5x + 2)

The first algebraic expression is simplified as follows;

-5x - 2 + 5x + 2

collect similar terms;

(-5x + 5x) + (-2 + 2)

= 0 + 0

= 0

The second algebraic expression is simplified as follows;

5x - 2 - (5x + 2)

= 5x - 2 - 5x - 2

collect similar terms;

= (5x - 5x) + (-2 - 2)

= 0 - 4

= - 4

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The excess amount in the form of interest is K58,784.92.

To calculate the monthly installment amount and the excess amount in the form of interest, we can use the loan amount, interest rate, and tenure.

Loan amount: Total expenditure - Medical insurance coverage

Loan amount = K85,800 - K20,000

Loan amount = K65,800

Interest rate per month: 17% / 12 months = 1.42%

Tenure: 12 years × 12 months

= 144 months

Monthly interest rate = 1.42% = 0.0142

Number of months = 144

Monthly installment = (K65,800 × 0.0142) / (1 - (1 + 0.0142)⁻¹⁴⁴)

Monthly installment = K763.43

So, the monthly installment amount is approximately K763.43.

To calculate the excess amount in the form of interest, we can subtract the total interest paid from the loan amount.

Total interest paid = (Monthly installment × Number of months) - Loan amount

Total interest paid = (K763.43 × 144) - K65,800

Total interest paid= K58,784.92

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Part 1: Oliver must sell more than 33 pineapples to make a profit.

Part 2: Oliver must sell at least 33 pineapples to cover the cost of producing 50 pineapples and make a profit.

Part 1:

The inequality is 6p > 200.

To solve for p, we divide both sides of the inequality by 6. This gives us p > 33.33.

Therefore, Oliver must sell more than 33 pineapples to make a profit.

Part 2:

To cover the cost of producing 50 pineapples, Oliver must sell at least 50 * $6 = $300 worth of fruit.

Since he must sell more than $200 worth of fruit to make a profit, he must sell at least 200 / 6 = 33.33 pineapples.

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The parent function for the given function is y=[tex]x^\frac{1}{3}[/tex].

The given function is [tex]f(x)=\sqrt[3]{27x-81}[/tex].

The parent function of a family of functions is the simplest one that satisfies the definition of that particular type of function. For example, the simplest linear function would be y = x which is the parent function of the linear family of functions.

The parent function y=[tex]x^\frac{1}{3}[/tex], horizontally shrink by a factor of 27 shift 3 units to the right.

Therefore, the parent function for the given function is y=[tex]x^\frac{1}{3}[/tex].

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Answer:

2/3 * 660

Step-by-step explanation:

If we convert 65% to a decimal, we get 0.65.

First, it will helpful to find exactly what is 65% of 668:  

0.65 * 668 = 434.2 and thus 65% of 668 is exactly 434.2.

Similarly, if you convert 2/3 to a decimal, you get 0.66 repeating.

2/3 * 660 = 440 which is only 10.2 units larger than 434.2.  Thus, 2/3 * 660 is the most accurate estimate of 65% of 668.

Answer:

Step-by-step explanation:

If the diameter is 4 meters, then the radius has to be 2 because the radius is half of the diameter.

The cube root of -2i,

⇒ ∛2[ cos(π/6) + i sin(π/6) ]

We can represent -2i in polar form as,

r(cosθ + i sinθ)

by computing its magnitude and angle.

The magnitude of -2i is 2

Since the absolute value of any imaginary number is equal to its magnitude.

To find the angle θ,

We can use the fact that the tangent of an angle is equal to the ratio of the opposite side to the adjacent side.

In this case,

The opposite side is -2 and the adjacent side is 0.

Therefore, we have tanθ = -2/0, which is undefined.

However,

We can use the fact that the cube root of a complex number is equal to the cube root of its magnitude times exp(iθ/3) to find the cube root of -2i.

So, the cube root of -2i is equal to the cube root of 2 times exp(iθ/3).

Now, we need to find the value of θ/3. Since θ is undefined,

we will represent it as π/2 + 2πn,

where n is any integer.

So, θ/3 = (π/2 + 2πn)/3 = π/6 + 2πn/3.

Therefore, the cube root of -2i is equal to

⇒  ∛2 [ cos(π/6 + 2πn/3) + i sin(π/6 + 2πn/3) ]

Now put n = 0

⇒ ∛2[ cos(π/6) + i sin(π/6) ]

This is the final form of the cube root of -2i in the required form.

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The solution to the equation 3x + 10x = 8x is x = 2

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

3x + 10x = 8x

Collect the like terms

So, we have

8x - 3x = 10

When the like terms are evaluated, we have

5x = 10

Divide both sides by 5

x = 2

Hence, the solution to the equation is x = 2

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The probability that Ms. Browning will select a blue marker both times is 1/9.

To calculate the probability that Ms. Browning will select a blue marker both times, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Ms. Browning has 3 markers in the box: 1 red, 1 blue, and 1 yellow. Since she selects a marker, uses it, and puts it back, the total number of possible outcomes for the first selection is 3.

For each outcome of the first selection, Ms. Browning again has 3 markers to choose from for the second selection.

Therefore, the total number of possible outcomes for the second selection is also 3.

To calculate the probability of selecting a blue marker both times, we need to determine the number of favorable outcomes. There is only 1 blue marker in the box, and Ms. Browning needs to select it twice.

Therefore, the number of favorable outcomes is 1.

The probability of an event is given by the ratio of favorable outcomes to total outcomes.

In this case, the probability of selecting a blue marker both times is:

Probability = (Number of favorable outcomes) / (Number of total outcomes)

= 1 / (3 × 3)

= 1 / 9

Therefore, the probability that Ms. Browning will select a blue marker both times is 1/9.

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The probability that a student is on the sports team, given that the student plays an instrument, is approximately 35.3% when rounded to one decimal place.

To find the probability that a student is on the sports team given that the student plays an instrument, we can use conditional probability.

Let's denote:

A = Event that a student plays an instrument

B = Event that a student is on the sports team

We are given the following information:

P(A) = 68% = 0.68 (probability of a student playing an instrument)

P(A ∩ B) = 24% = 0.24 (probability of a student playing an instrument and being on a sports team)

The conditional probability P(B|A) represents the probability of event B occurring given that event A has already occurred. It is calculated as:

P(B|A) = P(A ∩ B) / P(A)

Substituting the given values:

P(B|A) = 0.24 / 0.68 ≈ 0.3529

To express the probability as a percentage, we multiply by 100:

P(B|A) ≈ 0.3529 * 100 ≈ 35.3%

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The transformation of f(x) to g(x) is f(x) is shifted down by 4 units to g(x) and shifted right by 5 units

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

The functions f(x) and g(x)

Where, we can see that

f(x) = |x|

g(x) = |x + 5| - 3

So, we have

vertical difference = 0 - 3 = -3

horizontal difference = 5 - 0 = 5

This means that the transformation of f(x) to g(x) is f(x) is shifted down by 4 units to g(x) and shifted right by 5 units

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The Fourier series representation of X(t) is:

X(t) = -1 for 0 ≤ t ≤ T/2

= 1 for T/2 < t < T

To solve the Fourier series equation for the given periodic function X(t), we can follow these steps:

Step 1: Determine the fundamental frequency (ω0) and period (T) of the function X(t).

The period of X(t) is given as T.

The fundamental frequency (ω0) can be calculated as ω0 = 2π / T.

Step 2: Express X(t) as a Fourier series using complex exponential form.

The Fourier series representation of X(t) can be written as:

X(t) = A0 + Σ[Ak × cos(kω0t) + Bk × sin(kω0t)]

Since X(t) is an even function, all the sine terms will be zero. So, the series simplifies to:

X(t) = A0 + Σ[Ak × cos(kω0t)]

Step 3: Calculate the Fourier coefficients (Ak) for k = 0, 1, 2, ...

The Fourier coefficients can be calculated using the following formulas:

A0 = (1/T) × ∫[X(t)]dt

Ak = (2/T) × ∫[X(t) × cos(kω0t)]dt, for k > 0

Step 4: Calculate the Fourier coefficients A0 and Ak for the given function X(t).

Since X(t) is a piecewise function, we need to evaluate the integrals separately for each interval.

For 0 ≤ t ≤ T/2:

A0 = (1/T) × ∫[-2]dt = (1/T) × [-2t] (integrating from 0 to T/2)

= -2/T × (T/2 - 0) = -1

Ak = (2/T) × ∫[-2 × cos(kω0t)]dt = (2/T) × [-2/kω0 × sin(kω0t)] (integrating from 0 to T/2)

= -4/(kπ) × [sin(kπ) - sin(0)]

= -4/(kπ) × [0 - 0]

= 0

For T/2 < t < T:

A0 = (1/T) × ∫[2]dt = (1/T) × [2t] (integrating from T/2 to T)

= 2/T × (T - T/2) = 1

Ak = (2/T) × ∫[2 × cos(kω0t)]dt = (2/T) × [2/kω0 × sin(kω0t)] (integrating from T/2 to T)

= 4/(kπ) × [sin(kπ) - sin(kπ/2)]

= 4/(kπ) × [0 - (-1)^k]

= (-1)^(k+1) × (4/(kπ))

Step 5: Write the final Fourier series representation of X(t) using the calculated coefficients.

Since Ak = 0 for all k, except when k = 0, the series simplifies to:

X(t) = A0

= -1 for 0 ≤ t ≤ T/2

= 1 for T/2 < t < T

Therefore, the Fourier series representation of X(t) is:

X(t) = -1 for 0 ≤ t ≤ T/2

= 1 for T/2 < t < T

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The value of x and y is x ≈ 7.87 and y ≈ 25.38, the correct option is B.

We are given that;

Hypotenuse is 27 base is y and height is x the angle between base and hypotenuse is 17 degree

Now,

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2  

To find x and y, we can use the Pythagorean theorem and the trigonometric ratios for a right triangle. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The trigonometric ratios relate the angles and sides of a right triangle.

Using the Pythagorean theorem, we can write:

y^2 + x^2 = 27^2

y^2 + x^2 = 729

Using the trigonometric ratios, we can write:

sin(17°) = x/27

cos(17°) = y/27

Solving for x and y, we get:

x = 27 sin(17°) ≈ 7.87

y = 27 cos(17°) ≈ 25.38

Therefore, by pythagoras theorem answer will be x ≈ 7.87 and y ≈ 25.38.

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The values of θ  for different conditions were calculated with the help of trigonometric functions.

The solution of trigonometric functions is the values of angles where the function value becomes zero.

Given function is:

A) f (θ) = 2 sin θ + √3

f (θ) = 2 sin θ + √3 = 0

2 sin θ = -  √3

sin θ = - √3 / 2

θ = nπ + π/3

where n=1,3,5,7......

So, at θ = nπ + π/3,  pogo stick's spring will be equal to its non-compressed length.

B)If the angle was doubled, the function will look like this,

f (θ) = 2 sin 2θ + √3

2 sin 2θ + √3 = 0

2 sin 2θ = -  √3

sin 2θ = - √3 / 2

θ = nπ/2 + π/6

where  n=1,3,5,7....

if n=1,  θ = 2π/3

n=2,  θ = 7π/6

n=3,  θ = 5π/6

So, These are solution in [0,2π}.

C) y = 2 cos θ + 1

And, y = sin2 θ - 1

Hence, Equate both equation,

2 cos θ + 1 = sin2θ - 1

2 cos θ = 2 sinθ cos θ - 2

cos θ = sinθ cosθ - 1

cosθ (1 - sin θ) = - 1

cosθ = - 1

θ = nπ

where n=1,2,3.....

So, θ = nπ , the lengths of springs from the original pogo stick and the toddler's pogo stick are equal.

Hence, the values of θ  for different conditions were calculated with the help of trigonometric functions.

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Answer:

x>-30

Step-by-step explanation:

1x+31>1

x+31>1

The angle (to the nearest tenth of a degree) of the terminal side through the point P is approximately 39.2 degrees.

To find the angle θ (in degrees) associated with the point P = (√7/3, √2/3) on the unit circle, we can use the trigonometric identities for sine and cosine.

Let x = √7/3 and y = √2/3 be the coordinates of the point P.

We can see that x = cos(θ) and y = sin(θ) based on the definitions of cosine and sine in relation to the unit circle.

From x = √7/3, we have cos(θ) = √7/3.

From y = √2/3, we have sin(θ) = √2/3.

To find the angle θ, we can take the inverse cosine (cos⁻¹) or inverse sine (sin⁻¹) of the given values.

cos⁻¹(√7/3)= 39.2 degrees (rounded to the nearest tenth of a degree)

sin⁻¹(√2/3) = 62.2 degrees (rounded to the nearest tenth of a degree)

Since we want the angle 0 ≤ θ < 360, we need to determine the correct quadrant for the point P.

The point P = (√7/3, √2/3) lies in the first quadrant of the unit circle (where both x and y are positive), so the angle associated with it is 39.2 degrees.

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Starting with the given equation: 2 sin x cos x = cos x

By dividing both sides by cos x, we may simplify: 2 sin x = 1

Dividing both sides by 2:

sin x = 1/2

The values of x that fulfil sin x = 1/2 must now be found, and they are:

x = π/6 + 2πn or x = 5π/6 + 2πn, where n is any integer.

Therefore, the general solution is:

x = π/6 + 2πn or

x = 5π/6 + 2πn, where n is any integer.

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The compound inequality representing the range for the skull size of cats is: 39.32 ≤ x ≤ 43.01.

To find the compound inequality that represents the range for the skull size of cats, we need to solve the given compound inequality:

8 ≤ 1.03x - 32.4 ≤ 12

Let's solve it step by step:

Add 32.4 to all parts of the compound inequality:

8 + 32.4 ≤ 1.03x - 32.4 + 32.4 ≤ 12 + 32.4

40.4 ≤ 1.03x ≤ 44.4

Divide all parts of the compound inequality by 1.03 (the coefficient of x):

40.4/1.03 ≤ (1.03x)/1.03 ≤ 44.4/1.03

39.32 ≤ x ≤ 43.01

Therefore, the range for the skull size of cats can be represented by the compound inequality:

39.32 ≤ x ≤ 43.01

Rounded to the nearest hundredth, the compound inequality representing the range for the skull size of cats is:

39.32 ≤ x ≤ 43.01

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Paul will spend $1382.4 constructing the patio.

To calculate how much Paul will spend constructing the patio, we need to determine the area of the patio and then multiply it by the cost per square foot.

Looking at the scale provided, we can see that 1 cm represents 3 ft. We can use this scale to find the dimensions of the patio in feet.

The length of the patio is given as 8 cm, so the actual length in feet would be:

Length = 8 cm × 3 ft/cm = 24 ft.

Similarly, the width of the patio is given as 6.4 cm, so the actual width in feet would be:

Width = 6.4 cm × 3 ft/cm = 19.2 ft.

Now, we can calculate the area of the patio in square feet by multiplying the length and width:

Area = Length × Width = 24 ft × 19.2 ft = 460.8 sq ft.

The cost to construct the patio is $3 per square foot, so we can calculate the total cost by multiplying the area by the cost per square foot:

Total Cost = Area × Cost per square foot = 460.8 sq ft × $3/sq ft.

Total Cost = $1382.4.

Therefore, Paul will spend $1382.4 constructing the patio.

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By algebra properties, the simplified form of the rational equation 3 / (x + 1) - 1 / (x - 1) - 2 · x / (x² - 1) is equal to - 4 / (x² - 1). (Correct choice: C)

In this question we find a rational equation, whose simplified form must be found by algebra properties. First, write the entire expression:

3 / (x + 1) - 1 / (x - 1) - 2 · x / (x² - 1)

Second, factor all denominators:

3 / (x + 1) - 1 / (x - 1) - 2 · x / [(x + 1) · (x - 1)]

Third, use sum of fractions with different denominators:

[3 · (x - 1) - (x + 1) - 2 · x] / [(x + 1) · (x - 1)]

Fourth, simplify the resulting expression:

(3 · x - 3 - x - 1 - 2 · x) / [(x + 1) · (x - 1)]

- 4 / [(x + 1) · (x - 1)]

- 4 / (x² - 1)

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The angle m∠J  in the right angle triangle is 58.1 degrees.

One of the angle of a right tangle triangle is 90 degrees. The sum of

angles in a triangle is 180 degrees.

Therefore, the side length LK can be found using Pythagoras's theorem and the angle can be found using trigonometric ratios.

Hence,

tan ∠J = opposite / adjacent

tan ∠J = 15.1 / 9.4

∠J = tan⁻¹ 1.60638297872

∠J = 58.0909229196

Therefore,

m∠J = 58.1 degrees

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There are approximately 3.08 × 10²⁵ nanometers in each parsec.

To find out how many nanometers are there in each parsec, we need to first calculate the total number of meters in one parsec, and then convert that value to nanometers.

Given information:

3.26 light years per parsec

1 light year = 9.46 × 10¹⁵ meters

1 nanometer = 10⁻⁹ meters

To convert from light years to parsecs, we'll use the conversion factor: 3.26 light years per parsec.

1 parsec = 1 × (3.26 light years/1 parsec) = 3.26 light years

Now, we'll calculate the total number of meters in one parsec:

1 parsec = 3.26 light years = 3.26 × (9.46 × 10¹⁵ meters/light year)

Parsing the numbers:

3.26 × (9.46 × 10¹⁵) = 3.08 × 10¹⁶ meters

Finally, we'll convert the result to nanometers:

1 meter = 1 × (10⁹ nanometers/1 meter) = 10⁹ nanometers

Therefore, the total number of nanometers in one parsec is:

3.08 × 10¹⁶ meters × (10⁹ nanometers/1 meter) = 3.08 × 10²⁵ nanometers

So, there are approximately 3.08 × 10²⁵ nanometers in each parsec.

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The probability that a car chosen at random is not a red car is 51%

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

Cars = 60%

Red cars = 15%

The probability that a car chosen at random is not a red car is calculated as

P = (1 - Red cars) * Cars

substitute the known values in the above equation, so, we have the following representation

P = (1 - 15%) * 60%

Evaluate

P = 51%

Hence, the probability that a car chosen at random is not a red car is 51%

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There are 10% of the 60 students which is 6 students who are 18 years old or younger.

To get number of students who are 18 years old or younger, we have to determine percentage of students who fall into this category.

The percentage of students who are 18 years old or younger will be derived by subtracting the sum of the percentages of students who are 19 years old, 30 years old and over 20 years old from 100%.

The percentage of students who are 18 years old or younger is:

= 100% - (20% + 30% + 40%)

= 100% - 90%

= 10%.

Translated question:

A university course has 60 students. If 20% are 19 years old, 30% 30 and 40% over 20 years old, how many students can there be 18 years old or younger?

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Answer:

To solve the inequality 8x + 2 < 10x - 4, we can start by subtracting 8x from both sides to get 2 < 2x - 4. Then, we can add 4 to both sides to get 6 < 2x. Finally, we can divide both sides by 2 to get 3 < x. This means that the solution set for the inequality is all values of x that are greater than 3. In interval notation, the solution set is (3, ∞).

Step-by-step explanation:

The equation of the line on the graph passing through the points (-3, 3) and (3, -1) is  [tex]y = -\frac{2}{3}x + 1[/tex].

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

From the image, the line runs through points (-3, 3) and (3, -1).

First, we determine the slope (m) using the given points:

[tex]m = \frac{y_2 -y_1}{x_2 - x_1} \\\\m = \frac{-1 - 3}{3-(-3)} \\\\m = \frac{-4}{3+3} \\\\m = \frac{-4}{6} \\\\m =-\frac{2}{3}[/tex]

Now, plug a point (-3,3) and the slope m = -2/3 into the point-slope form and solve for y:

y - y₁ = m( x - x₁ )

[tex]y - 3 = -\frac{2}{3}( x - (-3)) \\\\y - 3 = -\frac{2}{3}( x + 3) \\\\y - 3 = -\frac{2}{3}x - 2\\\\y = -\frac{2}{3}x - 2+3\\\\y = -\frac{2}{3}x + 1\\[/tex]

Therefore, the equation of the line is [tex]y = -\frac{2}{3}x + 1[/tex].

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