Picture attached! 4 For x 20, which equation is false?
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1)
(x2)2 = 4/3
2)
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3) √
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4)
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The equation of the line parallel to y = x - 5 that goes through the point (7, 0) is y = x - 7.

This line has the same slope as the given line and passes through the specified point.

To find the equation of a line parallel to the given line y = x - 5, we know that parallel lines have the same slope.

The slope of the given line is 1, as it has the coefficient of x.

Therefore, the parallel line we are looking for will also have a slope of 1.

We can use the point-slope form of a linear equation to find the equation of the line.

The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is a point on the line and m is the slope.

We are given the point (7, 0), so we can substitute x₁ = 7 and y₁ = 0 into the equation.

Also, since we want a parallel line with a slope of 1, we have m = 1. Substituting these values, we get:

y - 0 = 1(x - 7)

Simplifying, we have:

y = x - 7.

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Answer:

x = 5

Step-by-step explanation:

4x - 8 = 12

4x - 8 + 8 = 12 + 8    correct

4x = 20     correct

Now, multiply both sides by 1/4.

¼ × 4x = ¼ × 20

x = 5

Answer: X = 5

Step-by-step explanation:

4X - 8 = 12

4X = 12 + 8

4X = 20

X = 20/4

X = 5

Answer:

Step-by-step explanation:

El área de un trapecio se calcula multiplicando la suma de sus bases por la altura y dividiendo el resultado entre 2. En este caso, la base mayor es de 30 cm y la base menor es de 2/3 de la mayor, lo que equivale a 20 cm. La altura es de 0,8 m o 80 cm. Por lo tanto, el área del trapecio es ((30 + 20) * 80) / 2 = 2000 cm².

(1) The integral of the function is (1/10)x⁵ - (1/8)x⁴ + (1/6)x³ + C.

(2) The integral is (1/4)(sec x)⁴ + eˣ(sec x) + (1/2)(sec x)² + C.

(3) The integral of cot²x dx is 1/sin(x) - sin(x) + C

(4)The integral of the function is  [tex]\frac{3}{7} x^{7/3} - \frac{3}{5}x^{10/3} \ + \ 21x^{1/3} \ + C[/tex]

(5) The shaded area under the curve is 7.22 sq units.

(1) The integral of (x⁶ - 2x⁵ + x⁴) / 2x² is determined as follows;

(x⁶ - 2x⁵ + x⁴) / 2x² = (x⁴(x² - 2x + 1)) / 2x²

= (x⁴(x - 1)²) / 2x²

= (x²(x - 1)²) / 2

∫(x²(x - 1)²) / 2 dx

= (1/2) ∫x²(x - 1)² dx

= (1/2) ∫x²(x² - 2x + 1) dx

= (1/2) ∫(x⁴ - 2x³ + x²) dx

= (1/2)(1/5)x⁵ - (1/2)(1/4)x⁴ + (1/2) (1/3)x³ + C

Simplifying further we will have;

= (1/10)x⁵ - (1/8)x⁴ + (1/6)x³ + C

(2) The integral of (sec³x + eˣsecˣ + 1) / (sec x) dx, is calculated as follows;

(sec³x + eˣsecˣ + 1) / (sec x) = (sec³x + eˣsecˣ + 1)(sec x / sec x)

= (sec⁴x + eˣsec²x + sec x) / sec x

Note; sec x as 1/cos x

= sec⁴x/cos x + eˣsec²x/cos x + sec x/cos x

= sec³x/cos x + eˣsec x + sec x/cos x

Integrate by substitution method.

u = sec x

du = sec x tan x dx.

∫(sec³x + eˣsec x + sec x/cos x) dx

= ∫(u³ + eˣu + u) du

= (1/4)u⁴ + eˣu + (1/2)u² + C

Substitute u back in terms of sec x;

= (1/4)(sec x)⁴ + eˣ(sec x) + (1/2)(sec x)² + C

(3) The integral of cot²x dx;

cot²(x) = (cos²(x))/(sin²(x))

Let u = sin(x)

du = cos(x) dx

= ∫(1-u²)/u² du

= ∫(1/u²) - 1 du

= ∫u⁻² - 1 du

= -1/u - u + C

= -1/sin(x) - sin(x) + C

(4) The integral of the function is;

∫(x² - 2x³ + 7)/∛x dx =  ∫x²/∛x dx - ∫2x³/∛x dx + ∫7/∛x dx

= [tex]x^{4/3} \ dx \ - \ 2x^{7/3}\ dx \ + \ 7x^{-2/3}\ dx[/tex]

[tex]= \frac{3}{7} x^{7/3} - (\frac{3}{10} \times 2)x^{10/3} \ + \ (3 \times 7)x^{1/3} \ + \ C\\\\= \frac{3}{7} x^{7/3} - \frac{3}{5}x^{10/3} \ + \ 21x^{1/3} \ + C[/tex]

(5) The shaded area under the curve is calculated as follows;

the given function;

[tex]y = x^{1/2} - x^2 + 2x[/tex]

The integral of the functions;

∫y = A =  [tex]\frac{2}{3} x^{3/2} - \frac{1}{3} x^{3} + x^2[/tex]

the limits = 2 and 0

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

A = 1.89 - 2.67 + 8

A = 7.22 sq units

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The value of x is 67. 3 degrees

To determine the value of the angle labelled x, we need to know that there are six different trigonometric identities.

These identities are listed as;

From the information given, we have that;

The angle = x

The opposite side = 43

The adjacent side = 18

Using the tangent identity, we have;

tan x = 43/18

Divide the values, we have;

tan x = 2. 3888

Find the tangent inverse, we get;

x = 67. 3 degrees

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(a) P = mt + b

(b) The exact percentage of defective cars cannot be determined without the values of m and b.

(c) The slope (m) represents the rate of change in the percentage of defective cars per unit change in the production rate. Its sign and magnitude determine the direction and steepness of the change.

(a) To write the equation for the percentage of cars P that are defective if t toys are produced an hour, we can use the concept of a linear relationship between the production rate and the percentage of defective cars. The equation can be written as:

P = mt + b

Where P represents the percentage of defective cars, t represents the number of toys produced per hour, m represents the slope of the line (change in percentage per change in production rate), and b represents the y-intercept (the percentage of defective cars when no toys are produced).

(b) Using the equation from part (a), if 2,500 cars are produced an hour (t = 2500), we can substitute this value into the equation to find the percentage of defective cars:

P = m(2500) + b

To calculate the exact percentage, we need the values of m and b. Unfortunately, the values are not provided in the given information. Therefore, without knowing the specific values of m and b, we cannot determine the exact percentage of defective cars.

(c) The slope of the equation represents the rate of change in the percentage of cars that are defective per unit change in the production rate. It quantifies how the percentage of defective cars increases or decreases as the production rate varies.

Unfortunately, the value of the slope (m) is not provided in the given information, so we cannot determine it directly. However, we can make some general observations about the slope:

If the slope is positive, it means that as the production rate increases, the percentage of defective cars also increases.

If the slope is negative, it means that as the production rate increases, the percentage of defective cars decreases.

The magnitude of the slope indicates the rate at which the percentage of defective cars changes with the production rate. A larger magnitude indicates a steeper change, while a smaller magnitude indicates a gentler change.

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The expression tan√3 tanø + 1 simplifies to the value of 2.

To find the value of tan√3 tanø + 1, we need to use the given information that 2sinø = 1 and 2cosø = √3.

We can start by rearranging the equations to solve for sinø and cosø individually.

From 2sinø = 1, we can divide both sides by 2 to get sinø = 1/2.

From 2cosø = √3, we can divide both sides by 2 to get cosø = √3/2.

Now, we can use these values to find the value of tanø. We know that tanø = sinø / cosø.

Substituting the values we found earlier:

tanø = (1/2) / (√3/2)

To simplify this expression, we multiply the numerator and denominator by the reciprocal of √3/2, which is 2/√3:

tanø = (1/2) * (2/√3)

tanø = 1 / √3

To further simplify, we rationalize the denominator by multiplying both the numerator and denominator by √3:

tanø = (1 * √3) / (√3 * √3)

tanø = √3 / 3

Now, we can substitute this value of tanø into the expression tan√3 tanø + 1:

tan√3 tanø + 1 = tan(√3) * (√3 / 3) + 1

Using the value of √3 as the square root of 3:

tan√3 tanø + 1 = (√3 * √3 / 3) + 1

tan√3 tanø + 1 = (3 / 3) + 1

tan√3 tanø + 1 = 1 + 1

tan√3 tanø + 1 = 2

Therefore, the value of tan√3 tanø + 1 is 2.

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Note the correct and the complete question is

If 2sinø=1 &2cosø= √3 then find the value of tan√3 tanø+1​ ?

The point (-√2,1) can also be represented as (√3, 5.18) in polar coordinates.

To find the polar coordinates of the rectangular coordinates (-√2,1), we can use the following formulas:

r = √(x² + y²)

θ = tan^⁻1(y/x)

Plugging in the given values of (-√2,1), we get:

r = √((-√2)² + 1²) = √(2 + 1) = √3

θ = tan^⁻1(1/(-√2)) ≈ 2.0344 radians

Note that since the point (-√2,1) is in the second quadrant, we need to add π to the value of θ obtained from the inverse tangent in order to obtain an angle in the interval [0,2π). Thus, we have:

θ ≈ 2.0344 + π ≈ 5.1779 radians

Rounding to 2 decimal places as needed, we get the polar coordinates of (-√2,1) as (r,θ) ≈ (√3, 5.18).

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The linear function that describes the data in the table for this problem is given as follows:

C. P(h) = h + 11.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

From the table, we have that when h increases by 1, P(h) also increases by 1, hence the slope m is given as follows:

m = 1/1 = 1.

Hence:

P(h) = h + b.

When h = 4, P(h) = 15, hence the intercept b is given as follows:

15 = 4 + b

b = 11.

Hence the rule is:

P(h) = h + 11.

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The equation for the line perpendicular to the tangent line at the point (4,1) is y = (-1/32)x + 9/8

First, you find the slope of the tangent line.

To find the slope of the tangent line, we take the derivative of the curve equation:

y = x^3 - 16x + 1

dy/dx = 3x^2 - 16

Evaluating the derivative at x = 4, we get:

dy/dx = 3(4)^2 - 16 = 48 - 16 = 32

The slope of the tangent line at the point (4,1) is 32.

Since the line perpendicular to a given line has a slope that is the negative reciprocal of the given line's slope, the slope of the line perpendicular to the tangent line is -1/32.

Using the point-slope form of a linear equation, we have:

y - 1 = (-1/32)(x - 4)

Simplifying, we get the equation for the line perpendicular to the tangent line as:

y = (-1/32)x + 9/8

Therefore, the equation is y = (-1/32)x + 9/8.

To find the smallest slope on the curve, we need to find the minimum value of the derivative of the curve equation.

dy/dx = 3x^2 - 16

To find the minimum value of this derivative, we set it equal to zero and solve for x:

3x^2 - 16 = 0

Using the quadratic formula, we get:

x = ±√(16/3)

Since we are looking for the point on the curve, we can disregard the negative square root value since it falls outside the x-intercepts of the curve.

So, the smallest slope occurs at x = √(16/3).

Substituting this value back into the curve equation, we get:

y = (√(16/3))^3 - 16(√(16/3)) + 1

Simplifying, we get:

y = 1/3 - 64/3 + 1 = -62/3

Therefore, the smallest slope on the curve is -62/3, and it occurs at the point (√(16/3), -62/3).

To find the equation for the tangent lines at the points where the slope of the curve is 32, we need to find the x-values where the derivative of the curve equation is equal to 32.

Setting the derivative equal to 32, we have:

3x^2 - 16 = 32

Solving for x, we get:

3x^2 = 48

x^2 = 16

x = ±4

So, the curve has a slope of 32 at the points (4,1) and (-4,1).

To find the equations for the tangent lines at these points, we can use the point-slope form of a linear equation.

At the point (4,1), the equation for the tangent line is:

y - 1 = 32(x - 4)

Simplifying, we get:

y = 32x - 127

Therefore, the equation for the tangent line at the point (4,1) is y = 32x - 127.

At the point (-4,1), the equation for the tangent line is:

y - 1 = 32(x + 4)

Simplifying, we get:

y = 32x + 129

Therefore, the equation for the tangent line at the point (-4,1) is y = 32x + 129.

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In a 30-60-90 triangle, the special relationship between the side lengths is based on the ratios of the sides.

Let's denote the length of the shorter leg (opposite the 30-degree angle) as "x," the length of the longer leg (opposite the 60-degree angle) as "y," and the length of the hypotenuse as "z."

The special relationship can be described as follows:

The length of the shorter leg (opposite the 30-degree angle) is always x.

The length of the longer leg (opposite the 60-degree angle) is always √3 times the length of the shorter leg, which can be written as y = √3x.

The length of the hypotenuse is always twice the length of the shorter leg, which can be written as z = 2x.

To summarize:

Shorter leg: x

Longer leg: √3x

Hypotenuse: 2x

These ratios hold true for any 30-60-90 triangle.

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Polynomial: 6x^3 + 12x^2 - 18x

Form 1: 6(x^3 + 2x^2 - 3x)

Explanation: This form was created by factoring out the GCF of 6 from each term in the polynomial.

Form 2: 6x(x^2 + 2x - 3)

Explanation: This form was created by factoring out the GCF of 6x from each term in the polynomial.

In both forms, the GCF of 6 allows us to factor out common factors and simplify the polynomial expression while preserving its original meaning.

To create a factorable polynomial with a greatest common factor (GCF) of 6, we can start by considering the common factors of the terms. Let's construct a polynomial:

Polynomial: 6x^3 + 12x^2 - 18x

To rewrite this polynomial in two other equivalent forms, we can factor out the GCF from each term and simplify.

Form 1: 6(x^3 + 2x^2 - 3x)

In this form, we factored out the GCF of 6 from each term: 6x^3/6 = x^3, 12x^2/6 = 2x^2, and -18x/6 = -3x.

Form 2: 6x(x^2 + 2x - 3)

In this form, we factored out the GCF of 6x from each term: 6x^3/6x = x^2, 12x^2/6x = 2x, and -18x/6x = -3.

We created each form by identifying the common factors in the polynomial and factoring them out. This process allows us to rewrite the polynomial in equivalent forms that emphasize different aspects.

In Form 1, we factored out the GCF of 6, leaving the remaining polynomial inside the parentheses. This form highlights the fact that the polynomial can be written as the product of the GCF and the remaining terms.

In Form 2, we factored out the GCF of 6x, again leaving the remaining polynomial inside the parentheses. This form emphasizes the fact that the polynomial can be written as the product of the GCF and another factor, in this case, x.

By rewriting the polynomial in these two forms, we have created equivalent expressions that emphasize the presence of the GCF and demonstrate the polynomial's factorability.

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Answer: 28

Step-by-step explanation:

In this scenario, we can consider the independent variable to be the number of hours and the dependent variable to be the total cost charged by Superior Segway Tours

As per the given situation, the cost charged by Superior Segway Tours is a one-time fee of $60, plus $28 per hour

So, the cost (y) can be calculated using the equation:y = 28x + 60 where x is the number of hours of the sightseeing tour.

The slope of this situation is the coefficient of x, which is 28. Therefore, the slope of this situation is 28.

Answer:

[tex]\langle53.24,37.28\rangle[/tex]

Step-by-step explanation:

[tex]u=65\langle\cos35^\circ+\sin35^\circ\rangle=\langle65\cos35^\circ,65\sin35^\circ\rangle\approx\langle53.24,37.28\rangle[/tex]

If Triangle SRTs angle R is 59° angle T is 79°  the length of ST to the nearest 10th of a yard is 6.1

Since we have given that

ΔSRT is a triangle with measures :

SR = 7 yd

∠T = 79°

∠R = 59°

We need to find the side ST .

To find the length of ST, we can use the Law of Sines, which states:

sin(T) / SR = sin(R) / ST

sin(79°) / 7 = sin(59°) / ST

0.14 = sin(59°) / ST

ST =  sin(59°)/0.14 ⇒ 0.8572 / 0.14 ≈ 6.1229

Therefore, the length of ST is approximately 6.1 yards to the nearest tenth of a yard

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Answer: c

Step-by-step explanation:

Im guessing

The y-intercept of the LSRL for the given data, with x = 12 representing the year "1912," is approximately 80.28.

To find the y-intercept of the Least Squares Regression Line (LSRL) for the given data, we can use linear regression to fit a line to the data points.

The LSRL equation is in the form y = mx + b, where y represents the response variable (in this case, the gold medal times), x represents the explanatory variable (in this case, the year represented by x = 12 for "1912"), m represents the slope of the line, and b represents the y-intercept.

First, let's assign the given data to the variables x and y, where x represents the year and y represents the gold medal times:

x = [12, 24, 32, 52, 60, 68, 76, 84, 92]

y = [82.2, 72.4, 66.8, 66.8, 61.2, 60.0, 55.65, 55.92, 54.64]

Next, we perform linear regression to find the equation of the LSRL. Using statistical software or calculators, we can find that the equation of the LSRL is y ≈ -0.29x + 80.28.

Since we are interested in the y-intercept, we set x = 0 and solve for y:

y-intercept = -0.29(0) + 80.28 = 80.28

Therefore, the y-intercept of the LSRL for the given data, with x = 12 representing the year "1912," is approximately 80.28. This value represents the predicted gold medal time in seconds for the women's 100-meter freestyle event in the year 1912, based on the regression line fitted to the available data.

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Answer:

3x^2

Step-by-step explanation:

3x^2(9x)^0

Calculate 9x to the power of 0 and get 1.

3x^2 * 1

Multiply 3 and 1 to get 3.

3x^2

Step-by-step explanation:

if you are not sure what a word means, use the general internet.

that is much faster than putting such a question in here and then waiting for an answer.

e.g.

a pentagon has 5 corners and 5 sides connecting these corners.

as penta is Greek for 5.

for a decagon, well, deca means 10.

so, a decagon has ... ... 10 corners and 10 sides.

the perimeter is the whole way around the object, so, it is the sum of all 10 sides.

therefore one side is

85 in / 10 = 8.5 in

Answer:

the value of x that makes the equation true is x = 3.5.

Step-by-step explanation:

To find the value of x that makes the equation 18x + 5 - 3 = 65 true, we need to simplify the equation and solve for x.

Starting with the equation:

18x + 5 - 3 = 65

First, combine like terms:

18x + 2 = 65

Next, isolate the term with x by subtracting 2 from both sides:

18x = 65 - 2

18x = 63

Finally, divide both sides of the equation by 18 to solve for x:

x = 63 / 18

x = 3.5

Therefore, the value of x that makes the equation true is x = 3.5.

The answer is:

Steps & work :

First, I focus only on the left side.

Combine like terms:

[tex]\sf{18x+5-3=65}[/tex]

[tex]\sf{18x+2=65}[/tex]

Subtract 2 from each side:

[tex]\sf{18x=63}[/tex]

Now, divide each side by 18:

[tex]\sf{x=\dfrac{63}{18}[/tex]

Clearly, this fraction is not in its simplest terms, and we can divide the top and bottom by 9:

[tex]\sf{x=\dfrac{7}{2}}[/tex]

[tex]\therefore\:\:\:\:\:\:\stackrel{\bf{answer}}{\boxed{\boxed{\tt{x=\frac{7}{2}}}}}}[/tex]

1: The probability of collecting a specific dinosaur is very unlikely.

2: The number of spins that it takes before you had at least one of each dinosaur in

Trial 1 is: 25 spins

Trial 2 is: 14 spins

Trial 3 is: 25 spins

3: The  number of spins correlates to the boxes of cereal by giving you a good representation on how many you will need to buy to collect all the dinosaurs.

5: The difference between experimental and theoretical probability is the experimental results can be different the theoretical results.

6: If someone bought eight boxes of cereal and got all eight dinosaurs I would be very surprised.

7: The probabilities change by starting at 25 then 14 then back up to 25.

8: The advantages of of using a simulation is that you do not have to waste as much money.

1: The probability of collecting a specific dinosaur is very unlikely.

2: The number of spins that it takes before you had at least one of each dinosaur in Trial 1 is: 25 spins

The number of spins that it takes before you had at least one of each dinosaur in Trial 2 is: 14 spins

The number of spins that it takes before you had at least one of each dinosaur in Trial 3 is: 25 spins

3: The  number of spins correlates to the boxes of cereal by giving you a good representation on how many you will need to buy to collect all the dinosaurs.

4: The experimental probability for each dinosaur from Trial 1 is: 25 spins

Trial 2: 14 spins

Trial 3: 25 spins

5: The difference between experimental and theoretical probability is the experimental results can be different the theoretical results.

6: If someone bought eight boxes of cereal and got all eight dinosaurs I would be very surprised because getting it is only eight boxes is highly unlikely but not impossible.

7: The probabilities change by starting at 25 then 14 then back up to 25.

8: The advantages of of using a simulation is that you do not have to waste as much money.

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The spinner and description of how it works is as shown in the attached files.

6. The value of P(7) = 1/10

7. P(less than 5) = 2/5

8. P(odd) = 1/2

9. P(less than 1) = 0

10. P(greater than 10) = 0

11. P(divisible by 2 or 3) = 3/5

Let's consider each probability separately:

P(7):

Since Dave's number is a whole number greater than 0 and less than 11, there are 10 possible numbers he could have chosen (1, 2, 3, 4, 5, 6, 7, 8, 9, 10).

Out of these 10 numbers, only one is 7.

Therefore, the probability that Dave's number is 7 is 1/10.

P(less than 5):

Out of the 10 possible numbers (1, 2, 3, 4, 5, 6, 7, 8, 9, 10), there are four numbers that are less than 5 (1, 2, 3, 4).

Hence, the probability that Dave's number is less than 5 is 4/10, which simplifies to 2/5.

P(odd):

Out of the 10 possible numbers, there are five odd numbers (1, 3, 5, 7, 9). Therefore, the probability that Dave's number is odd is 5/10, which simplifies to 1/2.

P(less than 1):

Since the number must be greater than 0, it cannot be less than 1.

Thus, the probability of choosing a number less than 1 is 0.

P(greater than 10):

Since the number must be less than 11, it cannot be greater than 10.

Thus, the probability of choosing a number greater than 10 is 0.

P(divisible by 2 or 3):

Out of the 10 possible numbers, there are six numbers that are divisible by 2 or 3 (2, 3, 4, 6, 8, 9).

Therefore, the probability that Dave's number is divisible by 2 or 3 is 6/10, which simplifies to 3/5.

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Answer:

$1.26

Step-by-step explanation:

After the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

Before the 2:30 stop, the bus let off 15 people and let on 9 people. The total change in the number of people at that stop is -15 (let off) + 9 (let on) = -6.

Therefore, there are 6 fewer people on the bus after the 2:30 stop compared to before that stop.

Ten minutes later, the bus makes another stop and lets off 4 more people. This additional change needs to be considered.

Since the previous calculation only accounted for the changes up until the 2:30 stop, we need to adjust the total change by including the subsequent stop.

Adding the change of -4 (let off) to the previous total change of -6, we get a new total change of -10.

Therefore, after the second stop, there are 10 fewer people on the bus compared to the number of people on the bus before the 2:30 stop.

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The facts that are not needed to solve the problem are:B.

The wait to ride the roller coaster was 40 minutes.C.

It was Tuesday.D.

The roller coaster is the fastest ride at the fair. Option B, C, D

To determine the facts that are not needed to solve the problem of estimating the waiting time for a roller coaster, we can examine the information provided and identify the essential elements for solving the problem.

The problem asks how long one would expect to wait if the line was 50 meters long. The key factor for estimating the waiting time is the length of the line, so the relevant information is:

A. The line of people was 100 meters long. This information is needed because it provides the basis for estimating the waiting time.

B. The wait to ride the roller coaster was 40 minutes. This information is not necessary to solve the problem because it refers to the waiting time on a specific day, which is not directly related to the length of the line.

C. It was Tuesday. This information is not necessary to solve the problem because the day of the week does not affect the relationship between line length and waiting time.

D. The roller coaster is the fastest ride at the fair. This information is not necessary to solve the problem because the speed or type of the ride does not directly influence the waiting time based on the line length.

Option B, C , D

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The correct answer is b. Same.

Two regression lines are parallel to each other if their slope is the same.

Justification:

In linear regression, the equation of a regression line is given by y = mx + c, where m represents the slope of the line. The slope (m) determines the direction and steepness of the line.

When two regression lines are parallel, it means they have the same direction and do not intersect. This implies that the change in y for a given change in x is the same for both lines, indicating that their slopes are equal.

Hence, the correct answer is b. Same.

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The minimum hours for Company B to be a better deal is 9 hours.

An equation is an expression that shows how numbers and variables are related to each other.

A linear function is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

Let y represent the total charge for x hours.

Company A charges a $80 annual fee plus a $10/hr car share fee. Hence:

y = 10x + 80

Company B charges $125 plus $5/hr. Hence:

y = 5x + 125

For company B to be a better deal, hence:

5x + 125 < 10x + 80

-5x < -45

x > 9

The minimum hours for Company B to be a better deal is 9 hours.

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The kite is approximately 57.6 feet above the ground.To find the height of the kite above the ground, we can use trigonometry and the given information about the angle of elevation and the length of the string.

Let's denote the height of the kite above the ground as h.

We can use the tangent function, which relates the angle of elevation to the opposite and adjacent sides of a right triangle:

tan(angle) = opposite / adjacent

tan(29°) = h / 110

To isolate h, we can multiply both sides of the equation by 110:

110 * tan(29°) = h

Using a calculator, we find:

h ≈ 57.6 feet

Note: When rounding the final answer, it is important to consider the given precision and units of measurement. In this case, rounding to the nearest tenth of a foot is appropriate.

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Answer:

x² + 12x + 36 = 0

(x + 6)² = 0

x = -6 is not in the domain of h(x).

The length of an edge of the cube is 3 cm.

The value of x is 9.

The value of "n" is 32.

If the mode of a set of data is 20 and each value in the data is increased by two, the new mode will also be increased by two. Therefore, the mode of the new data will be 22.

Given the lengths of the three sides of a triangle as 8x, 6x, and 5x cm, and the perimeter of the triangle as 36 cm, we can set up an equation to find the value of x:

8x + 6x + 5x = 36

19x = 36

x = 36/19

To find the lengths of the triangle sides, we substitute the value of x into the expressions:

Side 1: 8x = 8 * (36/19) cm

Side 2: 6x = 6 * (36/19) cm

Side 3: 5x = 5 * (36/19) cm

To find the area of the triangle, we can use Heron's formula, which states that the area of a triangle with sides a, b, and c is given by:

Area = √(s(s-a)(s-b)(s-c))

where s is the semiperimeter of the triangle, given by s = (a + b + c)/2.

Plugging in the values, we can calculate the area.

The median of the values x-4, x, 2x, and +12 is 9. To find the value of x, we arrange the numbers in ascending order:

x-4, x, 2x, +12

The median is the middle value when the numbers are arranged in order. In this case, the middle value is x, so we have:

x = 9

Therefore, the value of x is 9.

The lateral surface area of a cube is given by the formula 4a^2, where a is the length of an edge. In this case, we are given that the lateral surface area is 36 cm^2, so we can set up the equation:

4a^2 = 36

Dividing both sides by 4:

a^2 = 9

Taking the square root of both sides:

a = 3

Therefore, the length of an edge of the cube is 3 cm.

The total surface area of a cube is given by the formula 6a^2, where a is the length of an edge. Substituting the value of a:

6(3^2) = 6 * 9 = 54

Therefore, the total surface area of the cube is 54 cm^2.

In an "n" sided regular polygon, the ratio of each interior angle to each exterior angle is 15. The sum of the interior and exterior angles of a polygon is 180 degrees. Since the ratio of the interior angle to the exterior angle is 15, we can set up the equation:

Interior angle = 15 * Exterior angle

Interior angle + Exterior angle = 180

Substituting the first equation into the second equation:

15 * Exterior angle + Exterior angle = 180

16 * Exterior angle = 180

Exterior angle = 180/16 = 11.25 degrees

The sum of the exterior angles of a polygon is always 360 degrees. So, we can set up the equation:

360 = n * Exterior angle

Substituting the value of the exterior angle:

360 = n * 11.25

Solving for n:

n = 360/11.25 = 32

Therefore, the value of "n" is 32.

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