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PQ and RS are in the same plane and do not intersect. What geometric term describes PQ and RS?
perpendicular lines
complementary lines
skew lines
parallel lines

Answer:

74

Step-by-step explanation:

So, sec(t) = -1/cos(t) lies in Quadrant II.

The sign of a trigonometric function is determined by the signs of the coordinates of the points on the angle's terminal side. Knowing which quadrant the terminal side of an angle is in allows you to determine the signs of all trigonometric functions. The terminal side of an angle can be found in any of the four quadrants or along the axes in either the positive or negative direction (the quadrantal angles). For the signs of the trigonometric functions, each scenario indicates something different.

In Quadrant II, the value of t is between 90 and 180 degrees. In this quadrant, sine is negative, so tangent and secant are also negative.

For the given expressions:

sec(t) = 1/cos(t)

tan(t) = sin(t)/cos(t)

Since sine is negative in Quadrant II, cosine is also negative, so the reciprocal of cosine, which is secant, is negative in this quadrant.

So, sec(t) = -1/cos(t) in Quadrant II.

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the statement is disproved. If \(\(f(n)=O(g(n))\) and \(f(n)=\Omega(g(n))\)\),

then it is NOT necessarily true that \(\(f(n)=\Theta(g(n))\\).

Explanation: Let's take an example, Suppose\(\(f(n)=2n\) and \(g(n)=n\\), then:

\(\(f(n)=2n \leq 2n\)\), so

\(\(f(n)=O(g(n))\)(i) \(f(n)=2n \geq n\)\), so

\(\(f(n)=\Omega(g(n))\)(ii)\)

Now, for \(\(f(n)\)\) to be in \(\(\Theta(g(n))\)\),

we need to find constants c1 and c2 such that \(\(0 \leq c_{1}g(n) \leq f(n) \leq c_{2}g(n)\)\) for all values of n greater than some minimum value \(\(n_{0}\)\).

Now, take \(\(c_{1}=1\)\) and \(\(c_{2}=3\)\)(or any other constants), then:

\(c_{1}g(n)=n\)\(c_{2}g(n)=3n\) So,

\(\(c_{1}g(n)=n \leq 2n = f(n) \leq 3n = c_{2}g(n)\)\)

Thus, we can say that if\(\(f(n)=O(g(n))\) and \(f(n)=\Omega(g(n))\)\),

then it is not necessarily true that \(f(n)=\Theta(g(n))\).

Therefore, the statement is disproved.

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The slope of the curve at the given point is -1.33.

To find the slope of the curve at the point (-1, 1) using implicit differentiation, we need to differentiate the given equation with respect to x. Let's proceed with the steps:

Step 1: Differentiate both sides of the equation with respect to x.

d/dx(y³ + yx² + x² - 3y²) = d/dx(0)

Step 2: Apply the chain rule to differentiate each term.

d/dx(y³) + d/dx(yx²) + d/dx(x²) - d/dx(3y²) = 0

Step 3: Simplify the derivatives.

3y²(dy/dx) + 2xy + 2x - 6y(dy/dx) = 0

Step 4: Rearrange the equation to solve for dy/dx, which represents the slope.

(3y² - 6y)(dy/dx) = -2xy - 2x

dy/dx = (-2xy - 2x) / (3y² - 6y)

Step 5: Substitute the given point (-1, 1) into the expression for dy/dx to find the slope at that point.

dy/dx = (-2(-1)(1) - 2(-1)) / (3(1)² - 6(1))

= (2 + 2) / (3 - 6)

= 4 / (-3)

≈ -1.33

Therefore, the slope of the curve at the point (-1, 1) is approximately -1.33.

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Answer:

above sea level

Step-by-step explanation:

a) The median number of hours per week these Year 12 students spend doing homework is 4 hours.

b) If 10% of Year 12 students spend more than k hours per week doing homework, then the value of k is 5.75 hours.

The median is a central value or a middle value in a distribution. The number of values in a dataset is an important factor that determines the calculation of the median. It is a value that cuts the data set into two equal parts.

The data set consists of 20 Year 12 students. Sort the data in ascending order (or descending order) and find the middle value. Then, use the formula for calculating the median. 

a)The number of hours per week the Year 12 students spend doing homework is given as:

3, 3, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4.5, 5, 5, 5.5, 6, 7, 8, 8.5

Arrange the data in ascending order:

3, 3, 3, 3, 3, 3, 3.5, 3.5, 4, 4, 4, 4, 4.5, 5, 5, 5.5, 6, 7, 8, 8.5

Now count the data, which gives us 20 numbers. The middle value is the 10th and the 11th numbers, which are both 4.

So the median of the number of hours per week Year 12 students spend doing homework is 4 hours.

b) If 10% of Year 12 students spend more than k hours per week doing homework, then the value of k can be found using the following formula:

100% - 10% = 90%

So, 90% of students study for k hours or less.

So, the value of k can be found using the median. The median value is 4 hours, and 90% of students are studying for k hours or less. Therefore, 10% of students study for more than k hours.

k = 10% more than the value of the 90th percentile value, which is given by: k = 5.5 + ((8-5.5)/10)*1 = 5.5 + 0.25 = 5.75 hours.

Therefore, 10% of Year 12 students spend more than 5.75 hours per week doing homework.

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Answer:

\(\mathrm{a=-50,\ d=7,\ general\ formula=7(n-1)-50}\)

Step-by-step explanation:

\(\mathrm{Solution,}\\\mathrm{Given,}\\\mathrm{15^{th}\ term(t_{15})=48}\\\mathrm{or,\ a+14d=48.........(1)}\\\mathrm{And\ 40^{th}\ term(t_{40})=223}\\\mathrm{or,\ a+39d=223......(2)}\\\mathrm{n^{th}\ term(t_n)=\ ?}\\\mathrm{Subtracting\ equation(1)\ from\ (2),}\\\mathrm{25d=175}\\\mathrm{or,\ d=7}\\\mathrm{Now,\ a+14d=48\ or,\ a=48-14d=48-14(7)}\\\mathrm{\therefore a=-50}\)

\(\mathrm{t_n=a+(n-1)d}\\\mathrm{or,\ t_n=-50+(n-1)7}\\\mathrm{\therefore general\ formula=7(n-1)-50}\)

Answer to question 1 is   \(\text{y} \le -\frac{2}{5}\text{x}+100\)

=========================================================

Explanation:

The first task is to find the equation of the line through the given points in the table.

Pick any two points you want. I'll pick (0,100) and (50,80)

Determine the slope:

\((x_1,y_1) = (0,100) \text{ and } (x_2,y_2) = (50,80)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{80 - 100}{50 - 0}\\\\m = \frac{-20}{50}\\\\m = -\frac{2}{5}\\\\\)

The slope is -2/5.

The y intercept is b = 100 because of the point (0,100)

We go from \(\text{y} = m\text{x}+b\) to \(\text{y} = -\frac{2}{5}\text{x}+100\)

Each point from the table is found on this line. For instance, let's check the point (140,44)

\(\text{y} = -\frac{2}{5}\text{x}+100\\\\44 = -\frac{2}{5}*140+100\\\\44 = -56+100\\\\44 = 44\\\\\)

This confirms (140,44)

I'll let you check the other points.

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

Any point on the line mentioned represents a scenario where César spends all of the $50.

If he goes above the line, then he'll spend more than $50. If he goes below, he spends less than $50.

This means we want to shade the region below the boundary line \(\text{y} = -\frac{2}{5}\text{x}+100\)

We'll replace the equal sign with a "less than or equal" sign

We arrive at \(\text{y} \le -\frac{2}{5}\text{x}+100\) as the final answer to question 1.

Answer: Answer to question 1 is   =========================================================Explanation:The first task is to find the equation of the line through the given points in the table. Pick any two points you want. I'll pick (0,100) and (50,80) Determine the slope:The slope is -2/5.The y intercept is b = 100 because of the point (0,100)We go from  to Each point from the table is found on this line. For instance, let's check the point (140,44)This confirms (140,44)I'll let you check the other points.------------------Any point on the line mentioned represents a scenario where César spends all of the $50.If he goes above the line, then he'll spend more than $50. If he goes below, he spends less than $50.This means we want to shade the region below the boundary line We'll replace the equal sign with a "less than or equal" signWe arrive at  as the final answer to question 1.

Step-by-step explanation:

Answer:

62 degrees

Step-by-step explanation:

Answer:

52

Step-by-step explanation:

i know how to subtract

The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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Using a moving average of order p = 3, a forecast for time period 6 is 46.

The moving average is a mathematical method for calculating a series of averages using various subsets of the full dataset. It is also known as a rolling average or a running average. The moving average smoothes the underlying data and lowers the noise level, allowing us to visualize the underlying patterns and patterns more readily. In other words, a moving average is a mathematical calculation that employs the average of a subset of data at various time intervals to determine trends, eliminate noise, and better forecast future outcomes. Answer: 46.

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The answers to all the equations are:

So, f(x):

(A) f(x) = x + 3 when f(4)

(B) f(x) = 2x - 9 when f(5)

(C) f(x) = -6x + 2 when f(-3)

Therefore, the answers to all the equations are:

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(a) The number of ways that the event can occur is 6.

(b) Probabilities are :

1) 1/2, 2) 1/6 and 3) 1/3.

(a) Given a bag of different shapes.

Total number of shapes = 6

So, if we select one shape from random,

total number of ways that the event can occur = 6

(b) Number of squares in the bag = 3

Probability of choosing a square = 3/6 = 1/2

Number of circles in the bag = 1

Probability of choosing a circle = 1/6

Number of stars in the bag = 2

Probability of choosing a star = 2/6 = 1/3

Hence the required probabilities are found.

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Answer:

5

Step-by-step explanation:

8-1-(18-2)÷8

PEMDAS says parentheses first

8-1-16÷8

Then divide

8-1-2

Then subtract from left to right

7-2

5

Answer: Um, where is your picture to answer to this question? Please show me this picture to answer the question!

Step-by-step explanation:

Answer:

Step-by-step explanation:

Please your question is Incomplete please edit the question

From the probability, the quantity of various passwords that are conceivable assuming each character might be any lowercase letter or digit is 2,821,109,907,456 passwords

The most effective method to ascertain the probability

The accompanying information can be concluded:

Number of lower case letters = 26

Number of digits = 10

Total Characters = 26 + 10 = 36

Length of secret word = 8

The quantity of various passwords are conceivable assuming each character might be any lowercase letter or digit will be:

= (26+10)⁸ various passwords

= 2,821,109,907,456 passwords

The quantity of various passwords that are conceivable assuming each character might be any lowercase letter or digit, and something like one person should be a digit will be:

= 36⁸ - 26⁸

= 2,612,282,842,880 passwords

Finally, the probability that a substantial secret phrase will be produced will be:

= (36⁸ - 26⁸)/36⁸

= 0.93

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Answer: 90 degrees

Step-by-step explanation: ez

Answer:

Yes you divide 28/80 by 4 and you get 7/20

Step-by-step explanation:

Answer:

For my answer what I got was -118

If its wrong im sorry but I hope this helps :3

Answer: A: 288 in cubed B: 180 in cubed

Step-by-step explanation: Volume is length * height * width.

The Acme Company manufactures widgets, and the distribution of widget weights is bell-shaped. The mean weight of the widgets is 43 ounces, and the standard deviation is 10 ounces.

A bell-shaped distribution is often referred to as a normal distribution or a Gaussian distribution. In this case, the weights of the widgets follow this distribution pattern. The mean weight of 43 ounces represents the central tendency of the distribution, indicating that the most common or average weight of the widgets is around 43 ounces.
The standard deviation of 10 ounces represents the measure of variability or spread in the widget weights. It quantifies how much the weights of the widgets vary around the mean. A larger standard deviation suggests a wider spread of weights, while a smaller standard deviation indicates a narrower range.
The bell-shaped distribution, with its mean and standard deviation, allows the Acme Company to understand the typical range of widget weights and make informed decisions. It provides valuable insights into the variability and consistency of the manufacturing process, helping ensure that the widgets meet the desired specifications and quality standards.

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Answer:

489

Step-by-step explanation:

3423 divide 7

To know the number of data points, simply count the number of values in the data, these values are separated by a comma

Option A: 18, 91, 93, 55, 57, 18. is not correct (it has 6 data points)

Option B: 25, 26, 28, 91, 18, is not correct ( it has 5 data points)

Option C: 9, 12, 8,5, 12, 9, 7. is correct (it has 7 data points)

Option D: 7,5, 9, 11, 13, 4, 9, 18. is not correct ( it has 8 data points)

Option E: 95, 91, 87, 99, 95, 84, 77​. is correct (it has 7 data points)

Options C and E are correct

The y-intercept is 2

Answer:

-0.75

Step-by-step explanation:

Answer: 407

Step-by-step explanation: Given :

                                  Thursday                Friday                

School play                  300                         x                        

Band concert               184                         250

To Find : value of x

Solution

Since we are given that there is an association

So,  

Thus the value of x is 407

Answer:

A,B, and E

Step-by-step explanation:

edge 2021

If a building was photographed using an aerial camera from a flying height of 1000 m.

1.  The height of the building is 5.5 meters.

2. The photographic scale of the building top point is  5.50067e-07.

1. Height of the building:

Height of the building = Flying height * (Measured distance / Focal length)

Converting the measured distance from mm to meters:

Measured distance = 82.501 mm * (1 m / 1000 mm)

Measured distance = 0.082501 m

Substituting the values into the formula:

Height of the building = 1000 m * (0.082501 m / 150 m)

Height of the building = 5.5 m

Therefore the height of the building is 5.5 meters.

2. Photographic scale:

Photographic scale = Measured distance / Ground distance

Using the formula for the photographic scale:

Photographic scale = Measured distance / (Flying height * Focal length)

Photographic scale = 82.501 mm / (1000 m * 150 m)

Converting the measured distance from mm to meters:

Measured distance = 82.501 mm * (1 m / 1000 mm)

Measured distance = 0.082501 m

Photographic scale = 0.082501 m / (1000 m * 150 m)

Photographic scale = 5.50067e-07

Therefore the photographic scale of the building top point is  5.50067e-07.

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a)  The equation for the exponential distribution of waiting times is given by \(f(x) = \lambda e^{-\lambda x}\)

b) The probability of waiting less than 2 minutes to check out is 0.427

c) The probability of waiting between 4 and 6 minutes is 0.242

d) The probability of waiting more than 5 minutes to check out is 0.082

a. The equation for the exponential distribution of waiting times is given by:

\(f(x) = \lambda e^{-\lambda x}\)

where λ is the rate parameter of the distribution, and e is the natural logarithmic constant (approximately equal to 2.71828). The graph of the exponential distribution is a decreasing curve that starts at λ and approaches zero as x approaches infinity. The mean waiting time, denoted by E(X), is equal to 1/λ.

b. To find the probability that a customer waits less than 2 minutes to check out, we need to calculate the area under the exponential distribution curve between zero and 2 minutes. This can be expressed mathematically as:

P(X < 2) = \(\int_0^2 \lambda e^{-\lambda x} dx\)

Solving this integral yields:

P(X < 2) = 1 - \(e^{(-2\lambda)}\)

Substituting the given average waiting time of 2.5 minutes into the formula for the mean waiting time, we can calculate λ as:

E(X) = 1/λ

2.5 = 1/λ

λ = 0.4

Therefore, the probability of waiting less than 2 minutes to check out is:

P(X < 2) = 1 - \(e^{-2*0.4}\)

P(X < 2) ≈ 0.427

c. To find the probability of waiting between 2 and 4 minutes, we need to calculate the area under the exponential distribution curve between 2 and 4 minutes. This can be expressed mathematically as:

P(2 < X < 4) =\(\int_2^4 \lambda e^{(-\lambda x)} dx\)

Solving this integral yields:

P(2 < X < 4) = \(e^{(-2\lambda)} - e^{(-4\lambda)}\)

Substituting the value of λ obtained in part (b), we get:

P(2 < X < 4) = \(e^{(-20.4)} - e^{(-40.4)}\)

P(2 < X < 4) ≈ 0.242

d. To find the probability of waiting more than 5 minutes to check out, we need to calculate the area under the exponential distribution curve to the right of 5 minutes. This can be expressed mathematically as:

P(X > 5) = \(\int_5^{ \infty} \lambda e^{(-\lambda x)} dx\)

Solving this integral yields:

P(X > 5) = \(e^{(-5\lambda)}\)

Substituting the value of λ obtained in part (b), we get:

P(X > 5) = \(e^{(-5*0.4)}\)

P(X > 5) ≈ 0.082

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Answer:

x=0

Step-by-step explanation:

8x +9-3x=8+5x+1

5x+9=9+5x

5x -5x = 9-9

0=0

Answer:

75

Step-by-step explanation:

\(\frac{250}{2}\)-50

125-50

=75