1. In school lottery to win a price for "Free Domino's Pizza" it is required to select 5 numbers (in any order) out of 40 numbers.

What is the probability of winning?


2. Your sock drawer has 18 folded pairs of socks, with 8 pairs of white, 6 pairs of black, and 4 pairs of blue.

What is the probability, without looking in the drawer, that you will first select and remove a black pair, then select either a blue or a white pair?

To find the point on the line -5x + 7y + 1 = 0 that is closest to the point (1, 5), we can use the concept of perpendicular distance.

The line -5x + 7y + 1 = 0 can be rearranged to the standard form of a line: y = (5/7)x - 1/7.

We want to find a point (x, y) on this line that is closest to the point (1, 5). The distance between two points can be calculated using the distance formula:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the coordinates of the two points, we have:

Distance = sqrt((x - 1)^2 + (y - 5)^2)

We need to minimize this distance. Since the point (x, y) lies on the line -5x + 7y + 1 = 0, we can substitute the expression for y in terms of x from the line equation:

Distance = sqrt((x - 1)^2 + ((5/7)x - 1/7 - 5)^2)

Simplifying further:

Distance = sqrt((x - 1)^2 + ((5/7)x - 36/7)^2)

To find the minimum distance, we can take the derivative of the distance function with respect to x, set it equal to zero, and solve for x.

Differentiating the distance function:

d/dx [Distance] = d/dx [sqrt((x - 1)^2 + ((5/7)x - 36/7)^2)]

Setting the derivative equal to zero:

0 = (x - 1) + ((5/7)x - 36/7) * (5/7)

Solving the equation for x:

0 = x - 1 + (25/49)x - (180/49)

Multiplying through by 49 to eliminate the denominator:

0 = 49x - 49 + 25x - 180

0 = 74x - 229

74x = 229

x = 229/74

Substituting this value of x back into the line equation, we can find the corresponding value of y:

y = (5/7)(229/74) - 1/7

Simplifying the expression:

y = 115/74 - 1/7

To obtain the closest point on the line, the coordinates are approximately:

(x, y) ≈ (229/74, 827/518)

Therefore, the point on the line -5x + 7y + 1 = 0 that is closest to the point (1, 5) is approximately (229/74, 827/518).

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The vector field f(x, y, z) = i + 2j + 3k represents a constant vector field that points in the direction of the positive x-axis with magnitude 1, positive y-axis with magnitude 2, and positive z-axis with magnitude 3.

The plot of this vector field would consist of parallel arrows pointing in the same direction, where each arrow represents the magnitude and direction of the vector at a specific point in space. The arrows would be evenly spaced and extend indefinitely in the positive x, y, and z directions. The length of the arrows would represent the magnitude of the vector, with longer arrows indicating larger magnitudes.

In summary, the plot of the vector field f(x, y, z) = i + 2j + 3k would consist of evenly spaced, parallel arrows pointing in the positive x, y, and z directions, representing a constant vector field with magnitudes 1, 2, and 3 along the respective axes.

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Answer:

|-3| > 1

Step-by-step explanation:

Well |-3| = 3

3 > 1

1 < 3

(you can replace 3 for |-3| in those up there^)

The translations performed are

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

f(x) = ln(x)

g(x) = -ln(x + 1) - 3

First, we have the transformation to be:

From f(x) = ln(x) to f(x) = -ln(x)

This means a reflection across the x-axis

Next, we have

From f(x) = -ln(x) to f(x) = -ln(x + 3)

This means the function is translated left by 3 units

Next, we have:

From f(x) = -ln(x + 3) to f(x) = -ln(x + 3) - 3

This means the function is translated down by 3 units

Hence, the translation is 3 units left and 3 units down

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Answer:

4

explanation:

I took the test

The constant of proportionality  is 4.

The constant value of the ratio between two proportional quantities is the constant of proportionality. When either their ratio or their product gives a constant, two varying quantities are said to be in a relation of proportionality. The type of proportion between the two given quantities determines the value of the proportionality constant: Variation in both a direct and inverse manner.

given relation

x 1  2  3  4

y 4 8 12 16

the equation is

y = 4x

1 * 4 = 4

2 * 4 = 8

3 * 4 = 12

and so on...

Hence the constant is 4.

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In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.

The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.

We have to find the product of tan A and tan C.

In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.

So, we have, tan A = tan C

Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.

Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.

Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.

Answer: `(BC)^2/(AB)^2`.

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The correct answer is -60

When you look at -70 it looks like it would be higher then -60 but -60 is actually higher then -70 because it has a negative line.

Therefore, the correct answer is -60

Your answer is the center image.

hope this helps.

The stem-and-leaf plot reveals that 54 and 99 are the smallest and biggest values, respectively. Hence, the range is: range = 99 - 54 = 45

The range of a number collection or data points in mathematics is the difference here between biggest and smallest values. It is a measurement of the data's dispersion or variability. The range is frequently employed in descriptive statistics and can serve to provide information about the data's distribution.

given

Certainly! The data are shown in a stem-and-leaf plot as follows:

5 | 4

6 | 0 1 2 2

7 | 1 2 4 6 8

8 | 2 3 4 4 6 7

9 | 0 5 5 9

The difference between the largest and smallest values is the data's range.

The stem-and-leaf plot reveals that 54 and 99 are the smallest and biggest values, respectively. Hence, the range is: range = 99 - 54 = 45

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The overall percentage increase in price is 1.5, which means that the price of the solution has increased by 150%. This means that if the original price of the solution was $300, the new price after the increase would be $750.To find the overall percentage increase in price, we need to use the ratio of ingredients a and b, which is 2:1.

This means that for every 2 units of ingredient a used, 1 unit of ingredient b is used.

Let's assume that the original unit price of ingredient a was $100 and the original unit price of ingredient b was $200. After the increase, the unit price of ingredient a would be $110 (10% increase) and the unit price of ingredient b would be $250 (25% increase).

To find the overall percentage increase in price, we need to calculate the weighted average of the two ingredients based on their ratios. This can be done by multiplying the percentage increase in each ingredient by its weight in the ratio and adding them together.

The weighted average percentage increase in price can be calculated as follows:

[(2/3) x 10%] + [(1/3) x 25%] = (20/30) + (25/30) = 45/30 = 1.5

Therefore, the overall percentage increase in price is 1.5, which means that the price of the solution has increased by 150%. This means that if the original price of the solution was $300, the new price after the increase would be $750.

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Answer:

11=y÷6

Step-by-step explanation:

by the way i'm du/mb

Answer:

true false false true true

Answer:

f(x)=-1/3x+7 2/3

Step-by-step explanation:

Find the slope:

m= -1/3

Find the y-intercept:

b= -7 2/3

The exact values of cosθ and sinθ for an angle measure of 60° are cosθ = 0.5 and sinθ = 0.866. The angle of 60° is an acute angle, which means it is less than 90°. Acute angles lie in Quadrant I of the unit circle, where both the sine and cosine functions are positive.

The sine function of an angle is represented by the y-coordinate of a point on the unit circle that is rotated by that angle. The cosine function of an angle is represented by the x-coordinate of the same point.

When the angle is 60°, the point on the unit circle that is rotated by that angle has a y-coordinate of 3/2 and an x-coordinate of 1/2. Therefore, cosθ = 0.5 and sinθ = 0.866.

Here is a table of the values of cosθ and sinθ for some common angle measures:

Angle cosθ sinθ

0° 1 0

30° √3/2 1/2

45° 1/√2 1/√2

60° 1/2 √3/2

90° 0 1

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b. The statement "the probability that x falls between 10 and 20" is false.

A continuous random variable X has a uniform distribution between 5 and 15 (inclusive), meaning it can take any value between 5 and 15 with equal probability.

We need to find the probability that X falls between 10 and 20. Since the range of X is only between 5 and 15, we can only consider the range of 10 to 15 within this interval.

For a uniform distribution, the probability density function (pdf) is:

f(x) = 1 / (b - a)

where 'a' and 'b' are the lower and upper limits of the distribution, respectively. In this case, a = 5 and b = 15, so:

f(x) = 1 / (15 - 5) = 1 / 10

Now, to find the probability that X falls between 10 and 15, we can integrate the pdf over this interval:

P(10 ≤ X ≤ 15) = ∫[1/10]dx from 10 to 15

P(10 ≤ X ≤ 15) = [x/10] from 10 to 15

P(10 ≤ X ≤ 15) = (15/10) - (10/10) = 1/2

So, the probability that X falls between 10 and 20 is 1/2, not 1.0. Therefore, the statement is the probability that x falls between 10 and 20 is false.

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The function used to represents the time spend by Jasmine in biking for a distance of d miles is given by f(d) = d / 18.

The time Jasmine spends biking is indeed a function of the distance she bikes.

The formula to calculate the time Jasmine takes to bike a certain distance is equal to,

time = distance / speed __(1)

Here the speed is the rate at which Jasmine bikes = 18 miles per hour.

Let us consider 'd' be the distance representing the number of miles Jasmine bikes.

This implies,

The function that represents the time Jasmine spends biking in terms of the distance .

Function f(d)  representing the time Jasmine spends biking for a distance of d miles

Substitute all the values in the formula (1) we get,

⇒ f(d) = d / 18

Therefore, the function representing the time spend by Jasmine for distance d is equal to f(d) = d / 18.

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The above question is incomplete , the complete question is:

The time Jasmine spends biking is a function of the distance she bikes. Jasmine bikes 18 miles per hour. Assume she bikes at a constant rate.

Write the function representing the time Jasmine spends biking in terms of the distance?

Answer:

x

Step-by-step explanation:

equals 4 you can do rest

The solution to the linear system is x₁ = 0, x₂ = -5/4, and x₃ = 3/2.

We start with the augmented matrix:

[1 2 3 | 2]

[-1 2 5 | 5]

[2 1 3 | 9]

First, we eliminate the variable x₁ from the second and third equations by adding the first equation to them:

[1 2 3 | 2]

[0 4 8 | 7]

[0 -3 -3 | 5]

Next, we eliminate the variable x₂ from the third equation by adding 3/4 times the second equation to it:

[1 2 3 | 2]

[0 4 8 | 7]

[0 0 3 | 18/4]

Now, we have the system in row echelon form. We can perform backward substitution to find the values of the variables. Starting from the last equation, we have:

3x₃ = 18/4 -> x₃ = 18/4 / 3 = 3/2

Substituting this value back into the second equation, we have:

4x₂ + 8(3/2) = 7 -> 4x₂ + 12 = 7 -> x₂ = -5/4

Finally, substituting the values of x₂ and x₃ into the first equation, we have:

x₁ + 2(-5/4) + 3(3/2) = 2 -> x₁ - 5/2 + 9/2 = 2 -> x₁ = 0

Therefore, the solution to the linear system is x₁ = 0, x₂ = -5/4, and x₃ = 3/2.

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The statistic is interquartile range.

Interquartile range is a measure of dispersion that is calculated by subtracting the lower quartile (Q1) from the upper quartile (Q3). To calculate the interquartile range for the 10 dental practices, the insurance company first needs to organize the cash (non-insurance) prices for the procedure at each practice in ascending order. The lower quartile (Q1) is the median of the first 5 values and the upper quartile (Q3) is the median of the last 5 values. The interquartile range is then calculated by subtracting the lower quartile (Q1) from the upper quartile (Q3). In this case, the interquartile range is $74

The interquartile range is the range of values between the 25th and 75th percentiles. In this case, the statistic is the interquartile range for the cash price for filling a cavity across 10 dental practices in California. The interquartile range is $74, meaning that the price for filling a cavity at the 25th percentile is $74 lower than the price at the 75th percentile.

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Porosity calculated as ratio of pore to total vol. Plot of porosity vs averaging length scale (edge of square used for averaging). Rep. elemental vol = vol of square used for averaging.

The porosity as a function of the averaging length scale can be calculated as follows:

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Answer:

the population variance is 2 and the population standard deviation is approximately 1.41.

Step-by-step explanation:

To calculate the variance and standard deviation of a population, you can use the following formulas:

Population variance = (Σ(x - μ)²) / N

Population standard deviation = √(Σ(x - μ)² / N)

Where:

Σ is the sum of

x is each individual score in the population

μ is the population mean

N is the number of scores in the population

To begin, we need to find the population mean (μ):

μ = (6 + 2 + 3 + 0 + 4) / 5 = 3

Next, we can calculate the variance:

Population variance = ((6-3)² + (2-3)² + (3-3)² + (0-3)² + (4-3)²) / 5

Population variance = (9 + 1 + 0 + 9 + 1) / 5

Population variance = 2

Finally, we can calculate the standard deviation:

Population standard deviation = √((6-3)² + (2-3)² + (3-3)² + (0-3)² + (4-3)²) / 5

Population standard deviation = √(9 + 1 + 0 + 9 + 1) / 5

Population standard deviation = √2

Therefore, the population variance is 2 and the population standard deviation is approximately 1.41.

The variance of the given set of scores is 4 and the standard deviation is 2. Both are measures of how spread out the data is in statistics. The variance is calculated by acquiring the average squared deviation from the mean, while the standard deviation is the square root of the variance.

This is a question about the notions of variance and standard deviation in statistics. Variance is a measure of how spread out the numbers in a data set are. Standard deviation, on the other hand, is the square root of the variance, indicating the amount of deviation (or variation) you can expect in your data.

Here are the steps for calculating variance and standard deviation for given set of scores: 6, 2, 3, 0, 4

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The correct answer is  about 15.87% of the class scored lower than your friend based on the given z-score of -1.

(a) A z-score of 2.20 in an exam means that your score is 2.20 standard deviations above the mean score of the class. It indicates that your performance on the exam was relatively high compared to the average performance of the class.

(b) To determine the percentage of the class that scored lower than your friend, we can use the standard normal distribution table or a statistical software. Assuming a standard normal distribution, we can find the area under the curve to the left of a z-score of -1.

From the standard normal distribution table or using a statistical software, we find that the area to the left of a z-score of -1 is approximately 0.1587. This means that approximately 15.87% of the class scored lower than your friend.

Therefore, about 15.87% of the class scored lower than your friend based on the given z-score of -1.

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Answer:

603 cm³

Step-by-step explanation:

v = πr²h

v = π(4²)12

v = 3.14 * 16 * 12

v = 602.88

rounded

603 cm³

If Ariana removes the $4,800 rent from the set, the mean and median of the remaining rents will decrease because $4,800 is a very high value compared to the other rents.

Before removing the $4,800 rent, the mean can be calculated by adding up all the rents and dividing by the total number of rents (5):

Mean = (1,000 + 1,200 + 1,300 + 1,400 + 4,800) / 5 = 2,540

The median is the middle value in the set, which is 1,300.

After removing the $4,800 rent, the new mean can be calculated by adding up the remaining rents and dividing by the new total number of rents (4):

New Mean = (1,000 + 1,200 + 1,300 + 1,400) / 4 = 1,225

The new median is still 1,300 because it is the middle value in the remaining set.

Therefore, removing the $4,800 rent will decrease both the mean and median of the remaining rents.

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Answer: There are 80 ounces in 5 pounds

there are 80 ounces in 5 pounds

At t = 3, the rate οf change οf y with respect tο x is:

dy/dx = (dy/dt) / (dx/dt) = (3/5) / 9 = 1/15

The prοcess οf differentiatiοn cοmpares the rate οf change οf the functiοn tο the rate οf change οf the independent variable. The οutcοme οf differentiating a functiοn is referred tο as the functiοn's derivative. It prοvides each pοint's slοpe οn the functiοn's graph.

Tο find the rate οf change οf y with respect tο x, we need tο find dy/dx at t = 3. We can use the chain rule tο express dy/dx in terms οf derivatives with respect tο t:

dy/dx = (dy/dt) / (dx/dt)

We can find dx/dt and dy/dt as follows:

dx/dt = 3t² - 6t

dy/dt = (1/2)(t² + 16\()^{(-1/2)\) * 2t

Substituting t = 3, we get:

dx/dt = 3(3)² - 6(3) = 9

dy/dt = (1/2)((3)² + 16\()^{(-1/2)\) x 2(3) = 3/5

Therefore, at t = 3, the rate of change of y with respect to x is:

dy/dx = (dy/dt) / (dx/dt) = (3/5) / 9 = 1/15

So the answer is 1/15.

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Answer:

b). Examine relationships between two categorical variables

Step-by-step explanation:

True. Exception reports show a greater level of detail than is included in routine reports.

Exception reports are reports that help in identifying data that does not conform to expected patterns. Exception reports show information about an exception in the data set.

This helps to identify irregularities or anomalies in data or system operations.Exception reports are used to analyze system performance, monitor resource consumption, and to detect unusual activity.

This type of report is important to identify issues or errors, where the routine reports or standard reports would not provide enough detail or insight to do so.

It provides detailed information on any unusual event or anomaly that occurred beyond the usual course of events or processes.Exception reports are generated and distributed when the data is not expected or when an event occurs that is outside of what is considered typical.

For example, a financial system might generate an exception report if a transaction is entered that exceeds the maximum allowed amount. This report would show the details of the transaction and highlight the exception.

The purpose of exception reports is to provide users with a higher level of detail than they would find in routine reports. Exception reports are used to highlight significant data, which will be used for further analysis or action.

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The statement that shows a discrepancy between the check register and bank statement is: C. Gavin: The balance in his check register is $500 and the balance in his bank statement is $510.

The check register shows a balance of $500, while the bank statement shows a balance of $510.

In the case of Gavin, where the balance in his check register is $500 and the balance in his bank statement is $510, there is a $10 discrepancy between the two.

A possible explanation for this discrepancy could be outstanding checks or deposits that have not yet cleared or been recorded in either the check register or the bank statement.

For example, Gavin might have written a check for $20 that has not been cashed or processed by the bank yet. Therefore, the check register still reflects the $20 in his balance, while the bank statement does not show the deduction. Similarly, Gavin may have made a deposit of $10 that has not yet been credited to his account in the bank statement.

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