six distinct integers are picked at random from . what is the probability that, among those selected, the second smallest is ?

Using the division,

a) 363 ÷ 14 = 25 13/14

b) 636 ÷ 21 = 30 2/7

c) 908 ÷ 52 = 17 11/13

a) 363 ÷ 14, we first divide 363 by 14 to get a quotient of 25 with a remainder of 13. We then use the que board with 14 beads to represent this division. We start with the first digit of the dividend, which is 3. We count out 2 sets of 14 beads, which we move to the top of the board. We then move 1 more bead to the top, representing the remaining 13. The final result is 25 with a remainder of 13/14.

b) 636 ÷ 21, we divide 636 by 21 to get a quotient of 30 with a remainder of 6. We then use the que board with 21 beads to represent this division. We start with the first digit of the dividend, which is 6. We count out 3 sets of 21 beads, which we move to the top of the board. We then move 3 more beads to the top, representing the remaining 6. The final result is 30 with a remainder of 6/21, which can be simplified to 2/7.

c) 908 ÷ 52, we divide 908 by 52 to get a quotient of 17 with a remainder of 44. We then use the que board with 52 beads to represent this division. We start with the first digit of the dividend, which is 9. We count out 17 sets of 52 beads, which we move to the top of the board. We then move 44 more beads to the top, representing the remaining part of the dividend. The final result is 17 with a remainder of 44/52, which can be simplified to 11/13.

Learn more about division here

brainly.com/question/825875

#SPJ4

To estimate the number of new subscribers in Charlottesville and Albemarle County, we'll use the given joint probability density function (pdf) f(x,y).

Here's a step-by-step explanation:
1. Identify the random variables: In this case, X represents the number of new subscribers (in thousands) in Charlottesville, and Y represents the number of new subscribers (in thousands) in Albemarle County outside of Charlottesville.
2. Understand the joint probability density function (pdf): The function f(x,y) describes the probability of having a specific number of new subscribers in both areas. The joint pdf is used to find the probability of a particular combination of X and Y values.
3. Determine the desired outcome: In this case, you want to estimate the number of new subscribers in both Charlottesville (X) and Albemarle County (Y) next year.
4. Calculate the probabilities: To find the probability of a specific combination of X and Y values, you'll need to evaluate the joint pdf f(x,y) at those values.
5. Analyze the results: Based on the probabilities you've calculated using the joint pdf, you can make informed estimates about the number of new subscribers in both areas next year.
By following these steps and using the joint probability density function f(x,y), you can estimate the number of new subscribers for F XYZ finity Cable in Charlottesville and Albemarle County next year.

For more questions on probability density

https://brainly.com/question/23286309

#SPJ11

The function f(x) = x² - 7 is an example of a function that is neither even nor odd, as it does not exhibit either type of symmetry.

To determine whether a function is even, odd, or neither, we need to examine its algebraic form and look for a particular type of symmetry.

Let's apply this concept to the given function, f(x) = x² - 7. To determine whether f(x) is even or odd, we need to evaluate f(-x) and compare it to f(x).

f(-x) = (-x)² - 7 // substitute -x for x

= x² - 7 // simplify

Comparing f(-x) to f(x), we can see that they are not equal:

f(-x) = x² - 7

f(x) = x² - 7

Since f(-x) is not equal to f(x), the function is not even. To determine whether it is odd, we need to evaluate f(-x) + f(x) and see if the result is zero.

f(-x) + f(x) = (x² - 7) + (x² - 7) // substitute -x for x in the second term

= 2x² - 14

Since f(-x) + f(x) is not equal to zero for all values of x, the function is not odd either.

Therefore, we can conclude that the given function, f(x) = x² - 7, is neither even nor odd.

To know more about function here

https://brainly.com/question/28193995

#SPJ4

The distance from S to the plane x+y+z=0 is sqrt(105)/7.

To find the distance from the sphere S to the plane x+y+z=0, we need to first find the center of the sphere S. We know that the center of the sphere S is (1, 2, 3) and the radius of the sphere is 1. We can use the equation of the plane x+y+z=0 to find the distance from the center of the sphere to the plane.

We can use Lagrange multipliers to find the distance from the center of the sphere to the plane. We need to minimize the function [tex]f(x, y, z) = (x-1)^2 + (y-2)^2 + (z-3)^2[/tex] subject to the constraint x+y+z=0. Using Lagrange multipliers, we get the following system of equations:

2(x-1) = λ

2(y-2) = λ

2(z-3) = λ

x+y+z = 0

Solving these equations, we get x = 1-λ/2, y = 2-λ/2, and z = 3-λ/2. Substituting these values into the equation x+y+z=0, we get λ = 12/7. Substituting this value of λ into x, y, and z, we get the coordinates of the point on the plane closest to the center of the sphere: (5/7, 4/7, -9/7).

To find the distance from the center of the sphere to the plane, we can use the distance formula. The distance from the center of the sphere to the plane is given by the length of the vector connecting the center of the sphere to the point on the plane closest to the center of the sphere. Therefore, the distance from the sphere S to the plane x+y+z=0 is:

d = sqrt[(5/7 - 1)^2 + (4/7 - 2)^2 + (-9/7 - 3)^2] = sqrt[105/49] = sqrt(105)/7.

Learn more about distance: https://brainly.com/question/26550516

#SPJ11

Answer:

10 + 2x

also,

2x + 10

Step-by-step explanation:

"a number value" is the unknown, so use a variable (letter) I used x, but could be almost any letter (avoid e and i, they have other math meanings)

"10 more than" means to add on 10. You can do that up front or at the end. Order is way more important for subtracting, so no worries here.

"product" means multiplying. So the "product of 2 and a number" is 2x.

So to translate this word phrase into an algebraic expression, you get:

10 + 2x

but also 2x + 10 is the same thing.

a.  The cost of renting the gym and paying for supplies, which is $300. b. $10, c. y = 10x - 300 d. $200 e.  30 tickets f. the slope of the line is 1/6.

The slope of a line is the ratio of the change in the y-coordinate to the change in the x-coordinate. It represents the rate of change of the line. A positive slope indicates that the line is increasing, while a negative slope indicates that the line is decreasing. A slope of zero indicates that the line is horizontal.

The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is equal to zero.

Linear equations can be solved algebraically or graphically. In algebra, the goal is to isolate the variable and find its value. In graphing, the equation is plotted on a coordinate plane and the solution is the point where the line intersects with the x- or y-axis.

a. The constant in this situation is the cost of renting the gym and paying for supplies, which is $300.

b. The rate in this situation is the cost per ticket, which is $10.

c. Let x be the number of tickets sold and y be the total profit. The linear equation that represents this situation is:

y = 10x - 300

d. If Amanda sells 50 tickets, then the profit is:

y = 10(50) - 300 = $200

e. To break even, the profit must be 0. So we can set y = 0 and solve for x:

0 = 10x - 300

10x = 300

x = 30

Therefore, Amanda needs to sell 30 tickets to break even.

f. The graph of the linear equation is:

graph{y=10x-300 [-10, 50, -500, 500]}

To calculate the slope of a line that goes through points (10, 6) and (-2, 4), we can use the slope formula:

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

Substituting the given values, we get:

slope = (4 - 6) / (-2 - 10) = -2 / -12 = 1/6

Therefore, the slope of the line is 1/6.

To know more about slope  visit:

https://brainly.com/question/29181869

#SPJ1

The probability that the number of phone calls between 2:00 pm and 2:10 pm is exactly 25 is 1/110,592,893.

To calculate this probability, use the Poisson distribution formula: P(x) = (e^-λ * λ^x) / x!, where λ = 3 x 10 = 30. Therefore, P(25) = (e^-30 * 30^25) / 25! = 1/110,592,893.

The probability that the number of phone calls between 2:00 pm and 2:10 pm is more than 25 is the sum of probabilities of all calls more than 25. That is, the probability is 1 - (e^-30 * (30^0 + 30^1 + 30^2 + ... + 30^25)) / (0! + 1! + 2! + ... + 25!).

By using the same Poisson distribution formula, the probability is 1 - 0.99988822 = 0.00011178.

To know more about Poisson distribution formula click on below link:

https://brainly.com/question/30388228#

#SPJ11

As per integration, the height of the water in the barrel at time = 2 hours is 1.672 feet (option C).

The formula is r(t) = 47-15, where t is the time in hours since the rain began. This formula tells us how fast the water level is changing at any given time t.

In this case, we're asked to find the height of the water in the barrel at t = 2 hours, given that the height at t = 1 hour is 0.75 feet. To solve this problem, we'll integrate the rate formula from t = 1 to t = 2, and add the starting height of 0.75 feet.

∫(47-15)dt from t=1 to t=2 = [47t-15t] from t=1 to t=2 = 0.922

So the total increase in height from t=1 to t=2 is 0.922 feet. Adding this to the starting height of 0.75 feet, we get the height of the water at t=2:

0.75 + 0.922 = 1.672 feet

Therefore, the correct option is (C).

To know more about integral here

https://brainly.com/question/18125359

#SPJ4

b + 2p = 10 ,we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. if Evelyn buys two purses, she also buys six bracelets.

Let's start by defining our variables. We'll let "b" represent the number of bracelets that Evelyn buys and "p" represent the number of purses she buys.

We know that each bracelet costs $6 and each purse costs $12. We also know that her total purchase is $60.

Using this information, we can create an equation:

6b + 12p = 60

Now we want to solve for "b", which represents the number of bracelets. To do this, we need to isolate "b" on one side of the equation. We can start by simplifying the equation by dividing both sides by 6:

b + 2p = 10

Now we have an equation that relates the number of bracelets to the number of purses and the total cost of the purchase. We can use this equation to find the value of "b" given any value of "p". For example, if Evelyn buys two purses, we can substitute "p = 2" into the equation and solve for "b":

b + 2(2) = 10

b + 4 = 10

b = 6    

So if Evelyn buys two purses, she also buys six bracelets.

In general, we can see that the equation tells us that for every two purses that Evelyn buys, she buys one less bracelet. This makes sense because purses are more expensive than bracelets, so as she buys more purses, she can afford fewer bracelets.

To know more about cost of the purchase. click here:

brainly.com/question/28446697

#SPJ4

On average, 50% of athletes are able to begin activity 90 days after a knee operation, with a standard deviation of 15 days.

This means that the median time for 50% of athletes to be able to participate is 75 days, rounded to the nearest day.

The average time for an athlete to begin activity after a knee operation is 90 days, and the standard deviation is 15 days.

Standard deviation is a measure of how spread out the data points are in a data set; a larger standard deviation means that the data points are more spread out.

In this case, 50% of athletes can begin activity within 75 days, which is the median. By rounding to the nearest day, this would be 75 days. Therefore, 50% of athletes are able to participate within 75 days, rounded to the nearest day.

To know more about standard deviation click on below link:

https://brainly.com/question/23907081#

#SPJ11

Answer:

$1.90

Step-by-step explanation:

16.80 - 1.60 = 15.20, since we are finding the price of each bottle of juice.

1) Set up and equation equated to 15.20.

8x = 15.20

x = 15.20/8

x = 1.90

Therefore, each bottle of juice costs $1.90.

Answer:

For problem a: 0,4 0,5 0,6

For Problem B: 1,0 2,0 3,0

Step-by-step explanation:

Graph each equation on a graph Figure out either solid or dotted line. Then depending on <=,<,>,>= is whre you shade on your graph. The spot where both lines meet when shaded is your solution area and you pick any spot on that. You can check your answer by plugging in ordered pairs for your X,Y values in the system.

The answer is one intersection.

What is a function?

A function is a relationship or expression involving one or more variables.  It has a set of input and outputs.

The graph of the function f(x) = 0.8x is a straight line with slope 0.8 passing through the origin (0, 0). The graph of the function g(x) = ⌊x⌋ is the collection of all points (x, y) where y is the greatest integer less than or equal to x. This function is not continuous and has a discontinuity at each integer.

To find the intersections between the two graphs, we need to determine where the values of f(x) and g(x) are equal.

we need to find the integer values of x where 0.8x and x are equal.

0.8x = x

0.2x = 0

x = 0

Thus, the two graphs intersect at the point (0, 0). There are no other intersections between the two graphs, since they have different slopes and one is continuous while the other is not. Therefore, the answer is one intersection.

To know more about function visit,

https://brainly.com/question/11624077

#SPJ1

Answer:

Step-by-step explanation:

We can use the standard normal distribution to solve this problem by standardizing the score.

z = (x - mu) / sigma

Where:

x = 70 (score we are interested in)

mu = 60 (mean score)

sigma = 7 (standard deviation)

z = (70 - 60) / 7 = 1.43

Using a standard normal distribution table or calculator, we can find the probability that z is greater than 1.43. The probability is approximately 0.0764.

Therefore, the probability that a randomly selected student scored more than 70 on the exam is 0.0764 (or about 7.64%).

The gorilla has a heart rate that is four times faster than the chimpanzee's when they are resting.

Expression in math is a combination of numbers, variables, operations and/or symbols that represent a value, quantity or an equation. It can either be a single term, or several terms connected by mathematical operations such as addition, subtraction, multiplication and division. Expressions are typically used in equations, formulas and problems to help solve them.

To calculate the heart rate of the gorilla, we use the power function given: H(m) = 240m. Substituting in m = 200, we get H(200) = 240(200) = 48,000 beats per minute.

To calculate the heart rate of the chimpanzee, we use the same power function: H(m) = 240m. Substituting in m = 50, we get H(50) = 240(50) = 12,000 beats per minute.

Therefore, the gorilla has a heart rate that is four times faster than the chimpanzees when they are resting.

To know more about expression in math click-
https://brainly.com/question/1859113
#SPJ1

Answer:

153

Step-by-step explanation:

The relationship in the row is below

4³ +2³ +1³ =64 + 8 +1 = 72

1³ + 2³ +6³= 1 + 8 + 216

3³ + 1³ + 5³ = 27 +1 +125 = 153

All numbers below the first level are raised to power 3 and added together

Probability that exactly four workers carpool to work is 0.214990847, or approximately 21.5%.

We must apply the binomial distribution formula to resolve this issue. The number of successes in a certain number of independent trials that all have the same chance of success are described by the binomial distribution, which is a type of probability distribution. In this scenario, the number of successes is the number of workers who carpool, and the probability of success is 0.1.

The binomial distribution's formula is:

[tex]P(X=k) = to (n pick k) * p*k*1-p (n-k)[/tex]

Where n is the total number of trials (in this case, 8), p is the success probability (0.1), and (n choose k) is the binomial coefficient, which is equal to [tex]n! / (k! * (n-k)![/tex] and P(X=k) is the probability of obtaining exactly k successes.

This formula can be used to determine the likelihood that four employees will carpool to work:

[tex]P(X=4) = (8 pick 4) * 0.14 * 0.94 * 0.214 = 0.214990847.[/tex]

Learn more about probability here:

https://brainly.com/question/30034780

#SPJ4

Answer:

y = -2/3x + 1/3

Step-by-step explanation:

2x + 3y = 1

3y = -2x + 1

y = -2/3x + 1/3

To sketch:

Pretend x is 3. y would be -1 2/3.

Now that you have this point, draw through the point (0, 1/3).

There ya go

To find two divergent series, summation from n equals 1 to infinity of a_n and summation from n equals 1 to infinity of b_n, such that their product converges, we can consider the following series:

1. Summation from n equals 1 to infinity of a_n = ∑(1/n)
2. Summation from n equals 1 to infinity of b_n = ∑n

Solution:

1. The first series, ∑(1/n), is known as the harmonic series. It is a famous example of a divergent series, meaning that its sum approaches infinity as n approaches infinity.

2. The second series, ∑n, is an arithmetic series where the terms increase linearly. This series is also divergent, as the sum increases without bound as n approaches infinity.

Now, we need to verify that the product of these series converges:

3. Summation from n equals 1 to infinity of (a_n * b_n) = ∑((1/n) * n)

4. Simplifying the expression, we get ∑(1), which is a constant series with all terms equal to 1.

5. The sum of the constant series converges, as it approaches a finite value when n approaches infinity.

In conclusion, the two divergent series summation from n equals 1 to infinity of a_n = ∑(1/n) and

summation from n equals 1 to infinity of b_n = ∑n, have a product that converges, as their product ∑((1/n) * n) simplifies to a constant series ∑(1), which has a finite sum.

To know more about divergent series:

https://brainly.com/question/15415793

#SPJ11

The average rate of change of f(x) from x = -3 to x = 6 is 7.

What is meant by average?

The term "average" is used to describe a number that represents the central or typical value in a set of data. There are several different types of averages, including the mean, median, and mode.

To find the average rate of change of a function, we need to compute the difference between the function values at the two given points, and then divide by the difference in the input values.

For the function [tex]f(x) = x^2 + 4x - 15[/tex], the value of the function at [tex]x = -3[/tex] is:

[tex]f(-3) = (-3)^2 + 4(-3) -15 = 9 - 12 - 15 = -18[/tex]

The value of the function at [tex]x = 6[/tex] is:

[tex]f(6) = 6^2 + 4(6) - 15 = 36 + 24 - 15 = 45[/tex]

The difference in the function values is:

[tex]f(6) - f(-3) = 45 - (-18) = 63[/tex]

The difference in the input values is:

6 - (-3) = 9

Therefore, the average rate of change of f(x) from x = -3 to x = 6 is:

average rate of change = [tex](f(6) - f(-3)) / (6 - (-3)) = 63 / 9 = 7[/tex]

So, the average rate of change of f(x) from x = -3 to x = 6 is 7.

To learn more about average visit:

https://brainly.com/question/20118982

#SPJ1

There are 100,947 ways to assign the tasks to the 7 people.

This problem can be solved using combinations. We need to choose 17 tasks from a total of 17, which can be done in one way, and then assign each of these tasks to one of the 7 people. We can do this by considering all possible combinations of tasks that each person could be assigned.

Let's use the stars and bars method to count the number of ways to distribute the tasks. We can represent the tasks as stars and the people as bars, with each bar representing a separate person. For example, if person 1 is assigned 4 tasks, person 2 is assigned 2 tasks, and person 3 is assigned 1 task,

The number of ways to distribute the tasks is then the number of ways to arrange the 17 stars and 6 bars, which is

(17 + 6) choose 6 = 23 choose 6 = 100947

Learn more about combination here

brainly.com/question/28720645

#SPJ4

The calculated value of y when x is -4 is -10 given that the variation is a direct variation

Direct variation is a mathematical concept that describes the relationship between two variables that change in proportion to each other.

More formally, two variables x and y are said to vary directly if their ratio is constant. This can be expressed mathematically as:

y = kx

So, we have

20 = -8k

This gives

k = -2.5

This means that

y = -2.5x

When the value of x is -4 we have

y = -2.5 * -4

Evaluate

y = 10

Hence, the value of y when x is -4 is -10

Read more about direct variation at

https://brainly.com/question/6499629

#SPJ1

Answer:

To find the probability of the next customer ordering peanut butter cup, we need to determine the total number of ice cream cones and the number of cones that are peanut butter cup.

The total number of cones is:

4 + 5 + 2 + 3 + 2 = 16

The number of cones that are peanut butter cup is 2.

Therefore, the probability of the next customer ordering peanut butter cup is:

2/16 = 0.125

So, the probability of the next customer ordering peanut butter cup is 0.125 or 12.5%.

The compound inequality is -7 < y/3 - 2 < 4 and the solution is -15 < y < 18

To write the compound inequality that represents the statement, we can first translate the words into symbols:

The quotient of a number y and 3, less 2: y/3 - 2

Is between -7 and 4: -7 < y/3 - 2 < 4

So the compound inequality that represents the statement is:

-7 < y/3 - 2 < 4

To solve this compound inequality, we can first add 2 to all parts of the inequality:

-7 + 2 < y/3 - 2 + 2 < 4 + 2

Simplifying, we get:

-5 < y/3 < 6

To isolate y/3, we can multiply all parts of the inequality by 3:

-15 < y < 18

Therefore, the solution to the compound inequality is: -15 < y < 18

Read more about compound inequality at

https://brainly.com/question/234674

#SPJ1

The given equation 3x + 7y = 11 is equal to (1,-2).

The given equation is 3x + 7y = 11.

To find the solution of the equation, we need to consider the given options:

(6,-1)(1,-2)(0,4)

Now substitute each value of x and y in the given equation, we get,

If x = 6 and y = -13(3 × 6) + (7 × -1) = 18 - 7 = 11 ≠ 11

If x = 1 and y = -2(3 × 1) + (7 × -2) = 3 - 14 = -11 ≠ 11

If x = 0 and y = 4(3 × 0) + (7 × 4) = 0 + 28 = 28 ≠ 11

Therefore, the given equation 3x + 7y = 11 is equal to (1,-2).

for such more question on equation

https://brainly.com/question/17145398

#SPJ11

The expression or equation that correctly represents the situation given is y = 2x.

Based on the table, for each package of cashews 2 cans of peanuts are required. Here are some examples:

Based on this relationship and assuming y represents the cans of peanuts and x represents the packages of cashews a possible equation to represent this situation would be y = 2x.

Note: This question is incomplete; below I attach the missing information:

Write an equation to represent this relationship:

Learn more about equations in https://brainly.com/question/29657992

#SPJ1

Answer:2

Step-by-step explanation:

1+1=2

The value of angle x in the right triangle KJI is approximately 63.4 degrees.

What is trigonometric ratios ?

Trigonometric ratios are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The three primary trigonometric ratios are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.

These ratios are defined as follows:

Sine (sin) of an angle is the ratio of the length of the side opposite to the angle to the length of the hypotenuse.

Cosine (cos) of an angle is the ratio of the length of the adjacent side to the angle to the length of the hypotenuse.

Tangent (tan) of an angle is the ratio of the length of the side opposite to the angle to the length of the adjacent side.

Finding the value of x :

We can use the trigonometric ratios to find the value of angle x in the right triangle KJI.

First, we can use the Pythagorean theorem to find the length of the hypotenuse KI:

[tex]KI^2 = KJ^2 + JI^2[/tex]

[tex]KI^2 = 27^2 + 48^2[/tex]

[tex]KI^2 = 729 + 2304[/tex]

[tex]KI^2 = 3033[/tex]

[tex]KI =\sqrt{3033}[/tex]

Next, we can use the sine function to find the value of angle I:

[tex]sin(I) = JI / KI[/tex]

[tex]sin(I) = 48 / \sqrt{3033}[/tex]

[tex]I = sin^-1(48 / \sqrt{3033})[/tex]

[tex]I = 63.4[/tex] degrees

Therefore, the value of angle x in the right triangle KJI is approximately 63.4 degrees.

To know more about angle visit :

brainly.com/question/28451077

#SPJ1

Answer:

slope of 3/4 = line C

undefined slope = line A

Step-by-step explanation:

remember that slope is [tex]\frac{rise}{run}[/tex]. Pick any two points on the graph and count up and over to find the rise/run.

OR

use the slope formula [tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex] to plug the two points into and find the slope.

- vertical lines are always undefined.

- horizontal lines have a slope of 0

The sum of the first $20$ terms of the arithmetic sequence is $420$.

In an arithmetic sequence, the sum of the second and eighth terms is $5$, and the product of the fourth and fifth terms is also $5$. The sum of the first $20$ terms of this sequence can be calculated using the following formula:

Sum of the first $20$ terms = $20$/2($a_1 + a_{20})$, where $a_1$ is the first term of the sequence and $a_{20}$ is the twentieth term of the sequence.

Therefore, we need to find the first term of the sequence and the twentieth term of the sequence. To find the first term, we use the following equation:

$5 = a_2 + a_8$, where $a_2$ is the second term and $a_8$ is the eighth term.

To find the twentieth term, we use the following equation:

$5 = a_4 \times a_5$, where $a_4$ is the fourth term and $a_5$ is the fifth term.

Solving both equations, we get $a_2 = 1$ and $a_{20} = 40$. Then, we can calculate the sum of the first $20$ terms of the sequence:

Sum of the first $20$ terms = $20$/2($1 + 40$) = $420$.

Therefore, the sum of the first $20$ terms of the arithmetic sequence is $420$.

To Know more about arithmetic sequence, refer here:

brainly.com/question/12108818#

#SPJ11