This is the question

There are 37,837,800 ways to distribute 15 distinguishable objects into five distinguishable boxes so that the boxes have one, two, three, four, and five objects in them, respectively.

We are trying to find the number of ways to distribute 15 distinguishable objects into five distinguishable boxes so that each box has 1, 2, 3, 4, and 5 objects in them, respectively.

We can use the formula for combination to solve this problem. The number of ways to distribute n distinct objects into r distinct boxes where the first box has k1 objects, the second box has k2 objects, ..., and the last box has kr objects is:

n! / (k1! * k2! * ... * kr!)

Where n! is the factorial of n, k1! is the factorial of k1 and so on.

In this case, we have 15 distinct objects and 5 distinct boxes where the first box has 1 object, the second box has 2 objects, the third box has 3 objects, the fourth box has 4 objects, and the fifth box has 5 objects.

So, the number of ways to distribute 15 distinguishable objects into five distinguishable boxes so that the boxes have one, two, three, four, and five objects in them, respectively is:

15! / (1! * 2! * 3! * 4! * 5!) = 15! / (1×2×6×24×120)

= 37,837,800

To know more on combination

https://brainly.com/question/29223146

#SPJ4

The values of b that makes the lines parallel are given as follows:

b = ± 3/2.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

When two lines are parallel, they have the same slope.

Given two points, the slope is given as the change in y divided by the change in x.

This means that the slopes for each line are given as follows:

As they are parallel, the value of b is obtained as follows:

4b/3 = 3/b.

4b² = 9

b² = 9/4

[tex]b = \pm \sqrt{\frac{9}{4}}[/tex]

b = ± 3/2.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

x- intercept:  x = -1.33, y- intercept: y = log 4 + 2

Suppose that the line considered be of the form  y=f(x)

The equation for y-axis is x = 0

Thus, intersection between both the curves is obtained by putting x = 0 in the considered function.

We get x=0 and y=f(0)

Thus, the coordinate point of intersection with y-axis is (0,f(0))

And the equation for x-axis is y=0

Thus, its intersection with given function is at y= 0 and y such that

f(x)=0

Given equation,

y = log (3x+4) + 2,

For x - intercept,

y = 0,

0= log(3x+4) +2

-2= log(3x+4)

10^-2= 3x+4 ([tex]log_{m}[/tex]a=b => a=m^b)

0.01= 3x+4

0.01-4=3x

x= -3.99= -1.33

For y-intercept,

x = 0,

y=log(3(0)+4)+2= log4+2

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ1

The answer to the first, third and fourth part is inductive reasoning and the answer to the second and fifth part is deductive reasoning.

The first example is an example of Inductive reasoning because it is based on a pattern or trend of a sequence of numbers (2, 4, 6, 8) and uses that pattern to make a prediction or generalization about the next number in the sequence (10). This is a common use of inductive reasoning, where observations or data are used to make generalizations about future events or situations.

The second example is an example of Deductive reasoning because it starts with a general statement (all plants need water) and applies it to a specific case (Water Hyacinth) to reach a logical conclusion (Water Hyacinth needs water). This is the classic form of deductive reasoning, where the conclusion follows logically from the premises and can be proven to be true if the premises are true.

The third example is an example of Inductive reasoning because it is based on a pattern or trend of a sequence of numbers (dots in squares) and uses that pattern to make a prediction or generalization about the next number in the sequence (16 dots in the next square).

The fourth example is an example of Inductive reasoning because it is based on a pattern or trend of a sequence of events (pre-school, grade 1, grade 2) and uses that pattern to make a prediction or generalization about the next event in the sequence (the child's next teacher will be female).

The fifth example is an example of Deductive reasoning because it starts with a general statement (all football players are muscular) and applies it to a specific case (Peter) to reach a logical conclusion (Peter is a football player). This is the classic form of deductive reasoning, where the conclusion follows logically from the premises and can be proven to be true if the premises are true.

To know more on Inductive Reasoning or Deductive Reasoning

https://brainly.com/question/2437643

#SPJ4

Answer:

JF

Step-by-step explanation:

There is a rule where if the angle in a triangle is facing the smallest side, that angle is the smallest of the other 2 angles in the triangle, and vice versa. If the angle in a triangle is facing the biggest side, well, you can see where this is going(the angle is the biggest)

So if we look at this beautiful drawing that I drew :

Angle <JFR is 180 - 115, which is 65.

And the last angle is 180 - 65 - 35 = 80

Angle R is the biggest angle.

So the side that is facing R is the longest side, which is JF

Given an infinite grid, initial cell position (x, y) and a sequence of other cell position which needs to be covered in the given order.

The task is to find the minimum number of steps needed to travel to all those cells.

Note: Movement can be done in any of the eight possible directions from a given cell that is from cell (x, y) you can move to any of the following eight positions:(x-1, y+1), (x-1, y), (x-1, y-1), (x, y-1), (x+1, y-1), (x+1, y), (x+1, y+1), (x, y+1) is possible

Examples:

Input: points[] = [(0, 0), (1, 1), (1, 2)]

Output: 2

Move from (0, 0) to (1, 1) in 1 step(diagonal) and

then from (1, 1) to (1, 2) in 1 step (rightwards)

Input: points[] = [{4, 6}, {1, 2}, {4, 5}, {10, 12}]

Output: 14

Move from (4, 6) -> (3, 5) -> (2, 4) -> (1, 3) ->

(1, 2) -> (2, 3) -> (3, 4) ->

(4, 5) -> (5, 6) -> (6, 7) ->

(7, 8) -> (8, 9) -> (9, 10) -> (10, 11) -> (10, 12)

Since all the given points are to be covered in the specified order.

Find the minimum number of steps required to reach from a starting point to next point, then the sum of all such minimum steps for covering all the points would be the answer.

One way to reach from a point (x1, y1) to (x2, y2) is to move abs(x2-x1) steps in the horizontal direction and abs(y2-y1) steps in the vertical direction, but this is not the shortest path to reach (x2, y2).

The best way would be to cover the maximum possible distance in a diagonal direction and remaining in horizontal or vertical direction.

If we look closely this just reduces to the maximum of abs(x2-x1) and abs(y2-y1).

Traverse for all points and summation of all diagonal distance will be the answer.

To know more about  rectangular grid visit brainly.com/question/12377139

#SPJ4

The graph of 2x + 3y = 1470 have a y intercept of 490

An equation is a expression that shows the relationship between numbers and variables.

The standard form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept

Let x represent the number of sandwich and y represent the number of wraps.

The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. Hence:

2x + 3y = 1470

The graph is attached

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

The reason why parallel line is so important in our everyday lives is that help us to understand the path of the objects and sides of the various shapes.

Because they allow us to construct congruent angle pair relationships, parallel lines and transversals are crucial to the study of geometry.

Understanding the movement of objects and the sides of various forms is made easier with the aid of parallel lines. For instance, the opposing sides of parallelograms, squares, and rectangles are parallel to one another. The parallel line is frequently employed in the building sector.

Learn more about parallel line at:

https://brainly.com/question/24607467

#SPJ1

Answer:

a) The function to represent the scenario would be:

f(x) = 56 - 8x

b) To find out how many sips Anna can take before she needs to refill, we need to find when the water bottle is empty.

To do this, we can set f(x) = 0 and solve for x:

0 = 56 - 8x

8x = 56

x = 7

So, Anna can take 7 sips before she needs to refill.

c) A graph to represent this situation would be a straight line with a slope of -8 and y-intercept of 56.

d) The domain of the function is the set of all possible input values, or in this case, the number of sips Anna takes.

As Anna can take any whole number of sips, the domain of the function is the set of all non-negative integers:

{x | x ∈ Z, x ≥ 0}

We can represent how many sips Anna takes from her water bottle with the function y = 56 - 8x. Anna can take 7 sips before she needs a refill. The graph of this function is a straight line that starts at (0, 56) and ends at (7, 0). The domain in set notation is {x|x is an integer and 0 <= x <= 7}.

a) We can represent this scenario with a function, where the amount of water in the bottle depends on how many sips Anna has taken. This is a linear function because each sip Anna takes decreases the amount of water in the bottle by a constant amount. The function could be written as: y = 56 - 8x, where y represents the amount of water in the bottle, and x represents the number of sips Anna has taken.

b) To find out how many sips Anna can take before she needs to refill the bottle, we set y to 0 in our function: 0 = 56 - 8x. Solving for x gives us x = 7. Therefore, Anna can take 7 sips before she needs to refill the bottle.

c) A graph representing this situation would be a straight line starting at (0, 56) on the y-axis, and going down 8 units for each step along the x-axis, until reaching x=7.

d) The domain in set notation for this function would be {x|x is an integer and 0 <= x <= 7}.

https://brainly.com/question/31353350

#SPJ3

The 100th number of the sequence 1, 4, 7, 10..., is 298.

The given series 1, 4, 7, 10..., is an AP.

Arithmetic Progression (AP) is a sequence of numerals in order, in which the difference between any two consecutive digits is a constant value. A progression is a type of sequence for which it is possible to get a formula for the nth term.  

The Arithmetic Progression is the most generally used sequence in maths with easy-to-understand formulas. The nth-term formula of the AP (arithmetic progression) is

aₙ = a₁+ d(n-1)

Where

n = number of terms

a = first term

d = common difference

Here, n = 100, d = 3 and a₁ = 1

[tex]a_{100}[/tex] = 1 + 3(100-1)

[tex]a_{100}[/tex] = 1 + 3(99)

[tex]a_{100}[/tex] = 1 + 297

[tex]a_{100}[/tex] = 298

--The given question is incorrect, the correct question is

''If we count by 3's starting with 1, the following sequence is obtained: 1, 4, 7, 10..., what is the 100th number in this sequence?"--

To know more about arithmetic progression, here

https://brainly.com/question/16947807

#SPJ4

The solution is Option B , Option D.

The equations are z/6 + w = 11 and 5y + 4 = 16 + y

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

a)

( 10 + a ) / ( 3a + 1 )  

Now , it is an expression because the "=" sign and terms on both sides must always be present when writing an equation.

b)

z/6 + w = 11   be equation (1)

Now , the equation is having = sign along with coefficients and variables

c)

( z-2 ) / 3 < 15

The < sign represents an inequality relation

So , it is not an equation

d)

5y + 4 = 16 + y   be equation (2)

Now , the equation is having = sign along with coefficients and variables

e)

x² + 3x + 7

Now , it is an expression because the "=" sign and terms on both sides must always be present when writing an equation.

f)

5y + 1 ≤ y

The ≤ sign represents an inequality relation

So , it is not an equation

Hence , the equations are solved

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

The intersection between the sphere and the plane is the is diameter.

A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the centre of the sphere, and r is the sphere's radius.

Given that, segment MN has endpoints on a sphere. If segment MN does not pass through the center of the sphere.

A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.

So, the most specific name for segment MN is chord.

Here, segment MN lies on a plane that intersects the center of a sphere.

A diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.

Therefore, the intersection between the sphere and the plane is the is diameter.

Learn more about the sphere here:

https://brainly.com/question/12390313.

#SPJ1

If you went to college and earned a four-year degree, then 70% more money would you expect to earn each year than if you did not graduate from high school.

The pursuit of a college education is such a crucial life goal that it has taken center stage in the "American Dream." Attend college, secure a career, purchase a home, and start a family. Even if it isn't usually that easy, it all begins with your college education.

According to a study conducted across the country and released by the State Higher Education Executive Officers Association (sheeo.org), the average pay for high school graduates is close to $30,000. Graduates with a bachelor's degree typically make a little over $50,000 per year.

The average annual salary for those with higher level degrees (master's, doctoral, or professional) is also close to $70,000. This results in a sizable wage discrepancy over the course of a person's lifetime.

Hence, if you went to college and earned a four-year degree, then 70% more money would you expect to earn each year than if you did not graduate from high school.

To learn more about earning after graduation link is here

brainly.com/question/14449197

#SPJ4

He need 12 cup of water.

Algebra is a branch of mathematics that studies the manipulation of symbols in equations. It is used to solve problems involving unknowns, such as finding the solution to equations or determining the unknown value of a variable. Algebra is used in many areas of mathematics, science, and engineering. It is also used to understand and analyze functions, graphs, and other mathematical relationships. Algebra has applications in fields such as finance, physics, chemistry, and engineering.

To solve this problem, we can set up a proportion. Since the ratio of water to sugar is 4 to 1, and the ratio of sugar to lemon juice is 2 to 1, we can write the proportion 4/1 = 2/x, where x is the amount of water. Solving for x, we get x = 4/2 = 2. Multiplying this by the amount of lemon juice, 3 cups, gives us our answer of 12 cups of water.

To know more about Algebra click-
https://brainly.com/question/22399890
#SPJ4

To write an absolute value inequality from a line graph, we need to identify the inequality sign and determine the interval(s) of x-values that make the inequality true.

Here are the steps to write an absolute value inequality from a line graph:

Identify the inequality sign: If the graph is a solid line, the inequality is "equals to", if the graph is dashed, the inequality is "not equal to", if the graph is a solid line to one side and a dashed line to the other side, the inequality is "greater than or equal to" or "less than or equal to".

Determine the interval(s) of x-values that make the inequality true: The x-values for which the graph is above the x-axis represent the solution set of the inequality when the inequality sign is "greater than" or "greater than or equal to", and the x-values for which the graph is below the x-axis represent the solution set of the inequality when the inequality sign is "less than" or "less than or equal to"

Write the inequality: Using the information from step 1 and 2, we can write the inequality in the form of |x-h| operator k, where h is the x-coordinate of the vertex, k is the distance of the vertex to the x-axis and operator is the inequality sign determined in step 1.

To know more on absolute value inequality

https://brainly.com/question/30201926

#SPJ4

As per the unitary method, the place of marks in the water level in the cooler is 2.0 and 2.2 respectively.

Here we have given  cooler contains 4 l of water. the cooler has marks on it at every 0.2 l.

And here we also know that water bottles are filled with water from the cooler, and each bottle holds approximately 4/9 l.

Then the marking on the cooler are written as 0.2, 0.4, 0.6, 0.8, ...

Here we know that the water bottle will hold 4/9l of water

Here we have to convert the fraction into decimal form, then we get,

=> 4/9

=> 0.44

Then the water that can be filled on 4 bottle is calculated as,

=> 4 x 0.44

=> 1.76

Then the remaining water is calculated as,

=> 4 - 1.76

=> 2.24

Then the level of water mark in the cooler is 2.0 and 2.2

To know more about unitary method here.

https://brainly.com/question/28276953

#SPJ4

Answer: x=10

Step-by-step explanation:

120=6x

120+6x=+180=360

300+6x=360

6x=60

x=10

Answer:

0.25 or 1/4

Step-by-step explanation:

To find the common ration in a geometric sequence, divide the second number by the first number.  In this case, divide 6 by 24.

P. S. If you find my answer the most helpful could you please choose it as the Brainliest?  Have a great night!

Answer:

a is the correct answer because it is in the center of the shape

Answer: Information given below…

Step-by-step explanation:

Answer:

QR =40

Step-by-step explanation:

25÷5=5

35÷7=5

They are similar so we can conclude that QPR is 5 times bigger than ABC

Therefore

8^5= 40

And that's the answer

The shortest distance between points A and B on the cylinder is 6 inches.

This problem uses the Pythagorean Theorem to calculate the shortest distance between points A and B. The Pythagorean Theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In this problem, the hypotenuse is the shortest distance between points A and B and the other two sides are the radius and height of the cylinder.

Step 1: Calculate the radius of the cylinder by dividing the circumference of the base (18 inches) by 2π (3.14159):

r = 18 inches / 2π = 2.827 inches

Step 2: Calculate the height (h) of the cylinder by subtracting the radius from the total height (12 inches):

h = 12 inches - 2.827 inches = 9.173 inches

Step 3: Calculate the shortest distance between points A and B by multiplying the height (h) by 2:

d = 9.173 inches x 2 = 18.346 inches

Step 4: Round the result to the nearest whole number:

d = 18.346 inches ≈ 6 inches

To learn more about Pythagorean Theorem refer :

brainly.com/question/14930619

#SPJ1

The value of x is equal to 0.660441.

In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as For x > 0, a > 0, and a ≠1, y= logₐ x if and only if x = a^y Then the function is given by f(x) = logₐ x The base of the logarithm is a. This can be read it as log base a of x.

Given here: The exponential function 2(3e)ˣ=8

Simplifying further we get, (3e)ˣ=4

Taking log both sides we get x (ln3+1)=ln4

                                              x×2.0986=1.386

                                                       x=0.660441

Hence, The value of x is equal to 0.660441.

Learn more about logarithmic function here:

https://brainly.com/question/30085872

#SPJ1

Answer:

y = x + 5

Step-by-step explanation:

You can see that x is increasing at exactly the same rate as y. That rate is 1. This gives the graph a slope of 1. Now we can determine by subtracting 1 from y when x = 1 that the y intercept is 5. Slope intercept is y = mx+b. The y intercept is b which is five and the slope is m which is one.

That's  0.20833 of one day./

(5/24 of a day)

In the given question, none of the function exhibits an end behavior

The end behavior of a polynomial is the way the graph of the polynomial behaves as the input values become very large or very small. Generally, the end behavior of a polynomial is either up, down, or a combination of both. If the highest degree term has a positive coefficient, the end behavior is up; if the highest degree term has a negative coefficient, the end behavior is down. If the highest degree term has a coefficient of zero, the end behavior is a combination of up and down.

In the functions given, we can find the end behavior of each of these functions.

1)

y = √x

The leading coefficient test requires a polynomial and this function is not a polynomial.

2)

y = √(x - 5) - 6

The leading coefficient test requires a polynomial and this function is not a polynomial.

3)

y = -3√(x + 3) + 7

The leading coefficient test requires a polynomial and this function is not a polynomial

Learn more on end behavior of a polynomial here;

https://brainly.com/question/1402861

#SPJ1

Answer:

50%

1 2 = 1 × 50 2 × 50 = 50 100 . . So the answer is 50%

please mark me as a brainalist

The slope formula, when two points are on a line, the Slope-intercept formula, Point-slope formula, are the 3 types of slope formulas.

The slope of a line is defined as the change in the y coordinates with respect to the change in the x coordinate of that line.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of the line in the coordinate plane.

Slope formula:  m = (y₂ - y₁) / (x₂ - x₁), when two points on a line,

Slope-intercept formula: y = mx + b, the slope, and y-intercept of a line

Point-slope formula: y - y1 = m(x - x1), the slope of a line and a point on the line.

To know more about slope formulas:

https://brainly.com/question/6497976

#SPJ4

The population mean  of interest for this example is all of the tire pressure gauges in the shipment of 2000.

1. The problem states that 2000 tire pressure gauges were shipped to an automotive company warehouse.

2. Fifty of the tire gauges were randomly selected from various parts of the shipment and the percent of those that were defective was determined.

3. If the percentage of defective tire gauges was greater than 5%, the shipment was sent back.

4. Therefore, the population of interest for this example is all of the tire pressure gauges in the shipment of 2000.

This example involves an automotive company warehouse receiving a shipment of 2000 tire pressure gauges. Fifty of the tire gauges were randomly selected from various parts of the shipment and the percent of those that were defective was determined. If the percentage of defective tire gauges was greater than 5%, the shipment was sent back. Therefore, the population of interest for this example is all of the tire pressure gauges in the shipment of 2000 since this is the sample from which the percentage of defective gauges was determined.

Learn more about population mean here

https://brainly.com/question/19538277

#SPJ4

An expression to represent the sum of three consecutive odd integers is 3n + 3

The term expression in math is known as a sentence with a minimum of two numbers or variables and at least one math operation.

Here we have given that an expression to represent the sum of three consecutive odd integers in which n is the least number.

As here we have given that since the smallest integer is n,

And then it can be written as n+1 and n + 2 are the consecutive integers after that.

And then finally here we have to know that if you add them all up, then it becomes (n) + (n+1)+(n + 2) or simply 3n+3.

To know more about expression here.

https://brainly.com/question/14083225

#SPJ4

Answer:

Step-by-step explanation:

m= 3/1

y-int=-5