if there are 12 strangers in a room, what is the probability that no two of them celebrate their birthday in the same month?

Step-by-step explanation:

a)

any prime number has only 2 (1 and the number itself).

almost every even number has 1, 2, a factor of 2 and the number itself. so that did not work either.

following that line of thought, the only possible solutions are square numbers of prime numbers :

4, 9, 25, 49

they have only 1, its square root and the number itself as factors.

b)

in the same line of thinking it must be powers of 4 of prime numbers :

2⁴ = 16

with the factors 1, 2, 4, 8, 16

3⁴ = 81

with the factors 1, 3, 9, 27, 81

c)

and so, it must be a power of 6 of a prime number.

the only one possible is

2⁶ = 64

with the factors 1, 2, 4, 8, 16, 32, 64

Answer: 825 workers altogether

Step-by-step explanation:

well, if the ratio is 4.5 men to every woman, we just have to multiply 150 by 4.5, which means there will be 675 male workers and 150 female workers.

Answer:

Area = 15a^3b^6

Perimeter: 10a^2b^4+6ab^2

Step-by-step explanation:

Formula For Area: L*W

Input The Numbers: 5a^2b^4 * 3ab^2

5a^2b^4 * 3ab^2 = 15a^3b^6

Area = 15a^3b^6

Formula for perimeter: P=2(l+w)

Input the Numbers: P = 2(5a^2b^4 + 3ab^2)

2(5a^2b^4 + 3ab^2) = 10a^2b^4+6ab^2

Perimeter: 10a^2b^4+6ab^2

Hope this helped!

Using the given linear equation, we found the altitude of the plane at different time periods and the altitude of airplane at 5 and 30 minutes is found to be 250 feet and 0 feet respectively.

What is a linear equation?

A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. A linear equation's graph almost always takes the shape of a straight line.

The linear equation which shows the altitude of an airplane is as follows,

y = -10x + 300

where y = altitude (in feet)

           x = time of descend ( minutes)

a) when x = 0

     y = 300 feet

  when x = 5 minutes

    y = -10 * 5 + 300 = 250 feet

 when x = 8 minutes

   y = -10 * 8 + 300 = 220 feet

when x = 10 minutes

 y = -10 * 10 + 300 = 200 feet

when x = 30 minutes

y = -10 * 30 + 300 = 0 feet.

the table is as follows:

x (minutes)     0         5          8          10       30

y(feet)            300    250     220     200       0

b) From the above table, we can see that at 5 minutes the altitude is 250 feet and at 30 minutes, the altitude is 0 feet. There is a decrease in altitude, which suggests the plane is descending and finally landed when the time was 30 minutes.

Therefore using the given linear equation, we found the altitude of the plane at different time periods and discussed the altitude of airplane at 5 and 30 minutes.

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The dimensions will be as follows;

width is 5cm while the length is 20cm.

Let width = w

Let length = 4w (according to question)

Perimeter = 50cm

Perimeter formula for a rectangle = 2 (l +w)

Substituting in the variables (width and length)

2(w + 4w) = 50

2(5w) = 50

10w = 50

w = 5

Remember that length = 4w

length = 4w

length = 4(5)

length = 20cm

Therefore, the dimensions of the rectangle are 5cm by 20 cm.

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Answer:

Step-by-step explanation:

make the inequality y=3x-7 to get the linear line then find x=0 with is -7 and anything below that line or on the line is not part of the inequality therefore remember to graph with a dotted line instead of a solid.

Answer:

Step-by-step explanation:

The perimeter of the rectangle: We know that the frame is equal to 2(L+B)

therefore, the edge of a rectangle is 2[5a^2b^4 + 3ab^2]

                        = 2[ab^2(5ab^2 + 3)]

The area of a rectangle is L * B

                       =  (5a^2b^4) * (3ab^2)

                       =  15a^3b^6

Answer:

Step-by-step explanation:

The required equation that can be used to determine the price of each gallon of gas is 8.4x = 23.94. Option A is correct.What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.here,Let the cost of gas per gallon be x,Now according to the question,Cost of 8.4 gallons of fuel = 8.4xfrom the question,8.4x = 23.94Thus, the required equation that can be used to determine the price of each gallon of gas is 8.4x = 23.94. Option A is correct.

One solution exists for the following system of equations. In this question, correct answer is option (5) which states the solution is point

(3 , 2).

There are many various ways to define an equation. The definition of an equation in algebra is a mathematical statement that illustrates the equality of two mathematical expressions.

As we know that when the system of equations are given in graph form ,

then the solution to them is the number of points they intersect each other.

Now in the given question,

In the given graph it can be clearly seen that graphs of equations meet at one point. The point at which the graph meets is (3 , 2).

We can see that option (5) is correct.

So the given system of equations have one solution.

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A helium tank shaped like a cylinder has 2,401π in³ of space inside the tank. If the diameter of the helium tank is 14 inches,  its height is 1 inch.

Volume is a measure of the amount of space occupied by a three-dimensional object or a region of space. It is usually measured in units such as cubic meters (m³), cubic centimeters (cm³), cubic inches (in³), or liters (L).

For a solid object, such as a cube, cylinder, or sphere, volume is calculated by measuring the length, width, and height of the object and using a formula that is specific to that shape. For irregularly shaped objects, such as rocks or trees, volume can be determined by using techniques such as water displacement.

The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

In this case, we are given the diameter of the cylinder, which is 14 inches. The radius of the cylinder is half of the diameter, so r = 7 inches.

We are also given the volume of the cylinder, which is 2,401π cubic inches.

Using the formula for the volume of a cylinder, we can set up the following equation:

2,401π = π(7)²h

Simplifying this equation, we get:

2,401 = 49h

Dividing both sides by 49, we get:

h = 49/49 = 1

Therefore, the height of the helium tank is 1 inch.

However, this answer seems unlikely since the height of the tank should be greater than its radius. Therefore, there may be an error in the given volume or diameter of the tank.

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the answer is A its height is 49

Answer:

1.25 laps per minute

Step-by-step explanation:

5 laps in 4 minutes so distance over time is equal to rate so

5/4=1.25

The number of pieces in a jigsaw puzzle and the number of minutes required for a person to complete are not directly related. The time it takes for a person to complete a jigsaw puzzle depends on several factors, including the person's experience with puzzles, the level of difficulty of the puzzle, the size of the puzzle pieces, and the person's level of concentration.

For example, a 500-piece puzzle might take one person several hours to complete, while another person might be able to finish it in just a few hours. Similarly, a 1000-piece puzzle might take one person a full day to complete, while another person might be able to finish it in just a few hours.

In general, the larger the number of pieces in a puzzle, the more time it will take to complete. However, the actual time required can vary greatly depending on the individual and the specific puzzle.

The incidence rate of active cases of tb for the 6-month period was  0.00014

An incidence rate describes how quickly disease occurs in a population.

Incidence rate is the rate of new occurrence of a particular disease divided by the population of people at risk of the disease.

So for this question

The number of new  active cases of tb occurring between January 1 and June 30, 2012 was 26

Population at risk  in Baltimore is 183,000

Incidence rate = 26/183,000

The incidence rate of active cases of tb for the 6-month period was           0.00014 or 14 per 100,000 population.

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The area of the right triangular puppy pen found using the formula 1/2(b.h²) is 4900.90 feet².

What is a triangle?

A polygon with three edges and three vertices is called a triangle. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. A right triangle is a specific kind of triangle that has one angle that is exactly 90 degrees.

Given,

 The length of OY = 12 feet

The length of DY = 31 feet

m∠OYD = 65°

Since SDOG is a rectangle, m∠DOY = 90°.

So the ΔDOY is a right triangle.

Area of right triangle = 1/2 * b * h²

where b = base length

          h = height

From the given figure,

b = OY = 12

h = OD

h can be found using Pythagoras' theorem.

DY² = OD² + OY²

OD² = DY² - OY² = 31² - 12²  = 817

OD = √817 = 28.58 feet = h

Therefore the area of the right triangle ΔDOY is

area =  1/2 * b * h² = 0.5 * 12 *28.58² = 4900.90 feet².  

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The value of the inverse relation is y'(0) = 1/6

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

The point (1/6,0) is on the curve

The notation (y^-1)' (0) is an inverse notation

Using the above as a guide, we have the following:

(1/6,0) means y(1/6) = 0

This also means that

y'(0) = 1/6

Hence, the solution is 1/6

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The measure of the other angle of the parallelogram is 22 degrees.

Opposite angles of a parallelogram are equal (or congruent).

Let the missing angle be represented by x.

Since the opposite angles of a parallelogram are equal (or congruent).

x = 2x - 22

Solve for x

2x - 22 = x

2x = 22 + x

2x - x = 22

x = 22°

Therefore, 22 degrees is the measure of the other angle.

Option C) 22° is the correct answer.

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The function g(x) can be written as -

g(x) = f(x - 1)

Graph translation is a process of moving the graph over the dimensional plane either vertically, horizontally or both.

A translation can take place either horizontally or vertically as -

Given are the graphs of exponential functions f(x) and g(x).

We can write the exponential function g(x) as -

g(x) = f(x - 1)

Therefore, the exponential function g(x) can be written as -

g(x) = f(x - 1).

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Answer:

n = 3

Step-by-step explanation:

Starting equation:

2n + 4 = n + 7

Subtract by n on both sides:

n + 4 = 7

Subtract 4 on both sides

n = 3

Check to see if the answer works:

2(3) + 4 = 3 + 7

6 + 4 = 3 + 7

10 = 10

The solution works

n = 3

ANSWER is one- incher=1 while two inch binder=2.By using simultaneous equation.

Answer: 0.03, 0.243, 0.3, 0.42, 0.5

Step-by-step explanation:

Hope this helps you!

Answer:

Step-by-step explanation:

0.243, 0.03, 0.3, 0.42, 0.5

Answer: x = -3, 1/2

Step-by-step explanation:

Answer:

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

Given measurements:

Bring all to same unit, grams, then compare;

Order them from smallest to largest:

Answer:

The order of the measurements from smallest to largest is:

Step-by-step explanation:

The three given measurements of mass are:

Therefore, to be able to order the three given measurements from smallest to largest, first convert them to the same unit of mass (grams):

⇒ 3,000 g = 3,000 g

⇒ 60,000 mg = 60,000 × 0.001 = 60 g

⇒ 1.5 kg = 1.5 × 1000 = 1,500 g

Therefore, the order of the measurements in grams from smallest to largest is:

So, the order of the measurements in their original units from smallest to largest is:

The linear equation that passes through the two given points is:

y = -2x +  4

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Particularly, if a line passes through the points (x₁, y₁) and (x₂, y₂) then the slope will be:

a = (y₂ - y₁)/(x₂ - x₁)

Here we know that the line passes through (-1, 6) and (4, -4), then the slope is:

a = (-4 - 6)/(4 + 1) = -2

y = -2x + b

To find the value of b, we can replace the values of any of the points in the equation, if we use (-1, 6) we will get:

6 = -2*-1 + b

6 = 2 + b

6 - 2 = b = 4

The linear equation is y = -2x +  4

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Answer:

So the polynomial function is

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

Step-by-step explanation:

A polynomial function of lowest degree in standard form with roots x = 1, 3, and 2i can be written as (x - 1), (x - 3), and (x - 2i),

From the above data we can get,

k(x) = (x - 1)(x - 3)(x - 2i)

After expanding the equation ,

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

So the polynomial function is

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

Answer:

x=10

Step-by-step explanation:

First, add 5 to both sides of the equation, getting rid of the -5 on the left side but still making them equal.

5x=3x+20

Then, do the same with 3x, Subtract from both sides.

2x=20

Lastly, Divide both sides by 2 and you'll get your answer

x=10

Answer:

[tex] \sf \: x = 10[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 5x - 5 = 3x + 15

Then the value of x will be,

→ 5x - 5 = 3x + 15

→ 5x - 3x = 15 + 5

→ 2x = 20

→ x = 20 ÷ 2

→ [ x = 10 ]

Hence, the value of x is 10.

Number of child tickets were sold on Wednesday is 33 if three times as many adult tickets as child tickets were sold.

According to the question

At the city museum, child admission is $6.30 and adult admission is $9.80. On Wednesday, three times as many adult tickets as child tickets were sold, for a total sales of $ 1178.10

Number of Child admission = x

Number of Adult admission = y

On Wednesday ;

y = 3x

9.80y + 6.30x = 1178.10

9.80(3x) + 6.30x = 1178.10

29.40x + 6.30x = 1178.10

35.70x = 1178.10

x = 1178.10 / 35.70

x = 33

So, 33 child tickets were sold on Wednesday.

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The complete question is

At the city museum, child admission is $6.30 and adult admission is $9.80. On Wednesday, three times as many adult tickets as child tickets were sold, for a total sales of $ 1178.10 . How many child tickets were sold that day?

Sarah should blend 80.5 pounds of the high-quality beans and 39.5 pounds of the cheaper beans to make 120 pounds of blended coffee.

In this problem, we are given that Sarah Meeham needs to prepare 120 pounds of blended coffee beans to sell at a rate of $4.17 per pound. She plans to blend two types of coffee beans: a high-quality bean costing $5.25 per pound and a cheaper bean costing $2.00 per pound.

Let x be the number of pounds of the high-quality coffee beans needed and y be the number of pounds of the cheaper coffee beans needed. Since we need 120 pounds of the blended coffee, we have:

x + y = 120

The cost of the blended coffee is $4.17 per pound. This means that the total cost of the blended coffee is:

4.17(120) = 501.6

We can also find the cost of the high-quality and cheaper beans in terms of x and y:

5.25x is the cost of the high-quality beans

2.00y is the cost of the cheaper beans

The total cost of the two types of beans is the sum of their individual costs:

5.25x + 2.00y

Since we need 120 pounds of the blended coffee, we can set up the following equation using the above expressions for total cost:

5.25x + 2.00y = 501.6

Now, we can use the system of equations consisting of x + y = 120 and 5.25x + 2.00y = 501.6 to solve for x and y. One way to do this is by substitution:

x = 120 - y (from the first equation)

5.25(120 - y) + 2.00y = 501.6 (substituting x in the second equation)

Simplifying and solving for y, we get:

630 - 5.25y + 2.00y = 501.6

3.25y = 128.4

y ≈ 39.5

Now we can use this value of y to find x:

x = 120 - y

x = 120 - 39.5

x ≈ 80.5

Therefore, Sarah needs to blend approximately 80.5 pounds of the high-quality coffee beans and 39.5 pounds of the cheaper coffee beans to make 120 pounds of blended coffee that she can sell for $4.17 per pound.

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Answer:

[tex]-22.8[/tex]

Step-by-step explanation:

[tex]\int^{1}_{0} f'(x) \text{ } dx=f(1)-f(0)=f(1)-3 \\ \\ \\ B=\int^{5}_{1} f'(x) \text{ } dx=12 \implies f(5)-f(1)=12 \\ \\ -7.8-f(1)=12 \implies f(1)=-19.8 \\ \\ \therefore f(1)-3=-19.8-3=-22.8[/tex]