Volume of rectangular prism

We take the positive root:

n = (-3 + 27) / 2 = 12. Therefore, there were 12 people in the original group of winners.

Let's assume that there were n people in the original group of winners, and each person's share was x dollars. Then we know that:

n * x = $90,000,000

After three more winners are declared, the total number of winners becomes n + 3. Each person's share is then reduced by $1,000,000, so the new share per person is (x - $1,000,000). We can then write:

(n + 3) * (x - $1,000,000) = $90,000,000

Expanding the equation, we get:

nx - $1,000,000n + 3x - $3,000,000 = $90,000,000

Simplifying, we get:

nx + 3x = $1,000,000n + $93,000,000

Factoring out x and n, we get:

x(n + 3) = $1,000,000(n + 3) + $90,000,000

Dividing both sides by (n + 3), we get:

x = $1,000,000 + ($90,000,000 / (n + 3))

We can substitute this expression for x in the first equation:

n * ($1,000,000 + ($90,000,000 / (n + 3))) = $90,000,000

Expanding and simplifying, we get:

[tex]$n^2$[/tex]+ 3n - 270 = 0

Using the quadratic formula, we get:

n = [tex](-3\± \sqrt{(729)) / 2[/tex]

n = (-3 ± 27) / 2

Since n has to be positive, we take the positive root:

n = (-3 + 27) / 2 = 12

Therefore, there were 12 people in the original group of winners.

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Answer:

To solve this problem, we need to find the present value of the cash flow stream using a discount rate of 12%. We can use the present value formula:

PV = CF1/(1+r)^1 + CF2/(1+r)^2 + CF3/(1+r)^3 + CF4/(1+r)^4

where PV is the present value, CF1, CF2, CF3, and CF4 are the cash flows at time 1, 2, 3, and 4 respectively, and r is the discount rate.

Substituting the values given in the problem, we get:

PV = 690/(1+0.12)^1 + 365/(1+0.12)^2 + 220/(1+0.12)^3 + 330/(1+0.12)^4

PV = 690/1.12 + 365/1.2544 + 220/1.4049 + 330/1.5735

PV = 616.07 + 290.76 + 156.51 + 209.38

PV = 1272.72

Therefore, the present value of the cash flow stream is $1,272.72.

Step-by-step explanation:

On Julie's door, the images will span 210 square inches.

As Julie printed six images, the total space that the images cover is:

6 x 35 square inches = 210 square inches

Inches are measured as 1/36 of a yard in both British Imperial and American Customary measurement systems. According to some sources, the term "inch" comes from the Old English "ince" or "ynce," which in turn is said to have originated from the Roman "uncia" unit.

The name of another English unit, the ounce, is derived from the Roman word uncia. According to legend, King David I of Scotland defined the old English word "ynce" as the width of a man's thumb at the base of the nail in the year or thereabouts 1150 AD.

From the question:

Six images total, each measuring 5 by 7 inches, were printed by Julie. We must first calculate the area of each image in order to add up the overall area that these photographs cover.

One image's area is as follows:

5 inches x 7 inches = 35 square inches

As Julie printed six images, the total space that the images cover is:

6 x 35 square inches = 210 square inches

Consequently, 210 square inches of Julie's door will be covered by the images.

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After answering the presented question, we can conclude that As a rectangle result, the wall's length is approximately 18.67 metres.

In Euclidean geometry, a rectangle is a parallelogram with four small angles. It can also be described as a fundamental rule hexagon or one in which all of the angles are equal. Another option for the parallelogram is a straight angle. Four of the vertices in a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle." A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.

To begin, we can use the formula for the area of a rectangle, which is:

length x width Equals area

We know the wall's area is 39.2 m2, and we want to know how long it is. We are also given the wall's breadth, which is 2.1 m.

As a result, we can rearrange the formula to find the length:

width = Area length

length = 39.2 2.1 cm

a length of 18.67

As a result, the wall's length is approximately 18.67 metres.

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Best answer for the statement are Linear, Nonlinear.

A linear function is a type of mathematical function that has the following form:

f(x) = mx + b

where "m" and "b" are constants. "m" represents the slope of the line, or the rate at which the function changes .

Linear functions have a constant rate of change and when graphed form a straight line. Nonlinear functions do not have a constant rate of change, can be graphed with one or more curves or a "v-shape".

Therefore, the best answer to complete the sentence is:

Linear functions have a constant rate of change and when graphed form a straight line. Nonlinear functions do not have a constant rate of change, can be graphed with one or more curves or a "v-shape".

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Answer:

Step-by-step explanation:

Answer:

Mark gets $4800
Sofia gets $2400

Step-by-step explanation:

Let M, S and T represent the amounts that Mark, Sofia and Tina get respectively

We have the following

M = 2S
S = M/2

T = S/2 = M/2 ÷ 2 = M/4

Therefore the ratio of M : S; T can be expressed in terms of M as
M : M/2 : M/4

Multiplying throughout by 4 gives
4M : 2M : M

Removing the common M the proportion is

4 : 2 : 1

If T = 1200 then from T = S/2, s = 2T = 2 x 1200 = 2400

Since M = 2S, M = 2 x 2400 = 4800

So

Mark gets $4800
Sofia gets $2400

The ratio of the amounts obtained
4800: 2400: 1200

Dividing by 1200 gives us
4800/1200: 2400/1200: 1200/1200

= 4 : 2 : 1

Answer:

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

Since angle α is between 0° and 90°, it is in the first quadrant and therefore all sin α, cos α and tan α are positive numbers.

Use the following identities:

Given tan α = 2.4. Using identities, find cosine as follows:

Find sine:

Answer:

Step-by-step explanation:

If 24, x and 18 are in proportion, then we have:

24 : x = x : 18

This can be rewritten as:

x^2 = 24 x 18

x^2 = 432

Taking the square root of both sides, we get:

x = ± 20.7846

However, we also know that (x - 1) is in proportion with 24 and 18. Therefore:

24 : (x - 1) = (x - 1) : 18

This can be rewritten as:

(x - 1)^2 = 24 x 18

(x - 1)^2 = 432

Taking the square root of both sides, we get:

x - 1 = ± 20.7846

Solving for x in each case, we get:

x = 21.7846 or x = -19.7846

However, we can see that the value x = -19.7846 does not make sense in the context of the problem (since we cannot have a negative value for the number of something). Therefore, we can reject it as an extraneous solution.

Hence, the value of x is:

x = 21.7846

Answer: 21.7846

Answer:

70

Step-by-step explanation:

Answer: 4500

Step-by-step explanation:

1st 0, 1, 2, 3 ,5 ,6 ,7 ,8 ,9

2nd 0, 1, 2 ,3 ,4 ,5 ,6 ,7 ,8 , 9

3rd 0, 1, 2 ,3 ,4 ,5 ,6 ,7 ,8 , 9

4th 1, 3, 5, 7, 9

9 x 10x 10 x 5= 4500

Answer:

Parts of the expression:

b: a variable representing a quantity that can vary or change.

12: a constant representing a fixed value.

r: a variable representing a quantity that can vary or change.

Word expression:

"Add twelve times the quantity of r to b."

Step-by-step explanation:

Imhotep can pain the pyramid in 256 different ways, and his assistant can make 64 different models of the pyramid, as explained below.

There are 4 sides to paint, and each side can be painted with one of 4 colors. So the total number of different ways Imhotep can paint the Great Pyramid is:

4 x 4 x 4 x 4 = 256

Therefore, Imhotep can paint the Great Pyramid in 256 different ways. However, as pointed out, many of these ways are just rotations of each other. Specifically, there are 4 different rotations for each way of painting the pyramid. Therefore, the number of distinct models can be seen below:

256 / 4 = 64

Therefore, Imhotep's assistant only needs to make 64 different models.

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Answer:

Look explain

Step-by-step explanation:

Give the following outcomes for each of the events with a set of 1,2,3,4,5,6,7,8:

Event A: The number can be 1,2,3 because it has to be less than 4

Event B: The number can be 2,4,6,8 because those are the only even numbers

Both Event A&B: The marble must be even and between 1,2,3 so only 2 is correct and must be marble #2

I hope this helps :)

It is also important to communicate effectively with any individuals involved in the procedure to ensure that everyone is on the same page and working towards the same goal.

The procedure can refer to a variety of things depending on the context. If you are referring to a medical procedure, it is important to first consult with a healthcare professional to determine the specific procedure that is needed.

If you are referring to a legal or administrative procedure, it is important to review the guidelines and protocols set forth by the governing body or organization.

In general, the procedure typically involves a set of steps or instructions that must be followed in order to achieve a specific outcome. These steps may include gathering information, completing forms, submitting documents, or performing specific tasks.

It is important to carefully follow each step of the procedure to ensure that the desired outcome is achieved.

If you need a procedure completed by 12pm today, it is important to prioritize your tasks and ensure that you have all necessary resources and information available. Depending on the specific procedure, you may need to work quickly and efficiently in order to meet the deadline.

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The average speed in mph is 2 mph

Average Speed is the total distance that something has traveled by the total amount of time it took it to travel that distance. It is also the total distance traveled by the moving object and the amount of total time the object spent moving.

Average speed = Distance traveled/Time taken

Where Distance traveled = 4/10 mile

Time taken = 1/5 of an hour

To get the average speed in mph,

Average speed = (4/10)/(1`/5)

Average speed = 4/10 * 5/1

Average speed = 20/10

Average speed = 2 mph

Therefore, the average speed is 2mph

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Answer:

divide the numbers and you'll get 1×10^5

The two locations on the inverse function graph where the tangent lines to both functions are perpendicular are as a result: P(0.3807, 1.9337) and Q (0.6677, 0.6129).

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

[tex]y = f(x) = 1/(x^2+1) + (1-2x)^(1/3)\\y - 1/(x^2+1) = (1-2x)^(1/3)\\(y - 1/(x^2+1))\\y^3 = 1-2x\\x = (1 - (y - 1/(x^2+1))^3)/2\\g(y) = (1 - (y - 1/(x^2+1))^3)/2\\[/tex]

[tex]f(x) = 1/(x^2+1) + (1-2x)^(1/3)\\f'(x) = -2x/(x^2+1)^2 - (1-2x)^(-2/3)/3\\g(y) = (1 - (y - 1/(x^2+1))^3)/2\\g'(y) = -3(y - 1/(x^2+1))^2/(2(x^2+1)^2)\\-2x/(x^2+1)^2 - (1-2x)^(-2/3)/3 * -3(y - 1/(x^2+1))\\x^2/(2(x^2+1)^2) = -1\\2x/(x^2+1)^2 = 1/((1-2x)^(2/3)(y - 1/(x^2+1))^2)\\4x^2 = (x^2+1)\\x^2 / ((1-2x)^(4/3)(y - 1/(x^2+1))^2)\\(x^2-2x+1)(x^2+2x+1)\\(y - 1/(x^2+1))^2 = 16x^2(1-2x)^(4/3)\\x = 0.3807 or x = 0.6677\\y = 1.9337 or y = 0.6129\\[/tex]

The two locations on the inverse function graph where the tangent lines to both functions are perpendicular are as a result: P(0.3807, 1.9337) and Q (0.6677, 0.6129).

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Using arithmetic operation it is obtained that the cost of the car 4 years ago was $5750.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

Let C be the cost of the car 4 years ago.

According to the problem, the current cost of the car is 60% of the cost 4 years ago, so we can write -

3450 = 0.6C

Use the arithmetic operation of division -

To solve for C, we can divide both sides of the equation by 0.6 -

C = 3450/0.6

C = 5750

Therefore, the cost of the car 4 years ago was $5750.

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The (x, y) is translated tο (x-1, y-6).

Resizing an οbject is accοmplished thrοugh a change called dilatiοn. The οbjects can be enlarged οr shrunk via dilatiοn. A shape identical tο the sοurce image is created by this transfοrmatiοn. The size οf the fοrm dοes, hοwever, differ. A dilatatiοn οught tο either extend οr cοntract the οriginal fοrm. The scale factοr is a phrase used tο describe this transitiοn.

The scale factοr is defined as the difference in size between the new and οld images. An established lοcatiοn in the plane is the center οf dilatatiοn. The dilatiοn transfοrmatiοn is determined by the scale factοr and the centre οf dilatiοn.

the cοmpοsitiοn οf

(x, y) --> (x+4, y-1) and (x, y) --> (x-5, y-5)

(x, y) --> (x-5, y-5)

(x+4-5, y-1-5) = (x-1, y-6)

Therefοre, the cοmpοsitiοn οf (x, y) --> (x+4, y-1) and (x, y) --> (x-5, y-5) is (x, y) --> (x-1, y-6).

In οther wοrds, the translatiοn rule fοr the cοmpοsitiοn is:

Hence, The (x, y) is translated tο (x-1, y-6).

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Answer:

(x, y) --> (x-1, y-6)

Step-by-step explanation:

Answer:

1. Start with the dolphin’s initial position, which is -30 feet below the surface of the water. We can use a negative sign to indicate that the dolphin is below the surface.

2. Add 23 feet to the dolphin’s position to represent her first rise. This gives us -30 + 23 = -7 feet. The dolphin is now 7 feet below the surface of the water.

3. Add another 7 feet to the dolphin’s position to represent her second rise. This gives us -7 + 7 = 0 feet. The dolphin is now at the surface of the water.

Therefore, the answer is that the dolphin is now at the surface of the water.

Answer:

6

Step-by-step explanation:

16 Ounces in a pound

6x8=48

48/8=6

Answer:

3 pounds

Step-by-step explanation:

total pie = 8

weight of 1 pie = 6 ounces

weight of 8 pie = 6 ounces × 8

                         =  48 ounces

ounce into pound

1 ounce =0.0625 (divide ounces by 16)

48 ounces ÷ 16

=3 pounds

the baker made 3 pounds od apple pie

The image after the reflection over the line x = 2 is (11, -3)

Here we have the point T which has coordinates (-7,  -3), and we apply a refletion across the line x = 2.

This reflection will only chane the value of x in our point, such that the initial value x = -7

Is at the same distance of the line x = 2 than the final x-value

The distance between these values is:

d = |-7 - 2| = 9

Then the new x-value will be:

x = 2 + 9 = 11

Thus, the image after the reflection is (11, -3)

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Answer:

11

Step-by-step explanation:

because 11+11=22 so there are no different with two 11s

Answer:

Where is the expression bro

Answer: Without additional information about the trap, it is not possible to determine the value of m or any other measurements of the shape. Could you please provide more information or context for the problem?

Answer:basically if 23x45 is 35 then u times that to 15 and theres ur asnwer

23x45=35

Using the information shown on the auger shell. The value of x is found as 16.

Fractions and ratios can both be stated as reciprocals of one another. Similar rules apply to proportions, which are just the equivalence of two ratios.

For the given values in question:

8.8 mm

11 mm

20 mm

Value of x.

Using proportion of the numbers:

8.8 / 11 = x / 20

x = 8.8*20 / 11

x = 16

Thus, using the information shown on the auger shell.  The value of x is found as 16.

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Hence,[tex]110a^6b^6[/tex] is the simplified expression as by multiplying 5x11 using the distributive property .

A mathematical expression seems to be a combination of digits, symbols, and operators (like +, -,, and ) that denotes a relation or quantity. A single figure or variable can constitute an expression, as can a collection of several numbers, constants, and operators. It is possible to depict mathematical connections, functions, and processes using expressions. There are various categories into which expressions can be divided, including numerical, algebraic, polynomial, rational, and exponential expressions. These can be assessed by carrying out the relevant operations in the mathematical operation order, i.e., parentheses operations first, multiplication or division second, addition or subtraction third.

given

[tex]5x11ab^2(2a^5b^4)[/tex]

We may multiply 5x11 using the distributive property, and then multiply the variables using exponentiation rules to simplify the formula

[tex]5x11ab^2(2a^5b^4):[/tex]

[tex]55ab^2(2a^5b^4)[/tex] is equal to [tex]5x11ab^2(2a^5b^4)[/tex]

= [tex]110a^(1+5)b^(2+4)[/tex] (using the product rule of exponents)

= [tex]110a^6b^6[/tex]

Hence,[tex]110a^6b^6[/tex] is the simplified expression as by multiplying 5x11 using the distributive property .

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[tex]\left[\begin{array}{ccc}Answr:\\=&=&=\\1&6&.\end{array}\right][/tex]

Step-by-step explanation & Answer

In order to find chau’s height we would only need to subtract:

40 - 24 = ?

? = 16

But it determines what you are putting it in as well.

You can put it in, feet, meters, or inches.

So I do not know but looking at the question it seems like I do not need to know. ( Saying thing because you might actually have the measurements but I do not know / I cannot see. )

Thus the answer to your problem is, 16

Answer:

Step-by-step explanation:

To find the magnitude of the cross product of vectors a and b, we can use the formula:

|a x b| = |a| |b| sin(θ)

where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.

First, let's calculate the cross product of vectors a and b:

a x b = (2i + j + 8k) x (i + 3j + 4k)

= (j)(4k) - (8k)(3j) - (i)(4k) - (j)(2i) + (8k)(i) - (2i)(i + 3j)

= -10i - 20j - 20k

Next, let's find the magnitudes of vectors a and b:

|a| = √(2^2 + 1^2 + 8^2) = √(69)

|b| = √(1^2 + 3^2 + 4^2) = √(26)

Finally, we need to find the angle θ between vectors a and b. We can use the dot product to find cos(θ):

a · b = (2i)(i) + (1j)(3j) + (8k)(4k) = 2 + 3 + 32 = 37

|a| |b| cos(θ) = a · b

cos(θ) = a · b / (|a| |b|)

cos(θ) = 37 / (√(69) √(26))

cos(θ) ≈ 0.893

Using the fact that sin^2(θ) + cos^2(θ) = 1, we can solve for sin(θ):

sin(θ) = √(1 - cos^2(θ))

sin(θ) ≈ 0.449

Substituting the values we found into the formula for the magnitude of the cross product, we get:

|a x b| = |a| |b| sin(θ)

|a x b| = √(69) √(26) (0.449)

|a x b| ≈ 26.81

Therefore, the magnitude of the cross product of vectors a and b is approximately 26.81.