The Rodriguez family and the Barnes family each used their sprinklers last summer. The Rodriguez family's sprinkler was used for 15 hours. The Barnes family's sprinkler was used for 35 hours. There was a combined total output of 1050 L of water. What was the water output rate for each sprinkler if the sum of the two rates was 50 L per hour?

Rodriguez family's sprinkler:
Barnes family's sprinkler:

The solution for the system of equation -2y=-6x-18 3x-4y=27 is (x, y) = (-3, 9).

A system is an organized set of components that work together to achieve an overall goal. It could be a physical system, such as an automobile, or an abstract system, such as an economic system.

The first step is to isolate one of the variables in one of the equations. To do this, we can multiply both sides of the first equation by -3. This will give us: 6y = 18x + 54.
Next, we need to subtract this equation from the second equation. Doing so gives us: 3x - 6y = -27.
Now we can isolate the variable y. To do this, we can divide both sides of the equation by -6. This will give us: y = -3x - 9.
We have now isolated the variable y in both equations, so we can substitute y = -3x - 9 in the first equation. Doing so gives us: -2(-3x - 9) = -6x - 18.
We can then simplify this equation to get: 6x + 18 = -6x - 18.
Finally, we can solve this equation for x. Doing so gives us x = -3. We can then substitute this value into either equation to find the value of y: y = -3(-3) - 9 = 9.
Therefore, the solution for the system of equation -2y=-6x-18 3x-4y=27 is (x, y) = (-3, 9).

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The value g left parenthesis 4 right parenthesis divided by f left parenthesis 3 right parenthesis is 2.

What is parenthesis?

Parenthesis, also known as round brackets, are a type of punctuation used in writing to enclose additional information within a sentence that is not essential to the meaning of the sentence, but can provide clarification, emphasis, or further explanation. They are usually shown as two curved lines facing each other, like this: ().

For example, consider the sentence: "The concert, which was held at the arena last night, was sold out (as expected)." The words "as expected" are enclosed in parentheses, indicating that they are not necessary to the main meaning of the sentence, but provide additional information that may be of interest to the reader.

Parentheses can also be used to enclose mathematical equations, citations, or references in writing.

In this problem, we first need to substitute the given values of x in the functions f(x) and g(x).

f(x) = x - 2

f(3) = 3 - 2 = 1

g(x) = 2x - 6

g(4) = 2(4) - 6 = 2

So, [tex] \frac{g(4)}{f(3)} = \frac{2}{1} = 2[/tex]

Therefore,the value of g(4)/f(3) is 2.

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After Simplifying, we get:  [tex]5x^3y^2 + xy - 2xy^4[/tex]

Pοlynοmials are algebraic expressiοns made up οf cοefficients and variables. Occasiοnally, variables are referred tο as indeterminates.

Fοr pοlynοmial expressiοns, additiοn, subtractiοn, multiplicatiοn, and pοsitive integer expοnents are all pοssible; hοwever, divisiοn by variable is nοt. x²+x-12 is an illustratiοn οf a single-variable pοlynοmial. Three terms are invοlved in this example: x², x, and -12.

The Greek wοrds "pοlynοmial" and "nοminal," which tοgether mean "many terms," are the sοurce οf the English wοrd pοlynοmial. There is nο limit tο the number οf terms that a pοlynοmial can have.

When we add the twο pοlynοmials term by term, we get:

[tex](3x^3y^2 - 5xy^4 - 2xy) + (2x^3y^2 + 5xy^4 + 3xy) = 3x^3y^2 + 2x^3y^2 - 5xy^4 + 5xy^4 - 2xy + 3xy[/tex]

Simplifying, we get: [tex]5x^3y^2 + xy - 2xy^4[/tex]

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Answer:

5x^3y^2+xy (C)

Step by Step:

(3x^3y^2 − 5xy^4 − 2xy) + (2x^3y^2 + 5xy^4 + 3xy) =

3x^3y^2 − 5xy^4 − 2xy + 2x^3y^2 + 5xy^4 + 3xy =

(3 + 2)x^3y^2 + (-5 + 5)xy^4 + (-2 + 3)xy =

5x^3y^2 + xy

hope this helps (btw it's C)

The correct answer for the expression is -5(1) - 3(-4) = 7 and -2p + r = 4.

The algebraic approach to solving simultaneous linear equations is known as substitution technique. The value of one variable from one equation is substituted in the second equation in this procedure, as the name implies. By doing this, a pair of linear equations are combined into a single equation with a single variable, making it simpler to solve.

The given expression is: -5m - 3n for m = 1, n.= -4 and -2p + r for p = -3, and r = -2.

The correct steps are:

For, -5m - 3n substitute the value of m = 1 and n = -4:

-5(1) - 3(-4)

-5 + 12 = 7

For -2p + r:

-2(-3) + (-2)

6 - 2 = 4

Hence, the correct answer for the expression  is -5(1) - 3(-4) = 7 and -2p + r = 4.

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The height and the radius of the figure will remain unchanged as the figure is being just rotated around the axis and not transformed.

A function transformation "moves," "resizes," or "reflects" the parent function's graph, depending on the case. Function transformations can be broadly divided into three categories:

Translation

Dilation

Reflection

Dilation is the only one of these changes that modifies the original shape's size; the other two just change the shape's placement.

Here in the question,

The figure is being rotated not dilated so the dimensions of the new figure will remain the same.

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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:

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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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.

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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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: Since the spinners have 5 and 6 numbers respectively, the total number of outcomes is 5 x 6 = 30.

If we get the same number as a previous spin, it means that the first spin is irrelevant, and we only care about the second spin. Therefore, the probability of getting the same number as a previous spin is the same as the probability of getting any specific number on the second spin, which is 1 out of 6.

Therefore, the probability of getting the same number as a previous spin is 1/6, or approximately 0.17 to two decimal places.

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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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.

The probability that a 42 person shift will put together between 193.2 and 201.6 computers per hour is given as follows:

0.0006 = 0.06%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 4.2, \sigma = 0.8, n = 42, s = \frac{0.8}{\sqrt{42}} = 0.1234[/tex]

The probability that a 42 person shift will put together between 193.2 and 201.6 computers per hour is equivalent to the probability of a sample mean between 193.2/42 = 4.6 and 201.6/42 = 4.8.

The probability is the p-value of Z when X = 4.8 subtracted by the p-value of Z when X = 4.6, hence:

Z = (4.8 - 4.2)/0.1234

Z = 4.86

Z = 4.86 has a p-value of 1.

Z = (4.6 - 4.2)/0.1234

Z = 3.24

Z = 3.24 has a p-value of 0.9994.

Hence:

1 - 0.9994 = 0.0006 = 0.06%.

The missing section is given by the image presented at the end of the answer.

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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

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: 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:

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

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:

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

23x45=35

Answer:

The surface area of an object is the total area of all its faces. For a cube with sides of length 9 inches, the surface area can be calculated as follows:

The cube has six faces, all of which are identical squares.

The area of one square face is 9 inches x 9 inches = 81 square inches.

Therefore, the total surface area of the cube is 6 x 81 square inches = 486 square inches.

So the surface area of a cube with sides of 9 inches is 486 square inches.

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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(1.5)x + 1.5 = 30 and 1.5x = 28.5 are the correct equations that Beverly could use to determine how many marbles are in the bag.

Let x be the number of marbles in the bag.

Each marble weighs 1.5 grams and the bag weighs 1.5 grams.

Therefore, the total weight of the marbles and the bag is 1.5x + 1.5 grams.

But we know that the total weight is 30 grams.

So, we can write the equation:

1.5x + 1.5 = 30

Simplifying this equation, we get:

1.5x = 28.5

Therefore, the number of marbles in the bag is x = 19.

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Answer:

11

Step-by-step explanation:

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

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:

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:

c

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

First, the shape is wrong

2(8×3)+2(8×4)+2(3×4)=

2(24)+2(32)+2(12)=

48+64+24=136

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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Therefore, the volume of the truncated cuboid is approximately 68 + 4*√(30) cubic meters.

Volume is a measure of the amount of space occupied by a three-dimensional object. It is the amount of three-dimensional space enclosed by the boundaries of an object. Volume is typically measured in cubic units, such as cubic meters (m³) or cubic centimeters (cm³).

Here,

The truncated cuboid is a solid figure that is obtained by cutting off the top of a rectangular prism (cuboid) with a plane that is parallel to the base. The formula for the volume of a truncated cuboid is:

V = h/3 * (A + √(A*B) + B)

where V is the volume, h is the height of the truncated portion, A is the area of the top face, and B is the area of the base face.

In this case, the height of the truncated portion is 3 m, the top face has an area of 5 m x 8 m = 40 m², and the base face has an area of 8 m x 1.5 m = 12 m². Therefore:

A + B = 40 + 12 = 52 m²

√(AB) = √(4012) = √(480) = 4*√(30)

Substituting these values into the formula, we get:

V = 3/3 * (52 + 4√(30) + 12)

V = 68 + 4√(30)

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