A set of two or more equations with the same variables is called a system of equations. When you set the
two expressions that are equal to the same variable equal to each other, like you did in the previous lesson,
you are using the Equal Values Method of solving a system of equations. Use the Equal Values Method to
solve the following problem.
It is time to cool off on a hot summer day! Team Sunshine is filling an inflatable kiddie pool from a garden
hose. The pool has 30 gallons in it and Team Sunshine is adding 8 gallons per minute with a garden hose.
Next door, Team Breeze's pool is already filled with 180 gallons of water. They are emptying the pool at 5
gallons per minute with buckets.
Write two equations to represent the situation. Use the equations to find how long it takes until both pools
have the same amount of water. Check your calculations.

Answer:

Frederick Winslow Taylor

Step-by-step explanation:

Answer:

[tex]512\ \text{in}^2[/tex]

Step-by-step explanation:

x = Length and width of base

y = Height of box

Volume of the box is [tex]16384\ \text{in}^3[/tex]

[tex]x^2y=16384\\\Rightarrow y=\dfrac{16384}{x^2}[/tex]

Surface area is given by

[tex]s=x^2+4y\\\Rightarrow s=x^2+4\times \dfrac{16384}{x^2}\\\Rightarrow s=x^2+\dfrac{65536}{x^2}[/tex]

Differentiating with respect to x we get

[tex]s'=2x-\dfrac{131072}{x^3}[/tex]

Equating with 0 we get

[tex]0=2x^4-131072\\\Rightarrow x=(\dfrac{131072}{2})^{\dfrac{1}{4}}\\\Rightarrow x=16[/tex]

[tex]s''=2+\dfrac{393216}{x^4}[/tex]

at [tex]x=16[/tex]

[tex]s''=2+\dfrac{393216}{16^4}=8>0[/tex]

So the function is minimum at x = 16

[tex]y=\dfrac{16384}{x^2}=\dfrac{16384}{16^2}\\\Rightarrow y=64[/tex]

The material required is

[tex]s=x^2+4y=16^2+4\times 64\\\Rightarrow s=512\ \text{in}^2[/tex]

The minimum amount of material required is [tex]512\ \text{in}^2[/tex].

Given:

Consider the below figure attached with this question.

The given data set is:

66, 65, 66, 70, 66, 68, 63, 60, 66, 68, 63, 65

To find:

The correct box plot for the given data set.

Solution:

We have,

66, 65, 66, 70, 66, 68, 63, 60, 66, 68, 63, 65

Arrange the data set in ascending order.

60, 63, 63, 65, 65, 66, 66, 66, 66, 68, 68, 70

Divide the data set in 4 equal parts by using the parenthesis.

(60, 63, 63), (65, 65, 66), (66, 66, 66), (68, 68, 70)

Minimum value = 60

First quartile: [tex]Q_1=\dfrac{63+65}{2}[/tex]

[tex]Q_1=64[/tex]

Median: [tex]M=\dfrac{66+66}{2}[/tex]

[tex]M=66[/tex]

Third quartile: [tex]Q_3=\dfrac{66+68}{2}[/tex]

[tex]Q_3=67[/tex]

Maximum value = 70

It means the end points of the box plot are 60 and 70. The box lies between 64 and 67. Line inside the box at 66.

The box plot in option A is the only box plot that satisfy the above conditions.

Therefore, the correct option is A.

Answer:

The average daily maximum temperature in March is of 61 degrees.

Step-by-step explanation:

The average daily maximum temperature in his hometown in x months after January is given by:

[tex]f(x) = 12.2\cos{(\frac{\pi x}{6})} + 54.9[/tex]

What is the average daily maximum temperature in March?

March is 3 - 1 = 2 months after January, so this is f(2).

[tex]f(2) = 12.2\cos{(\frac{\pi*2}{6})} + 54.9 = 61[/tex]

The average daily maximum temperature in March is of 61 degrees.

Answer:

60

Explanation:

The new superset list is

2, 2, 3, 5

Multiply these factors together to find the LCM.

LCM = 2 x 2 x 3 x 5 = 60

In exponential form:

LCM = 22 x 31 x 51 = 60

LCM = 60

Therefore,

LCM(4, 5, 6) = 60

Answer:

3

Step-by-step explanation:

3 occurs the most in this data set

Answer:

The mode is 3.

Step-by-step explanation:

Answer: 6000+700+00+0

I hope that helps you

Answer:7 quarters and 6 dimes

Step-by-step explanation:

Answer:

For any two given points (x1,y1) and (x2,y2), the slope = (y2-y1)/(x2-x1)

Let's take the points (15,3) and (30, 6):

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

= (6-3)/(30-15)

=3/15

=1/5 =0.2

The slope, in general, means the rate of change of y, relative to x. In the context of this question, the slope tells us that the amount of concrete that can be poured (in yards) is a fifth of the time taken (in minutes).

Answer:

I believe it is C

Step-by-step explanation:

the answer is supposed to be 3/2 but i dont know

Answer:

20

Step-by-step explanation:

Answer:

1/2 + 10/12. = 1/2 × 6/6 =6/12. 6/12 + 10/12 =16/12. 16/12 = 1 4/12 = 1 1/3

Answer:

1) Congruent

2) Vertical angles

3) 12x - 18 = 8x + 10

4) x = 7

Step-by-step explanation:

1)

Congruent because they're vertical angles.

2)

Vertical angles

3)

12x - 18 = 8x + 10

4)

12x - 18 = 8x + 10

12x - 8x = 10 + 18

4x = 28

x = 7

Answer:

least to greatest is how number appear on a number line. numbers less than 0 or indicated with a negative number. if the number is greater than 0 it's indicated without the negative as the plus is implied.

-11, -5, -2 ,4 , 7

[tex] log_{2}(x + 5) + log_{2}(x - 5) = log_{2}(11) \\ = > log_{2}(x + 5) (x - 5) = log_{2}(11) \\ = > log_{2}( {x}^{2} - 25) = log_{2}(11) \\ cancel \: \: \: out \: \: \: log_{2} \: \: \: from \: \: \: both \: \: \: sides \\ {x}^{2} - 25 = 11 \\ = > {x}^{2} = 11 + 25 \\ = > {x}^{2} = 36 \\ = > x = \sqrt{36} \\ = > x = 6[/tex]

x = 6

Hope it helps.

Do comment if you have any query.

Answer:

The statement that is accurate is csc(θ)=1.06

Step-by-step explanation:

Looking at the reference angle in this triangle, we can see that the side that is 47 units is opposite of it, the side that is 50 units is the hypotenuse, and the side that is 17 units is adjacent to it.

Because we know this, we can plug our sides into the formula for cscθ, secθ, and cotθ.

So:

cotθ=adjacent/opposite = 17/47= 0.36

cscθ=hypotenuse/opposite = 50/47=1.06

Now without even looking at the other statements, we can see that the second one is correct as cscθ=hypotenuse/opposite = 50/47=1.06

Therefore, the statement that is accurate is csc(θ)=1.06.

Answer:

Step-by-step explanation:

Each installment is 1/12 of a yearly income:

Annual salary=32000

Monthly salary

Answer:

∠4 = 22

Step-by-step explanation:

Hello There!

The angles shown are consecutive interior angles

If you didn't know consecutive interior angles are supplementary angles meaning that the sum of the two angles is 180

So we can find the missing angle by subtracting the given angle (158 in this case) from 180

180 - 158 = 22

so we can conclude that ∠4 = 22

180.timr3fzgncvdfccfxdfdxxfhk

180-158=22

the measure is 44

Answer: There are 69 adults and 72 children went to the concert.

Step-by-step explanation:

Let x be the number of adults, and y be the number of children.

x + y = 141

3.5x + 2.5y = 421.5

x + y =141

x = 141 - y

3.5(141 - y) + 2.5y = 421.5

493.5 - 3.5y + 2.5y = 421.5

493.5 - y = 421.5

-y = -72

y = 72

x + y = 141

x + 72 = 141

x = 69

Answer:

Quadratic functions are those where their rate of change changes at a constant rate. Exponential functions are those where their rate of change is proportional to itself.

An example of a quadratic function would be the shape that a ball makes when you throw it. Gravity causes a constant acceleration, the ball slows down as it is moving up, and then it speeds up as it comes down.

An example of an exponential function would be the population of a bacterium as long as there is enough space and nutrients or how your money grows with compound interest in a bank.

A quadratic function is one in the form

f(x)=ax2+bx+c  

It’s rate of change (first derivative) is linear.

f′(x)=2ax+b  

The rate of the rate of change (second derivative) is constant.

f′′(x)=2a  

Quadratics are then the solutions to the differential equation

f′′=C  

An exponential function is one in the following form.

g(x)=Aekx  

It’s rate of change is another exponential function.

g′(x)=Akekx  

So exponentials are the solutions to the differential equation

g′=kg

Step-by-step explanation:

Yes. : )

Answer:

The answer is the third one, 1,176

Step-by-step explanation:

Answer:

see bottom

Step-by-step explanation:

divide through by 4

x2 - 2x - 3 = 0

x2 - 3x + x - 3 = 0

(x2 - 3x) + (x - 3) = 0

x(x - 3) + 1(x - 3) = 0

(x + 1) (x - 3) = 0

x + 1 = 0 and x - 3 = 0

x = -1 and x = 3

Answer:

a triangle that may not have the same dimensions as the bases

Step-by-step explanation:

The cross section of the figure that is perpendicular to the triangular bases and passes through a vertex of the triangular bases would be a triangle that may not have the same dimensions as the bases.

Divide the number of cubic feet that it can circulate by the number cubit feet per cubic yard. That gives the number of cubic yards that it can circulate. It can circulate about 10.37 cubic yards per minute.

The air conditioning system can be circulate in 15.92 cubic yards of air per minute.

Here,

An air conditioning system can circulate 430 cubic feet of air per minute.

We have to find the cubic yards of air which can be circulate in per minute.

What is the value of cubic yard in cubic feet?

1 cubic yard = [tex](3 ft)^3[/tex] = 27 cubic feet.

Now,

1 cubic yard = [tex](3 ft)^3[/tex] = 27 cubic feet.

Hence, Cubic yards of air circulate in per minute = 430/27 = 15.92

So, The air conditioning system can be circulate in 15.92 cubic yards of air per minute.

Learn more about the cubic feet visit:

https://brainly.com/question/27530276

#SPJ2

Answer:

p = 43 :)

Your welcome DaBaby

Answer:

68 in^2

Step-by-step explanation:

the shape is a trapezoid

A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs

Characteristics of a trapezoid

It has 4 vertices and edges

If both pairs of its opposite sides of a trapezoid are parallel, it becomes a parallelogram

Area of a trapezoid =   x (sum of the lengths of the parallel sides) x height

the dimension of the height is not given. We have to determine the value of the height using Pythagoras theorem

The Pythagoras theorem : a² + b² = c²

where a = length

b = base

c =  hypotenuse

10² = 6² + height²

100 = 36 + height²

height = 64

the square root of 64 is 8

the height is 8

1/2 x (8 + 9) x 8 = 68in^2

Answer:

0.606531 = 60.6531% probability that it will take between 2 and 132 minutes for the student to arrive at the library parking lot.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

Mean of 4 minutes

This means that [tex]m = 4, \mu = \frac{1}{4} = 0.25[/tex]

Find the probability that it will take between 2 and 132 minutes for the student to arrive at the library parking lot:

This is:

[tex]P(2 \leq X \leq 132) = P(X \leq 132) - P(X \leq 2)[/tex]

In which

[tex]P(X \leq 132) = 1 - e^{-0.25*132} = 1[/tex]

[tex]P(X \leq 2) = 1 - e^{-0.25*2} = 0.393469[/tex]

[tex]P(2 \leq X \leq 132) = P(X \leq 132) - P(X \leq 2) = 1 - 0.393469 = 0.606531[/tex]

0.606531 = 60.6531% probability that it will take between 2 and 132 minutes for the student to arrive at the library parking lot.

Answer:

3) Not equivalent

4) Equivalent multiply by 2

5) Equivalent multiply by 2

Answer:

4x-20

Step-by-step explanation:

2+5x-1x-22

First, rearrange to make life temporarily easier.

5x-1x+2-22

Then combine like terms.

5x-1x=4x

2-22=-20

So we have 4x-20

That is simplified as far as it can.

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hope it helps