Problem Situation: Eric is adding water to a 60-gallons pool. a The pool already has 12 gallons of water, and he wants to fill it to at least 27 gallons. The water flows at a rate of 6 gallons per minute. How many minutes, x, will it take for Eric to fill the pool with at least 27 gallons of water? Inequality that represents this situation: 27 < 12 +63 To solve the inequality, you can begin by solving the equation as shown. Drag a diagram to each row of the table to show which number line represents all of the solutions for the inequality and which number line represents all of the solutions for the problem situation​

Answer:

can you make it look better

Step-by-step explanation:

The quality

Answer:

a) 7 in

b) 72 steps

Step-by-step explanation:

Angle of elevation formula:  [tex]tan(\theta)=\dfrac{y}{x}[/tex]

where [tex]\theta[/tex] is the angle of elevation, y is the vertical distance (rise) and x is the horizontal distance.

a)  Given:

[tex]\implies tan(32)=\dfrac{y}{12}[/tex]

[tex]\implies y=12tan(32)[/tex]

[tex]\implies y=7 \ \textsf{in (nearest inch)}[/tex]

b)  Given:

⇒ Total height = 21 + 21 = 42 feet

1 foot = 12 inches

⇒ 42 feet = 42 x 12 = 504 inches

Using vertical rise of 7 in per step found in part (a):

Number of steps = 504 ÷ 7 = 72

Increased accuracy

Using unrounded vertical rise of 12tan(32):

Number of steps = 504 ÷ 12tan(32) = 67 steps to the nearest step

x = 2

y = -1/2

multiply 1st equation by 2 to get common coefficient

6x + 4y = 10

2x + 4y = 2

‐-------------- subtract equation

4x = 8

x = 2

substitute

3×2 + 2y = 5

6 + 2y = 5

2y = -1

y = -1/2

Answer:

B. nonlinear

Step-by-step explanation:

Difference                        Difference

   in x                x     y            in y

                         0   -2

       1                                         1

                         1     -1

       1                                         7

                        2      6

       1                                         19

                       3     25

The difference between any two consecutive x-coordinates is 1. Each difference between any two consecutive y-coordinates is different. This means it is a nonlinear function.

The number of days for which the money is left to reach the 20,400$ mark is; 21.28 days

The final amount to be reached is; $20400

The principal amount is; $8,000 and at. rate of 4.75 % compounded.

Hence, it follows that;

Divide both sides of the equation by 8000; we have;

Take log of both sides;

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The correlation coefficient of the number of employees and the number of products is 0.1.

The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.

A result of zero indicates no relationship at all, therefore, independent variable.

A.) In order to find the correlation between the two quantities we need to know the mean of the two values, therefore, the mean of the number of employees can be written as,

The mean of the  number of employees

[tex]\text{Mean of the number of employees} = \dfrac{0+50+100+150+200+250+300+350+400}{9}[/tex]

[tex]\text{Mean of the number of employees} = 200[/tex]

The mean of the  number of products

Mean of the number of Products [tex]= \dfrac{100+1100+2100 +3100+ 4100 +5100+ 6100+ 7100+ 8100}{9}\\\\\\=4100[/tex]

Now, the table can be written in the following manner as shown below, using the formula of the correlation,

[tex]r =\dfrac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}[/tex]

[tex]r =\dfrac{(30 \times 10^4)}{\sqrt{(15 \times 10^4)\times (60 \times 10^6)}}\\\\r = 0.1[/tex]

B.) The given data follows the linear relationship, therefore, the function of the given data will follow the general equation of a line.

y = mx + C

If we look at the value of y when the value of x was 0,

[tex]y = mx +C \\\\100 = m(0) + C\\\\C = 100[/tex]

Substitute the value of C in any other data point we will get,

[tex]y = mx+C\\\\1100 = m(50) +100\\\\m = 20[/tex]

Hence, the function that best fits the data is y=20x+100.

C.)  The slope and y-intercept of the plot indicate that as the number of employees in the organization increases the number of products increases as well. The y-intercept shows us that if there are no employees in the company at that point the company will be able to produce 100 products on its own.

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Answers:

16 chickens

35 pigs

========================================================

Explanation:

x = number of chickens

y = number of pigs

There are 51 heads, so x+y = 51 which solves to y = 51-x

2x = number of legs just from the chickens (2 legs per chicken)

4y = number of legs just from the pigs (4 legs per pig)

2x+4y = 172 legs total

----------

Plug in y = 51-x and solve for x.

2x+4y = 172

2x+4(51-x) = 172

2x+204-4x = 172

-2x+204 = 172

-2x = 172-204

-2x = -32

x = -32/(-2)

x = 16

Now use this to find y

y = 51-x

y = 51-16

y = 35

Since x = 16 and y = 35, this means there are 16 chickens and 35 pigs.

----------

Check:

x+y = 16+35 = 51 which works

2x+4y = 2*16+4*35 = 172 and that also works.

Both equations are confirmed.

Answer:

11/61

Step-by-step explanation:

cos b = adj side/hypotenuse

=11/61

Answer:

CosB = B/H

Base(B)= 11

Perpendicular (P)=60.

Hypotenuse (H)= 61

CosB = B/H

CosB= 11/61

Answer:

the answer is x=12√2

hope it helps

Answer:

Story

Jane is 1.7 m tall.  She stands 250 m away from the base of the Eiffel tower and looks up at the top of the building.  The angle of elevation from her eyeline to the top of the building is 45°.

Question

Calculate an estimate of the height of the building. Give your answer to the nearest meter.

Calculation

Label the sides of the triangle O, A and H (where O is the side opposite to the angle, A is the side adjacent to the angle and H is the hypotenuse).

In the triangle, the angle and side A is known, and O must be calculated.

Therefore, use the trig ratio tan(x) = O/A:

⇒ tan(40) = O/250

⇒ 250tan(40) = O

⇒ O = 209.7749078...

Assume Jane's eye-level is approximately 1.5 m above the ground.

Therefore, the Eiffel tower is approximately:

209.7749078... + 1.5 = 211.2749078.. meters tall

Rounding to the nearest meter ⇒ 211 m

Answer:

7 X = 30 + 2(x + 5)

7x = 30 + 2x + 10

7x = 40 + 2x

7x - 2x = 40 + 2x -2x

5x = 40

x=8

Answer:

x=8

Step-by-step explanation:

7 X = 30 + 2(x + 5)

7x = 30 + 2x + 10

7x = 40 + 2x

7x - 2x = 40 + 2x -2x

5x = 40

x=8

Answer:

There are two ways to do this problem algebraically or trigonometrically.

Algebraically/geometrically

The ratios of the sides of a 30/60/90 tri. are x, x√3, 2x (short leg, long leg, hyp). Therefore, if the long leg is 6 'units'. then 6 = x√3. x = 6√3.

The hyp is 2x then the hypotenuse is 2(6√3) = 12√3, rationalizing is 12√3/3 = 4√3

Using Trig.

We can use sinx = y/r = opp/hyp. The long leg of 6 is opposite 60 degrees (pi/3).

Therefore, sin(pi/3) = 6/r =

r = 6/sin(pi/3) = 6/(√3/2) = 12/√3, when you rationalize you get 12√3/3 = 4√3

The sine and cosine ratios for a 30°–60°–90° triangle with a hypotenuse of 6, when θ = 60° are  6√3 and 4√3.

This is defined as the longest side of a right-angled triangle and is opposite to the right angle.

The ratios of the sides of a 30/60/90 triangle are x, x√3, 2x (short leg, long leg, hyp). We can infer that the long leg is 6 'units' which is

6 = x√3

x = 6√3.

The hypotenuse is 2x then the hypotenuse is 2(6√3)

= 12√3 when rationalized

= 12√3/3 = 4√3.

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Step-by-step explanation:

8x+ 14y= 4

-6×-7y= -10

For elimination method we can decide to eliminate either the y or x variable I'm going to eliminate the x variable so either of the one am eliminating we multiply the first equation by the coefficient of the variable we are eliminating in other words

8x +14y=4.....*-6

-6×-7y= -10......*8

-48x-84y= -24

-48x-56y= 80

then we multiply the second equation all through by -1

-48x-84y= -24

48x+ 56y= -80

28y=-104

y= 26/7

x= 8/3

Answer:

37

Step-by-step explanation:

（x+10)+x+(3x-5)=180

5x=185

x=37

The sum of angles in the triangle is 180 degrees. Therefore, the value of x in the triangle is 35

The sum of angles of a triangle is 180 degrees. This simply implies the sum of the three angles in a triangle is equals to 180 degrees.

Therefore,

x + 10 + 3x - 5 + x = 180

combine like terms

x + x + 3x + 10 - 5 = 180

5x + 5 = 180

subtract 5 from both sides of the equation

5x + 5 - 5 = 180 - 5

5x = 175

divide both sides by 5

5x / 5 = 175 / 5

x = 35

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Answer:

e= 2.15

Step-by-step explanation:

Subtract both sides by 6

2.15=e

Thus e is 2.15

Hope this helps!

Answer:

10 miles

Step-by-step explanation:

Distance walked in 1 hour = 4 miles

So, distance walked in 2.5 hours

= 4 miles × 2.5

= 10 miles

Answer:

last one "kiki" is true...

Answer:

Option 2 and 4

Step-by-step explanation:

2) Number of science questions = (3/4) of total questions

                              = [tex]\dfrac{3}{4}*24[/tex]

4) Number of marbles in the jar = (3/4) of the total marbles

                  [tex]=\dfrac{3}{4}*24[/tex]

Answer:

Step-by-step explanation:

sin 44° = [tex]\frac{63}{ST}[/tex]

ST = [tex]\frac{63}{sin44}[/tex]

ST ≈ 90.7

Answer:

The 4th term is geometric

Step-by-step explanation:

For geometry series we use Tn = a•r^n-1

r = -3

a = 3

Use the equation Tn = 3(-3)^n-1 and you'll see that it's geometric.

Answer:

Step-by-step explanation:

Let the width is x, then the length is 2x.

Area of rectangle:

Dimensions are:

Perimeter is:

Let dimensions be x and 2x

Now

Now

Breadth=3

Length=2(3)=6

Perimeter

Answer:

-28, -20, -12, 4, 4

Step-by-step explanation:

I really dont know how to explain this but yeah pretty much thats the answer.

Answer:

= B

[tex]\frac{16}{40} +\frac{15}{40} = \frac{31}{40} \\\\\frac{2}{5} +\frac{3}{8} =\frac{31}{40}[/tex]

It should cut into

2 ne t is accurate

Answer:

A)  net A

B) AB = 3 in    BC = 5 in    CD = 8.6 in

C) 106.6 in²

Step-by-step explanation:

Part A:  

Part B:

From inspection of the diagram:

Part C:

Area of a rectangle = width x length

Area of a triangle = 1/2 x base x height

Surface area = 2(4 x 8.6) + (3 x 8.6) + 2(1/2 x 4 x 3)

                     = 68.8 + 25.8 + 12

                     = 106.6 in²

Answer:

Question 1 is A  (7/10) Question 2 is b (39/56)

Step-by-step explanation:

Answer:

Yo hope you do not get in trouble for plagiarism

Step-by-step explanation:

Answer: 1) 36 m and 60 m^2     2) 15π/2 + 10 m and 75π/4 m^2

Step-by-step explanation:

Using the pythagorean theorem in the first question, we get that the slope is 10 m so the perimeter = 10 + 14 + 6 + 6 = 36 m and the area is

(14 + 6)*6/2 = 60 m^2

So in the next question, the arc of the circle has a length of

2π*5*3/4 = 15π/2

So the perimeter is 15π/2 + 5 + 5 = 15π/2 + 10 m

And the area is 3/4*π*5*5=75π/4 m^2

Hope it helps

Chaos theory has a wide range of real-world applications and is used in fields such as weather prediction, finance, and biology.

Chaos theory is a branch of mathematics that studies the behavior of systems that are highly sensitive to initial conditions. The "butterfly effect" is a popular term used to describe the idea that small variations in initial conditions can lead to vastly different outcomes over time. This theory has many real-world applications in various fields.

One of the fields that makes use of chaos theory is weather prediction. Meteorologists use chaos theory to understand how small variations in atmospheric conditions can lead to large-scale weather patterns. They use computer simulations to model how different initial conditions can lead to different weather outcomes. This helps them make more accurate weather predictions and plan for extreme weather events.

Another field that uses chaos theory is finance. Financial analysts use chaos theory to understand how small fluctuations in financial markets can have a significant impact on the economy. They use mathematical models to analyze stock prices and interest rates and determine how small changes can lead to large market movements. This helps them make informed investment decisions and minimize risk.

Chaos theory is also used in biology to study the behavior of populations of animals, plants, and microorganisms. Biologists use chaos theory to understand how small changes in the environment can have a major impact on the growth and survival of populations. This helps them make informed decisions about the conservation and management of natural resources.

In conclusion, chaos theory has a wide range of real-world applications and is used in fields such as weather prediction, finance, and biology. The idea that small variations in initial conditions can lead to vastly different outcomes over time is a powerful tool for understanding complex systems and making informed decisions.

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