Jason left a bin outside in his garden to collect rainwater. he notices that 1 over 5 gallon of water fills 2 over 3 of the bin. write and solve an expression to find the amount of water that will fill the entire bin

The equation of P(e₁ ∪ e₂) describes the condition that the mutually exclusive event stands one of the events occurs, or both occur.

Mutually Exclusive events are described as in probability the particular addition rule exists practical when two occurrences exist incompatible with one another. It claims that the probability of either event exists equivalent to the probability of each possibility separately.

If e₁ and e₂ stand said to be mutually exclusive events then the probability of an event e₁ happening or the probability of event e₂ occurring exists given as P(e₁) + P(e₂) :

P(e₁ ∪ e₂) = P(e₁) + P(e₂)

Therefore, the equation of P(e₁ ∪ e₂) describes the condition that the mutually exclusive event stands for one of the events that happens, or both happen.

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Answer:

Step-by-step explanation:

120:220

2 will go into 120 60 times and go into 220 110 times. So your answer comes down to;

60:110

10 will go into 60 6 times and go into 110 11 times So your answer comes down to;

6:11

That is your final answer 6:11

Answer:

-(10/7)

Step-by-step explanation:

See attached graphic. The slope of the Green Line is cut off in the problem photo, but can be calculated from the graph to find the slope of the Red Line. The answer options are on drugs; pick the one that looks closest.

Answer:

-4/3

Step-by-step explanation:

Answer:

There are 7 two bed bedroom apartments.

Step-by-step explanation:

Solution Given:

let the one bedroom apartment be x and two bedroom apartment be y.

By the question we can make an equation as

x+y=12

or y=12-x............................[1]

Again:

$360x+$450y=$4,950

Now substituting value of y, we get

$360x+$450(12-x)=$4,950

Opening Bracket

$360x+$5400-$450x=$,4,950

solving equation

-90x=-450

dividing both side by -90,we get

x=5

again,

substituting value of x in equation 1,we get

y=12-5=7 two bed bedroom apartments.

Let, x represents the number of one bedrooms and 12 - x represents the number of two bedrooms.

According to the question,

[tex]360x + 450(12 - x) = 4950[/tex]

[tex]360x + 5400 - 450x = 4950[/tex]

[tex]5400 - 4950 = 450x - 360x[/tex]

[tex]450 = 90x[/tex]

[tex] \frac{450}{90} = x[/tex]

[tex]5 = x[/tex]

Therefore, one bedrooms = x = 5

For number of two bedrooms which is equal to 12 - x

= 12 - 5

= 7

So your required answer is 7

Expanding the digits, we have

[tex]3205_6 \equiv 3\cdot6^3 + 2\cdot6^2 + 0\cdot6^1 + 5\cdot6^0 = \boxed{725}[/tex]

Answer:  the average rate of change of the function is 23.

Step-by-step explanation:

[tex]h(x)=x^2-10x+21\ \ \ \ \ -1\leq x\leq 10 \ \ \ \ A(x)=?\\\displaystyle\\A(x)=\frac{\Delta y}{\Delta x}=\frac{h(x-g)-h(x)}{g} \\g=x_{max}-x_{min}\\g=10-(-1)\\g=10+1\\g=11.\ \ \ \ \ \Rightarrow\\A(x)=\frac{(x-11)^2-10*(x-11)+21-(x^2-10x+21)}{11} \\A(x)=\frac{x^2-22x+121-10x+110+21-x^2+10x-21}{11} \\A(x)=\frac{231-22x}{11}\\ A(x)=\frac{11*(21-2x)}{11}\\ A(x)=21-2x.\\x=x_{min}\ \ \ \ \ \Rightarrow\\A(x)=21-2*(-1)\\A(x)=21+2\\A(x)=23.[/tex]

The probability that a student chose football given that they like watching sports is: c. 0.27.

Using this formula

P[Like (Football)/Like (Sport)]

Where:

P=Probability

Like (Football)=0.23

Like (Sport)=0.23+0.18+0.26+0.17=0.84

Let plug in the formula

P[Like (Football)/Like (Sport)]=0.23/0.84

P[Like (Football)/Like (Sport)]=0.27

Therefore the probability that a student chose football given that they like watching sports is: c. 0.27.

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Answer:

C.

Step-by-step explanation:

The simplified product of (√6x² +4√8x³)(√9x-x√5x^5) is 3x√6x  + 24x^2√2 - x^4√30x - 8x^5√10

The product expression is given as:

(√6x² +4√8x³)(√9x-x√5x^5)

Evaluate the exponents

(√6x² +4√8x³)(√9x-x√5x^5) = (x√6 +8x√2x)(3√x - x^3√5x)

Expand the brackets

(√6x² +4√8x³)(√9x-x√5x^5) = x√6 * 3√x + 8x√2x * 3√x - x√6 * x^3√5x - 8x√2x * x^3√5x

This gives

(√6x² +4√8x³)(√9x-x√5x^5) = 3x√6x  + 24x^2√2 - x^4√30x - 8x^5√10

Hence, the simplified product of (√6x² +4√8x³)(√9x-x√5x^5) is 3x√6x  + 24x^2√2 - x^4√30x - 8x^5√10

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Check the picture below.

The value of angle x of the given cyclic segment is; 49.5°

We are given the measure of the angle of  arc QS as (4x – 18)°

Now, to find the measure of arc QS, this angle is to be equal to 180° and as such;

Thus;

(4x – 18)° = 180°

4x - 18 = 180

4x = 180 + 18

4x = 198

x = 198/4

x = 49.5°

The angle subtended by the arc at the center of a circle with center C is the angle of the arc. It is denoted by. m AB, where A and B are the endpoints of the arc. With the help of the arc length formula, we can find the measure of arc angle.

The formula to measure the length of the arc is;

Arc Length Formula (if angle θ is in degrees); s = 2πr (θ/360°)

Arc Length Formula (if θ is in radians) s = ϴ × r.

Thus, the value of x of the given cyclic segment is; 49.5°

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Answer: x = 0 ; y = -7

Step-by-step explanation:

Given equation:

1) 3x + 8y = -56

2) 2x - y = 7

Subtract 2x on both sides of 2) equation to isolate y-value

2x - y - 2x = 7 -2x

-y = 7 - 2x

Divide -1 on both sides of 2) equation

-y / -1 = (7 - 2x) / -1

y = 2x - 7

Current system

1) 3x + 8y = -56

2) y = 2x - 7

Substitute 2) equation into the y-value of 1) equation

3x + 8 (2x - 7) = -56

Simplify by distributive property

3x + 8 × 2x - 8 × 7 = -56

3x + 16x - 56 = -56

Combine like terms

19x - 56 = -56

Add 56 on both sides

19x - 56 + 56 = -56 + 56

19x = 0

Divide 19 on both sides

19x / 19 = 0 / 19

[tex]\Large\boxed{x=0}[/tex]

Substitute the x-value into one of the equations to find the y-value

2x - y = 7

2 (0) - y = 7

0 - y = 7

-y = 7

[tex]\Large\boxed{y=-7}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Let C(x) = -0.75x + 20,000 and R(x)= -1.50x then the profit function exists noted as P(x) = R(x) - C(x)

P(x) = -1.50x - (-0.75)x + 20,000

P(x)  = -0.75x + 20000

Therefore, the profit function exists -0.75x + 20000.

The profit function can be estimated by subtracting the cost function from the revenue function. Let profit be expressed as P(x), the revenue as R(x), the cost as C(x), and x as the number of items traded. Then the profit function exists noted as P(x) = R(x) - C(x).

Given:

C(x) = -0.75x+20,000 and R(x)= -1.50x

P(x) = R(x) - C(x)

= -1.50x - (-0.75)x + 20,000

= -1.50x + 0.75x + 20,000

Apply rule -(-a) = a

= -1.5x + 0.75x + 20000

Add similar elements:

-1.5 x + 0.75x = -0.75x

P(x)  = -0.75x + 20000

Therefore, the profit function exists -0.75x + 20000.

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The equation of the inverse function of the function f(x) = x + 5 is f'1(x) = x - 5

Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function

The function f(x) is given as

f(x) = x + 5

As a general rule, we start by writing f(x) as a variable (say f(x) = y).

So, the equation of the function becomes

y = x + 5

The next step is to switch/swap the positions of x and y in the above equation y = x + 5

The equation becomes

x = y + 5

The next step is to make y the subject of the formula in the above equation x = y + 5

The equation becomes

y = x - 5

This is done by subtracting 5 from both sides of the equation.

So, we have:

y = x - 5

Express as an inverse function

f'1(x) = x - 5

Hence, the inverse function of the function f(x) = x + 5 is f'1(x) = x - 5

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The quarterly annuity payment is $582.46.

What is an ordinary annuity?

An ordinary annuity in case of investment is the one that pays its end-of-the period cash flows rather than at the beginning as it is case of annuity due.

The applicable formula in this case is the present value formula of an ordinary annuity as shown below:

PV=quarterly payment*(1-(1+r)^-N/r

PV=initial investment=$10,000

quarterly payment=unknown(assume it is X)

r=quarterly interest rate=1.5%

N=number of quarterly payments in 5 years=5*4=20(there are 4 quarterly payments in a year)

$10,000=X*(1-(1+1.5%)^-20/1.5%

$10,000=X*(1-(1.015)^-20/0.015

$10,000=X*(1-0.742470418223773)/0.015

$10,000=X*0.257529581776227/0.015

X=$10,000/(0.257529581776227/0.015)

X=quarterly payment=$582.46

Note that the unknown in this case is the annuity payment, the present value can also be the unknown as well.

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Eduro's mistake of solving the inequality -4x > 120 is adding 4 to both sides instead of dividing both sides by -4

minus four x greater than 120

-4x > 120

x < 120/-4

There is a change in the inequality sign from greater than to less than because the inequality is been divided by -4

x < -30

Check:

-4x > 120

-4(-30) > 120

120 > 120

Therefore, Eduro's mistake of solving the inequality -4x > 120 is adding 4 to both sides instead of dividing both sides by -4

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Answer:

Step-by-step explanation:

Answer:

176 square feet

Step-by-step explanation:

add the areas of the rectangle and triangle

rectangle area is

16 times 8 which is

128

rectangle area is

1/2 times 12 times 8 which is

48

then add them

128 plus 48 is

176 square feet

Answer:

11/15 km

Step-by-step explanation:

Simply sum the areas:

2/5 + 1/3 = (6 + 5)/15 = 11/15

The number that best represents the slope of the graphed line that is given is: -4.

The slope of a line is the ratio of the vertical distance to the horizontal distance across the line. It is calculated using the formula:

Slope (m) = rise/run = change in y / change in x = (y2 - y1)/(x2 - x1)

Given the two points on a coordinate plane as shown in the mage below, let:

(x1, y1) represent (0, 2)

(x2, y2) represent (0.5, 0)

Plug in the values

Slope (m) = change in y / change in x = (0 - 2) / (0.5 - 0)

Slope (m) = -2/0.5

Slope (m) = -4

Therefore, we can state that, the number that best represents the slope of the graphed line that is given is: -4.

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The actual answer is C.1/2

chust mee am a doktor

Answer: C

Step-by-step explanation:

A function only exists if each x-value has only one possible y-value.

C is the only function because each x-value has only one y-value.

The other answer choices have x-values that have multiple y-values. In answer choice A, it has (2,9) and (2,8). In answer choice B, the set has (1, 0) and (1,2). And in answer D, it has (1,3) and (1,2)

Answer + Step-by-step explanation:

let f be the relation that we are studying.

f is a function if it associates a unique output (number) to each input (number) .

A. {(2,9), (2,8), (-3,7), (-3,6))

Since f(-3) = 7 and f(-3) = 6

Then

f associates -3 to two different outputs 7 and 6.

Then

f cannot be a function.

B. ((-4,3), (1,0), (1,2), (2,3)}

Since f(1) = 0 and f(1) = 2

Then

f cannot be a function.

C. {(2,1), (4,2), (6,3), (8,4))

f is a function.

D. {(1,2), (-2,3), (1,3), (-2,2)

Since f(-2) = 3 and f(-2) = 2

Then

f cannot be a function.

Answer:

D.= √29

Step-by-step explanation:

The distance between the two complex numbers,

Z₁=a+bi and Z₂=c+di in the complex plane is

[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]

In the Cartesian plane, the distance between, one point and other is (x₁,y₁) and (x₂,y₂) is the distance formula is

[tex]d = \sqrt{(X₂-X₁)² + (Y₂-Y₁)²} [/tex]

To find the distance between the two complex numbers using the formula

[tex]d = \sqrt{(c - a) {}^{2} + (d - b) {}^{2} } [/tex]

where,

[tex]d = \sqrt{(a - b) {}^{2} + (d - b) {}^{2} } \\ d = \sqrt{(6 - 4) {}^{2} + ( - 2 - 3) {}^{2} } \\ d = \sqrt{(2) {}^{2} + ( - 5) {}^{2} } \\ d = \sqrt{4 + 25} = \sqrt{29 \\ } [/tex]

Inequality can be used to find the domain of f(x) is (B) 4x+9 greater-than-or-equal-to 0.

To find the domain:

Therefore, inequality can be used to find the domain of f(x) is (B) 4x+9 greater-than-or-equal-to 0.

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The correct question is given below:

If f (x) = start root 4 x 9 enroot 2, which inequality can be used to find the domain of f(x)?

(A) startroot 4 x endroot greater-than-or-equal-to 0                                        

(B) 4x+9 greater-than-or-equal-to 0

(C) 4 x greater-than-or-equal-to 0

(D) startroot 4 x 9 endroot 2 greater-than-or-equal-to 0

Answer:

(B)- 4X+9 greater than or equal to 0

Step-by-step explanation:

Answer:

output = 9

Step-by-step explanation:

add 5 to the input to obtain output

output = 4 + 5 = 9

Angles in quadrilateral add to 360

108 +67 +10 =185

4x + 3x = 7x

185 + 7x = 360

- 185

7x. = 175

÷ 7

x = 25

Check:

4x25 = 100

100 + 67 + 108 = 275

275 + (3x25) = 350 + extra 10 is 360

Hope this helps!

The answer is 40

you just times 23 by the number of photocopies you need with is 20

so 23x20 which is 460

500-460 is 40

The number of sheets of papers remain unused are 40.

Given that, Jean loads a ream of paper 500 sheets into the tray of her photocopier she has 23 sheets and need 20 copies each sheet.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Number of sheets used = 23×20

= 460

Remaining sheets = 500-460

= 40

Therefore, the number of sheets of papers remain unused are 40.

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Answer:

67

Step-by-step explanation:

All triangles have three angles. The sum of the three angles should equal up to 180 degrees.

108-104-37= 67

the average pay per year is $4 million

Answer:

The average is 4millon

Step-by-step explanation:

because 16 millon divide by 4 =4

ez

Answer: 6

Step-by-step explanation: Since we substitute the b with 7, 10-7= 3. Since the 2 is next to the parentheses, we multiply 3 by 2, getting 6.

Hey there!

2(10 - b)

= 2(10 - 7)

= 2(10) + 2(-7)

= 20 - 14

= 6

OR

2(10 - b)

= 2(10 - 7)

= 2(3)

= 6

Therefore, your answer should be: 6

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

Just multiply how much she waxes in 3/5 hour by 5/3.  Answer is 100/3 or 33.33 sq. meters per hour

See below for the solution to the systems of equations

System of equations 1

Here, we have

y = -5x/3 + 3

y = x/3 -3

We start by plotting the graph of both equations

Next, we write out the point of intersection of the equations

See attachment for the equation of the system

From the attached graph, the point of intersection of the equations is (3, -2)

Hence, the solution to the system is (3, -2)

System of equations 2

Here, we have

y = 4x + 3

y = -x -2

We start by plotting the graph of both equations

Next, we write out the point of intersection of the equations

See attachment for the equation of the system

From the attached graph, the point of intersection of the equations is (-1, -1)

Hence, the solution to the system is (-1, -1)

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