A 6,000-gallon pool is being filled at a rate of 20 gallons per minute. At this rate, how many minutes will it take to fill this pool?

r = 10

θ = tan^-1 (4/3)

Radius = 56.00

θ = 27.00o = 0.47 radians

z = 10 × (cos 53°7'48″ + i sin 53°7'48″)

z = 10[cos(53.13) + i sin (53.13]

A seems like the best option

Answer:

Step-by-step explanation:

y=-4

The average rate of the given function is 2.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

The given function is h(x)=-x²-x+5 and the interval is -6≤x≤2.

x={-6, -5, -4, -3, -2, -1, 0, 1, 2}

y=-x²-x+5

When x=-2

y=-(-2)²-(-2)+5

y=-4+4+5

y=5

When x=-1

y=-(-1)²-(-1)+5

y=5

When x=0

y=5

When x=1

y=-1-1+5

y=3

When x=2

y=-(2)²-(2)+5

y=-1

Now, rate using (1, 3) and (2, -1), we get

m =(-1-1)/(2-3)

m=2

Therefore, the average rate of the given function is 2.

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Answer:

5.75x = f(x)

22.99 + 2.09x = g(x)

Step-by-step explanation:

Divide them into two parts:

Normal drinks and commemorative drinks

- With normal, only $5.75 is related (Only one drink at a time so 5.75x)

- With commemorative, $22.99 and $2.09 are related (A one time fee of $22.99, then a refill of $2.09; so 22.99 + 2.09x)

Answer:

600

Step-by-step explanation:

6x10^2 = 600

Answer:

600

Step-by-step explanation:

Answer:

The number of fishes person b initially has is 0

The number of fishes person a initially has is x, where x is any natural number

Step-by-step explanation:

The given parameters are;

let x represent the number of fish person a catches and let y represent the number of fishes that person b catches, we have;

x - x/2 = y + x/2

2·x - x = 2·y + x

2·x = 2·y + 2·x

∴ y = 0

Therefore;

The number of fishes person b initially has = 0

The number of fishes person a initially has = x, where x is any natural number.

The estimated median price of a single-family home in Charleston/No. Charleston in the 1st Quarter of 2008 is $201,048. If the median price continues to decrease at the same rate for the next two years, the estimated median price of a single-family home in the 1st Quarter of 2011 would be $144,458.

(a) To estimate the median price of a single-family home in the 1st Quarter of 2008, we need to calculate the original price before the 8.15% decrease. Let's assume the original price was P. The price after the decrease can be calculated as P - 8.15% of P, which translates to P - (0.0815 * P) = P(1 - 0.0815). Given that the end of 1st Quarter of 2009 median price was $184,990, we can set up the equation as $184,990 = P(1 - 0.0815) and solve for P. This gives us P ≈ $201,048 as the estimated median price of a single-family home in the 1st Quarter of 2008.

(b) If the median price of a single-family home falls at the same rate for the next two years, we can calculate the price for the 1st Quarter of 2011 using the estimated median price from the 1st Quarter of 2009. Starting with the median price of $184,990, we need to apply an 8.15% decrease for two consecutive years. After the first year, the price would be $184,990 - (0.0815 * $184,990) = $169,805.95. Applying the same percentage decrease for the second year, the price would be $169,805.95 - (0.0815 * $169,805.95) = $156,012.32. Therefore, the estimated median price of a single-family home in the 1st Quarter of 2011 would be approximately $144,458.

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The given expression is,

10639/500+22

According to

Answer:

second one

Step-by-step explanation:

Answer:

10.7 in.

Step-by-step explanation:

perimeter = base1 + base2 + side1 + side2

side1 = side2 = side

side1 + side2 = 2 * side

25.9 in. = 1.7 in. + 2.8 in. + 2 * side

2 * side = 21.4 in.

side = 10.7 in.

The length of segment RS is given as follows:

RS = 24.

The angle addition postulate states that if two or more angles share a common vertex and a common angle, forming a combination, the measure of the larger angle will be given by the sum of the measures of each of the angles.

The segment RT is the combination of segments RS and ST, hence:

RT = RS + ST.

Hence the length of segment RS is given as follows:

41 = RS + 17

RS = 24.

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Answer: 3/2

Did this on I ready

The speed of Becca for the given data is 3/2 miles per hour.

The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other terms, it is a measurement of an object's motion's speed without direction The term "velocity" refers to the combination of direction and speed.

Given the hiking distance of Becca = 9/10 miles

time taken = 3/5 hours

to find the speed,

speed = distance/time

speed = (9/10) ÷ (3/5)

speed = 9/10 x 5/3

speed = 3/2 miles per hour

Hence the speed of Becca is 3/2 miles per hour.

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4/3 of a number is more than 3/4 of its number by 1 . find the number .

According to question 4/3 of a number is equal to :

\( \longmapsto \: \frac{4}{3} \times x\)

Which means ,

\(\longmapsto \: \frac{4x}{3} \)

According to question 3/4 of a number is equal to :

\(\longmapsto \: \frac{3}{4} \times x\)

Which means ,

\(\longmapsto \: \frac{3x}{4} \)

Now , forming equation :

As the question says that 4/3 of a number is more than 3/4 of its number by 1 . So :

\(\longmapsto \: \frac{4x}{3} = \frac{3x}{4} + 1\)

Now , transposing 3x/4 to left hand side :

\(\longmapsto \frac{4x}{3} - \frac{3x}{4} = 1\)

Now , taking L.C.M :

\(\longmapsto \: \frac{4(4x) - 3(3x)}{12} = 1\)

Now by calculating :

\(\longmapsto \: \frac{16x - 9x}{12} = 1\)

Now Subtracting 16x with 9x and transposing 12 to right hand side :

\(\longmapsto \: 7x = 12\)

So ,

\(\longmapsto \: \boxed{ \bold{ x = \frac{12}{7} }}\)

Answer:

Step-by-step explanation:

To determine the value of ∑ i=134​ (2i^2 + 3i - 7), we can use the properties of summation and the given formula for the sum of squares.

First, let's simplify the expression inside the summation:

2i^2 + 3i - 7

Expanding the summation notation:

∑ i=1^34​ (2i^2 + 3i - 7)

We can split the summation into three separate summations:

∑ i=1^34​ 2i^2 + ∑ i=1^34​ 3i - ∑ i=1^34​ 7

Using the formula for the sum of squares:

∑ i=1^n​ i^2 = 6n(n-1)(2n-1) / 6

We can substitute this formula into the first summation:

2 * (∑ i=1^34​ i^2)

Using the formula, we have:

2 * [6 * 34 * (34-1) * (2*34-1)] / 6

Simplifying:

2 * [6 * 34 * 33 * 67] / 6

Next, let's evaluate the second summation:

∑ i=1^34​ 3i

We can use the formula for the sum of arithmetic series:

∑ i=1^n​ i = n(n+1) / 2

Substituting n = 34, we have:

3 * (∑ i=1^34​ i) = 3 * [34 * (34+1)] / 2

Finally, let's evaluate the third summation:

∑ i=1^34​ 7 = 7 * 34

Now, let's combine all three summations:

2 * [6 * 34 * 33 * 67] / 6 + 3 * [34 * (34+1)] / 2 - 7 * 34

Simplifying further will give us the final result.

Note: The final result may vary depending on the calculation precision used.

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Answer:

Slope of a line perpendicular to a line  = \(\frac{1}{6}\)

Step-by-step explanation:

(x₁ , y₁ ) = (3 , -5)      & (x₂, y₂) = (1 , 7)

\(slope = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\)

        \(= \frac{7-[-5]}{1-3}\\\\=\frac{7+5}{1-3}\\\\=\frac{12}{-2}\\\\= - 6\)

Slope of the perpendicular line = \(\frac{-1}{m}\)

                                                    \(= \frac{-1}{-6}\\\\= \frac{1}{6}\)

The table represents the exponential function as f(x) = a(b)^3

When the expression of function is such that it involves the input to be present as exponent (power) of some constant, then such function is called exponential function. There usual form is specified below. They are written in several such equivalent forms.

Here we have the table:

Year       number of new college programs

2005     3

2006     22

2007     27

2008     66

2009     100

Few things that are useful to identify this as an exponential equation are:

f(x) = a(b)^3

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Answer:

√200

Step-by-step explanation:

An irrational number is a number that can not be represented as a fraction

√81 = 9 = 9/1

√-16 = 4i

√-64 = 8i

√200 = ~14.14213

Answer:  its 53

Step-by-step explanation:

Answer:

53

Step-by-step explanation:

3(22)= 66

66-13=53

Answer:

Y = 0x-2.

Step-by-step explanation:

I don't want the question of my teachers being in my b or I am a good time wi and I am

Answer:

1/5

Step-by-step explanation:

rise = 2 ft

run = 10 ft

slope = rise/run = 2/10 = 1/5

Answer: 1/5

Answer:

1/5

Step-by-step explanation:

The slope is the rise over the run

Y / x

2/10

1/5

Answer:

10 x 10 = 100

6 x 6 = 36

:)

Answer:

10*10=100 | 6*6=36

Step-by-step explanation:

Well, 100/10=10

36/6=6

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

10+10+10+10+10+10+10+10+10+10=50+50=100

6+6+6+6+6+6=18+18=36

The number of possible seating arrangements depends on the conditions specified in the problem is 435,456,000

Permutation is the arrangement of objects in a specific order.

a. The mathematics majors occupy the first 6 seats:

The number of permutations of the mathematics majors is simply 6! (6 factorial), since they all have to sit together in a block. After the mathematics majors are seated, we have 12 chairs left for the chemistry and physics majors, who can be arranged in (5 + 7)! / (5! x 7!) ways.

Finally, the total number of permutations for the mathematics majors to occupy the first 6 seats is

=>  6! x (5 + 7)! / (5! x 7!).

=> 570240

b. The mathematics majors cannot occupy the first 6 seats:

In this case, the number of permutations of the mathematics majors is (18 - 6)! / (6! x (12 - 6)!). This is because they cannot occupy the first 6 seats and have to be arranged in the remaining 12 chairs.

Next, the number of permutations for the chemistry majors is (12 - 6)! / (5! x (12 - 6 - 5)!).

Finally, the number of permutations for the physics majors is (12 - 6 - 5)! / 7!.

The total number of permutations for this scenario is

=> (18 - 6)! / (6! x (12 - 6)!) x (12 - 6)! / (5! x (12 - 6 - 5)!) x (12 - 6 - 5)! / 7!.

=> 668250

c. Students with the same major sit in a block:

In this case, the number of permutations of the chemistry majors is simply 5! since they have to sit together in a block.

Similarly, the number of permutations of the mathematics majors is 6! and the number of permutations of the physics majors is 7!.

Finally, the total number of permutations for students with the same major to sit in a block is

=> 5! x 6! x 7!.

=> 435456000

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Answer:

A hexagon

Step-by-step explanation:

A hexagon - - - the allen wrench has 2 hexagonal heads. See attached pic.

The geometric shape that forms the hole that fits an allen wrench is a hexagon, which is a six-sided polygon with straight sides and angles.

The geometric shape hexagon-shaped hole in an allen wrench, also known as a hex key, is designed to fit tightly over the hexagonal socket of a screw or bolt head. A hexagon is a six-sided polygon, meaning it has six straight sides and angles. In the case of an allen wrench, the hexagon has internal angles of 120 degrees and opposite sides that are parallel.

The hexagonal shape of the hole in the wrench allows for a tight and secure fit onto the corresponding hexagonal socket of the screw or bolt head. This design ensures that the wrench can apply a significant amount of torque to the fastener without slipping, which is essential for many applications in construction, mechanics, and other industries.

The use of a hexagonal shape also allows for greater precision and control when turning the screw or bolt, making it easier to achieve the desired level of tightness. Overall, the hexagon is an ideal shape for the hole in an allen wrench due to its strength, stability, and precision.

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Answer:

-3x+y=14

Step-by-step explanation:

add the x and -4x which gives you -3x

add the -y and 2y which is y

then -14 and 28 add up to 14

Answer:

Side b = 20.68325

Step-by-step explanation:

Because the angles of a triangle will always equal 180 we can determine that angle a is 50 because 82+48+x=180. Then we use the law of sines and figure out that sin82/b=sin50/16. Then you cross multiply and get your answer.

To determine the change in angular momentum (ΔL) of a cylinder from t = 0 to t = t0, a student can use the equation:

ΔL = I * Δω

where ΔL is the change in angular momentum, I is the moment of inertia of the cylinder, and Δω is the change in angular velocity.

To calculate Δω, the student needs to know the initial and final angular velocities, ω0 and ωt0, respectively. The change in angular velocity can be calculated as:

Δω = ωt0 - ω0

Once Δω is determined, the student can use the moment of inertia (I) of the cylinder to calculate ΔL using the equation mentioned earlier.

The moment of inertia (I) depends on the mass distribution and shape of the cylinder. For a solid cylinder rotating about its central axis, the moment of inertia is given by:

I = (1/2) * m * r^2

where m is the mass of the cylinder and r is the radius of the cylinder.

By substituting the known values for Δω and I into the equation ΔL = I * Δω, the student can calculate the change in angular momentum (ΔL) of the cylinder from t = 0 to t = t0.

It's important to note that this method assumes that no external torques act on the cylinder during the time interval. If there are external torques involved, the equation for ΔL would need to include those torques as well.

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Option B: 4x²-x+3

(4x³ + 11x² + 0x + 9) + (x+3) [here, we will include 0x to do long division]

Divide 4x³ by x to get first term of the quotient, 4x³

Then, take 4x² and multiply it with 3 and you will get 4x² + 12

Subtract 4x² + 12 from 4x³ + 11x².

Then, you will get the remainder as -x² + 0x

Now you have to repeat the same same process, divide -x² by x to get second term of quotient, -x

Then take -x and multiply with 3 and you will get -x²- 3x

You will get the remainder as 3x+ 9

Divide 3x by x to get the third term of quotient, 3

Then, take 3 and multiply with 3 and you will get 3x + 9

Subtract and you will get the remainder as 0.

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The first term, a1, in the geometric series is -3.

What is Geometric Series?

A geometric series is a series for which the ratio of two consecutive terms is a constant function of the summation index. The more general case of a ratio and a rational sum-index function produces a series called a hypergeometric series. For the simplest case of a ratio equal to a constant, the terms have the form

To find the first term, a1, in a geometric series given the sum, Sn = 93, the common ratio, r = 2, and the number of terms, n = 5, we can use the formula for the sum of a geometric series:

Sn = a1 * (1 - r^n) / (1 - r)

Plugging in the given values, we have:

93 = a1 * (1 - 2^5) / (1 - 2)

Simplifying the expression:

93 = a1 * (1 - 32) / (-1)

93 = a1 * (-31)

Now we can solve for a1 by dividing both sides of the equation by -31:

a1 = 93 / -31

a1 = -3

Therefore, the first term, a1, in the geometric series is -3.

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The value of the middle of the three is 25.

Let x be the first odd integer, then the next two consecutive odd integers are x+2 and x+4. The sum of these three consecutive odd integers is given as 75, so we can write the equation:

x + (x+2) + (x+4) = 75

Simplifying the left side of this equation gives:

3x + 6 = 75

Subtracting 6 from both sides gives:

3x = 69

Dividing by 3 gives:

x = 23

So the first odd integer is 23, and the next two consecutive odd integers are 25 and 27. The middle of these three is the second consecutive odd integer, which is 25. Therefore, the value of the middle of the three is 25.

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Answer:

x = 3z(y - 2)

Step-by-step explanation:

Given

\(\frac{x}{3z}\) = y - 2 ( multiply both sides by 3z to clear the fraction )

x = 3z(y - 2)