The ________________ manages water resources in a 16-county region that stretches from Orlando to the Florida Keys, serving a population of 8.1 million (hint: Remember the water conservation calculator

1. The number of gallons of water produced is 460 gallons

2. The amount in cm the sea would increase after 6 years is 392 cm

We'll begin by by converting 1.9 m³ to cm³. This is illustrated below:

1 m³ = 1×10⁶ cm³

Therefore,

1.9 m³ = 1.9×10⁶ cm³

Next, we shall determine the volume of water produced from 1.9 m³ (i.e 1.9×10⁶ cm³) of ice. This is illustrated below:

From the question given,

1 cm³ of ice = 0.92 cm³ of water

Therefore,

1.9×10⁶ cm³ of ice = 1.9×10⁶ × 0.92

1.9×10⁶ cm³ of ice = 1.748×10⁶ cm³ of water

Finally, we shall determine the number of gallons produced. This is illustrated below:

From the question given,

3800 cm³ of water = 1 gallon

Therefore,

1.748×10⁶ cm³ of water = 1.748×10⁶ / 3800

1.748×10⁶ cm³ of water = 460 gallon

Thus, 460 gallons were produced

From the question given above,

1000 Km³ = 364 cm

Therefore,

179.4 Km³ = (179.4 × 364) / 1000

179.4 Km³ = 65.3016 cm per year

To obtain the increase after 6 years, multiply 65.3016 by 6 as shown below:

65.3016 × 6 = 392 cm

Thus, the sea will increase 392 cm after 6 years

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The Fall (drop)  of drainage piping is: A. 5".

In order to determine the fall (drop) of drainage piping we would need to multiply the drainage piping by the inch per feet.

Hence:

Using this formula

Fall (drop) of drainage piping = Drainage piping× inch per feet

Where:

Drainage piping=20

Inch per feet=1/4"

Let plug in the formula

Fall (drop) of drainage piping =20×1/4"

Fall (drop) of drainage piping =5"

Therefore the correct option is A. 5".

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The given polynomial function has 1 relative minimum and 1 relative maximum.

The given function is

f(x) = 2x³ - 2x² + 1

derivating the above function,

f'(x) = 6x² - 4x

At slope = 0, f'(x) = 0 (for maximum and minimum values)

⇒ 6x² - 4x = 0

⇒ 2x(3x - 2) = 0

2x = 0 or 3x - 2 = 0

∴ x = 0 or x = 2/3

Then the y-coordinates are calculated by substituting these x values in the given function,

when x = 0;

f(0) = 2(0)³ - 2(0)² + 1 = 1

So, the point is (0, 1)

when x = 2/3;

f(2/3) = 2(2/3)³ - 2(2/3)² + 1 = 19/27

So, the point is (2/3, 19/27)

Since y = 1 is the largest value, the point (0, 1) is the relative maximum for the given function.

So, y = 19/27 is the smallest value, the point (2/3, 19/27) is the relative minimum for the given function.

Thus, option A is correct.

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Multiply by 6

And

Multiply by 3

eq(1)-eq(2)

Then

From Equation 1

[tex] \dfrac{x}{2} + \dfrac{2y}{3} = - 1 [/tex]

[tex] \dfrac{3x + 4y}{6} = - 1[/tex]

[tex]3x + 4y = - 6 [/tex]

From Equation 2

[tex]x - \dfrac{y}{3} = 3 [/tex]

[tex] \dfrac{3x - y}{3} = 3[/tex]

[tex]3x - y = 9[/tex]

By eliminating ;;

For that multiply equation 2 by 4

12x - 4y = 36 _(3)

By taking equation (1) and (3)

3x + 4y = -6

12x - 4y = 36

__________

15x = 30

x = 30/15

x = 2

Putting the value of x in 2

[tex]3(2) - y = 9[/tex]

[tex]6 - y = 9[/tex]

[tex]6 - 9 = y[/tex]

[tex]-3 = y[/tex]

So The value of x = 2 and y = -3

These series show convergence of series which are

sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfraction

sigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction)

According to the statement

we have given the some series and we have to find that the out of these series which series is convergent.

So, For this purpose we have to check the convergence of series.

So,

we know that the for the convergent of series there is a one condition and if those condition will satisfy on the series then the series is convergent and if not then series is divergent.

So, the condition for convergent is a series converges if the absolute value of the sum of any finite number of sequential terms can become arbitrary small by starting the addition from a term which is far enough. So, if this condition is not satisfied the series diverges.

When we apply this condition on all given series then only 2 series satisfy this condition which is

So, These series show convergence of series  which are

sigma-summation underscript n = 1 overscript infinity endscripts startfraction 2 n over n 1 endfraction

sigma-summation underscript n = 1 overscript infinity endscripts 3 (startfraction 1 over 10 endfraction)

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Answer:

B. The series converges because it has a sum of 2/3

Here are the answers for the rest of the assignment:

C.

B.

C and D

A and C

B and D

C.

B. 0.31 and A. 0.0025

B. 1.0317 and C. 1.9683

(please read below)

Step-by-step explanation:

Had the assignment and these are the correct answers, enjoy :)

p.s Take a break here for a second, this was your last assignment before the unit test and finals, pre-calc is a very hard subject to master and calc is going to be even harder so I just want to say that I am proud of you, you have done a great job this year.

I have also taken the course(and many others) and answered countless questions for brainly (you have probably seen some of them if you took pre-calc) and this is my final answer for edge(might do one or 2 more for the finals) and it has been my greatest pleasure to bring you guys edge answers for 3 years strait but sadly this is where my road ends, I have tried my hardest to make your lives easier with my answers as others have for me. I hope some of y'all continue on my legacy and continue bringing good to the world 1 answer at a time.

So long fellows, thank you for taking the time to listen I hope y'all do well in life :)

rhumbos

it is the most precise name because it gives more information about the quadrilateral

The number from the grid that fulfills all the given clues is; 12

The grid is shown in the attached image.

Now, we are told that Manju and Arif are thinking of a number on the grid and the clues are;

It is a multiple of 3.

It is even.

It is in the third row.

Now, looking at the third row, we see the numbers as;

11, 12, 13, 14, 15

Now, the only number that fulfills all the given clues is 12.

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Answer:

Step-by-step explanation:

Considerando la definición de una ecuación, el número desconocido es 50.

Una ecuación es la igualdad existente entre dos expresiones algebraicas conectadas a través del signo de igualdad en la que figuran uno o varios valores desconocidos, llamadas incógnitas, además de ciertos datos conocidos.

Los miembros de una ecuación son cada una de las expresiones que aparecen a ambos lados del signo igual.

En este caso, "La suma de un número con su mitad es igual a 75" puede ser expresado mediante una ecuación, donde consideras que "x" es la incógnita, que representa el número desconocido.

Teniendo en cuenta que la mitad de un número se calcula dividiendo el número por 2, entonces la ecuación queda expresada como:

x + x÷2= 75

O lo que es lo mismo

x + [tex]\frac{1}{2}[/tex]x= 75

Resolviendo:

[tex]\frac{3}{2}[/tex]x= 75

x= 75 ÷[tex]\frac{3}{2}[/tex]

x= 75×[tex]\frac{2}{3}[/tex]

x=50

Finalmente, el número desconocido es 50.

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The dive of the Peregrine falcon took 7.5 seconds

How to solve such time related questions?

The key concept for solving such questions is the relationship between speed, distance and time.

The relationship between them is Distance = Speed X Time

Assuming the top speed of  a Peregrine falcon is 240mph.

Distance travelled by the Peregrine falcon = 0.5 miles

By using the formula we get

0.5 = 240 x time

time = [tex]\frac{1}{480}[/tex] hours

time = [tex]\frac{3600}{480}[/tex] seconds = 7.5 seconds

∴ The dive of the Peregrine falcon took 7.5 seconds

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Common significance levels are 0.01 and 0.05. Because the observations in the sample do not come from a random pool, it is impossible to conduct a test based on a population percentage by utilizing the normal approximation approach. This is further explained below.

Generally, The possibility of an occurrence may be quantified using the concept of probability. There are many occurrences that cannot be foreseen with complete accuracy.

In conclusion, Both 0.01 and 0.05 are considered to be significant values. It is not feasible to perform a test based on a population percentage using the normal approximation technique because the observations in the sample do not originate from a random pool. This makes it impossible to utilize the normal approximation approach.

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Answer:

3 cups for 60 biscuits

60/3=20

1 cup for 20 biscuits

95/20=4.75

4.75 cups of flour

Hope This Helps!!!

Answer:4.75

Step-by-step explanation: If 3 cups equals 60 biscuits then how much with you need for 95 biscuits

60/3 equals 20 95/20 equals 4.75 just to make sure lets multiply

475x20 equals 9500 now put the decimal back in place   95.00

Answer:

A). 0

Step-by-step explanation:

If you look at the graph, you can see that the only time it passes through the X- Axis is at (0, -20). Therefore, the solution to y=g(x) where g is negative, would be 0.

One of the numbers would be 321. Hence option B is true.

Used the concept of the Number system that states,

A writing system used to express numbers is known as a number system. It is the mathematical notation used to consistently express the numbers in a particular set using digits or other symbols.

Given that,

The ratio of the two numbers is 2/3, and their sum is 535.

Let us assume that,

The two numbers are x and y.

Hence we have;

[tex]\dfrac{x}{y} = \dfrac{2}{3}[/tex]  .. (i)

And, [tex]x + y = 535[/tex]   .. (ii)

From equation (i);

[tex]\dfrac{x}{y} = \dfrac{2}{3}[/tex]

[tex]x = \dfrac{2y}{3}[/tex]

Substitute the above value of x in (ii);

[tex]x + y = 535[/tex]

[tex]\dfrac{2y}{3} + y = 535[/tex]

[tex]2y + 3y = 535 \times 3[/tex]

[tex]5y = 1605[/tex]

[tex]y = 321[/tex]

From equation (i);

[tex]x = \dfrac{2y}{3}[/tex]

[tex]x = \dfrac{2\times 321}{3}[/tex]

[tex]x = 214[/tex]

Therefore, the number is 321. So option B is true.

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Answer:

1. Cube

2. Square-based pyramid

Step-by-step explanation:

Answer:

Below.

Step-by-step explanation:

a) Cube

b Pyramid

The congruency proof that can be used to show that ∠P≅∠R is as given in the steps below.

From the figure as seen online, we can see that;

The figure shows the same triangles PQS and RQS as in the beginning of the task. Angles SPQ and SRQ are highlighted in red.

Thus, the 2 column proof to show that ∠P≅∠R is;

Statement 1; ∠SPQ≅∠SRQ

Reason 1; Given

Statement 2; SQ bisects ∠PSR

Reason 2; Given

Statement 3; ∠PSQ≅∠QSR

Reason 3; Definition of angle bisector

Statement 4; SQ ≅ SQ

Reason 4; Reflexive Property of Congruence

Statement 5; △PQS≅△RQS

Reason 5; Angle - Angle Side (AAS) Congruency Postulate

Statement 6; PS ≅ SR

Reason 6; CPCTC (Corresponding parts of congruent triangles are congruent)

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Answer:

a) x = 1, x = -7

b) (-3, -48)

c) x = -3

d) upwards

Step-by-step explanation:

Given quadratic equation:

[tex]y=3(x-1)(x+7)[/tex]

Intercept form of a quadratic equation:  

 [tex]y=a(x-p)(x-q)[/tex]

where:

Comparing the formula with the given equation:

⇒ p = 1

⇒ q = -7

Therefore, the x-intercepts of the given equation are x = 1 and x = -7.

The midpoint between the two x-intercepts is the x-coordinate of the vertex.

[tex]\implies \textsf{Midpoint}=\dfrac{x_2+x_1}{2}=\dfrac{1+(-7)}{2}=-3[/tex]

Therefore, the x coordinate of the vertex is -3.

To find the y-coordinate of the vertex, substitute this into the given equation:

[tex]\implies y=3(-3-1)(-3+7)=-48[/tex]

Therefore, the coordinates of the vertex are (-3, -48).

The x-coordinate of the vertex is the axis of symmetry.

Therefore, the axis of symmetry is x = -3.

If the leading coefficient of a quadratic equation is positive, the parabola opens upwards.

If the leading coefficient of a quadratic equation is negative, the parabola opens downwards.

From inspection of the given equation, the leading coefficient is 3.

Therefore, the parabola opens upwards.

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The equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.

In the question, we have been asked for the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury.

First, we will find the equations showing the level of mercury in each body of water.

For the first water body:

Initial measure of mercury = 0.05 ppb.

Rate of rising = 0.1 ppb each year.

Number of years = y.

Thus, the equation showing level of mercury = 0.05 + 0.1y.

For the second water body:

Initial measure of mercury = 0.12 ppb.

Rate of rising = 0.06 ppb each year.

Number of years = y.

Thus, the equation showing level of mercury = 0.12 + 0.06y.

We are looking for the equation, to find y, the year in which both bodies of water have the same amount of mercury.

As they will have the same amount of mercury, their respective equations showing the level of mercury should be equal, that is:

0.05 + 0.1y = 0.12 + 0.06y, which is the required equation.

Thus, the equation that can be used to find y, the year in which both bodies of water have the same amount of mercury is 0.05 + 0.1y = 0.12 + 0.06y. Hence, the 3rd option is the right choice.

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For the complete question, refer to the attachment.

1. The force necessary to gain a velocity of 60 m/s within 5 mins is 40 N

2. The velocity gained by the object at the end of the second minute is 30 m/s

F = m(v –u) / t

F = 200(60 – 0) / 300

F = 40 N

F = m(v –u) / t

Cross multiply

m(v –u) = Ft

Divide both sides by m

v - u = Ft / m

v - 0 = (150 × 120) / 600

v = 30 m/s

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In the right angled triangle ACD shown with isosceles triangle ABC and ADC, AB = AC = AD

An equation is an expression that shows the relationship between two or more numbers and variables.

A triangle is a polygon that has three sides and three angles. Types of triangles are isosceles, equilateral and scalene.

In the diagram shown:

AB = AC = AD

In the right angled triangle ACD shown with isosceles triangle ABC and ADC, AB = AC = AD

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Answer:

The answer to your question is 5500

Step-by-step explanation:

[tex]50x 110 = 5500\\[/tex]

I hope this helps and have a good day!

The zero of polynomials is -2. The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex].

According to the question,

The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex]. In order to find the zero of polynomials only if we substitute the value and polynomials become zero.

p(-2) = [tex]3(-2)^{3} - 16 (-2) - 8[/tex]

= 3(8) + 32 -8

= 0

Hence, the zero of polynomials is -2. The polynomials is p(y) = [tex]3y^{3} - 16 y - 8[/tex].

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The Lena has no common ratio for the sequence 1.0 1.5 2.5 2.0

According to the question,

1.0  1.5  2.5  2.0

a = 1.0

r = 1.5/1 = 1.5

r = 2.5/1.5 = 1.6667

r = 2/2.5 = 0.8

common ratio is different, so given sequence is not geometric sequence.

Hence,  the Lena has no common ratio for the sequence 1.0 1.5 2.5 2.0.

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Answer:

D) f(x) = (1/2)^x

Step-by-step explanation:

at least that is what I think answer D is supposed to be.

I guess the other answer options are actually

A) f(x) = -2^x

B) f(x) = 2^x

C) f(x) = (1/2)^-x

let's look at the most interesting point here : (1, 1/2).

when x=1, then y = 1/2

A fails. because for x = 1 we get y = -2.

B fails. because for x = 1 we get y = 2.

C fails. because for x = 1 we get (1/2)^-1

and that is 1 / 1/2 = 2

so, the only function giving us (1, 1/2) is D, as

(1/2)¹ = 1/2

equation of a line is y=mx+ c

where m is that gradient and c is y intercept

so first we find the gradient (m)

M= change in y intercept ÷change in x

M=4-2÷5-1

M=2÷4=1/2(as a fraction)(you can also use o.5)

there 1/2is the gradient

then to find the equation of the line

y= 1/2x +c (from coordinates 1,2 we substitute)

2=1/2(1)+c

2-1/2=c

c=1.5

or

from the coordinates 5,4

4=1/2(5) +c

4=5/2+ c

c=4-5/2

c=1.5

equation of the line=y=0.5x + 1.5

or y=1/2x +1.5

hope it helps you^_^

The weight of each small tables and chairs in the United States is 15lbs and 3.5lbs respectively.

Let

3x + 5y = 62.5

3x + 2y = 52

5y - 2y = 62.5 - 52

3y = 10.5

y = 10.5/3

y = 3.5 lbs

Substitute y = 3.5 into

3x + 2y = 52

3x + 2(3.5) = 52

3x + 7 = 52

3x = 52 - 7

3x = 45

x = 45/3

x = 15 lbs

Therefore, the weight of each small tables and chairs in the United States is 15lbs and 3.5lbs respectively.

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