it took 2/3 minute to fill a barrel 1/4 full of water. find the unit fate in barrels per minute

The derivative of the function [tex]f(x) = \sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}[/tex] will be given below.

[tex]f'(x) = \dfrac{1 + (0.5x^2 + 2x + 1)(1.5x^3 + 4x^2 + 2x + 2)}{\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}}[/tex]

The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decrease.

The equation of the function will be given as,

[tex]f(x) = \sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}[/tex]

The derivative of the function will be given as,

[tex]f'(x) = \dfrac{d}{dx} \ \sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2} \\\\\\f'(x) = \dfrac{2 + 2(x^2 + 1)(0.5x^2 + 2x + 1) \cdot (x + 2) + (0.5x^2 + 2x + 1)^2 \cdot 2x}{2\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2} }\\\\\\f'(x) = \dfrac{2 + (0.5x^2 + 2x + 1)[2(x^2 + 1)(x + 2) + (0.5x^2 + 2x + 1) \cdot 2x]}{2\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2} }\\[/tex]

Solve the equation further, then we have

[tex]f'(x) = \dfrac{1 + (0.5x^2 + 2x + 1)[(x^2 + 1)(x + 2) + (0.5x^2 + 2x + 1) \cdot x}{\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}}\\\\\\f'(x) = \dfrac{1 + (0.5x^2 + 2x + 1)(x^3 + 2x^2 + x + 2 + 0.5x^3 + 2x^2 + x)}{\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}}\\\\\\f'(x) = \dfrac{1 + (0.5x^2 + 2x + 1)(1.5x^3 + 4x^2 + 2x + 2)}{\sqrt{2x + (x^2 + 1) (0.5x^2 + 2x + 1)^2}}[/tex]

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The equation that can be used to represent the proportional relationship between time and the distance a greyhound dog can travel is:

y = 44x.

A direct proportional relationship is a function in which the output variable is found with the multiplication of the input variable and the constant of proportionality, as follows:

y = kx.

In which k is the constant of proportionality, also representing the rate between the output and the input for any pair of (input, output) except (0,0).

From the table of distances and time given in this problem, the constant is found as follows:

k = 220/5 = 440/10 = 660/15 = 44.

Hence the constant is of 44 and the relation is given by:

y = 44x.

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Equation is y = 2x² + 4x + 1.

A parabola is an approximately U-shaped, mirror-symmetrical planar curve. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.

Given Data

Standard form of quadratic equation

Y = ax² +bx + c

Given points

(3,9), (30,-9). (0,1)

Equating points in formula

9= a(3)² + b(3) + c

9 = 9a + 3b +c

-9 = a(30)² + 3(30) + c

-9 = 900a + 90 + c

1 = a(0)² + b(0) + c

c = 1

Equating c in the equation

9 = 9a + 3b +1

8 = 9a + 3b

-9 = 900a + 90b +1

-10 =  900a + 90b

Multiplying both sides by 100

800 = 900a + 300b

-10    = 900a + 90b

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

790 = 210b

b = 4 (rounding off)

Putting values of b into equation

8 = 9a + 3(4)

20 = 9a

a = 2 (rounding off)

Equation is y = 2x² + 4x + 1.

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Answer:

x

Step-by-step explanation:

2x + 5 + 7x = 8x -11  Combine like terms

9x + 5 = 8x -11  Subtract 8x from both sides of the equation

x + 5 = -11  Subtract 5 from both sides of the equation.

x= -16

Answer: -16

Step-by-step explanation:

2x+5+7x = 8x-11 simplifies into 9x+5 = 8x -11.

Move 8x to the other side - put like terms together : 9x-8x+5 = -11

Which is simplified into x+5 = -11

Move 5 to the other side to isolate x: x = -11 -5

Combine -11 and -5

x = -16

Samuel's average speed during his morning routine is  24.3 miles per hour.

Average speed measures how fast an object or a person is travelling with respect to time. Average speed is the ratio of total distance travelled and total time travelled.

Average speed = total distance / total time

Total distance = 4.5 + 2/3 + 9

= 4.5 + 9 + 0.67 = 14.2 miles

Total time = 30 + 20 + 45 = 95 minutes = 1 hour 35 minutes  = 1 7/12 hours = 1.6 hours

Average speed = 14.2 / 1.6 = 24.3 miles per hour

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Answer: n = 1/2; m = 2/3

Step-by-step explanation:

A ⇒ 12 y = 6x + 24

[tex]y=\frac{n}{2}+2[/tex]

[tex]n=\frac{1}{2}[/tex]

B ⇒ 3y = 2x + 18

[tex]y=\frac{2}{3}n+6[/tex]

[tex]m=\frac{2}{3}[/tex]

∴ Lines are neither because slop diff.

the answer:

9-5x+2=4-5x

Step-by-step explanation:

as there is -5X in the two sides

Answer:

32°

Step-by-step explanation:

Angle A + angle B = angle ACD

Since it is an isosceles triangle angle a = angel b

2(2x + 16) = 5x +24  distribute the 2

4x + 32 = 5x + 24  Subtract 4x from both sides

32 = x + 24  Subtract 24 from both sides

8 = x

Now plug in 8 for x in 2x + 16

2(8) + 16

16+ 16 = 32

Answer:

1a. 10 cups of dry rice will serve 30 people.

1b. 15 cups of dry rice will serve 45 people.

2. 30 spring rolls = 15 people

40 spring rolls = 20 people

56 spring rolls = 28 people

Step-by-step explanation:

1a. To find a constant, the equation is y/x. When 6 is divided by 2, you get 3 and from there the input increases by 3.  So, you multiply 10 by 3 to find how many people it can serve.

1b. To find this answer, you divide 45 by 3 to get 15. So 15 cups will serve 45 people.

2. Any number in the second column is divided by .5 to get the number in the first column. Any number in the first column is multiplied by .5 to get the number in the second column.

I hope that helps :)

Answer: 1725714.28571

Answer:

12080000/7 or 1725714.28571

Step-by-step explanation:

The mean and median of the data are equivalent and the value is 6.

The mean (average) of a data set can be calculated by adding up all the numbers in the collection and dividing by the total number of values in the set.

Let us find the mean of the data set :

mean =  (4 + 5 + 6 + 7 + 8) ÷ 5 = 30÷ 5 = 6

Median = 6 middle value.

Therefore the mean and median are equivalent.

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Answer:

Step-by-step explanation:

-2=3/2(0)+5

Hello!

Part (A)

[tex]\text{Mean} = \dfrac{\text{sum of all salaries}}{\text{number of workers}} =\dfrac{13500 + 27500+13750 + 79000+ 19250 + 29000+21000}{7} \\\\\text{Mean}= 29000 \text{ dollars}[/tex]

Part (B)

 ==> The mean of other six worker's salary

  [tex]\text{Mean}= \dfrac{\text{sum of the 6 worker's salary}}{\text{number of workers} }=\dfrac{13500+27500+13750+19250+29000 + 21000}{6} \\\\ \text{Mean}= \dfrac{124000}{6}=20,666.67 \text{ dollars}[/tex]

Hope that helps!

Roxanne claims that all linear equations represent proportional relationships. So, this statement "Yes, because all linear equations have graphs that are straight lines." makes him correct.

When there is a proportionate relationship between two variables, the other variable changes at a consistent pace regardless of how the first variable changes, grows or shrinks. A constant ratio between the two variables can be thought of as the constant rate.

Equations, graphs, and tables that use proportions can be used to show proportional relationships. A broad structure is followed by the proportional relationship equation, which will be taught in this session. Straight lines are used to illustrate the graphs. The tables are sets of numbers that are always paired in the same ratio.

Hence the correct option is A

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Answer:

v=4,−2

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor equal to zero.

Answer:

[tex]{ \sf{ {v}^{2} - 2v - 8 = 0}} \\ { \sf{(x + 2)(x - 4) = 0}} \\ { \tt{x = - 2 \: \: or \: \: 4}}[/tex]

Answer:

I would say corresponding angles are converse

Step-by-step explanation:

I'm not that sure though, but I'm looking at my notes and it's kind of similar to the fact that it's corresponding

y value of the kilo

 y =  (1/1000) x

imagine

x = 20

y = x / 1000

20 / 1000 = 0.020

The range of x values that define the expression is known as the domain. The collection of all legal y values constitutes the range. To determine the range, use the graph.

How are domain and range determined?

The Equation's Domain and Range in order to identify the values of the independent variable x and acquire the domain, we simply solve the equation y = f(x). Simply put, x=g(y) will calculate the function's range after we identify g's domain (y)

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The standard form of (5 times 10^3) x (9 times 10^7) is 45x10^10

(5 times 10^3) x (9 times 10^7)

=5x10^3 x 5x10^7

=5x9 x 10^(3+7)

=45x10^10

The answer can also be written in the Decimal Point format,

=4.5x10^11

This answer can be elaborated by using the Product of Powers rule of exponents. In this rule, we add exponents when multiplying powers with the same base.

Exponent = The number of multiplications by itself.  It is represented as written above and to the right of a number.

For example:

10^7, where 10 is the base and 7 is an exponent.

Product of Powers rule of Exponents:

a^b x a^c = a^(b+c)

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Answer:

c

Step-by-step explanation:

the product (multiply ) of y and 12 is 12y and 4 less than 12y is

12y - 4

Answer:

12y - 4.

Step-by-step explanation:

The product is 12y and we subtract 4 from it.

The values from the least to greatest is 160%, 1.8, 2.1, 220%, 16/5 .

In the question ,

it is given that

the values 9/4 , 160%, 1.8, 16/5 , 220%, and 2.1

to arrange the values , we first need to simplify all the values .

(i) the value 9/4 = 2.25

(ii) 160% = 160/100 = 1.60

(iii)the value 1.80

(iv) Simplifying 16/5 , we get 3.20

(v) Simplifying 220% = 220/100 = 2.20

(vi) the value 2.10

the least value is 1.60 which is 160%.

the greatest value is 3.20 which is 16/5 .

Therefore ,the values from the least to greatest is 160%,1.8,2.1,220%,16/5  .

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Answer:

z = 54

Step-by-step explanation:

The sum of all interior angles in a polygon is given by the formula :

(n-2) × 180  (Where n is the number of sides) .  

There are 5 sides so the sum of all interior angles will be :

(5-2) × 180 = 540°

So :

108 + 130 + 140 + 2z + z = 540

Simplify :

378 + 3z = 540

Subtract 378 from both sides :

3z = 540 - 378

3z = 162

Divide both sides by 3 :

z = 162 ÷ 3

z = 54

Hope this helped and have a good day

Answer:−2.9 and −1.1

Step-by-step explanation:

If the actual mean is 18 ounces, there is a 0.0003 chance that the sample mean was 18.2 ounces or more.

Given that 18 ounces are what Kellogg estimates to be the typical weight of a box of Frosted Flaked. The average weight of the 30 cartons they sampled was 18.2 ounces. According to past data, the filling procedure's standard deviation is 0.32 ounces.

Let Y be a box weights random variable.

μ = 18 ounces

SD = 0.32 ounces

The sample size and mean are provided as,

Sample size (n)  = 30

Sample mean (y) = 18.2

Y then follows roughly the standard deviation N(μ = 18, SD = 0.32)

Z score appears as:

[tex]z = \frac{\sqrt{n}(y-u)} {SD}[/tex]

where z is a normal standard variable having a mean of 0 and a standard deviation of 1.

Since sample size n is 30 and the standard deviation is given. y follows approximately Normal distribution

If the actual mean is 18 ounces, the likelihood that the sample mean will have been 18.2 ounces or more is given as,

[tex]P[Y \geq 18.2] = P [\frac{\sqrt{n(y - u)} }{SD} \geq \frac{\sqrt{30}(18.2- 18) }{0.32}\\ \\ =P [z\geq \frac{\sqrt{30}* 0.2 }{0.32}]\\ \\= P [z\geq \frac{1.0954}{0.32}]\\ \\=P [z\geq 3.4233]\\\\= 0.0003[/tex]

Therefore, if the actual mean is 18 ounces, there is a 0.0003 chance that the sample mean was 18.2 ounces or more.

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Answer:

48 orange marbles

Step-by-step explanation:

[tex] \frac{6}{5} = \frac{x}{40} [/tex]

[tex]5x = 240[/tex]

[tex]x = 48[/tex]

Answer:

its d i got it right

Step-by-step explanation:

Hey you man what are you doing here go to there

Answer:

answer is c

Step-by-step explanation:

5x+2=10

Answer:

Step-by-step explanation:

20

Answer: B

Step-by-step explanation:

Assuming we mean biconditional statements. A biconditional must always be true. B is the only answer choice were both p and q are true. A young cow is a calf, and calfs are cows. Hope this helps!