Group of 5 people can do a piece of work in 6hrs- Calculate the time a group of 8 people working half the rate of first group could take​

To simplify the equation, we have y = [tex]\frac{3}{4x^2 + 24x} + 8[/tex]

Given the expression

y-8 = 3/4x [x-(-6)]

First, expand the bracket

[tex]y - 8[/tex]= [tex]\frac{3}{4x^2 + 24x}[/tex]

Make 'y' the subject of formula

y = [tex]\frac{3}{4x^2 + 24x} + 8[/tex]

Thus, to simplify the equation, we have y = [tex]\frac{3}{4x^2 + 24x} + 8[/tex]

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Answer:

Step-by-step explanation:

Solution

17 = a + b

b =  a + 1                    Substitute b into the top equation

17 = a + a+1                Combine

17 = 2a + 1                  Subtract 1 from both sides

17-1 = 2a+1-1               Combine

16 = 2a                       Divide both sides by 2

16/2 = 2a/2

a = 8

b = 8 + 1 = 9

Answer

a = 8

b = 9

A percentage is a way to describe a part of a whole. The relative change from last year to this year is 3.7%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

28.6% of city employees ride the bus to work, therefore, the final value is 28.6. While Last year, 29.7% of city employees rode the bus to work, therefore, the initial value is 29.7.

Since relative change means change with respect to some value. Thus, the relative value with respect to last year is,

Relative value = (29.7-28.6)/29.7 = 0.037 = 3.7%

Hence, the relative change from last year to this year is 3.7%.

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Answer: 3/4

Step-by-step explanation:

Answer:

The area for the trapezoid is

A=h/2(a+b)

A=8/2(10+15)

A=100 cm square

Hope it helps!

Answer:

V = (s^3)/6  (Answer B )

Step-by-step explanation:

If the length of a side of the base is s, then the height of the pyramid is half that, or s/2.

The volume of a pyramid with a square base and base side length S and height H is V = (1/3)(S^2)(H).

In this case, the formula is V = (1/3)(s^2)(s/2), or V = (s^3)/6  (Answer B)

The function g(x) is obtained by the transformation of the function f(x) is translated towards left by 1 unit.

A statement, principle, or policy that creates the link between two variables is known as a function.

The function f(x) is given below.

f(x) = 2ˣ

Then the function g(x) is given as

[tex]\rm g(x) = 2^{x + 1}[/tex]

The function g(x) is obtained by the transformation of the function f(x) is translated towards left by 1 unit.

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Answer:

They could make at most 5 teams and its not possible to make everyone on team.

Step-by-step explanation:

If there are 4 players on a team, then we use 23 ÷ 4 = 5.75, 0.75 is not enough for 1, so there are 3 players remaining after making 5 teams.

Answer:

3.8918

round the 1 from the 8 to get 2

3.892

Using Chebyshev's Theorem, the minimum percentage of commuters in has a commute time within 2 standard deviations of the​ mean is of 75%.

When we have no information about the population distribution, Chebyshev's Theorem is used. It states that:

Hence, the minimum percentage of commuters in has a commute time within 2 standard deviations of the​ mean is of 75%.

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The weight of the chocolate frosting if it is 55% cocoa powder will be 272.25 grams.

The quantity of anything is stated as though it were a fraction of a hundred.

Mama bear wants to bake a cake with chocolate frosting for her twin's birthday party.

She uses a package containing 495 grams of cocoa powder for the frosting.

Then the weight of the chocolate frosting if it is 55% cocoa powder will be

⇒ 0.55 × 495

⇒ 272.25 grams

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The two types of transformations that can be used to transform f(x) to g(x).  g (x) = f(x) + 16 and g (x) = f(x + 8)

ABC has vertices at A (12, 8), B (4, 8)

f(x)= 0, -1 ,5,14

g(x)= -6, -1, -1, 14

g(x)=f(x)+k

-6= 0+k

k= -6

A) g (x) = f(x) + 16 and

g(x) = f(x + 8)

B) g(x)=f(x)+k

-1= -1+ k

k= -1+1=0

g(x)=f(x)+k

-1= 5+k

k= -1-5=-6

g(x)=f(x)+k

14= 14+k

k= 0

k= -6,0,-6,0

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Answer: 2

Step-by-step explanation:

[tex]a_{n}=2(2)^{n-1}\\\\a_{1}=2(2)^{1-1}=2\\\\a_{2}=2(2)^{2-1}=4[/tex]

Average rate of change:

[tex]\frac{4-2}{2-1}=\boxed{2}[/tex]

Answer:

length=22 [cm].

Step-by-step explanation:

1) if the length is 'l' and the width is 'w', then it is possible

2) to write the given perimeter: 62=2(l+w), - this is the 1st equation of system;

3) to write the condition 'the length of a rectangle is 5 cm less than 3 times its width' as 3w-5=l, - this is the 2d equation of the system.

4) using two equations above it is possible to make up the next system:

[tex]\left \{ {{2(w+l)=62} \atop {3w-5=l}} \right. \ = > \ \left \{ {{w+l=31} \atop {3w-l=5}} \right. \ = > \ \left \{ {{l=22} \atop {w=9}} \right.[/tex]

5) finally, the length=22 [cm].

Answer:

Two functions which satisfies the H(x) are f(x) = 2x - 4, (x)    = x⁵  and

f(x)  = 2x,  g(x)  = x⁵ - 2

Step-by-step explanation:

The given question is based on the decomposition of a given function into two functions

Decomposition of a function :- functional decomposition is the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed from those parts by function composition

so the function given in the question is H(x) = 2x⁵ - 4

now by using the concept of decomposition of a function we can find two functions f and g

therefore,

f(x) = 2x - 4

and    g(x)    = x⁵

similarly we can find another pair which satisfies the function H(x)

f(x)  = 2x

and g(x)  = x⁵ - 2

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Answer:

its $95 dollars

Step-by-step explanation:

Answer:

A = { x:x >3 ,where x --> R}

B = { x:x <4, where x --> R}

Y = { x:x is month of year with more than 30 days}

W = { x:x is all days of a week}

Answer:

a)  initial height = 0 m

b)  8 s

c)  vertex = (4, 32)

    maximum height = 32 m

Step-by-step explanation:

Given equation:

[tex]h=-2t^2+16t[/tex]

where:

The initial height of the arrow will be at the beginning of its journey, so when t = 0

Substitute t = 0 into the equation and solve for h:

[tex]\implies h=-2(0)^2+16(0)[/tex]

[tex]\implies h=0[/tex]

Therefore, the initial height of the arrow is 0 m.

The arrow will hit the ground when the height is 0 m.

Substitute h = 0 into the given equation:

[tex]\implies -2t^2+16t=0[/tex]

Factor out -2t:

[tex]\implies -2t(t-8)=0[/tex]

Therefore:

[tex]\implies -2t=0 \implies t=0[/tex]

And:

[tex]\implies t-8=0 \implies t=8[/tex]

Therefore, the arrow will hit the ground at 8 seconds.

The vertex is the turning point of a parabola - it's minimum or maximum point.

As the leading coefficient for the given equation is negative, the parabola opens downwards and so its vertex is its maximum point.

There are different ways to find the vertex of a parabola. The easiest way to find the x-coordinate is by calculating the midpoint of the x-intercepts.

We have determined that the arrow has a height of 0 m at 0 seconds and 8 seconds.  Therefore, t = 0 and t = 8 are the x-intercepts.  The midpoint is halfway between zero and 8, so the midpoint is t = 4

To find the y-coordinate, substitute t = 4 into the equation and solve for h:

[tex]\implies h=-2(4)^2+16(4)[/tex]

[tex]\implies h=-32+64[/tex]

[tex]\implies h=32[/tex]

Therefore, the coordinates of the vertex are (4, 32)

The maximum height is the y-coordinate of the vertex.

Therefore, the maximum height is 32 m

Answer: 72

Step-by-step explanation:

[tex]\sum^{3}_{t=0} (6t^{2}-3)=(6(0)^{2}-3)+(6(1)^{2}-3)+(6(2)^{2}-3)+(6(3)^{2}-3)=\boxed{72}[/tex]

Answer:

51° and 39°

Step-by-step explanation:

x + 4x - 165 = 90

5x = 90 + 165

5x = 255

x = 255 / 5

x = 51

4 x 51 = 204

204 - 165 = 39

2 angles are 51 and 39

Answer: The graph crosses the x-axis at x = 2.

Step-by-step explanation:

The root has a multiplicity of 3, meaning that it crosses the x axis at x=2.

The ranges of batting averages were least common among the players is 0.320-0.329 and 0.360-0.369 , Option D is the correct answer.

Average is the middle value of a set of data points , calculated by summing all the data points and then dividing by the number of points.

It is given that , 30 best batting averages for a semi-pro baseball league.

The ranges of batting averages were least common among the players

To find this , it has to be observed that which range has the lowest frequency

The range 0.320-0.329 and 0.360-0.369 has frequency of 1 which is the least among all

Hence Option D is the correct answer.

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The degree of dispersion in your data collection is indicated by variance.
It is given by the formula:
[tex]\overline{d}= \sum_{i=1}^{i=n}\frac{|x_i-\overline{x}|^2}{n}[/tex]

To determine the values of a certain set of scattered data, the standard deviation formula is utilized. The dispersion of the quantities or data from the mean is how the standard deviation is simply defined. The conclusion drawn from a lower standard deviation is that the results are fairly near to the average. Higher values, on the other hand, indicate a significant dispersion from the mean. The standard deviation number can never be negative, it should be positive.

It is given by the formula:

[tex]s_d = \sqrt{\sum_{i=1}^{i=n}\frac{|x_i-\overline{x}|^2}{n}} =\sqrt{\overline{d}}[/tex]

We have that the mean of the values is:  

at 8 AM [tex]\overline{x}=\frac{97.9+99.3+97.9+97.6+97.4}{5}=98.02[/tex]

at 12 AM [tex]\overline{x}=\frac{98.5+99.7+98+97.4+97.6}{5}=98.24[/tex]

Using the above definitions we have that

at 8 AM [tex]\overline{d}=\frac{(98.02-97.9)^2+(98.02-99.3)^2+(98.02-97.9)^2+(98.02-97.6)^2+(98.02-97.4)^2}{5}=0.4456[/tex]

[tex]s_d=\sqrt{\overline{d}}=\sqrt{0.4456}=0.6675[/tex]

at 12 AM

[tex]\overline{d}=\frac{(98.24-98.5)^2+(98.24-99.7)^2+(98.24-98)^2+(98.24-97.4)^2+(98.24-97.6)^2}{5}=0.6744[/tex]

[tex]s_d=\sqrt{\overline{d}}=\sqrt{0.6744}=0.8212[/tex]

In general, [tex]\mu_d[/tex] represents the mean of the differences from the population of matched data.

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For the function F(x)=[tex]a(x+k)^{1/n}+C[/tex] the value of a is less than zero and the correct option is option d.

Given the value of function  F(x)=[tex]a(x+k)^{1/n}+C[/tex].

We have to put the function equal to 0 for finding the nature of a and C is a fixed number in the function :

a[tex](x+k)^{1/n}[/tex]+C=0

a[tex](x+k)^{1/n}[/tex]=-C

a=-C/[tex](x+k)^{1/n}[/tex]

Since negative sign is coming before a and the value of rest of the expression cannot be negative so the value of a should b negative which means less than 0. The rest of the expression cannot be negative because it has a power of 1/n which only gives positive values like modulas.

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The graph of the parent absolute value function decreases over Option B(–∞, 0) interval.

An absolute value function is defined as a function that contains an algebraic expression within absolute value symbols.

The absolute value function is f(x) = |x| is defined as,

f(x )

x = x < x = 0 < x = -x

Observe that the graph is V-shaped.

The vertex of the graph is (0,0).

The domain is the set of all real numbers.

The x-intercept and the y-intercept are both 0.

Hence, The graph of the parent absolute value function decreases over Option B(–∞, 0) interval.

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Answer:

1.6

Step-by-step explanation:

4,4-2.8 = 1.6

6-4.4 = 1.6

7.6-6 = 1.6

Then common difference is 1.6