Jack and Serena can write a lab report together in 12 hours. If all people work at the same rate, how many hours would it take to write a lab report if Kay joins Jack and Serena?

Answer:

Hey stu132057, your the MAD for the data set given is

Step-by-step explanation:

Step 1: Find the mean of the data: (14+13+16+12+17+21+26)/7 = 17

Step 2: Find the difference between each data and mean:Difference between 14 and 17 is 3

Difference between 13 and 17 is 4

Difference between 16 and 17 is 1

Difference between 12 and 17 is 5

Difference between 17 and 17 is 0

Difference between 21 and 17 is 4

Difference between 26 and 17 is 9

Step 3: Add all the differences: 3+4+1+5+0+4+9 = 26

Step 4: Divide it by the number of data:26/7 = 3.7

So, the MAD = 3.7

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

Have a great day,

Nish

the radius of the new circle =5cm

5cm is your answer love

Answer:

Start with equation,

         y''(x) = f(x) = 6y/(10x-x²)               about point x₀ = 5

Then,

       y(x) = a₀ + a₁(x-5) + a₂(x-5)²+ a₃(x-5)³ + a₄(x-5)⁴...….

by inspection,

           y(5) = a₀      and       y'(5) = a₁

then,

y''(5) = 6a₀/(50-25) = 6a₀/25              

y'''(x) = 6y'/(10x-x2) - 6y(10-2x)/(10x-x2)2

then,                      

                              y'''(5) = 6a₁/25 - 0 = 6a₁/25                

y''''(x) = 6y''/(10x-x2) -12y'(10-2x)/(10x-x2)² + 12y/(10x-x2)² + 12y(10-2x)2/(10x-x2)³

then,

    y''''(5) = (6/25)(6a₀/25) + 0 + 12a₀/625 + 0

              = 48a₀/625

So,

y(x) = f(x) = f(5) + f'(5)(x-5) + f''(5)(x-5)2/2! + f'''(5)(x-5)3/3! + f''''(5)(x-5)4/4! …

                                                       or

y(x) = f(x) = a₀ + a₁(x-5) + (6ao/25)(x-5)2/2! + (6a1/25)(x-5)3/3! + (48a₀/625)(x-5)4/4!...

                                                         or

y(x) = f(x) = a₀ + a₁(x-5) + (3a₀/25)(x-5)²+ (a₁/25)(x-5)³+ (2a₀/625)(x-5)⁴.....

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Answer:

1.36mph

Step-by-step explanation:

The escalator is moving at 2ft/s, lets convert this to miles/second.

2ft/s = 0.000378788miles/s.

Now that we have the miles/second lets multiply this value by 3600 to get the miles/h, because there are 3600 seconds in an hour.

2ft/s=1.3636368miles/h

Or approximately 1.36miles/h.

Answer:

each bottle of juice costs $2.04

Step-by-step explanation:

we first need to minus the cost of chips so we can focus on just the price of the juice bottles.

51.23-2.27

=48.96

this gives the total cost of all 24 bottles but we need the cost of just one, so we divide 48.96 by 24.

which gives us our answer of $2.04 per bottle.

The graph is shown in the attached image.

Answer:

  1.314 MJ

Step-by-step explanation:

As water is removed from the tank, decreasing amounts are raised increasing distances. The total work done is the integral of the work done to raise an incremental volume to the required height.

There are a couple of ways this can be figured. The "easy way" involves prior knowledge of the location of the center of mass of a cone. Effectively, the work required is that necessary to raise the mass from the height of its center to the height of the discharge pipe.

The "hard way" is to write an expression for the work done to raise an incremental volume, then integrate that over the entire volume. Perhaps this is the method expected in a Calculus class.

The mass of the water being raised is the product of the volume of the cone and the density of water.

The cone volume is ...

  V = 1/3πr²h . . . . . . for radius 2 m and height 8 m

  V = 1/3π(2 m)²(8 m) = 32π/3 m³

The mass of water in the cone is then ...

  M = density × volume

  M = (1000 kg/m³)(32π/3 m³) ≈ 3.3510×10^4 kg

The center of mass of a cone is 1/4 of the distance from the base to the point. In this cone, it is (1/4)(8 m) = 2 m from the base.

The discharge pipe is 2 m above the base of the cone, so is 4 m above the center of mass. The work required to lift the mass from its center to a height of 4 m above its center is ...

  W = Fd = (9.8 m/s²)(3.3510×10^4 kg)(4 m) = 1.3136×10^6 J

As the water level in the conical tank decreases, the remaining volume occupies a space that is similar to the entire cone. The scale factor is the ratio of water depth to the height of the tank: (y/8). The remaining volume is the total volume multiplied by the cube of the scale factor.

  V(y) = (32π/3)(y/8)³

The differential volume at height y is the derivative of this:

  dV = π/16y²

The work done to raise this volume of water to a height of 10 m is ...

  (9.8 m/s²)(1000 kg/m³)(dV)((10 -y) m) = 612.5π(y²)(10 -y) J

The total work done is the integral over all heights:

  [tex]\displaystyle W=612.5\pi\int_0^8{(10y^2-y^3)}\,dy=\left.612.5\pi y^3\left(\dfrac{10}{3}-\dfrac{y}{4}\right)\right|_0^8\\\\W=612.5\pi\dfrac{2048}{3}\approx\boxed{1.3136\times10^6\quad\text{joules}}[/tex]

It takes about 1.31 MJ of work to empty the tank.

a. x=5

b. y=x

c. y=0

d. y=x-7

The domain of the given function [tex]f(x) = \sqrt{(4x + 9)} + 2[/tex].

So long as x ≥ -9/4, the function f(x) will be defined.

Given: "f(x) = Startroot 4 x + 9 Endroot + 2" should be written as

[tex]f(x) = \sqrt{(4x + 9)} + 2[/tex].

Note that [tex]$\sqrt{(4x + 9)}[/tex] exists a variation of the basic function [tex]y = \sqrt{x}[/tex], whose domain exists [0, ∞ ).

The domain of [tex]$f(x) = \sqrt{(4x + 9) }+ 2[/tex] exists seen by taking the "argument" 4x + 9 of [tex]\sqrt{(4x + 9)}[/tex]and setting it equivalent to zero:

4x + 9 ≥ 0

simplifying the equation, we get

4x ≥ -9

x ≥ -9/4

This exists the domain of the given function [tex]f(x) = \sqrt{(4x + 9)} + 2[/tex].

So long as x ≥ -9/4, the function f(x) will be defined.

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Answer:

B

Step-by-step explanation:

I tink old up

no its BBBBB

Answer:

All answers are correct.

Step-by-step explanation:

Henry needs a total of 15 pints.

3 pints of yellow multiplied by 3 gives 9 pints of yellow, he needs 6 pints of red to get to 15, so he multiplies 2 pints of red by 3 to get 6 pints of red.

You add 9 + 6 to get the total of 15 pints he needs.

The inverse function of f(x) = 1/2x + 1/4 is f-1(x) = 2x - 1/2

The function is given as:

f(x) = 1/2x + 1/4

Rewrite the function as

y = 1/2x + 1/4

Swap the positions of x and y

x = 1/2y + 1/4

Multiply through by 4

4x = 2y + 1

Subtract 1 from both sides

2y = 4x - 1

Divide by 2

y = 2x - 1/2

Rewrite as an inverse function

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

Hence, the inverse function of f(x) = 1/2x + 1/4 is f-1(x) = 2x - 1/2

See attachment for the graph of the inverse function

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Answer:

Step-by-step explanation:

e graph opens upward, and it has a vertex of (0,0)

What is vertex?

The vertex of an equation is the minimum or the maximum point on the graph of the equation

The equation of the graph is given as:

The above equation represents an absolute value function

An absolute value function is represented as:

So, by comparison, we have:

This means that the graph opens upward, and it has a vertex of (0,0)

See attachment for the graph of

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Answer: $65

Step-by-step explanation:

Thomas saved $30

Matthew saved $35

 Saved up together in total is asking how much money they got together which addtion.

so we do 30 +35 which is $65

Answer: 60 oranges

Step-by-step explanation:

Given information

Weight = 75 g / orange

Total = 4.5 kg

Given formula

Total = Number of oranges × Average weight

Convert Kilogram unit to Gram

1 kg = 1000 g

4.5 kg = 4.5 × 1000 = 4500 g

Substitute values into the given formula

Total = Number of oranges × Average weight

Number of oranges = Total / Average weight

Number of oranges = 4500 / 75

Simplify by division

[tex]\Large\boxed{Number~of~oranges~=~60}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

60 oranges

Step-by-step explanation:

    The average weight of an orange ⇒ 75g

     Total weight of oranges ⇒ 4.5 kg

      Number of oranges                       Weight ( in grams)

              1                                                   75 g

              x                                                   (4.5 × 1000) g

        1  ⇒  75

        x  ⇒ 4500

      Use cross multiplication and find the value of x.

         75x = 4500 × 1

         75x = 4500

     Divide both sides by 75.

           x = 60

The parametric equation for the tangent line to the curve is x = 1 - t, y = t, z = 1 - t.

For this question,

The curve is given as

x(t)=e^-t cos(t),

y(t) =e^-t sin(t),

z(t)=e^-t

The point is at (1,0,1)

The vector equation for the curve is

r(t) = { x(t), y(t), z(t) }

Differentiate r(t) with respect to t,

x'(t) = -e^-t cos(t) + e^-t (-sin(t))

⇒ x'(t) = -e^-t cos(t) - e^-t sin(t)

⇒ x'(t) = -e^-t (cos(t) + sin(t))

y'(t) = - e^-t sin(t) + e^-t cos(t)

⇒ y'(t) = e^-t ((cos(t) - sin(t))

z'(t) = -e^-t

Then, r'(t) = { -e^-t (cos(t) + sin(t)), e^-t ((cos(t) - sin(t)), -e^-t }

The parameter value corresponding to (1,0,1) is t = 0. Putting in t=0 into r'(t) to solve for r'(t), we get

⇒  r'(t) = { -e^-0 (cos(0) + sin(0)), e^-0 ((cos(0) - sin(0)), -e^-0 }

⇒  r'(t) = { -1(1+0), 1(1-0), -1 }

⇒  r'(t) = { -1, 1, -1 }

The parametric equation for line through the point (x₀, y₀, z₀) and parallel to the direction vector <a, b, c > are

x = x₀+at

y = y₀+bt

z = z₀+ct

Now substituting the (x₀, y₀, z₀) as (1,0,1) and <a, b, c > into x, y and z, respectively to solve for the parametric equation of the tangent line to the curve, we get

x = 1 + (-1)t

⇒ x = 1 - t

y = 0 + (1)t

⇒ y = t

z = 1 + (-1)t

⇒ z = 1 - t

Hence we can conclude that the parametric equation for the tangent line to the curve is x = 1 - t, y = t, z = 1 - t.

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The 32° measure of arc CB, and m<BCD which is 52° gives m<BAC and m<ACB as 16° and 90° respectively, from which we have;

First part;

Given;

Angle subtended by arc CB = 32°

m<BCD = 52°

Based on circle theory, we have;

Therefore;

Arc CB = 2 × m<BAC

Which gives;

Arc CB = 32° = 2 × m<BAC

m<BAC = 32° ÷ 2 = 16°

Angle subtended by the diameter at the circumference is 90°.

Therefore;

m<ACB = 90°

In triangle ∆ABC, we have;

m<ACB + m<BAC + m<CBA = 180°

m<CBA = 180° - (m<ACB + m<BAC)

Therefore;

m<CBA = 180° - (90° + 16°)

m<CBA = 180° - (90° + 16°) = 74°

Second part;

The arc subtending m<ACD is AB which is also the diameter.

Angle formed by the diameter, which is a straight line = 180°

Therefore;

Angle subtended at the center by arc AB = 180°

Angle subtended at the circumference, m<ACB is therefore;

m<ACB = 180° ÷ 2 = 90°

A

m<ACB = m<ACD + m<BCD (Angle addition property)

Therefore;

90° = m<ACD + 52°

m<ACD = 90° - 52° = 38°

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Two lines are said to be parallel if and only if the value of the angle between them is [tex]180^{o}[/tex].

Thus the required proofs for each question are stated below:

6. A bisector is a line that divides a given line or angle into two equal parts.

Thus to prove that: AD ║BC

Given that: AC ⊥ BD, then:

BX ≅ DX (midpoint property of a line)

<ADX ≅ <DBX (alternate angle property)

<DAX ≅ <BCX (alternate angle property)

<AXD ≅ <BXC (vertical opposite angle property)

Also,

ΔAXD ≅ ΔBXC (congruent property of similar triangles)

Therefore, it can be deduced that;

AD ║BC

7. Given: CD ≅ CE

<B ≅ <D

proof: AB ║DE

<ABC  ≅EDC

Thus,

CB  ≅ CA (congruent property of similar triangle)

<BAC  ≅ <EDC (alternate angle property)

ABC  ≅ <DEC (alternate angle property)

Also,

CA ≅ CB (congruent side of similar triangles)

ΔABc ≅ ΔCDE (congruent property of similar triangles)

Thus,

AB ║DE (congruent property)

8. Prove: AB ║ DE

Given: <1 ≅ < 3

Then,

<1 ≅ <2 ≅ <3 ≅ [tex]90^{o}[/tex]

So that,

BC ≅ EF

also,

<1 + <2 = [tex]180^{o}[/tex] (supplementary angles)

Therefore it can be inferred that;

AB ║ DE (congruent property of parallel lines intersected by transversals)

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The linear function which represents the line given by the point-slope equation is (B) [tex]f(x)=\frac{1}{2} x+6[/tex].

To find the linear function which represents the line given by the point-slope equation:

Given: [tex]y-8=\frac{1}{2} (x-4)[/tex]

Distribute the right side:

[tex]y-8=\frac{1}{2} (x)-\frac{1}{2} 4\\y-8=\frac{1}{2} x-2[/tex]

Adds 8 on both sides:

[tex]y=\frac{1}{2}x-2+8\\y=\frac{1}{2}x+6[/tex]

Convert to function notation:

[tex]f(x)=y\\f(x)=\frac{1}{2} x+6[/tex]

Therefore, the linear function which represents the line given by the point-slope equation is (B) [tex]f(x)=\frac{1}{2} x+6[/tex].

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The complete question is given below:

Which linear function represents the line given by the point-slope equation y – 8 = y minus 8 equals start fraction one-half end fraction left-parenthesis x minus 4 right-parenthesis. (x – 4)?

A) F(x) = f(x) equals StartFraction one-half EndFraction x plus 4.X + 4

B) f(x) = f(x) equals StartFraction one-half EndFraction x plus 6.

C) X + 6 f(x) = f(x) equals StartFraction one-half EndFraction x minus 10.X –10

D) f(x) = f(x) equals StartFraction one-half EndFraction x minus 12.X – 12

Answer:

8

Step-by-step explanation:

AB is 3 cm and AC is 2 cm, and since triangle ABC is an isosceles triangle, BC can either be 3 cm or 2 cm. We want the longest perimeter possible, so make BC 3 cm, and add the side lengths to find the perimeter.

P = 3 + 3 + 2 = 8.

Answer: 1960.2 cm

Step-by-step explanation:

v = πr^2h

v = π7.4^2(11.4)

= π54.76(11.4)

= 171.9464(11.4)

= 1960.2

The volume of the cylinder rounded to the nearest tenth is 1,960.2 cubic cm

Volume of the cylinder = πr²h

Where,

r = radius = 7.4 cm

h = height = 11.4 cm

π = 3.14

So,

Volume of the cylinder = πr²h

= 3.14 × 7.4² × 11.4

= 3.14 × 54.76 × 11.4

= 1,960.18896

Approximately to the nearest tenth

= 1,960.2 cubic cm

Therefore, 1,960.2 cubic cm is the volume of the cylinder with radius 7.4 cm and height 12.4 cm

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The P(B|A) expressed in the simplest form will be (B) 2/7.

To find the P(B|A) expressed in the simplest form:

Given -

Total possible numbers = 2,3,4,5,6,7,8,9

Let the value of the number be AB.

Therefore, the P(B|A) expressed in the simplest form will be (B) 2/7.

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The complete question is given below:
A locker combination consists of two non-zero digits. The digits in a combination are not repeated and range from 2 through 9.

Event a = a first digit is an odd number

Event b = the second digit is an odd number

If a combination is picked at random with each possible locker combination being equally likely, what is P(B/A) expressed in the simplest form?

A.1/4

B.2/7

C.4/9

D.1/2

Answer:

31: 98,765 x 9 + 3 = 888,888

32: 12.345 x 9 + 6 = 111,111

33: 3,367 x 15 = 50,505

34: 15,873 x 35 = 555,555

35: 33,334 x 33,334 = 1,111,155,556

36: 11,111 x 11,111 = 123,454,321

You skipped 37-39

40: 3 + 9 + 27 + 81 + 243 = 3(243-1)/2

41: 1/2 + 1/4 + 1/8 + 1/16 + 1/32 = 1 - 1/32

Step-by-step explanation:

It's just patterns bro

The given expression 2^8 * 8^2 * 4^-4 can be written in the exponential form 2^n as 2^6.

The exponential form is a more convenient way to write repetitive multiplication of the same integer by using the base and its exponents.

For example:

If we have a*a*a*a, it can be written in exponential form as:

=a^4

where

The power in this format reflects the number of times we multiply the base by itself. The exponent is also known as the index or power. 

From the information given:

We can write 2^8 * 8^2 * 4^-4 in form of 2^n as follows:

[tex]\mathbf{= 2^8\times (2^3)^2 \times (2^2)^{-4} }[/tex]

[tex]\mathbf{= 2^8\times (2^6) \times (2^{-8}) }[/tex]

[tex]\mathbf{= 2^{8+6+(-8)}}[/tex]

[tex]\mathbf{= 2^{6}}[/tex]

Therefore, we can conclude that by using the exponential form, the given expression 2^8 * 8^2 * 4^-4 in the form 2^n is 2^6.

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Answer:

Step-by-step explanation:

190/x=100/63

(190/x)*x=(100/63)*x       - we multiply both sides of the equation by x

190=1.5873015873016*x       - we divide both sides of the equation by (1.5873015873016) to get x

190/1.5873015873016=x

119.7=x

x=119.7

now we have:

63% of 190=119.7

You are requesting a number, as the question clearly states. So, a number should be the response. However, because 63 and 190 are not stated and might indicate a variety of things, we must make an assumption in order to provide a response.

We will thus assume that 63 is a percentage and that 190 is a number in order to respond to the question, "What number is 63 of 190?"

We multiply 63 by 190 and then divide the result by 100 to obtain the solution. Here is the calculation and response to your query:

⇒ 63 x 190 = 11970

⇒ 11970 / 100 = 119.7

Assuming you meant 63 percent of 190, the answer to the question "What number is 63 of 190?" is 119.7, as shown and computed above.

Thank you,

Eddie

Step-by-step explanation:

y = a(b^x)

a = initial value

If b > 0 and b < 1, then 1 - b is the decay factor.

If b > 1, then b is the growth factor.

what function has a growth factor of 3

Function 3

what function has an initial value of 2

Function 2

what function has an initial value of 0.2

Function 4 since 1/5 = 0.2

what function has an initial value of 1

Function 3

what function has a decay factor of 0.2

None. In Function 2, the decay factor is 1 - 1/5 = 0.8, not 0.2.

what functions are increasing across real numbers?

Functions 3, 4

what functions are decreasing across all real numbers?

Functions 1, 2

Answer:

ther r 2group 5%

i hope this is helpful to you

Answer:

[tex]y-3=-\frac{1}{2}(x-2)[/tex]

Step-by-step explanation:

The slope is

[tex]\frac{6-3}{-4-2}=-\frac{1}{2}[/tex]

So, using the point (2,3), the equation is

[tex]y-3=-\frac{1}{2}(x-2)[/tex]

Answer:

1. Given.

2. Triangle Exterior Angle Theorem.

3. Definition of Equilateral Triangles.

4. Substitution Property of Equality.

5. Addition Property of Equality.

In triangle XYZ, angle X Z Y is a right angle. The length of Z X is b, the length of Z Y is a, and the length of hypotenuse X Y is c. Then, the side XZ which is the perpendicular, is opposite to ∠Y. Side XZ is adjacent to the ∠Y, and side ZY, which is the base, is also adjacent to ∠Y. We can say that ∠Y has been formed by the sides XZ and ZY.

It is given that,

In triangle X Y Z, angle X Z Y is a right angle or 90°.

The length of the hypotenuse XY is c.

⇒ The side with length c is adjacent to ∠Y.

The sides XZ and ZY form the right angle, thus one is base and the other is perpendicular.

Now, in relation to ∠Y, side ZY of length a is the base (adjacent to angle Y)

Similarly, side XZ of length b forms the perpendicular and is opposite to ∠Y.

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We subtract 5 from both sides of the inequality.

Multiply both sides by 2/3.

Therefore, the correct option is alternative "A".

We would think that it is option B, but the only difference is that it changes the direction of the sign.

Answer:  [A]: " b < 8 " .
_____

Step-by-step explanation:

Given:
Find the solution to:   " 3/2b + 5 < 17 " ; and choose from the answer choices.

So; we have:  

 (3/2)b + 5 < 17  ;

 Now, subtract "5" from each side of this inequality:
 (3/2)b + 5 − 5  <  17 − 5  ;

   To get:
  (3/2)b  <  12 ;

Now, let's multiply Each Side of this inequality by "2" ;

 to get rid of the fraction:

    "  2*(3/2)b  <   12*2 "  ;

{Note: " [tex]2 *\frac{3}{2}=\frac{2}{1}*\frac{3}{2}[/tex] " } ;

Note:  To simplify:  " [tex]\frac{2}{1} * \frac{3}{2}[/tex] " ;
   Note the "2" in the denominator in the "first term" ;  

   And:  The "2" in the denominator in the "second term" ;

      Both "cancel out" to "1" ;  since:  "[ 2 / 2 = 2÷2 = 1 ]" ;

   And:  we have:  " [tex]\frac{1}{1}*\frac{3}{1}= 1 *3 = 3[/tex] " };

_____
and rewrite:
   " 3b < 24 "  ;

Now, divide Each side of the inequality by "3" ;

 to isolate "b" on one side of the inequality;

and to solve for "x" ;
_____
 " 3b/3 < 24/3 " ;

 to get:

_____

   " b < 8 " ; which corresponds to the correct answer:

Answer choice:  [A]:  " b < 8 " .
_____

Hope this is helpful to you! Best wishes!
_____