A manager drew this box-and-whisker plot to represent the ages of the company's 240 employees.

Box-and-whisker plot ranging from 34 to 58 with ticks at increments of 1. Plot defined by points at 35, 42, 49, 54, 57.

How many employees are younger than 42?

Select from the drop-down menu to correctly complete the statement.

About
Choose... 24,48,60,75
employees are younger than 42.

Given :

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Now , x = a ( θ + sin θ )

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Now y = a ( 1-cosθ)

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Diff w.r.t " θ " we get .

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From eqn ( 1 ) & ( 2 )

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Hope Helps!:)

Answer:

13. True, False, True

14. False, True, True

15. All true

[tex]\textit{volume of a hemisphere}\\\\ V=\cfrac{1}{2}\cdot \cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=74466 \end{cases}\implies 74466=\cfrac{1}{2}\cdot \cfrac{4\pi r^3}{3} \\\\\\ 74466=\cfrac{2\pi r^3}{3}\implies 223398=2\pi r^3\implies \cfrac{22398}{2\pi }=r^3\implies \cfrac{111699}{\pi }=r^3 \\\\\\ \sqrt[3]{\cfrac{111699}{\pi }}=r~\hfill \stackrel{\textit{diameter = 2r}}{2\sqrt[3]{\cfrac{111699}{\pi }}\implies \sqrt[3]{\cfrac{893592}{\pi }}}~~ \boxed{\approx~~65.77}[/tex]

Answer:

  5 m

Step-by-step explanation:

The length of the side of a square is the root of the area of the square. The area of this square is the difference between the trapezoid area and the triangle area.

__

  square area = trapezoid area - triangle area

  square area = 57.5 m² -32.5 m² = 25 m²

Then the side length is ...

  side length = √(square area) = √(25 m²)

  side length = 5 m

The length of a side of the square is 5 m.

Answer:

(0,6) to (4,10) it might be the answer..........

The equation of the line passing through the points (0, 6) and (4, 10) is y = x + 6.

Here, we have,

To find the equation of the line passing through the points (0, 6) and (4, 10), we can use the slope-intercept form of a linear equation, which is given by:

y = mx + b,

where m is the slope of the line, and b is the y-intercept.

First, let's calculate the slope (m) using the formula:

m = (y₂ - y₁) / (x₂ - x₁),

where (x₁, y₁) = (0, 6) and (x₂, y₂) = (4, 10).

m = (10 - 6) / (4 - 0) = 4 / 4 = 1.

Now that we have the slope (m = 1), we can substitute it into the slope-intercept form along with one of the given points to find the y-intercept (b).

Using the point (0, 6), we have:

6 = 1(0) + b,

b = 6.

Therefore, the y-intercept (b) is 6.

Now we can write the equation of the line using the slope-intercept form:

y = mx + b,

y = 1x + 6,

y = x + 6.

Hence, the equation of the line passing through the points (0, 6) and (4, 10) is y = x + 6.

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Answer:

x=4, perimeter is 30.

Step-by-step explanation:

Let's calcualte the perimeter of the two figures. I'm assuming the pentagon is regular else the problem lacks information.

[tex]5(x+2) = 3x+(2x-1)+(x+7)\\5x+10=6x+6\\4=x[/tex]

At this point the easiest to compute is the pentagon, one side is 6, the whole perimeter is 30.

Answer:

x=-1/7

Step-by-step explanation:

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

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

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

[tex]\frac{3x^2-10x+1}{3x-3} =x[/tex]

[tex]\frac{3x^2-10x+1}{3x-3} =\frac{x(3x-3)}{3x-3}[/tex]

[tex]\frac{3x^2-10x+1}{3x-3} =\frac{3x^2-3x}{3x-3}[/tex]

[tex]3x^2-10x+1=3x^2-3x[/tex]

[tex]-10x+1=-3x[/tex]

[tex]-7x=1[/tex]

[tex]x=-1/7[/tex]

22 + 22 x r = 30

22 x r = 30 - 22

r = 8 : 22

r = +36,36%

r = increase rate

Answer:

Step-by-step explanation:

Refer to the definition of a function. I'll just give you a layman's definition to be concise.

For something to be a function, there needs to be exactly 1 output for every input. You cannot have a case where you input 1 value, and get 2 or more values as an output.

In math we call all the possible input values the domain, and we call all the possible output values the range.

Let's take a look at each situation on your worksheet.

1. Is a function. This is because only one arrow stems from each input value. There are cases where the different input values give the same output, sure, but each input returns 1 discrete thing, not an array of things.

(Think of it this way, if i had a machine that could answer any question I had with yes, no or maybe. I wouldn't want the machine to give me "yes and maybe" or "yes and no" as the result when I ask it a question. That doesn't make sense and I would think the machine is broken. What could happen, is that I ask the machine different questions, and for those different questions, it gave me the same answer, like "yes" and "yes" respectively. in that case, it would be acceptable, because it isn't contradicting itself for any individual question.)

2. Not a function. There are 2 different output values for b.

(Refer back to my machine analogy. The "machine" in this question is contradicting itself. I gave the machine one input, and the machine is telling me, "it's this and actually it's this other thing too")

3. Is a function for the same reasons as 1.

4. Isn't a function.

(It's basically telling you, the machine reads -6 as -4, but it also reads -6 as 0, and also 2. And it also tells you the machine reads -4 as -3, but it also reads it as 8. Again, the machine should only read 1 input in 1 way and not contradict itself. )

Answer:

He did not put the numbers in order.

Explanation:

The numbers need to be in order from smallest to largest before you find the median.

Answer:

4

Step-by-step explanation:

By the triangle midsegment theorem, 2(WY)=VZ.

So, 2(7s)=s+52, meaning s=4.

Answer:

13x + 14

Step-by-step explanation:

5x + 6 + 3x = 8x + 6.

8x + 6 + x + 1 + x + 1 + 2= 10x + 10

10x + 10 + (2²)(i think) = 10x + 14

10x + 14 + 3x = 13x + 14

final answer

Answer:

[tex]13x+14[/tex]

Step-by-step explanation:

First take all the sides and add:

[tex]5x+6+3x+3x+2+2+2+x+1+x+1[/tex]

Then Combine Like terms:

[tex]5x+3x+3x+x+x+6+2+2+2+1+1[/tex]

There is your answer:

[tex]13x+14[/tex]

(If I misunderstood the handwriting, please tell me, and I will fix my mistakes)

Answer:

Step-by-step explanation:

4x + y = 2

y = -4x + 2

Answer:

Step-by-step explanation:

<A and <B are alternate interior angles. That means they are in the interior of the parallel lines and they are on opposite sides of the transversal.

When that happens <A = <B

8x + 78 = 2x + 114                      Subtract 2x from both sides.

8x - 2x + 78 = 2x - 2x + 114       Combine

6x + 78 = 114                              Subtract 78 from both sides

6x + 78 - 78 = 114 - 78

6x = 36                                       Divide by 6

6x/6 = 36/6

x = 6

I think you are asked for B

<B = 2x + 114

<B = 2*6 + 114

<B = 12 + 114

<B = 126

Answer:

5(7b+3c-2)

Step-by-step explanation:

Common factor of 5

35b/5= 7b
15c/5= 3c
-10/5= -2

Take the common factor and multiply it by the quotients
5(7b+3c-2)

Answer:

[tex]\boxed{33.5 \ \text{feet/second}}[/tex]

Step-by-step explanation:

To find the unit rate, we need to find out how much distance does the cyclist travel in 1 second. For that, we need to use the unitary method. A unitary method is a method that determines the unit rate of an object.

Note: Since the cyclist travels at a constant rate, unitary method can be used.

[tex]\rightarrow 837 \dfrac{1}{2} \ \text{feet in 25 seconds}[/tex]

[tex]\rightarrow 837.5 \ \text{feet} = 25 \ \text{seconds}[/tex]

Divide both sides by 25:

[tex]\rightarrow \dfrac{837.5}{25} \ \text{feet} = \dfrac{25}{25} \ \text{seconds}[/tex]

[tex]\rightarrow 33.5 \ \text{feet} = 1 \ \text{seconds}[/tex]

[tex]\rightarrow \boxed{33.5 \ \text{feet/second}}[/tex]

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Answer:

B - 2093 in cubed

Step-by-step explanation:

Use the formula 4/3 * pi * r^3 to find the volume of one basketball, using 5 as the radius. Next, multiply this number by 4 to find the volume of 4 basketballs. The answer should be option B.

Hopefully this helps- let me know if you have any questions!

Answer:V≈268.08

Step-by-step explanation:Volume of a sphere: V = (4/3)πr. times 4 equals V≈268.08. i think this is it!! i hope it works loe you have an amazing day:) -marina mae

If two pentagons are similar, then their sides are proportional. To find PT, we'll need to set up a proportion.

AE / PT = AB / PQ

---There are many ways to set up this proportion, it just depends on what side lengths you have and ensuring that they match up on both shapes.

6 / x = 5 / 12.5

5x = 75

x = 15

Length of PT = 15 cm

Option C

Hope this helps!

Step-by-step explanation:

if I understand correctly, then we have

h(x) = 2 × cubic root(x - 10) + 4

the x-intercept is the x value where y or h(x) = 0.

0 = 2 × cubic root(x - 10) + 4

0 = cubic root(x - 10) + 2

-2 = cubic root(x - 10)

-8 = x - 10

x = 2

The intercept is the point where a line or curve crosses the axis. The x-intercept of the function is (2,0)

The intercept is the point where a line or curve crosses the axis. Given the function below:

h(x) = 2(∛x-10) + 4

For the x-intercept, it is the point where h(x) = 0.

Substitute

2(∛x-10) + 4 = 0

2(∛x-10)  = -4

(∛x-10)  = -2

Take the cube of both sides

x-10 = (-2)^3
x -10 = -8

x = -8 + 10

x = 2

Hence the x-intercept of the function is (2,0)

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Answer:

  C, E

Step-by-step explanation:

Here, we want to change the equation of a circle from general form to standard form. This is done by making the leading coefficients 1, completing the squares, and then rewriting the equation in standard form.

The leading coefficients of the given equation are 2, so we first want to divide by 2. This gives ...

  x² +y² -4x -6y +8 = 0

Subtracting 8 puts us in better position to complete the squares.

  x² +y² -4x -6y = -8

Now, we can add the squares of half the coefficients of the linear terms.

  (x² -4x +4) +(y² -6x +9) = -8 +13 . . . . . . matches C

And we can simplify this to the standard form equation:

  (x -2)² +(y -3)² = 5 . . . . . matches E

The equation 100 = 100 + y is an algebraic equation

The operation is subtraction property of equality, and the value of y is 0

The equation is given as:

100 = 100 + y

To solve for y, we apply the following operation

Operation: subtraction property of equality

So, we have:

100 - 100 = 100 - 100 + y

Evaluate the differences

0 = y

Rewrite as:

y = 0

Hence, the operation is subtraction property of equality, and the value of y is 0

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The triple integral that is bounded by a paraboloid x = 4y2 4z2 given as 16.762

Parabloid, x = 4y² + 4z²

plane x = 4

x = 4y² + 4z²

x = 4

4 = 4y² + 4z²

4 = 4 (y² + z² )

1 = y² + z²

from polar coordinates

y = r cos θ

z = r sin θ

r² = y² + z²

0 ≤ θ ≤ 2π

4r² ≤ x ≤ 4

0 ≤ r ≤ 1

[tex]\int\limits\int\limits\int\limits {x} \, dV = \int\limits^1_0\int\limits^a_b\int\limits^c_d {x} \, dx ( rdrdz)[/tex]

where

a = 4

b = 4r²

c = 2r

d = 0

The first integral using limits c and d gives:

[tex]2pi\int\limits^1_0\int\limits^a_b {xr} \, dx[/tex]

The second integral using limits a and b

[tex]pi\int\limits^1_0 {16 } } \, rdr - pi\int\limits^1_0 {16r^{5} \, dx[/tex]

[tex]16pi\int\limits^1_0 { } } \, rdr - 16pi\int\limits^1_0 {r^{5} \, dx[/tex]

[tex]16pi\int\limits^1_0 { } } \, [r-r^{5}]dr[/tex]

The third integral using limits 1 and 0 gives: 16.762

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The triple integral that is bounded by a paraboloid x = 4y2 4z2 given as 16.762

Integration is defined as adding small parts to form a new significant part.

Parabloid, x = 4y² + 4z²

plane x = 4

x = 4y² + 4z²

x = 4

4 = 4y² + 4z²

4 = 4 (y² + z² )

1 = y² + z²

from polar coordinates

y = r cos θ

z = r sin θ

r² = y² + z²

The limits of the integral

0 ≤ θ ≤ 2π

4r² ≤ x ≤ 4

0 ≤ r ≤ 1

[tex]\int\int\intxdV = \int_0_1\int_b_a\int_d_cxdx(rdrdz)[/tex]

where

a = 4

b = 4r²

c = 2r

d = 0

The first integral using limits c and d gives:

[tex]2\pi\int_0^1\int_b^axydx[/tex]

The second integral using limits a and b

[tex]\pi \int_0^116rdr-\pi\int_0^116r^5dx[/tex]

[tex]16\pi \int_0^1rdr-16\pi\int_0^1 r^5dx[/tex]

[tex]16\pi\int_0^1[r-r^5]dr[/tex]

The third integral using limits 1 and 0 gives: 16.762

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Answer:

C. parallelogram

D. rectangle

E. kite

Step-by-step explanation:

Cannot be the square because all sides are the same. A trapezoid can have two sides the same, but not two pairs of equal sides. The remaining shapes can have two pairs of equal length sides. see image.

Answer:

60 days.

Step-by-step explanation:

This is  a proportion question. You compare two ratios. Unfortunately it is an inverse ratio.

12 = k/100                   Multiply both sides by 100

1200 = k

20 = k/x                       Multiply both sides by x

20x = k

20x = 1200                 Divide by 20

20x/20 = 1200/20

x = 60 days.  

An inverse proportion works by making a constant k. The  constant k makes the days shorter when the number of people increases. You should expect that. More people , less time.

They are corresponding angles

Step-by-step explanation:

We know that x=75⁰ because

[tex]180 - 105 = 75[/tex]

75⁰ is angle EFB

Since we know this, and because we know that AD//EH,

We can conclude that x=75⁰(AD is parallel to EH and angle CBA or x and angle EFB are corresponding angles)

Answer:

1t = 1000kg

22.69 x 1000= 22690 kg

22690 kg ÷ 100 = 226.9

I would usually round it to 227 but I would say 226, since they are asking how many full bags she sold.

Answer:

the anwer is b

I did the math