Find the inter-quartile range of the given data set. 3, 16, 18, 25, 26, 29, 31, 50 13 15 47

Answers

Answer 1

Answer: I did this in my lesson and the answer you are looking for is 13! Hope this helped you or anyone else. :)

Answer 2

Answer:

The answer to your question is 13.

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Three balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 13 cm. a. What is the volume of the cylinder? Explain your method for finding the volume.
b. What is the total volume of the three balls? Explain your method for finding the total volume.
c. What percent of the volume of the container is occupied by the three balls? Explain how you would find the percent.

Answers

We know the following:
Cylinder volume: V₁ = π r² h
Ball (sphere) volume:V₂ = $(4)/(3)$ π r³
where:
V - volume
r - radius of base of cylinder and diameter of ball
h - height of cylinder.

R = 13 cm ⇒ r = 13 ÷ 2 = 6.5
π = 3.14

a) Since balls touch all sides of cylinder (as shown in image), it can be concluded that height of cylinder is equal to sum of diameters of 3 balls and that radius of base of cylinder is equal to radius of ball:
h = 3 × r = 3 × 13 cm = 39 cm
r = 6.5 cm
So,
V₁ = π r² h
V₁ = 3.14 × (6.5 cm)² × 39 cm
V₁ = 5,173.9 cm³

b. The total volume of three balls is the sum of volumes of each ball:
Vₐ = 3 × V₂
Vₐ = 3 × $(4)/(3)$ π r³
Vₐ = 3 × $(4)/(3)$ 3.14 (6.5 cm)³
Vₐ = 3,449.3 cm³

c. Percentage of the volume of the container occupied by three balls ould be expressed as ratio of volume of three balls and volume of cylinder:
V = $( V_(1))/( V_(a) )$ ×100
V = $(3,449.3)/(5,173.9)$ ×100
V = 0.6666 ×100
V = 66.66%

A. The volume of the cylinder can be computed because the statement "The balls just touch the top, bottom, and sides of the cylinder" gives a clue of the height and radius of the cylinder. The height is equal to 3 times the diameter of the balls, and its radius is the same as the balls' radius.

Vcylinder = πr^2h = π(13/2)^2 (3*13) = 5176.56 cm^3

B. The volume of the three balls is computed using the equation of V for spheres:

Vball = 3*4*π*r^2/3 = 3451.05 cm^3

C. The answer is the equal to the total volume of the balls divided by the volume of the cylinder

3451.05(100%)/5176.56 = 66.67%

Brian bought beverages for his coworkers. One day he bought 3 lemonades and 4 iced teas for $12.00. The next day he bought 5 lemonades and 2 iced teas for $11.50. Find the cost of 1 lemonade and 1 iced tea, to the nearest cent.

Answers

Let's take lemonade's price as 'x' and iced tea's price as 'y'.

$\left \{ {{3x+4y=12} \atop {5x+2y=11.5}} \right. \n \left \{ {{x=4-y} \atop {5(4-y)+2y=11.5}} \right. \n \left \{ {{x=4-y} \atop {20-3y=11.5}} \right. \n \left \{ {{x=4-y} \atop {y=2.83}} \right. \n \left \{ {{x=1.17} \atop {y=2.83}} \right.$

Price of lemonade is $2.83, iced tea's $1.17.

Distance between (0,2) and (0,4)

Answers

There are many ways to do this, I prefer the distance formula it looks like this:
$√((x_2-x_1)^2+(y_2-y_1)^2)$
We are given 2 pairs of coordinates: (0,2) and (0,4)
0=x1
2=y1
0=x2
4=y2
We take the numbers and sub in the values above in place of the variables:
$√((0-0)^2+(4-2)^2)$
Simplfy it:
$√((0)^2+(2)^2)$
0^2=0
2^2=4
We are left with :
$√(4)$
$√(4) =2$
Final answer: 2

D= √(x sub2 - x sub1)^2 + (y sub2 - ysub1)

D= √(0-0)^2 + (4-2)^2

D= √0^2 + 2^2

D= √0 + 4

D= √4

D = 2

How do you factor: x^3 - 8 (x cubed minus 8)

Answers

$x^3 - 8 =x^3-2^3 = (x-2) (x^2 + 2x + 2^2)=(x-2) (x^2 + 2x + 4)\n \n \na^3 - b^3 = (a - b) (a^2 + ab + b^2)$

Answer: (x - 2)(x² + 2x + 4)

Step-by-step explanation: In this problem, we're asked to factor x³ - 8.

Notice that x³ is a perfect cube and 8 is a perfect cube because 8 is 2 × 2 × 2 or 2³. So we have the difference of two cubes.

To factor the difference of two cubes, we use the following formula.

a³ - b³ can be factored as (a - b)(a² + ab + b²) and in this problem, since a³ is represented by x³, the value of a is x and since b³ is represented by 8, the value of b is 2.

So substituting x and 2 into the formula for a and b, we have

[(x) - (2)][(x)² + (x)(2) + (2)²] and notice that we changed the parentheses in the formula to brackets so that we're not dealing with too many sets of parentheses.

Next, simplifying inside the second set of brackets and changing the brackets back to parentheses, we have (x - 2)(x² + 2x + 4) which is our final answer.

88% of 56.25 is what number?

Answers

Your answer is 88% of 56.25 is 49.5

Hope this helps.

My book said 88% of 56.25 is 49.5?

What is 37.025 written in word form

Answers

thirty-seven and twenty-five thousanths

37.025 in written form is:

Thirty-seven and twenty-five thousandths

Hope I Helped You!!! :-)

Have A Good Day!!!

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