24. Four golf 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 4cm.

Answers

Answer 1

the complete question is
Four golf 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 4cm.
1) What is the volume of the cylinder rounded to the nearest cubic centimeter?
2) What is the total volume of the four balls rounded to the nearest cubic centimeter?
3) What percent of the volume of the container is occupied by the four balls?

Part 1) volume of the cylinder=pi*r²*h
r=4/2----> 2 cm
h=4*4----> 16 cm
volume of the cylinder=pi*2²*16----> 200.96 cm³----> 201 cm³

the answer Part 1) is 201 cm³

Part 2) volume of a sphere=(4/3)*pi*r³ ( is equal to volume of one golf ball)
r=2 cm
volume of a sphere=(4/3)*pi*2³ ----> 33.49 cm³
so
volume of four golf ball-----> 4*33.49----> 133.97 cm³----> 134 cm³

the answer part 2) is 134 cm³

part 3)
volume of cylinder=201 cm³
volume of the four golf ball=134 cm³
so
if 201 cm³-----------> 100%
134 cm³--------> x
x=134*100/201----> x=66.67%

the answer part 3) is 66.67%

Related Questions

Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).

Answers

Hello!

The formula for the area of a sector can be written as follows:

Area = [tex] \frac{1}{2} [/tex][tex]r^{2} [/tex](R)

In the above formula, “r” represents the radius while “R” represents the radian measure of a sector. The radius is given to us in the image above as 10 inches. However, we still need the radian measure of the two sectors. To find this measure, we can use the following conversion:

1 degree = [tex] \frac{pi}{180} [/tex] radians

Because the two sectors have a given measure of 72 degrees, we need to multiply both sides of the above conversion by 72:

72 degrees = [tex] \frac{72pi}{180} [/tex]

Reduce the fraction on the right side of the equation:

72 degrees = [tex] \frac{2pi}{5} [/tex]

We now have the radian measure of both sectors. Now simply insert this and any other known values into the “area of a sector” formula above:

Area = [tex] \frac{1}{2} [/tex][tex]10^{2} [/tex]([tex] \frac{2pi}{5} [/tex])

Simplify the right side of the equation to get the following answer:

Area = 20 pi

We have now proven that the area of one sector is equal to 20 pi.

If, however, you need the combined area of the two identical sectors, simply multiply the proven area by 2 to get a total area of 40 pi.

I hope this helps!

Answer: 40 pi

Step-by-step explanation:

At a pie-eating contest, Isla ate 1⁄4 of a pie before time was called. Alexa only finished 1⁄8 of a pie. How much more pie did Isla eat than Alexa?

Answers

Hi there!

Isla - 1/4

Alexa - 1/8

The problem is set up below:

Isla - Alexa =

1/4 - 1/8 =

In order to subtract we need to make both fractions have the same denominator. To do that we will multiply by how many times 4 goes into 8.

1 2 2
- x - = -
4 2 8

Therefore,

2/8 - 1/8 = 1/8

Your answer- 1/8

Hope this helps you!

~DL

A wheel spins at 300 revolutions per minute. What is the angular velocity of the wheel, in radians per second? Round the answer to the nearest hundredth.

Answers

Angular velocity = 300 revolutions per minute

1 revolution = 2π radians.

So, we can write:

Angular velocity = 300 x 2π radians per minute = 600π radians per minute

1 minute = 60 seconds.

So,

Angular velocity = 600π radians per 60 seconds
⇒
Angular velocity = 10π radians per second
Angular velocity = 31.42 radians per second

Thus, rounding of to nearest hundredth, the angular velocity will be 31.42 radians per second.

Answer:

31.42

Step-by-step explanation:

Which best describes a triangle with side lengths of 6 inches 8 inches and 9 inches?

Answers

It is an acute scalene triangle.

tanθ=sinθ/cosθ

True or False

Answers

If;
A = Adjacent
O = Opposite
H = Hypotenuse

Then,
Sin Ф = O/H
Cos Ф = A/H
Therefore,
(Sin Ф)/Cos Ф) = (O/H)/(A/H) = (O/H)*(H/A) = O/A

Now,
tan Ф = O/A ----

Therefore, it is true that
tan Ф = SinФ/CosФ

Take a right angled triangle with side lengths x, y, and z, where x is the hypotenuse.
sin θ=z/x
cos θ=y/x
sinθ/cosθ=(z/x)/(y/x)=z/y=tan θ
the statement is true.

What is the standard form of the equation of a circle given by x^2 + y^2 - 18x + 8y + 5 = 0

Answers

Completing the square:

x^2 - 18x + y^2 + 8y = -5
x^2-18x +81 - 81 + y^2 + 8y + 16 - 16 = -5.

Then, (x-9)^2 + (y+4)^2 = -5 + 81 + 16 = 92

Then the desired equation is (x-9)^2 + (y+4)^2 = 92.

Answer:

x-9,y+4,92

Step-by-step explanation:

Find the area of the parallelogram with vertices at (−2,3),(−2,3), (6,14),(6,14), (−14,1),(−14,1), and (−6,12).(−6,12).

Answers

C is your answer your welcome

Sally has x books that weigh 2 pounds each and 8 books that weigh 3 pounds each. the total weight of her books is 62 pounds. which equation below could be used to find how many 2-pound books sally has?

Answers

if Sally has x books that are 2 pounds then her x books weights a total of 2x lbs.

8 books of 3 lbs weights 8*3=24lbs

All them add up to 62, therefore we can conclude to the equation :
2x+24=62
or we can simplify to
2x=38
or even
x=19

write a number sentence to compare 7.17 and 7.170

Answers

Both of these values are the same, so the number sentence would state:

7.17 = 7.170

You can place any number of zeros to the very end on the right side (when there is a decimal point) without changing the value of the number.

7.1700000 = 7.17 also

Answer:

They are equal

Step-by-step explanation:

Circle 1 is centered at (-4, 5) and has a radius of 2 centimeters. Circle 2 is centered at (2, 1) and has a radius of 6 centimeters. What transformations can be applied to circle 1 to prove that the circles are similar? The circles are similar because you can translate circle 1 using the transformation rule ( x, x) and then dilate it using a scale factor of ( ).

Answers

we know that
Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another.
In this problem to prove circle 1 and circle 2 are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another.

we have that

Circle 1 is centered at (-4, 5) and has a radius of 2 centimeters
Circle 2 is centered at (2, 1) and has a radius of 6 centimeters

step 1
Move the center of the circle 1 onto the center of the circle 2
the transformation has the following rule
(x,y)--------> (x+6,y-4)
so
(-4,5)------> (-4+6,5-4)-----> (2,1)
so
center circle 1 is now equal to center circle 2
The circles are now concentric (they have the same center)

step 2
A dilation is needed to increase the size of circle 1 to coincide with circle 2

scale factor=radius circle 2/radius circle 1-----> 6/2----> 3

radius circle 1 will be=2*scale factor-----> 2*3-----> 6 cm
radius circle 1 is now equal to radius circle 2

A translation, followed by a dilation will map one circle onto the other, thus proving that the circles are similar

the answer is

The circles are similar because you can translate circle 1 using the transformation rule ( x+6,y-4) and then dilate it using a scale factor of (3 )

Can someone please help me

Answers

No, the two rectangles are not similar. Similar rectangles will have the same ratio of shortest to longest side lengths.
3 : 4 ≠ 5 : 6

What value of y makes the equation true?

Answers

Hi there!

First, we'll need to solve the equation for y. In order to solve for y, we can use our properties. The property we can use in order to solve for y is the subtraction property. Using this property, we can subtract 2.9 from each side. This gives us the value of y as 8.1. Therefore, the answer is A - 8.1.

Hope this helps!! :)
If there's anything else that I can help you with, please let me know!

Concerned about graffiti, mayors of nine suburban communities instituted a citizen community watch program. community monthly incidents after monthly incidents before burr oak 2 7 elgin corners 3 2 elm grove 6 2 greenburg 4 3 huntley 5 11 north lyman 3 9 south lyman 3 5 pin oak 5 7 victorville 2 3 click here for the excel data file (a) choose the appropriate hypotheses to see whether the number of graffiti incidents declined. assume μd is the mean difference in graffiti incidents before and after.

Answers

Just to be clear, the data are reported in the picture attached.

We set the difference in graffiti incidents between before (B) and after (A) as:
d = A - B
If the number of incidents has indeed reduced, then d will be negative.

In order to choose the hypothesis, we need to recall that the null hypothesis H₀ represents the statement that we want to prove wrong, while the alternative hypothesis H₁ represents the statement that we want to prove right.
Therefore, we want μd to be strictly negative (= 0 would mean that the number of incidents stayed constant).

Hence:
H₀ : μd ≥ 0
H₁ : μd < 0

Final answer:

The appropriate hypotheses to determine if graffiti incidents declined involve a null hypothesis where the mean difference is greater than or equal to zero and an alternative hypothesis where the mean difference is less than zero. The μd represents the mean difference in graffiti incidents before and after the institution of the community watch program.

Explanation:

The appropriate hypotheses to test whether the number of graffiti incidents declined in the suburban communities after the institution of a citizen community watch program are as follows:

H0: μd ≥ 0 (Null hypothesis: The mean difference in graffiti incidents before and after is greater than or equal to 0, indicating no decrease.)Ha: μd < 0 (Alternative hypothesis: The mean difference in graffiti incidents before and after is less than 0, indicating a decrease.)

Here, μd (mu-sub-d) represents the mean difference between the number of incidents before the program and after the program was implemented. To test these hypotheses, we would typically conduct a paired t-test if the samples are normally distributed or a Wilcoxon signed-rank test if the distribution is not normal.

Assuming μd is the mean difference in graffiti incidents before and after, the test will determine if there is statistically significant evidence to support that the community watch program resulted in a reduction of graffiti incidents.

Marcus drew a quadrilateral with only 1 pair of parallel sides. Which quadrilateral did Marcus draw?

Answers

That would be a trapezoid

a trapezoid!
Hope this helps! <3

When no more than 110 units are produced, the cost of producing y units is given by c(x). c(x)equals0.2 x cubed minus 24 x squared plus 1524 x plus 31 comma 272 how many units should be produced in order to have the lowest possible average cost?

Answers

Given that the cost of production is modeled by:
c(x)=0.2x^3-24x^2+1524x+31272
for lowest average cost, we calculate c'(x)=0
thus:
From c(x), we shall have:
c'(x)=0.6x^2-48x+1524
solving for x we get:
x=40+/- 30.6594i
but since we are looking for a definite number of units, we shall do away with the complex part such that we shall remain with:
x=40 units
hence the minimum number of units will be 40 units

Tory plans to enter the path at mile marker 1 and hike for 4 miles. Tory is a beginner hiker, so he wants to choose the path that is less steep on average.

Which path should he choose? Why?

Answers

If you need help visualizing this, you might draw vertical lines at distance = 1 and at distance = 5. Look at the points where those lines cross f(x). The vertical difference is perhaps 350 ft. Look at where the lines cross g(x). That vertical distance may be about 200 ft.

The vertical change from 1 to 5 is considerably less for g(x) than for f(x).

Tory should choose path ...
g(x)

Use right triangle DCB to find the trig values for angle D.

sinD =

cosD =

tanD =

Answers

sin D= opp./hyp. = 35/37
cos D= adj./hyp. = 12/37
tan D= opp./ adj. = 35/12

Answer: sinD = 0. 9459

cosD =0. 3243 tanD=2. 917

Step-by-step explanation:

From the figure above;

opposite = 35

adjacent = 12

hypotenuse = 37

sin D = opposite/hypotenuse

sinD = 35/37 = 0. 9459

cosD = adjacent/hypotenuse

= 12/37 = 0. 3243

tanD = adjacent/opposite

= 35/12 = 2. 9167

[tex] \frac{10.5}{1.79} [/tex]
[tex] \frac{16}{2.19} [/tex]
How would I find out the unit rate for these two equations?

Answers

well, we can see this case like this, say let's find out how much is it for just 1oz in each case.

[tex]\bf \begin{array}{ccll} oz&\$\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 10.5&1.79\\ 1&x \end{array}\implies \cfrac{10.5}{1}=\cfrac{1.79}{x}\implies x=\cfrac{1\cdot 1.79}{10.5}\implies x\approx 0.17048 \\\\\\ \begin{array}{ccll} oz&\$\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 16&2.19\\ 1&y \end{array}\implies \cfrac{16}{1}=\cfrac{2.19}{y}\implies y=\cfrac{1\cdot 2.19}{16}\implies \boxed{y = 0.136875}[/tex]

so, the one with less $/oz is the better deal, because is less bucks per ounce.

A professor teaching a discrete math course gives a multiple-choice quiz that has ten questions, each with four possible responses: a, b, c,
d. what is the minimum number of students that must be in the professor's class in order to guarantee that at least three answer sheets must be identical? (assume that no answers are left blank.)3

Answers

Each question has three possible distinct answers.
Ten questions have 3^10 possible distinct answers sheets.
=>
(3^10)+3 will guarantee that at least 3 answer sheets are identical.

Numerically,
(3^10)+3 = 59049 +3 = 59052

The correct minimum number of students required to guarantee that at least three answer sheets must be identical is 5.

To solve this problem, we can use the pigeonhole principle. The pigeonhole principle states that if you have more pigeons than pigeonholes, at least one pigeonhole must contain more than one pigeon.

In this scenario, each question can be thought of as a pigeonhole, with the possible answers (a, b, c, d) as the pigeons. Since there are four possible answers for each question, we have four pigeonholes for each of the ten questions.

Now, let's consider the number of students (pigeons) and the number of unique answer sheets (pigeonholes). We want to find the minimum number of students such that at least three of them have identical answer sheets.

For two students, there are [tex]$4^{10}$[/tex] possible combinations of answers for the ten questions. For three students, the number of possible combinations of answers is [tex]$4^{10} \times 4^{10}$[/tex]. In general, for [tex]$n$[/tex] students, the number of possible combinations is [tex]$4^{10} \times 4^{10} \times \ldots \times 4^{10}$ ($n$ times)[/tex].

We need to find the smallest [tex]$n$[/tex] such that the number of combinations exceeds the number of ways to distribute the answer sheets without having three identical ones.

The number of ways to distribute the answer sheets without having three identical is given by the sum of the combinations of choosing 1, 2, ...,[tex]$n-1$[/tex] students out of [tex]$n$[/tex] to have unique answer sheets, and then multiplying by [tex]$4^{10}$[/tex] for each unique combination. This is because we are allowing for the possibility that some students have the same answer sheets, but not more than two.

The sum is given by:

[tex]\[ \binom{n}{1} \times 4^{10} + \binom{n}{2} \times 4^{10} + \ldots + \binom{n}{n-1} \times 4^{10} \][/tex]

We want to find the smallest [tex]$n$[/tex] such that:

[tex]\[ \binom{n}{1} \times 4^{10} + \binom{n}{2} \times 4^{10} + \ldots + \binom{n}{n-1} \times 4^{10} < 4^{10n} \][/tex]

For [tex]$n = 4$[/tex], we have:

[tex]\[ \binom{4}{1} \times 4^{10} + \binom{4}{2} \times 4^{10} + \binom{4}{3} \times 4^{10} = 4 \times 4^{10} + 6 \times 4^{10} + 4 \times 4^{10} = 14 \times 4^{10} \][/tex]

For [tex]$n = 5$[/tex], we have:

[tex]\[ \binom{5}{1} \times 4^{10} + \binom{5}{2} \times 4^{10} + \binom{5}{3} \times 4^{10} + \binom{5}{4} \times 4^{10} \][/tex]

[tex]\[ = 5 \times 4^{10} + 10 \times 4^{10} + 10 \times 4^{10} + 5 \times 4^{10} = 30 \times 4^{10} \][/tex]

Now, we compare [tex]$30 \times 4^{10}$ with $4^{10 \times 5}$[/tex]. Since [tex]$4^{10 \times 5}$[/tex] is much larger than[tex]$30 \times 4^{10}$[/tex], we can see that for [tex]$n = 5$[/tex], the number of possible combinations exceeds the number of ways to distribute the answer sheets without having three identical ones.

Therefore, the minimum number of students required to guarantee that at least three answer sheets must be identical is 5.

Explain how you can use a model to find 4x 3/8

Answers

4 rectangles split it on 8 part then shade 3 of the 8 parts, them count every rectangle shades and add the all together, you will get 12/8, is the same if you multiply 4*3/8 you will get 12/8 simplified is 1/2!

The area of a rectangular patio is 5 and 5/8 square yards, and its length is 1 and 1/2 yards. What is the patio's width in yards?

Answers

area = length * width

width = area/length

area = 5 5/8 sq yd = 5.625 sq yd
length = 1 1/2 yd = 1.5 yd

width = area/length = (5.625 sq yd)/(1.5 yd) = 3.75 yd

width = 3.75 yd = 3 3/4 yd

Hello!

We can use the equation to find the area of a rectangle

The equation is l * w = A

l is length
w is width
A is area

Put in the values you know
1 1/2 * w = 5 5/8

Divide both sides by 1 1/2

w = 3 3/4

The answer is 3 3/4 yards

Hope this helps!

What is the area of a figure whose vertices are (-2,1), (3,1), (2,-3), and (-3,-3)?

Answers

check the picture below, you can pretty much count the units off the grid.

what is the tenth rule for A(n)=-9+5(n-1)

Answers

Given that the sequence follows the formula
A(n)=-9+5(n-1)
the tenth term will be given as follows:
From
A(n)=-9+5(n-1)
substitute n=10 in the equation we get:
A(10)=-9+5(10-1)
A(10)=-9+5(9)
A(10)=-9+45
A(10)=36

Answer: 36

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

a2 − 2a − 224 = 0

8, –28

16, –14

–16, 14

–8, 28

Answers

For this case we have the following equation:
a2 - 2a - 224 = 0
Applying the resolver we have:
A = (- b +/- root (b ^ 2 - 4 * a * c)) / (2 * a)
Substituting values we have:
A = (- (- 2) +/- root ((- 2) ^ 2 - 4 * 1 * (- 224))) / (2 * (1))
Rewriting:
A = (2 +/- root (4 + 896)) / (2)
A = (2 +/- root (900)) / (2)
A = (2 +/- 30) / (2)
The roots are:
A1 = (2 + 30) / (2)
A2 = (2 - 30) / (2)
Rewriting:
A1 = 16
A2 = -14
Answer:
16, -14

The answer is Answer:

16, -14

Leslie is a biologist. She is going to randomly select one animal from her lab to study. There are 5 salamanders, 3 crayfish, and 12 minnows in her lab. What is \text{P(salamander}

Answers

Since there are a total of 20 animals (5+3+12) and there are 5 salamanders, the probability she chooses a salamander is 5/20 -> 1/4, 25%, or .25

The sample space contains three types of animals; 5 salamanders, 3 crayfish, and 12 minnows.

So population of sample space would be, n(S) = Salamanders + Crayfish + Minnows.

n(S) = 5 + 3 + 12 = 20.

She wants to randomly select an animal and check if it is Salamander or not.

population of favourable outcomes would be, n(salamander) = 5.

Now the probability for selecting a salamander would be :-

[tex]P(salamander) = \frac{n(salamander)}{n(S)} \\\\ P(salamander) = \frac{5}{20} \\\\ P(salamander) = \frac{1}{4} \;or\; 0.25 \;or\; 25\%[/tex]

Explain how you can tell when a formula represents a length an area or a volume

Answers

Do you mean how you can tell between an area formula and a volume formula? Well usually like on a reference sheet it says the shape and the letter a or v, a representing area and v representing volume. I hope this helps, if it doesn't please tell me in the comment section

Area and volume are both used to determine the amount of space.

While area is used for two-dimensional shapes, volume is used for three-dimensional shapes.

The difference between the given parameters are:

Length is often represented as the difference between points.Area is represented as the product of two dimensions or the square of a dimensionVolume is represented as the product of three dimensions or the cube of a dimension

For instance:

[tex]\mathbf{Length = b -a}[/tex]

[tex]\mathbf{Area = ab}[/tex]

[tex]\mathbf{Volume= abc}[/tex]

Read more about lengths, areas and volumes at:

https://brainly.com/question/13608425

the volume of water in a bowl is given by V=1/3pih^2(60-h), where h is the depth of the water in centimeters. If the depth is increasing at the rate of 3cm/sec when the water is 10 cm deep, how fast is the volume increasing at that instant

Answers

[tex]\bf V=\cfrac{1}{3}\pi h^2(60-h)\implies V=\cfrac{1}{3}\pi h^260-\cfrac{1}{3}\pi h^3 \\\\\\ V=20\pi h^2-\cfrac{\pi }{3}h^3\implies \cfrac{dV}{dt}=20\pi \left(\stackrel{chain~rule}{2h\frac{dh}{dt}} \right)-\cfrac{\pi }{3}(\stackrel{chain~rule}{3h^2\frac{dh}{dt}}) \\\\\\ \begin{cases} \frac{dh}{dt}=3\\ h=10 \end{cases}\implies \cfrac{dV}{dt}=20\pi [2(3)(10)]-\cfrac{\pi }{3}[3(10)^2(3)] \\\\\\ \cfrac{dV}{dt}=1200\pi -300\pi \implies \cfrac{dV}{dt}=\stackrel{\frac{cm}{sec}}{900\pi }[/tex]

PLEASE HELLPPPP!!!!!!!!!!!!
Figure BMHF is rotated how many degrees clockwise?

Answers

Asked and answered elsewhere.
https://brainly.com/question/9953496

T-shirts at a clothing store cost $19 each Rory bought several T-shirts at this price and paid $57 how many t-shirts did Rory buy

Answers

one t-shirt = $19

Number of t-shirts = $57 ÷ $19 = 3

Answer: 3 t-shirts

The other guy is correct

Which of the following graphs shows a negative linear relationship with a correlation coefficient, r, relatively close to -1

Answers

Graph B is the correct answer as of July 2018

The graph that shows a negative linear relationship that has a correlation coefficient, r, that is closer to -1 is: B. graph B.

What is a Negative Linear Relationship Graph?

A graph that shows a negative linear relationship has a trendline that slopes downwards from your left to the right.

The closer the data points are to each other along the trendline in a negative linear graph, the closer the correlation coefficient, r, is to -1.

Therefore, the graph that shows a negative linear relationship and has a correlation coefficient, r, that is closer to -1 is: B. graph B.

Learn more about negative linear relationship graph on:

https://brainly.com/question/17088993

#SPJ2

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