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.
What is the volume of the cylinder rounded to the nearest cubic centimeter?
What is the total volume of the four balls rounded to the nearest cubic centimeter?
What percent of the volume of the container is occupied by the four balls?
Answers
Please, see the attached files.
Thanks.
Related Questions
A quality control expert randomly samples 60 pairs of sunglasses and finds 5 defective pairs. predict how many defective pairs will be in a shipment of 420 sunglasses.
Answers
7*5=35 sunglasses
For this case the first thing you should do is find the percentage of sunglasses that are defective.
For this, we make the following rule of three:
60 pairs -------------------> 100%
5 pairs ---------------------> x
From here, we clear the value of x.
We have then:
[tex] x = (\frac{5}{60}) * (100)
x = 8.3%
[/tex]
We now look for the amount of sunglasses that may come with defects.
We have then:
[tex] N = (0.083) * (420)
N = 34.86
[/tex]
Rounding to the nearest whole number:
[tex] N = 35
[/tex]
Answer:
About 35 defective pairs will be in a shipment of 420 sunglasses
The size of a television is given by the length ofthe diagonal of the screen. the ratio of the height to the width of wide flat-screen tv is 8:15. find expressions for the width and height of a wide-screen tv in terms of the length of its diagonal.\
Answers
suppose:
width=8x
length=15x
let d be the diagonal
thus; using Pythagorean theorem:
d^2=(8x)^2+(15x)^2
=64x^2+225x^2
=289x^2
d=17x
or x=d/17
width=8x=8d/17
length=15x=15d/17
What is the radius of the circle given the equation x2 - 6x + y2 + 10y - 2 = 0?
Answers
[tex]\text{We have:}\\\\x^2-6x+y^2+10y-2=0[/tex]
[tex]\text{Use:}\ (a\pm b)^2=a^2\pm2ab+b^2[/tex]
[tex]\underbrace{x^2-2\cdot x\cdot3+3^2}_{(x-3)^2}-3^2+\underbrace{y^2+2\cdot y\cdot5+5^2}_{(y+5)^2}-5^2-2=0\\\\(x-3)^2+(y+5)^2-9-25-2=0\\\\(x-3)^2+(y+5)^2-36=0\ \ \ \ |+36\\\\(x-3)^2+(y+5)^2=36[/tex]
[tex]\text{coordinates of the center of the circle (3; -5)}\\\\\text{a radius}\ r=\sqrt{36}=6[/tex]
Part A: Factor 5x2b2 + 14xb2 − 3b2. Show your work.
Part B: Factor x2 − 18x + 81. Show your work.
Part C: Factor x2 − 121. Show your work.
Answers
We have the following expression:
5x2b2 + 14xb2 - 3b2
Rewriting we have:
b2 (5x2 + 14x - 3)
b2 (5x-1) (x + 3)
Part B:
We have the following expression:
x2 - 18x + 81
Rewriting we have:
(x-9) (x-9)
(x-9) ^ 2
Part C:
We have the following expression:
x2 - 121
Rewriting we have:
(x-11) (x + 11)
Akikos dogs has three puppies. They weigh 2.6pounds, 2.74 pounds, and 3.1 pounds. How much more does the heaviest puppy weigh than the lightest puppy?
Answers
Solve the system of equations. { 13x−y=90 y=x^2−x−42
Answers
(6, -12)
(8, 14)
You can get these by taking the second equation and plugging it in for y in the first equation. Then solve using the quadratic formula.
The first painter can finish a paint job in 2 hours. The second painter can finish the same job in 8 hours. How long would it take them to finish the job if they were working together?
Answers
If two painters who can individually finish a painting job in 2 hours and 8 hours respectively work together, they will be able to finish the job in 1.6 hours.
Explanation:The question is about determining how fast two painters can finish a paint job if they work together, given their individual working speeds. This is related to the field of mathematics and specifically to the concept of rates. The first painter can finish the job in 2 hours, so, his rate of working is 1/2 of the job per hour. The second painter can finish the job in 8 hours, so his rate of working is 1/8 of the job per hour. When they work together, their rates are added together. So, the combined rate of both painters is 1/2 + 1/8 = 5/8 of the job per hour. To find out how long it would take them to finish the job together, we take the reciprocal of this, which gives us 8/5 or 1.6 hours.
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Working together, the two painters would take approximately 1.6 hours or 1 hour and 36 minutes to finish the job.
Explanation:To find how long it would take the two painters to finish the job together, we can use the concept of work rates. The first painter can finish the job in 2 hours, so they have a work rate of 1/2 job per hour. Similarly, the second painter can finish the job in 8 hours, so their work rate is 1/8 job per hour.
When the two painters work together, their combined work rate is the sum of their individual work rates. So, the total work rate when they work together is 1/2 + 1/8 = 5/8 job per hour.
To find the time it would take them to finish the job, we can use the formula time = 1 / work rate. Substituting in the combined work rate of 5/8 job per hour, we get:
time = 1 / (5/8) = 8/5 = 1.6
Therefore, it would take the two painters approximately 1.6 hours or 1 hour and 36 minutes to finish the job if they were working together.
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use the formulas to find the lateral area and the surface area of the given prism round your answer to the nearest whole number 5.39m 26m 5m 2m
the choices for the answer is
322m2 327m2
296m2 342m2
296m2 332m2
322m2 332m2
Answers
Answer:
for connexus 322m^2, 332m^2
Step-by-step explanation:
PLEASE HELP ME WITH THIS ILL MARK AS BRAINIEST
What is the value of h when the function is converted to vertex form?
Note: Vertex form is f(x)=a(x−h)2+k .
f(x)=x2+10x+35
Enter your answer in the box.
Answers
f(x)=x^2+10x+35
Complete the square: f(x)=x^2+10x+25-25+35 = (x+5)^2 +10
or y-10=(x+5)^2, so the vertex is at (-5,10). h has the value -5.
Answer:
h = -5
Step-by-step explanation:
What is the value of w?
w + 3
4
=
w - 2
2
Answers
A gardener wants to plant 122500 trees in his field in such a way that the number of trees in a row is equal to the number of rows .How many trees will he plant in each row?
Answers
Thus the total number of trees will be:
Total=(number of rows)*(number of trees in each row)
hence:
122500=x×x
122500=x²
hence
x=√122500
x=350
thus the number of rows will be 350 and the number of trees in each row will be 350
Irma needs to rent a car for a business trip from phoenix to san jose (720 miles one way). she will drive round trip and will be gone a total of 8 days. the car rental company charges $65.00 per day and allows for 1,600 miles for irmas's trip. there will be an additional charge of $0.24 per mile over the 1,600 miles allowed. how many total miles can she drive without exceeding her budget of $600.00?
Answers
Daily rate + cost per mile over 1600 = total cost
(65 x 8) + 0.24m = 600
520 + 0.24m = 600
-520 -520
0.24m = 80
0.24 0.24
m = 333.33... miles
The maximum number of whole miles she can drive would be 1933 miles (1600 + 333).
YO!NEED THIS!!!!!POINTS!!!!!!WILL GIVE THE BRAIN!!!!
Answers
Since the two ends of graph are in opposite direction, the exponent of variable has to be odd. For an even exponent of leading term, the two ends are in same direction.
Since the graph is falling on left and rising on right, this indicates that the coefficient of leading term is positive.
So, the leading term must have:
1) Odd exponent
2) Positive Coefficient
Thus, option Fourth is the correct answer
Pollsters take a survey of people at a ball game to collect and analyze data about favorite leisure activities of star city’s residents. Would this study be biased Why or why not?
Answers
Answer:
Yes, it will be a biased study.
Step-by-step explanation:
Given is that -
Pollsters take a survey of people at a ball game to collect and analyze data about favorite leisure activities of star city’s residents.
This study will be biased and it will produce biased results.
Firstly, few people at ball game do not represent the whole population of the city and it is not necessary that all the people at ball park will respond to the question in the survey.
Answer:
Yes, it is biased. The sample of people at the ball park is not representative of Star City’s residents.
The answer is D.
what is the length of the diagonal AC in the rectangle below?
Answers
Then use Pythagorean Theorem to find BD (the hypotenuse of right triangle DCB). So Pythag here would be:
[tex]BC^2+DC^2=BD^2[/tex]
See attached picture for full work.
Line segment AB has endpoints A(10, 4) and B(2, 8). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4. A) (6, 6) B) (2, 56 5 ) C) ( 24 5 , 42 5 ) D) ( 42 5 , 24 5 )
Answers
Write each of the equations below in standard form (i.e. y = ax^2+bx+c y=ax 2 +bx+c):
a. y = 3(x-7)(x+4) y=3(x−7)(x+4)
b. y = 2(x-3)^2 + 5 y=2(x−3) 2 +5
c. y = -2(x+3)(x+5) y=−2(x+3)(x+5)
d. y = -3(x-4)^2 + 8y=−3(x−4) 2 +8
Answers
Hope it helps
What transformation matrix would result in a 300 degrees counterclockwise rotation about the origin?
i cant type all of the options, but they all look like fractions inside brackets, some with square root signs.
Answers
[tex]\begin{pmatrix}cos\:\theta &-sin\:\theta \\ sin\:\theta &cos\:\theta \end{pmatrix}[/tex]
The given angle is θ=300°.
The values we need are
[tex]cos\left(300^{\circ} \right)=\frac{1}{2}[/tex]
[tex]sin\left(300^{\circ} \right)=-\frac{\sqrt{3}}{2}[/tex]
Substituting these into the given transformation matrix, we have
[tex]\begin{pmatrix}\frac{1}{2}&\frac{\sqrt{3}}{2}\\ -\frac{\sqrt{3}}{2}&\frac{1}{2}\end{pmatrix}[/tex]
the answer is B
hope this helps :)
A circular mirror has a diameter of 12 inches. part a what is the area, in square inches, of the mirror?
a. 6 π
b. 12 π
c. 36 π
d. 72 π part b a circular frame that is 3 inches wide surrounds the mirror. what is the combined area, in square inches, of the circular mirror and the frame?
a. 9 π
b. 18 π
c. 54 π
d. 81 π
Answers
2nd part is d
I BELIEVE
Final answer:
The area of the circular mirror is 36π square inches, and the combined area of the mirror and frame is the difference between the total area with the frame (81π square inches) and the mirror alone, resulting in 45π square inches.
Explanation:
Part A: Area of the Circular Mirror
To find the area of the circular mirror, we use the formula for the area of a circle, which is A = πr², where r is the radius of the circle. Since the diameter of the mirror is given as 12 inches, the radius would be half of that, which is 6 inches. Plugging the radius into the formula, we get:
A = π(6 inches)² = 36π square inches
Part B: Area of the Circular Mirror and Frame
The frame adds 3 inches to the radius on all sides, making the overall radius of the mirror and frame 9 inches (6 inches + 3 inches). Using the area formula again, A = π(9 inches)² = 81π square inches.
To find the combined area of the mirror and frame, we subtract the area of the mirror from the total area. Hence, combined area = 81π square inches - 36π square inches = 45π square inches.
Determine whether quantities vary directly or inversely and find the constant of variation. A teacher grades 25 students essays in 4 hours. Assuming he grades at the same speed, how long will it take him to grade 35 essays?
Answers
The number of essays graded varies directly with the number of hours worked, with a constant rate of 6.25 essays per hour. Therefore, it will take approximately 5.6 hours for a teacher to grade 35 essays at this rate.
The scenario presented describes a situation where the number of essays graded is directly proportional to the number of hours worked. This means that as the number of essays increases, the hours required to grade them also increase, assuming the grading speed (rate) is constant. To find the constant of variation (or rate of grading), we divide the number of essays by the number of hours.
If a teacher grades 25 essays in 4 hours, the rate would be 25 essays÷4 hours = 6.25 essays per hour. To find out how long it will take to grade 35 essays at this rate, we divide the number of essays by the rate:
35 essays ÷ (6.25 essays per hour) = 5.6 hours.
So, it will take the teacher approximately 5.6 hours to grade 35 essays given the constant grading speed.
Find the volume of each sphere or hemisphere. Round to the nearest tenth.
sphere: circumference of a great circle = 26m
Answers
volume of a sphere=(4/3)*pi*r³
in this problem
circumference=26 m
circumference=2*pi*r
so
26=2*pi*r----------> r=26/(2*pi)----> 4.14 m
volume of a sphere=(4/3)*pi*(4.14)³---> 297.08 m³------> 297.1 m³
the answer is
volume of a sphere is equal to 297.10 m³
A. 99
B. 100
C. 121
D. Cannot be determined
Answers
Corresponding parts of congruent figures
what is the area of the circle if DF=20 in.
Answers
DF is the diameter of the circle
so
radius r=DF/2----->20/2-----> r=10 in
area of the circle=pi*r²------> pi*10²-----> 100*pi in²-----> 314 in²
the answer is
100*pi in² or 314 in²
15 Points!
Describe how to transform the graph of f into the graph of g.
A) Shift the graph of f left 3 units.
B) Shift the graph of f right 7 units.
C) Shift the graph of f right 3 units.
D) Shift the graph of f left 7 units.
Answers
Answer:
D) Shift the graph of f left 7 units.
Look at the picture.
Group A represents males on the football team at Grizzly High School. Group B represents the men’s cross country team at Grizzly High School. Both teams are played during the same season. What can you conclude about the groups A and B?
A.
There are not any students who play in either football or run cross country.
B.
There are not any students who run only cross country .
C.
There are not any students who play only football..
D.
There are not any students who are in both sports, football and cross country.
Answers
You actually can't tell if their is a team with no one and the other team has players. B and C are wrong for the same reason A was wrong..
Your answer from this bunch is D but it's not clear that it is right. One team could practice on Tuesdays and Thursdays and the other on Mondays and Wednesdays. I don't know what you'd do on game day. But schools have worked that problem out, I'm sure. There would not be a conflict.
D <<<<<<< answer
Answer:
D.
There are not any students who are in both sports, football and cross country.
Step-by-step explanation:
An insect flies 20 feet in 1 second. how fast does the insect fly in miles per hour?
Answers
All of the units cancel other than miles divided by hours which is what we need.
Now we do (20 * 60 * 60 * 1) / 5280 which is 13.636363 (repeating) or 13.6364 miles per hour.
A number is mutiplied by 10. Then 32 is added to the product. This sum is then devised by 4. The answer is 28. What was the original number?
Answers
I went in a did the opposite of what it said (so I multiples 28 by 4, subtracted 32, and then divided by 10). Hope this helps!
Use graphs and tables to find the limit and identify any vertical asymptotes of the function.
Answers
Vertical asymptote: x=8
Answer:
The limit of the function is [tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex] and the vertical asymptotes is x=8.
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{1}{x-8}[/tex]
We need to find the value of
[tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}[/tex]
The graph of the function f(x) is attached below.
From the graph it is clear that the function approaches to -∞ as x approaches to 8 from left. So, by the graph we can say that
[tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex]
The table of values is attached below. From the table it is clear that the value of f(x) decreasing as the value of x is closed to 8 from left. So, by the table we can say that
[tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex]
To find the vertical asymptotes equate denominator, equal to 0.
[tex]x-8=0[/tex]
[tex]x=8[/tex]
Therefore the limit of the function is [tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex] and the vertical asymptotes is x=8.
What is the y-intercept of x^2+2x+6
Answers
y = x^2 + 2x + 6
Let x = 0
y = 0^2 + 2 * 0 + 6
y = 6
Answer: 6
so
y=x²+2x+6=0²+2*0+6=6
y=6
So y-intercept is (0,6)
Another question for math. ill give mad points, the question is in attachment
Answers
y = (- 2, 5)
z = (1, 3)
Therefore, the vector yz is given by:
yz = z - y = (1, 3) - (-2, 5)
yz = ((1 - (- 2)), (3-5))
yz = ((1 + 2), -2)
yz = (3, -2)
Then, the magnitude is given by:
lyzl = root ((3) ^ 2 + (-2) ^ 2)
lyzl = root (9 + 4)
lyzl = root (13)
Answer:
yz = (3, -2)
lyzl = root (13)
option A