Given a soda can with a volume of 21 and a diameter of 6, what is the volume of a cone that fits perfectly inside the soda can? (Hint: only enter numerals in the answer blank).
Answers
it looks like
6.688=r^2h
that means we must find 3^2
that basically means 3x3 which is 9
then you have to divide that from 6.688
then you get 0.743
that is your height.
now we must find the volume of the cone. The formula for that is
V=пr^2(h/3)
now lets plug in our info
V=(3.14)(9)(0.743/3)
you get 6.999
Answer:
Volume of the cone = 7 unit³
Step-by-step explanation:
Soda can has the shape of a cylinder.
Volume of soda can = πr²h
where r = [tex]\frac{6}{2}=3[/tex] units
and volume = 21 unit³
We put the values in the formula to get the value of h.
21 = πr²h
[tex]h=\frac{21}{\pi r^{2} }[/tex]
Now If we fit a cone inside the can, radius of the cone will be equal to the radius of the cylinder and height of the cylinder will be equal to the height of the cone fit inside.
By the formula of volume of cone
Volume = [tex]\frac{1}{3}\pi r^{2}h[/tex]
= [tex]\frac{1}{3}\pi r^{2}( \frac{21}{\pi r^{2} })[/tex]
= [tex]\frac{21}{3}=7[/tex] units³
Volume of the cone is 7 unit³
Related Questions
21. Compare the numbers 5/9 and 0.5. use the symbols <, >, or =.
A) 5/9=0.5
B) 5/9>0.5
C) 5/9<0.5
Answers
Now the the 2 fractions are easy to compare.
1/9 is a larger fraction than 1/10
Therefore 5/9 > 5/10
B
Answer:
B) [tex]\frac{5}{9}>0.5[/tex]
Step-by-step explanation:
We are asked to compare the numbers 5/9 and 0.5.
Let us convert 0.5 as a fraction. We will divide and multiply 0.5 by 10 as:
[tex]0.5\times \frac{10}{10}=\frac{5}{10}=\frac{1}{2}[/tex]
Now, we will make a common denominator for both numbers as:
[tex]\frac{1*9}{2*9}=\frac{9}{18}[/tex]
[tex]\frac{5*2}{9*2}=\frac{10}{18}[/tex]
Therefore, [tex]\frac{5}{9}>0.5[/tex] and option B is the correct choice.
3y = 2x-6
x + y =8
Solve algebraically.
Answers
x + y = 8 Subtract x from both sides
y = 8 - x
Now, substitute this y value (8 - x) into the other given equation and solve for x.
3y = 2x - 6 Replace y with 8 - x
3(8 - x) = 2x - 6 Multiply 3 (8 - x)
24 - 3x = 2x - 6 Add 3x to both sides
24 = 5x - 6 Add 6 to both sides
30 = 5x Divide both sides by 5
6 = x Flip the equation to make it easier to read
x = 6
Now, use the x + y = 8 equation, replace the x with 6, and solve for y.
x + y = 8 Substitute x for 6
6 + y = 8 Subtract 6 from both sides
y = 2
Check your answers in both equations.
3y = 2x - 6 Replace x and y with 6 and 2
3(2) = 2(6) - 6 Simplify 3(2)
6 = 2(6) - 6 Simplify 2(6)
6 = 12 - 6 Subtract
6 = 6
x + y = 8 Replace x and y with 6 and 2
6 + 2 = 8 Add
8 = 8
So, the answers to your system of equations are x = 6 and y = 2 .
How many boys are in a class of thirty-five student if the girls outnumber boys by five
Answers
There are total 35 students in the classroom. If the number of girls is 5 more than the number of boys, then the number of boys in the class is 15.
What is fraction?An object or total number of some objects can be fractionated into two more fractions where the sum of these fractions equals to the total number. Let s be the total number of pearls in a glass. Let x be the number of white pearls and y be that of black pearls in it.
then s = x +y.
It is given that, the total number of students in the class is 35. The number of girls outnumber boys by 5. Let the number of boys be x then the number of girls will be x +5.
Now, the total number of students is the sum of number of boys and girls.
x + (x +5) = 35
2x + 5 = 35
2x = 35 - 5 = 30
x = 30/2 = 15.
Therefore, the number of boys is 15 and the number of girls is 20.
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what percentage is $7,360 of $78,000
Answers
divide 7360 by 78000
7360/78000 = 0.943589
= 9.44%
A figure is translated using the vector (-2,4) What translation vector would move the image back to its original position?
Answers
A translation formation is one of the simplest transformation since all it does is just to move the position of the figure without changing the size, the angles, or any other characteristics other than the position along.
So a translation by a vector (-2, 4) means that all points of the given figure is moved by:
(x – 2, y + 4)
Meaning that the whole figure is moved to the left by 2 units and moved to top by 4 units
So to revert this back into the original figure, we simply have to move again by:
(x + 2, y – 4)
Therefore move the whole figure to the right by 2 units and to the bottom by 4 units. So the translation to use is a vector (2, -4)
Answer:
(2, -4)
What is 1 / (0! - 1!)
Answers
Identify the measure of arc PQ
Answers
Line segment SQ=180, because it is a straight line
90+28=118
180-118=62
hope this helps:)
Write the product as a trinomial.(k – 1)(k – 4)
Answers
Use FOIL to solve this.
First
k * k
Outer
k * -4
Inner
-1 * k
Last
-1 * -4
k^2 - 4k - 1k + 4
k^2 - 5k + 4 is the trinomial.
A random sample of 49 statistics examinations was taken. the average score, in the sample, was 84 with a variance of 12.25. the 95% confidence interval for the average examination score of the population of the examinations is
Answers
Given a random sample of 49 exams with an average score of 84 and variance of 12.25, the 95% confidence interval for the average score for the all exams is between 82.4 and 85.6.
Explanation:Based on the given problem, a random sample of 49 statistics exams was examined. The statistics from this sample recorded an average score of 84 with a variance of 12.25. Using this information, we can establish a 95% confidence interval for the average score for the entire population of statistics exams - that's our goal here.
To calculate this, we take the sample mean (84) and add and subtract the standard deviation (sqrt(12.25)=3.5) multiplied by the z value for 95% confidence level (which is about 1.96).
The confidence interval calculation should look like this: [84 - (1.96*3.5/sqrt(49)), 84 + (1.96*3.5/sqrt(49))]. Obtaining 82.4 and 85.6 as the lower and upper limits, we can see that our 95% confidence interval estimate for the population's average exam score is from 82.4 to 85.6.
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Which of the following is a measurement conversion that you may need to make when comparing energy and mass in nuclear reactions? (A)degrees Celsius to Kelvin (B) grams to tons (C)kilojoules to joules (D)meters per second to miles per hour
Answers
Answer:
C
Step-by-step explanation:
Duncan shares 20 percent of all of his sales commissions with his personal assistant. If Duncan earns x dollars in commissions and gives his assistant y dollars, which equation correctly models this situation? mc011-1.jpg
Answers
if x = the total commissions, and 20% goes to his assistant, you would need to multiply your total sales commissions by 0.2 to find 20%, and that would be the total given to the assistant.
Hope this helps
Answer:
X * (0.2)y
Step-by-step explanation:
In how many ways can we seat 6 people around a round table if Fred and Gwen insist on sitting opposite each other? (Two seatings are considered equivalent if one is a rotation of the other.)
Answers
Fred and Gwen are seated opposite each other, and we name the 4 remaining seats 1, 2, 3, 4, starting from the right of Fred.
There are 4 options for seat 1,
then 3 for the seat 2, after one is seated in the 1.st seat
2 options for the seat 3,
and 1 for the seat 4.
That is, the 4 friends can sit in 4*3*2*1=24 different ways.
Answer: 24
Answer:
24
Step-by-step explanation:
PLEASE HELP IM IN A HURRY
Answers
The graph of f(x) = x^2 has been shifted into the form f(x) = (x − h)^2 + k
What is the value of h?
Answers
[tex]\bf \bullet \textit{ stretches or shrinks horizontally by } {{ A}}\cdot {{ B}}\\\\ \bullet \textit{ flips it upside-down if }{{ A}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the x-axis} \\\\ \bullet \textit{ flips it sideways if }{{ B}}\textit{ is negative}\\ \left. \qquad \right. \textit{reflection over the y-axis}[/tex]
[tex]\bf \bullet \textit{ horizontal shift by }\frac{{{ C}}}{{{ B}}}\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is negative, to the right}\\\\ \left. \qquad \right. if\ \frac{{{ C}}}{{{ B}}}\textit{ is positive, to the left}\\\\ \bullet \textit{ vertical shift by }{{ D}}\\ \left. \qquad \right. if\ {{ D}}\textit{ is negative, downwards}\\\\ \left. \qquad \right. if\ {{ D}}\textit{ is positive, upwards}\\\\ \bullet \textit{ period of }\frac{2\pi }{{{ B}}}[/tex]
with that template in mind, let's see, it went to the right 2 units, and then up 3 units.
that simply means, C = -2, D = 3.
Answer: h=2
hope this helps
Which number can each term of the equation be multiplied by to eliminate the fractions before solving? 6 –3/4x +1/3 =1/2 x + 5
Answers
This works as the fractions are the same value, they are just bigger numbers.
Answer:
The number is 12.
Step-by-step explanation:
Given: [tex]6-\dfrac{3}{4}x+\dfrac{1}{3}=\dfrac{1}{2}x+5[/tex]
We need to find a number multiply to each term to get rid of fraction.
We will find LCD of denominator.
First we see the numbers at denominator
Denominators are 4,3,2
Now, we will find the LCD of 2,3, and 4
Factor of 2: 2x1
Factor of 3: 3x1
Factor of 4: 2x2x1
LCD = 2x2x3 = 12
If we multiply by 12 to each term to eliminate the fraction.
Simplest equation:
[tex]12\cdot 6-12\cdot \dfrac{3}{4}x+12\cdot \dfrac{1}{3}=12\cdot \dfrac{1}{2}x+12\cdot 5[/tex]
[tex]72-9x+4=6x+60[/tex]
Hence, The number is 12.
Last year Jill was 5.1 feet tall she grew 8% taller in 1 year how tall is she know
Answers
A flat-screen television has a rectangular screen that is 29 inches high and 32 inches wide. What is the surface area of the screen?
A. 120 sq. in.
B. 60 sq. in.
C. 784 sq. in.
D. 928 sq. in.
Answers
multiply height by width
29 x 32 = 928 sq in
Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = 4 - 3 sin θ
Answers
Answer:
Symmetry about y-axis
Step-by-step explanation:
We are given that
[tex]r=4-3sin\theta[/tex]
When the graph is symmetric about x- axis then the point (x,y) change in to (x,-y) and the function remain same.
The point[tex] (r,\theta,)[/tex] is replaced by [tex]( r,-\theta)[/tex]
Substitute the value then we get
[tex]r=4-3 sin(-\theta) [/tex]
[tex]r=4+3sin\theta[/tex] ([tex]sin(-\theta)=-sin\theta)[/tex]
The value of function changes .Hence , the function is not symmetric about x- axis.
When the function is symmetric about y-axis then the point [tex](r,\theta) [/tex] change into point [tex](r,\pi-\theta)[/tex] and function remain same
Substitute the value
[tex]r=4-3sin(\pi-\theta)[/tex]
[tex]r=4-3 sin\theta[/tex] ([tex]sin(\pi-\theta)=sin\theta[/tex])
The value of function does not change when point change ,Hence, the function is symmetric about y- axis.
When the graph is symmetric about origin then the point [tex](\theta,r)[/tex] change into point[tex](r,\pi+\theta)[/tex] and the value of function remain same.
Substitute the value then we get
[tex]r=4-3sin(\pi+\theta)[/tex]
[tex]r=4+3sin\theta [/tex]
[tex]r=4+3sin\theta [/tex]
Hence, the graph has symmetry about y-axis .
When constructing a circle inscribed in a triangle, what is the purpose of constructing a perpendicular segment from the incenter to a side of the triangle?
To determine the center of the circle
To determine the radius of the circle
To connect the midpoints of each side of the triangle
To connect the arc markings from the angle bisectors
Answers
When a circle is inscribed in a triangle, it means that the circle is drawn inside a triangle such that the midpoints of each side of the triangle are tangent to the circle. By doing this, you draw the biggest circle that could fit inside a triangle.
Now, the circle and the triangle have the same center illustrated here by the red dot. When you connect all sides of the triangle to the center (yellow lines), you create three equal angles. This is equal to 360 (one revolution) divided by 3, equals 120°. But when you create a perpendicular bisector from the center (black line), the angle is halved. It will now be 120/2 = 60°. Usually you are given the sides of the triangle. By using pythagorean theorems, you can find, therefore, the radius of the circle. To illustrate, the radius is equal to (s/2)/tan60.
Thus, the answer is: To determine the radius of the circle.
If Julie invests $9,250 at a rate of 7%, compounded weekly, find the value of the investment after 5 years. $13,455.78
Answers
Use this formula
[tex]A=P(1+ \frac{r}{n} ) ^{(n)(t)} [/tex] where A is the ending amount, P is the starting amount, n is the number of times it compounds a year, and t is the number of years. We have all we need to set it up:
[tex]A=9,250(1+ \frac{.07}{52} ) ^{(52)(5)} [/tex]
First divide and add inside the parenthesis:
[tex]A=9,250(1.001346) ^{(52)(5)} [/tex]
then multiply the exponents:
[tex]A=9,250(1.001346) ^{260} [/tex]
raise the value inside the parenthesis to the power of 260:
[tex]A=9,250(1.418676)[/tex]
and finally multiply to get A = $13,122.76
What is the value of x in the isosceles trapezoid below
Answers
(That graphic is very blurry. I hope I can read it correctly.)
14x + 3x + 10 = 180
17x = 170
x = 10
Answer:
X=10
Step-by-step explanation:
In order to solve this problem you just have to remember that in rectangles and trapezoids opposite angles are suplemmentary, in this case you can equal those to 180º, your equation would be:
[tex]14x+3x+10=180\\17x+10=180\\17x=180-10\\[/tex]
[tex]17x=170[/tex]
[tex]x=\frac{170}{17}[/tex]
[tex]x=10[/tex]
So the answer is X equals to 10.
Last month, a company had receipts totaling $3,700. The company had overhead costs of $444. What is the rate of overhead? A. 11% B. 10% C. 13% D. 12
Answers
divide the overhead by total receipts
444/3700 = 0.12
0.12 = 12%
The tides around Cherokee Bay range between a low of one foot to a high of 5 feet. The tide is at its lowest point when time, t, is 0 and completes a full cycle over a 24 hour period. What is the amplitude, period, and midline of a function that would model this periodic phenomenon
A. Amplitude = 4 feet; period = 24 hours; midline: y = 3
B. Amplitude = 2 feet; period = 12 hours; midline: y = 2
C. Amplitude = 2 feet; period = 24 hours; midline: y = 3
D. Amplitude = 4 feet; period = 24 hours; midline: y = 2
Answers
Answer:
its C
Step-by-step explanation:
How would I graph these equations?
a. 2x + 3y = 12
b. x = 7
Answers
A
For Part A, we must first put this in Slope Intercept Form (SIF), which is y=mx+b where "m" is the slope and "b" is the y-intercept. To do this, we should solve like a normal equation for y.
2x+3y=12
-2x -2x
3y=-2x+12
/3 /3
y=-2/3x+4
Now that we have the proper equation, it is simply to graph! We should simply make a point at (0, 4), and then go down 2, right 3 until you are satisfied with your line.
B
Part B is a simple x value, which means you will draw a vertical line through 7 on the x-axis.
Below I have attached a clearly labeled graph that shows you examples of these lines. The red markings indicate x=7. The yellow circle shows you the y-intercept in Part A, while the yellow dots show you the slope in Part A.
Determine the factors of x2 − 8x − 12.
a. (x − 6)(x + 2)
b. (x + 3)(x − 4)
c. Prime
d. (x + 6)(x − 2)
Answers
Pretty sure its C because none of the other options factor to x^2-8x-12
Answer:
The correct option is: c. Prime
Step-by-step explanation:
The given expression is: [tex]x^2 -8x-12[/tex]
First we will take each given option and simplify them using FOIL method to see if we get the original given expression. So.....
[tex]a.\ \ \ (x-6)(x+2)\\ \\ =x^2+2x-6x-12\\ \\ =x^2-4x-12\\ \\ \\ b.\ \ \ (x+3)(x-4)\\ \\ =x^2-4x+3x-12\\ \\ =x^2-x-12\\ \\ \\ d.\ \ \ (x+6)(x-2)\\ \\ =x^2-2x+6x-12\\ \\ =x^2+4x-12[/tex]
We can see that options [tex]a, b\ and\ d[/tex] doesn't give the original given expression.
So, the expression [tex]x^2 -8x-12[/tex] is Prime.
list the sides of triangle WXY in order from smallest to largest
Answers
The sides of triangle WXY can be listed from smallest to largest as YW, WX, XY, by matching the side lengths to a set of Pythagorean triplets (5, 12, and 13 cm). This corresponds to option A of the provided choices.
To list the sides of triangle WXY in order from smallest to largest, we can use the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
According to the given information, we have two right triangles with sides 5 cm, 12 cm, and 13 cm.
Recognizing these are Pythagorean triplets, where 5 and 12 are the legs and 13 is the hypotenuse, it indicates that the side measures 13 cm is the longest side, followed by the 12 cm side, and then the 5 cm side is the shortest.
Therefore, if we match these lengths to the sides of triangle WXY, we can list the sides from smallest to largest based on their corresponding lengths, with the assumption XY matches the 13 cm side (as it is not specified and must be inferred).
The correct listing of triangle sides from smallest to largest would be: YW, WX, XY. This correlates to option A in your list.
The probable question may be:
list the sides of triangle WXY in order from smallest to largest
A. YW, WX, XY
B. XY, YW,WX
C. WX,XY,YW
D. XY, WX,YW
The regular price of a child's entry ticket to a water park is $6 less than that for an adult's. The park offers half off all entry tickets during the off-peak season. The Sandlers paid a total of $78 for 1 adult ticket and 2 child's tickets to the water park during the off-peak season. The following equation represents this situation, where x represents the regular price of an adult ticket: 78 = one-half x + (x − 6)
Answers
the expression for the child's ticket is [tex]x-6[/tex]
The price of adult's ticket during off-peak season is [tex] \frac{1}{2}x [/tex]
The price of child's ticket during off-peak season is [tex] \frac{1}{2}(x-6) [/tex]
The total cost paid by The Sandlers is $78
The equation is [tex]78= \frac{1}{2}x- \frac{1}{2}(2(x-6)) [/tex] = [tex] \frac{1}{2}x+(x-6) [/tex]
rearranging to solve the equation
[tex]78= \frac{1}{2}x+x-6 [/tex]
[tex]78= \frac{3x}{2} -6[/tex]
[tex]78+6= \frac{3x}{2} [/tex]
[tex](84)(2)=3x[/tex]
[tex] \frac{168}{3} =x[/tex]
[tex]x=56[/tex]
The price of one adult's ticket is $56 (normal price) and the price of one child's ticket is $50
How to calculate ten percent of something?
Answers
you do .10 * 50 to get 5.
Every minute, the first letter of each word is moved to the other end of the word. After how many minutes will the original sentence first reappear?
Answers
To find the time it takes for the original sentence to reappear, we need to find the least common multiple (LCM) of the cycle counts of each word. The LCM of the cycle counts gives us the number of minutes for the original sentence to reappear.
Explanation:To find the number of minutes it takes for the original sentence to reappear, we need to analyze the pattern of the letters in a word. Let's take an example sentence: 'The quick brown fox jumps over the lazy dog.' After the first minute, the sentence becomes 'ehT uickq norwb foxp smuj revo eht yzal god.' Notice that each word has its first letter moved to the end. So, each word becomes a cyclic permutation of itself, with a period equal to the number of letters in the word.
Now, let's count the number of cycles for each word in the original sentence. 'The' has one cycle, 'quick' has five cycles, 'brown' has five cycles, 'fox' has three cycles, 'jumps' has five cycles, 'over' has four cycles, 'the' has one cycle, 'lazy' has four cycles, and 'dog' has three cycles. To find the time it takes for the original sentence to reappear, we need to find the least common multiple (LCM) of these cycle counts. The LCM of 1, 5, 5, 3, 5, 4, 1, 4, and 3 is 60.
Therefore, it will take 60 minutes for the original sentence to first reappear.
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If one coin is flipped and then a second coin is flipped, what is the probability that both coins turn up tails? question 18 options:
Answers
1/2 x 1/2 = 1/4