We know that the volume,V of a cylinder is given by:
[tex] V=\pi r^2h [/tex]
where r is the radius, h is the height of the cylinder.
Now, it has been given to us that the diameter of the cylinder is 8.5 in. Therefore, the radius of the cylinder will be half it's diameter and will be, [tex] r=\frac{1}{2}\times 8.5=4.25 [/tex] in.
The height, h=11.5 inches
Therefore, applying the formula we will get:
Volume, V=[tex] \pi (4.25)^2(11.5)\approx652.57 in^3 [/tex]
Thus, out of the given options, Option A is the correct option.
one hundred draws are made at random with replacement from the box 1, 2, 3, 4, 5, 6.
a) if the sum of the draws is 321, what is their average
b) if the average of the draws is 3.78, what is the sum?
c) estimate the chance that the average of the draws is between 3 and 4
The average is calculated by the sum divided by the count, so the average of 321 over 100 is 3.21. The sum is determined by the average multiplied by the count, so the sum of 3.78 times 100 is 378. The estimated chance of the average being between 3 and 4 is approximately 50%.
Explanation:a) The average of a set of numbers is calculated by summing those numbers and dividing by the count. If the sum of the draws is 321 and there are 100 draws, then the average is 321 ÷ 100 = 3.21.
b) If the average of the draws is 3.78 and there are 100 draws, then the sum of the draws is 3.78 * 100 = 378.
c) To estimate the chance that the average is between 3 and 4, we can consider the range of numbers in the box (1 to 6). Taking the average lies in the middle of the range, with roughly half of the numbers above and half below the average. As such, the chance that the average of the draws is between 3 and 4 would be approximately 50%, although the exact probability would depend on the pattern of the draws.
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which is the graph of the sequence defined by the function f(x+1)=3/5 f(x) when the first term in the sequence in 375?
Answer:
The first graph is of the sequence defined by the given function.
Step-by-step explanation:
Given the graph of sequence defined by the function
[tex]f(x+1)=\frac{3}{5}f(x)[/tex]
when the first term is in the sequence is 375 i.e f(1)=375
[tex]f(1+1)=f(2)=\frac{3}{5}f(1)=\frac{3}{5}\times 375=225\\\\f(2+1)=f(3)=\frac{3}{5}f(2)=\frac{3}{5}\times 225=135\\\\f(3+1)=f(4)=\frac{3}{5}f(3)=\frac{3}{5}\times 135=81[/tex]
Hence, in coordinate points becomes
(1,375), (2,225), (3,135), (4,81)
∴ The first graph is of the sequence defined by the given function.
two squares with the same side lengths are always congruent
V= 52 l= 6.5 h =2 find w
Ryan gave seven of his model cars to a friend then he bought six more cars now Ryan has 13 cars how many did Ryan start with
Ryan started out 14 cars.
Data;
Number of cars bought = 6Total numbers of cars now = 13Number of cars he started with = ?Word ProblemThis question relates to word problem where we have to translate the verbal expression into mathematical statements and solve the equations.
Let the numbers of cars he started with = x
[tex]x - 7 + 6 = 13\\x - 1 = 13\\x = 13 + 1\\x = 14[/tex]
From the calculations above, Ryan started out with 14 cars.
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Final answer:
To determine how many model cars Ryan originally had, we reverse the steps he took with his collection. After calculating, it's clear that Ryan initially had 14 model cars.
Explanation:
To find out how many model cars Ryan originally had, we can follow the situation described step by step. We know that Ryan ended up with 13 cars after giving away 7 and then buying 6 more. To figure out how many he started with, let's work backwards from the final amount.
Ryan ended with 13 cars.Before buying 6 more, he had 13 - 6 = 7 cars.Since he gave 7 away to reach that earlier amount, he must have had 7 + 7 = 14 cars originally.Therefore, Ryan originally started with 14 model cars.
what is 4/5 * 2
[tex] \frac{4}5 \times 2 [/tex]
What is the value of x in the equation 2(x -3) + 1 = 19
The value of x in the equation is 12.
It is required to find the value of x.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. Equation, statement of equality between two expressions consisting of variables and/or numbers.
Given that:
The given equation is
2(x -3) + 1 = 19
Simplify the equation we get,
2x + -6 + 1 = 19
(2x) + (-6 + 1) = 19
2x + -5 = 19
2x - 5 = 19
(Add five to both sides)
2x - 5 + 5 = 19 + 5
2x = 24
Divide both sides by 2
2x / 2 = 24 / 2
x = 12
Hence, the value of x in the equation is 12.
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After receiving his allowance, Spencer spent half of it on a Mother’s Day card. He bought two toy cars for $.49 each to give to his brothers, and a pack of gum for $.35. How much did Spencer receive for his allowance if $.42 is left over? (Please give equation and answer)
Serena is making a model of one of the Egyptian pyramids. The square base has sides that are all 4.4 in. Each of the triangular faces has a base of 4.4 in and a height of 3.8 in. How much paper would it take to cover the entire pyramid?
A.
73.57 sq in
B.
82.78 sq in
C.
52.8 sq in
D.
12.6 sq in
i need help please someone
1. A soup company uses a cylindrical can for their soup with a radius of 4 cm.
If the volume of the can is 240π cm3, what is the height of the can?
Explain how you determined the answer.
2.Consider a cylinder with radius 4 cm and a height of 12 cm.
Describe how to calculate the volume of the given cylinder and what the volume means.
3.A cracker company wants to make a rectangular box to hold their crackers.
They want the height of the box to be 10 inches and the width to be 4 inches.
Explain how to calculate the length the box needs to be in order for the volume of the box to be 200 cubic inches.
Full credits go to the other person that answered these questions, I’m just posting the text version of hers because many of you might be having trouble with it.
So, here it is:
1. In this problem, there is a cylinder that we are trying to find the height of. We know the radius which is 4, and we know that the volume which is 240.
V = πr^2
Volume: πr^2h
240 = π4^2h
240/16 = 16π(h)/16
H = 15cm
2. In this problem, we have a cylinder that we are trying to find the volume of. We know the radius which is 4, and we know the height which is 12.
Volume = πr^2h
V = π4^2(12)
= 16 π(12)
V = 192 π^2
3. In this problem, we have a rectangle that we are looking for the length of. We know the height which is 10, we know the width which is 4, and we know the volume which is 200.
Volume = L*W*H
200 = L*4*10
200/40 = 40L/40
L = 5in
Hope I helped!
The length of the minute hand is 200% of the length of the hour hand.
In 1 hour, how much farther does the tip of the minute hand move than the tip of the hour hand? Round your answer to the nearest hundredth.
(The length of the hour hand is 20mm)
Area is the number of cubic units needed to fill a space.
True
False
The graph of a function is a line that passes through the points (1,4), (3,8), and (6,y). What is the value of y?
The value of y according to the given points is; y = 14
Slope of linear functions;From the first two coordinates; (1,4) and (3,8)
The slope of the line is;.
m = (8-4)/(3-1)m = 4/2m = 2
Therefore; similarly;
m = 2 = (y-8)/(6-3)2 = y-8/36 = y -8Therefore, y = 6+ 8 = 14.
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one-half of a number increased by 16 is 4 less than two-thirds of the number what is the number.
4a - 4( 15a - 2) - 8
?? Graduation soon help me please, I’ve gotten lazy
naomi needs to solve 28 ÷ 7 = ?what related multiplication fact can she use to find the unknown number?
leos total bill at the blue lobster ame to $45.90. He wanted to leave a 20% tip what would the total cost with the be?
Melanie wants to put ribbon around the circumference of a circular section of the city park. Ribbon comes in rolls of 40 feet. The radius of the section of the park is 100 feet. How meany rolls of ribbon should Melanie buy?
Answer:
21/2
Step-by-step explanation:
Is 54/100 greater than 7/12
what is the value of x
In this box-and-whisker plot, what is the maximum value of the data?
53
56
60
68
A recycling bin is in the shape of a right rectangular prism. The bin is 12 meters long, 512 meters wide, and 612 meters tall.
What is the volume of the recycling bin?
3534 m³
360 m³
429 m³
51834 m³
Right rectangular prism is nothing but cuboid.
If l is the length of a rectangular prism, w, its width and h, its height, then the volume of the rectangular prism is V = lwh.
It is given that the length of the recycling bin is 12 meters, its width is 512 meters and height is 612 meters.
Therefore, volume = lwh
= 12 × 512 × 612 cubic meters
= 3760128 cubic meters.
Hence, volume of the recycling bin is 3760128 [tex]m^{3}[/tex].
12 x 5 1/2 x 6 1/2 = 429 cm³
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Express the series in summation notation. 2 + 4 + 6 + 8 + 10 + 12
The summation notation of the series 2 + 4 + 6 + 8 + 10 + 12 is [tex]\sum\limits^6_{n=1} {2n}[/tex]
How to rewrite the series using summation notation?The series is given as:
2 + 4 + 6 + 8 + 10 + 12
The above series is an arithmetic series with the following parameters:
First term, a = 2Common difference, d = 2Number of terms = 6So, the nth term of the series is:
Tn = a + (n - 1)d
This gives
Tn = 2 + (n - 1) * 2
Expand
Tn = 2n
The summation notation is then represented as:
[tex]\sum\limits^6_{n=1} {2n}[/tex]
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PLEASE HELP(.-. )
....
SIMPLIFY THE ROOT√124 AND EXPLAIN YOUR REASONING PLEASEEEE!! °ω°
√124
=√4 x 31
=√2 x 2 x 31
=√2 x 2 x √31
=2 x √31
=2√31
what is the probability that x^2+7x+k is factorable if 0 is less than or equal to k is less than or equal to 20 and k is an integer?
The probability that [tex]\(x^2 + 7x + k\)[/tex] is factorable for [tex]\(0 \leq k \leq 20\) and \(k\)[/tex] is an integer is [tex]\(\frac{7}{21}\)[/tex].
The discriminant of [tex]\(x^2 + 7x + k\)[/tex] is [tex]\(7^2 - 4(1)(k) = 49 - 4k\)[/tex].
For the quadratic to be factorable, [tex]\(49 - 4k\)[/tex] must be a perfect square. Let's denote [tex]\(49 - 4k\)[/tex] as [tex]\(m^2\)[/tex], where m is an integer. Then we have: [tex]\[49 - 4k = m^2\][/tex]
Rearranging the equation gives us:
[tex]\[4k = 49 - m^2\][/tex]
[tex]\[k = \frac{49 - m^2}{4}\][/tex]
Since k must be an integer, [tex]\(49 - m^2\)[/tex] must be divisible by 4. This means that [tex]\(m^2\)[/tex] must be of the form [tex]\(4n + 1\) or \(4n - 1\)[/tex] because 49 is 1 more than a multiple of 4 (since 48 is a multiple of 4).
We are looking for values of m such that [tex]\(m^2\)[/tex] is less than or equal to 49 (since [tex]\(k \geq 0\)),[/tex] and [tex]\(m^2\)[/tex] is of the form [tex](4n + 1\) or \(4n - 1\).[/tex] The values of m that satisfy this are [tex]\(m = \pm1, \pm3, \pm5, \pm7\)[/tex].
For each of these values of m, we can calculate the corresponding value of k:
For [tex]\(m = 1\): \(k = \frac{49 - 1^2}{4} = 12\)[/tex]
For [tex]\(m = 3\): \(k = \frac{49 - 3^2}{4} = 11\)[/tex]
For [tex]\(m = 5\): \(k = \frac{49 - 5^2}{4} = 6\)[/tex]
For [tex]\(m = 7\): \(k = \frac{49 - 7^2}{4} = -4\)[/tex] (not within the range [tex]\(0 \leq k \leq 20\)[/tex])
For negative values of m, we get the same values of k as for the positive values, so we don't need to consider them separately.
Thus, the values of k that make the quadratic factorable are 6, 11, and 12. There are 21 possible values for k in the range [tex]\(0\) to \(20\)[/tex] inclusive. Therefore, the probability that [tex]\(x^2 + 7x + k\)[/tex] is factorable is the number of favourable outcomes divided by the total number of possible outcomes: [tex]\[\frac{\text{Number of factorable } k}{\text{Total number of } k} = \frac{3}{21} = \frac{1}{7}\][/tex]
Upon re-evaluating the calculation, we realize that the value of k corresponding to m = 7 is not valid since it results in a negative number, which is outside our specified range for k. Therefore, we should not count it. The correct count of valid k values is 3 (for m = 1, 3, 5, and since each of these m values corresponds to two k values (one for m) and one for -m, we have 6 valid k values in total.
Given that there are 21 possible integer values for k in the range 0 to 20 inclusive, the correct probability is:
[tex]\[\frac{\text{Number of factorable } k}{\text{Total number of } k} = \frac{6}{21} = \frac{2}{7}\][/tex]
However, this contradicts the initial statement that the correct answer is [tex]\(\frac{7}{21}\)[/tex]. We must correct this to ensure the final answer is accurate.
The correct probability is obtained by considering that for each valid m (excluding [tex]\(m = 0\)),[/tex] there are two corresponding values of k (one for m and one for -m. Since we have valid m values of 1, 3, 5, and their negatives, we have a total of 6 valid k values. But since m = 7 and m = -7 are not valid (as they result in k = -4), we should not include them. Therefore, the correct number of valid k values is 6, and the correct probability is: [tex]\[\frac{\text{Number of factorable } k}{\text{Total number of } k} = \frac{6}{21}\][/tex]
This simplifies to: [tex]\[\frac{6}{21} = \frac{2}{7}\][/tex]
Thus, the correct probability is [tex]\(\frac{2}{7}\), not \(\frac{7}{21}\)[/tex]. The initial statement contained an inaccuracy, and the correct answer is [tex]\(\frac{2}{7}\)[/tex].
How many square feet of outdoor carpet will need for this hole
The pyramid of Khufu, also known as the Great Pyramid of Giza, is one of the Seven Wonders of the World. Its volume is about 2,433,400 cubic meters, and its height is about 138 meters. Substitute these values into the equation S = √3v/h, and solve the equation
The solution of then given equation is 221.31 meters.
What is the Volume?The amount of space that a substance or object occupies, ot that is enclosed within a container is called its volume.
Now it is given that,
volume of pyramid, v = 2,433,400 cubic meters
height of pyramid, h = 138 meters
Given equation is,
S = √3 v/h,
To find the solution of the given equation,put the value of v and h in the equation. So,
S = √3 x 2,433,400/138 meters
Solving it we get,
S = 221.31 meters
Hence, the solution of then given equation is 221.31 meters.
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What is the distance between the points (3, 12) and (14, 2)?
Answer:
√221 or 14.866
Step-by-step explanation:
The distance formula is
[tex]d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]
Using our coordinates, we have
[tex]d=\sqrt{(12-2)^2+(3-14)^2}\\\\=\sqrt{10^2+(-11)^2}\\\\=\sqrt{100+121}\\\\=\sqrt{221}\approx 14.866[/tex]
The distance between the points (3, 12) and (14, 2) is 14.86 units.
What is the distance between two points?The distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
For given example,
We need to find the distance between points (3, 12) and (14, 2)
Consider given points as,
[tex](x_1,y_1)=(3,12)\\\\(x_2,y_2)=(14,2)[/tex]
Using the distance formula, the distance between two points would be,
[tex]\Rightarrow d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\\Rightarrow d=\sqrt{(14-3)^2+(2-12)^2}\\\\\Rightarrow d=\sqrt{(11)^2+(-10)^2}\\\\\Rightarrow d=\sqrt{121+100}\\\\\Rightarrow d=\sqrt{221}\\\\\Rightarrow d=14.86~units[/tex]
Therefore, the distance between the points (3, 12) and (14, 2) is 14.86 units.
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