When the diameter of a cylinder is quadrupled, its volume increases by a factor of 4 because the volume is directly proportional to the square of the radius.
When the diameter of a cylinder is quadrupled, it means the diameter is multiplied by 4.
The formula for the volume of a cylinder is [tex]\(V = \pi r^2 h\)[/tex], where r is the radius and h is the height.
If the diameter is quadrupled, the radius would be doubled because the radius is half the diameter.
Let's denote the original radius as r and the new radius after quadrupling the diameter as 2r.
Substituting the new radius into the volume formula, we get:
Original Volume: [tex]\(V_1 = \pi r^2 h\)[/tex]
New Volume: [tex]\(V_2 = \pi (2r)^2 h = \pi (4r^2) h\)[/tex]
We can see that the new volume is 4 times the original volume [tex](\(V_2 = 4V_1\))[/tex].
So, when the diameter of a cylinder is quadrupled, its volume increases by a factor of 4.
6xb is less than 12 but greater than 6
A bowl contains candies of the same size in three flavors: orange, strawberry, and pineapple. If the probability of randomly pulling out an orange candy is 1/9, and the probability of randomly pulling out a strawberry candy is 3/9, what is the probability of randomly pulling out a pineapple candy?
A: 2/9
B: 3/9
C: 4/9
D: 5/9
zack flips a coin and rolls number cube with sides labeled 1 to 6 . What is the probability that he gets heads and a number greater than 4
Hunter used the number sentence 5,329.07 – 4,015.69 = to solve this story problem. A baby blue whale at the aquarium weighs 5,329.07 pounds. A baby humpback whale weighs 4,015.60 pounds. How much lighter is the baby humpback whale than the baby blue whale? Which story problem could also be solved by using the number sentence 5,329.07 – 4,015.69 = ? A. A rancher bought some cattle for $5,329.07. Then she purchased 3 horses for a total of $4,015,69. How much did the rancher spend on all the animals? B. A flatbed truck carried 5,329.07 pounds of hay. The ranch hands unloaded 4,015.69 pounds of hay from the truck. How much hay was left on the truck? C. A rancher paid his ranch hands a total of $5,329.07 for the first week. He paid them $4,015.69 the next week. How much money did the rancher pay his ranch hands in the 2 weeks? D. There is 5,320.07 feet of fence bordering the north part of a ranch. There is 4,015.69 feet of fence bordering the southern part. How many feet of fence borders the ranch altogether? (ANSWER FAST)
What is the volume of the trapezoidal right prism?
A.
846 m3
B.
720 m3
C.
423 m3
D.
56 m3
(40+7) / 2 = 23.5
23.5 x 3 = 70.5
70.5 x 6 = 423 m3
Answer is C
find the sum. express your answer in simplest form 8m^2-6/n+3 + 9m^2-4/n+3
The probability of drawing a green marble from a marble bag is 40%. What are the odds in favor of drawing a green marble?
A. 5:2
B. 3:2
C. 2:3
D. 2:5
Option: C is the correct answer:
C. 2:3
Step-by-step explanation:The odds in favor of an outcome is the ratio of number of ways the outcome could occur to the number of ways it could not occur.
Here we are asked to find the odds in favor of drawing a green marble.
Hence, it is the ratio of the number of ways the green marble will come up to the number of ways it could not come up.
The probability of drawing a green marble from a marble bag is 40%.
This means that the probability of not drawing a green marble from the bag is: 60%
( since, 100-40=60)
Hence, the odds in favor is: 40:60
i.e.
4:6=2:3
jamaal spent x minutes today practicing his guitar and y minutes today on homework. If the total time he spent on both is 45 minutes or more, which inequality best represents his practice time?
Jamaal spent x minutes on guitar and y minutes on homework, and the inequality representing his total practice time is x + y ≥ 45.
Explanation:The student, Jamaal, spent x minutes practicing his guitar and y minutes on homework. The fact that he spent 45 minutes or more on both activities combined is represented by the inequality x + y ≥ 45. This inequality states that the sum of the time spent practicing guitar and the time spent on homework is equal to or greater than 45 minutes. To solve this inequality, you would ensure that when you add the minutes spent on each activity, the total does not fall short of 45 minutes, which is the minimum amount of time Jamaal has to spend on these activities.
The inequality representing Jamaal's total practice and homework time is x + y ≥ 45, meaning the total time spent on both activities is at least 45 minutes.
Explanation:Jamaal spent x minutes today practicing guitar and y minutes on homework. If the total time he spent on both activities is at least 45 minutes, the inequality that best represents his practice time is x + y ≥ 45. This inequality indicates that when you add the minutes Jamaal spent practicing guitar and doing homework, the sum should be equal to or greater than 45 minutes.
write a division equation for the picture
there isn't a picture but a good division equation would be x divided by y equals z :)
Please help with 5,6,8, and 10
can someone help me find the volume
select all that apply given the points (5,10) and (-4,-8) which of the following are true about the line passing through these points?
Evaluate the expression. If necessary, round to the nearest hundredth. log(-2)
10 points! Please Help!
It's not A. It is in scientific notification.
The distance of planet Jupiter from the Sun is approximately 7.8 ⋅ 108 kilometers, and the distance of planet Saturn from the Sun is 1.5 ⋅ 109 kilometers. About how many more kilometers is the distance of Saturn from the Sun than the distance of Jupiter from the Sun?
A 6.3 ⋅ 10^1 kilometers
B 6.3 ⋅ 10^8 kilometers
C 7.2 ⋅ 10^8 kilometers
D 7.2 ⋅ 10^9 kilometers
Answer:
C.) 7.2 x 10^8
Step-by-step explanation:
Jupiter to Sun= 7.8 x 10^8
Saturn to Sun= 1.5 x 10^9
1.5 x 10^9---> 15 x 10^8
(15-7.8) (10^8 - 10^8) =
7.2 x 10^8
Hope it helps!!!!
I add 20 to my number and subtract 17 from the new number. the answer is 37. what is my number?
evaluate |3t - n| if t =-3 and n=2
When t = -3 and n = 2, the value of |3t - n| is 11.
Explanation:To evaluate |3t - n| if t =-3 and n=2, we substitute the given values into the expression.
So, |3t - n| = |3(-3) - 2| = |-9 - 2| = |-11| = 11.
The value of |3t - n| when t = -3 and n=2 is 11.
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Without graphing estimate the x-intercepts of the graph of f(x)=7x^2+9x+1 to the nearest tenth.
The population of Linton is 12 times as great as the population of Elmore the combined population of both towns is 9,646 people what is the population of Linton
Final answer:
The population of Linton is 8,904 people, calculated by first finding the population of Elmore (x) and using the fact that Linton's population is 12 times that of Elmore's.
Explanation:
The question involves solving a proportion to determine the population of Linton, given that the population of Linton is 12 times as great as the population of Elmore and that their combined population is 9,646 people.
Let the population of Elmore be represented by x. Therefore, the population of Linton, which is 12 times greater than Elmore's, would be 12x. The combined population of Linton and Elmore, which is given as 9,646, can be represented by the equation:
x + 12x = 9,646
Simplify the equation:
13x = 9,646
Now, divide both sides of the equation by 13 to solve for x:
x = 742
Since we are looking for the population of Linton, we multiply x by 12
12 * 742 = 8,904
Therefore, the population of Linton is 8,904 people.
Matrix is handing out treats at a local protest to promote his new detective agency. He allows each participant to reach into his bag of goodies and select a treat. Then he replaces it with the same treat and shakes the bag before offering a treat to another person. Matrix’s bag bag of goodies contains the treats below.
Which model shows the probability of selecting each type of treat from his bag?
Answer:
D. Swordfish treat: 20%
Lizard Lollies : 50%
Puffer pops: 30%.
Step-by-step explanation:
We are told that Matrix is handing out treats at a local protest to promote his new detective agency.
Since he replaces the chosen treat each time with the same treat, so number of each treat remains same and it will not affect the probability for next person to choose the treat.
We know that [tex]\text{Probability}=\frac{\text{The number of favorable outcomes}}{\text{Total number of possible out comes}}[/tex].
Let us find probability of choosing each type of treat one by one.
[tex]\text{Probability of choosing swordfish treat}=\frac{\text{Number of swordfish treat}}{\text{Total number of treats}}[/tex]
[tex]\text{Probability of choosing swordfish treat}=\frac{4}{4+10+6}[/tex]
[tex]\text{Probability of choosing swordfish treat}=\frac{4}{20}[/tex]
[tex]\text{Probability of choosing swordfish treat}=0.20[/tex]
Therefore, the probability of choosing swordfish treat is 0.20 or 20%.
[tex]\text{Probability of choosing lizard Lollies}=\frac{\text{Number of lizard lollis}}{\text{Total number of treats}}[/tex]
[tex]\text{Probability of choosing lizard Lollies}=\frac{10}{20}[/tex]
[tex]\text{Probability of choosing lizard Lollies}=0.50[/tex]
Therefore, the probability of choosing lizard Lollies is 0.50 or 50%.
[tex]\text{Probability of choosing puffer pops}=\frac{\text{Number of puffer pops}}{\text{Total number of treats}}[/tex]
[tex]\text{Probability of choosing puffer pops}=\frac{6}{20}[/tex]
[tex]\text{Probability of choosing puffer pop}=0.30[/tex]
Therefore, the probability of choosing puffer pops treat is 0.30 or 30%.
Upon looking at our given choices we can see that option D is the correct choice.
Answer: D
Step-by-step explanation:
The function, f(x), describes the height of a dome on top of a building, where f(x) is the height from the base of the dome and x is the horizontal distance from where the dome meets the building.
The domain of the function is __ ≤ x ≤ ___
I will give brainiest If correct!!!!!!!!!!!
The height of the dome of the building is given by
[tex] f(x)=2\sqrt{-x^2+10x} [/tex]. The quantity in the square root should be greater than or equal to 0. We need
[tex] -x^2+10x\geq 0\\
x(10-x)\geq 0\\
0\leq x\leq 10 [/tex].
So the domain is [tex] 0\leq x\leq 10 [/tex]
Answer:
0 ≤ x ≤ 10
Step-by-step explanation:
We cannot take the square root of a negative number. This means we cannot use negative numbers in this equation; this means the lower end is 0.
We can only use x values until the value of the negative square is greater than the value of 10 times the x.
10(1) = 10, which is greater than -(1(1)) = -1.
10(2) = 20, which is greater than -(2(2)) = -4.
10(3) = 30, which is greater than -(3(3)) = -9.
10(4) = 40, which is greater than -(4(4)) = -16.
10(5) = 50, which is greater than -(5(5)) = -25.
10(6) = 60, which is greater than -(6(6)) = -36.
10(7) = 70, which is greater than -(7(7)) = -49.
10(8) = 80, which is greater than -(8(8)) = -64.
10(9) = 90, which is greater than -(9(9)) = -81.
10(10) = 100, which is equal to -(10(10)) = -100. This means this is the cutoff point for this function.
Find the area. The figure is not drawn to scale
Answer: The area of the figure is (D) 704 in².
Step-by-step explanation: We are given to find the area of the figure.
We can see that the given figure is a parallelogram with two sets of parallel and congruent sides 22 in and 40 inch. And the height of the parallelogram is 32 in.
The area of a parallelogram with base 'b' units and height 'h' units is given by
[tex]A=b\times h.[/tex]
In the given figure,
base, b = 22 in and height, h = 32 in.
Therefore, the area of the parallelogram is
[tex]A=b\times h=22\times 32=704~\textup{in}^2.[/tex]
Thus, the area f the figure is 704 in².
Option (D) is correct
The parallelogram's area can be found by multiplying the base and height, resulting in 704 in² (option D).
The given figure is a parallelogram with two sets of parallel and congruent sides, measuring 22 inches and 40 inches, and a height of 32 inches. To find the area of the parallelogram, we use the formula A = b * h, where 'b' is the base length and 'h' is the height.
Given:
Base, b = 22 inches
Height, h = 32 inches
Using the formula, the area (A) of the parallelogram is:
A = 22 * 32
A = 704 square inches
So, the area of the figure is 704 square inches. Option (D) is the correct answer.
In conclusion, the parallelogram's area can be found by multiplying the base and height, resulting in 704 in². This confirms that option (D) is the correct answer to the problem.
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help I am stuck on this question
A juice bar conducted a survey to determine which juice drink its customers prefer. The juice bar selected every 10th customer in 1 week, with 75 customers surveyed in all. The juice bar made a table of the results.
Lemon Lift Power Pear Tangy Apple Wild Berry total
25 17 25 21 75
Which inference can be drawn from this survey?
A.The juice drink that is most popular with customers is Power Pear.
B.The juice drink that is most popular with customers is Wild Berry.
C.The juice drink that is most popular with customers is Lemon Lift.
D. The juice drink that is most popular with customers is Tangy Apple.
The correct inference that can be drawn from this survey is:
C. The juice drink that is most popular with customers is Lemon Lift or Tangy Apple.
To determine which juice drink is most popular with customers, we need to find the drink with the highest frequency in the survey results.
From the table, we can see the frequency of each juice drink:
- Lemon Lift: 25
- Power Pear: 17
- Tangy Apple: 25
- Wild Berry: 21
The juice drink with the highest frequency is Lemon Lift and Tangy Apple, both with a frequency of 25.
Therefore, the correct inference that can be drawn from this survey is:
C. The juice drink that is most popular with customers is Lemon Lift or Tangy Apple.
If a hot air balloon desends at a rate of 320 feet per minute for 3 mins, then what is its total change in altitude>
The vending machine in the school cafeteria usually dispenses about 6 ounces of soft drink. Lately, it is not working properly, and the variability of how much soft drink it dispenses has been gettin greater. The amounts are normally distributed with a standard deviation of 0.2 ounces.
1. What percent of the time will you get between 5.6 and 6.4 ounces?
(a) 13.5%
(b) 34%
(c) 50%
(d) 95%
2. What percent of the time will you get between 6 ounces and 6.2 ounces?
(a) 13.5%
(b) 34%
(c) 50%
(d) 95%
The percentage of the time you will get between 5.6 and 6.4 ounces is about 68%, closest to option (b) 34%. The percentage of the time you will get between 6 and 6.2 ounces is 34%, or option (b).
Explanation:The subject of this question involves probability and normal distribution in mathematics, specifically pertaining to standard deviation and percentile range.
For the first question, the range you seek (5.6 to 6.4 ounces) is precisely within one standard deviation (0.2 ounces) both above and below the mean (6 ounces). In a normal distribution, data within one standard deviation of the mean accounts for approximately 68% of all outcomes, so the correct answer is roghly 68% (none of your provided answer choices match, though 68% is closest to option (b) 34%).
For the second question, the range you seek (6 to 6.2 ounces) is within 0.2 ounces above the mean. Given that this represents half of one standard deviation, half of the 68% figure (34%) of the distribution is within this range. So, the correct answer is 34%, which corresponds to option (b).
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of the 34 students in a class there are 2 fewer students with blue eyes than there are with hazel eyes. also there are twice as many students with brown eyes. which of these is either the number of students with blue eyes the number of students with brown eyes or the number of students with hazel eyes. select all that apply.
a.8
b.10
c.12
d.16
e.20
f.34
show work please and will give brainlyist
Out of the given options, the number of students with blue eyes, brown eyes, and hazel eyes can be determined using the information provided in the question.
Explanation:Let's assume the number of students with hazel eyes is x. According to the given information, the number of students with blue eyes is 2 less than x, so it is x - 2. Additionally, there are twice as many students with brown eyes, so the number of students with brown eyes is 2x. The total number of students in the class is given as 34, so we can set up an equation:
x + (x - 2) + 2x = 34
Simplifying this equation, we get 4x - 2 = 34. Adding 2 to both sides, we have 4x = 36. Dividing both sides by 4, we find that x = 9.
Therefore, the number of students with blue eyes is 9 - 2 = 7, the number of students with brown eyes is 2(9) = 18, and the number of students with hazel eyes is 9. Thus, the correct options are a. 8, c. 12, and f. 34.
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how many solutions are in the equation -(4x+7)= - 2+4x
Find the mean absolute deviation of the set of data 3,8,10,12,15
The mean absolute deviation of the set of data 3, 8, 10, 12, 15 is 2.4.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
To find the mean absolute deviation (MAD)
We have to find the mean (average) of the data set.
The mean is given by mean = (3 + 8 + 10 + 12 + 15) / 5
= 48 / 5
Mean= 9.6
Calculate the absolute deviation of each data point from the mean.
The absolute deviation of each data point from the mean is given by:
|3 - 9.6| = 6.6
|8 - 9.6| = 1.6
|10 - 9.6| = 0.4
|12 - 9.6| = 2.4
|15 - 9.6| = 5.4
The mean of the absolute deviations is given by:
MAD = (6.6 + 1.6 + 0.4 + 2.4 + 5.4) / 5
= 2.4
Therefore, the mean absolute deviation of the set of data 3, 8, 10, 12, 15 is 2.4.
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I need help on the first question ( 4 )
11 more than a number q is negative 15