As sand leaks out of a hole in a contaimer, it forms a conical pile whose altitude is always the same as its radius. If the height of the pile is increasing at a rate of 6in/min, find the rate at which sand is leaking out when the altitude is 10 inches.
The rate at which sand is leaking out when the altitude is 10 inches is
600π inches³ / min.
What is a cone?It is a shape of a Christmas tree where there is a base of radius r and a top point called the apex.
The volume of a cone is (1/3)πr²h.
We have,
A conical pile formed due to a leak out of a hole whose radius is equal to its height.
dh/dt = 6 in/min
The rate at which the sand is leaking when height is 10 inches.
We have,
Volume = (1/3)πr²h and h = 10 inches
V = 1/3 πh²h
V = 1/3 πh³
Differentiating both sides.
dV/dt = 1/3 x π x 3 x h² (dh/dt)
dV/dt = π x h² x 6
dV/dt = π x 10² x 6
dV/dt = 600π inches³ / min
Thus,
The rate at which sand is leaking out when the altitude is 10 inches is
600π inches³ / min.
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In a sample of 200 students, what is the probability that over 31% of the sample has ap credit?
It costs $2.80 to make a sandwich at the local deli shop. To make a profit, the deli sells it at a price that is 170% of the cost. The sandwich sells for $ .
commutative
property of addition of 93+ (68+7)
You have 2/3 of a pizza. You divide the remaining pizza into 4 equal pieces. What fraction of the pizza is each piece?
A number cube is rolled with these results: 64 ones, 67 twos, 73 threes, 59 fours, 72 fives, and 71 sixes. What is the experimental probability of rolling an even number?
Write your answer as a percent, to the nearest tenth of a percent.
A. 51.9%
B. 48.5%
C. 53.6%
D. 46.8%
Answer: B. [tex]48.5\%[/tex]
Step-by-step explanation:
Given : A number cube is rolled with these results:
64 ones, 67 twos, 73 threes, 59 fours, 72 fives, and 71 sixes.
Even numbers : 2,4,6
The number of times of rolling even number = [tex]67+59+71=197[/tex]
Total outcomes = [tex]64+67+73+59+72+71=406[/tex]
Now, the experimental probability of rolling an even number :-
[tex]\dfrac{197}{406}[/tex]
In percent, [tex]\dfrac{197}{406}\times100=48.52216748\approx48.5\%[/tex]
Hence, the experimental probability of rolling an even number = [tex]48.5\%[/tex]
Marko currently has 20 tulips in his yard. Each year he plants 5 more. Write an explicit formula for the number of tulips Marko has.
Predict the number of tulips Marko will have in 7 years.
To write an explicit formula for the number of tulips Marko has, use the formula n = a + (x-1)d, where n represents the number of tulips, a is the initial number of tulips, x is the number of years, and d is the change in number of tulips each year. The explicit formula for Marko's tulips is n = 20 + 5(x-1). To predict the number of tulips Marko will have in 7 years, substitute x = 7 into the formula and solve for n, giving Marko will have 50 tulips in 7 years.
Explanation:To write an explicit formula for the number of tulips Marko has, we can use the formula: n = a + (x-1)d. Here, n represents the number of tulips, a is the initial number of tulips (20), x is the number of years, and d is the change in number of tulips each year (5). So, the explicit formula is n = 20 + 5(x-1).
To predict the number of tulips Marko will have in 7 years, we can substitute x = 7 into our formula: n = 20 + 5(7-1). Solving this equation, we get n = 20 + 5(6) = 20 + 30 = 50. Therefore, Marko will have 50 tulips in 7 years.
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The school theater department made $2142 and the department sold the same number of tickets each night and each ticket cost $7. How many tickets did the theater department sell each night?
You should get your answer of 306 :)
[tex]\sqrt[7]{2142}[/tex]
^online division .-.
Translate “the perimeter of a rectangle is equal to 2 times the length plus twice the width
The required translated string of “the perimeter of a rectangle is equal to 2 times the length plus twice the width" is,
Perimeter = 2 * length + 2 * width.
Given that,
To translate “the perimeter of a rectangle is equal to 2 times the length plus twice the width."
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
What is the perimeter?Perimeter is the measure of the figure on its circumference.
Here, the given string, “the perimeter of a rectangle is equal to 2 times the length plus twice the width" can be translated in the mathematical form is,
Perimeter = 2 * length + 2 * width.
Thus, the required translated string of “the perimeter of a rectangle is equal to 2 times the length plus twice the width" is,
Perimeter = 2 * length + 2 * width.
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Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1) and from (9, 1) to (10, 0)
To evaluate the given line integral, you need to parameterize the curve composed of two segments. Then, you solve the integrals along the two separate segments and take the sum.
Explanation:To evaluate the line integral where the curve c consists of line segments from (0, 0) to (9, 1) and from (9, 1) to (10, 0) for the function (x + 9y) dx + x² dy, we need to parameterize the curve and solve the integral.
First, we parametrize the line segments. For the segment from (0, 0) to (9, 1), we have x = 9t and y = t for t in [0, 1]. For the segment from (9, 1) to (10, 0) let x = 9 + s and y = 1 - s for s in [0, 1].
Then, we integrate along the first and second segments separately with respect to t. For the first segment, the integral is ∫(9t + 9t) d(9t) + ∫(81t²) dt = ∫18t dt + ∫81t² dt. For the second segment, the integral is ∫(9 + s + 9(1 - s)) ds + ∫(81 + 2 * 9 * s + s²) d(1 - s) = ∫ds + ∫s² ds.
We then evaluate these integrals over the respective bounds, sum them up and that gives the line integral along the path described.
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paige mows 1/6 acre in 1/4 hour.How many acres does paige mow per hour?
A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 lower than in the first. The tax in the first city was 3.5% , and the tax in the second city was 7.5% . The total hotel tax paid for the two cities was $347.50 . How much was the hotel charge in each city before tax?
Amy Jo found that the perimeter of a square was 53.2 square inches. What is the side length of the square?
perimeter of a square is 4 times side length (4s)
to find the length of a side divide the perimeter by 4
53.2 / 4 = 13.3
so each side is 13.3 inches
A two year degree that focuses on natural science, engineering, and mathematics is called an
Associate of science
Answer:
Assosiate in science
Step-by-step explanation:
An Associate of Science (AS) is a 2-year degree offered by most community colleges. Most AS degrees are transfer degrees and provide an academic foundation, but not specific career training. The A.S. degree is intended for students planning to pursue a bachelor’s degree in the areas of math or science.
I hope you find this information useful and interesting! Good luck!
The table shows the amount of money in your bank account over a period of 5 weeks. The account does not pay interest. You plan to keep saving at the same rate until you have $650 in the account. Which equation could you use to find the number of weeks, n, it would take to reach your goal?
Answer:
35*n+100=650
Step-by-step explanation:
I got the question right on TTM
If a polynomial function f(x) has roots 3 and mc001-1.jpg, what must also be a root of f(x)?
The Complex Conjugate Root Theorem dictates that if -4 is a root of f(x), then 4 must also be a root. This theorem applies to polynomials with real coefficients, ensuring non-real complex roots appear in conjugate pairs.
Explanation:If a polynomial function f(x) has roots 3 and -4, then by the Complex Conjugate Root Theorem (also known as the Conjugate Pairs Theorem), if the polynomial has real coefficients, which is the usual assumption unless stated otherwise, the complex roots must come in conjugate pairs. Therefore, if -4 is a root, its complex conjugate 4 must also be a root of f(x). This applies to all non-real complex roots of a polynomial with real coefficients.
The Complex Conjugate Root Theorem is essential for understanding the behavior of polynomial functions with complex roots. In general, if a polynomial has a complex root a + bi, where a and b are real numbers and i is the imaginary unit (the square root of -1), its conjugate a - bi is also a root. This is true because polynomial equations with real coefficients have the property that their roots are either real or occur in complex conjugate pairs.
Answer:
A: -5 - √3i
This should be correct on edge
Can someone explain this a little better?
Answer:
1. 76,000
2. 8050
3. 240000
Step-by-step explanation:
We know that
1 tens = 10 ones
1 hundreds = 100 ones
1 thousand = 1000 ones
10 thousands = 10000 ones
Using these conversions we get,
1 : [tex]760\text{ hundreds}=760\times 100=76,000[/tex]
2 : [tex]805\text{ tens}=805\times 10=8050[/tex]
3 : [tex]24\text{ ten thousands}=24\times 10000=240000[/tex]
Table can be filled as shown below:
Thousands Ones
Q. no. Hundreds Tens Ones Hundreds Tens Ones
1. 7 6 0 0 0
2. 8 0 5 0
3. 2 4 0 0 0 0
the average marks of shahid first four papers is 88 how much mark should he get in the fifth paper so that the average of five papers becom 90?
a.92
b.94
c.96
d.98
Answer with Step-by-step explanation:
The average marks of Shahid first four papers is 88.
Let a,b,c and d be the marks in first four papers
⇒ [tex]\dfrac{a+b+c+d}{4}=88[/tex]
⇒ a+b+c+d=88×4
=352
Let marks in fifth paper be x
The average of five papers become 90
⇒ [tex]\dfrac{a+b+c+d+x}{5}=90[/tex]
⇒ a+b+c+d+x=90×5
⇒ 352+x=450 (since a+b+c+d=352)
⇒ x=450-352
⇒ x=98
Hence, Correct option is:
d.98
6578 divided 34
20\5
A bottle of medicine contains 40 doses. How many doses are in 3 1/3 bottles?
To calculate the total number of doses in 3 1/3 bottles of medicine, multiply the fraction of bottles (10/3) by the number of doses per bottle (40). The result is 133 1/3 doses.
Explanation:The student is asking how many doses are in 3 1/3 bottles of medicine if one bottle contains 40 doses. To find the answer, we need to multiply the number of bottles by the number of doses per bottle.
Here is the step-by-step calculation:
First, convert 3 1/3 bottles to an improper fraction: 3 1/3 = (3 × 3 + 1)/3 = 10/3 bottles.Next, multiply this value by the number of doses in one bottle to find the total number of doses: (10/3) × 40 doses = 400/3 doses.Finally, simplify the fraction: 400/3 doses = 133 1/3 doses.So, there are 133 1/3 doses in 3 1/3 bottles of medicine.
Please help.. I got stuck on this question please help and explain
Sam earned $150 last week. Jay earned $130 last week. They combined their money and decided to donate ¼ of their total amount to a charity. Then, they spent 40% of the remaining amount at an amusement park. Jay claims that they only have 35% of their original combined total left.
Is jay right or wrong?
The wall in the family room is exactly 12 feet long. Your couch is 10 feet and 6 inches long. Once the couch is placed, how much room is left for your end table?
inches
find two possible factors for the estimated product 2,800
Marisol is preparing a care package to send to her brother. The package will include a board game that weighs 4 lb and several 14 lb snack packs. The total weight of the care package must be less than 25 lb.
Drag and drop the answer into the box.
Question Answer
Which statement describes the solution to this inequality?
Marisol must send less than 1 snack pack.Marisol must send fewer than 21 snack packs.Marisol must send fewer than 84 snack packs.Marisol must send fewer than 100 snack packs.
If it snows on game day there is a 32% chance the Jets will win. If it does not snow on game day there is a 41% chance the jets will win. There is a 29% chance that it will snow on game day.
a. What is the probability the Jets will win?
b. What is the probability that it snows on game day and the Jets win?
c. What is the probability that it snows on game day given that the Jets win?
To find the probability the Jets will win, we use the Law of Total Probability. The probability that it snows on game day and the Jets win is found using the definition of conditional probability. Lastly, to find the probability that it snows on game day given that the Jets win, Bayes' theorem is used.
Explanation:To solve this problem, we can use the concept of conditional probability. Let's define the following events:
A = it snows on game day
B = the Jets win
We are given:
P(B|A) = 0.32 (the probability of the Jets winning if it snows)
P(B|A') = 0.41 (the probability of the Jets winning if it doesn't snow)
P(A) = 0.29 (the probability of it snowing on game day)
To find the probability of the Jets winning, we can use the Law of Total Probability:
P(B) = P(B|A)P(A) + P(B|A')P(A')
P(B) = 0.32 * 0.29 + 0.41 * (1 - 0.29)
P(B) = 0.0928 + 0.1059
P(B) ≈ 0.1987
To find the probability that it snows on game day and the Jets win, we can use the definition of conditional probability:
P(A and B) = P(A) * P(B|A)
P(A and B) = 0.29 * 0.32
P(A and B) ≈ 0.0928
To find the probability that it snows on game day given that the Jets win, we can use Bayes' theorem:
P(A|B) = (P(B|A) * P(A)) / P(B)
P(A|B) = (0.32 * 0.29) / 0.1987
P(A|B) ≈ 0.4643
Gina wrote the number 43,628. Then she used the same digits to write a new number. In the new number, she moved the digit 6 one place to the left. Which is the value of 6 in Gina's new number?
John and Jeremy are the local names for two lighthouses that guard a particularly dangerous part of the coast. John blinks every 6 seconds and Jeremy blinks every 4 seconds. They blink together at midnight. How many seconds will pass before they blink together again?
A number, one-third of that number , and one-fourth of that number are added. The result is 19 what is the original number
HELP ASAP PLEASE!!!!!!!!!!!!!!
Product of prime factors for 60 = 2x2x3x5
How do i write this in index form?
I have tried by simplifying so it is 2 to the power of 2 x 3 x 5
It stills says it is incorrect, anyone know?
The correct index form for the product of prime factors of 60, which is 2x2x3x5, is 2^2 x 3 x 5.
Explanation:The product of prime factors for 60 is indeed 2x2x3x5. To write this in index form, we group the same numbers together and count how many there are. Then we use the base and exponent form to write it. Here, 2 is repeated twice. So, 2x2 can be written as 2^2. The primes 3 and 5 are each given once, so, we do not write powers for them. Therefore, the correct index form is 2^2 x 3 x 5.
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