The water level in a paper cup shaped like a cone with radius 3 cm and height 10 cm, filled at a rate of 2 cm³/s, rises at approximately 0.025 cm per second when the water is 5 cm deep.
Explanation:This question involves related rates, a concept in Calculus. We know that the volume, V, of a cone with a radius r and height h is given by the formula V = (1/3)πr²h. Given that the shape of the cup is conical, the radius and the height of the water in the cup are proportional, so we can express r as r=3h/10.
Thus, we can rewrite the volume formula in terms of h: V = 1/3 * π * (3h/10)² * h = πh³/100. Differentiating both sides with respect to time t, we get dV/dt = πh² dh/dt. We want to find dh/dt (the rate at which the water level rises) when h=5 cm and given that dV/dt (the rate at which water is poured into the cup) is 2 cm³/s.
Plugging these values into the differentiated formula, we get: 2 = π(5)² * dh/dt. Solving for dh/dt, we find that dh/dt = 2/(25π) or about 0.025 cm/s. So, the water level is rising at a rate of approximately 0.025 cm per second when the water is 5 cm deep.
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Please help me with this question
two fractions have the same denominator. Which is greater fraction: the fraction with the greater
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Which statements about the ellipse are true? Check all that apply.
The center is at (−2, −5).
The distance between the center and each vertex is 10 units.
The covertices are at (−2, −4) and (−2, −6).
The distance between the center and each focus is units.
The directrices are horizontal lines approximately 5.1 units from the center.
1.) The center is at (-2,-5).
3.) The con vertices are at (-2,-4) and (-2,-6).
4.) The distance between the center and each focus is 2√6 units.
Statements 1,3 and 4 about the ellipse are true. Ellipse is the result of carving a cone with an oblique plane that does not intersect the base.
What is an ellipse?The asymmetrical oval shape is drawn by a spot advancing along a plane so that the sum of its distance from foci is kept the same known as an ellipse.
1.) The center is at (-2,-5).
3.) The cone vertices are at (-2,-4) and (-2,-6).
4.) The distance between the center and each focus is 2√6 units.
Hence statements 1,3 and 4 about the ellipse are true.
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Mary Ann is buying miniature cars. She wants to buy 20 cars total for a big race she and her friends are having. Black cars $6 dollars each. If she spends $104, how many white cars did she buy?
A minor league baseball team plays 101 games in a season. If the team won 17 more than twice as many games as they lost, how many wins and losses did the team have? How many games did the team lose? How many games did they win?
find the domain of the following function below. f(x)=3x-5/2
How many sequences of outcomes are possible if one rolls two identical dice 10 successive times?
a new truck that sells for $29000 depreciates 12% each year. Write a function that models the value of the truck
An individual head of a sprinkler system covers a circular area of grass with a radius of 25 feet. The yard has 3 sprinkler heads that each cover a circular area with no overlap. What is the approximate total area that will be watered?
Answer:
Approximate Total area that will be watered is 5887.5 feet²
Step-by-step explanation:
Radius of the Circular area that sprinkler cover , r = 25 feet
Number of sprinkler = 3
Area covered by 1 sprinkler = Area of circle
= πr²
= 3.14 × (25)²
= 3.14 × 625
= 1962.5 feet²
Area covered by 3 sprinkler = 3 × 1962.5 = 5887.5 feet²
Therefore, Approximate Total area that will be watered is 5887.5 feet²
The approximate total area that will be watered will be 5887.5 feet². Square centimeters and other similar units are used to measure area.
What is the area?The space filled by a flat form or the surface of an item is known as the area.
The number of unit squares that cover the surface of a closed-form is the figure's area.
The given data in the problem is;
r is the radius of the Circular area that sprinkler cover = 25 feet
n is the number of sprinklers = 3
The sprinkler executes a circular motion ;
Area covered by sprinkler = Area of the circle
The area covered by sprinklers is found as;
[tex]A_S = \pi r^2 \\\\ A_S = 3.14 \times (25)^2 \\\\\ A_S = 3.14 \times 625 \\\\ A_S= 1962.5 \ feet^2[/tex]
The area covered by the three sprinklers will be;
[tex]\rm A_S = 3 \times 196.25 \\\\ \rm A_S =5887.5 \ feet^2[/tex]
Hence approximate total area that will be watered will be 5887.5 feet².
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How many ways can you pick 4 students from 10 students (6 men, 4 women)?
Answer:
There are 210 ways in which you can pick 4 students from 10 students (6 men, 4 women).
Step-by-step explanation:
We use the combination formula because the order does not matter.
For example, John, Laura,... is the same way as Laura, then John, then ...
Combinations formula
[tex]C_{n,x}[/tex] is the number of different combinatios of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
Combinations of 4 students from a set of 10. So
[tex]C_{10,4} = \frac{10!}{4!(10-4)!} = 210[/tex]
There are 210 ways in which you can pick 4 students from 10 students (6 men, 4 women).
Find an for the arithmetic series with s16 = -288 And a1 =-21
Given the sum of the sequence and the first term, we rearrange the formula for the sum to solve for 'd', the common difference. This will allow us to calculate the term at any given point in the arithmetic sequence.
Explanation:In an arithmetic sequence, the nth term can be represented by the formula a + (n-1)d where 'a' is the first term, 'n' is the number of terms and 'd' is the common difference between the terms.
The sum, 's', of the first 'n' terms in an arithmetic sequence is given by the formula s = n/2 * (2a + (n - 1)d).
Given the sum, 's', and the first term in the sequence, 'a', we can rearrange the sum formula to find 'd', the common difference, which will then allow us to find any term in the sequence.
We have s16 = -288 and a1 = -21. So, our problem reduces to solve for 'd' in s = n/2 * (2a + (n - 1)d) The solution with most relevance to the student's question will be the calculated 'd' value.
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Omar owns a sandwich shop, and his best selling sandwich is the BLT. When making BLT sandwiches, it takes of a pound of bacon to make 4 sandwiches. He uses pounds of bacon for every 2 tomatoes used and 5 tomatoes for every full head of lettuce used.
If Omar is making enough BLT sandwiches to use 2 full heads of lettuce, then he is going to use pounds of bacon and will make a total of BLT sandwiches.
When making enough BLT sandwiches to use 2 full heads of lettuce, Omar will be using 2.5 pounds of bacon and will end up making a total of 40 BLT sandwiches.
Explanation:The subject of this question is Mathematics, specifically ratios and proportions. Given that Omar uses one full head of lettuce for every 5 tomatoes, for 2 heads of lettuce, he will use 10 tomatoes (2*5). Since he uses 1/2 pound of bacon for every 2 tomatoes, then for 10 tomatoes, he will need 2.5 pounds of bacon (10/2*0.5). Finally, since it takes 1/4 pound of bacon to make 4 sandwiches, with 2.5 pounds of bacon he will make 40 sandwiches (2.5/0.25*4). Therefore, Omar will use 2.5 pounds of bacon and make a total of 40 BLT sandwiches.
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fractions that name the same number are
These are called "Equivalent Fractions."
Equivalent fractions may look different from each other, but all equivalent fractions have he same value.
Jessica is going to paint her patio. It is made up of two rectangles. One measures 7 ft x 4 ft x 5 ft, and the other measures 10ft x 8ft x 6ft. What is the total area of her patio?
Answer:
Jessica patio is made up of two rectangles.
Dimension of one rectangle which is in the shape of cuboid = 7 ft x 4 ft x 5 ft,
Dimension of Second rectangle which is also in the shape of cuboid =10 ft x 8 ft x 6 ft
→Total Area of Patio=Total Surface Area of Cuboid having Dimension 7 ft x 4 ft x 5 ft,+ Total Surface Area of Cuboid having Dimension 10 ft x 8 ft x 6 ft
= 2 ×[7×4+4×5+5×7]+2×[10×8+8×6+10×6]
=2×[28+20+35]+2×[80+48+60]
=2×83 +2×188
=166+376
=542 square feet
Upper face of larger cuboid is partially covered , with smaller cuboid.
Area of Lower face of smaller cuboid =7 ×4=28 square feet
Total Area of patio = 542- (Area of lower face of smaller cuboid)
= 542 - 28
=514 square feet
A particular security's default risk premium is 2 percent. for all securities, the inflation risk premium is 1.75 percent and the real risk-free rate is 3.5 percent. the security's liquidity risk premium is 0.25 percent and maturity risk premium is 0.85 percent. the security has no special covenants. calculate the security's equilibrium rate of return.
The equilibrium rate of return is 8.3%.
The equilibrium rate of return of a security is the sum of the real risk-free rate, the inflation risk premium, the default risk premium, the liquidity risk premium, and the maturity risk premium.
In this case, the equilibrium rate of return is:
3.5% + 1.75% + 2% + 0.25% + 0.85% = 8.3%
So the answer is 8.3%.
Here is a breakdown of the calculation:
The real risk-free rate is the rate of return that investors would expect to earn on an investment with no risk of default or inflation.
The inflation risk premium is the additional return that investors demand to compensate them for the risk of inflation.
The default risk premium is the additional return that investors demand to compensate them for the risk of default on a security.
The liquidity risk premium is the additional return that investors demand to compensate them for the difficulty of selling a security quickly and easily.
The maturity risk premium is the additional return that investors demand to compensate them for the risk that the value of a security will decline as it approaches maturity.
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Find the volume v of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x − 1 , y = 0, x = 9; about the x-axis v = incorrect: your answer is incorrect.4
Seven friends picked 7 quarts of blueberries. Three of the friends will share 4 quarts blueberries equally and the other 4 friends will share 3 quarts of the blueberries equally. In which group does each friend get a greater amount of blueberries? Explian your reasoning
A stretch of highway that is 12 1/4 kilometers long has speed limit signs every 7/8 of a kilometer. How many speed limit signs are on this stretch of highway?
Answer:
the answer is 14 speed limit signs
Step-by-step explanation:
Bowling costs $4.50 per game (g). Shoe rental costs $3.75 each. The total cost is a function of the number of games. What function rule models the total cost of games and shoe rental? Evaluate the function for three games.
The cost function is an illustration of linear functions
The cost function is [tex]C(x) = 3.75 + 4.50x[/tex]The cost for three games is $17.25From the question, we have:
[tex]G = 4.50[/tex] --- cost per game
[tex]R = 3.75[/tex] --- cost per shoe rent
Since the cost is a function of number of games, it means that;
The cost of shoe rent is a fixed cost
Let x represents the number of games.
So, the cost function is:
[tex]C(x) = R + G \times x[/tex]
This gives
[tex]C(x) = 3.75 + 4.50 \times x[/tex]
[tex]C(x) = 3.75 + 4.50x[/tex]
Substitute 3 for x; to evaluate the function for 3 games
[tex]C(3) = 3.75 + 4.50 \times 3[/tex]
[tex]C(3) = 3.75 + 13.50[/tex]
[tex]C(3) = 17.25[/tex]
Hence, the cost for three games is $17.25
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It takes 484848 minutes for 777 people to paint 777 walls. How many minutes does it take 202020 people to paint 202020 walls?
Answer:
Approximately 391 minutes taken by 20 people to paint 20 walls.
Step-by-step explanation:
Given : It takes 48 minutes for 7 people to paint 7 walls.
To find : How many minutes does it take 20 people to paint 20 walls?
Solution :
7 people to paint 7 walls in 48 minutes.
So, 1 people to paint 7 walls in [tex]\frac{48}{7}[/tex] minutes.
and 1 people to paint 1 walls in [tex]\frac{48}{7\times 7}[/tex] minutes.
Now, We have to find minutes does it take 20 people to paint 20 walls.
20 walls will be painted in [tex]\frac{48\times 20}{7\times 7}[/tex] minutes.
20 people to paint 20 walls in [tex]\frac{48\times 20\times 20}{7\times 7}[/tex] minutes.
i.e. [tex]\frac{48\times 20\times 20}{7\times 7}=\frac{19200}{49}=391.83[/tex]
Therefore, Approximately 391 minutes taken by 20 people to paint 20 walls.
according to a meteorologist rain gauge 2.785 centimeters of rain fell. which shows a way to represent the 7 in this number
[tex] \frac{3}{4} - \frac{3}{8} \\ [/tex]
The function ƒ(x) is modified as follows: It is multiplied by –3. x is replaced by x + 3. The new function is graphed. Which of the following effects on the graph of ƒ(x) are needed to produce the new graph? Choose all that apply.
horizontal translation
vertical translation
dilation
reflection over the x-axis
reflection over the y-axis
Answer:
Horizontal Translation, Dilation and Reflection along y-axis
Step-by-step explanation:
submitting an online payment
Four consecutive integer numbers add to 2. What are the numbers?
The numbers are consecutive, meaning they are in arithmetic progression.
Sum of Arithmetic Progression = (n/2)[2a + (n- 1)d]
Where, n = total number of numbers and d = common difference between two successive numbers
Therefore n = 4 and d = 1 ( as the numbers are consecutive )
now (4/2)(2a + (4 - 1)1) = 2
i.e. 2(2a + 3) = 2
i.e. 4a + 6 = 2
i.e. 4a = - 4
i.e. a = - 1
Therefore nos are -1, -1+1 , -1+1+1 , -1+1+1+1
i.e. -1, 0 , 1 , 2
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Find the thirtieth term of the following sequence.
-6, -4, -2, 0, ...
52
64
66
Answer:
The thirtieth term of sequence is 52
Step-by-step explanation:
Given the A.P series
-6, -4, -2, 0, ...
we have to find the thirtieth term of the following sequence.
The A.P is -6, -4, -2, 0, ...
which implies
Common difference, d=-4-(-6)=-4+6=2
First term=a=-6
n=30
[tex]a_n=a+(n-1)d[/tex]
[tex]a_{30}=a+29d[/tex]
[tex]a_{30}=-6+29(2)=-6+58=52[/tex]
hence, the thirtieth term of sequence is 52
Leo bought a used car for x dollars. one year later the value of the car was 0.88x. which expression is another way to describe the change in the value of the car?
A)0.12% decrease
B)0.88% decrease
C)12% decrease
D)88% decrease
Initial price of car = $x
After one year the price of car = $0.88x
to find the change in price we subtract the price after one year from initial price.
It means change in price = (x-0.88x)= 0.12x
By this we can easily see that , price dropped by 0.12
Or we can say that price dropped by 12%
So option C is the correct answer
C) 12% decrease
how to find the area of 2 half circles and a rectangle
The data set below consists of the scores of 15 students on a quiz. for this data set, which measure of variation do you think is more appropriate, the range or the standard deviation? explain your thinking. 90 90 91 91 89 90 89 91 91 90 60 90 89 90 91
In the given data set, the standard deviation is the more appropriate measure of variation as it takes all the scores into account and provides a better insight into the data compared to the range.
Explanation:In the given data set, both range and standard deviation can be used to measure the variation. However, the standard deviation might be a better measure in this instance. The standard deviation provides a numerical measure of the overall amount of variation in the data set. It indicates how far the values are from their average, or mean. In contrast, the range only provides the difference between the highest and lowest values, potentially overlooking the distribution of all the values.
When calculating the standard deviation for your dataset, it becomes evident that most scores are concentrated around the 90s, but there's one score dramatically lower at 60. This single score skews the data set and increases the standard deviation, indicating a larger spread around the mean than what might first be observed. As such, the standard deviation gives us a more detailed understanding of the spread within this set of quiz scores, making it the more useful measure in this case compared to the range.
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Future googling man, am I ever gonna get married?