The rate of the increase of the radius of the disk of the cylinderical tank is found to be 59.173 m/hr.
V=(h)(r2)/2 is the formula for the cylinder's volume.
both sides of the derivative
dV/dt=(dh/dt)(πr2)/2+(h)(πr)(dr/dt)
Let's now apply what we know.
dV/dt equals 0.11 metres cubic per hour
dh/dt = 0. Rate is 0 since the height isn't moving.
We must now determine the value that r should have. To do this, we'll apply the original volume formula. Keep in mind that it has been seeping for five hours.
5 hours (at a rate of 0.11 metres each hour equals 0.55 metres.
V=(h)(πr^2)/2
0.55 = (10⁻⁶)(πr²)/2
= 391.17 metres
Let's now connect everything for the difference
dV/dt=(dh/dt)(πr2)/2+(h)(πr)(dr/dt)
0.11=(0)(π)(591.727)2+(10-6)(π)(591.727)(dr/dt)
= 59.173 m/hr
Hence the radius rate is changing at 59.173 m/hr.
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does this table represent a functon?
Answer:
no, because each y value corresponds to multiple x values. And the x values repeat each other.
Step-by-step explanation:
Answer:
No, because there is more than one of the same x value
Step-by-step explanation:
What is meant in statistics by "scores having a central tendency"?
In statistics, the "central tendency" refers to a single value which represents middle or center of a set of data. The 3 common measures of central tendency are named as mean, median, and mode.
When scores have a central tendency, it means that most of the scores in a set of data are clustered around a particular value.
For Example, if we have a data set of test scores, and most of the scores are around 70, then 70 would be the central tendency of the data set.
The central tendency is an important concept in statistics because it provides a way to summarize a large set of data with a single value.
It can help you understand the overall pattern of the data and make comparisons between different data sets.
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From the figure below, the coordinates for point z are:
HELP PLS
Answer:
(2a, 0)
Step-by-step explanation:
the distance from (a,0) and z from the origin and to each other is both 3. It’s in the middle of two points, there’s an equal distance between w to y and y to z. I hope that makes sense, so, to get the x coordinate multiply a by 2.
A salesperson at a jewelry store earns 6% commission each week. Last week, jarrod sold $680 worth of jewelry. How much did make in commission? How much did the jewelry store make from sales?
Answer:
1/ $ 4.08
2/ $675.92
Step-by-step explanation:
Take 68 times 0.06% = $4.08
680 - 4.08= 675.92
Answer:
Step-by-step explanation:
40.80 it told me the answer
Which rectangular equation represents the parametric equations x =t Superscript one-half and y = 4t? y = 4x2, for x ≥ 0 y = one-fourth x squared, for x greater-than-or-equal-to 0 y = 16x2, for x ≥ 0 y = StartFraction 1 Over 16 EndFraction x squared, for x greater-than-or-equal-to 0
Answer:
Answer is Option A
Step-by-step explanation:
the things people do for points smh :/
The rectangular equation which represents the parametric equations; x = t^(¹/2) and y = 4t is; y = 4x2, for x ≥ 0.
Rectangular Equation from Parametric equationsFrom the task content, it follows that the parametric equations given are;
x = t^(¹/2) and y = 4tHence, it follows that; t = x² and y= 4t
Ultimately, upon substitution of x² for t; the resulting rectangular equation is; y = 4t².
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How much would it cost for Mr. John to replace the tile in his kitchen if the cost for the tile is $1.50 per square foot? (Think about what shape the kitchen is to find the area of it)
Answer:
214.50
Step-by-step explanation:
A = lw
13 x 11 = 143 (13 is a guess)
143 x 1.50 = 214.50
im not 100 % but give it a try
hope this helps
pls mark brainliest
40% of the students passed both exams. 80% of the students passed the second exam. how many students (in percent) who passed the second exam also passed the first exam ? next
50%. students (in percent) who passed the second exam also passed the first exam.
Let's imagine that there are 100 kids in the teacher's class. We know that 40 of them passed BOTH tests, and 80 passed the second test.
Because if they weren't, they wouldn't have passed the first test and consequently wouldn't have passed both, we can be sure that the group of students who passed BOTH tests is only made up of the 80 who passed the second test.
Thus, both tests were passed by 40 of the 80 pupils who passed the second one:
40/80 = 1/2 = 50%.
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the property name for 20+0=20
Answer: Identity Property of Addition
Step-by-step explanation: The identity property holds true for addition.
The statement 20 + 0 = 20 represents the identity property of addition.
The identity property of addition says we add 0
to any number, the sum is equal to the original number.
In general terms, we can write the identity property of addition
as a + 0 = a where a is a variable that represents any number.
Solve for x. round to the nearest tenth
Answer:
x ≈ 11.1
Step-by-step explanation:
Using the cosine ratio in the right triangle.
cos42° = \(\frac{adjacent}{hypotenuse}\) = \(\frac{x}{15}\) ( multiply both sides by 15 )
15 × cos42° = x, then
x ≈ 11.1 ( to the nearest tenth )
which terms are used to describe events that have NO outcomes in COMMON?
Events that have no outcomes in common are said to be disjoint or mutually exclusive.
Two sets are known to be mutually exclusive when they have no common elements. Mutually exclusive events are those that cannot take place at the same moment.
If two events are considered disjoint events, then the probability of both events occurring at the same time will be zero.
Set A = {2, 4, 6, 8, 10, 12, 14, 16}
Set B = {1, 3, 5, 7, 9, 11, 13, 15}
A and B do not have any numbers in common, so P (A ∩ B) = 0. Therefore, A and B are mutually exclusive.
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What is the slope of the line that contains points (2, 9) and (8, 7)?
Answer:
-1/3
Step-by-step explanation:
m = y2-y1/x2-x1 formula for slope
m = 7-9/8-2 Plug in the numbers
m = -2/6 Subtract 7-9 and 8-2
m = -1/3 Simplify
An airline company advertises that 100% of their flights are on time after checking 5 flights from yesterday and finding that these 5 were on time.
a) What is population of interest?
b) What is the sample?
c) Was this a representative sample? Explain.
d) How should the company determine the percentage of their flights that are on time?
Answer with explanation:
Given: An airline company advertises that 100% of their flights are on time after checking 5 flights from yesterday and finding that these 5 were on time.
a) population: A large group of observations have characteristics related to the point of the study.
Here, population: "All flights operated by the company"
b) Sample: It is a subset of the population.
Here, Sample: "5 flights from yesterday"
(c)
Since the number of flights per day operated by an airline company is much larger than 5 ( generally in hundreds).
i.e. the sample is too small to be able to assure that the results are true.
Hence, this is not a representative sample.
(d) To determine the percentage of their flights that are on time we use the following formula:
(Number of flights are on time) ÷ (Total flights) x 100
If $800 is deposited into a new savings account with a simple interest rate of 1.8%, what will be the total amount in the account after 15 years?
Answer:
Step-by-step explanation:
I = prt
I = 800 × 1.8% x 15
I = $216
Remember the percent sign for the rate or write it as a decimal (multiplier)! In this case the multiplier would be 0.018!
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5
Select the correct answer.
Simplify the expression.
3x √648x4y8
O A. 18x2y2√3xy²
1
O B. 18ry2 3x²y²
O c. 9x²y 2xy²
OD. 18x2y2 √2xy²
The correct simplified expression is 18xy^7√2. Therefore, the correct answer is not D. 18x^2y^2√2xy^2, as stated earlier.
To simplify the expression 3x √648x^4y^8, we can start by simplifying the square root of 648. The square root of 648 can be expressed as the square root of 9 times the square root of 72.
The square root of 9 is 3, and the square root of 72 can be simplified as the square root of 36 times the square root of 2. The square root of 36 is 6, so the square root of 72 is 6√2.
Now we can rewrite the expression as 3x(6√2x^4y^8).
Next, we can simplify the coefficients and the variables. The coefficient 3 multiplied by 6 gives us 18. The variables x^4 and x cancel out, leaving us with x^0, which is equal to 1. Similarly, the variables y^8 and y cancel out, leaving us with y^7.
Therefore, the simplified expression is 18xy^7√2.
The correct answer is D. 18x^2y^2√2xy^2.
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1. Congratulations! You are going to be a contestant on a new game show with a chance to win some money. You
will spin the two spinners shown below to see how much money
you will win.
a. Make an area model or tree diagram of all the possible outcomes
of spinning the two spinners. If a tree diagram, at the ends of the
branches, on the far right, write the amount you would win for
each combination of spins.
$100 $300
$1500
Keep Your Winnings
Double
Your
Winnings
The tree diagram shows the potential number of winning possible
What is a tree diagram with all the possible outcomes of spinning the two spinnersHere's a tree diagram showing all the possible outcomes of spinning the two spinners:
|------ $100 ---- Keep Your Winnings
|
Spin 1 ----|------ $300 ---- Keep Your Winnings
|
|------ $1500 --- Keep Your Winnings
|
|------ Double --|------ $100 ---- $200
|
|------ $300 ---- $600
|
|------ $1500 --- $3000
|
|------ Keep ---- Keep Your Winnings
The diagram starts with the first spinner, which can land on $100, $300, or $1500. Then, for each of these outcomes, the second spinner can land on one of four options: Keep Your Winnings, Double Your Winnings, $100, or $300. If the second spinner lands on Double Your Winnings, the amount won is doubled based on the outcome of the first spinner.
At the far right of each branch, the amount you would win for each combination of spins is shown. For example, if the first spinner lands on $100 and the second spinner lands on $300, you would win $300. If the first spinner lands on Double and the second spinner lands on $1500, you would win $3000.
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I need help asap!!
Solve for d and show your work:
16d- (4 -5d) =-67
Step-by-step explanation:
16d-4+5d= -67
21d-4= -67
21d= -67+4
d= -63/21
d = -3
hope it helps
Answer: d = -3
Step-by-step explanation:
⇒16d -(4-5d) = -67
⇒16d -4 +5d = -67
⇒21d = -67+4
⇒21d = -63
⇒d = -63/21
⇒d = -3
Therefore d = -3
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A forecasting method has produced the following over the past five months. What is the mean absolute deviation?.
List of four quantitative forecasting methods.
Moving averages, exponential smoothing, trend projection, and linear regression are all in the list. (Forecasting strategies, medium)
The average distance between observations and their mean is indicated by the variability metric known as mean absolute deviation . It uses the data original units to facilitate interpretation. Greater values imply a bigger divergence from the mean. Lower values, on the other hand, are related to the data surrounding it clustering. The average absolute deviation and the mean deviation are other names for the mean absolute deviation.
The next three procedures are necessary to calculate the mean absolute deviation.
1.By adding up all the observations and dividing by the sample size,
you can determine the sample average.
2.Discover the total deviation from the mean of each data point. When
negative signals appear, ignore them and instead deduct the
observed values from the mean
3.Divided the total value of above step
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This shows the trapezoid cut into two triangles.
2 mm
4 mm
4 mm
What are the areas of the two triangles?
square millimeters and
What is the area of the trapezoid?
square millimeters
square millimeters
The areas of the two triangles are 4 square millimeters and 8 square millimeters, and the area of the trapezoid is 12 square millimeters.
How to find the areas of the two trianglesFirst we need to use the formula for the area of a triangle:
Area = 0.5 x base x height
The height of each triangle is 4 mm, and the bases are 2 mm and 4 mm. Therefore, the areas of the two triangles are:
Area of triangle 1 = 0.5 x 2 mm x 4 mm = 4 square millimeters
Area of triangle 2 = 0.5 x 4 mm x 4 mm = 8 square millimeters
To find the area of the trapezoid, we can add the areas of the two triangles together:
Area of trapezoid = Area of triangle 1 + Area of triangle 2
Area of trapezoid = 4 square millimeters + 8 square millimeters
Area of trapezoid = 12 square millimeters
Therefore, the areas of the two triangles are 4 square millimeters and 8 square millimeters, and the area of the trapezoid is 12 square millimeters.
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What is the OUTCOME of tossing a penny and spinning a spinner?
A.3
B.4
C.6
D.8
A ream of A4 paper contain 500 sheets the size of each paper is 297mm long and 210mm wide the volume of the ream is 3742.2cm find the thickness of each sheet of paper answer in millimeters
The thickness of each sheet of paper is 0.0012mm.
To find the thickness of each sheet of paper answer in millimeters.
What is mensuration?The act of measuring geometry applied to the computation of lengths, areas, or volumes from given dimensions or angles.
Given that:
A ream of A4 paper contain 500 sheets the size of each paper is 297mm long and 210mm wide the volume of the ream is 3742.2cm.
To convert cm in mm.
3742.2cm=37422 mm
Surface 1 sheet:
(297mm) X 210mm) =
62370\(mm^{2}\)
Volume 1 sheet:
37422mm : 500 =
74.844mm
Thickness of 1 sheet:
74.844mm : 62370mm =
0.0012mm
So, the thickness of each sheet of paper is 0.0012mm.
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in the right triangle abc, the median to the hypotenuse has a length of 15 units and the altitude to the hypotenuse has a length of 12 units. what is the length of the shorter leg of the triangle abc?
The length of the shorter leg of the triangle ABC is approximately 24.49 units. Let's denote the right triangle ABC, where C is the right angle.
Let D be the midpoint of AB, and E be the foot of the altitude from C to AB. Then we have:
CD = 1/2 AB (definition of median)
CE = 12 (given altitude to the hypotenuse)
Let x be the length of the shorter leg of the triangle ABC. Then we have:
AE = x (definition of altitude)
EB = AB - x (definition of complementary leg)
By the Pythagorean theorem, we have:
AC^2 = AB^2 + BC^2
(2CD)^2 = AB^2 + x^2
AB^2 = 4CD^2 - x^2
By the similarity of triangles AEC and ABC, we have:
CE/AC = AE/AB
12 / (AB + BC) = x / AB
AB = x / (12/x + 1)
Substituting AB into the previous equation, we get:
4CD^2 - x^2 = x^2 / (12/x + 1)^2
Simplifying and solving for x, we get:
x^4 - 576x^2 - 14400 = 0
This is a quadratic equation in x^2, so we can solve for it using the quadratic formula:
x^2 = [576 ± sqrt(576^2 + 4*14400)] / 2
x^2 = [576 ± 624] / 2
Since x is a length, we take the positive square root:
x^2 = 600
x ≈ 24.49
Therefore, the length of the shorter leg of the triangle ABC is approximately 24.49 units.
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45% of a 300ml drink is concentrated pineapple juice. The rest is water. Find the volune of water that must be added so that 40% of the drink is concentrated pineapple juice.
The volume of water that must be added so that 40% of the drink is concentrated pineapple juice will be 37.5 mL.
What is the unitary method?Unitary method is a mathematical method used in arithmetic to perform conversions between different units of measurement.
Given;
45% of a 300ml drink is concentrated pineapple juice.
If x is the volume of water, then we get;
(0.45)(300) + (0)(x) = (0.40)(300 + x)
135 = 120 + 0.40x
15 = 0.40x
x = 37.5
Therefore, The volume of water that must be added so that 40% of the drink is concentrated pineapple juice will be 37.5 mL.
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Solve for x: 3x + 4 = 9x + 3
Answer:
Step-by-step explanation:
3x+4=9x+3, we will add and subtract the variable and the numbers so we have, x in one side and the numbers on the other side
4-3=9x-3x
1=6x
x=1/6
Answer:
x = 1/6
Step-by-step explanation:
1. Add and subtract the variable and the numbers.
So far: 4 - 3 = 9x - 3x
4 - 3 = 9x - 3x
2. Simplify.
4 - 3 = 1.
9x - 3x = 6x.
To do addition with variables, delete the variables, which now is 9 - 3, easy, 6, add the x back (only to the answer), so 6x.
Since 1 is on 1 part of the equal side, because 4 - 3 = 1.
And is 1 = 6x.
1/6 then is your final answer.
Elimination Method2x+ 4y=10X+ y=15
1) Let's pick the 2nd equation and to eliminate the x variable, multiply by -2 then add both equations like this
2x+ 4y=10
-2X+ -2y=-30
---------------------------------
2y = -20
y = -10
2) Now let's plug that y=-10 into one equation, usually the simpler one.
x +y = 15
x -10 = 15 add 10 to both sides
X = 15 +10
x=25
3) So the solution is S ={25, -10}
The sun of the arithmetic sequence is equal to three times the sum of the infinite geometric sequence.
Answer:9
Step-by-step explanation:sun *3
Pedro and Amelia share a common investment goal and once they reach their goals, they will withdraw their money.
Amelia starts out with twice as much money as Pedro and it takes Pedro 6 times longer than Amelia to reach this goal.
They both use the same bank that provides a 4% annual interest rate compounded quarterly.
Work out how long it takes Pedro to reach his investment goal.
The number of years that Pedro took to reach his investment goal will be 52.5 years.
What is compound interest?A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.
We know that the compound interest is given as
A = P(1 + r)ⁿ
Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.
Amelia and Pedro have the same financial objective, and if they achieve it, they will withdraw their funds. Pedro starts off with twice as much money as Amelia, but it takes him six times as long to get there. Both of them use the same bank, which offers a 4% annual interest rate that is compounded every three months. Next, we have
n' = 4n
r/4 = 2 x 0.04 / 4 = 0.02
Let x be the amount of money invested by Pedro. Then the amount of money invested by Amilia will be 2x.
Let n be the number of years. Then for Pedro, the number of years will be 6n.
Then the equation when investment gets doubled will be
4x = 2x(1 + 0.02)⁴ⁿ
2 = 1.02⁴ⁿ
Taking log on both sides, then we have
ln 2 = 4n ln 1.02
4n = 35
n = 8.75 years
Then the number of years that Pedro took to reach his investment goal will be
6n = 6 x 8.75 = 52.5 years
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Right triangle ABC is located at A (-1,-2), B(-1, 1), and C (3, 1) on a coordinate plane. What is the equation of a circle A with radius AC?
Olx + 1)2 + y + 2)2 = 9
O(x + 1)2 + (y + 2)2 = 25
OOX - 3)2 + y - 12 = 16
Ox - 3)2 + (y - 142 = 25
Answer:
(x +1)^2 + (y +2)^2 = 25
Step-by-step explanation:
A diagram of the given triangle shows you it has side lengths of 3 and 4, so the square of the hypotenuse is ...
(AC)^2 = (AB)^2 +(BC)^2 = 3^2 +4^2
(AC)^2 = 25
The center of the circle is at A(-1, -2), so the equation is ...
(x -h)^2 +(y -k)^2 = r^2
for the circle centered at (h, k) with radius r.
We know that the square of the radius (r^2) is 25, so we can write the equation as ...
(x +1)^2 +(y +2)^2 = 25
Answer:
(x + 1)2 + (y + 2)2 = 25
Step-by-step explanation:
Hope this helps :)
What percent of 56 is 21?
A)3/8%
B) 3 3/4%
C) 3 7/12%
D)375%
Step-by-step explanation:
100% = 56
1% = 100%/100 = 56/100 = 0.56
21 is that many % as 1% fits into it.
so,
21/0.56 = 37.5% = 37 1/2 %
i think that is actually the third answer option (but you wrote it wrongly).
Marta’s math textbook weighs Four-fifths of a pound less than 4 times the weight of the book she is reading for her language arts class. If the weight of the math textbook is 2 and one-fifth pounds, which shows the correct equation and value of x, the weight of Marta’s book for language arts?
4 x + four-fifths = 2 and one-fifth; x = StartFraction 7 over 20 EndFraction of a pound
4 x minus four-fifths = 2 and one-fifth; x = three-fourths of a pound
4 x + four-fifths = 2 and one-fifth; x = three-fourths of a pound
4 x minus four-fifths = 2 and one-fifth; x = StartFraction 7 over 20 EndFraction of a pound
Answer:
C
Step-by-step explanation:
Determine the equation of the line that passes through (-8,9) and (2,-6)
Express you answer as a fraction in lowest terms.
The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.
We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.
Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.
Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.
The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.
Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.
Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.
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