The answer is 2000000$ . Victoria need to sell 2000000$ this year to achieve $60000 this annum.
As per the question , 3 percent of her yearly is equivalent to $30000 ,
If 3 percent is equivalent to $30000 , then 100 % is equal to , ( 30000 × 100/3 = 1000000 $ )
Now , we can conclude , the realtor sold worth of 1000000 $.
If Victoria want to earn 60000$ then She has to sell ( 60000 ×100/3 = 2000000 $ ) as only 3 % is equivalent to 60000 $ .
This year 2000000$ will she need to sell .
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Help pleaseeee It's the task for now
The probability of the next customer paying in cash is approximately 0.421 or 42.1%.
What is ratio ?
A ratio is a mathematical relationship between two quantities or values that indicates how many times one value is contained within the other. It is a way of comparing two values by expressing their sizes relative to each other. Ratios are usually written in the form of a fraction, using a colon, or with the word "to" between the two values being compared.
For example, if there are 20 red marbles and 30 blue marbles in a bag, the ratio of red marbles to blue marbles is 20:30, which can be simplified to 2:3. This means that there are two red marbles for every three blue marbles in the bag.
Given by the question:
The total number of customers yesterday is:
Total customers = cash customers + debit card customers + credit card customers
Total customers = 40 + 16 + 39
Total customers = 95
The number of customers who paid in cash is 40.
The probability that the next customer pays in cash can be calculated as the ratio of the number of cash-paying customers to the total number of customers:
Probability of paying in cash = Number of cash-paying customers / Total number of customers
Probability of paying in cash = 40 / 95
Probability of paying in cash = 0.421 (rounded to three decimal places)
Therefore, the probability of the next customer paying in cash is approximately 0.421 or 42.1%.
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The coordinates of the four vertices of quadrilateral ABCD are listed below
4
• A(-3,3)
.
.B(2,6)
. C(5, 1)
. D(-5,-5)
Which statement proves whether or not this quadrilateral is a rectangle?
OA
The slope of CD is-
rectangle
OB The slope of AB is
-5-1
-5-5
OD. The slope of AB is
6-3
2-(-3)
3
5
6-3
2-(-3)
3
and the slope of DA IS
OC. The slope of BC is and the slope of CD is
rectangle
3-(-5)
-3-(-5)
and the slope of BC is These two segments are perpendicular, so the shape is a rectangle.
These two segments are not perpendicular, so the shape is not a
These two segments are not perpendicular, so the shape is not a
and the slope of CD is-7
These two segments are perpendicular, so the shape is a rectangle.
For the quadrilateral ABCD the statement which proves that this quadrilateral is not a rectangle is (a) The slope of CD is "(-5-1)/(-5-5) = 3/5", and the "slope of DA is [3-(-5)]/[-3-(-5)] = 8/2", these "two-segments" are not perpendicular , so the shape is not a rectangle;
The coordinates of the "four-vertices" of the quadrilateral ABCD are :
A(-3,3), B(2,6), C(5, 1), D(-5,-5);
To prove whether the quadrilateral is a rectangle or not, we need to show that its adjacent sides are perpendicular and its diagonals are congruent.
In this question, we are given the coordinates of the four vertices of the quadrilateral.
To determine if it's a rectangle, we use the slope formula to find the slopes of the sides of the quadrilateral. If slopes of adjacent sides are "negative-reciprocals" of each other, then they are perpendicular. If the slopes of the diagonals are equal, then they are congruent.
Using the given coordinates, we find that the slope of CD is = (-5-1)/(-5-5) = 3/5, and
The slope of DA is = [3-(-5)]/[-3-(-5)] = 8/2. These two slopes are not negative reciprocals of each other, so CD and DA are not perpendicular.
So, the quadrilateral is not a rectangle.
Therefore, the correct option is (a).
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The given question is incomplete, the complete question is
The coordinates of the "four-vertices" of the quadrilateral ABCD are :
A(-3,3), B(2,6), C(5, 1), D(-5,-5);
Which statement proves whether or not this quadrilateral is a rectangle?
(a) The slope of CD is (-5-1)/(-5-5) = 3/5, and the slope of DA is 3-(-5)/-3-(-5)=8/2, these two segments are not perpendicular , so the shape is not a rectangle;
(b) The slope of AB is (6-3)/(2-(-3) = 3/5, and slope of BC is (6-1)/(2-5) = -5/3, these two segments are perpendicular , so the shape is a rectangle;
(c) The slope of BC is (6-1)/(2-5) = -5/3, and slope of CD is (-5-1)/(-5-5) = 3/5, these two segments are not perpendicular, so the shape is not a rectangle;
(d) The slope of AB is (6-3)/(2-(-3) = 3/5, and slope of CD is (-5-1)/(-5-5) = 3/5, these two segments are perpendicular , so the shape is a rectangle;
How do you write 0.53 as a whole number
Answer:
Step-by-step explanation:
0.53 cannot be written as a whole number, but it can be written as the ratio 53/100, which is the ratio of two whole numbers (53 and 100).
given rhombus and square have equal area and one of diagonal of rhombus is one side of square if length of square is 10 cm find a) diagonals of rhombus if one is half of the othe b)area of square c)area of rhombus d) perimeter of square
Answer:
a) 10 cm and 20 cm
b) 100 cm^2
c) 100 cm^2
d) 40 cm
Step-by-step explanation:
Given:
\(a(rhombus) = a(square)\)
\(l(square) = 10 \: cm\)
\(diagonal1 = 2 \times diagonal2\)
Find:
a) Diagonals of the rhombus
We already know the length of one diagonal (which is 10 cm, since it was said, that is is equal to a square's length)
Now, we can find the other one (d2 is the second diagonal):
10 cm = 0,5 × d2 (divide both sides from 0,5)
d2 = 20 cm
b) Area of the square
\(a(square) = {l}^{2} = {10}^{2} = 100 \: {cm}^{2} \)
c) Area of the rhombus:
\(a(rhombus) = \frac{1}{2} \times d1 \times d2 = \frac{1}{2} \times 10 \times 20 = 100 \: {cm}^{2} \)
d) Perimeter of the square (we multiply one side's length by 4, since square has 4 identical sides):
\(p(square) = l \times 4 = 10 \times 4 = 40 \: cm\)
A gardener uses exactly 500 feet of fencing to completely enclose a rectangular
area in her backyard. If the width of her garden is 50 feet less than the length,
what will be the area of her garden?
Answer:
Step-by-step explanation:
Let's start by assigning variables to the dimensions of the rectangular garden.
Let L be the length and W be the width.
From the problem statement, we know that the width is 50 feet less than the length, so we can write:
W = L - 50
We also know that the perimeter of the garden is 500 feet, which means:
2L + 2W = 500
Substituting W with L - 50, we get:
2L + 2(L - 50) = 500
Simplifying this equation, we get:
4L - 100 = 500
Adding 100 to both sides:
4L = 600
Dividing both sides by 4:
L = 150
Now that we know the length, we can find the width:
W = L - 50 = 150 - 50 = 100
The area of the garden is:
A = L × W = 150 × 100 = 15,000 square feet.
Therefore, the area of the garden is 15,000 square feet.
what is the result of the following expression? 10 + 5 * 3 - 20
a tutor charges $5 for each class he takes per day that lasts for an hour. for each additional hour he tutors he charges $3. match the number of hours he tutors for in the first column with the money he makes from it.
the hours: 4,2,5,3
Answer:
u need to show the column
Express this number in scientific notation: 0.0002077
Given the number:
0.0002077
Let's express in scientific notation.
To express the number in scientific notation, move the decimal point so that there is only one non-zero number to the left of the decimal point.
Then, the number of decimal places you move will be the exponent on 10.
If the decimal point is moved to the right, the exponent will be negative.
If the decimal pointt is moved to the left, the exponent will be positive.
In this case the decimal point will be moved to the right.
Using this description, we have the scientific notation below:
\(undefined\)Answer:
2.077 x \(10^{-4}\)
Step-by-step explanation:
First, move the decimal place until we have a single digit between 1 and 10 to the left of the decimal point. In this problem, if we keep moving the decimal point to the right in 0.0002077 we will get 2.077.
Next, count how many places we moved the decimal point. If we have to move the decimal place to the right, the exponent will be negative. If we had moved the decimal place to the left, the exponent would be positive. In this case we had to move it 4 places to the right to change 0002077 to 2.077. We show that we moved it 4 places to the right by noting that the number should be multiplied by \(10^{-4}\).
The figure shows two vectors T⃗ and U⃗ separated by an angle θTU.You are given that T⃗ =(3,1,0), U⃗ =(2,4,0), and T⃗ ×U⃗ =V⃗ .1) Express V⃗ as an ordered triplet of values, separated by commas.2) Find the magnitude of V3) Find the sine of the angle between T⃗ and U⃗ .
The \(\vec{v}\) as an ordered triplet of values, separated by commas is ( 0 , 0 , 10 )
The magnitude of V is 10 units.
The sine of the angle between \(\vec{T}\) and \(\vec{U}\) is \(45^{\circ}\).
As per the given data the value of \(\vec{T}\) is ( 3, 1, 0 ) and \(\vec{U}\) is ( 2, 4, 0 )
Firstly we have to determine the value of \(\vec{v}\).
The value of \(\vec{v}\) is given by \(\vec T \times \vec U\)
\(& v=\left|\begin{array}{lll}\hat{i} & j & \hat{k} \\3 & 1 & 0\\2 & 4 & 0\end{array}\right|\)
\(=\hat{k}(12-2)\)
\(=10 \hat{k}\)
Therefore \(\vec{v}\) = ( 0 , 0 , 10 )
Now we have to determine the value of magnitude of V.
Magnitude of V is represented by \($|\vec{v}|\)
\($|\vec{v}|=\sqrt{100}\)
\($|\vec{v}|\) = 10 units
Therefore the magnitude of V is 10 units.
Now we have to determine the value of sine of the angle between \(\vec{T}\) and \(\vec{U}\).
\(|\vec{v}|=|\tilde{T}||\tilde{U}| \sin \theta_{T U}\)
\(\Rightarrow \theta_{T U}=\sin ^{-1}\left(\frac{|\vec{v}|}{|\vec{T}| |\vec{U}|}\right)\)
\(=\sin ^{-1}\left(\frac{10}{\sqrt{200}}\right)\)
\(=45^{\circ}\)
Therefore value of sine of the angle between \(\vec{T}\) and \(\vec{U}\) is \(45^{\circ}\)
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Two runners start the race at the same time. The first runner's speed is 4/5 of the speed of the second runner. After 30 minutes, the runners are 2 miles apart. What is the speed of each runner?
The speed of the second runner is x = 40/9 miles per hour. The speed of the first runner is (4/5)x = (4/5)*(40/9) = 16/9 miles per hour.
Let the second runner's speed be x. Then the first runner's speed is 4/5 * x = (4/5)x.Therefore, the speed of the first runner is (4/5)x and the speed of the second runner is x.After running for 30 minutes, the first runner would have covered a distance of (4/5)x * 1/2 = (2/5)x miles.
The second runner would have covered a distance of x * 1/2 = (1/2)x miles. Since the runners are 2 miles apart, we can write an equation:(2/5)x + (1/2)x = 2. Multiplying both sides of the equation by 10 to eliminate fractions, we get: 4x + 5x = 40.
Simplifying the equation, we get: 9x = 40. Dividing both sides of the equation by 9, we get: x = 40/9. Therefore, the speed of the second runner is x = 40/9 miles per hour. The speed of the first runner is (4/5)x = (4/5)*(40/9) = 16/9 miles per hour.
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What is a function f of three variables?
The domain of f is the set of all real numbers f(x,y) as (x,y) varies throughout the domain D with three variables.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
The functions of a point (or vector) in R2 or R3 that have real values will now be looked at. These functions will typically be defined on sets of points in R2, but there will be occasions when we utilise points in R3 and when it is more convenient to think of the points as vectors (or terminal points of vectors).
Each point f(x,y) in D is given a real number f(x,y) according to a real-valued function f defined on a subset D of R2. The domain of f is the set of all real numbers f(x,y) as (x,y) varies throughout the domain D, and the range of f is the greatest set D in R2 on which f is defined.
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(a) how many paths are there from the point (0, 0) to the point (110, 111) in the plane such that each step either consists of going one unit up or one unit to the right? (b) how many paths are there from (0,0) to (210, 211), where each step consists of going one unit up or one unit to the right, and the path has to go through (110, 111)?
(a) The number of pathways in the plane from point (0, 0) to point (110, 111) when each step consists of walking one unit up or one unit to the right is known as the number of ways to go to a point in a grid using just right and up moves.
This is a classic combinatorial problem known as a binomial coefficient. The binomial coefficient C(110+111, 110) = C(221, 110) = 221!/(110!111!) is the number of ways to travel from (0, 0) to (110, 111).
(b) The number of paths from (0, 0) to (210, 111) where each step consists of walking one unit up or one unit to the right and the path must pass through (110, 111) is the product of two binomial coefficients.
First, as calculated in section 1, the number of pathways from (0, 0) to (110, 111) is C(110+111, 110) = C(221, 110). Second, there are C(210+211, 210) ways to get from (110, 111) to (210, 111). (210, 211). (421, 210). C(221, 110) * C is the total number of paths found by multiplying these two binomial coefficients (421, 210).
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Alicia wants to help children out local shelters by providing them with toys throughout the year. She started with 1345 toys and gives away 25 each week. How many toys will she have remaining after 22 weeks
Answer:
795 toys
Step-by-step explanation:
if she gives away 25 toys each week for 22 weeks, that will be a total of 550 toys in 22 weeks
And now we simply minus 550 from 1345 to get 795 toys remaining after 22 weeks
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What will be the location of the x value of R' after using the translation rule (x + 4, y - 7), if the pre-image R is located at ( 24, -13)
The location of the x value of R' after using the translation rule is 28
What will be the location of the y value of R' after using the translation rule?The translation rule is given as:
(x + 4, y - 7)
The pre-image of R is located at (24, -13)
Rewrite as
R = (24, -13)
When the translation rule is applied, we have:
R' = (24 + 4, -13 - 7)
Evaluate
R' = (28, -20)
Remove the y coordinate
R'x = 28
Hence, the location of the x value of R' after using the translation rule is 28
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I need some help with this
Answer:
12
Step-by-step explanation:
i think its right
PLEASE CAN I HAVE HELP
Answer:
1.28
is the answer :) since the number after 7 is 5 you round up
Answer: 1.28
The 7 is in the hundredth's place, and since there is a 5 after it, we round up.
use traces to sketch the surface. 9x2 + 4y2 + z2 = 36
Using these traces, we can sketch the surface as an ellipsoid in three dimensions centered at the origin, with semi-major axis of length 6 along the z-axis, semi-major axis of length 3 along the y-axis, and semi-major axis of length 2 along the x-axis.
To sketch the surface 9x^2 + 4y^2 + z^2 = 36 using traces, we can fix values of x, y, and z and plot the resulting curves. When we fix x = 0, we get 4y^2 + z^2 = 36, which is an ellipse in the yz-plane centered at the origin with semi-major axis of length 6 along the z-axis and semi-minor axis of length 3 along the y-axis.
When we fix y = 0, we get 9x^2 + z^2 = 36, which is also an ellipse in the xz-plane centered at the origin with semi-major axis of length 6 along the z-axis and semi-minor axis of length 2 along the x-axis. When we fix z = 0, we get 9x^2 + 4y^2 = 36, which is a horizontal ellipse in the xy-plane centered at the origin with semi-major axis of length 2 along the x-axis and semi-minor axis of length 3 along the y-axis.
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One angle measures 170°, and another angle measures (6k 44)°. if the angles are vertical angles, determine the value of k. k = 12 k = 20 k = 21 k = 126
Answer: the answer is 21
Step-by-step explanation:
If one angle measures 170°, and another angle measures (6k + 44)° and both are vertical angles that means the second angle should be the same as the first angle.
Vertical angles are congruent meaning they have an equal measure.
Now we have to find k
(6k + 44) = 170
subtract 44 - 44 and 170 - 44
(6k) = 126
divide 6 by 6, that leaves with just k on the left.
126 divided by 6 equals to 21
k = 21
Hope this helps!
Application (12 marks) 9. For each set of equations (part a and b), determine the intersection (if any, a point or a line) of the corresponding planes. x+y+z=6=0 9a) x+2y+3z+1=0 x+4y+8z-9=0 160
9b) 1
The set of equations in 9a) and 9b) represents three planes in three-dimensional space. The planes in 9a) intersect at a single point. The planes in 9b) do not intersect at a single point, resulting in no solution.
Let's solve the system of equations in 9a) and 9b) to find the intersection of the planes. We can start by using the method of elimination to eliminate variables.
Considering the equation set 9a), subtract the first equation from the second equation, we get: (x+2y+3z+1) - (x+y+z) = 0 - 6, which simplifies to y+2z+1 = -6. Similarly, subtracting the first equation from the third equation gives us: (x+4y+8z-9) - (x+y+z) = 0 - 6, which simplifies to 3y+7z = -3.
Now we have two equations in the variables y and z. By solving these equations, we find that y = -1 and z = 0. Substituting these values back into the first equation, we can solve for x: x + (-1) + 0 = 6, which gives x = 7. Therefore, the intersection of the planes is the point (7, -1, 0).
Since the three planes intersect at a single point, it can be represented as a point in three-dimensional space.
Considering the equation set 9b), multiply the first equation by 3 and subtract it from the second equation, we get: (3x-y+14z-6) - (3x+3y+6z+6) = 0 - 0, which simplifies to -4y-8z = 0. Next, subtracting the first equation from the third equation, we have: (x+2y+5) - (x+y+2z+2) = 0 - 0, which simplifies to y+2z+3 = 0. Now we have two equations in the variables y and z. By solving these equations, we find that y = -2z-3 and y = 2z. However, these two equations are contradictory, meaning there is no common solution for y and z. Therefore, the system of equations does not have a unique solution, and the planes do not intersect at a single point or form a line.
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Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary.
Age (yr) when award was won Frequency
15-24 27
25-34 33
35-44 14
45-54 4
55-64 6
65-74 1
75-84 1
Lower class limits are 15, 25, 35, 45, 55, 65, 75, Upper class limits are 24, 34, 44, 54, 64, 74, 84, Class width are 10 (all classes have a width of 10), Class midpoints are 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, Class boundaries are [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) and Number of individuals included in the summary is 76.
Here are the details for the given frequency distribution:
Lower class limits are the least number among the pair
Here, Lower class limits are 15, 25, 35, 45, 55, 65, 75 respectively.
Upper class limits are the greater number among the pair
Here, upper limit class are 24, 34, 44, 54, 64, 74, 84 respectively.
Class width is the difference between the Lower class limits and Upper class limits which is 10 (all classes have a width of 10).
Class midpoints is the middle point of the lower class limits and Upper class limits which is 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5 respectively.
Class boundaries are the extreme points of the classes which are [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) respectively.
Number of individuals = 27 + 33 + 14 + 4 + 6 + 1 + 1
= 76
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What outcome is likely to occur for a hypothesis test evaluating a treatment that has a very large and robust effect?
For the given statement, we have to correctly rejecting the null hypothesis.
According to the statement
we have to find the outcome when hypothesis test evaluating a treatment that has a very large and robust effect.
For this purpose, we know that the
A hypothesis is a testable statement about the relationship between two or more variables or a proposed explanation for some observed phenomenon.
And according to the given statement it is clear that the by this we have to rejected this hypothesis.
because this treatment and the large effects are not possible for the independent values of the hypothesis.
In other words, we can say that the we have to correctly rejecting the null hypothesis.
So, For the given statement, we have to correctly rejecting the null hypothesis.
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what is the relationship between the variance and the standard deviation? a) variance is twice the standard deviation. b) variance is the square root of the standard deviation. c) there is no constant relationship between the variance and the standard deviation. d) variance is the square of the standard deviation.
The relationship between the variance and standard deviation is: option a)The standard deviation is the square root of the variance.
What is variance?The variance of a random variable from its true population or sample mean is expected in probability theory and statistics. The term "variance" refers to a measurement of how widely apart a group of numbers are from one another.
Here,
Variance and standard deviation are both measures of spread. They calculate the deviation of each data point from the mean. The range of data increases with increasing variation. Using the original unit of measurement, the standard deviation measures the same thing as the variance (whereas variance is the original unit squared).
Therefore ,The relationship between the variance and standard deviation is: option a)The standard deviation is the square root of the variance.
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*PLEASEE ANSWER!! ASAP!! , NEED HELP *
The GDP for a hypothetical economy is determined to be 6 billion dollars in year 1 and 7.5 billion dollars in year 2. What is the growth rate of GDP from year 1 to year 2?
A.) 1.5%
B.) 125%
C.) 150%
D.) 25%
Answer:
answer is d
Step-by-step explanation:
25%of 6billion is 1.5 billion that's the difference in money from year one and two
The growth rate of GDP from year 1 to year 2 for the considered hypothetical economy is given by: Option D: 25%
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
\(\dfrac{a}{100} \times b\)
Growth rate (in percentage) of GDP is the percent of previous years GDP the next year GDP is.
For first year, GDP = $6 billion
For second year, GDP = $7.5 billion
So the difference is of 1.5 billion dollar increment in GDP.
Thus, the rate of growth of GDP from first year to second year is $1.5 billion per year.
Now we need to find out how much 1.5 billion dollars increment is in comparison to the first year GDP (so as to know how much percent is increased).
Let we have: 1.5 billion is P% of 6 billion
Then, we get:
\(\dfrac{6000000000}{100} \times P = {1500000000}\\\\60000000 \times P = 1500000000\\\\\text{Dividing both the sides by 60000000, we get:}\\\\P = \dfrac{1500000000}{60000000} = 25 \: \rm (in \: percent)\)
So second year's GPD is 25% incremented compared to the first year's GDP.
Thus, the growth rate of GDP from year 1 to year 2 for the considered hypothetical economy is given by: Option D: 25%
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Solve please don’t know how to get the answer
Answer:
5.9 mph
Step-by-step explanation:
The boat's speed is 15 mph
Given the current's speed is x, then
Boat's speed going upstream: 15 - x
=> time going upstream = 130/(15 - x)
Boat's speed going downstream: 15 + x
=> time going downstream = 130/(15 + x)
Total time
130/(15 - x) + 130/(15 + x) = 20.5
130(15 + x) + 130(15 - x ) = 20.5(15 + x)(15 - x)
130(15 + x + 15 - x) = 20.5(225 - x^2)
20.5(225 - x^2) = 130(30)
225 - x^2 = 3900/20.5
x^2 = 225 - 3900/20.5
x = square root of (225 - 3900/20.5)
x = ±5.895 or ±5.9
since speed can't be negative, speed of current is 5.9
if a 10-pound turkey costs $20.42.how much does a 21-pound turkey cost
Answer:
$42.88
Step-by-step explanation:
Let's create a proportion using the following setup:
cost/pounds=cost/pounds
We know that it costs $20.42 for a 10 pound turkey.
$20.42/10 pounds= cost/pounds
We don't know how much a 21 pound turkey costs, so we can say that it costs $x for a 21 pound turkey.
$20.42/ 10 pounds= $x/ 21 pounds
20.42/10=x/21
We want to find x, by getting x by itself.
x is being divided by 21. The inverse of division is multiplication. Multiply both sides by 21.
21*(20.42/10)=(x/21)*21
21* 20.42/10=x
21*2.042=x
42.882=x
Round to the nearest cent, or hundredth.
42.88=x
x= $42.88
A 21 pound turkey costs $42.88
The volume of a cone is 27 cm3. What is the volume of a cylinder that shares the same radius and height as the cone?
HELP NOW PLS!!!
Answer:
81 cm3
Step-by-step explanation:
The volume of a cylinder is three times that of a cone, as long as it has the same radius and height. Their formulas prove it.
Hope this helps
Answer:
81 cm³
Step-by-step explanation:
V-cylinder = πr²h
V-cone = πr²h/3
You can see from the formulas that the volume of a cone is 1/3 the volume of a cylinder with the same radius (r) and height (h).
Therefore:
πr²h/3 = 27
πr²h = 27(3) = 81 = volume of the cylinder
Sam has a rectangular field whose length and breadth are in the ratio 8:7. He wants to fence the field with bamboo to make it an extremely sustainable resource. If the cost of fencing the field at the rate of Dhs16 per metre is Dhs12000, find the dimensions of the field.
Answer:
Length = 200 m
Breadth = 175 m
Step-by-step explanation:
Perimeter of the rectangular field = Total cost ÷ rate per metre
= 12000 ÷ 16
= 750 m
Length : breadth = 8 : 7
Length = 8x
Breadth = 7x
Perimeter = 750
2*(length + breadth) = 750
2*(8x + 7x) = 750
2* 15x = 750
30x = 750
x = 750/30
x = 25
Length = 8x = 8*25 = 200 m
Breadth = 7*25 = 175 m
According to a survey of workers, 5/50
of them walk to work, 4/50
bike, 20/50
carpool, and 9/50
alone. What percent of workers walk or bike to work?
Answer:
45 percent like to walk or bike
Step-by-step explanation:
Solve the given differential equation x^3 y"' - 6y = 0 y(x) = ______ , x > 0
The solution to the given differential equation is:
\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]\)
How did we get the value?To solve the given differential equation
\(x^3y'''\ -\ 6y\ =\ 0,\)
we can use the method of power series. Let's assume a power series solution of the form
\(y(x)\ =\ \sum_{n=0}^{\infty} a_nx^n.\)
Differentiating y(x) with respect to x gives:
\(\[y'(x)\ =\ \sum_{n=0}^{\infty} n a_n x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+1) a_{n+1} x^n\]\)
Differentiating again gives:
\(\[y''(x)\ =\ \sum_{n=0}^{\infty} (n+1)na_{n+1}x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+2)(n+1)a_{n+2}x^n\]\)
Differentiating one more time gives:
\(\[y'''(x)\ =\ \sum_{n=0}^{\infty} (n+2)(n+1)na_{n+2}x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^n\]\)
Substituting these expressions into the differential equation, we have:
\(\[x^3 \sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^n - 6 \sum_{n=0}^{\infty} a_n x^n\ =\ 0\]\)
Rearranging the terms and combining like powers of x, we get:
\(\[\sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^{n+3} - 6 \sum_{n=0}^{\infty} a_n x^n\ =\ 0\]\)
Now, let's equate the coefficients of like powers of x to zero:
For n=0:
\(\[(3)(2)(1)a_3 - 6a_0 = 0 \implies 6a_3 - 6a_0 = 0 \implies a_3 = a_0\]\)
For n=1:
\(\[(4)(3)(2)a_4 - 6a_1 = 0 \implies 24a_4 - 6a_1 = 0 \implies a_4 = \frac{1}{4}a_1\]\)
\(For \: n\geq 2:
\[(n+3)(n+2)(n+1)a_{n+3} - 6a_n = 0 \implies a_{n+3} = \frac{6a_n}{(n+3)(n+2)(n+1)}\]
\)
Now we can write the solution as:
\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{6a_{n-2}}{n(n-1)(n-2)}x^{n+3}\]
\)
Simplifying the series, we get:
\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_
1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]
\)
Therefore, the solution to the given differential equation is:
\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]\)
where a₀ and a₁ are arbitrary constants to be determined based on the initial conditions or boundary conditions given in the problem.
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9) Refer to the table which summarizes the results of testing for a certain disease.
Positive Test Negative Test
Result Result
Subject has the disease
Subject does not have the disease
111
11
4
172
one of the results is randomly selected, what is the probability that it is a false negative (test
indicates the person does not have the disease when in fact they do)? What does this probability
suggest about the accuracy of the test?
A) 0. 591, The probability of this error is high so the test is not very accurate.
B) 0. 0348, The probability of this error is low so the test is fairly accurate.
C) 0. 0134; The probability of this error is low so the test is fairly accurate.
D) 0. 0369; The probability of this error is low so the test is fairly accurate.
The probability that it is a false negative (test indicates the person does not have the disease when in fact they do) is 0.0348.
This probability indicates that the test's accuracy is 0. 0348; as the likelihood of this inaccuracy is minimal, the test is quite accurate.
The likelihood that a randomly chosen result will be a false negative, meaning that the test will show that the person does not have the condition while in fact they do:
\(P(NP|D) = \frac{4}{115} \\\\P(NP|D) = 0.0348\)
We may infer that the occurrence is unlikely to occur and that the test is reasonably accurate because the probability is less than 0.0500.
Probability is simply the possibility that something will happen. When we don't know how something will turn out, we might talk about the possibility of one result or the likelihood of several. The study of occurrences that fit into a probability distribution is known as statistics.
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