A distribution is negatively skewed if the mode is larger than the mean. The final answer is C.
In a negatively skewed distribution:
A. the median is larger than the mode.
B. the mean is larger than the mode.
C. the mode is larger than the mean.
D. the mean is larger than the median.
Negatively Skewed Distribution:
left skewed distributions occur when the long tail is on the left side of the distribution. Statisticians also refer to them as negatively skewed. This condition occurs because probabilities taper off more slowly for lower values. Therefore, you’ll find extreme values far from the peak on the low side more frequently than the high side.
The distribution is negatively skewed if the data values are clustered on the right side of the curve causing it to have a peak on the right but a flatter tail on the left side. This happens when the data set has more frequently occurring higher values than lower values.
When the median is closer to the box’s higher values and the lower whisker is longer, it’s a left skewed distribution. Notice that the longer tail extends towards the lower values, making it negatively skewed.
To find out if the data set follows a normal or skewed distribution, the three measures of central tendency (mean, median, and mode) can be compared.
The mean is greater than the median. The mean overestimates the most common values in a positively skewed distribution
The distribution is negatively skewed if the mean is lesser than the median and the median is lesser than the mode.
The given scenario is the same as negatively skewed I if the mode is larger than the mean. The final answer is C.
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Are polynomials closed under addition?
Polynomials form a system like to that of integers hence they are closed under the operations of addition and subtraction.
Exponents of polynomials are whole numbers.
Hence the resultant exponents will be whole numbers , addition is closed for whole numbers. As a result, polynomials are closed under addition.
If an operation results in the production of another polynomial, the resulting polynomials will be closed.
The outcome of subtracting two polynomials is a polynomial. They are also closed under subtraction as a result.
The word polynomial is a Greek word. We can refer to a polynomial as having many terms because poly means many and nominal means terms. This article will teach us about polynomial expressions, polynomial types, polynomial degrees, and polynomial properties.
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What happens when a function tries to assign or change a value of a variable that has been defined at the module level
When Python constructs a function, it also generates a temporary variable with the same name, and only the function can access the value of that variable.
What is Using a temporary variable?Using a temp variable is the quickest and easiest way to switch the values of two variables. Using the formula temp = a, the first variable's value is stored in the temp variables. By doing this, you can change the values of the two variables so that a = b before assigning the value of temp to the second variable.Tuple packing and sequence unpacking are two additional methods for changing the values of two variables without the usage of a temporary variable. Using commas to divide up the pieces in a tuple is one method of creating a tuple. Additionally, Python examines a task's right side before its left. As a result, the variables are packed into a tuple on the right side of the statement by using commas to separate them, and they are unpacked on the left side using the same number of target variables separated by commas.As long as the statement has the same number of variables on both sides as there are variables, this approach of variable swapping and permutation can be applied to more than two variables.To Learn more About temporary variable Refer To:
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A financial advisor has recommended two possible mutual funds for investment: Fund A and Fund B. The return that will be achieved by each of these depends on whether the economy is good, fair, or poor. A payoff table has been constructed to illustrate this situation:
STATE OF NATURE
INVESTMENT GOOD ECONOMY FAIR ECONOMY POOR ECONOMY
Fund A $10,000 $2,000 –$5,000
Fund B $6,000 $4,000 0
Probability 0. 2 0. 3 0. 5
Draw the decision tree to represent this situation.
Perform the necessary calculations to determine which of the two mutual funds is better. Which one should you choose to maximize the expected value?
Suppose there is a question about the return of Fund A in a good economy. It could be higher or lower than $10,000. What value for this would cause a person to be indifferent between Fund A and Fund B (i. E. , the EMVs would be the same)?
$21,500 this would be cause a person to be indifferent between Fund A and Fund B (i. E. , the EMVs would be the same)
EMV 1 = 0.2*10,000 + 0.3*2,000 + 0.5*-5,000 = $100EMV 2 = 0.2*6,000 + 0.3*4,000 + 0.5*-0 = $2,400.
Comparing both funds based on EMV calculations, Fund B shows a higher EMV. Therefore, to maximize expected value, we should invest in Fund B with an expected value of $2,400. First, his EMV for Fund A is not the same as Fund A's return being higher or lower in good economic conditions. Therefore, the EMC can also be higher or lower. But obviously the economy changes quickly sometimes. You don't always get the same return. So relying solely on returns is risky. Relying heavily on favorable economic conditions makes Fund A vulnerable to change and increases investor risk, so investors need to be more diversified. We can do the calculation:
Fund A return in good economy = Difference between A and B: EMV (Fund A) = EMV (Fund B) 0.2*X + 0.3(2,000) + 0.5(- 5,000) = 2 4,000.2X = 4,300X = $21,500.
Therefore, if the economy is good, Fund A's return should be $21,500 for there to be indifference between Fund A and the fund B.
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Miguel has three times as many dimes as he has quarters. He has as many nickels.as he has dimes and quarters.combined. The total amount of money he has is $3.00. How many of each coin does Miguel have?
Answer:
Step-by-step explanation:
fter solving the algebraic equation, Miguel has 4 quarters, 12 dimes and 16 nickels.
What is algebra?
One of the earliest areas of mathematics that deals with number theory, geometry, and analysis is algebra. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols.
The number of quarters is taken to be x, then the number of dimes will be 3x, and the number of nickels will be 3x + x = 4x
$3.00 when converted to cents is 300 cents.
The value of nickels is 5 x 4x=20x.
The value of dimes is 10 x 3x=30x.
The value of quarters is 25x.
As the total value of money Miguel has is 300 cents, then the algebraic equation will be -
20x + 30x + 25x = 300
Solve to get the value of x -
75x = 300
x = 4
Therefore, the amount of quarters is x = 4 quarters.
The amount of dimes is x = 3x = 3 x 4 = 12 dimes.
The amount of nickels is 4x = 4 x 4 = 16 nickels.
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What is the greatest possible quotient of any two distinct members of the set $\left\{\frac{2}{5}, \frac{1}{2},5,10\right\}$? Specifically, we wish to maximize $\frac{x}{y}$, where $x$ and $y$ are chosen from the previous set.
The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required is; 25.
What is the maximum possible quotient of any pair of numbers from the set?It follows from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.
On this note, since the quotient which is to be maximised is hypothetically; x / y;
To maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.
On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;
10 / (2 / 5)
= ( 10 × 5 ) / 2
= 25.
Ultimately, the greatest possible quotient as required is; 25.
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The equations that are equivalent to each other will be 2 + x = 5, x + 1 = 4, and - 5 + x = - 2. Then the correct options are A, B, and E.
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
Simplify all the equations, then we have
A. 2 + x = 5, to simplify the equation, then we have
2 + x = 5
x = 3
B. x + 1 = 4, to simplify the equation, then we have
x + 1 = 4
x = 3
C. 9 + x = 6, to simplify the equation, then we have
9 + x = 6
x = - 3
D. x + (- 4) = 7, to simplify the equation, then we have
x - 4 = 7
x = 11
E. - 5 + x = - 2, to simplify the equation, then we have
- 5 + x = - 2
x = 3
The equations that are equivalent to each other will be 2 + x = 5, x + 1 = 4, and - 5 + x = - 2. Then the correct options are A, B, and E.
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For the functions below, what is the direction of fastest increase at (1, 1, 1)? (a) f(x, y, z) = 1/x² + y² + 22
(b) f(x, y, z) = 4xy + 4yz + 4xz 6 (c) f(x, y, z) x2 + y2 + z2
Answer: For all three functions, the direction of fastest increase at the point (1, 1, 1) is the direction of the gradient vector of the function at that point.
For function (a), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:
[2/x³, 2y, 22] = [2, 2, 22].
The direction of this gradient vector is given by the direction in which each of its components is increasing the most rapidly. In this case, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.
For function (b), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:
[4y + 4z, 4x + 4z, 4x + 4y] = [4, 4, 4].
Again, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.
For function (c), the gradient vector at (1, 1, 1) is given by the partial derivatives of the function at that point:
[2x, 2y, 2z] = [2, 2, 2].
As before, all three components are increasing at the same rate, so the gradient vector points in the direction of the positive x, y, and z axes.
Therefore, for all three functions, the direction of fastest increase at (1, 1, 1) is the direction of the positive x, y, and z axes.
Step-by-step explanation:
A bag contains 9 red marbles, 4 blue marbles, and 7 yellow marbles. You randomly select three marbles from the bag. a. What is the probability that all three marbles are red when you replace each marble before selecting the next marble? Round your answer to the nearest tenth. about % b. What is the probability that all three marbles are red when you do not replace each marble before selecting the next marble? Round your answer to the nearest tenth. about %
Answer:
A) 9.1%
B) 7.4%
Step-by-step explanation:
Part A
Because you are replacing each marble before selecting the next, the probability of choosing one red marble remains the same, so choosing 3 red marbles with replacement would mean the probability gets multiplied by itself 3 times:
[tex]\displaystyle P(\text{Red+Replace})=\biggr(\frac{9}{20}\biggr)^3=\frac{9}{20}*\frac{9}{20}*\frac{9}{20}=\frac{729}{8000}\approx9.1\%[/tex]
Part B
[tex]\displaystyle P(\text{Red+No Replace})=\frac{C(9,3)C(4,0)C(7,0)}{C(20,3)}=\frac{\frac{9!}{3!(9-3)!}}{\frac{20!}{3!(20-3)!}}=\frac{\frac{9*8*7}{3*2*1}}{\frac{20*19*18}{3*2*1}}=\frac{9*8*7}{20*19*18}=\frac{7}{95}\approx7.4\%[/tex]This can also be calculated with [tex]\frac{P(9,3)}{P(20,3)}[/tex] because the order does matter in which you pick the 3 red marbles with no replacement.
Answer:
9.1%
7.4%
Step-by-step explanation:
(a+b+c)(a-b+c)=a2+b2+c2 prove
Answer:
There might be an error in the question, the result below should be the correct answer. It is not possible for a^2+b^2+c^2 to be the answer.
(a+b+c)(a-b+c) = a^2 +2ac - b^2 + c^2
Step-by-step explanation:
(a+b+c)(a-b+c) = a^2 - ab +ac + ba - b^2 +bc + ca - cb + c^2 (expanding the two terms in brackets first)
Since ab = ba, ac = ca and bc = cb,
-ab and ba can be cancelled out
bc and -cb can be cancelled out
Hence, (a+b+c)(a-b+c) = a^2 +2ac - b^2 + c^2
This is what I have obtained through expansion, then simplification by cancelling out the common terms.
Could you help check the question again?
Kyle earns 11.2% commission on his sales at the electrical retail store. He made sales worth $8571 this month. how much commission has he earned? Give your answer to the nearest dollar.
Answer:
Sales=8571$
Commission=11.2% of Sales
=11.2/100 × 8571$
=(11.2×8571)/100 $
=959.952$ Which is nearly equal to 960$.
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Hello can someone please help me with this please What is the best possible geometric model for a set of rail tracks?
Ray ----Point ---- Line --- Plane
Fine the measure of an angle that is supplement to ABC if m < ABC is 82?
100 ---- 8---------278------
Fine the measure of an angle that is complementary to ABC is 32?
328------148------58------32
The intersection of two lines is a ?
Quadrilateral--------Point--------Line--------Plane
A rail track is composed by multiple lines, however all the lines are in the same plane, hence a plane is the best geometric model for the rail track.
How to obtain the supplement of an angle?Two angles are supplementary if the sum of their measures is of 180º, hence the supplement of an angle is obtained subtracting 180º by the angle measure.
This means that the supplement of ABC = 82º is given as follows:
180º - 82º = 98º.
How to obtain the complement of an angle?Two angles are complementary if the sum of their measures is of 90º, hence the complement of an angle is obtained subtracting 90º by the angle measure.
This means that the supplement of ABC = 90º is given as follows:
90º - 32º = 58º.
Where do two lines intersect?Two lines intersect at a single point, which is the solution to the system of equations involving the two lines.
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Find the inverse of the function f(x) = 2÷3x -6
Answer:
f⁻¹(x) = 3/2x +9
Step-by-step explanation:
You want the inverse of the function f(x) = 2/3x -6.
Inverse functionThe inverse function can be found by solving for y:
x = f(y)
Here, that is ...
x = 2/3y -6
x +6 = 2/3y . . . . . . . . . . . . . . add 6
y = 3/2(x +6) = 3/2x +9 . . . . multiply by 3/2
The inverse function is f⁻¹(x) = 3/2x +9.
__
Additional comment
Sometimes the division symbol ÷ is used to mean "divided by everything after this symbol." If that is the intended meaning, the function should be written as f(x) = 2/(3x -6) or f(x) = 2÷(3x -6).
We have interpreted the symbol according to the order of operations, which tells us that 2÷3x-6 means ((2÷3)·x)-6.
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What is a polynomial of degree 4 called?
A polynomial of degree 4 is called bi-quadratic polynomial.
Bi-quadratic polynomial
A biquadratic equation is a polynomial equation with degree 4, and it strictly does not consist of any term with degrees 3 and 1.
Polynomial
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division
Degree of polynomial
The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial.
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Find the product of the factors 8.075*0.08
Answer: 8.075: gotta get somebody else to do this one...sorry. and 0.08 = 8
Step-by-step explanation:
Did this with a classmate couple months ago. Hope this helps. :)
I have 460 less than dotun.altogether we have 1280.how much do we each have
The main unknown at this point is "the number of adult tickets." The "number of children's tickets" is another factor that is unknowable. In order to assign two variables, do as follows:
Let a = # of adult tickets
and c = # of children's tickets.
What is meant by variables?Any traits, figures, or amounts that may be gauged or counted are considered variables. Another name for a variable is a data item. Variables include things like age, sex, business income and expenses, birthplace, capital expenditures, class grades, eye color, and vehicle type.
Setting up the equations using the unknowns that follow the word problem is the next step. Here are the details:
There are 460 tickets total because there are an adult ticket and a child ticket.
a + c = 460.
Now that we know we want to find the number of adult tickets, we can translate the basic equation a + c = 460 into terms of a:
a + c = 460
-a = -a (For example, use -a to delete a from the left side of the equation on either side.)
c = 460 - a
We can now enter the equation c into the other equation, 8.75a + 3.50c = 3143, since we have the equation c expressed in terms of a.
Now, we need to find the value of c in the first equation so that we can plug it into the second equation:
292 + c = 460
-292 = -292
c = 168
(8.75 × 292) + (3.50 × 168) = 3143
2555 + 588 = 3143
3143 = 3143
Therefore, We each have 3143
The complete question is:
For a show adult tickets are $8.75 and children's tickets are $3.50. 460 tickets were sold for a total of 3143 how many adults tickets were sold?
Adult ticket = 8.75
child ticket = 3.50
460 tickets we're sold totaling 3143
how many adults tickets were sold
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Convert the number into standard form, please!
Convert from number format to standard form as a decimal multiplied by a power of 10.
What is standard form?Standard form is a way of writing a number so it is easier to read. It is often used for very large or very small numbers. Standard form is like scientific notation and is typically used in science and engineering.A number is written in standard form when it is represented as a decimal number times a power of 10.As an example, consider the speed of light which travels at about 671,000,000 miles per hour. Written in standard form this number is equivalent to 6.71 x 108.step 1
convert 1.5806*10rais to 4
Convert to decimal notation
1.5806*10^4
The exponent is 4, making it 10 to the power of 4. As the exponent is positive, the solution is a number greater than the origin or base number. To find our answer, we move the decimal to the right 4 time(s)
1.5806 ->15806
step 2
final result
15806
Simplify the expression
1.581*10^4
Simplify exponents and square roots
1.581*10^4
10 ^4 = 10 × 10 × 10 × 10 = 10,000
1.581*10000
Perform any multiplication or division, from left to right:
1.581*10000
15806
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What does y 3x 3 look like on a graph?
On a graph, y 3x 3 would be a line that is 3 units below the line y = 3x. It would have the same slope but lower y-intercept.
To graph y 3x 3, we can first graph y = 3x. To do this, we can pick any two points along the line and plot them. For example, if we choose (0,0) and (1,3), the line would look like this:
(0,0) -------------------------- (1,3)
Now, to graph y 3x 3, we want to move the line 3 units down. Therefore, the new points that we plot should be (0,-3) and (1,0). The graph should look like this:
(0,-3) -------------------------- (1,0)
This line is 3 units below the line y = 3x. It has the same slope, but a lower y-intercept.
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Is P 3 2 and Q 2 3 represent the same point justify?
It is Justified that P and Q are different point.
What is cartesian coordinate plane?The coordinate plane where a location of a point is represented in the form of X and Y coordinate pair, is termed as cartesian plane. In this plane two reference axes are used which are perpendicular to each other.
What is the location of two point stated above?In the question, two-point P (3, 2) and Q (2, 3) are given. As per the cartesian coordinate system a location of a point is represented by a pair of numerical terms. The first numerical terms denote the X coordinate of the point, and the next terms refers the Y coordinate of that point.
Therefore, P and Q are two different points on the cartesian plane. The point p (3, 2) where 3 is the X coordinate and the distance from Y axis is 3 and 2 is the Y coordinate and distance from X axis is 2.
Similarly for the point Q (2, 3), 2 denotes the X coordinate of the point Q and 3 is the Y coordinate.
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Can a polynomial have no real roots?
Odd degree polynomials can have no real roots.
A polynomial of even degree can have any number from 0 to n distinct real roots. A polynomial of odd degree can have any number from 1 to n distinct real roots.
polynomials
A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.
Real root
A real root is a solution to an equation which is also a real number.
Real number
Real numbers are numbers that include both rational and irrational numbers. Rational numbers such as integers (-2, 0, 1), fractions(1/2, 2.5) and irrational numbers such as √3, π(22/7), etc., are all real numbers.
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The population of Smallville in the year 1890 was 6250. Assume the population increased at a rate of 2.75% each year. a) Estimate the population in 1915 and 1940. b) Predict when the population reached 50,000
If the population grew 2.75% each year then each year the population was multiplied by 1+2.75%=1+0.0275=1.0275
What is the population of Smallville in 1890 was 6250?Population in the year 1890 = 6250. Population increased at the rate of 2.75% per year or increased by 11400 , which will become 411400 after the increaseif you were to do it a step at a time it would mean multiplying 6250 by 0.0275(2.75%), and adding the result to 6250, then repeating the operation with the new number for each year until you reached the amount of years required (25 and 50 years).Now an easier way to do that first step would be multiplying by 1.0275, which already takes care of adding the original number. Now just do that for each of the intervals (25 and 50) required.
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In the figure below, side AC of ABC lies on line l.
A. 25
B. 30
C. 22
D. 24
Neegan paddles a kayak 21 miles upstream in 4.2 hours. the return trip downstream takes him 3 hours. what is the rate that neegan paddles in still water? what is the rate of the current?
The speed of Neegan paddles in still water will be 6 miles/Hr, while the rate of the current will be 1 mile/Hr.
Neegan paddles a kayak 21 miles upstream in 4.2 hours.
As he is moving in Upstream, so during returning the flow will be downstream
Downstream refers to the direction of the flow's termination, which is at the other end of the canal from the source. You are travelling upstream, for instance, if you are sailing from Kingston to Toronto. You are travelling downstream if you are moving from Kingston to Cornwall.
Let the speed of Neegan paddles in still water = x miles/Hr.
Let the rate of the current be = y miles/Hr.
As Speed = Distance/Time
So, for Upstream speed, Speed will be = x-y
For downstream, the speed will be = x+y
From question,
(x-y) = 21/4.2 = 5-----(i)
(x+y)= 21/3 = 7 -----(ii)
Solving (i) and (ii)
2x = 12
=> x = 6
So, the value of y (From (i), will be = (x-5) = 6-5 = 1
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If a scuba diver swam from the surface at −12 1/2 feet per minute, for 4 1/2 minutes, what would be the diver’s change in elevation?
The change in elevation would be -225/4 feet
What is a mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.
Given here, Speed of scuba diver as -12¹/₂=-25/2 and time in minutes 4¹/2=9/2
Thus distance traversed -25/2 × 9/2 = -225/4
Hence, the change in elevation is -225/4 feet
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•50 POINTS• don’t explain
-A
-B
-C
Answer:
C. Neither------------------------------------
There is no indication that the given triangles are congruent.
We can see one angle of each triangle is marked as congruent and that is is. No more evidences of congruence and therefore we state the triangles are not congruent.
This is a choice C.
A triangle ha an area of 142. 74 quare feet and a height of 18. 3 feet. What i the length of the bae?
A triangle having an area of 142. 74 ft^2 and a height of 18. 3 ft, has a base of 15.6 ft.
What is the area of a triangle?
In a two-dimensional plane, a triangle's area is the area that it completely encloses. A triangle is a closed shape with three sides and three vertices, as is common knowledge. The entire area occupied by a triangle's three sides is referred to as its area. Half of the product of the triangle's base and height provides the general formula for calculating the area of the triangle.
The area of the triangle is 142.74 ft^2.
The height of the triangle is 18.3 ft.
Let the base of the triangle be x.
The formula for area of a triangle is -
Area = (height × base)/2
Plugging in the values in the equation -
142.74 = (18.3 × x)/2
142.74 = 18.3x/2
18.3x = 285.48
x = 285.48/18.3
x = 15.6
Therefore, the base of the triangle measures 15.6 ft.
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What is vertically opposite angles in maths class 7?
When two lines intersect each other, then the opposite angles formed are called vertical angles or vertically opposite angles.
A pair of vertically opposite angles are equal to each other. Also, a vertically opposite angle and its adjacent angle are supplementary angles, i.e., they add up to 180 degrees. For example, if two lines intersect and make an angle, say X=35°, then its opposite angle is also equal to 35°. And the adjacent angle to angle X will be equal to 180 – 35 = 145°
In the given figure, ∠QOR and ∠SOP form a pair of vertically opposite angles and similarly ∠SOQ and ∠POR form such a pair. Therefore,
∠QOR = ∠SOP
∠SOQ = ∠POR
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Find the area of the surface obtained by rotating the circle
x2 + y2 = r 2
about the line
y = r.
The area of the surface obtained by rotating the circle [tex]x^2 + y^2 = r^2[/tex] about the line y = r is π²r² square units.
To find the area of the surface obtained by rotating the circle
[tex]x^2 + y^2 = r^2[/tex] about the line y = r, we can use the method of cylindrical shells.
The circle [tex]x^2 + y^2 = r^2[/tex] is centered at the origin (0, 0) with a radius r. The line y = r is the line y-axis but shifted up by r units.
When we rotate the circle about the line y = r, it forms a 3D shape called a torus or a donut shape.
Consider a small strip on the circle at a distance y from the line y = r.
This small strip is at a distance r - y from the y-axis.
The length of this strip is the circumference of the circle at y, which is 2πy (since the circumference of a circle is 2π times its radius).
The width of this strip is the change in x, which we can denote as dx.
The area of this small strip is then given by the product of its length and width, which is 2πy dx.
Now, to find the total surface area, we integrate this area over the range of y values from -r to r (since the circle is symmetric about the y-axis):
Total Surface Area = ∫[from -r to r] 2πy dx
Now, we need to express y in terms of x using the equation of the circle [tex]x^2 + y^2 = r^2:\\y^2 = r^2 - x^2[/tex]
y = ±√(r² - x²)
Since we are considering the upper half of the circle, we take the positive square root:
y = √(r² - x²)
Now, we can rewrite the integral with respect to x:
Total Surface Area = ∫[from -r to r] 2π√(r² - x²) dx
To solve this integral, we can make a trigonometric substitution:
Let x = r sin(θ), then dx = r cos(θ) dθ.
When x = -r, θ = -π/2, and when x = r, θ = π/2.
Now the integral becomes:
Total Surface Area = ∫[from -π/2 to π/2] 2π√(r² - (r sin(θ))²) (r cos(θ)) dθ
Total Surface Area = 2πr² ∫[from -π/2 to π/2] √(1 - sin²(θ)) cos(θ) dθ
Now, we can use the trigonometric identity:
sin²(θ) + cos²(θ) = 1
√(1 - sin²(θ)) = cos(θ)
Total Surface Area = 2πr² ∫[from -π/2 to π/2] cos²(θ) dθ
Now, use the trigonometric identity: cos²(θ) = (1 + cos(2θ))/2
Total Surface Area = 2πr² ∫[from -π/2 to π/2] (1 + cos(2θ))/2 dθ
Total Surface Area = 2πr² [θ/2 + (sin(2θ))/4] [from -π/2 to π/2]
Total Surface Area = 2πr² [(π/2 + sin(π) - (-π/2 + sin(-π)))/4]
Since sin(π) = 0 and sin(-π) = 0:
Total Surface Area = 2πr² [(π/2 - (-π/2))/4]
Total Surface Area = 2πr² (π/2)
Total Surface Area = π²r²
So, the area of the surface obtained by rotating the circle [tex]x^2 + y^2 = r^2[/tex] about the line y = r is π²r² square units.
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Question 10: Let the graph of f(x) represent the cost in thousands of dollars to feed the zoo animals daily, where x is the number of animals measured in hundreds. What does the solution to the function (2, 12) represent?
Cost (in thousands)
20
15
(2. 12)
10
5
Number of Animals (in hundreds)
• There are 200 animals, and the cost is $12,000 daily.
• There are 2,000 animals, and the cost is $1,200 daily.
• There are 1,200 animals, and the cost is $2,000 daily.
• There are 12,000 animals, and the cost is $200 daily.
Answer: I believe is the first one
Step-by-step explanation: It says animal in hundreds right. so looking at it 200 animals is right. But also x = 2 and y = 12
Hope this helps I'm sorry if it does not help
An object is moving at a speed of 11 yards every 6 months. Express this speed in centimeters per hour.
Speed of the given object in centimeters per hour
= 0.23 cm / hour
What is unit conversion?Unit conversion is a process with multiple steps that involves multiplication or division by a numerical factor or, particularly a conversion factor. The process may also require selection of the correct number of significant digits, and rounding. Different units of conversion are used to measure different parameters.
Like 1 yard = 91.44 cm
1 month = 730 hrs.
Given,
Distance covered by the object = 11 yards
Distance covered in cm = 11 × 91.44 = 1005.84 cm
Time taken to cover 11 yards = 6 months
Time taken in hours = 6 × 730 = 4380 hrs.
Speed of the object = distance covered by the object / Time taken
Speed of the object = 1005.84/4380 = 0.2296 ≈ 0.23 cm per hour
Hence, in centimeters per hour,
the speed of the object is 0.23 cm / hour.
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What is the product of 2p 7 3p2 4p 3?
The product of 2p 7 3p2 4p 3 is 756p7.
What is product in math?Product in math is the result of multiplying two or more numbers, variables, or algebraic expressions together. It is often denoted by the symbol 'x' or by juxtaposition, such as writing "ab" instead of "a x b". The product of two numbers is the same as the result of the first number multiplied by the second. Product is a fundamental concept in mathematics and is used in many different types of equations and calculations.
This can be calculated by multiplying the terms together.
First, multiply the terms in each parenthesis.
2p 7 is 14p, 3p2 is 9p2, and 4p 3 is 12p3.
Then, multiply the three terms together, 14p x 9p2 x 12p3, which equals 756p7.
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