Answer:
i ) $96120
ii ) Singular adult fee in 2012: $186.91
Step-by-step explanation:
( i )
To find the costs of all 560 peoples you:
Multiply the amount of people by the fee,
440 × 198 = $87120
120 × 120 = $9000
Add these go get the sum of member fees: $96120
( ii )
First calculate what 1% of the adult fee would be:
198 ÷ 100 = 1.98 = 1%
Then calculate what 0.1% of the fee:
1.98 ÷ 10 = 0.198 = 0.1%
Now multiply 5 by the value of 1% to get 5% :
5 × 1.98 = 9.9
Then multiply 6 by the 0.1% to get 0.6% :
0.198 × 6 = 1.188
Add these numbers together to get:
1.188 + 9.9 = $11.088 = 5.6%
Due to the fact this question is referring to money we will round this number 2 decimal places (as money does not exceed 2dp)
$11.09
We now subtract this from the 2013 fee to find out the 2012 fee
$198 - $11.09 = $186.91
$186.91 was the cost of a singular adult fee in 2012
x557x55 is divisible by 11. find the value of x
Step-by-step explanation:
A number is divisible by 11 if and only if the difference between sum of alternate digits is divisible by 11.
Here the number is x557x55. The difference between the sum of alternate digits is,
[tex]\longrightarrow S=(x+5+x+5)-(5+7+5)[/tex]
[tex]\longrightarrow S=2x-7[/tex]
By statement, the number x557x55 is divisible by 11 if and only if [tex]S=2x-7[/tex] is divisible by 11.
Let,
[tex]\longrightarrow 2x-7=11a[/tex]
[tex]\longrightarrow 2x=11a+7\quad\dots(1)[/tex]
We separate the RHS as the following.
[tex]\longrightarrow 2x=10a+a+6+1[/tex]
[tex]\longrightarrow 2x=10a+6+a+1[/tex]
[tex]\longrightarrow 2x=2(5a+3)+(a+1)[/tex]
In this question, the LHS is an even integer since x is a digit, i.e., integer. So RHS should also be an even integer.
Since [tex]2(5a+3)[/tex] is even, [tex]a+1[/tex] must be even. So let,
[tex]\longrightarrow a+1=2k[/tex]
[tex]\longrightarrow a=2k-1[/tex]
Then (1) becomes,
[tex]\longrightarrow 2x=11(2k-1)+7[/tex]
[tex]\longrightarrow 2x=22k-4[/tex]
[tex]\longrightarrow x=11k-2\quad\dots(2)[/tex]
So this is expression for x, for any integer k.
As x is a digit of x557x55, x is a single digit integer, so its value lies in between 1 and 9 [x ≠ 0 because it is also the left most digit of x557x55], i.e.,
[tex]\longrightarrow 1\leq x\leq 9[/tex]
From (2),
[tex]\longrightarrow 1\leq 11k-2\leq 9[/tex]
Adding 2,
[tex]\longrightarrow 3\leq 11k\leq 11[/tex]
Dividing by 11,
[tex]\longrightarrow\dfrac{3}{11}\leq k\leq 1[/tex]
Since k is an integer, we get,
[tex]\longrightarrow k=1[/tex]
Then from (2),
[tex]\longrightarrow x=11(1)-2[/tex]
[tex]\longrightarrow\underline{\underline{x=9}}[/tex]
Hence the value of x is 9.
What is the domain of the function y 3x 1?
We calculated the domain of this function is all the real numbers of independent variable X such as 0, 1, 2, 3, 4, 5, 6 etc.
What is function?An expression that indicates a relationship between an independent variable and dependent variable. A function consists of two variables with or without numbers. A function has symbols but equal sign is mandatory.
What is domain of a function?The domain of a function is the set of all possible value of independent variables. It is also called the input of a function.
What is the domain of the function y= 3x-1?In the above function, the domain is all real number of independent variable x.
For each value of x that means for each domain, we get a value of y. The set of y values are called ranges.
we put x= 0, 1, 2, 3, 4, 5, 6 and so on.
we get y = 3×0-1 = -1
y = 3×1-1 = 2
y =3×2-1 = 5
y = 3×3-1 = 8
y= 3×4-1 = 11
y = 3×5-1 = 14
y= 3×6-1= 17
The set of domains are {0, 1, 2, 3, 4, 6}
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(x+y)(x2+xy+y2)
pls solve step by step
Answer:
[tex]x {}^{3} + 2x {}^{2} y + 2xy {}^{2} + y {}^{2} [/tex]
Step-by-step explanation:
Greetings !
Given expression:-[tex](x + y)( x{}^{2} + xy + y {}^{2}) [/tex]
stepsDistribute parentheses
[tex] = xx {}^{2} + xxy + xy {}^{2} + yx {}^{2} + y {}^{2}x + y {}^{2} [/tex]
simply[tex] = x {}^{3} + x {}^{2} y + xy {}^{2} + yx {}^{2} + y {}^{2} x + y {}^{2} [/tex]
Collect Like terms and further simplification
[tex] = x {}^{3} + 2x {}^{2} y + 2xy {}^{2} + y {}^{2} [/tex]
Hope it helps!!!
If you have any questions and suggestions tag it on the comments. thanks
The product of (x+y)(x²+xy+y²) gives x³ + 2x²y + 2xy² + y³.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
(x+y)(x²+xy+y²)
Multiplying the terms
= x(x²+xy+y²)) + y(x²+xy+y²)
= x³ + x²y + xy² + yx² + xy² + y³
= x³ + 2x²y + 2xy² + y³
Hence, the expression gives x³ + 2x²y + 2xy² + y³.
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Collin states that 8+(16+9)=(8+16)+9 is always true. which of the following properties would prove Collin is correct?
Transitive Property
Associative Property of Multiplication
Associative Property of Addition
Commutative Property of Addition
What are the zeros of the polynomial 4x 2 }+ 52 √ 2x 3 ?`?
The zeros of the polynomial are 1/2√2 and -3/√2.
What is a zero of a polynomial?The zeros of a polynomial are all the x-values that make the polynomial equal to zero.
Given, the polynomial is 4x² + 5√2x - 3.
We have to find the zeros of the polynomial,
Let 4x² + 5√2x - 3 = 0
On factoring,
= 4x² + 6√2x - √2x - 3
= 2√2x(√2x + 3) - (√2x + 3)
= (2√2x - 1)(√2x + 3)
Now, 2√2x - 1 = 0
2√2x = 1
x = 1/2√2
Also, √2x + 3 = 0
√2x = -3
x = -3/√2
Therefore, the zeros of the polynomial are 1/2√2 and -3/√2.
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Is 1 the biggest prime number?
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself, so 1 is not consider as a prime number.
Therefor 1 is not the biggest prime number.
What is a prime number?A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.
What is whole number?Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.
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What is the ordered pair for Point N?
Enter the coordinates in the boxes.
The ordered pair for Point N is (6,9).
What is the ordered pair?
An ordered pair in mathematics is a set of two things. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples or 2-length sequences.
Here, we have
Given the graph and we have to find the coordinates of all points.
N = (6,9)
M = (5,7)
R = (9,8)
D = (2,6)
C = (1,4)
B = (2,1)
A = (6,2)
Q = (7,5)
Hence, the ordered pair for Point N is (6,9).
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Question In picture
this was an accident how do I delete?
Marvin is playing a solitaire game with marbles. There are n bowls (for some positive integer n), and initially each bowl contains one marble. Each turn, Marvin may eitherremove a marble from a bowl, orchoose a bowl A with at least one marble and a different bowl B with at least as many marbles as bowl A, and move one marble from bowl A to bowl B.The game ends when there are no marbles left, but Marvin wants to make it last as long as possible.Prove that the game must end after at most n(n+1)/2 turns.Prove that for every positive integer k, there is an n such that Marvin can make the n-bowl game last for at least kn turns.Marisa comes along and asks to join the game. Marvin and Marisa revise the rules: they will alternate taking turns, starting with Marisa. When the game ends, whoever took the last turn is the winner.Prove that among any three consecutive values of n, there is at least one value for which Marvin has a winning strategy.
Among any three consecutive values of n, there is at least one value for which Marvin has a winning strategy.
For the first part of the problem, we can prove that the game must end after at most n(n+1)/2 turns by induction. Base case: When there is only one bowl, Marvin can remove the single marble in one turn, so the game ends after one turn.
Inductive step: Suppose the game ends after at most k(k+1)/2 turns when there are k bowls. We will show that the game ends after at most (k+1)(k+2)/2 turns when there are k+1 bowls. If Marvin removes a marble from a bowl, then the number of bowls decreases by one and the game must end after at most k(k+1)/2 turns by the inductive hypothesis.
If Marvin moves a marble from bowl A to bowl B, where bowl A has at least one marble and bowl B has at least as many marbles as bowl A, then the number of marbles in bowl A decreases by one and the number of marbles in bowl B increases by one. Since bowl B has at least as many marbles as bowl A, the number of bowls remains unchanged. Thus, the game must still end after at most k(k+1)/2 turns.
In either case, the game ends after at most k(k+1)/2 turns, so the game must end after at most (k+1)(k+2)/2 turns when there are k+1 bowls, as desired.
For the second part of the problem, we can prove that for every positive integer k, there is an n such that Marvin can make the n-bowl game last for at least kn turns by constructing a strategy.
Suppose Marvin wants to make the n-bowl game last for at least kn turns. He can do this by making sure that there are always at least k marbles in each bowl. To do this, Marvin can start by placing k marbles in the first bowl, k-1 marbles in the second bowl, and so on, down to 1 marble in the nth bowl.
On each turn, Marvin can choose a bowl with at least k marbles and move one marble to a bowl with fewer than k marbles. For example, if there are k+1 marbles in the first bowl and k marbles in the second bowl, Marvin can move one marble from the first bowl to the second bowl. This keeps the number of marbles in each bowl at least k. Since Marvin can take at least one turn per bowl, the game will last for at least kn turns.
For the third part of the problem, we can prove that among any three consecutive values of n, there is at least one value for which Marvin has a winning strategy.
Let n be a positive integer. We will show that either Marvin has a winning strategy for the n-bowl game or Marisa has a winning strategy for the (n+1)-bowl game.
If Marvin has a winning strategy for the n-bowl game, then he can win the n-bowl game by following his winning strategy.
If Marvin does not have a winning strategy for the n-bowl game, then Marisa has a winning strategy for the n-bowl game. In this case, Marvin can adopt Marisa's winning strategy for the n-bowl game as his own winning strategy for the (n+1)-bowl game.
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How can you use a square root to relate the side length and area?
Therefore , we can calculate the side of the length of the square by finding the square root of the given area.
The square root of an integer, which is the outcome of multiplication alone, gives the initial number. Squares and square roots are a few of examples of exponents. Think about the number 36. Furthermore, this can be written as 6x6.
Here,
The base length times the height of any quadrilateral yields the area of that shape.
Since the shape is square, we can be certain that all of its sides are equal in length.
Using this information, we can work backwards to determine the length of one side by taking the square root of the area.
For example : Square having area of 25
We can find its length by taking square root of 25
Which comes out to be √25 = 5
Thus , 5 is a length of the side of the square.
Therefore , we can calculate the side of the length of the square by finding the square root of the given area.
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Duncan works at a banquet hall and is setting tables for a wedding reception. He starts with a pile of 144 salad plates, and he places 10 salad plates on every table he sets. Write an equation that shows how the number of salad plates remaining, y, depends on the number of tables Duncan sets, x.
The equation that shows the number of plates that is remaining would be = Y = (Total salad plate/X) - 4.
What is a banquet hall?A banquet hall is a building constructed is a way that various celebrations and functions can be held in such a place such as wedding receptions.
The total number of salad plates available = 144
The number of salad plate per every table set = 10
The number of salad plates remaining = y
The number of tables set by Duncan = x.
If 1 table = 10
X tables = 144
make X tables the subject of formula;
X tables = 144/10
X tables = 14 tables (approximately)
But 14 × 10 = 140 salad for the 14 tables
The remaining salad plates is 4 plates.
Y = (Total salad plate/X) - 4
Therefore, the number of salad plates remaining which is 4 depends on the number of tables Duncan sets which is 10.
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Hi! i need some help:)
Answer:
y=1/2x+-2
Step-by-step explanation:
What is the slope and y-intercept of y =- 3x 4?
The slope of the linear equation y = -3x + 4 is -3, and the y-intercept is 4.
To calculate the slope of a linear equation, the formula is m = (y2 - y1) / (x2 - x1). The slope is calculated by selecting two points on the line, (x1, y1) and (x2, y2), and then subtracting the first point's y-value from the second's and dividing the result by the first point's x-value minus the second's. For the equation y = -3x + 4, the y-intercept is 4, which is the b-value in the equation y = mx + b. The y-intercept is the point where the line crosses the y-axis. To calculate the y-intercept, set x = 0 and solve for y. For the equation y = -3x + 4, when x = 0, y = 4. Therefore, the y-intercept is 4.
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Two right angle triangles are joined toghether to. Make triangle acD
Answer:
transversitile multistelular projection
Answer:
Step-by-step explanation:
The perimeter of triangle ACD that is formed by two right-angle triangles ACB and DCB, approximated to 1 decimal place is: 40.1 cm.
a 17-tooth spur pinion has a diametral pitch of 8 teeth/in, runs at 1150 rev/min, and drives a gear at a speed of 575 rev/min. find the number of teeth on the gear and the theoretical center-to-center distance.
No. of teeth on the pinion(TP)=17.
Diametral pitch(pd)=8 teeth/in.
Rotational speed of the pinion(NP)=1120 rev/min or 1120 rpm.
Rotational speed of the gear(NG)=544 rev/min or 544 rpm.
To calculate:
No. of teeth on gear(TG) & theoretical centre to centre distance(C).
Solution:
We know that;
Diametral pitch(pd)=No. of teeth in the gear/Diameter of the gear
For pinion,
pd=TP/DP
Pittiong the values in above eq.
8 teeth/in =17/DP =>DP=17/8 in.
or DP=2.125 in.
Gear ratio(G)=(NP/NG)=(TG/TP)=(DG/DP)
=>(NP/NG)=(TG/TP)
=>1120/544 =TG/17 =>TG=35
No. of teeth the gear(TG)=35 {Ans}
Also from gear ratio formula,
(NP/NG)=(DG/DP)
=>1120/544=DG/2.125
=>DG=4.375 in.
In the next fig. I have drawn a rough diagram of the pinion and gear arrangement which will help you to understand how to calculate the centre to centre distance(C)
centre to centre distance,C=rP+rG {Where rP and rG are the radii of pinion and gear respectively}
=>C=(DP+DG)/2
Diameter =2*radius}
=>C=(2.125+4.375)/2 in. =3.25 in.
Theoretical centre to centre distance (C)=3.25 in.
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What are the 3 parameters of range function?
Three parameters, start value, stop value, and step value, are required for the range() method in Python to function. After incrementing the values by the amount specified in the step value .
what is range ?The range of values between a given data collection's top and lowest values is known as the statistical range. The difference between the highest and lowest observation is another method of expressing the range. By deducting the highest value from the lowest, one may calculate the sample interval. A crucial indicator of variability for continuous variables is the sample range.
here
startNumber (optional): The series of integers that are returned begins with this number.
stopNumber: The list of integers that range() provides comes to an end before this one.
stepValue (opportunity): a number that is an integer and represents the difference between each integer in the series.
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What is the mean of 4 6 8 10 12 14 *?
The mean of the given observation is 9.
What are the mean, median, and example?
The ratio between the total number of observations in a data set and the sum of all observations is known as the mean in statistics. The most frequent number, or the one that happens the most frequently, is known as the mode.
Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
Mean = Sum of all the observations/Number of observations
Mean = 4+6+8+10+12+14/6
Mean = 54/6
Mean = 9
Hence, the mean of the given observation is 9.
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A delivery driver earns a fixed amount for each delivery she makes, and yesterday her average hourly wage was $16. 50 an hour. If she worked 6 hours yesterday and made 11 deliveries, how much does she earn for each delivery made?.
Answer:
let x= amount she earn for each delivery
6(16.5) = 11x
99 = 11x
x = 9
Each delivery she earned $9.CHECKING:$16.5 per hour * 6 hours = $99
11 deliveries * $9 = $99
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Which of the following is quadratic equation 3x2 5x 9 x2 7x 3?
Yes, the given equation is quadratic equation.
Here it has been given that,
3x² - 5x + 9 = x² - 7x + 3
Now, after solving above equation further we obtain,
2x² + 2x + 6 = 0
From the above equation the factor 2 is taken out as it is common and now the equation looks like : x² + x + 3 = 0
The coefficients of the quadratic equation are compared and if it meets the criteria then it is quadratic equation otherwise not.
Now as we can see, the above equation clearly represents a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = 1 and c = 3.
Hence, the above given equation is a algebraic quadratic equation.
Which of the following is quadratic equation 3x² - 5x + 9 = x² - 7x + 3 ?
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If this net were to be folded into a cube, which number would be opposite of the number 1
Answer:
Number 5
Step-by-step explanation:
When the net is folded, 3 will be folded left and up, with 4 being the base. 6 will be folded right, with 2 being the top of the cube.
So, we have pairs
2 and 4
6 and 3
1 and 5
So, the opposite of the number 1 is the number 5
Solve for x and graph the solution on the number line below.
1≥-x-1 and -x-1≥ −13
The solution to both inequality is 2 ≥ -x and -x≥ 14
How to calculate inequality ?The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities1, is at the core of social justice theories. However, because it frequently has diverse meanings to different people, it is prone to misunderstanding in public discourse.
We have the equation 1≥-x-1 and -x-1≥ −13
Let us solve the inequality
1 ≥ - x - 1
1 + 1 ≥ -x
2 ≥ -x
Now, let us solve the inequality
-x-1≥ −13
-x+13 ≥ -1
-x≥ 14
Therefore the solution to both inequality is 2 ≥ -x and -x≥ 14
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How do you find the discontinuity of a hole?
The process of finding the discontinuity of a hole is explained below.
The term discontinuity in statistics is defined as a point on the graph that is undefined or is unfit for the rest of the graph.
In order to find the discontinuity of the hole we have to perform the following steps,
The first and foremost thing is to factor out the numerator and the denominator
Next we have to determine the common factors in the numerator and the denominator
After that we have to set the common factors equal to zero and find the value of x.
Then the final steps is to plot the graph and mark the point with a hole
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if Z1=(x1,y1) and Z2=(x2,y2) where Z1 and Z2€C then Z1 + Z2=?
Answer:
Step-by-step explanation:
If Z1 = (x1, y1) and Z2 = (x2, y2) are complex numbers, then their sum is given by:
Z1 + Z2 = (x1 + x2, y1 + y2)
For example, if Z1 = (3, 4) and Z2 = (-2, 5), then their sum is:
Z1 + Z2 = (3 + (-2), 4 + 5) = (1, 9)
In general, to add two complex numbers, we add their real parts and their imaginary parts separately.
The value of [tex]z_1[/tex] + [tex]z_2[/tex] = ( [tex]x_1[/tex] + [tex]x_2[/tex] )+ i ( [tex]y_1[/tex] + [tex]y_2[/tex])
What is Complex Number?Complex Numbers. Complex numbers are those that are expressed as a+ib, where a and b are real numbers and I is a imaginary number called a "iota."
Given:
[tex]Z_1=(x_1,y_1)[/tex] and [tex]Z_2=(x_2,y_2)[/tex]
Also, we know by Complex number
[tex]z_1[/tex] = [tex]x_1[/tex] + i [tex]y_1[/tex]
and, [tex]z_2[/tex] = [tex]x_2[/tex] + i [tex]y_2[/tex]
Then, [tex]z_1[/tex] + [tex]z_2[/tex]
= ( [tex]x_1[/tex] + i [tex]y_1[/tex]) + ( [tex]x_2[/tex] + i [tex]y_2[/tex])
= ( [tex]x_1[/tex] + [tex]x_2[/tex] )+ i ( [tex]y_1[/tex] + [tex]y_2[/tex])
Hence, the addition gives ( [tex]x_1[/tex] + [tex]x_2[/tex] )+ i ( [tex]y_1[/tex] + [tex]y_2[/tex]).
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Why do we calculate the mean?
Mean is calculated to get an idea of the average of the observations in the data set.
The average value of the observations in a data set is called the mean or average . It is calculated by dividing the sum of observations by the number of observations i.e.
u = (x1 + x2 + x3 + .... + xn)/n
where u is the mean , x1 , x2 ..., xn are data observations and n is the number of observations.
For example, we have values as 1,2,3,4,5 and we want to calculate the mean . Then it is calculated by
u = (1+2+3+4+5) / 5 = 3.
So, the mean is 3.
Therefore, mean is calculated to get an average or an idea of a certain number of observations.
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How many numbers between 50 and 100 are divisible by 3?
On solving the provided question, we can say that - If you put all the numbers together by digits, the total must be a multiple of three. so answer is 17
what is divisibility test?The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.
[tex]51, 54, 57\\60, 63, 66, 69\\72, 75, 78\\81, 84, 87\\90, 93, 96, 99[/tex]
If you put all the numbers together by digits, the total must be a multiple of three. so answer is 17
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2. A swimming pool has a volume of 32,700 cubic feet. How many gallons of water doesthe pool hold?A. 4,371.66 galB. 239,360 galC. 244,596 galD. 4,278.07 gal
The pool holds about 245,000 gallons. Therefore, option (c) 244,596 gal is correct.
To find the number of gallons of water the pool holds, we need to convert the volume in cubic feet to gallons.
One cubic foot is equal to 7.4805194805 gallons, so to find the number of gallons in the pool, we can multiply the volume in cubic feet by the conversion factor:
1 cubic foot= 7.4805194805 gallons
gallons = 32,700 cubic feet * 7.4805194805 gallons/cubic foot
= 244,999.99968 gallons
Rounded to the nearest gallon, the pool holds about 245,000 gallons.
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One cubic foot is equal to 7.4805194805 gallons, so to find the number of gallons in the pool, we can multiply the volume in cubic feet by the conversion factor:
1 cubic foot= 7.4805194805 gallons
gallons = 32,700 cubic feet * 7.4805194805 gallons/cubic foot
= 244,999.99968 gallons
Rounded to the nearest gallon, the pool holds about 245,000 gallons.
Work out the length of AB.
Give your answer to 3 significant figures.
A (-1, 6)
B (5, 3)
Answer:
AB = 6.71
Step-by-step explanation:
See the attached worksheet.
Find the lengths of the two sides of the right triangle:
CB = (5 - (-1)) = 6
CA = (6-3) = 3
Use the Phythagorean Theorem to find AB.
6^2 + 3^2 = AB^2
AB^2 = 45
AB = 6.71
Is 0 and 1 are prime?
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. 0 is not a positive integer and 1 is not greater than 1, so they are not considered a prime number.
What is a prime number?A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.
What is whole number?Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.
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Michael breeds chickens and ducks. Last month, he sold 505050 chickens and 303030 ducks for \$550$550dollar sign, 550. This month, he sold 444444 chickens and 363636 ducks for \$532$532dollar sign, 532.
The price of a single chicken is $8 and the price of a single duck is $5.
The prices can be determined by forming the linear equation in two variables.
Given that,
Michael sold last month, 50 chickens and 30 ducks for $550.
This month, he sold 44 chickens and 36 ducks for $532.
Let the price of single chicken be 'a' and the price of a single duck be 'b'. Then the linear equation will be:
50a+30b=550 ____________(1)
44a+36b=532 ____________(2)
Solving equation (1) for the value of 'b'.
b=550-50a/30
b=55/3 - 5a/3 ____________(3)
Putting the value of 'b' in equation (2).
44a+36(55/3 - 5a/3) = 532
128 = 16a
a=8
Putting the value of a in equation (3).
b= 55/3 - 5*8/3
b=5
Thus, The price of a single chicken is $8 and the price of a single duck is $5.
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Michael sold last month, 50 chickens and 30 ducks for $550.
This month, he sold 44 chickens and 36 ducks for $532.
50a+30b=550
44a+36b=532
Solving equation (1) for the value of 'b'.
b=550-50a/30
b=55/3 - 5a/3
Putting the value of 'b'
44a+36(55/3 - 5a/3) = 532
128 = 16a
a=8
Putting the value of a
b= 55/3 - 5*8/3
b=5
Thus, The price of a single chicken is $8 and the price of a single duck is $5.
a flea collar for dogs contains an active ingredient that evaporates at a rate proportional to the amount still present. half of the ingredient evaporates in the first 20 days after the collar is removed from the protective packaging. if the collar becomes ineffective after 70% of the active ingredient has evaporated, how many days does the collar remain effective?
Therefore ,the collar remain effective for 26.44 days.
Who defines order?In mathematics, there are numerous ways to use the word "order." It most frequently refers to the quantity of elements in (for example, conjugacy class order, graph order, group order, etc.) or describes the biggest term (for example, curve order, surface order, or polynomial order) that appears in a mathematical object.
Here,
=>Rate of evaporation=k=dr/dt
=> amount still present=R.
Thus ,It's a first order reaction.
So, half life=0.693/k.
20=0.693/k.
=> k=0.0346
Now,
60% of active ingredient has been evaporated.
So, 40% left.
Time taken=T=(2.303/k)log(R/0.4R)
T=(2.303/0.0346)log(5/2)
T=66.56(log5-log2)
T=66.56(0.699-0.301)
T=66.56(0.398)
T=26.44 days.
Therefore ,the collar remain effective for 26.44 days.
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