This statement best describes the coefficient, 3,700 is "the amount of the initial deposit". which is the correct answer would be option (C).
What is an exponential function?An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.
The exponential function is given in the question as:
3700(1.05)^4t
This expression is for the amount that will be in the account, in dollars, after t years.
As per the question,
The coefficient, 3,700 represents the amount of the initial deposit in the given exponential function
Thus, the correct answer would be an option (C).
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a rectangular poster is to contain 200 square inches of print. the margins at the top and bottom of the poster are to be 2 inches, and the margins on the left and right are to be 1 inch. what should the dimensions of the poster be so that the least amount of poster is used?
dimensions of the poster with margin are L = 12 in and h = 24 in
What is the area of a rectangular poster?The shape/polygon of a rectangle is two dimensional, having four sides, four vertices, and four right angles. The rectangle's two opposing sides are equal and parallel to one another. The space a rectangle occupies is known as its area. The area of a rectangle can also be defined as the region inside its border.
We utilise the unit squares to calculate a rectangle's area. Rectangle ABCD should be divided into unit squares. The total number of unit squares that make up a rectangle ABCD is its area.
Rectangle area equals length times width.
SolutionLet call length of printed area of the poster be " x " and height of printed area of the poster be " y ".
Area of the poster = length and height
200 = x*y
y = 200/x
We also know that dimensions of the poster with margin is:
L = x + 2 in and H = y + 4 in
Therefore area of the poster is:
A(p) = ( x + 2 ) * ( y + 4 )
And area as function of x is:
A(x) = ( x + 2 ) * ( 200/x + 4 )
A(x) = 200 + 4*x + 400 /x + 8
Taking derivatives on both sides of the equation we have:
A´(x) = 4 - 400/x²
By taking A´(x) = 0
4 - 400/x² = 0 ⇒ 4*x² - 400 = 0
x² = 400 / 4
x² = 100
x = 10 in
and y = 200/x ⇒ y = 20
The second derivative A´´(x) = 400/x4 which is > 0
there is a minimum for the function at the point x = 10
As x and y are dimensions of the printing area of the poster, dimensions of the poster with margin are
L = x + 2 = 10 + 2 = 12 in and
h = y + 4 = 20 + 4 = 24 in
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plumeria island is an island in the indian ocean. the island is 4,000 square kilometers in size. currently, 500,000 people live there. last year, 150,000 children were born and 50,000 people immigrated. 100,000 people died and 10,000 emigrated. it is believed that the island could support up to 350 people per square kilometer. the current population density is .
The current population density is 125 people / square kilometers.
Given :
plumeria island is an island in the indian ocean. the island is 4,000 square kilometers in size. currently, 500,000 people live there. last year, 150,000 children were born and 50,000 people immigrated. 100,000 people died and 10,000 emigrated. it is believed that the island could support up to 350 people per square kilometer.
Total people = 500000
Area = 4000 square kilometers
we know that ,
Population density = total people / area
= 500000 / 4000
= 500 / 4
= 125
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A bicycle manufacturing company makes a particular type of bike. Each child bike requires 4 hours to build and 4 hours to test. Each adult bike requires 6 hours to build and 4 hours to test. With the number of workers, the company is able to have up to 120 hours of building time and 100 hours of testing time for a week. If c represents child bikes and a represents adult bikes, determine which system of inequality best explains whether the company can build 10 child bikes and 12 adult bikes in the week.
a. No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100
b. No, because the bike order does not meet the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
c. Yes, because the bike order meets the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤
d. 100 Yes, because the bike order meets the restrictions of 4c + 4a ≤ 120 and 6c + 4a ≤ 100
Answer:
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100.
Step-by-step explanation:
According to the described situation, the system of inequalities that best explains whether the company can build 20 child bikes and 6 adult bikes in the week is given by:
What is the system of inequalities?
Considering the variables c and a, for the number of child and adult bikes, respectively, we have that, considering the building time:
testing time When c = 20, a = 6:
Hence, the correct option is:
No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100.
Mav has xx nickels and yy dimes. She has no more than 28 coins worth a minimum of $2 combined. Solve this system of inequalities graphically and determine one possible solution.
inequality #1-
inequality #2-
mav could have __ nickles and __ dimes
Inequality #1: x + y ≤ 28
Inequality #2: 0.05x + 0.1y ≥ 2
Mav could have 5 nickles and 20 dimes.
Step-by-step explanation:It's given that Mav has less than or equal to 28 coins, so we can write the following inequality:
x + y ≤ 28
We know that a nickel is work 0.05 and a dime is worth 0.1. Using the given information, the following inequality is true since the coins must be greater than or equal to $2 combined:
0.05x + 0.1y ≥ 2
Now, we will graph them. Both graphed lines will use solid lines since both include equal to. We will shade below #1 and above #2. I used Desmos Graphing Calculator, you can find it online for free. Once we type in our equations, we get the needed graph.
The overlapping portion contains our possible solutions. There are many, but one possible solution is (5, 20), with 5 nickels and 20 dimes.
How do you solve 2^(x) − 2^(−x) = 5 ?
The solution for the expression 2^(x) − 2^(−x) = 5 is x = log2(10)
Substitute 2^(−x) for 5 and solve for x, which is log2(10).
The given expression ,
2^(x) − 2^(−x) = 5
2^(x) = 5 + 2^(−x)
2^(2x) = (5 + 2^(−x))^2
2^(2x) = 25 + 10*2^(−x) + 2^(−2x)
25 + 10*2^(−x) + 2^(−2x) = 2^(2x)
25 − 2^(2x) = 10*2^(−x) − 2^(−2x)
25 − 2^(2x) = 10*2^(−x) − 2^(−2x) + 2^(2x)
25 = 10*2^(−x) + 2^(2x) − 2^(−2x)
25 = 10*2^(−x) + 2^(−2x) (2^(2x) - 2^(−2x))
25/(2^(−2x) (2^(2x) − 2^(−2x))) = 10*2^(−x)
25/(2^(2x) − 2^(−2x)) = 10*2^(−x)
2^(x) = 10
x = log2(10)
Substitute 2^(−x) for 5 and solve for x, which is log2(10).
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the lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. what is the probability that a pregnancy will last at least 300 days? question 16 options: 0.9835 0.4834 0.0179 0.0165
To solve this problem, we can use the standard normal distribution and the Z-score formula to find the probability that a pregnancy will last at least 300 days.
The Z-score is a measure of how many standard deviations a value is from the mean. We can use the Z-score to standardize a value, which means we can express it in terms of how many standard deviations it is from the mean of the distribution.
The Z-score formula is:
Z = (x - μ) / σ
Where x is the value we are standardizing, μ is the mean of the distribution, and σ is the standard deviation of the distribution.
To find the probability that a pregnancy will last at least 300 days, we can use the Z-score formula to standardize 300 days:
Z = (300 - 268) / 15 = 4
This means that 300 days is 4 standard deviations above the mean of 268 days.
To find the probability that a pregnancy will last at least 300 days, we can use a Z-table or a calculator to find the area under the standard normal curve that is greater than or equal to 4 standard deviations.
Using a calculator or a Z-table, we find that the probability that a pregnancy will last at least 300 days is approximately 0.0165, which corresponds to answer choice D: 0.0165.
9. What are the point and slope given by the equation y + 2 = -7(x-1)? HELP ME PLEASE MY FINAL IS TMR
Hello,
I hope you and your family are doing well!
To find the point and slope given by the equation y + 2 = -7(x-1), we can start by rearranging the equation to solve for y:
y + 2 = -7(x-1)
y = -7(x-1) - 2
y = -7x + 7 + (-2)
y = -7x - 9
This is the slope-intercept form of the equation, where y = -7x - 9 is the slope and (-9, 0) is the y-intercept.
The slope of the line is -7, and the point on the line is (-9, 0).
Therefore, the point and slope given by the equation y + 2 = -7(x-1) are (-9, 0) and -7, respectively.
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Which of the expressions below has a 8 in the ones place of the sum? Select all that apply.
A) 34.56 + 24.89
B) 72.35 + 45.81
C) 9.56 + 9.41
D) 12.34 + 15.42
The expression that shows the number 8 in one's place will be 72.35 + 45.81 and 9.56 + 9.41. Then the correct options are B and C.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The expression that shows the number 8 in one's place.
Let's check all the options, then we have
A) 34.56 + 24.89 = 59.45
In the number 59.45, the one's place is 9. So, it is incorrect.
B) 72.35 + 45.81 = 118.16
In the number 118.16, the one's place is 8. So, it is correct.
C) 9.56 + 9.41 = 18.97
In the number 18.97, the one's place is 8. So, it is correct.
D) 12.34 + 15.42 = 27.76
In the number 27.76, the one's place is 7. So, it is incorrect.
The expression that shows the number 8 in one's place will be 72.35 + 45.81 and 9.56 + 9.41. Then the correct options are B and C.
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Find BE if EC =12, BD=21, AD=18
and DE || AC?
Hello,
I hope you and your family are doing well!
To find the length of BE, we can use the Pythagorean theorem to find the length of AC, and then use the fact that DE is parallel to AC to find the length of BE.
First, we use the Pythagorean theorem to find AC:
AC^2 = AD^2 + DC^2
Substituting the known values, we get:
AC^2 = 18^2 + 12^2
AC^2 = 324
AC = sqrt(324) = 18
Since DE is parallel to AC, we can set up a proportion to find the length of BE:
BE/EC = AC/DC
Substituting the known values, we get:
BE/12 = 18/12
BE = (18/12) * 12
BE = 18/1
BE = 18
Therefore, the length of BE is 18.
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What is the indefinite integral of 1/xlnx?
In integration the bindefinite integral of 1/xlnx is
ln(|u|)+C=ln(|lnx|)+C with the aid of using parts, we've discovered whilst the specified formula.
The vital of the 2 capabilities are taken, with the aid of using thinking about the left time period as first feature and 2nd time period as the second one feature.
This technique is referred to as Ilate rule.The vital of xlnx is same to (x2/2) lnx - x2/4 + C, wherein C is the mixing constant. We can compare this vital the usage of the technique of integration with the aid of using parts.
We have the vital:
[tex]∫1xlnxdx
Use substitution. Let u=lnx so that du=1xdx . Note that each of those are presently gift withinside the vital.
∫1xlnxdx=∫(1lnx)1xdx=∫1udu
This is a not unusualplace vital:
∫1udu=ln(|u|)+C
Since u=lnx :
ln(|u|)+C=ln(|lnx|)+C[/tex]
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Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = x2y3zi + sin xyzj + xyzk, S is the part of the cone y2 = x2 + z2 that lies between the planes y = 0 and y = 3, oriented in the direction of the positive y-axis.
Why do we use the line integral form of stokes theorem to integrate this, instead of the stokes variation that uses the curl?
We can conclude that 2187π/4 is the required S curl F.ds using Stokes' Theorem.
What is the Stokes' Theorem?According to Stoke's theorem, where C = A closed curve, "the surface integral of the curl of a function across a surface limited by a closed surface is equal to the line integral of the particular vector function over that surface."
S = Any surface bordered by C.
So, by utilizing Stokes Theorem to calculate S curl F .dS.
[tex]\iint_s c u r l F \cdot d s=\int_c F d r[/tex]
Parameterize C now.
r(t) = (3 cos t, 3 - 3 sin t)
When t is in [0 2].
Now,
[tex]\begin{aligned}& \int_c F \cdot d r=\int_0^{2 \pi} F(3 \cos t, 3-3 \sin t) \cdot r^{\prime}(t) d t \\& =\int_0^{2 \pi}\left(\left(9 \cos ^2 t\right)(27)(-3 \sin t),(\sin t) \times(-27 \cos t \cdot \sin t) \cdot(-3 \sin t, 0-3 \cos t) d t\right. \\& =27 \int_0^{2 \pi} 81 \cos ^2 t \cdot t \sin ^2 t+3 \cos ^2 t . t \sin t d t \\& =27 \int_0^{2 \pi} \frac{81}{4} \sin ^2 2 t+27\left[-\cos ^3 t\right]_0^{2 \pi}\end{aligned}[/tex]
[tex]\begin{aligned}& =27 \times \frac{81}{4} \int_0^{2 \pi}\left(\frac{1-\cos 4 t}{2}\right) \\& =\frac{2187}{8}\left[t-\frac{1}{4} \sin 4 t\right]_0^{2 \pi} \\& =\frac{2187}{8}\left[2 \pi-\frac{1}{4} \sin 4(2 \pi)-0-\frac{1}{4} \sin 4(0)\right] \\& =\frac{2187 \pi}{4}\end{aligned}[/tex]
Therefore, we can conclude that 2187π/4 is the required S curl F.ds using Stokes' Theorem.
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Using the given points, determine Y . Type a numerical answer in the space provided.
(-3,-5) and (0,10)
The value of the notation Δy from the points (-3,-5) and (0,10) is 15
How to determine the slope of the points?The complete question is added at the end of this solution
From the question, we have the following parameters that can be used in our computation:
Points = (-3,-5) and (0,10)
Rewrite the above points properly
So, we have the following ordered pairs
(x, y) = (-3,-5) and (0,10)
The notation Δy represents the change in the y values of the given points
This notation can be extended to calculate the slope of the points
The slope of the line is then calculated using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (-3,-5) and (0,10)
Substitute the known values in the above equation
So, we have the following equation
Slope = (10 + 5)/(0 + 3)
Evaluate the sum
Slope = 15/3
The numerator represents Δy
i.e. Δy= 15
Evaluate the quotients
Slope = 5
Hence, the slope of the line is 5 and the value of the notation Δy is 15
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Complete question
Using the given points, determine Δy
Type a numerical answer in the space provided.
(-3,-5) and (0,10)
Evaluation
A family rents a truck to move from Buffalo to
Chicago. The rental has a base cost of $49.95,
plus, an additional
cost of $1.19 per mile driven.
The family also pays for gas,
which costs $3.89 per gallon.
The truck’s average gas mileage
is 18 miles per gallon.
The family decided to take a rest in Cleveland, what would be the distance travelled from Buffalo to Cleveland if the total cost of the move is $724.85?
The distance travelled from Buffalo to Cleveland if the total cost of the move is $724.85 is 479.97
How to solve for the distance traveledThe base cost of the rental is said to be 49.95 dollars + 1.19 per mile
The cost of the gas is $3.89. The mileage of the truck is 18 miles
There would be an extra cost of
$3.89/18 per mile.
= 0.216111
In x miles we would have the equation that is written as:
C(x) = 49.95 + (1.19 + 0.21611)x
C(X) = $724.85 this is the total cost. Hence we would have
$724.85 = 49.95 + 1.19x + 0.21611x
$724.85 - 49.95 = 1.40611x
674.9 = 1.40611x
divide through by 1.40611
674.9 / 1.40611 = x
x = 479.97
The distance traveled is 479.97
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What is the best unit to measure the capacity of a washing machine.
A) milliliter
B) liter
Answer:
Liter
Step-by-step explanation:
Milliliters are used for much smaller amounts of liquid.
Which of the following is equal to 505 ÷ 5 ?
A. (500+5) + (500 ÷ 5) B. (500-5) - (5 ÷ 5). C. (500+ 5) + (5 + 5) D. (500+5) + (5 ÷ 5)
Answer:
a.
Step-by-step explanation:
HELPP ITS FIE TOMORROW NOOOO
Answer: answer below
Step-by-step explanation:
4 (a). 900 grams of flour
work 150x6=900 grams
4 (b). 3 large eggs
work 450÷150=3
5 (a). 2.99
work 11.96÷4=2.99
5 (b). 26.91
work 2.99x9=26.91
6 (a). Can't help
6 (b). 6:12
6 (c). 16:8
6 (d). 10 paws
Can't help on problem 7
referring to question 1, what is the predicted strength of a weld with a diameter of 51? a. -812.72 b. -503.16 c. -81.82 d. we should not use the least squares regression line to calculate this value
The predicted strength of a weld with diameter of 51 is -503.16.
Given that diameter of weld is 51.
And we have to find predicted strength of a weld.
We know that the equation of predicted strength is,
strength = -941.6 + (8.598 × D)
where D id diameter = 51
⇒ strength = - 941.6 + (8.598 × 51)
strength = -941.6 + 438.4
strength = -503.2
Therefore predicted strength of a weld is -503.2 i.e option (b) -503.16.
A prediction equation predicts a value of the response variable for given values of the factors. The Delphi Survey technique is a popular method used in prediction. There are two types of prediction methods: qualitative and quantitative.
The Least square Regression Line is the line that makes the vertical distance from the data points to the regression line as small as possible. It is called a "least squares" because the best line of fit is one that minimizes the variance.
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if x=3 and y=-5 find the value of x-y^2
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{x - y^2}\\\mathsf{= 3 - (-5)^2}\\\mathsf{= 3 + \bf 5^2}\\\mathsf{= 3 + \bf 5\times5}\\\mathsf{= 3 + \bf 25}\\\mathsf{= 28}\\\\\huge\text{Therefore, your answer should be: \boxed{\textsf{28}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
which of the following factors is a factor of 3x^3+18x^2+27x
The factor of the given expression is (C) (x + 3).
What are the factors?In mathematics, a divisor of an integer n, often termed a factor of n, is an integer m that may be multiplied by some number to generate n.
In this scenario, one also asserts that n is a multiple of m.
A factor is a number that is multiplied by another number to produce the desired result.
A product is a solution to a multiplication problem.
Think of a multiplication problem as components being combined to find a product.
So, we have:
3x^3+18x^2+27x
Now, take the factors out as follows:
3x^3+18x^2+27x
3x(x²+6x+9)
3x(x+3)²
Factors: (x + 3)
Therefore, the factor of the given expression is (C) (x + 3).
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Complete question;
Which of the following is a factor of 3x3 + 18x2 + 27x?
a. 9x
b. x3
c. x + 3
d. x - 3
15+14+13+12+11+10+9+8+7+6+5+4+3+2+1
Answer:
120
Step-by-step explanation:
Don't know if this is a joke, but have a great day regardless!
Which ones are the correct answers
find the domain of the vector function. (enter your answer in interval notation.) r(t) = t − 1 t 1 i sin(t) j ln(81 − t2) k
(-9, 9) domain of the vector function. A vector valued function's domain is a subset of all real numbers at which the function is well-defined.
How do find the domain of a vector?Consider the function y = f(x) to have an independent variable x and a dependent variable y. If a function f provides a way to successfully produce a single value y using a value for x, that chosen x-value is said to belong to f's domain.
A vector-valued function is a rule that gives each member of a subset of R1 a vector. A function's domain is the set of all possible inputs to the function. The domain of f(x)=x2 is all real numbers, for example, and the domain of g(x)=1/x is all real numbers except x=0.
r(t) = t − 1 t 1 i sin(t) j ln(81 − t2) k
Lets find the domain of first which is given by,
t - 2 / t + 2
This function is defined at all values except, t equals to -2 as the function is not defined at,
t -= -2
Lets find the domain of first which is given by,
sin(t),
Two trigonometry function sine and cosine defined for all real number
This function is defined at all real numbers. Hence the domain of component j is.
Set the above argument greater than zero to find where the expression is defined.Thus,
(9 + t ) (9 - t) > 0
Therefore,
The domain of it should be (-9, 9)
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True or False?
need answer asap thanks
Answer: False
Step-by-step explanation:
Q1. Which of the following are quadratic equations? 11= - 4x2-x3
The given equation 11= - 4x^2-x^3 is not quadratic. It is a cubic.
What is quadratic?The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax^2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable.
Is a quadratic 2 or 4?Quadratic expressions are those involving powers of x up to the second power, not the fourth power, hence the prefix quad signifies "four" rather than "two."
As highest power with the variable is 3 so it is a cubic expression not a quadratic.
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A golf store purchases a driver at a wholesale price of $200. Mr. Nganga learned that the driver was marked up 100%. What is the retail price of the clubs?
The retail price of the driver of the clubs after will be $400.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A golf store buys a driver at a discount cost of $200. Mr. Nganga discovered that the driver was increased by 100 percent.
The retail price of the clubs will be given as,
⇒ $200 x (1 + 100%)
⇒ $200 x (1 + 1)
⇒ $200 x 2
⇒ $400
The retail price of the driver of the clubs after will be $400.
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How do I find the value of log1000?
Answer:
To find the value of log1000, you can use the logarithmic property that states that log(a^b) = b * log(a). In this case, we can rewrite 1000 as 10^3, so log1000 = log(10^3) = 3 * log(10) = 3.
A real estate agent sold a house for $315,000 last week. If her commission is 1.25% of the selling price of the home, find the amount of her commission?
The required amount of her commission is given as $3937.5.
Given that,
A real estate agent sold a house for $315,000 last week. The commission is 1.25% of the selling price of the home,
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Commission = 1.25% of $315000
Commission = 1.25× 315000/100
Commission = $3,937.5
Thus, the required amount of her commission is given as $3937.5.
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There are two option for tickets & admission to the carnival. Option #1 requires you to pay a $5 admission fee plus $0.30 per ride ticket. Option #2 requires you to pay a $3 admission fee plus $0.80 per ride ticket. Garrett chose option #1 and Meagan chose option #2. If they wound up paying the same amount of money, how many tickets did they each purchase?
The number of tickets they purchased is 4.
How many tickets did they purchase?The expression that would b used to represent the total cost at the carnival is a linear expression. A linear expression is an expression that has a single variable that is raised to the power of one.
The form of the linear expressions that can be used to represent the total cost at the carnival is:
Total cost = admission fee + (price per ride x number of rides)
Total cost in option 1 = $5 + 0.30r
Total cost in option 2 = $3 + $0.80r
Where r = number of rides
When they pay the same amount of money, the linear functions would be equal:
$5 + 0.30r = $3 + $0.80r
$5 - $3 = $0.80r - 0.30r
$2 = $0.50r
r = 2 / 0.5
r = 4
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huduko incorporated offers a number of computer services. one server handles its own web page. it receives requests for web pages at the rate of 79 per second. the standard deviation of these interarrival times is 0.02 second. what is the coefficient of variation of the interarrival times for this server?
Using the standard deviation value of these interarrival times, the coefficient of variation is 0.012.
What do you mean by Standard Deviation?The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
What is Coefficient of variation and formula to calculate it?The standard deviation to mean ratio, or coefficient of variation (CV), illustrates the degree of variability in proportion to the population mean. The dispersion increases with increasing CV.
Formula is given by:
[tex]CV = \frac {\sigma}{\mu}[/tex]
[tex]\sigma = 0.02[/tex]
Mean for the time of 0.02 sec is = 79 * 0.02
=1.58
CV= 0.02/1.58
=0.012
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Last week, the Lions
scored 52 points. This
week, they scored 42
points. What is the
percent decrease in
the Lions' scores?
Answer: 42 is a 19.231% decrease of 52.
gg against the jags yesterday
