for the post office in the previous problem, a second drive-through window is being considered. a single line would be formed and as a car reached the front of the line it would go to the next available clerk. the clerk at the new window works at the same rate as the current one. a) what is the average time a car is in the system? b) what is the average number of cars in the system? c) what is the average time cars spend waiting to receive service? d) what is the average number of cars in line behind the customer receiving service? e) what is the probability that there are no cars in the system? f) what percentage of the time are the clerks busy? g) what is the probability that there are exactly two cars in the system?
Answer: Option A is correct, What is the average time a car is in the system?
Answer: 1/30-24= ⅙ * 60 min =10 min
Step-by-step explanation:
Frank bought 10 pounds of dog food for $17. 50. At this rate how much would he pay for 15 pounds.
Answer:
[tex]\$26.25[/tex]
Step-by-step explanation:
Price of 10 pounds of dog food is= $17.50
Price of 1 pounds of dog food is= [tex]\$\frac{17.50}{10}[/tex]
This implies that price of 15 pounds of dog food is=[tex]\$ \frac{17.50}{10}\times 15[/tex]
Simplifying this, we obtain:
This implies that price of 15 pounds of dog food is= [tex]\$26.25[/tex]
Harley davidson offers 3 different motorcycle models. Each of these is available in 6 different colors. How many different combinations of model and color are available?.
There are 18 possible combinations for the model and color options.
According to the given information,
There are 3 motorbike manufacturers.
There are 6 different colors available.
Total combinations possible = Motorcycle count *color count
Total combinations possible=3*6
=18
Therefore, there are 18 possible combinations that are available.
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7/8 divided by 1/4 in simplest form
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1. The cheese production for 2006 is 7.76 billion.
2. The cheese produced in 2014 is 9.84 billion.
What is a function?It should be noted that a function is simply used to show the relationship between the variables that are given.
In this situation, there's a 3% growth per year and the function for the cheese production is modelled as:
y = 7.1(1.03)^x
y = cheese production
x = number of years after 2003.
1. Therefore, since 2006 is 3 years after 2003, this will be
y = 7.1(1.03)^x
y = 7.1(1.03)³
y = 7.1 × 1.093
y = 7.76 billion
The production is 7.76 billion.
2. The production in 2014 will be;
y = 7.1(1.03)^x
y = 7.1(1.03)^11
y = 7.1 × 1.385
y = 9.84 billion
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in a survey of 2300 t.v. viewers, 690 said they watch network news programs. find the margin of error for the 95% confidence interval used to estimate the population proportion.
Margin of error for the 95% confidence interval used to estimate the population proportion is 0.0187
It is given that out of 2300 tv viewers, 690 said they watch network news program.
Sample n=2300
Number that watch network program (x)=690
We now find the margin error:
For 95% confidence interval, z-value is 1.96 from Chi-square distribution
We now get the point estimate, p:
p=x/n, where x=690, and n=2300
=690/2300
=0.3
Margin of Error=[tex]z*\sqrt{\frac{p*(1-p)}{n} }[/tex]
[tex]=1.96*\sqrt{\frac{0.3*(1-0.3)}{2300} }[/tex]
=0.0187
Hence, the margin error is 0.0187
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Select the correct answer. Solve the equation using the method of completing the square. (3x)^2+24x-24=0
[tex](3x)^2+24x-24=0\\\\ \bold{(3x)^2+2\cdot3x\cdot4+4^2}-4^2-24=0\\\\(3x-4)^2-16-24=0\\\\\large\text{$\bold{(3x-4)^2-40=0}$}[/tex]
when 30 orange trees are planted on an acre, each will produce 500 oranges per year. for every additional orange tree planted, each tree will produce 10 fewer oranges. how many total trees should be planted to maximize the yield?
Answer:
40 trees per acre
Step-by-step explanation:
: If x is the number of trees beyond 30 that are planted on the acre, then
the number of oranges produced will be: Oranges(x) = (number of trees) (yield per
tree) = (30 + x)(500 – 10x) = 15,000 + 200x – 10x
2
. The derivative Oranges'(x) =
200 – 20x is zero when x = 10. Using the second derivative test, Oranges"(x) = –
20 is negative, so this is maximal. Thus, x = 10 more than 30 trees should be
planted, for a total of 40 trees per acre.
Jackson bought a used laptop for $400. He refurbishes the laptop and sells it for $750. What percentage markup is the laptop?
Answer:
58%
Step-by-step explanation:
Answer:
187.5%
Step-by-step explanation:
100/400=0.25
0.25 x 750= 187.5%
The table below represents points on a line.
X, -5 y, 16
X, -4 y, 13
X, -3 y, 10
X, -2 y, 7
What is the slope of this line?
slope of this line is -3.
Given table:
X, -5 y, 16
X, -4 y, 13
X, -3 y, 10
X, -2 y, 7
slope m = y2 - y1 / x2 - x1
Take any two points (-5,16) and (-4,13).
slope m = 13 - 16 / -4 - (-5)
= -3/-4+5
= -3/1
= -3
Therefore slope of this line is -3.
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the annual rainfall in a certain region is approximately normally distributed with mean 40.4 inches and standard deviation 5.8 inches. round answers to the nearest tenth of a percent. a) what percentage of years will have an annual rainfall of less than 43 inches?
67% of years will have an annual rainfall of less than 43 inches.
What is percentage ?In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often indicated by the percent sign '%', but the abbreviations 'pct.', 'pct', and 'pc' are also sometimes used. Percentages are dimensionless numbers. It has no units of measure.
Calculation we've got a population with a mean of 40.6 and the standard deviation of 5.3, we're told this is this follows a normal distribution. So if we want to find the probability That we're going to have less than 43, we're gonna use normal Cdef since we want less. Then we're gonna first put in a really, really, really small number for our lower bound, our upper bound is 43 are mean is 40.6. Standard deviation 5.3. So this gives us .6747. Next we want to find the probability that we're gonna be greater than 38. So we're gonna use normal C. D. F. This time since we went greater than 38 is our lower bound a really, really, really big numbers are upper bound, 40.6 is our means the innovation 5.3 and this gives us .6881. And then lastly, we want the probability That we're going to be greater than 37, but less than 42. So, normal CDF Lower bound 37. Upper bound 42, I mean 40.6 standard deviation 5.3 and this gives us a probability of .3557learn more about percentage here :
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Line a passes through (-3,4) and (3,6) line b passes through (-10,-3) and (-8,3) line c passes through (0,5) and (3,-4) line d passes through (4,-7) and (13,-4) determine which of the lines are parallel and which are perpendicular
Lines a and b are parallel lines.
Lines a and c are perpendicular lines
Lines d and c are perpendicular lines.
The formula to calculate the slope between two points is equal to
[tex]m = y2-y1/(x2-x1)[/tex]
Part 1) Find the slope of Line a
We have the points
(-3,4) and (3,6)
Substituting the value in the formula
[tex]m = 6-4/ (3-(-3))\\m = 2/6\\ma = 1/3[/tex]
Part 2) Find the slope of Line b
We have the points
(-10,-3) and (-8,3)
Substituting the value in the formula
[tex]m = 3-(-3)/ (-8-(-10))\\m = 6/(-8+10)\\mb = 6/2=3[/tex]
Part 3) Find the slope of Line c
We have the points
(0,5) and (3,-4)
Substituting the value in the formula
[tex]m = -4-5/ (3-0)\\m = -9/3\\mc = -3[/tex]
Part 4) Find the slope of Line d
We have the points
(4,-7) and (13,-4)
Substituting the value in the formula
[tex]m = -4-(-7)/ (13-(4))\\m = 3/9\\md = 1/3[/tex]
Part 5) Compare the slopes
Remember that
If lines are parallel then their slopes are equal.
If lines are perpendicular then their slopes are opposite reciprocal.
We've got,
[tex]ma = 1/3\\mb = 3\\mc = -3\\md = 1/3[/tex]
Lines a and b are parallel lines (slopes are the same).
Lines a and c are perpendicular lines (slopes are opposite reciprocal).
Lines d and c are perpendicular lines (slopes are opposite reciprocal).
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What is the Inverse of y=4x
Answer:
Step-by-step explanation:
f⁻¹(x) = x/4
An aquarium originally cost $60 but is on sale for 15% off. How much does the aquarium cost after the discount?
Answer:
$51
Step-by-step explanation:
Step 1. 0.15 x $60 = $9
Step 2. $60 - $9 = $51
PLEASE HELP QUICK
Which pair of radicals is a pair of like radicals?
The radical pair that is similar to one another is [tex]3\sqrt{7}[/tex] and [tex]11\sqrt{7}[/tex] and the right answer is (2).
Discover the radical pair.Two radicals must have the same number in the root operator in order for them to be comparable.
The following two radicals are similar:
[tex]a\sqrt{b}[/tex] and [tex]c\sqrt{b}[/tex]
Since [tex]a\sqrt{b}[/tex] and[tex]c\sqrt{b}[/tex] are like terms, arithmetic operations such as addition, subtraction, multiplication, and division can be carried out on them
Considering the options given, only [tex]3\sqrt{7}[/tex] and [tex]11\sqrt{7}[/tex] are in the form [tex]a\sqrt{b}[/tex] and [tex]c\sqrt{b}[/tex] because they have equal value inside the root operator.
Therefore, the pair of radicals that is a like pair is [tex]3\sqrt{7}[/tex] and [tex]11\sqrt{7}[/tex].
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7. The bill for 3 hotdogs and a juice box was $8.40. If the juice box cost $1.65, how much was each hot dog?
Answer:
2.25:)
Step-by-step explanation:
A line has a slope of 1/6 and includes the points (10,z) and ( – 2, – 10). What is the value of z?
Answer: -8
Step-by-step explanation:
The line has a slope of 1/6, which means the x coordinate increases by 6 for every 1 the y coordinate increases.
In these two points, the x coordinate is decreasing by 12.
We need to divide that by 6, because the y increases 1 for every 6 the x increases.
12/6 = 2, which means that between the x coordinates of 10 and -2, the y coordinate has decreased by two.
We need to add 2 to -10 to get our answer, which is -8.
- x + y = - 3
y=x-3
Substitution method
Substitution is the process of substituting numbers for letters in order to calculate the value of an expression.
What exactly is the Substitution method?The substitution method is an algebraic method for solving simultaneous linear equations. As the title suggests, the value of one variable from one equation is substituted in the other equation.The substitution method starts by determining the value of any one of the factors in one equation in terms of the other variable.For example, if we have two equations, x+y=7 and x-y=8, we can deduce that x=7-y from the first equation. This is the initial step in using the substitution method.The substitution method involves substituting the value of a variable from one equation into the second.Therefore,
x=-1 and y=-4
Equivalent two equal expressions is another method that will work well in this case. This is a variation on substitution.
Transpose both equations to give y=
equ 1. y = x-3 and equ 2. y=7 x+3
Note that y=y
7 x+3=x-3
6 x =-6
x =-1
Equ 1. y=-1-3 ⇒ y=-4
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A race is 36.9 miles long. There is a water station every 1 23/100 miles along the race route. What is the total number of water stations?
The total number of water stations is 30.
Given:
A race is 36.9 miles long. There is a water station every 1 23/100 miles along the race route.
Total number of water stations = 36.9/1 23/100.
= 36.9/100+23/100
= 36.9/123/100
= 36.9/1.23
= 369/10/123/100
= 369*100/123*10
= 369*10/123
= 3*10
= 30.
Therefore the total number of water stations is 30.
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7⁸x7³x7⁴/ 7⁹x7⁵ someone please help
Answer: 7
Step-by-step explanation:
To do this, we need to simplify the numerator.
This means we need to multiply 7^8 x 7^3 x 7^4
To multiply these, we add the exponents together.
This gives us 7^15.
Now, we need to simplify the denominator.
This means we need to multiply 7^9 x 7^5
This gives us 7^14.
Now that we have both the numerator and denominator simplified, we divide 7^15 and 7^14.
To divide 7^15 and 7^14, we need to subtract the exponents.
This gives us 7^1.
7^1 = 7.
K-
Use the formulas developed in this section to find the area of the
figure.
(Simplity your answer.)
13 in
10 in
22 in
17 in.
4
Grac
se
who are the potential candidates for entrepreneurship
4-1/2-1-3
What is the answer
Show all the mathematical steps required to calculate slope given two points. To earn full credit you must provide the slope formula, show the values substituted into the formula, steps to simplifying, and stating the final result. P1(-13, -4) and P2(-9, -32)
The equation of line is y = -7x - 95
What is an Equation of a line?
The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m of a line is a measurement of its steepness and direction.The slope of a line formula computes the "vertical change" to "horizontal change" ratio between two distinct points along a line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the two points be P1 and P2
P1 ( x₁ , y₁ ) = P1 ( -13 , -4 )
P2 ( x₂ , y₂ ) = P2 ( -9 , -32 )
Step 1 :
To calculate the slope m of the two points
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values of x₁ , y₁ , x₂ , y₂ in the equation , we get
m = ( -32 - (-4) ) / ( -9 - (-13) )
m = (-32 + 4 ) / ( -9 + 13 )
m = -28 / 4
m = -7
Therefore the slope is -7
Step 2 :
Now , the equation of the line is given by
y - y₁ = m ( x - x₁ )
Substituting the values of x₁ , y₁ and m in the equation , we get
y - (-4) = -7 ( x - (-13) )
y + 4 = -7 ( x + 13 )
y + 4 = -7x - 91
Subtracting 4 on both sides , we get
y = -7x - 95
Hence , the equation of line is y = -7x - 95
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Graph and label the functions: [tex]y=|2x|[/tex] and [tex]y=\frac{1}{2}x[/tex]. Summerize what each of the transformations do to the parent function: y=|x|. Please show the graph!!
According to the graph transformation, the function y = |2x| is compressed than the parent function y = |x| and the function y = 1/2x is drawn as straight line.
Graph transformation:
The graph transformation refers a process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph and it also shows the modification of algebraic equations.
Given,
Here we have the function y = |2x| and y = 1/2x.
Now, we need to find the transformations do to the parent function: y=|x|.
Here we need to plot the graph for each of the function.
And we have to plot the separate graph for the parent function.
While we compare these two graph we have identify the function y = |2x| is compressed than the parent function y = |x|.
And the function y = 1/2x makes the straight line on the graph but the parent function has v shaped graph so, it is not possible to compare them.
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How do you solve log6?.
The solution of the given logarithmic function log 6 is 1.78.
Define the term logarithmic function?The opposite of an exponential function is a logarithmic function. A log function as well as an exponential function both use the same base. An exponent is a logarithm. f(x) = bx is how the exponential function is expressed. The formula for such logarithmic function is f(x) = log base b of x.For the stated function;
= log 6
= log(2 x 3)
Using the multiplication property of log;
log (m x n) = log m + log n
= log(2) + log(3)
solve the value by calculator;
= 0.69 + 1.09
= 1.78
Thus, the solution of the given logarithmic function log 6 is 1.78.
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HELP PLEASE WILL GIVE BRAINLYEST FOR CORRECT ANSWER AND TO REMIND ME!
Answer: triangle, rectangle, pentagonal
Step-by-step explanation: b x h and length x width = base.
You and your friend are hiking down a mountain after a rigorous
ascent to the top. After 1 hour, your elevation is 6,650 feet. After 2
hours, your elevation is 5,985 feet. After 3 hours, your elevation is
5,320 feet. This pattern continues. Let n represent the number of
hours you I have been hiking.
Write a function f(n) to represent the elevation after n hours.
The function f(n) to represent the elevation after n hours is y = -665 x + 7315.
What is the point-slope form of a line?The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis may be found using the point-slope form. Every point on a line must satisfy the equation for the line in order for it to exist. This suggests that a linear equation in two variables can represent a line.
Let the x value represent hours and elevation is represented by y values.
So,
(x₁, y₁) = (1, 6650)
(x₂, y₂) = (2, 5985)
Find the slope by using the slope formula
m = (y₂-y₁)/ (x₂-x₁)
= (5985 - 6650) /(2 - 1)
= -665
So, the function f(n) to represent the elevation after n hours is given by
(y - 6650) = -665 (x - 1)
y - 6650 = -665x +665
y = -665 x + 7315
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mary is building a storage shed from wood panels in the shape of a regular polygon. each rectangular wall panel is 7 feet wide and 8 feet tall. she wants the shed to have the most walls possible so she can hang tools on them.
The shape of the shed and the process for arriving at the solution of the word problem are as follows;
a. The number of walls in the shed are 8 walls and the shape of the shed is an octagon
b. The amount Mary has budgeted for the storage shed is divided by the unit cost of a panel and one bracket for joining the bracket to find the number of panels, which indicates the shape of the shed Mary builds.
c. The door is assumed to cost the same as one panel
What is a word problem?A word problem is an exercise in math or science that consists of the background information to the problem being introduced using everyday language rather that mathematical equations.
Parts of the question information obtained from a similar question online includes;
The number of walls Mary wants = As most as possible
The cost of the panels = $0.89 per square foot
Cost of the brackets for joining the panels = $6.50
Her budget for the wall of the shed = $500
a. The number of walls Mary will be able to build is found as follows;
The cost of each rectangular wall panel = 7 ft × 8 ft × $0.89/ft² = $49.84
The cost of a panel and a bracket = $49.84 + $6.50 = $56.34
The number of panels in the shed, n = The ratio of her budget to the cost of a panel and bracket
[tex]n =\dfrac{\$500}{\$56.34} \approx 8.87[/tex]
The number of panels in the shed she will be able to build with her budget is 8 panels
The shape of the storage shed she can build is an octagon
b. The solution process is to find the cost of a unit of material which is the cost of a panel and a bracket, then dividing the budget by the unit cost to find the number of panels in the shed.
The number of panels indicates the polygon she forms by the shed
c. The assumption made is in the cost of the door, which is assumed to cost the same as a panel and a bracket
The parts of the complete question are;
a. The number of walls the shed can have within Mary's budget, and what shape is the storage shed
b. Provide a description of the process of finding a solution
c. The assumptions made
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which function increases faster?
f(x) function increases faster.
From the question, we have
g(x) =5/2x-3
At x =0, g(x) = -3
At x =1, g(x) = -1
Hence, f(x) function increases faster.
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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Please help me out, and do me a favor and don’t answer if you don’t know please
2. What is the solution to each equation? Show both positive and negative
solutions.
A. x² = 25
B. 3x² = 48
Answer:
lmfa you answer my questions i recently posted ill answer yours.
Step-by-step explanation:
kk
What is the solution to each equation? Show both positive and negative
solutions.
A. x² = 25
x = -5 or 5
_________________________________
B. 3x² = 48
divide both sides by 3:
3x²/3 = 48/3
x² = 16
x = -4 or 4