The arrival rate is found to be 30 emails per hour and the service rate is calculated to be 45 emails per hour.
It has been mentioned in the question that in every 2 minutes, customers send emails to a help desk of an online retailer, on an average, and the standard deviation of the inter-arrival time is also given to be 2 minutes. The online retailer has three employees for answering those emails.
It takes almost 4 minutes to write a response email to the customer, on average. The standard deviation (SD) of the service times is 2 minutes. This is a g/g/k type queue.
Therefore the arrival rate per hour is given by the following relation:
Arrival rate in 1 hr = No. of minutes in an hr / inter arrival time of email taken in minutes
Given here,
No. of minutes in an hour = 60 minutes
Inter arrival time of the email taken in minutes = 2 minutes
∴ Arrival rate in 1 hr = 60 / 2
= 30 emails / hr
Hence the arrival rate is 30 emails per hour.
Now for finding out the service rate we have the following formula:
Service rate = No. of minutes in an hr x No. of employes answering/ average time that is required to write response email
Given here,
No. of minutes in an hr = 60 minutes
No. of employes answering = 3
Average time that for writing response email = 2 minutes
∴ Service rate = 60 * 3 / 4
= 45 emails / hr
Hence the service rate is 45 emails per hour.
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The function -2x^2-8x+42 represents the approximate height of an object (x seconds) after it is thrown off the top of a building. How many seconds does it take for the object to hit the ground?
The function is given to be:
[tex]-2x^2-8x+42[/tex]The object hits the ground when the function is equal to zero:
[tex]-2x^2-8x+42=0[/tex]Solving the equation by factorization, we have:
[tex]\begin{gathered} 2(-x^2-4x+21)=0 \\ -x^2-4x+21=0 \\ -x^2-7x+3x+21=0 \\ -x(x+7)+3(x+7)=0 \\ \therefore \\ (-x+3)(x+7)=0 \\ Hence \\ x=3,x=-7 \end{gathered}[/tex]Since the time cannot be negative, then the time will be 3 seconds.
Therefore, it will take 3 seconds for the object to hit the ground.
Nathan eats the same amount of lunch meat everyday. If Nathan eats 2 pounds of lunch meat in 8 days, he eats pound(s) of lunch meat per day
Using fraction, He consumes 1/4 pound of lunch meat each day.
Describe fraction.A fraction, expresses a piece of a whole, a fraction, such as one-half, eight-fifths, or three-quarters, specifies the number of components of a respective size.
Given,
He consumes 2 pounds of beef in 8 days.
We need to determine how much meat he consumes each day.
To ascertain:
He consumes 2/4 of a pound of beef in a day.
= 1/4
He thus consumes 1/4 pound or less of lunch meat every day.
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1. A trapezoid is pictured on the right. Its bottom base a is not changing while its top base b is increasing at the rate of 3 inches per second while its height h is decreasing at the rate of 0.5 inches per second. How fast is the area of the trapezoid changing, measured in square inches per second, at this moment?
A) -2.5
B) -.75
C) 1
D) 2
(Please explain)
Answer:
the answer is A...
Step-by-step explanation:
Calculate Area (A):
The area formula for a square is denoted below:
A = s2
Taking the square root of both sides, we get:
s = √A
s = √3
s = 1.7320508075689
arcsin (-1)
compute the exact value
–π/2 is the exact value of arcsine (-1).
What is arcsine?The six main inverse trigonometric functions include arcsin. It is the sine function's inverse trigonometric function. The mathematical symbol for arcsin, commonly known as inverse sine, is arcsin x or sin-1x (read as sine inverse x). Sin-1x is not the same as (sin x)-1; that is, sin-1x is not the reciprocal function of sin x. This is an important distinction to make. We may use the six inverse trigonometric functions arccos, arcsin, arctan, arcsec, arccsc, and arccot to calculate angles. Arcsin x calculates the angle that corresponds to the right-angled triangle's perpendicular to hypotenuse ratio. We shall examine the idea of arcsin in this article and determine its formula. We'll also talk about the domain and range.
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i don't know non of this and i need help pls
By using the fact that ∠4 and ∠5 add up to 180° and ∠5 = ∠7, we conclude that the measures of the angles are:
∠5 = ∠7 = 56°.
How to find the measures of the angles?For angles formed by the interception between lines meet the following property.
If the angles are one next to the other, the measures add up to 180°.
If not, then the two angles have the same measure.
This means that:
∠5 = ∠7
∠8 = ∠6
And so on.
If the two horizontal lines are parallel, then:
∠5 = ∠1
And we know that:
∠4 + ∠1 = 180°
124° + ∠1 = 180°
∠1 = 180° - 124° = 56°
Then we get that:
∠5 = ∠7 = 56°.
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If you earn $7.50 per hour at your job how much will you earn if you work 25 hours?
Answer:
$187.5
Step-by-step explanation:
.
Answer:
187.50
Step-by-step explanation:
7.5(25)=187.50
hope this helped
have a good day^^
ASAP!!
4/3x + 2/3x = 1/3x +5
Solve the equation for X and include all steps to get Branliest.
Answer: x=3
Step-by-step explanation: Multiply both sides of the equation by 3 to get 4x+2x=x+15. Combine like terms. (underlined) 6x=x+15. Move variable to left side and change its sign. 6x-x=15. Combine like terms again. 5x=15. Divide both sides of the equation by 5 to get x=3.
simplify 0.027^2/3 PLEASE
Answer:
Hope the picture will help you
Answer:
2.718
Step-by-step explanation:
let x = .027^2/3
x=.027^.67
applying natural log on both sides
lnx = ln.027^.67
lnx = .67ln.027
lnx = 2.42004
applying antilog on both sides
x = e^2.42004
x = 2.718
thus, .027^2/3 = 2.718
can someone please help me answer this im really confused. Thank you so much if you help!!
Answer:
y=2X - 6
Step-by-step explanation:
find the slope using the 2 points
m = 8-2/7-3 = 2
substitute 4,2 in the equation y=mx+b and solve for b.
2 = 2x4+b
b=-6
y = 2x - 6
Answer:
Slope intercept formula: y = 2x -6
Point Slope formula y = 2x-6
Step-by-step explanation:
1) Find the slope
2) Choose a point and plug it into the equation y = mx+b
3) Solve for b
4) Plug-in new slope (m) and new y-intercept (b) into equation y = mx+b
Solving:
4 = x1
2 = y1
7 = x2
8 = y2
to find slope with slope formula:
m = y2-y1/x2-x1 = 8-2/7-4 = 6/3 = 2
now plug in,
y = 2x+b
to find b, take any one of the pair
(i will choose (4,2) )
2 = 2(4) + b
now solve for b,
2 = 8+b
b = -6
Slope intercept formula: y = 2x -6
for point slope: y-y1 = m(x-x1)
as we know our slope is 2 and points are (0,-6) where 0 is x1 and -6 is y1
now we plug in,
y-(-6) = 2(x-0)
y+6 = 2x
Point Slope formula y = 2x-6
Hope this helps! Please like!!
:)
Express as a trinomial. (x-9)(x+6)
The expression of (x-9)(x+6) as a trinomial is x² -3x - 54
what is a trinomial?A trinomial is an algebraic expression that has three non-zero terms.
In a simpler terms, the definition of a trinomial is a math equation that has three terms which are connected by plus or minus notations.
Therefore, let's express (x-9)(x+6) as a trinomial.
Hence,
(x-9) (x+6) = x² + 6x - 9x - 54
Finally,
x² + 6x - 9x - 54 = x² -3x - 54
Therefore, the trinomial form of (x-9)(x+6) is x² -3x - 54
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WILL MARK BRAINIEST Rewrite the radical expression as an expression with a rational exponent. 3 square root x 7
a x21
b x4
c x7/3
d x 3/7
I need help with this can someone please help?
HG is the answer.
hope this helps
The first one is GH Segment.
Both shapes are similar. The figure on the right is a scaled version of the figure on the left. The VU edge in the left figure corresponds to the GH edge in the right figure.
The second one is %[tex]150[/tex].
As can be seen, the VU edge is [tex]2[/tex] units long while the GH edge is [tex]3[/tex] units long. By proportioning these edges and multiplying by [tex]100[/tex], we find the scaling factor. It is [tex]\frac{3}{2}[/tex].
the product x squared and y increased by 4
3. A tomato sauce company currently sells tomato sauce in a
cylindrical can that has a radius of 5 cm and a height of 12 cm.
They have plans to use larger cans to sell tomato sauce in bulk.
The new cylindrical cans are to be similar to the original cans
and have a height of 60 cm.
If the original can holds 1487 cm³ of tomato sauce,
how much tomato sauce will the new can hold?
√x cm³
V=
Tomato sauce will the new can hold is 743[tex]cm^{3[/tex]
let take us take,
V = Sh
[tex]S_{1} =S_{2}[/tex]
[tex]h_{1[/tex] = 12 cm
[tex]h_{2}[/tex] = 60 cm
[tex]\frac{V_{1} }{V_{2} } = \frac{h_{1} }{h_{2} }[/tex]
[tex]\frac{1487}{v_2} } = \frac{12}{60}[/tex]
= 743[tex]cm^{3[/tex]
What is Height?Height means the vertical distance, either between the top and bottom of something or between the bottom and the thing above it. height refers to being tall or short as measured vertically.
Height is a way of measuring someone or something from the bottom to the top or from the head to the feet. In other words, height indicates how tall someone or something is. We can compare how tall we will be when we grow up. We often compare the average height of men and women in different countries.
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Dominoes region seven manager projects a net income of $725,000 the net income typically represents 30% of total annual sales based on his projections what will be the annual sales
We were informed that the net income will be $725,000, since that value represents 30% of the total annual sales we can apply a rule of three to solve the problem. We do that by making 30% represent $725,000 in the same proportion that 100% represents the total anual sales, x. We have:
[tex]\frac{30}{100}\text{ }\frac{\text{ \%}}{\text{ \%}}=\frac{725000}{x}[/tex]We can cross multiply to find the value of "x".
[tex]\begin{gathered} 30\cdot x=100\cdot725000 \\ x=\frac{72500000}{30} \\ x=2416666.667 \end{gathered}[/tex]The total annual sale on this year will be approximately $2,416,666.667.
7.
In the given image, the measure of 2x is
Only enter the number.
P
N
142°
90°
X
* REQUIRED
M
U
Answer:
Angle LMN = 180 - 142
= 38° (sum of angles on a straight line=180)
x = 180 - 90 - 38
= 52° (sum of angles in triangle=180)
A rectangle has an area of 40 square units. The length is
6 units greater than the width.
Mark this and return
What are the dimensions of the rectangle?
O 8 by 5
O 10 by 4
O11 by 9
O 13 by 7
Save and Exit
Next
Submit
The dimensions of the rectangle will be equal to 10 by 4.
A rectangle may be defined as the closed figure having four sides with the interior angles equal to 90°. it has two dimensions the length and the width. The area of a rectangle may be defined as the product of its length and width. According to the question the area of the rectangle is given as 40 square units. Let us assume the length as 'l' units and width as 'b' units. It is given that length is 6 units greater than the width that is l = (b + 6).
Now, the area of the rectangle = l×b
40 = (b + 6)×b
40 = b² + 6b
=> b² + 6b - 40 = 0
=> b = [-6 ± √(36 + 160)]/2
=> b = (-6 ± 14)/2
=>b = 4 units, since width cannot be negative.
Now, length = b + 6 = 10 units.
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A right pyramid has a surface area of 258 cm2. A right cone has a base radius of 4 cm. The cone and pyramid have equal surface areas. What is the height of the cone to the nearest tenth of a centimetre?
The height of the cone to the nearest tenth of a centimeter is 17.40 cm.
From the given information provided in the question, we can solve this problem by following a few steps.
The surface area of a right pyramid is 258 cm² according to the question.
The surface area of the cone is equal to the surface area of the right pyramid. Therefore the surface area of the cone is also 258 cm².
The surface area of a cone is denoted as ( πrh + πr² ).
Where h is denoted as the height and, r is denoted as the radius of the cone which is 4 cm.
Hence the surface area of the cone is,
SA = (π× 4× h+ π× 4² ) cm²
Now, we can generate an equation, as both represent the value of the surface area of the cone.
(π× 4× h+ π× 4² ) = 258
Or, (12.56h + 39.44) = 258 [ The value of π is 3.14 ]
Or, 12.56h = 258 - 39.44 [ subtracting 39.44 from both sides ]
Or, 12.56h = 218.56
Or, h = 218.56/12.56 [ dividing both sides by 12.56]
Or, h = 17.40
Now, we can conclude that the height of the cone is 17.40 cm.
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PLEASE HELP WHAT IS THE ANSWER
Triangle DAC is isosceles.
The correct option; Angle BAD is congruent to angle BCA, is requited to show ΔDBA ≅ ΔCBA by side-angle-side congruence theorem.
What is meant by congruence of triangles?If all 3 corresponding sides are equal as well as all 3 corresponding angles seem to be equal in measure, two triangles are said to be congruent.
These triangles could be moved, rotated, flipped, and turned to look exactly the same. They coincide if they are repositioned. ' is the symbol of congruence.side-angle-side congruence theorem: By SAS rule, two triangles are said to be congruent if any two sides and the angle would include between the sides with one triangle are equivalent to a corresponding two sides and also the angle would include here between sides of the second triangle.
For the given triangles;
ΔDBA and ΔCBA
Side AC = Side AD
Side AB = Side AB (common)
Thus, to make both triangles congruent the angles falling in between these two triangles must be equal.
Thus, Angle BAD is congruent to angle BCA,
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Please help!! It’s geometry and I just need the answer quick
Answer:
4.5
Step-by-step explanation:
Penny is going to make a donation to our local animal shelter. The price of each item she will donate is shown.
so far she has 30 cans of cat food 34 cans of dog food and 18 bags of cat she wants the value of her donation to be more than $380 how many bags of dog food does Penny need to donate to meet her goal?
Answer:
Second Choice: 8.73b + 171.48 > 381
Step-by-step explanation:
This is a tricky question because the first two choices both represent an inequality that satisfy the conditions
First, let's eliminate obvious wrong choices.
If b represents the number of bags of dog food and one bag costs $8.73, there should be term 8.73b somewhere in the inequality since 8.73b represents the total $ cost of b bags of dog food.
This means we can eliminate the last two choices
Let's deal with the knowns and compute the dollar amounts of each of the products being donated
30 cans of cat food at $0.57 per can = 0.57 x 30 = $17.10
34 cans of dog food at $0.84 per can = 0.84 x 34 = $28.56
18 bags of cat food at $$6.99 per bag = 6.99 x 18 = $125.82
The sum of these is $171.48
She is also donating b bags of dog food at $8.73 per bag = 8.73 x b = $8.73b
So the total cost of the donation =
8,73b + 171.48 which has to exceed 381
So the inequality is
8.73b + 171.48 > 381
Which is the choice you have selected and I believe it is correct
Now, the tricky part comes because if you subtract 171.84 from both sides of the inequality we get
8.73b > 318 - 171.48
Both inequalities are equivalent but we would not write an inequality of the type where the RHS is a mathematical expression. We would instead simplify the right hand side and write it as
8.73b > 209.52 (381-171.48 = 209.52)
I believe the way the question is worded is the LHS should be the $sum of all the donations and the RHS the minimum value.
So the best choice is choice 2: 8.73b + 171.48 > 381
i hope that helps.
The PTA prepared 10 gallons of punch to serve at their first meeting. If each serving is eight ounces, how many people can be served?
Based on mathematical operations, the number of people that 10 gallons of punch can serve is 192 persons.
How is the number determined?The number of people can be determined using mathematical operations of multiplication based on converting the gallons to ounces and division.
The number of gallons of punch to serve at the first meeting = 10 gallons
The quantity of punch per serving = 8 ounces
1 gallon = 153.722 ounces
10 gallons = 1537.22 ounces
The persons that can be served 8 ounces from the 10 gallons = 192 (1,537.22/8).
Thus, mathematically, from the 10 gallons of punch, the PTA can serve 192 persons.
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The half-life of a certain medication is 2 hours, and a patient takes a single 400-milligram dose of the medication.
After 6 hours, there will be X milligrams of medication left in the patient's body.
After 7 hours, there will be X milligrams of medication left in the patient's body. Round your answer to the nearest hundredth.
After 8 hours, there will be X milligrams of medication left in the patient's body.
The number of milligrams of medication medication left after 6 hours is; 50 milligrams.
The number of milligrams of medication medication left after 7 hours is; 35.36 milligrams.
The number of milligrams of medication medication left after 8 hours is; 25 milligrams.
What amount of medications is left in the body after each of the given time intervals?It follows from the task content that the amount of medications left in the patient's body be determined in each case.
Recall the formula for the amount of substance remaining for half life situations is as follows;
A = N (1/2)^(t/half-life)
Since half life = 2 hours and N = 400 milligrams;
Hence;
At t = 6hrs; A = 400(1/2)^(6/2) = 400(1/2)³ = 50millograms.At t = 7hrs; A = 400(1/2)^(7/2) = 400(1/2)^(3.5) = 35.36 millograms.At t = 8hrs; A = 400(1/2)^(8/2) = 400(1/2)⁴ = 25 millograms.Read more on half-life;
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Idil is deciding between two different movie streaming sites to subscribe to. Plan A costs $18 per month plus $1 per movie watched. Plan B costs $8 per month plus $3 per movie watched. Let AA represent the monthly cost of Plan A if Idil watches x per month, and let B represent the monthly cost of Plan B if Idil watches x movies per month. Write an equation for each situation, in terms of x, and determine which plan would be cheaper if Idil plans on watching 6 movies each month.
The cheaper plan here would be plan A. The equation that is written in terms of the plans on movies is 0 < x < 5
How to solve the equationFor the plan A, we would have the function to be given as
A = 1x + 18
This is due to thge fact that this plan is said to cost $18 per month plus $1 per movie watched.
For plan B the function would have to be:
B = 3x + 8
The equation that we would have here would be
1x + 18 < 3x + 8
= x - 3x < 8 - 18
= -2x < -10
x < 5
Hence we would have the equation as 0 < x < 5
Cheaper plan
1x6 + 18 = 24
3x 6+ 8 = 18 + 8 = 26
Plan A id cheaper
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Kelly drove 238 miles on 6 1/6 gallons of gasoline. Calculate how many miles per gallon she gets in her vehicle.
Kelly gets 38.59 miles per gallon of gasoline
Miles drove by Kelly = 238 miles
Gasoline used by the car = 6 1/6 gallons
Gasoline used in the car in improper fraction = 37/6 gallons
Average fuel economy: Average fuel economy of a car gives the distance covered by the car in one gallon of gasoline. This is an important factor to consider while buying or using a car as it is a major source of expenditure for the car.
To calculate miles per gallon we use the following formula:
Miles per gallon = Miles driven/ Gasoline used in the car
= 238/(37/6)
= 238*6/37
= 38.59
Miles per gallon = 38.59
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keisha's basketball team must decide on a new uniform. the seventh-graders will pick the color of the shorts (black or gold) and the eighth-graders will pick the color of the jersey (black, white, or gold), but the two groups of players will not confer together. if, for both garments, each possible color is equally likely to be chosen, what is the probability that the shorts will be a different color than the jersey? express your answer as a common fraction.
The probability that the shorts of the basketball team will be of a different color than the jersey is 2/3.
Probability can be found using the following formula;
probability = number of favorable outcomes or events ÷ total number of outcomes or events
In order to calculate the probability that the shorts will be of a different color than the jersey, we first determine the total number of combinations that are possible;
1- Black-Black
2- Black-White
3- Black-Gold
4- Gold-Black
5- Gold-White
6- Gold-Gold
Hence there are a total of 6 possible combinations of shorts and jerseys out of which 2 are the same and 4 are different.
Therefore the probability that the shorts will be of a different color can be calculated as follows;
probability = number of favorable outcomes or events ÷ total number of outcomes or events
probability = 4 ÷ 6
probability = 2/3
Hence, 2/3 is the probability that the shorts will be of a different color than the jersey.
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PLEASE HELP NOW!!! THX :))
You are baking doughnuts for your class. There are 8 total students in your class and you have baked 11 doughnuts. Write and solve an equation to find the additional number x of doughnuts you need to bake in order to have 4 doughnuts for each student. Write your equation so that the units on each side of the equation are doughnuts per student.
Answer: 4x + 11 = 4(8)
Step-by-step explanation:
[tex] x {6} \div x {15}[/tex]how to solve x to the 6th power divided by x to the 15th power
So, if we apply the power's rule, we notice that if the base is the same, the exponents can be substracted. Like this
So the answer is 1 / x to the 9th power
26 = -12u - 9 + 7u solve for u and simplify as much as possible
Answer:
u = -7
Step-by-step explanation:
26 = -12u - 9 + 7u
combine u terms on right side:
26 = -5u - 9
add 9 to both sides:
26 + 9 = -5u - 9 + 9
35 = -5u
divide both sides by -5:
35/-5 = -5u/-5
u = -7
(5x²+23x+16) + (x+4)
÷
Answer:
5x2 + 24x + 20
Step-by-step explanation: