Recall the definition of absolute value:
[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
Then we have a few cases to consider:
• If [tex]4x-5\ge0[/tex] and [tex]-x+5\ge0[/tex], the equation simplifies to
[tex]4x-5 = -x+5 \implies 5x=10 \implies \boxed{x=2}[/tex]
• If [tex]4x-5<0[/tex] and [tex]-x+5\ge0[/tex], we get
[tex]-(4x-5) = -x + 5 \implies -3x = 0 \implies \boxed{x=0}[/tex]
• If [tex]4x-5\ge0[/tex] and [tex]-x+5<0[/tex], then
[tex]4x-5 = -(-x+5) \implies 3x=0 \implies x=0[/tex]
but we already have this solution.
• If [tex]4x-5<0[/tex] and [tex]-x+5<0[/tex], then
[tex]-(4x-5) = -(-x+5) \implies -5x = -10 \implies x=2[/tex]
which we also already found.
graph the relation y=2x
NEED HELP RELATIONSHIP IN TRIANGLES
Answer:
Step-by-step explanation:
10x-13=17x-41
DO YOUR WORK
The manager of a grocery store in Decatur currently provides special service to people who still use checks to pay for food. They have a separate pay/bag line for people who insist on waiting for a dollar total to pull out their checkbook and start writing. On average, 30 customers per hour arrive at the checking pay/bag line and they can be modeled with a Poisson distribution. The clerk at this line can handle an average rate of 35 customers per hour and their service can be modeled with exponential distribution.
a. 67%.
b. 75%.
c. 33%.
d. 25%.
Utilization Average time a customer spends in the system
rho = λ/μ w = 1/μ - λ = L/λ
Average # of customers in the system Average time a customer spends in the queue
Ls = λ/μ - λ Wq = λ/μ(μ - λ) = Ls/λ
Average # of customers in queue Probability of n units in the syst
The correct option is: c. 33%. (The probability of having 36 customers in the system is approximately 0.00183%, which is approximately 0.033%, or 33%).
To find the utilization (ρ) of the clerk at the check/pay line, we can use the formula:
ρ = λ / μ
where:
ρ = Utilization
λ = Arrival rate (rate at which customers arrive at the line)
μ = Service rate (rate at which the clerk can handle customers)
Given in the problem:
Arrival rate (λ) = 30 customers per hour
Service rate (μ) = 35 customers per hour
Now, let's calculate the utilization (ρ):
ρ = 30 / 35 ≈ 0.8571
To convert this to a percentage, we multiply by 100:
ρ ≈ 0.8571 * 100 ≈ 85.71%
Since the utilization represents the percentage of time the clerk is busy, we need to find the percentage of time the clerk is idle (not busy). This can be calculated by subtracting the utilization from 100%:
Idle time = 100% - Utilization
Idle time ≈ 100% - 85.71% ≈ 14.29%
Now, let's find the average time a customer spends in the system (W) using Little's Law:
W = L / λ
where:
W = Average time a customer spends in the system
L = Average number of customers in the system (both in the queue and being served)
λ = Arrival rate (rate at which customers arrive at the line)
Given in the problem:
Arrival rate (λ) = 30 customers per hour
Now, we need to find the average number of customers in the system (L) to calculate the average time.
L = Ls + λ
where:
Ls = Average number of customers in the queue
Ls = λ / (μ - λ)
Given in the problem:
Service rate (μ) = 35 customers per hour
Ls = 30 / (35 - 30) = 30 / 5 = 6 customers
Now, calculate the average number of customers in the system (L):
L = Ls + λ
L = 6 + 30 = 36 customers
Now, calculate the average time a customer spends in the system (W):
W = L / λ
W = 36 / 30 = 1.2 hours per customer
Finally, let's find the probability of having n units in the system (both in the queue and being served). In this case, n would be the number of customers in the system (L):
Probability of having n units in the system = (ρ^n) * (1 - ρ)
Probability of having 36 units in the system (L):
Probability of L customers in the system = (0.8571^36) * (1 - 0.8571) ≈ 0.0000183
The question asks for the percentage, so we multiply by 100 to convert to percentage:
Probability ≈ 0.0000183 * 100 ≈ 0.00183%
Thus, the correct option is: c. 33%. (The probability of having 36 customers in the system is approximately 0.00183%, which is approximately 0.00183% * 18 ≈ 0.033%, or 33%).
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Professor Lee Xiao teaches an online class. She is paid $2,409 for up to 25 students,
plus an extra of $136 for every student beyond 25.
Professor Xiao is paid $3,262 for the class. How many students did she have? (Round
to the nearest integer).
acha
Answer:
25 + 6 = 31
Step-by-step explanation:
Her actual pay is 3262
Her base rate is 2409 Subtract to get the amount over the base
Amount of + 25 853
So how many student more does that amount to?
853 / 136 = 6.27
If you have to round to the nearest integer, the answer is 6.
Solve -2/3x > 8 or -2/3x < 4.
{x | x > -12 or x < -6}
{x | -12 < x < -6}
{x | x < -12 or x > -6}
{x | x < -12 or x > -6}
=========================================================
Explanation:
Let's solve the first inequality for x.
(-2/3)x > 8
-2x > 8*3
-2x > 24
x < 24/(-2)
x < -12
The inequality sign flips when we divide both sides by a negative value.
Let's do the same for the second inequality.
(-2/3)x < 4
-2x < 4*3
-2x < 12
x > 12/(-2)
x > -6
The conclusion of each section is that x < -12 or x > -6 which points us to choice C as the final answer.
Side note: The intervals x < -12 and x > -6 do not overlap in any way. There's a gap between the two pieces. We consider these intervals to be disjoint. The number line graph is below.
Jack’s school bag contains 8 books each of weight 3/8 pounds, and 6 folders of weight 1/2 pound. b) What fraction of the total weight is folders?
Answer:
6 pounds
Step-by-step explanation:
3/8×8/1=24/8=3
6/1×1/2=6/2=3
3+3=6
Which of the following sets is equal to {1, 2, 3, ...)?
{x| xER, x>1}
{x|xER, x> or equal to 1}
{x|xEN, x> or equal to 1}
Answer:
[tex]\{x~ | ~x\in \mathbb{N}, x \geq 1\}[/tex]
Step-by-step explanation:
(07.03 LC)
Identify the factors of x2 - 8x - 20. (1 point)
O (x + 4Nx - 5)
O (x + 5)(x - 4)
O (x - 10)(x + 2)
O (x-2)(x + 10)
Answer:
(x - 10)(x + 2)
Step-by-step explanation:
We are looking for two things that multiply together to give us
x^2 - 10x - 20
These things are binomials, such as (x+2) or (x-7) or (x+8) or (x-5)
We know the first term in the binomial has to be x, because x times x is x^2.
And then we are looking for two numbers that multiply to -20 but also add up to -8.
-10 and 2 multiply to make -20 and add up to -8 so we pick the answer (x-10)(x+2)
Answer:
Option C
Step-by-step explanation:
x² - 8x - 20
x² - (10x - 2x) - 20
x² - 10x + 2x - 20
x(x - 10) + 2(x - 10)
(x - 10)(x + 2)
Hence
Option C is correct
Name each polynomial by degree and number of terms .
1) -10x
2) -10r4- 8r2
3) 7
4)9a6 + 3a5 - 4a4 - 3a2 + 9
5)-3n3 + n2 - 10n + 9
6) 7x2 - 9x - 10
7) -4b
8) -9 + 7n3 - n2
Answer:
Polynomials are classified according to their number of terms. 4x3 +3y + 3x2 has three terms, -12zy has 1 term, and 15 - x2 has two terms. As already mentioned, a polynomial with 1 term is a monomial. A polynomial with two terms is a binomial, and a polynomial with three terms is a trinomial.
Twice the difference of a number and 4 is equal to three times the sum of the number and 10.
Answer:
2(x-4)=3(x+10)
Step-by-step explanation:
a plane flies 5.0km due north from a point O and then 6.0km on a bearing of 060° the pilot then changes course on a bearing of 120° for 4.0km. find how far and in what direction the plane is from the starting point?
The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.
A plane that travels a distance [tex]r[/tex], in kilometers, with a bearing of [tex]\theta[/tex] sexagesimal degrees can be represented in standard position by means of the following expression:
[tex]\vec r = r\cdot (\sin\theta, \cos \theta)[/tex] (1)
We can obtain the resulting vector ([tex]\vec R[/tex]) by the principle of superposition:
[tex]\vec R = \Sigma_{i=1}^{n} [r_{i}\cdot (\sin \theta_{i}, \cos \theta_{i})][/tex] (2)
If we know that [tex]r_{1} = 5\,km[/tex], [tex]\theta_{1} = 0^{\circ}[/tex], [tex]r_{2} = 6\,km[/tex], [tex]\theta_{2} = 60^{\circ}[/tex], [tex]r_{3} = 4\,km[/tex] and [tex]\theta_{3} = 120^{\circ}[/tex], then the resulting vector is:
[tex]\vec R = 5\cdot (\sin 0^{\circ}, \cos 0^{\circ}) + 6\cdot (\sin 60^{\circ}, \cos 60^{\circ}) + 4\cdot (\sin 120^{\circ}, \cos 120^{\circ})[/tex]
[tex]\vec R = (5\sqrt{3}, 6) \,[km][/tex]
The magnitude of the resultant is found by Pythagorean theorem:
[tex]\|\vec R\| = \sqrt{R_{x}^{2}+R_{y}^{2}}[/tex]
And the bearing is determined by the following inverse trigonometric relationship:
[tex]\theta_{R} = \tan^{-1} \left(\frac{R_{y}}{R_{x}}\right)[/tex] (3)
If we know that [tex]R_{x} = 5\sqrt{3}\,km[/tex] and [tex]R_{y} = 6\,km[/tex], then the magnitude and the bearing of the resultant is:
[tex]\|\vec R\| = \sqrt{(5\sqrt{3})^{2}+6^{2}}[/tex]
[tex]\|\vec R\| \approx 10.536\,km[/tex]
[tex]\theta_{R} = \tan^{-1} \left(\frac{6}{5\sqrt{3}} \right)[/tex]
[tex]\theta_{R} \approx 34.715^{\circ}[/tex]
The plane flies a distance of approximately 10.536 kilometers in straight line and with a bearing of approximately 035°.
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A pencil at a stationery store costs $1, and a pen costs $1.50. Shawn spent $12 at the store. He bought a total of 9 items. Which system of equations can be used to find the number of pencils (x) and pens (y) he bought? (5 points)
1.5x + y = 12
x = 9y
x + 1.5y = 12
x + y = 9
x + 9y = 12
x = 1.5y
9x + y = 12
x = 1.5y
Answer:
9 = x + y
1x + 1.5y = 12
Step-by-step explanation:
9 (number of items) = x (number of pencils) + y (number of pens)
1x (cost of x number of pencils) + 1.5y (cost of y number of pen s)= 12 (total cost)
HELP PLZ PLZ ITS DUE IN 30 MINUTES
Answer:
wouldn't that be...24x²?
What is the gradient of the graph shown?
Give your answer in its simplest form.
Answer:
Step-by-step explanation:
When it's clear, the easiest way to do the problem is to used the x and y intercepts.
This question is one of the clear one.
The x intercept is 2,0
The y intercept is 0,1
You want the slope.
m = (y2 - y1)/(x2 - x1)
y2 = 1
y1 = 0
x2 = 0
x1 = 2
m = (1 - 0)/(0 - 2)
m = 1 / -2
m = -1/2
In this case the slope and gradient have the same value -- - 1/2 or - 0.5
12 tenths+ 9 tenths = tenths = ones = tenths
6. Expand the brackets: a) 3(x - y) )
Answer:
3x-3y
Step-by-step explanation:
3(x-y)
open the brackets:
(3×x)-(3×y)
= 3x-3y
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 5 hours. Together they charged a total of $2750.
What was the rate charged per hour by each mechanic if the sum of the two rates was $205 per hour?
-Whats the First mechanic: $ -----per hour
-Whats the Second mechanic: $ ---- per hour
(−3, −1), (−1, 5) Find the slope of the line that passes through the pair of points.
[tex]slope = \frac{ 5 - ( - 1)}{ - 1 - ( - 3)} \\ [/tex]
[tex]slope = \frac{5 + 1}{ - 1 + 3} \\ [/tex]
[tex]slope = \frac{6}{2} \\ [/tex]
[tex]slope = 3[/tex]
Determine whether each graph shows a positive correlation, a negative
correlation, or no correlation. If there is a positive or negative correlation,
describe its meaning in the situation.
Answer:
Positive correlation.Step-by-step explanation:
From the graph we can see overall increasing trend.
It means there is a positive correlation.
The meaning of this is the more time you spend on study the better test score you get.
Answer:
Negative correlation
Step-by-step explanation:
As TV hours increase, exercise
hours decrease.
HELP
Lyndie is making reduced copies of a photo that measures 25 centimeters in height. She sets the copy machine to an 80% size
reduction.
PART A
Write a percent equation that represents
the relationship of the height of the first
copy to the height of the original photo.
PART B
Lyndie wants to make another copy that
will have a height of 17 cm. The copy
machine settings increase or decrease in
increments of 5%. Which photo should she
make her copy from, the original or her
first copy? Explain.
Answer: 5+ba*7= 88
Step-by-step explanation:
Izzo's Pizza sells four types of pizza crust. Last week, the owner tracked the number sold of each type, and this is what she found.
Type of Crust Number Sold
Thin crust
344
Thick crust
391
Stuffed crust 155
Pan style
185
Based on this information, or the next 3500 pizzas she sells, how many should she expect to be thin crust? Round your answer to the nearest whole number. Do
not round any intermediate calculations.
#3
Determine whether the ratios are equivalent.
5:2 and 30: 12
o equivalent
not equivalent
Answer:
yes
Step-by-step explanation:
Ratios are equivalent if they are multiples or divisors of each other.
5 : 2 ( multiply both sides by 6 )
= 30 : 12
or
30 : 12 ( divide both sides by 6 )
= 5 : 2
Thus 5 : 2 and 30 : 12 are equivalent ratios
Answer:
equivalent
Step-by-step explanation: 5 x 6 = 30 2 x 6 = 12
WHOEVER EXPLAINS FIRST GETS BRAINLIEST!!
Enter your answer and show all the steps that you use to solve this problem in the space provided. Solve.
-2/5x-9<9/10
what is 5y² if y= -1
Answer:
5
Step-by-step explanation:
Input all of the numbers and solve:
5×-1×-1
Start by solving -1*-1=1
5*1=5
Answer:
the answer for this question is 5
simplify.
|−6 + (−3)| (−3) + 8 ÷ 2
If the expression inside the absolute value bars which is -6 .Simplifying the expression |−6 + (−3)| (−3) + 8 ÷ 2 is: 9.
What is the expression?Let simplify the given expression step by step:
|-6 + (-3)| = |-9| = 9
First calculate the expression inside the absolute value bars which is -6 + (-3) = -9. Then take the absolute value of -9, which is 9.
(-3) + 8 ÷ 2 = (-3) + 4 = 1
We follow the order of operations (PEMDAS/BODMAS).
First perform the division:
8 ÷ 2 = 4
Add -3 to 4 which gives us 1.
Simplified expression :
9 * 1 = 9
Therefore the expression is 9.
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Sean has three dollars more than twice as much money as Peter if Sean has $10 how much money does Peter have
Answer:
peter has $3.50
Step-by-step explanation:
3.50 times 2 is 7 plus 3 is 10
How do I solve this
Answer:
Step-by-step explanation:
well, I'd just multiply each option out using FOIL
First, Outside, Inside, Last
A) (x + 2√3i)(x - 2√3i)
First x(x) = x²
Outside x(- 2√3i) = - 2x√3i
Inside x(2√3i) = 2x√3i
last (- 2√3i)(2√3i) = -(2²)(√3²)(i²) = -4(3)(-1) = 12
add them all up x² + 12 looks like it works for me
B) = x² + 36
C) = x² + 4√3 + 12
D) = x² - 12
88, 89, 86, 90, 83, 81, 89
What is the median number
A 88
B. 89
C 90
D. 86
Please answer this I really need help
Answer:
The answer is 90.
Step-by-step explanation:
90 is in the middle
Answer:
d
Step-by-step explanation:
cause i said so
The square below represents one whole.
What percent is represented by the shaded area?
I NEED HELP PLSSS GEOMETRY
Answer:
Its the first one (top left option)
Step-by-step explanation:
ur in a rush so i wont explain, pls give me brainliest