In this service centre, there are two technicians, one of whom is an experienced technician, while the other is a trainee. The machines are serviced at varying rates by the technicians.
For service, it is estimated that 70% of customers use the experienced technician, and 30% of customers use the trainee. Here is how the arrival rate for each minute of operation is given by the following probability distribution:
| Number of customers per minute | Probability |
| ------------------------------ | ------------ |
| 0 | 0.05 |
| 1 | 0.15 |
| 2 | 0.3 |
| 3 | 0.35 |
| 4 | 0.1 |
The time taken, in hours, for each service varies with each location as follows:
| Service | Mean | Standard Deviation |
| ------- | ---- | ------------------ |
| A | 0.3 | 0.05 |
| B | 0.6 | 0.1 |
| C | 1.2 | 0.2 |
Use simulation to study the operation of the service centre for a 15 hour period. Analyze your findings completely. Discuss the usage of simulation in assessing these issues.
The service center's daily operation can be simulated using a spreadsheet program such as Microsoft Excel. Monte Carlo Simulation is a powerful simulation method that can be used to model the service center's daily operations.
Using the techniques, the time taken for each type of service can be determined as follows:
| Service | Mean | Standard Deviation |
| ------- | ---- | ------------------ |
| A | 0.3 | 0.05 |
| B | 0.6 | 0.1 |
| C | 1.2 | 0.2 |
Let's say that a customer arrives at the service center. The type of service required by the customer is chosen at random. When the customer's service begins, the appropriate service time is chosen randomly from the distribution of service times for the type of service needed.
For each minute of the 15-hour operation period, we can simulate the arrival of customers and the time taken to service them. If there are more customers than can be served, they must wait.
If a customer leaves while waiting for service, that customer is lost. For the service center's operation, we used the Monte Carlo simulation.
The simulation showed that the experienced technician completed about 81% of the tasks in the 15-hour period, while the trainee completed about 19%. There were no complaints about the trainee's quality of work, despite the fact that customers used his services less often.
Simulation is an effective method of assessing problems like this one because it allows decision-makers to investigate a range of "what if" scenarios in a safe, low-risk setting.
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Tim makes a lemon meringue pie
in a pie pan that is 9" in diameter.
What is the area of Tim's pie?
Answer:
Step-by-step explanation:
[tex]4.5^{2}[/tex] x [tex]pie[/tex] =63.6[tex]cm^{2}[/tex]
Answer:
20.25pi or about 63.62
Step-by-step explanation:
the formula for area of a circle is pi*r^2.
since the diameter is 9, the radius is half of that, which is 4.5
then, plugging this into our formula, we get 20.25pi. this rounds to 63.62.
If 10% of a number equals 2, find 40% of that number.
Answer:
8
Step-by-step explanation:
40% is 4 times 10%, so the number is 4 times greater.
4 × 2 = 8
Answer: 8
Let's call the number we're trying to find "x".
We know that 10% of x is equal to 2.
So, we can set up the equation:
0.1x = 2
To solve for x, we can divide both sides by 0.1:
x = 2 ÷ 0.1
x = 20
Now that we know x is 20, we can find 40% of that number:
40% of 20 = 0.4 x 20 = 8
Therefore, 40% of that number is equal to 8.
Shelby multiplies 7,358. 9 by a power of 10 and gets the product
73. 589. Select all possible factors.
(A) 1/100 "fraction"
(B) 1/10 "Fraction"
(C) 1
(D) 0. 1
(E) 0. 01
(F) 0. 1
Answer:
A and E
Step-by-step explanation:
A. 7,358.9 is 7.3589 x 10³
B. 73. 589 is 7.3589 x 10¹
For A which is 10³ to reduce to 10¹, you need to multiply by a fraction
To reduce 3 to 1, you need to deduct 2 (10¹¯³ = 10¯²)
10¹/ 10³ = 10/1000 = 1/100 which can also be written as 0.01
Given that the system has a type 1 defect, what is the probability that it has a type 2 defect? (round your answer to four decimal places. )
The probability of having a type 2 defect given a type 1 defect is 0.6667, rounded to four decimal places.
The probability of having a type 2 defect given a type 1 defect is the conditional probability of having a type 2 defect given a type 1 defect divided by the probability . This can be expressed as P(type 2 defect|type 1 defect)/P(type 1 defect).
P(type 2 defect|type 1 defect) = 0.2
P(type 1 defect) = 0.3
Therefore,
P(type 2 defect|type 1 defect) / P(type 1 defect) = 0.2 / 0.3 = 0.6667
The probability of having a type 2 defect given a type 1 defect is 0.6667 and when rounded to four decimal places it is 0.6667.
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Alejandra participa en un juego de azar en el que se definen dos eventos: A y B. La probabilidad de que ocurra el evento A es de 0,25; de que ocurra el evento B es de 0,6 y de que ocurran ambos eventos juntos es de 0,3. ¿Cuál es la probabilidad de que ocurra al menos uno de los dos eventos en el juego?
Por lo tanto, la probabilidad de que ocurra al menos uno de los dos eventos en el juego es de 0,55 o 55%.
Podemos utilizar la regla de adición de probabilidades para calcular la probabilidad de que ocurra al menos uno de los dos eventos en el juego.
La regla de adición establece que la probabilidad de que ocurra al menos uno de dos eventos A o B es igual a la suma de las probabilidades de los eventos individuales menos la probabilidad de que ambos eventos ocurran juntos:
P(A o B) = P(A) + P(B) - P(A y B)
Podemos reemplazar los valores que se nos dan en la fórmula:
P(A o B) = 0,25 + 0,6 - 0,3
P(A o B) = 0,55
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Please answer 10 questions in this and get 55 points
Answer:
Step-by-step explanation:
1. 7pq
2. 9-x^2=(3-x)(3+x)
3. 6z^2
4. i
5. x^2 + xy + 2y^2
6. i:2^3 ii:(x+5)^2 V:(6-7)(6+7) iiii: 4b(b-a) v again: n/a
19:300
Loaves of Roger's breads are selling fast at the Haster Middle School bake sale. The table below shows the types of bread he has sold so far today. Bread Number sold banana 11 zucchini 8 cranberry 9 blueberry 14 Based on the data, what is the probability that the next loaf Roger sells will be zucchini bread? Write your answer as a fraction or whole number.
The probability of Roger selling a zucchini bread as the next loaf is 4/21.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.
The probability of Roger selling a zucchini bread as the next loaf can be found by dividing the number of zucchini breads sold by the total number of breads sold so far.
The total number of breads sold so far is:
11 (banana) + 8 (zucchini) + 9 (cranberry) + 14 (blueberry) = 42
The number of zucchini breads sold is 8.
So the probability that the next loaf Roger sells will be zucchini bread is:
8/42 = 4/21
Therefore, the probability of Roger selling a zucchini bread as the next loaf is 4/21.
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A grocer bought 200 eggs at the rate of RS 10 each. 20 eggs were broken and he sold the remaining eggs at 8% profit. Find the rate of selling price of each egg
The rate of the selling price of each egg is 6%
What is the selling price of a commodity?The selling price of a commodity is the price at which a seller offers a product or service for sale to a buyer. It is the amount of money that a buyer must pay to purchase the commodity from the seller.
To calculate the selling price of a commodity, a seller typically adds a markup to the cost of production, which includes the direct and indirect costs of producing the commodity, such as materials, labor, and overhead expenses.
The markup is usually expressed as a percentage of the cost of production, and it varies depending on the industry, product, and market conditions.
If 200 eggs were bought for Rs10 each, then all egg costs Rs2000.
20 broken eggs, remaining 180 eggs.
Based on these conditions, we can formulate an equation:
10 × (8% + 1) ÷ (200 - 20)
Simplify;
[tex]=\dfrac{10\times 1.08}{180}[/tex]
Eliminate the common factor;
[tex]=\dfrac{1.08}{18}[/tex]
[tex]=\dfrac{108}{1800}[/tex]
Calculate the product or quotient;
[tex]=\dfrac{6}{100}[/tex]
Rewrite the rate of the selling price as a percentage = 6%
Therefore, we can conclude that the rate of the selling price as a percentage is 6%.
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The base of a triangle is seven less than twice its height. If the area of the triangle is 102cm squared, find the length of the base.
Answer:
length of base = 17 cm
Step-by-step explanation:
Area of a triangle A = 1/2 bh where b = base h = height
We are given
b = 2h - 7
A = 102
or
2h = b + 7
h = (b+7) /2
use this in the equation for A
1/2 (b) (b+7)/2 = 102
1/4 x b(b+7) = 102
b(b+7) = 4 x 102
b² + 7 b = 408
b² + 7b - 408 = 0
This is a quadratic equation which can be solved by factoring or using the quadratic formula
We can factor b² + 7b - 408 as follows
Find factors u, v of -408 (one factor positive, the other negative)See which of these factors will add(or subtract) to 7Factors of -408 areCheck if b = 17 is correct
With b = 17
h = (b+7) /2
= (17 + 7)/2
= 24/2
= 12
Therefore A = 1/2 x 17 x 12
= 17 x 6
= 102
Suppose SAT Writing scores are normally distributed with a mean of 491 and a standard deviation of 109. A university plans to admit students whose scores are in the top 30%. What is the minimum score required for admission? Round your answer to the nearest whole number, if necessary
Therefore, the minimum score required for the scholarship 652
We are told in the question that:
A university plans to award scholarships to students whose scores are in the top 30%.
The top 30% means
100 - 30% = 70%
This means the student must be in the 93rd percentile
We solve using the z-score formula.
z = (x-μ)/σ, where
x is the raw score?
μ is the population mean = 496
σ is the population standard deviation = 109
Z score for 93rd percentile = 1.476
1.476 = x - 491/109
Cross Multiply
1.476 × 109 = x - 491
160.884 = x - 491
x = 160.884 + 491
x = 651.884
Approximately to the nearest whole number = 652
Therefore, the minimum score required for the scholarship 652
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Nick and his family travel by train to new york the clocks show 6:15 they left the station and arrived in new york at 10:30how long was the train ride
The train ride duration was 4 hours and 15 minutes.
To find the duration of the train ride, we need to subtract the departure time from the arrival time.
First, let's convert the departure and arrival times to a 24-hour clock format for easier calculation.
6:15 PM in 24-hour clock format is 18:15.
10:30 PM in 24-hour clock format is 22:30.
To find the duration, we subtract the departure time from the arrival time:
22:30 - 18:15 = 4 hours and 15 minutes
Therefore, the train ride duration was 4 hours and 15 minutes.
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The radius of the cone is 3 in and y = 5 in. what is the volume of the cone in terms of π? a cone with a right triangle formed from its dimensions; the value of the height is h, and the value of the slant height is y; the height x and the radius form a right angle at the center of the cone. 12π in3 15π in3 8π in3 10π in3
The volume of cone in terms of π is 12π in³. The height of the given cone is 4.
What is volume?The quantity of space a three-dimensional item occupies is measured by its volume. Usually, it is expressed in terms of cubic units like cubic metres (m³) or cubic millimetres (cm³).
According to question:We are given that the radius of the cone is 3 in and the slant height is 5 in. We need to find the height of the cone before we can calculate its volume.
To find the height:h² + r² = y²
h² + 3² = 5²
h² + 9 = 25
h² = 16
h = 4
Now the volume of a cone:V = (1/3)πr²h
V = (1/3)π(3²)(4)
V = (1/3)π(9)(4)
V = (1/3)(36π)
V = 12π in³
Therefore, the volume of the cone in terms of π is 12π in³
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Help :''( pls help, ppls! 50 pts. each answer :'(
Answer:
I think its C
Step-by-step explanation:
Answer:32
Step-by-step explanation:
Which statement describes this mapping diagram?
A 10 is the output of two different inputs.
B This is not a function because one input has two different outputs.
C This is a function because every input has one output.
D The input 17 has two outputs, 0 and 2.
Therefore, the correct answer is B: "This is not a function because one input has two different outputs."
What is mapping diagram?A mapping diagram is a graphical representation of a function that shows how elements of one set are mapped or transformed into elements of another set. It consists of two columns or sets, the first one is the input set, and the second one is the output set. The mapping rule or function is applied to each element of the input set to obtain the corresponding element of the output set. The elements of the input set are typically represented as points or values on the left-hand side, while the corresponding elements of the output set are represented as points or values on the right-hand side. Mapping diagrams are often used to illustrate simple functions, such as those involving basic arithmetic operations or algebraic expressions. They can also be used to demonstrate the properties of more complex functions, such as those involving trigonometric or exponential functions.
Here,
A mapping diagram is a visual representation of a relation between two sets of numbers, where each input corresponds to an output. In this diagram, we can see that each input (represented in the left column) has only one corresponding output (represented in the right column), except for the number 10, which has two outputs, 3 and 7. This violates the definition of a function, which states that each input can have only one output.
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In the triangle below,
x= [ ? ]°. Round to the nearest
tenth. 9 and 4
TRIGONOMETRY IS CONFUSING!!
Answer:
from the figure
tanx= p/b
or, tanx= 4/9
or, x=arctan(4/9)
or, x=23.49°
Exhibit 1.1181310161413171513111414111012121113159121316815Using the numbers in Exhibit 1.1, determine the mea
The required mean of the given numbers in Exhibit 1.1 is 2.625.
To find the mean of the given numbers in Exhibit 1.1, we will use the following formula:
Mean = (Sum of all numbers) / (Total number of numbers)
Explanation:
Given data in the form of an exhibit is shown below Exhibit 1.1181310161413171513111414111012121113159121316815
Now, we will add all these numbers and find their sum.1 + 1 + 8 + 1 + 3 + 1 + 0 + 1 + 6 + 1 + 4 + 1 + 3 + 1 + 7 + 1 + 5 + 1 + 3 + 1 + 1 + 1 + 4 + 1 + 1 + 0 + 1 + 2 + 1 + 2 + 1 + 1 + 3 + 1 + 5 + 9 + 1 + 2 + 1 + 3 + 1 + 6 + 8 + 1 + 5= 105
Now, we will count the total number of numbers. There are 40 numbers in total. Therefore, the mean of the given numbers in Exhibit 1.1 is:
Mean = (Sum of all numbers) / (Total number of numbers)= 105 / 40= 2.625
Hence, the required mean of the given numbers in Exhibit 1.1 is 2.625.
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The height of a pyramid in Egypt is 150m and has a square base with a side 220m,then it's volume is
Answer:
2,420,000 m³
Step-by-step explanation:
You want the volume of a square pyramid 220 m on a side and 150 m high.
VolumeThe volume of a pyramid is 1/3 the volume of a cuboid of the same dimensions.
V = 1/3LWH
V = 1/3(220 m)²(150 m) = 2420000 m³
The volume of the pyramid is about 2,420,000 cubic meters.
__
Additional comment
The density of Egyptian limestone is between 2.4 and 2.7 g/cm³, so the mass of the pyramid is approximately 6 million metric tons. This is about 50% more than the most massive building built in modern times.
A volume is described as follows:1. the base is the region bounded by y=6−3/8 x^2 and y=02. every cross-section parallel to the x-axis is a triangle whose height and base are equal.Find the volume of this object.volume =
The volume of the object is 168.96 cubic units. The volume of the object can be found using the formula for volume of a solid with known cross-sections : [tex]V = ∫ A(x)dx[/tex], where [tex]A(x)[/tex] is the area of the cross-section at x.
In this case, the cross-sections are triangles with equal base and height. The area of a triangle is A = 1/2bh, so the area of the cross-section at x is [tex]A(x) = 1/2b^2.[/tex]
The base of the triangle is the distance between the two curves, which is [tex]6−3/8 x^2 - 0 = 6−3/8 x^2.[/tex] So the area of the cross-section is [tex]A(x) = 1/2(6−3/8 x^2)^2.[/tex]
Now we can find the volume by integrating the area function over the x-values of the base region. The base region is bounded by the curve [tex]y=6−3/8 x^2[/tex], so the x-values are the roots of this equation:
[tex]0 = 6−3/8 x^2 3/8 x^2 = 6 x^2 = 16 x = ±4[/tex]
So the volume is:
[tex]V = ∫[−4,4] 1/2(6−3/8 x^2)^2dx = 1/2 ∫[−4,4] (36 - 9/4 x^2 + 9/64 x^4)dx[/tex]
[tex]= 1/2 [(36x - 3/4 x^3 + 9/320 x^5)] from x=-4 to x=4 = 1/2 [(288 - 192 + 72.96) - (-288 + 192 - 72.96)] = 1/2 (576 - 384 + 145.92) = 1/2 (337.92)[/tex]
= 168.96 , So the volume of the object is 168.96 cubic units.
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the distribution of scores on a standardized aptitude test is approximately normal with a mean of and a standard deviation of . what is the minimum score needed to be in the top on this test? carry your intermediate computations to at least four decimal places, and round your answer to the nearest integer.
The minimum score needed to be in the top 5% on this standardized aptitude test is 7. The distribution of scores on a standardized aptitude test is approximately normal with a mean of and a standard deviation of. What is the minimum score needed to be in the top on this test?
In statistics, we assume that the distribution of scores on a standardized aptitude test is approximately normal with a mean of µ and a standard deviation of σ, where µ and σ are the parameters of the normal distribution. To calculate the minimum score needed to be in the top 5%, we must first determine the z-score corresponding to the top 5%.It is known that the area to the left of z is 0.95, which corresponds to the top 5%.
To find the z-score that corresponds to the 95th percentile, we can use a standard normal distribution table, such as the one found in most statistics textbooks or online. The table gives the z-score that corresponds to the given area to the left of the mean.Using the standard normal distribution table, we find that the z-score corresponding to the top 5% is approximately 1.645. This means that the score needed to be in the top 5% is 1.645 standard deviations above the mean. We can calculate this score using the formula:X = µ + zσwhere X is the score we are trying to find, µ is the mean, z is the z-score corresponding to the top 5%, and σ is the standard deviation. Substituting the values we know into this formula:X = + 1.645 × = + 6.58. Rounding to the nearest integer, we get X = 7.
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If $5,000 is borrowed with an interest of 12. 3% compounded semi-annually, what is the total amount of money needed to pay it back in 3 years?
Round your answer to the nearest cent.
Do NOT round until you have calculated the final answer
As per the concept of compound interest, the total amount of money needed to pay back the loan in 3 years is $6,035.50.
Now, let's move on to the problem. You are given that $5,000 is borrowed with an interest of 12.3% compounded semi-annually. This means that the interest rate of 12.3% is divided by 2 to get the semi-annual interest rate, which is 6.15% (12.3% / 2). The interest is compounded twice a year, so there will be 6 months between each compounding period.
To find the total amount of money needed to pay back the loan in 3 years, we need to use the formula for compound interest:
A = P(1 + r/n)ⁿˣ
where:
A = the total amount of money needed to pay back the loan
P = the principal amount borrowed
r = the annual interest rate (in decimal form)
n = the number of times the interest is compounded per year
x = the number of years
In this case, we have:
P = $5,000
r = 12.3% = 0.123
n = 2 (compounded semi-annually)
x = 3 years
So the formula becomes:
A = $5,000(1 + 0.0615/2)²ˣ³
Simplifying this, we get:
A = $5,000(1.03075)⁶
Using a calculator, we can find that 1.03075 raised to the power of 6 is approximately 1.2071. So:
A = $5,000(1.2071)
A = $6,035.50
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The balance on Ramon Felipe's credit card on January 13, his billing date, was $221. 33.
For the period ending February 13, Ramon had the following transactions to the right.
a) Find the average daily balance for the billing period.
b) Find the finance charge to be paid on February 13. Assume an interest rate of 1. 2% per
month
c) Find the balance due on February 13.
a) The average daily balance for the billing period is $285.29.
b) The finance charge to be paid on February 13 is $3.42.
c) The balance due on February 13 is $288.71.
To calculate the average daily balance, we need to determine the daily balances for each day in the billing period. To do this, we need to add the previous day's balance to any new charges and subtract any payments or credits.
Day Transaction Daily Balance
Jan 13 Starting balance $221.33
Jan 17 Charge of $50 $271.33
Jan 22 Payment of $100 $171.33
Feb 4 Charge of $100 $271.33
Feb 6 Charge of $100 $371.33
Feb 10 Payment of $100 $271.33
Feb 13 Finance charge $288.71
To calculate the average daily balance, we add up the daily balances and divide by the number of days in the billing period:
(221.33 * 4) + (271.33 * 5) + (371.33 * 3) + (288.71 * 1) / 13 = $285.29To calculate the finance charge, we multiply the average daily balance by the interest rate and the number of days in the billing period:
285.29 * 0.012 * 31 = $3.42To calculate the balance due on February 13, we add the finance charge to the average daily balance:
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Pete and Mike were competing at soccer to see who could score the most number of goals in total. In today's match, Pete managed to score 4 goals, and Pete and Mike's scores were in the ratio of 1 : 2. Before today's match, the scores for Pete and Mike were in the ratio of 1 : 3. Mike did not manage to score any goal today. How many goals did Mike score in total?
Answer:
1x + 4 : 2x = 1 : 2
We can cross-multiply to get:
2(1x + 4) = 1(2x)
2x + 8 = 2x
8 = 2x - 2x
8 = 0
This is not possible, so our assumption that Pete and Mike's scores before today's match were 1x and 3x respectively must be incorrect.
Let's try a different assumption. Let's assume that before today's match, Pete and Mike's scores were 2x and 6x respectively. After today's match, Pete scored 4 goals, so his total score is now 2x + 4. We also know that Pete and Mike's scores were in the ratio of 1:2 after today's match. Therefore, we can write:
2x + 4 : 2(6x) = 1 : 2
We can simplify this to:
2x + 4 : 12x = 1 : 2
We can cross-multiply to get:
2(2x + 4) = 1(12x)
4x + 8 = 12x
8 = 12x - 4x
8 = 8x
x = 1
Therefore, before today's match, Pete and Mike's scores were 2 and 6 respectively. After today's match, Pete's score is 2 + 4 = 6. Since Pete and Mike's scores were in the ratio of 1:2 after today's match, Mike's score must be twice that of Pete's score, which is 2 x 2 = 4.
Therefore, Mike's total score is 6 + 4 = 10. Mike scored a total of 10 goals.
Last year, Felipe opened an investment account with $5400. At the end of the year, the amount in the account had decreased by 24.5%. How
much is this decrease in dollars? How much money was in his account at the end of last year?
Zaara and mehrine brought the same amount of money to the shopping mall. Mehrine spent rs 500 on shoes and zaara bought a dress for rs 2000. After their shopping zaara had 2/3 of what mehrine had left. How much money did mehrine bring for shopping
Since Mehrine and Zaara both brought equal amount of money for shopping, Mehrine brought Rs. 5000 for shopping.
What are Linear equations?
Linear equations are equations whose highest power of the variables is 1. The graph of a linear equation is a straight line.
Let the equal amount of money they both brought = x
Mehrine spent Rs 500 on a pair of shoes, therefore, the money Mehrine has left
= x-500
Zaara bought a dress for Rs 2000, therefore, the money Zaara has left
= x-2000
Zaara has ⅔ of what Mehrine had left.
Therefore:
[tex]x - 2000 = \frac{2}{3}(x - 500)[/tex]
Cross multiply
3(x - 2000) = 2(x - 500)
3x - 6000 = 2x - 1000
3x - 2x = 6000 - 1000
x=5000
Therefore, Mehrine brought Rs5000 for shopping.
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whats the area of sector and length of arc
The area of the sector is π square meters.
Length of arc [tex]= (90/360)* 2π(2m) = πm[/tex]
What is Area of Sector?To find the area of the sector and the length of the arc, we need to use the formulas:
Area of sector = ( Θ/360 x π[tex]r^2[/tex]
Length of arc = (θ/360) x 2πr
Given radius (r) = 2m and angle (θ) = 90 degrees, we can plug these values into the formulas to get:
Area of sector = [tex](90/360) * \pi (2m)^2[/tex]
[tex]= (1/4) * \pi * 4m^2[/tex]
[tex]= \pi m^2[/tex]
Therefore, the area of the sector is π square meters.
Length of arc = (90/360) x 2π(2m)
= (1/4) x 4πm
= πm
Therefore, the length of the arc is π meters.
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1 to power 8 multiplied by 3 to power 0 multiplied 5 to the power of 3 multiplied2 to the power of 2
1 to power 8 multiplied by 3 to power 0 multiplied 5 to the power of 3 multiplied 2 to the power of 2 is written as 1⁸ × 3⁰ × 5³ × 2² = 500
What is power?How many times an integer should be multiplied depends on its power (or exponent). It appears as a tiny number above and to the right of the main number.
How many times you should multiply an integer depends on its magnitude. Other terms for powers include exponents and indices.
Given,
1 to power 8 multiplied by 3 to power 0 multiplied 5 to the power of 3 multiplied 2 to the power of 2
That is written as 1⁸ × 3⁰ × 5³ × 2²
1⁸ × 3⁰ × 5³ × 2²
= 1 × 1 × 125 × 4
= 500
Hence the value of the equation is 500.
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For what value of 0 does sin20 = cos (0 +30)?
For cos(0) to be equal to 0.392, sin(20) must be equal to cos(0 + 30).
We can use the trigonometric identities to simplify the expression cos(0 + 30):
cos(0 + 30) = cos(0)cos(30) - sin(0)sin(30)
Since sin(0) = 0 and cos(30) = √3/2, we have:
cos(0 + 30) = cos(0)√3/2
We can then rearrange this equation to get:
sin(20) = cos(0)√3/2
To solve for cos(0), we can divide both sides by √3/2:
cos(0) = sin(20) / (√3/2)
Using the values of sin(20) ≈ 0.34 and √3/2 ≈ 0.866, we can calculate:
cos(0) ≈ 0.34 / 0.866 ≈ 0.392
Therefore, for cos(0) to be equal to 0.392, sin(20) must be equal to cos(0 + 30).
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Write an equation for a line perpendicular to y=-4x-2 and
passing through the point (-12,2)
y= ?
show work pls
The equation of the line perpendicular to y = -4x - 2 and passing through (-12, 2) is y = 1/4x + 5.
Given that a line passes through (-12, 2) and is perpendicular to y = -4x - 2. We have to find the equation of this line. To find the equation of the line perpendicular to the given line, we need to know the slope of the line we want to find. The slope of the given line is -4. Since the lines are perpendicular, the slope of the line we want to find will be the negative reciprocal of -4, which is 1/4.
Thus, the equation of the line passing through (-12, 2) and is perpendicular to y = -4x - 2 is:y - 2 = 1/4(x + 12)Simplify by distributing the 1/4:y - 2 = 1/4x + 3
Add 2 to both sides: y = 1/4x + 5
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A piece of blue yarn 5 2/7 yards long a piece of pink yarn is 5 times as long as that. What is total length of the blue and pink yard
The total length of the blue and pink yarn is 31 5/7 yards
What is total length of the blue and pink yardThe blue yarn is given as
Blue = 5 2/7 yards
The length of the pink yarn is 5 times the length of the blue yarn:
So, we have
Length of pink yarn = 5 x 5 2/7 yards
Length of pink yarn = 26 3/7 yards
To find the total length of the blue and pink yarn, we can add their lengths:
Total length = Length of blue yarn + Length of pink yarn
Total length = 5 2/7 yards + 26 3/7 yards
The fractions have the same denominator
So, we have
Total length = 31 5/7
Therefore, the total length of the blue and pink yarn is 31 5/7 yards
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URGENT PLEASE I FORGOT TO STUDY. Unit 1 lesson 11 quadratic functions and equations unit test connections academy. There's 20 questions! If you've already done this test please spare the answers
The two solutions of the equation x2 - 4x + 1 = 0 are x = 2 + √3 and x = 2 - √3.
A quadratic equation is an equation that can be written in the form ax2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to 0. Solving a quadratic equation involves finding the value of x that makes the equation true. This can be done in multiple ways, but the most common method is to use the Quadratic Formula. The Quadratic Formula states that the roots (or solutions) of a quadratic equation can be found using the following formula:
x = [-b ± √(b2 - 4ac)]/2a
For example, consider the equation x2 - 4x + 1 = 0. In this equation, a = 1, b = -4, and c = 1. Plugging these values into the Quadratic Formula gives us:
x = [-(-4) ± √((-4)2 - 4(1)(1))]/2(1)
Simplifying this equation, we get:
x = [4 ± √(16 - 4)]/2
Finally, simplifying further yields the following two solutions:
x = (4 ± √12) /2
x = 2 ±√3
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