the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute, is approximately 0.081 or 8.1%.
How to solve?
To solve this problem, we can use the Poisson distribution, which models the probability of a certain number of events occurring in a fixed interval of time or space, given the expected rate of occurrence.
Let lambda be the expected rate of customer arrivals per minute. If exactly two customers arrive in the first minute, then the expected number of customers to arrive in three minutes is lambda ×3. We can use this expected value to calculate the probability of at least seven customers arriving in three minutes:
P(X ≥ 7 | X ~ ∝(λ×3))
= 1 - P(X ≤ 6 | X ~ ∝(λ×3))
= 1 - ∑[k=0 to 6] (e²(-λ3) ×(lλ3)²k / k!)
where e is the mathematical constant approximately equal to 2.71828, and k! denotes the factorial of k.
To find lambda, we can use the fact that exactly two customers arrive in the first minute. The Poisson distribution assumes that the number of events in a fixed interval of time or space follows a Poisson distribution with parameter lambda, which represents the expected rate of occurrence. Therefore, lambda is equal to the number of customers arriving per minute, which is 2.
Substituting lambda = 2 into the formula, we get:
P(X ≥ 7 | X ~ ∝(2×3))
= 1 - P(X ≤ 6 | X ~ ∝(6))
= 1 - ∑[k=0 to 6] (e²(-6) ×6²k / k!)
Using a calculator or computer software, we can evaluate this expression to get:
P(X ≥ 7 | X ~ ∝(6)) ≈ 0.081
Therefore, the probability that at least seven customers arrive in three minutes, given that exactly two arrive in the first minute, is approximately 0.081 or 8.1%.
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2
5
8
11
14
17
3
9
✓
12
15
✓
18
Total Revenue ($)
1400
1200
1000
100-
600
400-
200-
100
200
300
Quantity Produced
400
500
What does the point (1, 3) represent on the graph?
It shows that for every 3 items produced the revenue is $1.
It shows that the revenue is a constant rate of $1.
It shows that for every 300 items produced the revenue is $100.
It shows that for every 1 item produced the revenue is $3.
The point (1, 3) represent on the graph is that D. It shows that for every 1 item produced the revenue is $3.
What does the graph implyThis chart contains two segments, the upper one depicting the amount of items generated and the lower segment indicating the total profits accumulated from those products.
Point (1, 3) does not align with any measurements in this illustration. Yet according to the determinable alternatives, it seems like the most practical figure to think of is that every product created incurs three dollars in returns. This elucidation resonates with the insights presented in the table as the revenue growths by $300 when the quantity conceived increases by 100 (from 400 to 500).
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What's the awnser for this question I'm really stuck :(
Answer:
120
Step-by-step explanation:
36x94=2700+120+540+24
if the probability of a 22% return is 70% and the probability of a 5% loss is 30%, what is the expected return to the nearest whole percentage? group of answer choices
By answering the presented question, we may conclude that The expected return is therefore 14 percent, which is the nearest entire percentage.
Describe probability.Calculating the likelihood that an event will happen or that a claim is true is the subject of probability theory, a branch of mathematics. A probability is a number between 0 and 1, where 0 denotes how probable an event is to occur and 1 denotes certainty.
An expression of chance or likelihood expressed in numbers is called a probability. Probabilities can be expressed as numbers between 0 and 1, or as percentages between 0% and 100%. the percentage of occurrences out of all equally likely scenarios that result in a specific event in comparison to all possible outcomes.
To compute the anticipated return, we must consider both the likelihood of a 22% return and the probability of a 5% loss. The following formula can be used:
Estimated return = probability of 22% return multiplied by 22% + probability of 5% loss multiplied by (-5%).
Return on investment = 0.7 x 22% + 0.3 x (-5%)
Return on investment = 15.4% - 1.5%
13.9% expected return
As a result, the predicted return to the closest whole percentage is 14 percent.
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(x-2)(x + 8) = 0
X=?
Answer: X = 2, -8
Step-by-step explanation: We need to find the values that make the values in the parenthesis 0. So for the first one, it has to be a 2. Next, to make the second parenthesis a zero, it has to be a -8.
Click and drag the domain and range in the left to their corresponding functions defined in the right. The function that assigns to each pair of positive integers the first integer of the pair The function that assigns to each positive integer its largest decimal digit The function that assigns to a bit string the number of ones minus the number of zeros in the string The function that assigns to each positive integer the largest integer not exceeding the squareroot of the integer The function that assigns to a bit string the longest string of ones in the string
The correct corresponding between the domain and range to their functions are as follows:
The function that assigns to each pair of positive integers the first integer of the pair = Domain: Z+ * Z+ and range: Z+The function that assigns to each positive integer its largest decimal digit = Domain: Z+ and range: {1, 2, 3, 4, 5, 6, 7, 8, 9}The function that assigns to a bit string the number of ones minus the number of zeros in the string = Domain: set of all bit strings, and range: ZThe function that assigns to each positive integer the largest integer not exceeding the square root of the integer = Domain: Z+ and range: Z+The function that assigns to a bit string the longest string of ones in the string = Domain: set of bit strings, and range: {λ, 1, 11, 111, ...}To summarize, each of these functions maps elements from a specific domain to a unique element in a corresponding range. The first two functions map positive integers to positive integers and decimal digits, respectively. The third function maps bit strings to integers, the fourth function maps positive integers to positive integers, and the fifth function maps bit strings to strings of ones.
Understanding the domains and ranges of functions is essential for determining the validity of operations and for ensuring the proper use of mathematical tools in solving problems. The domains and ranges of functions can be used to establish the set of values for which the function is defined and can provide insight into the possible output values of the function.
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on the final pass through the selection sorting algorithm two values are brought over from the unsorted list into the sorted list.
true or false
The statement "on the final pass through the selection sorting algorithm two values are brought over from the unsorted list into the sorted list" is false.
To answer your question regarding the selection sort algorithm: On the final pass through the selection sorting algorithm, only one value is brought over from the unsorted list into the sorted list. So, the statement is false.
In a selection sort algorithm, during each pass, the minimum (or maximum, depending on the order) value in the unsorted part of the list is selected and then swapped with the first unsorted value. This process continues until there is only one value left in the unsorted part of the list, which is then automatically considered sorted.
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15 points for both I need to turn it in tmr
Answer:
7) A
8) C
Step-by-step explanation:
7:
[tex]\frac{2}{3}[/tex]x + 6 = 16 Substitute 15 for x
[tex]\frac{2}{3}[/tex] x [tex]\frac{15}{1}[/tex] + 6 = 16
[tex]\frac{30}{3}[/tex] + 6 = 16
10+ 6 = 16
16 = 16 Checks
8)
3r - 2r - 8 = -8r + 10 Combine like terms
r - 8 = -8r + 10 Subtract r from both sides
r - r - 8 = -8r -r + 10
-8 = -9r + 10 Subtract 10 from both sides
-8 - 10 = -9r + 10 - 10
-18 = -9r Divide both sides by -9
2 = r
Helping in the name of Jesus.
Usted debe resolver los siguientes triángulos rectángulos empleando las
relaciones dadas para funciones trigonométricas, teorema de Pitágoras y teorema
de ángulos interiores de un triángulo. La suma de las medidas de los ángulos
interiores de un triángulo es 180°.
1. a =340 u.l. y α = 30°28
2. c = 458 u.l. y α =65°35'
3. a =202,56 u.l. y b = 337,98 u.l.
4. a = 2.867 u.l. y c = 8.234 u.l.
5. c = 305,02 u.l. y α = 58°10.6'
6. b = 4,310 u.l. y c = 6,320 u.l.
Answer: watch this video it will help a lot
ures+of+the+angles+interiors+of+a+triangle+is+180%C2%B0.+1.+a+%3D340+u.l.+and+%CE%B1+%3D+30%C2%B028+2.+c+%3D+458+u.l.+and+%CE%B1+%3D65%C2%B035%27+3.+a+%3D202.56+u.l.+and+b+%3D+337.98+u.l.+4.+a+%3D+2.867+u.l.+and+c+%3D+8.234+u.l.+5.+c+%3D+305.02+u.l.+and+%CE%B1+%3D+58%C2%B010.6%27+6.+b+%3D+4%2C310+u.l.+and+c+%3D+6%2C320+u.l.&aqs=chrome..69i57j69i64l2.386j0j7&sourceid=chrome&ie=UTF-8#fpstate=ive&vld=cid:af82eef0,vid:i3bjEOA5_zc
Step-by-step explanation:You must solve the following right triangles using the
relations given for trigonometric functions, Pythagorean theorem and theorem
of interior angles of a triangle. The sum of the measures of the angles
interiors of a triangle is 180°.
1. a =340 u.l. and α = 30°28
2. c = 458 u.l. and α =65°35'
3. a =202.56 u.l. and b = 337.98 u.l.
4. a = 2.867 u.l. and c = 8.234 u.l.
5. c = 305.02 u.l. and α = 58°10.6'
6. b = 4,310 u.l. and c = 6,320 u.l.
how do you interpret the statement z = 1.42, p > 0.05?
The interpretation of this statement z = 1.42, p > 0.05 is that there is not enough evidence to reject the null hypothesis at the 0.05 level of significance.
The statement 'z = 1.42, p > 0.05' indicates the results of a statistical test that uses a standard normal distribution, also known as the z-distribution.
The value of z is a standardized score that represents how many standard deviations a sample statistic is from the population mean.
In this case, the value of z is 1.42, which means that the sample statistic is 1.42 standard deviations above the population mean.
The value of p is the probability of obtaining a test statistic as extreme or more extreme than the observed value.
Assuming that the null hypothesis is true.
In this case, the statement 'p > 0.05' means that the p-value is greater than 0.05.
Which interpret that the observed sample statistic is not statistically significant at the 0.05 level of significance.
The null hypothesis is the statement that there is no significant difference between the sample statistic and the population parameter.
That any difference observed is due to chance.
The statement 'z = 1.42, p > 0.05' suggests that the observed difference is not significant and may be due to chance.
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A straight line has a gradient of 6 and passes through the point (3,19).
Work out the equation of the line.
Give your answer in the form y=mx+c
Answer:
y = 6x + 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope ( gradient ) = 6 , then
y = 6x + c ← is the partial equation
to find c substitute (3, 19 ) into the partial equation
19 = 6(3) + c = 18 + c ( subtract 18 from both sides )
1 = c
y = 6x + 1 ← equation of line
Ramada Company produces one golf cart model.
A partially complete table of company costs follows:
Required:
1. Complete the table:
Number of Golf Carts Produced and Sold 1500 Units 2000 Units 2500 Units
Total costs Variable costs $1,040,000 Fixed costs per year $600,000 Total costs $1,640,000
------------- ------------- -------------
Cost per unit Variable cost per unit Fixed cost per unit Total cost per unit ------------- ------------- -------------
Number of Golf Carts Produced and Sold 1500 Units 2000 Units 2500 Units
Total costs $1,640,000 $1,640,000 $1,640,000
Variable costs $1,040,000 $1,386,667 $1,733,333
Fixed costs per year $600,000 $600,000 $600,000
Cost per unit $1,093.33 $820 $656
To calculate the variable cost per unit, we divide the total variable costs by the number of units produced and sold. For example, for 1500 units, the variable cost per unit would be $1,040,000 / 1500 = $693.33.
To calculate the fixed cost per unit, we divide the total fixed costs by the number of units produced and sold. For example, for 1500 units, the fixed cost per unit would be $600,000 / 1500 = $400.
The total cost per unit is the sum of the variable cost per unit and the fixed cost per unit. For example, for 1500 units, the total cost per unit would be $693.33 + $400 = $1,093.33.
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the curvature of the helix r(t) i jbt k (a,b0) is . what is the largest value can have for a given value of b?
The curvature of the helix r(t) i jbt k (a,b0) is |b|.
The largest value it can have for a given value of b is when b is negative, resulting in a sharper curve. Curvature measures the degree of bending of a curve, and in this case, it is proportional to the magnitude of b. So, the larger the value of |b|, the sharper the curve.
However, the sign of b also plays a role in determining the direction of the curvature. When b is negative, the curvature is in the opposite direction of the tangent vector, resulting in a sharper curve. Therefore, the largest value of curvature can be achieved when b is the largest negative value.
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Activity 3: Finding endpoints in a standard normal distribution: Find end points on a standard normal distribution with the given property, and sketch the area. Note that you'll be able to use your answers from this activity in the following activities1. The area between ± z is 0.802. The area between z is 0.903. The area between ± z is 0.954. The area between ± z is 0.985. The area between ± z is 0.99
To find the endpoints in a standard normal distribution with the given properties, we'll use the z-table:
1. The area between ± z is 0.80: Look for 0.4000 in the z-table (0.80/2), which corresponds to a z-score of approximately ±1.28.
2. The area between ± z is 0.90: Look for 0.4500 in the z-table (0.90/2), which corresponds to a z-score of approximately ±1.645.
3. The area between ± z is 0.95: Look for 0.4750 in the z-table (0.95/2), which corresponds to a z-score of approximately ±1.96.
4. The area between ± z is 0.98: Look for 0.4900 in the z-table (0.98/2), which corresponds to a z-score of approximately ±2.33.
5. The area between ± z is 0.99: Look for 0.4950 in the z-table (0.99/2), which corresponds to a z-score of approximately ±2.58.
To summarize, the endpoints on a standard normal distribution with the given areas are approximately ±1.28, ±1.645, ±1.96, ±2.33, and ±2.58.
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QUESTION 1 If an eigenvalue has multiplicity greater than one. list the eigenvalue according to its multiplicity. For example, list an eigenvalue 14 0 0 Find the eigenvalues of the matrix 0 -3 LO-21 with multiplicity two twice. a. =-2 12 = -2, and iz = 4 b.1 = 2.12 = 3, and 13 =-3 c.=2,12=-2 and 13 = -3 o di = -2 12 = 3, and 13 = 4 o el=-3, 12 = 4, and 13 = 6
The eigenvalues of the matrix [0 -3; 1 -2] with multiplicity two twice are 2, 2, and -3.
The matrix given is:
[ 0 -3 ]
[ 1 -2 ]
To find the eigenvalues of this matrix, we need to solve the characteristic equation:
det(A - λI) = 0
where A is the matrix, λ is the eigenvalue, and I is the identity matrix. Substituting the given matrix, we get:
det([0 -3; 1 -2] - λ[1 0; 0 1]) = 0
Simplifying the above expression, we get:
det([-λ -3; 1 -2 - λ]) = 0
Expanding the determinant, we get:
(-λ) * (-2 - λ) - (-3) * 1 = 0
Simplifying the above expression, we get:
λ^2 - 2λ + 3 = 0
Solving the above quadratic equation, we get:
λ = (2 ± √(-8)) / 2 = 1 ± i√2
Since the given matrix has multiplicity two for one of the eigenvalues, the correct answer is (c):
λ = 2 (multiplicity two) and λ = -3.
Therefore, the eigenvalues of the matrix [0 -3; 1 -2] with multiplicity two twice are 2, 2, and -3.
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In a class of 100 students, what is the probability that at least 4 people will share the same birthday?
Enter as a percentage, but do not include the percent sign. Round to 1 decimal place.
Approximately 3.8 (rounded to one decimal place).
How to calculate the probability?To calculate the probability that at least 4 people share the same birthday in a class of 100 students, we can use the complementary probability method. This means finding the probability that no group of 4 or more people share the same birthday and subtracting it from 1.
Step 1: Calculate the probability that everyone has a unique birthday:
P(unique birthdays) = (365/365) * (364/365) * (363/365) * ... * (266/365)
Step 2: Calculate the probability that at least one pair shares the same birthday, but no group of 3 or more:
P(2 people share, rest unique) = 1 - P(unique birthdays)
Step 3: Calculate the probability that no group of 3 or more shares the same birthday:
P(no group of 3 or more) = P(unique birthdays) + C(100, 2) * (1/365) * P(98 people have unique birthdays)
Step 4: Calculate the probability that at least one group of 4 people share the same birthday:
P(at least 4 people share) = 1 - P(no group of 3 or more)
Step 5: Convert the probability to a percentage and round to 1 decimal place.
Using these steps, the probability that at least 4 people share the same birthday in a class of 100 students is approximately 3.8% (rounded to one decimal place). Your answer: 3.8.
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there are 5 performers who are to present their acts at a variety show. one of them insists on being the first act of the evening. if this request is granted, how many different ways are there to schedule the appearances?
Answer:
Step-by-step explanation:
0u
In the EAI sampling problem, the population mean is $71,800 and the population standard deviation is $4000. For n=30, there is a
0.5064 probability of obtaining a sample mean within $500 of the population mean. Use z-table.
a. What is the probability that is within $500 of the population mean if a sample of size 60 is used (to 4 decimals)?
b. Answer part (a) for a sample of size 120 (to 4 decimals).
The probability that is within $500 of the population mean if a sample of size 60 is used is 0.6680.
The probability that is within $500 of the population mean if a sample of size 120 is used is 0.8294
How to calculate the probabilityz = (x - μ)/σ
z1 = (71300 - 71800)/516.3978 = -0.97
z2 = (72300 - 71800)/516.3978 = 0.97
Therefore, we get
P(71300 <= X <= 72300) = P((72300 - 71800)/516.3978) <= z <= (72300 - 71800)/516.3978)
= P(-0.97 <= z <= 0.97) = P(z <= 0.97) - P(z <= -0.97)
= 0.834 - 0.166
= 0.6680
b)
Here, μ = 71800, σ = 365.1484, x1 = 71300 and x2 = 72300. We need to compute P(71300<= X <= 72300). The corresponding z-value is calculated using Central Limit Theorem
z = (x - μ)/σ
z1 = (71300 - 71800)/365.1484 = -1.37
z2 = (72300 - 71800)/365.1484 = 1.37
Therefore, we get
P(71300 <= X <= 72300) = P((72300 - 71800)/365.1484) <= z <= (72300 - 71800)/365.1484)
= P(-1.37 <= z <= 1.37) = P(z <= 1.37) - P(z <= -1.37)
= 0.9147 - 0.0853
= 0.8294
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PLEASE HELP ME SOLVE THE FOLLOWING WITH DETAILED EXPLAINATIONS .GOD BLESS YOU .
1.Find the value of y:
3(2raised to the power -y) all over 16 - 1 =1/2
2.A train passes through a station at a speed of 108km/h.
The length of the station is 120km.
The train takes 7 seconds to completely pass through the station .
Work out the length of the train.
3.Xavier's salary increases by 2% each year.
In 2010 , his salary was £40,100
i) Calculate his salary in 2015 and give your answer to the nearest pound.
ii) In which year did Xavier's salary first greater than £47,500
The value of y is 0.26 and the length of the train is 45m
[tex]3( 2^-^y) / (16 - 1) )= 1/2[/tex]
[tex]2^(^-^y^) = 5/6[/tex]
After applying log on both sides we get
-y × log(2) = log(5/6)
Divide both sides by log 2
y = -log(5/6) / log(2)
We get the value of y
y =- 0.2630344
Speed of train = 108 km/h
= (108×1000) m / (60 × 60) s
= 30 m/s
Length of station = 120 km = 120000 m
Let's assume that the length of the train is L
L/30 + (L + 120)/30 = 7
2L/30 + 4 = 7
2L/30 = 3
L = 45
Hence, the length of train is 45 m
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Find y as a function of t if y" – 4y - 5y = 0, y(0) = 7, y(1) = 8. yt) = Remark: The initial conditions involve values at two points.
The solution to the given differential equation y'' - 4y' - 5y = 0 with initial conditions y(0) = 7 and y(1) = 8 is y(t) = (15/4)[tex]e^-^t[/tex] + (1/4)[tex]e^5^t[/tex].
1. Identify the given equation as a homogeneous linear differential equation with constant coefficients: y'' - 4y' - 5y = 0.
2. Solve its characteristic equation: r² - 4r - 5 = 0, which factors to (r - 5)(r + 1) = 0, yielding roots r₁ = 5 and r₂ = -1.
3. Write the general solution: y(t) = C₁*[tex]e^5^t[/tex] + C₂*[tex]e^-^t[/tex].
4. Apply the initial condition y(0) = 7: 7 = C₁*e^(0) + C₂*e^(0) => 7 = C₁ + C₂.
5. Apply the initial condition y(1) = 8: 8 = C₁*e⁵ + C₂*e⁻¹.
6. Solve the system of linear equations to find C₁ = 1/4 and C₂ = 15/4.
7. Substitute the constants back into the general solution to get the final answer: y(t) = (15/4)[tex]e^-^t[/tex] + (1/4)[tex]e^5^t[/tex].
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In a class of students, the following data table summarizes how many students passed
a test and complete the homework due the day of the test. What is the probability that
a student chosen randomly from the class did not complete the homework?
Passed the test Failed the test
Completed the homework
Did not complete the homework
11
7
3
2
The probability that a student chosen randomly from the class did not complete the homework is 3/23, or approximately 0.13
Define the term probability?A measure of the likelihood or chance that a particular event will occur is called probability. It is represented by a number from 0 to 1.
To find the probability that a student chosen randomly from the class did not complete the homework, we need to use the information given in the table.
We can see from the table that there are a total of 11 + 7 + 3 + 2 = 23 students in the class. Out of these, 3 students did not complete the homework. Therefore, the probability of a student chosen randomly from the class not completing the homework is:
P(not completing homework) = 3 / 23
So, the probability that a student chosen randomly from the class did not complete the homework is 3/23, or approximately 0.13 (rounded to two decimal places).
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The ferris wheel has a diameter of 54 feet and the top for the wheel is 57 feet above the ground.
Two seconds into the ride you would be at the top of the wheel. Assume that y varies sinusoidaly
with time. The ferris wheel competes one revolution in 16-seconds.
a) Graph one period of the function and find the equation
b) At what hieght will you be on the ferris wheel reletive to the ground when: Round to the nearest tenth.
i. t = 10 seconds
ii. t= 18 seconds
iii. t = 43 seconds
The equation of the function is: y = 27sin((2π/16)(t - 2)) + 3.
At t = 10 seconds, you would be about 18.5 feet above the ground. At t = 18 seconds, you would be about 48.5 feet above the ground. And at t = 43 seconds, you would be about 3.0 feet above the ground.
How to Solve the Problem?a) To graph one period of the work, we ought to discover the sufficiency, period, stage move, and vertical move.
The plentifulness is half the remove between the greatest and least values of the work. Since the most elevated point on the wheel is 57 feet over the ground and the least point is 3 feet over the ground, the sufficiency is:
A = (57 - 3)/2 = 27 feet
The period is the time it takes for one total transformation of the wheel. We are told that the ferris wheel completes one transformation in 16 seconds, so:
T = 16 seconds
The stage move is the flat move of the work. Since the wheel is at the most elevated point when t = 2 seconds, the work is moved to the cleared out by 2 seconds:
C = 2 seconds
The vertical move is the normal esteem of the work. Since the most reduced point of the wheel is 3 feet over the ground, the vertical move is:
D = 3 feet
In this manner, the condition of the work is:
y = 27sin((2π/16)(t - 2)) + 3
b) To find the tallness at different times, we fair have to be plug within the values of t into the condition we found in portion a) and circular to the closest tenth.
i. t = 10 seconds
y = 27sin((2π/16)(10 - 2)) + 3
y ≈ 18.5 feet
ii. t = 18 seconds
y = 27sin((2π/16)(18 - 2)) + 3
y ≈ 48.5 feet
iii. t = 43 seconds
y = 27sin((2π/16)(43 - 2)) + 3
y ≈ 3.0 feet
Subsequently, at t = 10 seconds, you'd be almost 18.5 feet over the ground. At t = 18 seconds, you'd be almost 48.5 feet over the ground. And at t = 43 seconds, you'd be around 3.0 feet over the ground.
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Assume that the population proportion is 0.57. Compute the standard error of the proportion for sample sizes of n = 100, 200, 500, and 1000. What can you say about the size of the standard error of the proportion as the sample size is increased?
As the sample size increases, the standard error of the proportion decreases. This means that the precision of the sample proportion as an estimate of the population proportion improves with larger sample sizes.
The standard error of the proportion, you can use the following formula:
Standard Error (SE) = √(p(1-p)/n)
where p is the population proportion and n is the sample size.
For n = 100:
SE = √(0.57 × (1-0.57) / 100) = √(0.2451 / 100) = 0.0495
For n = 200:
SE = √(0.57 × (1-0.57) / 200) = √(0.2451 / 200) = 0.0350
For n = 500:
SE = √(0.57 × (1-0.57) / 500) = √(0.2451 / 500) = 0.0221
For n = 1000:
SE = √(0.57 × (1-0.57) / 1000) = √(0.2451 / 1000) = 0.0156
Therefore, As the sample size increases, the standard error of the proportion decreases. This means that the precision of the sample proportion as an estimate of the population proportion improves with larger sample sizes.
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find sin(2x), cos(2x), and tan(2x) from the given information. tan(x) = − 1 5 , cos(x) > 0
The value of trignometric function sin(2x) is 2√24/25, cos(2x) is -23/25 and tan(2x) is -10/9
Using the given information, we can determine that sin(x) = -√24/5 and cos(x) = √1-24/25 = √1/25 = 1/5.
To find sin(2x), we can use the double angle formula: sin(2x) = 2sin(x)cos(x) = 2(-√24/5)(1/5) = -2√24/25.
To find cos(2x), we can use the double angle formula: cos(2x) = cos²(x) - sin²(x) = (1/25) - 24/25 = -23/25.
To find tan(2x), we can use the identity: tan(2x) = (2tan(x))/(1-tan²(x)) = (2(-1/5))/(1-1/25) = -10/9.
In summary, sin(2x) = -2√24/25, cos(2x) = -23/25, and tan(2x) = -10/9. These calculations were made using the double angle formula and the identity for tan(2x).
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. What is the sum of −5x^2 + 8x – 3 and 6x^2 − 4x + 9 ?
Answer:
x² + 4x + 6
Step-by-step explanation:
- 5x² + 8x - 3 + 6x² - 4x + 9 ← collect like terms
= (- 5x² + 6x²) + (8x - 4x) + (- 3 + 9)
= x² + 4x + 6
Answer:
x^2+4x+6
Step-by-step explanation:
-5x^2+6x^2+8x-4x-3+9
=x^2+4x+6
What is the IQR of the boxplot?
Answer: 16
Step-by-step explanation: The IQR is Q3 - Q1.
In this case, it is 55 - 39, which equals 16
the major problem with point estimation is that it group of answer choices provides only a single point in its estimate. cannot be utilized to estimate population parameters. does not take sampling error into account. cannot be utilized with sample data.
The major problem with point estimation is that it provides only a single point in its estimate. This means that it does not take into account the possible variability or uncertainty that comes from sampling error when estimating population parameters.
The major problem with point estimation is that it provides only a single point in its estimate, which may not accurately represent the true population parameter. This is because point estimation relies on a single sample to estimate the parameter, and does not take into account the variability that could result from different samples.
Additionally, point estimation cannot be utilized to estimate population parameters directly, as it only provides an estimate for the specific sample used. However, point estimation can still be useful for obtaining rough estimates of parameters, particularly when more precise methods are not available or feasible. It is important to keep in mind that point estimation is subject to sampling error, which can affect the accuracy of the estimate. To minimize this error, it is often necessary to use larger sample sizes or employ other sampling techniques such as stratified sampling or random sampling.
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data show that the weight of an offensive linesman may be any weight between 200 and 350 pounds. the distribution of weight is based on aa. continuous random variableb. discrete random variablec. qualitative variabled. all the above
The distribution of weight is based on a continuous random variable.
What is Continuous Random Variable?
In statistics, a continuous random variable can take on any value within a certain range, as opposed to a discrete variable, which can only take on a finite number of values.
Qualitative variables are categorical variables that do not have a numerical value, but instead represent characteristics or qualities of a population or sample.
Therefore, the weight of an offensive linesman is an example of a continuous random variable.
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Two lines meet at a point that is also the vertex of an angle. Set up and
solve the appropriate equations to determine x and y.
x+ 32 = 90
x= 58°
y + x = 90°
y= 90-58
y =32°
5. to build the confidence interval for the mean of the delivery times from the data sheet, what is the appropriate probability table to use?
The confidence level is usually set at 95%, which corresponds to a significance level of 0.05.
What is the probability?Probability means to estimate or calculate how likely or "probable" something is to happen. The possibility of an event can be described with words like "certain", "impossible" or "probable". In mathematics, probabilities are always written as fractions, decimals, or percentages with values between 0 and 1.
A probability table is not normally used to construct a confidence interval for mean delivery times from a data sheet. Instead, you use statistical methods such as the t-distribution or z-distribution, depending on the sample size and whether or not the population standard deviation is known.
If the population standard deviation is known, you can use the z distribution to construct a confidence interval for the mean. However, if the population standard deviation is not known, as is often the case, the t-distribution must be used.
To use the T distribution, you must determine the degrees of freedom for your sample. The degrees of freedom are equal to the sample size minus one. If you have degrees of freedom, you can look up the appropriate t-value in a t-table or use statistical software to calculate it.
You can then create a confidence interval using the following formula:
Confidence interval for the mean = sample mean ± (t-value x standard error)
The standard error is calculated by dividing the sample standard deviation by the square root of the sample size. The confidence level is usually set at 95%, which corresponds to a significance level of 0.05.
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In Chapter 1 of the course textbook, you were introduced to the Academic Performance Index (API) measure used by the government of California to measure school performance. For the remaining questions, we drew a different random sample of 20 schools than the sample discussed in the text. For this sample: • the sum of the API scores, L:21 Y;, is 16,602 • the sum of squared deviations from the sample mean, L^l (Y; – Y)2, is 109,497.80. Use this information to answer the following questions. It is strongly recommended that you write down your answers to each question as you may need them for a later question. Question 16 1 pts What is the sample mean API score? Please round your answer to two decimal places. Question 17 1 pts What is the sample variance? Please round your answer to two decimal places.
Question 16:
The sample mean API score is given by the formula:
Y = L: Y; / n
where Y; represents the API score for each school and n is the sample size. Substituting the given values, we get:
Y = 16,602 / 20 = 830.10
Therefore, the sample mean API score is 830.10 (rounded to two decimal places).
Question 17:
The sample variance is given by the formula:
s² = L^l (Y; – Y)² / (n – 1)
where Y; represents the API score for each school, Y is the sample mean, n is the sample size, and L^l denotes the summation symbol. Substituting the given values, we get:
s² = 109,497.80 / (20 – 1) = 5,768.31
Therefore, the sample variance is 5,768.31 (rounded to two decimal places).
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