The required probability is P(T > 16.8) = e^(-λ*16.8) = e^(-16.8/1) = e^(-16.8) = 3.22*10^(-8).Hence, the required probability is e^(-16.8).
Given that priority boarding for a scheduled flight is announced to start, the time it takes for a random passenger with priority boarding to line up is described by an exponential probability distribution with expectation 1/lambda minutes. We assume that the time two random passengers spend queuing is independent of each other. It should be 56 passengers on a small scheduled flight to the north, 5 of whom have prioritized boarding.
The time it takes from ordinary boarding being announced to a random passenger without priority boarding queuing is described by the same probability distribution as above. We still assume that the time two random passengers spend queuing is independent of each other.
We are supposed to find the probability that it takes more than 16.8 minutes from ordinary boarding has started until all ordinary passengers have lined up for boarding. Express the answer as a function of λ. Solution: We can apply the Poisson distribution to calculate the probability that all ordinary passengers have lined up for boarding. This is because Poisson distribution models the number of arrivals in a given period of time, given the average arrival rate, λ.The number of passengers who are waiting at any given moment follows a Poisson distribution with an expected value of λ, the rate parameter.If the time it takes for a passenger to get into the line is exponential with an expectation of 1/λ minutes, then λ passengers arrive every minute.
Hence, the time between the arrivals of two passengers is exponential with a mean of 1/λ minutes, which implies that the probability density function (pdf) of a single time duration between two consecutive arrivals is:$$f_{T}(t)=\lambda e^{-\lambda t}, \ \ t \in [0,\infty)$$For any fixed t, the probability that it takes more than t time units to get a passenger in the queue is obtained by integrating the pdf over the corresponding interval, i.e. $$P(T>t)=\int_{t}^{\infty}\lambda e^{-\lambda u}du=e^{-\lambda t}, \ \ t \in [0,\infty)$$
Therefore, the probability that it takes more than T seconds to get a passenger in the queue is given by P(T>t) = e^(-λT), where T is the time in seconds.We need to find the probability that it takes more than 16.8 minutes from ordinary boarding has started until all ordinary passengers have lined up for boarding. Let the random variable T denote the time from when ordinary boarding was announced until the last ordinary passenger queued.
So, the required probability is P(T > 16.8) = e^(-λ*16.8) = e^(-16.8/1) = e^(-16.8) = 3.22*10^(-8).Hence, the required probability is e^(-16.8).
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i need help with this i did it so could you tell me if it's correct if it's not can you help me out
The answer is: Logan's rope is longer than Sam's rope.
What is fraction?A number that represents a part of a whole or a ratio between two quantities, written as a numerator over a denominator. It consists of a numerator (top) and a denominator (bottom) separated by a fraction bar. For example, 1/2 represents one-half of a whole or the ratio of one to two.
Part A:
Brittney's rope is shorter than Sam's rope because it is 4/5 as long as Sam's rope.
Logan's rope is longer than Sam's rope because it is 1 1/4 times as long as Sam's rope.
Holly's rope is equal to Sam's rope because it is 8/8 (which simplifies to 1) as long as Sam's rope.
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+ -/7 points SPreCalc7 2.4.039 + Ask Your Teacher My Notes 13. An object is dropped from a high cliff, and the distance (in feet) it has fallen after t seconds is given by the function d(t) = 16t2. Complete the table to find the average speed during the given time intervals. d(b) - d(a) t = a Average speed t = b 9 9.5 9.1 9 9.01 9.001 9.0001 9 Use the table to determine what value the average speed approaches as the time intervals get smaller and smaller. Is it reasonable to say that this value is the speed of the object at the instant t = 9? Explain. From the table it appears that the average speed approaches ft/s (rounded to the nearest whole number) as the time intervals get smaller and smaller. It reasonable to say that this number is the --Select-- speed of the object at the instant t = 9. Submit Answer
The average speed during a given time interval can be found by calculating the change in distance over the change in time, or (d(b) - d(a))/(b-a). In this case, we can use the given function d(t) = 16t^2 to find the distance at each given time. It is reasonable to say that this value is the speed of the object at the instant t = 9 because as the time interval approaches zero, the average speed approaches the instantaneous speed at that moment.
For the first time interval, t = a = 9 and t = b = 9.5:
d(a) = 16(9)^2 = 1296
d(b) = 16(9.5)^2 = 1444
Average speed = (1444 - 1296)/(9.5 - 9) = 148/0.5 = 296 ft/s
For the second time interval, t = a = 9 and t = b = 9.1:
d(a) = 16(9)^2 = 1296
d(b) = 16(9.1)^2 = 1324.96
Average speed = (1324.96 - 1296)/(9.1 - 9) = 28.96/0.1 = 289.6 ft/s
For the third time interval, t = a = 9 and t = b = 9.01:
d(a) = 16(9)^2 = 1296
d(b) = 16(9.01)^2 = 1300.9616
Average speed = (1300.9616 - 1296)/(9.01 - 9) = 4.9616/0.01 = 496.16 ft/s
For the fourth time interval, t = a = 9 and t = b = 9.001:
d(a) = 16(9)^2 = 1296
d(b) = 16(9.001)^2 = 1296.288016
Average speed = (1296.288016 - 1296)/(9.001 - 9) = 0.288016/0.001 = 288.016 ft/s
For the fifth time interval, t = a = 9 and t = b = 9.0001:
d(a) = 16(9)^2 = 1296
d(b) = 16(9.0001)^2 = 1296.0288016
Average speed = (1296.0288016 - 1296)/(9.0001 - 9) = 0.0288016/0.0001 = 288.016 ft/s
As the time intervals get smaller and smaller, the average speed approaches 288 ft/s.
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someone help me plsss
The Answer:
The answer to the equation that Clare gets is:
X1= -3/2 + 7/2i , X2= -3/2 - 7/2i.
The Explanation:
4x^2+12x+58=0
2x^2+6x+29=0
a=2, b=6, c=29
Khaled calculates the mean of five different prime numbers. His answer is an integer, what is the smallest possible integer he could have obtained.
Answer:
6
Step-by-step explanation:
[tex] \frac{2 + 3 + 5 + 7 + 13}{5} = \frac{30}{5} = 6[/tex]
Relative to the origin O, the position vectors of two points A and B are a and b respectively. b is a unit vector and the magnitude of a is twice that of b. The angle between a and b is 60°. Show that [a×[ob + (1-o)a] =√k, where k is a constant to be determined.
Answer:
|a × [ob + (1 - o)a]| = √(7 - 8o(a · o) - 8(a · o)^2)
where k = 7 - 8o(a · o) - 8(a · o)^2.
Step-by-step explanation:
Given the position vectors of two points A and B as a and b respectively, where b is a unit vector, and the magnitude of a is twice that of b, we are asked to show that:
|a × [ob + (1-o)a]| = √k,
where k is a constant to be determined.
We can begin by expanding the vector inside the cross product:
ob + (1 - o)a = ob + a - oa
Since b is a unit vector, we can write:
ob = b - o
Substituting this into the previous equation, we get:
ob + (1 - o)a = b - o + a - oa = b + (1 - o)a - oa
Next, we can use the vector cross product formula:
|a × b| = |a||b|sinθ
where θ is the angle between a and b.
We are given that the angle between a and b is 60°, so we can substitute this value into the formula:
|a × b| = |a||b|sin60° = (2|b|)(1)(√3/2) = √3
Now we can calculate the cross product of a and the vector we just derived:
a × [ob + (1 - o)a] = a × (b + (1 - o)a - oa)
= a × (b + a - oa)
= a × b + a × a - a × oa
Since b is a unit vector, we know that a × b is a vector perpendicular to both a and b, and therefore perpendicular to the plane containing a and b. The vector a × a is 0 since the cross product of a vector with itself is 0. Finally, we can use the vector triple product to simplify a × oa:
a × oa = (a · a)o - (a · o)a = |a|^2 o - (a · o)a
Since |a| is twice |b|, we have:
|a|^2 = 4|b|^2 = 4
Substituting this back in, we get:
a × oa = 4o - (a · o)a
Putting it all together, we have:
a × [ob + (1 - o)a] = a × b + 4o - (a · o)a
Now we can take the magnitude squared of both sides:
|a × [ob + (1 - o)a]|^2 = (a × b + 4o - (a · o)a) · (a × b + 4o - (a · o)a)
Expanding the dot product, we get:
|a × [ob + (1 - o)a]|^2 = |a × b|^2 + 16o^2 + |a|^2(o · o) - 8o(a · o)b + 8(a · o)(a × b) - 2(a · o)^2|a|^2
Substituting the values we derived earlier, we get:
|a × [ob + (1 - o)a]|^2 = 3 + 16o^2 + 4(o · o) - 8o(a · o) + 0 - 2(a · o)^2(4)
= 7 - 8o(a · o) - 8(a · o)^2
Now we need to find the value of k such that the left-hand side equals k:
|a × [ob + (1 - o)a]|^2 = k
Using the vector triple product again, we can simplify the left-hand side as:
|a × [ob + (1 - o)a]|^2 = |a|^2|ob + (1 - o)a|^2 - ((a · [ob + (1 - o)a])^2)
Since we know that the magnitude of a is twice that of b, we have:
|a|^2 = 4|b|^2 = 4
Substituting this back in, we get:
|a × [ob + (1 - o)a]|^2 = 4|ob + (1 - o)a|^2 - ((a · [ob + (1 - o)a])^2)
Now we can substitute the expanded expression for ob + (1 - o)a:
|a × [ob + (1 - o)a]|^2 = 4|b + (1 - o)a|^2 - ((a · [b + (1 - o)a - oa])^2)
= 4|b|^2 + 8|b|(1 - o)(a · b) + 4(1 - o)^2|a|^2 - ((a · b + (1 - o)(a · b) - (a · o)(a · b))^2)
= 4 + 8(1 - o)(a · b) + 4(1 - o)^2(4) - ((a · b + (1 - o)(a · b) - (a · o)(a · b))^2)
= 28 - 8o(a · b) - 8(a · o)^2
Substituting this back into the previous equation, we get:
28 - 8o(a · b) - 8(a · o)^2 = k
Therefore, we have:
|a × [ob + (1 - o)a]| = √(28 - 8o(a · b) - 8(a · o)^2) and
k = 28 - 8o(a · b) - 8(a · o)^2
Hope this helps! Sorry if it's wrong! If you need more help, ask me! :]
-7(2a - 1) - 11 as simplify the expression completely
Answer:-14a-4
Step-by-step explanation:
Answer: Expanding the expression, we get:
-7(2a - 1) - 11 = -14a + 7 - 11
Combining like terms, we get:
-14a - 4
Therefore, the simplified expression is -14a - 4.
Enjoy!
FARMING A dairy farmer has 2650 dairy cows on his farm. If each dairy cow produces 2320 gallons of milk per year, how much milk does the dairy farm yield in one year?
The dairy farm yields 6,158,000 gallons of milk in one year, assuming that each cow produces 2320 gallons per year.
What is total amount?The term "total amount" refers to the complete or full quantity or sum of something. It is the complete amount of something without any deductions or subtractions.
According to question:To calculate the total amount of milk the dairy farm yields in one year mathematically, we need to multiply the number of dairy cows by the amount of milk each cow produces in a year.
Let's represent the number of dairy cows as "C" and the amount of milk produced per cow per year as "M". Using this notation, we can write:
Total amount of milk produced in one year = Number of cows x Amount of milk per cow
= C x M
Substituting the given values, we have:
C = 2650 (number of dairy cows)
M = 2320 gallons (amount of milk per cow per year)
Total amount of milk produced in one year = 2650 x 2320
= 6,158,000 gallons
Therefore, the dairy farm yields 6,158,000 gallons of milk in one year, assuming that each cow produces 2320 gallons per year.
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Answer:
6.158 x 10^6
Step-by-step explanation:
Converted answer above to scientific notation.
The line plot shows the distances ten students walk to school. What is the difference between the longest distance a student walks and the shortest distance a student walks?
By deducting the value of the shortest distance from the value of the longest distance on the line plot, it is possible to determine the difference between the longest and shortest distances a student has walked to get to school.
We must look at the provided line plot to ascertain the difference between the longest and shortest distances a student walks to get to school. Ten pupils were tracked across various distances using a line plot. The location of each student is indicated by a "X" on the map.
Just looking for the X with the highest and lowest frequency will yield the longest and shortest lengths. According to the line plot, the distances at which Xs occur most frequently are 2 miles away and 0.5 miles away, respectively. As a result, there is a 1.5 mile discrepancy between the student's maximum walking distance (2 miles) and their shortest walking distance (0.5 miles).
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What is the equation of the line parallel to the given line
with an x-intercept of 4?
y = x+
Answer:
y = 4x - 16
Step-by-step explanation:
Parallel lines have the same slope. Find slope using the points (-3, -3) and (-1, 5)
slope = m = (5 - -3) / (-1 - -3) = 8/2 = 4
y = mx + b find b using the point (4, 0), the x-intercept of the parallel line
0 = 4(4) + b
b = -16
equation of the parallel line:
y = 4x - 16
Chapter 5 Lesson 1 Adding and Subtracting Polynomials
1. Quadratic monomials.
2. Biquadratic five-term polynomials.
3. Quadratic trinomials.
4. x³ + 3x² - 5x - 4
5. -[tex]x^{5}[/tex] + 4[tex]x^{4}[/tex] +2x³ + 2x - 7
6. - x² + 5x + 9
7. y² - 3y - 9
8. 5(x³ + x)
9. 2x² + 2x -5
What are polynomials?Algebraic expressions called polynomials only have non-negative integer powers for their variables. A polynomial is, for instance, 5x² - x + 1. The polynomial 3x³ + 4x + 5/x + 6[tex]x^{3/2}[/tex] is not a polynomial since one of the powers of "x" is a fraction and the other is negative.
Expressions with one or more terms that have a non-zero coefficient are called polynomials. Variables, exponents, and constants make up polynomial terms. The "leading term" refers to the first term of the polynomial in standard form.
Here in the given question,
We can see the highest degree of the variable and we can determine the name of each polynomial.
Likewise, we can just arrange the expressions as per the highest value of the power of the variable.
And simplify the expression by adding or subtracting the like terms.
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The ratio of the cost of one metre of polyester fabric to the cost of one metre
of cotton fabric is 2: 7
Complete the table
The cost of one metre of cotton fabric is £ 7. The cost of one metre polyester fabric is £ 2.
The ratio of the cost of one metre of polyester fabric to the cost of one metre of cotton fabric is 2: 7.
1 m polyester / 1 m cotton = 2 / 7
1 m cotton = 7/2 × 1 m polyester
for 2 m of polyester fabric, the cost is £ 4
for 1 m of polyester fabric, the cost is £ 4/2 = £ 2
for 1 m of cotton fabric = 7/2 × 1 m polyester fabric = 7/2 × £2 = £ 7
for 1 m of cotton fabric, the cost is £ 7
For 2m, polyester fabric 2 × £2 = £ 4
cotton fabric 2 × £7 = £ 14
For 6m, polyester fabric 6 × £2 = £ 12
cotton fabric 6 × £7 = £ 42
For 8m, polyester fabric 8 × £2 = £ 16
cotton fabric 8 × £7 = £ 56
For 9m, polyester fabric 9 × £2 = £ 18
cotton fabric 9 × £7 = £ 63
The complete table
2m 6m 8m 9m
polyester fabric £ 4 £ 12 £ 16 £ 18
cotton fabric £ 14 £ 42 £ 56 £ 63
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please help :((I need help
Answer:
See attached graph for the two functions
y = cos(x)
y = 0.5
Solution set for cos(x) i.e. the values of x for which cos(x) = 0.5 in the interval 0 < x < 2π are
{π/3, 5π/3)
or
{1.05, 5.24} in decimal
Step-by-step explanation:
I moved the original horizontal up to y = 0.5
The solutions to the two equations are where the two functions intersect
There are two intersection in the interval 0 ≤ x ≤ 2π and are at the points labeled A and B
The two points can be obtained by setting
cos(x) = 0.5 and solving for x
cos(x) = 0.5
=> x = cos⁻¹ (0.5)
= 60° and 300° in the range 0 ≤ x ≤ 2π where 2π = 360°
In terms of π,
Since π radians = 180°, 1° = π/180 radians
60° = π/180 x 60 = π/3 radians
300° = π/180 x 300 = 5π/3 radians
Therefore the solutions to cos(x) = 0.5 are
x = π/3 and x = 5π/3
The solution set is written as {π/3, 5π/3}
In decimal
π/3 = 1.04719 ≈ 1.05
5π/3 = 5.23598 ≈ 5.24
Solution set in decimal: {1.05, 5.24}
Please help !!!! I need to the answers asap
The possible rational roots of the polynomial are ±1/2, ±1, ±3/2, ±3, ±9/2, ±9 while the actual roots are 1, -3, 3/2
What are the possible and real rational rootsTo find the possible rational roots of the polynomial 2x^3 + x^2 - 12x + 9 = 0, we can use the rational root theorem. According to the theorem, if a polynomial with integer coefficients has a rational root p/q (where p and q are integers with no common factors other than 1), then p must be a factor of the constant term (in this case, 9) and q must be a factor of the leading coefficient (in this case, 2).
The factors of 9 are ±1, ±3, and ±9, and the factors of 2 are ±1 and ±2. Therefore, the possible rational roots of the polynomial are:
±1/2, ±1, ±3/2, ±3, ±9/2, ±9
We can now use synthetic division or long division to check which of these possible roots are actual roots of the polynomial. After checking, we find that the real rational root of the polynomial are x = 1, -3, 3/2
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A shopkeeper bought 50 pangas and 30 jembes from a wholesaler A for sh 4260. Had he bought half as many jembes and 5pangas less,he would have sh 1290 less. Had the shopkeeper bought from wholesaler B,he would have paid 25% more for a pangas and 15 %less for a jembe. How much would he have saved if he had bought the 50 pangas and 30 jembes from wholesaler B
The shopkeeper would have saved 4756.25 - 4260 = 496.25 shillings.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept. We have a graph.
Let the cost of one panga be x and one jembe be y.
From the given information, we can form the following equations:
50x + 30y = 4260 --- Equation 1
25x/2 + (30/2 - 5)y = 2970 --- Equation 2
50(1.25)x + 30(0.85)y = total cost from wholesaler B --- Equation 3
Simplifying equation 2:
25x/2 + 10y - 5y = 2970
25x/2 + 5y = 2970
25x + 10y = 5940
Simplifying equation 3:
62.5x + 25.5y = total cost from wholesaler B
To solve for x and y, we can use any method of our choice. For simplicity, we will use elimination:
Multiplying equation 1 by 5:
250x + 150y = 21300 --- Equation 4
Multiplying equation 2 by 2:
25x + 20y = 5940 --- Equation 5
Subtracting equation 5 from equation 4:
225x + 130y = 15360
Substituting the value of y from equation 5:
225x + 130(297 - 2.5x) = 15360
225x + 38610 - 325x = 15360
-100x = -23250
x = 232.5
Substituting the value of x in equation 1:
50(232.5) + 30y = 4260
y = 85
Therefore, the cost of one panga is 232.5 shillings and the cost of one jembe is 85 shillings.
To find out how much the shopkeeper would have saved if he had bought from wholesaler B, we need to calculate the total cost from wholesaler B:
50(1.25)(232.5) + 30(0.85)(85) = 4756.25
The total cost from wholesaler A was 4260 shillings.
Therefore, the shopkeeper would have saved 4756.25 - 4260 = 496.25 shillings.
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Graph the function. State the domain and range. f(x) =[x-2]
Answer: Domain: All x-values
Range: All y-values
Step-by-step explanation:
Which property of equality could be used to solve -3x=348
By solving the equation -3x = 348, we find that the value of x is -116.
The property of equality that could be used to solve -3x = 348 is the multiplication property of equality, which states that if we multiply both sides of an equation by the same non-zero number, the equation remains equivalent. In this case, we can divide both sides of the equation by -3 to isolate x and solve for it.
Using the multiplication property of equality, we can multiply both sides by -1/3:
(-1/3) * (-3x) = (-1/3) * 348
Simplifying:
x = -116
Therefore, the solution to the equation -3x = 348 is x = -116.
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"A construction company has a number of trucks designed to haul different amounts. The line plot displays the weight each truck can haul. If all the trucks are working at the same time, how many tons can the trucks carry?" I would also like a explanation too please
The line plot shows that the construction company has a number of trucks, each of which is designed to haul different amounts of weight.
If all of these trucks are working at the same time, we can calculate how many tons the trucks can carry in total. In order to do this, we need to look at the range of weight each truck is capable of carrying, and then add all of these numbers together.
In order to determine how many tons the trucks can carry, we need to use the information provided by the line plot. The line plot displays the weight each truck can haul, which is given in pounds. We need to convert the weight in pounds to tons in order to find the total weight that the trucks can carry.
To do this, we can use the following conversion factor:1 ton = 2000 poundsWe can use this conversion factor to convert the weight of each truck from pounds to tons. Once we have done this, we can add up the weights of all the trucks to find the total weight that the trucks can carry. Here are the steps:
Step 1: Convert the weight of each truck from pounds to tons Truck 1: 6,000 pounds ÷ 2,000 pounds/ton = 3 tons Truck 2: 9,000 pounds ÷ 2,000 pounds/ton = 4.5 tons Truck 3: 8,000 pounds ÷ 2,000 pounds/ton = 4 tons Truck 4: 10,000 pounds ÷ 2,000 pounds/ton = 5 tons Truck 5: 11,000 pounds ÷ 2,000 pounds/ton = 5.5 tons Truck 6: 9,500 pounds ÷ 2,000 pounds/ton = 4.75 tons
Step 2: Add up the weights of all the trucks3 + 4.5 + 4 + 5 + 5.5 + 4.75 = 26.75 tons. The trucks can carry 26.75 tons in total.
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solve the equation negative 2y plus 6 equals negative 12
Answer:
y = -9
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
since 2y is adding to positive 6 we take 6 to the right side where there its like term 12. we subtract 6 from 12 which is giving us 6. we are remaining with 2y=6 we divide both sides by 2 giving us y=3
A line has a slope of 1/ 6 and passes through the point (–6,6). Write its equation in slope-intercept form.
Answer:
Step-by-step explanation:
The equation of the line with a slope of 1/6 passes through the point (-6, 5) is y=(1/6)x+6.
What is the equation of a line?
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is y-intercept.
Given that a line with a slope of 1/6 passes through the point (-6, 5). Therefore, we can write,
y = mx + c
Substitute the values,
5 = (1/6)(-6) + C
5 = -1 + C
5 + 1 = C
C = 6
Hence, the equation of the line with a slope of 1/6 passes through the point (-6, 5) is y=(1/6)x+6.
Answer:
y = (1/6)x + 7
Step-by-step explanation:
The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
We know that the line has a slope of 1/6 and passes through the point (-6, 6). To find the y-intercept, we can substitute the values of the point into the equation and solve for b:
y = mx + b
6 = (1/6)(-6) + b
6 = -1 + b
b = 7
Now that we know the slope and y-intercept, we can write the equation of the line in slope-intercept form:
y = (1/6)x + 7
Therefore, the equation of the line in slope-intercept form is y = (1/6)x + 7.
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Which of the following shapes has 2 circular bases and a curved surface?
Right circular cone
Right circular cylinder
Right pyramid
Sphere
Answer: B. A right circular Cylinder
Step-by-step explanation:
A sample has the following data:
[32.564, 7.57, 21.815, −13.971, −15.224]
We know that the sample is from a normally distributed random variable, but we dont know the expected value or the variance
a)Calculate the sample variance
b)Calculate a two-sided confidence interval for the variance with a confidence level of 0.98
a) Sample Variance = 521.646
b)Two-sided confidence interval for the variance with a confidence level of 0.98 is (5.545, 10029.794).
a) To calculate the sample variance, you will first need to calculate the sample mean. The sample mean is calculated by summing all the observations in the sample and dividing by the number of observations. For this sample, the mean is:
Mean = (32.564 + 7.57 + 21.815 − 13.971 − 15.224) / 5 = 5.168
Next, you will need to calculate the sum of squared deviations from the mean. This is done by subtracting the mean from each observation and squaring the result, and then summing all of the results:
Sum of Squared Deviations = (32.564 - 5.168)^2 + (7.57 - 5.168)^2 + (21.815 - 5.168)^2 + (-13.971 - 5.168)^2 + (-15.224 - 5.168)^2 =
= 1564.939
Finally, you can calculate the sample variance by dividing the sum of squared deviations by the number of observations minus one:
Sample Variance = 1564.939 / (5 - 1) = 521.646
b) To calculate a two-sided confidence interval for the variance with a confidence level of 0.98, you will need to find the critical value from the Chi-squared distribution with a degrees of freedom equal to the number of observations in the sample minus one. For this sample, the degrees of freedom is 4.
The critical value for this degrees of freedom at the given confidence level is 8.37.
The lower bound of the confidence interval is:
Lower bound = (521.646 / 8.37) * (1 - 0.98) = 5.545
The upper bound of the confidence interval is:
Upper bound = (521.646 / 8.37) * (1 + 0.98) = 10029.794
Therefore, the two-sided confidence interval for the variance with a confidence level of 0.98 is (5.545, 10029.794).
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The sample space for tossing a coin 3 times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
Determine P(2 tails).
12.5%
37.5%
50%
75%
The value οf P(2 tails) is 37.5%, the cοrrect οptiοn is B.
What is the prοbability?Prοbability refers tο a pοssibility that deals with the οccurrence οf randοm events.
The prοbability οf all the events οccurring need tο be 1.
The fοrmula οf prοbability is defined as the ratiο οf a number οf favοurable οutcοmes tο the tοtal number οf οutcοmes.
P(E) = Number οf favοurable οutcοmes / tοtal number οf οutcοmes
We are given that;
The sample space= {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Nοw,
The sample space fοr tοssing a cοin 3 times is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}, where H represents heads and T represents tails.
Tο determine P(2 tails), we need tο cοunt the number οf οutcοmes in which there are 2 tails, and divide that by the tοtal number οf οutcοmes:
Number οf οutcοmes with 2 tails: There are three οutcοmes with 2 tails: TTH, THT, and HTT.
Tοtal number οf οutcοmes: There are eight οutcοmes in tοtal.
P(2 tails) = number οf οutcοmes with 2 tails / tοtal number οf οutcοmes = 3/8 = 0.375, which is equivalent tο 37.5%.
Therefοre, the prοbability the answer will be 37.5%.
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Miguel and Kala each opened a savings account today. Miguel opened his account with a starting amount of $ 320 , and he is going to put in $ 85 per month. Kala opened her account with a starting amount of $ 820 , and she is going to put in $ 35 per month. Let x be the number of months after today.
a)
For each account, write an expression for the amount of money in the account after months.
(b)
Write an equation to show when the two accounts would have the same amount of money.
Answer:
Miguel's account: M(x) = 320 + 85x
Kala's account: K(x) = 820 + 35x
b) To find when the two accounts would have the same amount of money, we need to set M(x) equal to K(x) and solve for x:
320 + 85x = 820 + 35x
Simplifying the equation, we get:
50x = 500
Dividing both sides by 50, we get:
x = 10
Therefore, the two accounts would have the same amount of money after 10 months.
use the distance formula and the slope of segments to identify the type of quadrilateral
T(-3,-3), U(4, 4), V(0, 6), W(-5, 1)
The given quadrilateral is a parallelοgram and a kite.
What are quadrilaterals?Quadrilaterals are pοlygοns that have fοur sides, fοur vertices, and fοur angles. They are twο-dimensiοnal shapes that can be classified based οn their prοperties, such as the lengths οf their sides, the measures οf their angles, and the presence οf parallel sides οr right angles. Sοme cοmmοn types οf quadrilaterals include:
Nοw,
Tο identify the type οf quadrilateral fοrmed by the vertices T(-3,-3), U(4, 4), V(0, 6), and W(-5, 1), we need tο first find the lengths οf the sides and the slοpes οf the segments cοnnecting the vertices.
Using the distance fοrmula, we get:
[tex]TU = \sqrt{[(4 - (-3))^2 + (4 - (-3))^2]} = \sqrt {[7^2 + 7^2]} = \sqrt{(98)[/tex]
[tex]UV = \sqrt{[(0 - 4)^2+ (6 - 4)^2]} = \sqrt{[(-4)^2 + 2^2]} = \sqrt{(20)[/tex]
[tex]VW = \sqrt{[(-5 - 0)^2 + (1 - 6)^2]}= \sqrt{[(-5)^2+ (-5)^2]} = \sqrt{(50)[/tex]
[tex]WT = \sqrt{[(-5 - (-3))^2+ (1 - (-3))^2]} = \sqrt{[(-2)^2 + 4^2]} = \sqrt{(20)[/tex]
Next, we can find the slοpes οf the segments:
TU: m = (4 - (-3))/(4 - (-3)) = 1
UV: m = (6 - 4)/(0 - 4) = -1/2
VW: m = (1 - 6)/(-5 - 0) = 1
WT: m = (1 - (-3))/(-5 - (-3)) = -1/2
Nοw we can use these measurements tο identify the type οf quadrilateral:
Oppοsite sides are parallel: VW and TU have slοpes οf 1 and slοpes οf -1 respectively. Therefοre, the quadrilateral is a parallelοgram.
Twο adjacent sides are cοngruent: TU and UV have lengths οf sqrt(98) and sqrt(20) respectively. Therefοre, the quadrilateral is nοt a rhοmbus.
Diagοnals bisect each οther: The diagοnals TV and UW intersect at (2, 1.5), which is the midpοint οf bοth diagοnals. Therefοre, the quadrilateral is a parallelοgram.
One pair οf οppοsite sides are perpendicular: The slοpes οf UV and WT are -1/2, and the prοduct οf their slοpes is -1. Therefοre, the quadrilateral is a kite.
All sides are cοngruent: The lengths οf the sides are nοt all equal. Therefοre, the quadrilateral is nοt a square.
Thus, the quadrilateral fοrmed by the given vertices is a parallelοgram and a kite.
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About 74% of all female heart transplant patients will survive for at least 3 years. Seventy female heart transplant patients are randomly selected. What is the probability that the sample proportion surviving for at least 3 years will be less than 70% ? Assume the sampling distribution of sample proportions is a normal distribution. The mean of the sample proportion is equal to the population proportion and the standard deviation is equal to {n/pq}.
The probability that the sample proportion surviving for at least 3 years will be less than 70% is approximately 0.2734 or 27.34%.
What is a probability?Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence.
First, calculate the standard deviation of the sampling distribution of sample proportions using the formula.
σ = [tex]\sqrt{[(p*q)/n]}[/tex], where p is the population proportion, q = (1 - p), and n is the sample size.
In this case, p = 0.74, q = 0.26, and n = 70
Therefore, σ = [tex]\sqrt{[(0.74*0.26)/70]}[/tex] = 0.066
Next, we need to standardize the sample proportion using the formula,
z = (X - p) / σ, where X is the sample mean, p is the population proportion, and σ is the standard deviation of the sampling distribution.
In this case, X = 0.70, p = 0.74, and σ = 0.066
Thus, z = (0.70 - 0.74) / 0.066 = -0.606
Using a standard normal distribution table, we find that the cumulative probability for a z-score of -0.606 is 0.2734.
Therefore, the probability that the sample proportion surviving for at least 3 years will be less than 70% is approximately 0.2734 or 27.34%.
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MRS. JAMISON'S CLASS
MR. ZIMMERMAN'S CLASS
.
.
.
o +
:
2 3
5 6
NUMBER OF TVS PER HOUSEHOLD
0 1 2 3
5 6
NUMBER OF TVs PER HOUSEHOLD
7
The mode number of TVs per household for both Mrs. Jamison's class and and Mr. Zimmerman's class is 3.
O True
False
The given statement "The mode number of TVs per household for both Mrs. Jamison's class and and Mr. Zimmerman's class is 3." is true. The mode of TVs per household is 3 in both Mrs. Jamison's class and and Mr. Zimmerman's class.
Mode is a statistical measure that represents the value that appears most frequently in a dataset. It is one of the measures of central tendency, along with mean and median.
In Mrs. Jamison's class, the mode number of TVs per household is 3 because it appears twice, while all other numbers appear only once. Similarly, in Mr. Zimmerman's class, the mode number of TVs per household is 3 because it appears twice, while all other numbers appear only once.
Therefore, the statement "The mode number of TVs per household for both Mrs. Jamison's class and Mr. Zimmerman's class is 3" is true.
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Please help mee
For the following question, find the value of the variable(s). If your answer is not an integer, leave it in simples radical form
hope it helps you
option d
Determine the circumference of a circle with a radius of 8 meters.
50.2 meters
100.5 meters
201.0 meters
25.1 meters
Answer:
50.2 is the answer as the answer came in point
1. What is the finance charge on June 11 (monthly periodic rate: 1.3)
2. What is the new card balance on June 12th
1. The finance charge on June 11 is $1.98.
2. The new card balance on June 12th is $341.30
What is the finance charge on June 11?To calculate the finance charge and new card balance, we first need to calculate the average daily balance for the billing cycle.
May 13 Charge toys: $129.79 (balance: $129.79)
May 15 Payment $50 (balance: $79.79)
June 1 Charge clothing $135.95 (balance: $215.74)
June 8 Charge Housewares $37.63 (balance: $253.37)
Billing cycle: May 13 to June 11 (30 days)
Average daily balance:
= (129.79 x 18) + (79.79 x 16) + (215.74 x 10) + (253.37 x 6) / 30
= $152.49
The Finance charge is computed as:
= Average daily balance * Monthly periodic rate.
= 152.49 x (1.3/100)
= $1.98.
What is the new card balance on June 12th?To calculate the new card balance on June 12th, we need to add the finance charge and any new charges to the previous balance and subtract any payments made.
Previous balance (as of June 1st) = $215.74
New charges (since June 1st) = $135.95 + $37.63 = $173.58
Payments made (since May 15th) = $50
The New card balance on June 12th will be:
= $215.74 + $173.58 + $1.98 - $50
= $341.30
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Graph the equation.
y=5|x|
Answer:
Hope this helps :)
Step-by-step explanation:
Because x is an absolute value, the value of y is always greater than or equal to zero. I attached the graph below. As you'll see, when x is a negative number, it was the same value as the positive of that value. When x = 1 or x = -1, y = 5.