(a) The probability that there is exactly one car and exactly one bus during a cycle is 0.020.
(b) The probability that there is at most one car and at most one bus during a cycle is 0.105.
(c) The probability that there is exactly one car during a cycle is 0.100, and the probability that there is exactly one bus during a cycle is 0.200. The probability that there is exactly one car is also 0.050.
(a) To find the probability that there is exactly one car and exactly one bus during a cycle, we need to look at the cell in the table where x = 1 and y = 1. This cell has a probability of 0.020. Therefore, the probability that there is exactly one car and exactly one bus during a cycle is 0.020.
(b) To find the probability that there is at most one car and at most one bus during a cycle, we need to add up the probabilities of the cells where either x = 0 or x = 1, and either y = 0 or y = 1. These cells are
x = 0, y = 0: 0.025
x = 0, y = 1: 0.010
x = 1, y = 0: 0.050
x = 1, y = 1: 0.020
Adding up these probabilities, we get
0.025 + 0.010 + 0.050 + 0.020 = 0.105
Therefore, the probability that there is at most one car and at most one bus during a cycle is 0.105.
(c) To find the probability that there is exactly one car during a cycle, we need to add up the probabilities of the cells where x = 1. These cells are
x = 1, y = 0: 0.050
x = 1, y = 1: 0.020
x = 1, y = 2: 0.030
Adding up these probabilities, we get
0.050 + 0.020 + 0.030 = 0.100
Therefore, the probability that there is exactly one car during a cycle is 0.100.
To find the probability that there is exactly one bus during a cycle, we need to add up the probabilities of the cells where y = 1. These cells are
x = 0, y = 1: 0.010
x = 1, y = 1: 0.020
x = 2, y = 1: 0.050
x = 3, y = 1: 0.060
x = 4, y = 1: 0.040
x = 5, y = 1: 0.020
Adding up these probabilities, we get
0.010 + 0.020 + 0.050 + 0.060 + 0.040 + 0.020 = 0.200
Therefore, the probability that there is exactly one bus during a cycle is 0.200.
Finally, the probability that there is exactly one car can also be obtained by summing the probabilities of the cells in the first row of the table
0.025 + 0.010 + 0.015 = 0.050
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Evaluate. Write your answer as a fraction or whole number without exponents.
6^–3 =
Answer:
i'm pretty sure it's 33
Step-by-step explanation:
6^= 36
36-3= 33
PLEASE HELP
Write and simplify a polynomial expression to find the area of 4 circles. Each circle has a radius of (4a-6)
Answer: 64πa^2-192πa+144
Step-by-step explanation:
Area of a circle: π •r^2
So then the area would be: 4•π(4a-6)^2
FOIL (4a-6)(4a-6) and get 16a^2-48a+36
Plug it in and get 4•π(16a^2-48a+36)
Distribute pi sign and get 4•(16πa^2-48πa+36π)
Distribute the 4 and you get 64πa^2-192πa+144
Answer: 64πa^2-192πa+144
assume that 90 million households in the u.s. turn on their televisions at 8:00 p.m. on a sunday night, and the total number of u.s. tb households is 119.9 million. calculate the households using television (hut) figure.
The households using television (HUT) figure is 75.06%.
The households using television (HUT) figure is a measure of the percentage of households that have turned on their televisions at a particular time. It is calculated by dividing the number of households watching TV by the total number of households and multiplying by 100%.
In this case, we are given that 90 million households in the US turned on their televisions at 8:00 p.m. on a Sunday night. The total number of US households is 119.9 million. Using this information, we can calculate the HUT figure as follows
Households using television (HUT) = (Number of households watching TV / Total number of households) x 100%
HUT = (90 million / 119.9 million) x 100%
HUT = 75.06%
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What is 35 to the nearest degree
I'm sorry, 35 is not a measure of angle and therefore cannot be rounded to the nearest degree. Are you asking for the sine, cosine, or tangent of 35 degrees?
165. 1% of 384. 7. Round to the nearest thousandth
Rounding to the nearest thousandth means rewrite the number and deleting all digits to the right of the rounded number. The percentage value for 165.1% of 384.7 is equals to the 42.917%.
In mathematics, a percentage is a number that represents a fraction of hundred. We have to calculate the value of 165.1% of 384.7. Percentage solution with steps:
Step 1: We make the assumption that 384.7 is 100% since it is our output value.
Step 2: We next represent the value we need with x. From step 1, it follows that 100% = 384.7.
Step 3: In the same sense, x% = 165.1.
Step 5: Now, we have a pair of simple equations:
100% = 384.7 --(1).
x% = 165.1 ---(2).
Step 6: By simply dividing equation (1) by equation 2 and taking note of the fact that both the LHS (left hand side) of both equations have the same unit (%); we have 100% /x% = 384.7/165.1.
Step 7: Taking the inverse or reciprocal in both sides, x% / 100% = 165.1/384.7
=> x = ( 165.1/384.7) × 100
=> x = 42.91655835716 ~ 42.917 (round to the nearest thousandth). Therefore, 165.1 is 42.917% of 384.7.
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Consider parallelogram ABCD below. Point E is the intersection of diagonals AC and BD.
Progress: 0/2
Part 1 of 2
4(-2,2)
D(-2,-10)
(a) Find the area of AABE.
cm
2
B (8.2)
C(8.-10)
suppose that a 17 ft ladder is sliding down a wall at a rate of 6 ft/sec. at what rate is the bottom of the ladder moving when the top is 8 ft from the ground?
The bottom of the ladder is moving at a rate of 1.333 ft/sec when the top is 8 ft from the ground
The bottom of the ladder is moving at a rate of 6 ft/sec when the top is 8 ft from the ground. This can be found by using the equation v = d/t, where v is the velocity, d is the distance, and t is the time. The distance is 8 feet (from the top of the ladder to the ground) and the time is 1/6 seconds (since the ladder is sliding down at a rate of 6 ft/sec). Therefore, the velocity of the bottom of the ladder when the top is 8 ft from the ground is 8/1/6 = 8/6 = 4/3 = 1.333 ft/sec.
To understand this concept more clearly, imagine a ball rolling along the ground. Its velocity is constant until it hits a slope and begins to move down the slope. At this point, its velocity increases as it moves further down the slope, and its velocity is higher when it is further down the slope.
This is the same concept as the ladder sliding down the wall; the bottom of the ladder is moving faster than the top, so the velocity of the bottom of the ladder increases as the top of the ladder gets closer to the ground.
In conclusion, the bottom of the ladder is moving at a rate of 1.333 ft/sec when the top is 8 ft from the ground. This can be found using the equation v = d/t, where v is the velocity, d is the distance, and t is the time. The distance is 8 feet and the time is 1/6 seconds since the ladder is sliding down at a rate of 6 ft/sec.
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Polygon WXYZ is dilated by a scale factor of 3 with vertex W as the center of dilation, resulting in polygon W’X’Y’Z’. The coordinates of point ware (3,2), and the coordinates of point X are (7,5).
So the coordinates of point X' after dilation are (15, 11).
Polygon WXYZ is dilated by a scale factor of 3, with vertex W as the center of dilation. This means that the distances from vertex W to the other vertices are multiplied by 3, while W remains unchanged. Given the coordinates of point W are (3,2) and point X are (7,5), we can find the coordinates of point X' after dilation.
To do this, first determine the change in the x and y coordinates from point W to point X:
Δx =[tex]7 - 3 = 4\\[/tex]
Δy =[tex] 5 - 2 = 3[/tex]
Now multiply these changes by the scale factor of 3:
Δx' =[tex] 4 * 3 = 12[/tex]
Δy' =[tex] 3 * 3 = 9[/tex]
Now add these new changes to the original coordinates of point W to get the coordinates of point X':
X'(x) =[tex] W(x) + Δx' = 3 + 12 = 15[/tex]
X'(y) = [tex]W(y) + Δy' = 2 + 9 = 11[/tex]
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Find x
Find y
Need explanation
Step-by-step explanation:
Well, since this is a 45, 45, 90 triangle, it means that the given side and y have the same length.
Y = 1.5sqrt(2)
this means that X, the hypotenuse is equal to 1.5sqrt(2)^2 + 1.5sqrt(2)^2 = X^2
X is equal to 2.44948974278
A rectangular tank measures 15 cm by 7 cm by 10 cm. How many milliliters of water are in the tank when it is full? How many liters?
The tank contains 1050 milliliters of water when full or 1.05 liters.
To calculate the volume of the tank in milliliters, we multiply the length (15 cm), width (7 cm), and height (10 cm) together:
15 cm x 7 cm x 10 cm = 1050 cm³
Since 1 milliliter equals 1 cubic centimeter (cm^3), we know that the tank can hold 1050 milliliters of water.
To convert milliliters to liters, we can divide the volume in milliliters by 1000:
1050 mL ÷ 1000 = 1.05 L
Therefore, when full, the tank can hold 1050 milliliters of water or 1.05 liters.
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The sum of two numbers is 18. Their difference is -8. Find the two numbers.
Part A
Write a system of equations that represents the situation.
x + y =
x-y =
Part B
Solve the system of equations. Express the coordinates as decimals if necessary.
Answer:
Step-by-step explanation: is 13 bc 13-8 is 5 and 5+1313is
the probability that a student at certain high school likes art is 35%. the probability that a student who likes art also likes science is 22%. find the probability that a student chosen at random likes science given that he or she likes art. round to the nearest tenth of a percent.
The probability that a student chosen at random likes science given that he or she likes art is 41.4%
In our case, we want to find P(Science|Art), which is the probability of a student liking science given that he or she likes art. Using Bayes' theorem, we have:
P(Science|Art) = P(Art|Science) x P(Science) / P(Art)
We know that P(Art) = 0.35 and P(Science|Art) = 0.22. To find P(Art|Science), we can use the formula:
P(Art|Science) = P(Science|Art) x P(Art) / P(Science)
We don't know P(Science) yet, but we can calculate it using the fact that:
P(Science) = P(Science|Art) x P(Art) + P(Science|Not Art) x P(Not Art)
where P(Not Art) is the probability that a student does not like art, which is 1 - P(Art) = 0.65. We are given that P(Science|Not Art) = 0.15, which is the probability that a student who does not like art likes science. Substituting these values, we get:
P(Science) = 0.22 x 0.35 + 0.15 x 0.65 = 0.1855
Now we can substitute all the values into Bayes' theorem:
P(Science|Art) = 0.22 x 0.35 / 0.1855 = 0.414 or 41.4%
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A randomized experiment was performed to determine whether two fertilizers, A and B, give different yields of tomatoes. A total of 33 tomato plants were grown; 16 using fertilizer A, and 17 using fertilizer B. The distributions of the data did not show marked skewness and there were no outliers in either data set. The results of the experiment are shown below.[table]Which of the following statements best describes the conclusion that can be drawn from this experiment?A. There is no statistical evidence of difference in the yields between fertilizer A and fertilizer B (p > 0.15).B. There is a borderline statistically significant difference in the yields between fertilizer A and fertilizer B (0.10 < p < 0.15).C. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.05 < p < 0.10).D. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).E. There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (p < 0.01).
Answer:
There is evidence of a statistically significant difference in the yields between fertilizer A and fertilizer B (0.01 < p < 0.05).
Step-by-step explanation:
There are 36 students in the school choir. The ratio of girls to boys in the choir is
5:4. Two girls are absent from practice on Monday. What is the ratio of girls to
boys at choir practice on Monday?
A 3:4
C 9:8
B 5:2
D 10:7
Answer:
C 9:8
Step-by-step explanation:
total students = 36
5+4=9
5:4 = 20:16
20-2=18
ratio for monday = 18:16
=9:8
You have$ 11.50 and you need ti make copies of a flyer at a store that changes $0.30 per copy
Answer:
56
Step-by-step explanation:
Answer:
56
Step-by-step explanation:
the answer is 56
A student starts a walk at (−6, 10). If the student walks 4 miles north, south, east, or west, which of the following could be their location at the end of the walk?
HELP ME PLEASE!!!
Answer: Assuming the student walks along a rectangular grid and not diagonally, the possible locations the student could end up after walking 4 miles in any direction would be the points that are 4 units away from the starting point in a north, south, east, or west direction.
Using this information, we can determine that the possible locations the student could end up at are:
(-2, 10)
(-6, 14)
(-10, 10)
(-6, 6)
Therefore, the answer is:
All of the above locations are possible endpoints.
Step-by-step explanation:
If the student walks 4 miles north, south, east, or west, the location at the end of the walk are respectively, (-6, 14). (-6, 6), (-2,10). (-10, 10).
What is a coordinate plane?The Cartesian plane, named after the mathematician René Descartes (1596 - 1650), is a plane with a rectangular coordinate system that associates each point in the plane with a pair of numbers.
Given that,
A student starts a walk at (-6, 10)
If the student walks 4 miles north, south, east, or west,
The location at the end of the walk =
Plotting dotted diagram,
East
|
North --------- |-------------- South
|
West
Suppose, he goes to north direction
Then, 4 will be added to y coordinate,
It can be written as,
(-6, 14)
Similarly, for South, (-6, 6),
East, (-2,10).
West, (-10, -10)
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the temperature at 12 noon was 10 degree Celsius above zero .if it decreases at the rate of 2 degree Celsius per hour until midnight ,at what time would the temperature be 8 degree Celsius below zero? what would be the temperature at midnight?
Answer:
The time will be 1:00pm(13 hours) at which the degree Celsius will drop down to 8degrees Celsius since the temperature at 12noon was 10 degree Celsius and it is dropping at the rate of 2 degree Celsius.
katherine spent 20\% of her hike going uphill. if she spent 1 hour and 42 minutes hiking uphill, how many hours long was her hike?
Katherine's hike was 4.7 hours long. She spent 1 hour and 42 minutes going uphill, which was 20% of her hike. This means that her entire hike was (1 hour and 42 minutes) / (20%) = 4.7 hours long.
To calculate this, we need to divide the amount of time spent hiking uphill (1 hour and 42 minutes) by the percentage of her hike spent going uphill (20%). 1 hour and 42 minutes is equal to 102 minutes. 102 minutes / 20% = 4.7 hours. Therefore, Katherine's hike was 4.7 hours long.
We can use the following equation to calculate the answer:
Hike time = (uphill time) / (percentage of uphill time)
Hike time = (102 minutes) / (20%) = 4.7 hours
It is important to note that the calculation can also be done using the amount of time spent going downhill as well. The amount of time spent going downhill will equal the total hike time minus the amount of time spent going uphill. In this case, the amount of time spent going downhill would equal 4.7 hours - 1 hour and 42 minutes = 2.28 hours.
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tanner is 2 years older than kiara. in 8 years the sum of their ages will be 80. how old is tanner now?
Tanner is currently 16 years old and Kiara is 14 years old. In 8 years, the sum of their ages will be 80, and Tanner will be 24 years old and Kiara will be 22 years old.
Tanner is currently 16 years old. Kiara is 14 years old. We can use algebra to solve this problem.
Let x be Tanner's age and y be Kiara's age. We can write the equation x + y = 80.
Since Tanner is two years older than Kiara, we can write x = y + 2. Substituting x for y + 2, we can write (y + 2) + y = 80.
Simplifying this equation, we get 2y + 2 = 80. We can subtract 2 from both sides of the equation, leaving us with 2y = 78. Dividing both sides by 2 gives us y = 39.
Since y represents Kiara's age, we know that Kiara is currently 39 years old. Since Tanner is two years older, we can say that Tanner is 41 years old.
Therefore, Tanner is currently 16 years old and Kiara is 14 years old. In 8 years, the sum of their ages will be 80, and Tanner will be 24 years old and Kiara will be 22 years old.
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Help please, If A= 3x^2+5x-6 and B= -2x^2-6+7, then A-B equals
A-B is equivalent to 5x2 + 11x - 13 as a result as [tex]A = 3x^2 + 5x - 6[/tex] and [tex]B = -2x^2 - 6x + 7[/tex] .
what is expression ?A mathematical expression is a grouping of digits, variables, operators, and symbols that denotes a mathematical amount or relationship. It can be analyzed or condensed using mathematical operations and rules, and it can be a single word or a group of terms. Numerous mathematical ideas, including equations, variables, functions, and formulas, can be represented by expressions. Standard form, factored form, extended form, and polynomial form are just a few of the different ways they can be expressed in writing.
given
We must deduct the expression B from the expression A in order to obtain A-B. To accomplish this, we subtract the appropriate coefficients from terms of the same degree. Here are the facts:
[tex]A = 3x^2 + 5x - 6\\B = -2x^2 - 6x + 7[/tex]
A - B =[tex](3x^2 + 5x - 6) (-2x^2 - 6x + 7)[/tex]
= 3x2 + (5x - 6) + (2x2 - 6) + (7x - 5x2 + 11x - 13 (distributing the negative sign)
A-B is equivalent to 5x2 + 11x - 13 as a result as [tex]A = 3x^2 + 5x - 6[/tex] and [tex]B = -2x^2 - 6x + 7[/tex] .
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Which of the filling best describes the expression 6(y+3)
Answer: 6y+18
Step-by-step explanation:
6 x y=6y
6 x 3= 18
Answer:
The product of a constant factor of six and a factor with the sum of two terms.
Step-by-step explanation:
Since we have given that
6(y+3)
It has sum of two terms i.e. y and 3.
Mathematically, it is expressed as
y+3
And the product of constant factor of six and a factor with the sum of two terms.
Mathematically, it is expressed as
6(y+3)
Hence, The product of a constant factor of six and a factor with the sum of two terms.
siona bought 10 outfits to wear to church. the shirt has a price of $3.50 and a pair of shorts has a price of $4.00. how many shirts and pairs of shorts did she buy when she spent a total of $36.50?
Siona bought 7 shirts and 3 pairs of shorts when she spent a total of $36.50. The problem can be solved using a system of equations.
Let's use a system of equations to solve this problem:
Let x be the number of shirts that Siona bought, and y be the number of pairs of shorts that she bought. Then we have:
Equation 1: x + y = 10 (Siona bought 10 outfits in total)
Equation 2: 3.50x + 4.00y = 36.50 (The total cost of the outfits is $36.50)
To solve for x and y, we can use substitution or elimination. Let's use substitution:
From Equation 1, we can solve for x in terms of y:
x = 10 - y
Substitute this expression for x into Equation 2:
3.50(10 - y) + 4.00y = 36.50
Simplify and solve for y:
35 - 3.50y + 4.00y = 36.50
0.50y = 1.50
y = 3
Now we can substitute y = 3 back into Equation 1 to solve for x:
x + 3 = 10
x = 7
Therefore, Siona bought 7 shirts and 3 pairs of shorts when she spent a total of $36.50.
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Please help I need this answer!! I’ll mark brainiest!!
Answer: 150 degrees
Step-by-step explanation:
It just is
Answer:
A) 150°Step-by-step explanation:
The measure of an angle in a regular dodecagon can be found using the formula:
angle = (n-2) x 180° / n
where n is the number of sides of the polygon. For a regular dodecagon, n = 12, so the formula becomes:
angle = (12-2) x 180° / 12 = 150°
Therefore, the measure of an angle in a regular dodecagon is 150 degrees. Answer: 150.
Sara cut a 2 1/2 meter rope to hang a swing for her sister. How many centimeters is the rope
Length of the Sara's rope of 2 1/2 meter in centimeter is 25 centimeters.
To convert 2 1/2 meters to centimeters, we can use the conversion factor 1 meter = 100 centimeters. This means that:
2.5 meters = 2.5 x 100 centimeters
= 250 centimeters
Therefore, the length of the rope is 250 centimeters. It's important to understand and be able to convert between different units of measurement, as this is a common task in many fields such as science, engineering, and finance. For example, in science, it's important to be able to convert between different units of length, mass, and volume when making measurements or analyzing data. Similarly, in finance, it's common to convert between different currencies or units of time when dealing with investments or loans. Being able to make these conversions accurately is essential to avoid errors or misunderstandings. In this case, converting the length of the rope from meters to centimeters allows us to work with a more convenient unit for the task at hand, which is hanging a swing for Sara's sister.
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The price of a 6-minute phone call is 1. 80. What is the price of a 18-minute phone call?
Answer:
5.40
Step-by-step explanation:
let X represent the price of a 18 minute phone call
X=18 ×1.80
6
= 5.40
rent-a-reck incorporated finds that it can rent cars if it charges for a weekend. it estimates that for each price increase it will rent three fewer cars. what price should it charge to maximize its revenue? how many cars will it rent at this price?
Rent-A-Reck Incorporated should charge $95 to maximize its revenue and the company will rent 45 cars at a price of $95.
To determine the price that will maximize Rent-A-Reck Incorporated's revenue, we need to consider the relationship between the price of renting a car and the number of cars that are rented.
Based on the information provided, we know that the demand for rental cars decreases as the price increases. Specifically, for each $5 increase in price, two fewer cars will be rented.
Let's denote the price of renting a car as P and the number of cars rented as Q. Then we can express the relationship between price and quantity as:
Q = 60 - 2(P - 80)/5
This equation tells us that as the price P increases, the number of cars rented Q decreases. We can also use this equation to find the price that will maximize revenue. Revenue is calculated by multiplying the price by the number of cars rented, so we can write the revenue function as:
R = P(Q) * Q
= P * (60 - 2(P - 80)/5)
To find the price that maximizes revenue, we need to find the value of P that makes R as large as possible. One way to do this is to take the derivative of R with respect to P and set it equal to zero:
dR/dP = (60 - 2(P - 80)/5) - 2P/5 = 0
Solving for P, we get:
P = $95
To find the number of cars that will be rented at this price, we can substitute P = $95 into the demand equation:
Q = 60 - 2($95 - $80)/5
= 45
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Complete question is:
Rent-A-Reck Incorporated finds that it can rent 60 cars if it charges $80 for a weekend. It estimates that for each $5 price increase it will rent two fewer cars. What price should it charge to maximize its revenue? How many cars will it rent at this price?
according to 2016 united states census data, women represent 50.8 % of the population. thus, do the percent of women in the stem field accurately represent the percent of women in the population? by how much do they differ? show your math!
Answer: 100000
Step-by-step explanation:
does the line ever match up perfectly? can the lines ever have the same slope? can the lines ever have the same y-intercept? why or why not?
No, the lines cannot ever match up perfectly because there is always some sort of difference between them. The lines can have the same slope if they have the same change in y-values for a given change in x-values. The lines can also have the same y-intercept if they cross the y-axis at the same point.
No, there will never be a perfect alignment between the lines since there will always be a discrepancy of some kind. However, the lines can have the same slope and y-intercept. This is possible because the slope and y-intercept are determined by the equation of the line, and if two lines have the same equation, then they will have the same slope and y-intercept.
If the lines intersect the y-axis at the same location, they can also have the same y-intercept. This means that the two lines have the same value of b in the equation y = mx + b. This means that the two lines have the same slope and the same y-intercept.
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when a person standing in neutral flexes their right shoulder so that their arm is horizontal with the ground, the center of gravity (mass) will
When a person standing in neutral flexes their right shoulder so that their arm is horizontal with the ground, the center of gravity (mass) will shift towards the left side of the body.
Explanation:
What is center of gravity?The point at which the weight of a body or an object is concentrated, that is, the point at which the mass of the body or the object is focused is known as the center of gravity. The center of gravity (CG) is the point where the weight of the body is supposed to act, which is the point about which the body remains in balance. The body's center of gravity is important because it affects its balance and stability
.When a person is standing in a neutral position, the center of gravity is in the midline of the body. When the person flexes their right shoulder and holds their arm horizontally, the center of gravity will shift towards the left side of the body. This is because the weight of the arm is now being supported by the left side of the body. The shift in the center of gravity will cause the person to adjust their posture to maintain balance and stability.
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The following table gives the probability distribution of a random variable X
X 1 2 3 4
P(x) ¼ C ½ 1/8
a) Find the value of the constant C
b) Find
The value of the constant C is 3/4.
Probability is a branch of mathematics that deals with the likelihood or chance of an event occurring. It is a measure of the likelihood that a specific event will occur, expressed as a value between 0 and 1
The sum of the probabilities for all possible values of X should equal 1
P(1) + P(2) + P(3) + P(4) = 1
Substituting the given values, we get:
C/4 + 1/2 + 1/8 + C/4 = 1
Simplifying the equation, we get:
C/2 + 5/8 = 1
Move 5/8 to right hand side of the equation
C/2 = 3/8
C = (3/8) x 2
C = 3/4
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