Answer: 34.65 miles at an angle of 325.39°
Step-by-step explanation:
Ok, the initial position is (0,0)
Then she flies 30 miles at an angle of 160°, if we count the angle counterclokwise from the x-axis, the new position will be:
p = (30*cos(120°), 30*sin(120°))
Then she travels another 15 miles at an angle of 205°, the new position is:
p = (30*cos(120°) + 15*cos(205°), 30*sin(120°) + 15*sin(205°))
p = (-28.59 , 19.64)
If she now travles X miles at an angle Y, we must have that the final position is the point (0,0)
this means that:
X*cos(Y) = -(-28.59) = 28.59
X*sin(Y) = -19.64
Now, we can find the quotient between those two equations and use that tan(x) = sin(x)/cos(x)
X*(sin(Y))/(X*cos(Y)) = -19.64/28.59
Tg(Y) = -0.69
Y = ATg(-0.69) = -34.61°
If we use only positive angles, this angle is equivalent to:
360° - 34.61° = 325.39°
now lets find the distance:
Xcos(325.39°) = 28.59
X = 28.59/cos(325.39°) = 34.65 miles.
A 5000-seat theater has tickets for sale at $28 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $153 comma 200?
Answer:
Let's denote:
x: number of ticket 28$
y: number of ticket 40$
Then, we have:
x + y =5000
28x + 40y = 153200
=> 28(5000 - y) + 40y = 153200
=> 12y = 153200 - 140000
=> 12y =13200
=> y = 1100 (ticket 40$)
=> x = 5000 - 1100 = 3900 (ticket 28$)
Find the mean, median, mode and range for each set of data. Calculator usage is encouraged!
1. 23, 87, 19, 34, 37, 87, 81, 5, 14, 100, 26 Please help thank you!
Answer:
mean: 46.63636
median: 34
mode: 87
range:95
How To:
Step 1 : To find Mean
Average = ( 1 + 5 + 5 + 7 + 8 + 10 ) / 6
=36 / 6
Mean = 6
Step 2 : To find Median
Middle value = ( 5 + 7 ) / 2
= 12 / 2
Median = 6
Step 3 : To find Mode
Mode = 5 (The number with more repetition, here 5 is repeated two times)
Step 4 : To find Range
Range = Largest number - Smallest number
= 10-1
= 9
Range = 9
Answer:
Mean: 46.6
Mode: 87
Median: 34
Range: 95
Step-by-step explanation:
Mean: (finding the average)
Median: (the middle number of the data set)
Mode: (the most number repeated from the data set)
Range: (is the difference between the highest value and the lowest value)
first arrange the following data set.
23, 87, 19, 34, 37, 87, 81, 5, 14, 100, 26
so:
5, 14, 19, 23, 26, 34, 37, 81, 87, 87, 100
Lets us first find the mean by adding up all the numbers and dividing it by the amount of numbers in the data set.
Mean: 5 + 14 + 19 + 23 + 26 + 34 + 37 + 81 + 87 + 87 + 100 = 513/11 = 46.6
Mode: 87
Median: 34
Range: 100 - 5 = 95
A bag contains 3 red marbles and 6 blue marbles. A second bag contains 6 green marbles and 4 yellow marbles. You choose a marble from bag A and then a marble from bag B, what would be the probability of selecting one blue marble and one yellow marble?
Answer:
4/15
Step-by-step explanation:
Bag A
3 red marbles and 6 blue marbles. = 9 marbles
P(blue) = blue/total =6/9 = 2/3
Bag B
6 green marbles and 4 yellow marbles. = 10 marbles
P(yellow) = yellow/total=4/10 = 2/5
P(blue,yellow) = 2/3 * 2/5 = 4/15
Which equation represents the hyperbola shown in the
graph?
10
8
(x - 2)2
(y + 3)
25
(-2,5) 6
(-7,3)
(1-21)
4-12-10 -8 -6 4-2
(3,3)
(x + 2)2
(y = 3) = 1
4
2 4 6
(x + 2)2
25
(y - 3)2
4
1
(232) - (7,31 = 1
(x - 2)2
25
Answer:
Step-by-step explanation:
A general equation of a hyperbola is
x^2 y^2
-------- - ------- = 1 (This applies only when the center of the hyperbola
a^2 b^2 is at (0, 0) ).
You must compare the given equations to this standard form to identify which represents the hyperbola shown, and also you must share the illustration of the hyperbola.
The equation represents the hyperbola shown in the graph is (y - 1)² / 9 - (x + 4)² / 4 = 1
What is a hyperbola?A hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set.
A hyperbola has two pieces, called connected components or branches, that are mirror images of each other and resemble two infinite bows.
Given that, a graph, showing hyperbola, we need to find the equation,
We have the general equation for up - down facing hyperbola as
(y - k)² / b²- (x - h)² / a² = 1.
Let's start listing the properties of this graph -
Taking a look at the graph we see that the center point of our hyperbola here is (- 4, 1).
Therefore, (h, k) = (- 4,1).
This is the semi distance from the center to one of the vertices. Here it will be the distance from points (- 4,1) and (- 4,4) or 3 unit difference.
Therefore, a = 3.
That gives asymptotes. Now remember that it will be in the form
y = ± b / a.
We already know a = 3, so we have to find b.
Looking at this graph we can say that another point besides (- 4,1) that lies on the "dotted line" is (- 2, - 2).
Calculating the slope of the dotted line would be as follows,
Given: (- 4,1) and (- 2, - 2)
Slope = - 2 + 4 / - 2 - 1 = 2 / 3
We have the equation y = 2 / 3x.
Therefore, b = 2.
Let's substitute to equation...
h = - 4, k = 1, b = 2, a = 3
(y - 1)² / (3)²- (x + 4)² / (2)² = 1
(y - 1)² / 9 - (x + 4)² / 4 = 1
Hence, the equation represents the hyperbola shown in the graph is (y - 1)² / 9 - (x + 4)² / 4 = 1
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The complete question is attached
How does Harrison Bergeron's physical description help to create satire?
Answer:
The absurdity of Harrison's exaggerated handicaps ridicules society's obsession with equality.Step-by-step explanation:
Answer:
Step-by-step explanation:
In the year 2081, the 211th, 212th, and 213th amendments to the Constitution dictate that all Americans are fully equal and not allowed to be smarter, better-looking, or more physically able than anyone else. The Handicapper General's agents enforce the equality laws, forcing citizens to wear "handicaps": masks for those who are too beautiful, loud radios that disrupt thoughts inside the ears of intelligent people, and heavy weights for the strong or athletic.
One April, 14-year-old Harrison Bergeron, an intelligent, athletic, and good-looking teenager, is taken away from his parents, George and Hazel Bergeron, by the government. They are barely aware of the tragedy, as Hazel has "average" intelligence (a euphemism for stupidity), and George has a handicap radio installed by the government to regulate his above-average intelligence.
Hazel and George watch ballet on television.They comment on the dancers, who are weighed down to counteract their gracefulness and masked to hide their attractiveness. George's thoughts are continually interrupted by the different noises emitted by his handicap radio, which piques Hazel's curiosity and imagination regarding handicaps. Noticing his exhaustion, Hazel urges George to lie down and rest his "handicap bag", 47 pounds (21 kg) of weights locked around George's neck. She suggests taking a few of the weights out of the bag, but George resists, aware of the illegality of such an action.
On television, a news reporter struggles to read the bulletin and hands it to the ballerina wearing the most grotesque mask and heaviest weights. She begins reading in her unacceptably natural, beautiful voice, then apologizes before switching to a more unpleasant voice. Harrison's escape from prison is announced, and a full-body photograph of Harrison is shown, indicating that he is seven feet (2.1 m) tall and burdened by three hundred pounds (140 kg) of handicaps.
George recognizes his son for a moment, before having the thought eliminated by his radio. Harrison himself then storms the television studio in an attempt to overthrow the government. He calls himself the Emperor and rips off all of his handicaps, along with the handicaps of a ballerina, whom he proclaims his "Empress". He orders the musicians to play, promising them nobility if they do their best. Unhappy with their initial attempt, Harrison takes control for a short while, and the music improves. After listening and being moved by the music, Harrison and his Empress dance while flying to the ceiling, then pause in mid-air to kiss.
Diana Moon Glampers, the Handicapper General, enters the studio and kills Harrison and the Empress with a ten-gauge double-barreled shotgun. She forces the musicians to put on their handicaps, and the television goes dark. George, unaware of the televised incident, returns from the kitchen and asks Hazel why she was crying, to which she replies that something sad happened on television that she cannot remember. He comforts her and they return to their average lives.
What can be determined by looking at the factored form of the polynomial f(x) = (x + 7)(x - 2) ?
A
The graph of the polynomial has zeros at (0,-7) and (0,2)
В
The graph of the polynomial has zeros at (7,0) and (-2,0)
C
The graph of the polynomial has zeros at (-7,0) and (2,0)
D
The graph of the polynomial has zeros at (0,7) and (0,-2)
Answer:
C . The graph of the polynomial has zeros at (-7,0) and (2,0)
Step-by-step explanation:
f(x) = (x + 7)(x - 2)
Zero's obtained:
(x+7)(x-2) = 0x+7 = 0 ⇒ x = -7x-2 = 0 ⇒ x = 2Coordinates:
(-7, 0) and (2, 0)Correct answer choice is:
C . The graph of the polynomial has zeros at (-7,0) and (2,0)
What is the difference between the two temperatures -13°C and 10°C
Answer:
23
Step-by-step explanation:
According to a Pew Research Center report from 2012, the average commute time to work in California is 27.5 minutes. To investigate whether the small city she lives in has a different average, a California high school student surveys 45 people she knows (her teachers, her parents, and their friends and co-workers) and finds the average commute time for this sample to be 24.33 minutes with a standard deviation of 9.53 minutes. The data are not too skewed. The null and alternative hypotheses of her study are: H0 : µ = 27.5 versus Ha : µ 6= 27.5
Required:
a. Identify the observational units for this study.
b. Identify the variable of interest and state whether it is categorical or quantitative.
c. Identify (in words and using an appropriate symbol) the parameter of interest
d. Use the 2SD approach to find a 95% confidence interval for the parameter.
e. Interpret the interval from part d. in context.
BRAINLIEST ASAP! LENGTH OF AC?
Answer:
2.33 units
Step-by-step explanation:
[tex]\tan 25\degree =\frac{AC}{5}\\\\0.46630 = \frac{AC}{5}\\\\AC = 0.46630 \times 5\\AC =2.3315\\AC = 2.33 \: units[/tex]
Bob, Paula and Sam invest $50000 in a business. Bob invests $4000 more than Paul does and Paul invests $5000 more than Sam does. If the total profit was $70000, select the correct answer. Note that the profit is distributed proportionally based on the respective amount each invested. A. The ratio of the investment of Bob, Paula and Sam is 11:15:10. B. The ratio of the investment of Bob, Paula and Sam is 12:17:21. C. The ratio of the investment of Bob, Paula and Sam is 12:5:4. D. The profit of Paula was $23,800
Answer:
D
Step-by-step explanation:
since sam invest the least, let a be the amount invested by sam
sam = a
paul = a + 5000
bob = a + 5000 + 4000
3a + 14000 = 50000
3a = 36000
a = 12000
thus sam is 12000, paul is 17000 and Bob is 21000
therefore the ratio of B:P:S is 21:17:12
profit by paula is 17/50 x 70000 = 23800
The profit by Paula is 17/50 x 70000 = 23800.
We have given that Bob, Paula and Sam invest $50000 in a business. Bob invests $4000 more than Paul does and Paul invests $5000 more than Sam does. If the total profit was $70000
Since sam invest the least, let a be the amount invested by sam
Therefore we get,
sam = a
What is the investment of Paul?
The investment of Paul = a + 5000
Bob = a + 5000 + 4000
3a + 14000 = 50000
3a = 36000
divide both sides by 3 so we get,
a=36000/3
a = 12000
Therefore, sam is 12000,
paul =5000+12000=17000 and
Bob =12000+9000= 21000
Therefore the ratio of B:P:S is 21:17:12
The profit by Paula is 17/50 x 70000 = 23800.
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BRAINLIST+11 Pts!!!
Jim just found a job with a take-home pay of $950 per month. He must pay $400 for rent and $100 for groceries each month. He also spends $100 per month on transportation. If he budgets $50 each month for clothing, $100 for restaurants and $50 for everything else, how long will it take him to save $1,800?
Answer:12 months
Step-by-step explanation:
400+400=800 so 950-800=150 1800/150=12
During one year Saul takes 15 credit hours for each three quarters. Tuition and fees amount to $608 per credit hour. Textbooks average $420 per quarter. The prorated monthly cost for tuition and fees and textbooks is?
Answer:
Total textbook cost of tuition fees per month will be $ 2,356 and 25 cents
Step-by-step explanation:
To solve the exercise, we will first define the total cost per quarter.
cost of 1 credit hour = $ 601
then we solve the following:
cost of 15 credit hours = $ 601 * 15 = $ 9015
textbooks = $ 410
then we solve the following:
total cost = 9015 + 410 = $ 9425
total cost for 3 quarters = 3 * $ 9425 = $ 28275 for 12 months
we calculate as follows
Total textbook cost of tuition fees per month will be
$ 28,275 / 12 = $ 2,356 and 25 cents
1. 10(.15)=1.5
2. 10-1.5=8.5
3. 8.5 (.15)=1.275
4. 8.5-1.275=7.225
Keep going until you get number 5 and below 1
!!!!!!!!!!!!!!!!!!!!!!!!
PLEASE MAN!
Answer:
6.14125(0.15) = 0.9211875 (below 1)
6.14125 - 0.92118 = 5.22007
Step-by-step explanation:
Given data
1. 10(.15)=1.5
2. 10-1.5=8.5
3. 8.5 (.15)=1.275
4. 8.5-1.275=7.225
continuation the sequence
5) 7.225 (0.15) = 1.08375
6) 7.225 - 1.08375 = 6.14125
7) 6.14125(0.15) = 0.9211875 (below -one)
8 ) 6.14125 - 0.9211875 = 5.2200625 (get number 5)
9) 5.2200625(0.15) = 0.783009
10) 5.2200625 - 0.783009 = 4.4370532
The altitude of an airplane is decreasing at a rate of 44 feet per second. What is the change in altitude of the airplane over a period of 34 seconds?
Answer:
1320 feet
Step-by-step explanation:
All we have to do is multiply the rate of change of altitude by the time it took the altitude to change.
The altitude of an airplane is decreasing at a rate of 44 feet per second. After 30 seconds, the change is altitude is:
44 * 30 = 1320 feet
The altitude of the airplane has changed by 1320 feet.
Which one of the following is not a fixed cost in owning a vehicle?
1 point
Gas
Insurance
Registration
Tags
Step-by-step explanation:
tags is not a fixed cost
What is the Surface Area of the figure below?
A
60 units2
B
60 units3
C
104 units2
D
104 units3
Answer:
D
Step-by-step explanation:
I'm really sry if it's wrong!
Nora made 15 gallons of lemonade for a community picnic.
Part A
Which of the following can be used to find the number of pints of lemonade that Nora made?
15 × 2 × 2
15 × 4 × 2
15 × 3 × 2
15 × 4 × 3
Part B
How many pints of lemonade did Nora make?
Enter your answer in the box.
pints
Answer:
I also belive for Part A the second one is the answer because it equals 120 Part B is 120 pints! Good Luck! And I hope this Helps!
Answer:
B
Step-by-step explanation:
Oil is leaking from an oil tanker, and an expanding circle of oil is spreading on the ocean. The radius, r, of
modeled by the function r(s)=315, where sis time in seconds.
The area of the spill when s=5 seconds is
1 square inches.
Reset
Reset
Next
Next
Answer:
[tex]45\pi$ square inches[/tex]
Step-by-step explanation:
The radius, r of the expanding circle of oil is modeled by the function:
[tex]r=3\sqrt{s}[/tex] , where s is time in seconds.
When s=5
Radius [tex]r(5)=3\sqrt{5}$ inches[/tex]
Area of a circle [tex]=\pi r^2[/tex]
Therefore, the area of the oil spill when s=5 seconds
[tex]=\pi* (3\sqrt{5})^2\\=45\pi$ square inches[/tex]
The area of the spill when s=5 seconds is 45pi square inches.
Christian and Megan want to purchase a new car. The car has a base price of $16,700, options totaling $1,095, and a destination charge of $325. They read in a consumer magazine that the dealer's cost for the car is 90 percent of the base price and 87 percent of the options price. What should they estimate as the dealer's cost?
1 point
$15,764.40
$15,806.65
$16,275.15
$16,307.65
Answer:
it's B
Step-by-step explanation:
because I took the test
An angle whose measure is -102° is in standard position. Which quadrant does the terminal side of the angle fall?
Quadrant 1
Quadrant 2
Cuadrant 3
Cuadrant 4
Answer:3
Step-by-step explanation:
edg
For the data 20, 40, 50, 20, 10, 70. What is there mean absolute deviation?
Answer:
18.333
Step-by-step explanation:
Determine which consecutive integers do not have a real zero of f(x) = x^3 + 9x^2 + 8x – 5 between them.
A.) (–8, –7)
B.) (4, 5)
C.) (0, 1)
D.) (–2, –1)
Answer:
Option B (4,5)
Step-by-step explanation:
The integers (4, 5) do not have real zero.
What is zero of a function?Knowing what zeros represent can assist us in determining when and how to locate the zeros of functions given their expressions and a function's graph. The value of x when the function itself reaches zero is typically referred to as a function's zero.
A function's zero can take many different forms, but as long as they have a y-value of zero, we will consider them to be the function's zero.
Given Expression
f(x) = x³ + 9x² + 8x - 5
to find which is not a real zero,
condition of real zero is for any function f(a , b) if f(a).f(b) < 0 the function have at least a zero.
1: (-8, -7)
f(-8).f(-7) = [(-8)³ + 9(-8)² + 8(-8) - 5][(-7³) + 9(-7)² + 8(-7) - 5]
f(-8).f(-7) = (-5)(37)
f(-8).f(-7) = -185 < 0 points have at least a zero
2: (4, 5)
f(4).f(5) = [(4)³ + 9(4)² + 8(4) - 5][(5³) + 9(5)² + 8(5) - 5]
f(4).f(5) = 235 x 385
f(4).f(5) = 94,475 > 0
points do not have any zeros
3: (0, 1)
f(0).f(1) = [(0)³ + 9(0)² + 8(0) - 5][(1³) + 9(1)² + 8(1) - 5]
f(0).f(1) = -5 x 13
f(0).f(1) = -65 < 0
points have a zero
4: (–2, –1)
f(-2).f(-1) = [(-2)³ + 9(-2)² + 8(-2) - 5][(-1³) + 9(-1)² + 8(-1) - 5]
f(-2).f(-1) = 7 x (-5)
f(-2).f(-1) = -35 < 0
points have a zero
Hence only point (4, 5) do not have a zero.
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if a line is perpendicular to y=-2/3x+2, will it be perpendicular to 2x+3y=12?
Answer:
3x + 2y = -2
Step-by-step explanation:
Given Equation is − 2 x + 3 y = 12
3 y = 2 x + 12
y = ( 2 /3 ) y + 12
Slope of this line is m = 2/ 3
Slope of Line A m a = 2
Slope of Line B m b = 2/ 3
Slope of Line C m c = − ( 2 /3 )
Slope of Line D m d = − ( 3 /2 )
since m d = − 1 /m , D is perpendicular to the given line
Which equation represents the black line?
Which equation represents the red line?
Explain a mathematical way to find the intersection of the lines without actually graphing the lines.
Answer:
Black Line y = 3 + 2x , y = 2x +3
Red Line y = -2 - .5x. y = -.5x -2
vice versa
Step-by-step explanation:
For the black line, the lines intersects y at coordinate (0,3) and that would be b. To find the slope, use the equation rise / run. It rises 4 and runs 2. Putting this into an equation 4/2, it would be 2 as the constant. In other words, it would be 2x. Therefore, the function for the black line is y = 3 + 2x
For the red line, using the same explanation from the black line, the line intersects y at -2, and the slope would be -.5x, since it runs downwards 2 and runs 4, and since it runs downwards, a negative sign would be necessary in front of the slope.
A teacher of statistics wants to know if a new teaching methodology that includes IT is efficient in terms of increased average score. He took a class with old methodology and a class with new methodology for samples and gave a same test. Open the file by clicking the file name above. Once you open the file and run Excel, you need not open it again. What is Ha? Find it from Excel output that you generate.
a) 0.62.
b) 0.5.
c) 0.31.
d) -0.5.
Answer:
The answer is 0.31
Step-by-step explanation:
Old Method New Method .
Mean 73.5625 Mean 75.70588
Standard Error 3.143736 Standard Error 2.923994
Median 72 Median 75
Mode 90 Mode 64
Standard deviation 12.57494 Standard deviation 12.05594
Sample Variance 158.1292 Sample Variance 145.3456
Kurtosis -1.14544 Kurtosis -0.76646
Skewness 0.171025 Skewness 0.091008
Range 39 Range 41
Minimum 55 Minimum 56
Maximum 94 Maximum 97
Sum 1177 Sum 1287
Count 16 Count 17
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: μNew< μOld
Alternative hypothesis: μNew > μOld
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the mean difference between sample means is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
[tex]SE=\sqrt{\frac{S_1^2}{n_1} +\frac{S_2^2}{n_2} } \\\\SE=4.29[/tex]
DF = 31
[tex]t = \frac{(x_1-x_2)-d}{SE} \\\\t = - 0.4997[/tex]
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.
The observed difference in sample means produced a t statistic of - 0.499. We use the t Distribution Calculator to find P(t < - 0.499) = 0.311
Therefore, the P-value in this analysis is 0.311.
Interpret results. Since the P-value (0.311) is greater than the significance level (0.05), we cannot reject the null hypothesis.
From the above test we do have sufficient evidence in the favor of the claim that new method is efficient than the old method.
In the right triangle shown DF=EF=3. How long is DE?
Answer:
4.24
Step-by-step explanation:
To solve this, use the Pythagorean therom. A^2 + b^2 = C^2
in this case a = 3 and b = 3
so 9 + 9 = sqrt 18
4.24
Answer:3√(2)
Step-by-step explanation:
DF=3
EF=3
DE=√(3^2 + 3^2)
DE=√(3x3 + 3x3)
DE=√(9+9)
DE=√(18)
DE=√(2 x 9)
DE=√(2) x √(9)
DE=√(2) x 3
DE=3√(2)
At Silver Gym, membership is $35 per month, and personal training sessions are $30 each. At Fit Factor,
membership is $85 per month, and personal training sessions are $20 each. In one month, how many
personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Sarah would have to buy
equal.
personal training sessions to make the total cost at the two gyms
Answer:
5 sessions each
Step-by-step explanation:
Let the personal training sessions be x.
Then at Silver Gym Sarah would spend:
35 + 30xAnd at Fit Factor she would spend:
85 + 20xSince total costs are same, the amounts will be equal:
35+30x = 85 + 20x30x - 20x = 85 - 3510 x = 50x= 50/10x= 5So Sarah would buy 5 training sessions for each of the gyms.
And she would spend $185 at each.
-5x+20<5 solve for x
Answer: x > 3
Step-by-step explanation: Just like any of your two-step equations, in this inequality, start by isolating the x term which in this case is -5x by subtracting 20 from both sides. That leaves you with -5x < -15.
To get x by itself, divide both sides by -5, but watch out.
If you divide both sides of an inequality by a negative number, you must switch the direction of the inequality sign.
So we have x > 3.
I have also graphed the inequality for you below.
Start with an open dot at 3. The reason for that is because x > 3 but x is not equal to 3 so we use an open dot.
Now, draw an arrow to the right to
represent all numbers greater than 3.
A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. (Round your answers to four decimal places.) (a) Compute the probability that 2 or fewer will withdraw. (b) Compute the probability that exactly 4 will withdraw. (c) Compute the probability that more than 3 will withdraw. (d) Compute the expected number of withdrawals.
Answer:
(a) Probability that 2 or fewer will withdraw is 0.2061.
(b) Probability that exactly 4 will withdraw is 0.2182.
(c) Probability that more than 3 will withdraw is 0.5886.
(d) The expected number of withdrawals is 4.
Step-by-step explanation:
We are given that a university found that 20% of its students withdraw without completing the introductory statistics course.
Assume that 20 students registered for the course.
The above situation can be represented through binomial distribution;
[tex]P(X =r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,......[/tex]
where, n = number of trials (samples) taken = 20 students
r = number of success
p = probability of success which in our question is probability
that students withdraw without completing the introductory
statistics course, i.e; p = 20%
Let X = Number of students withdraw without completing the introductory statistics course
So, X ~ Binom(n = 20 , p = 0.20)
(a) Probability that 2 or fewer will withdraw is given by = P(X [tex]\leq[/tex] 2)
P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 2)
= [tex]\binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}[/tex]
= [tex]1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}[/tex]
= 0.2061
(b) Probability that exactly 4 will withdraw is given by = P(X = 4)
P(X = 4) = [tex]\binom{20}{4} \times 0.20^{4} \times (1-0.20)^{20-4}[/tex]
= [tex]4845\times 0.20^{4} \times 0.80^{16}[/tex]
= 0.2182
(c) Probability that more than 3 will withdraw is given by = P(X > 3)
P(X > 3) = 1 - P(X [tex]\leq[/tex] 3) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)
= [tex]1-(\binom{20}{0} \times 0.20^{0} \times (1-0.20)^{20-0}+ \binom{20}{1} \times 0.20^{1} \times (1-0.20)^{20-1}+ \binom{20}{2} \times 0.20^{2} \times (1-0.20)^{20-2}+\binom{20}{3} \times 0.20^{3} \times (1-0.20)^{20-3})[/tex]
= [tex]1-(1 \times1 \times 0.80^{20}+ 20 \times 0.20^{1} \times 0.80^{19}+ 190\times 0.20^{2} \times 0.80^{18}+1140\times 0.20^{3} \times 0.80^{17})[/tex]
= 1 - 0.4114 = 0.5886
(d) The expected number of withdrawals is given by;
E(X) = [tex]n\times p[/tex]
= [tex]20 \times 0.20[/tex] = 4 withdrawals
A bag of colored marbles contains 16 blue marbles, 12 red marbles, and 8 yellow marbles.
What is the theoretical probability of drawing a red marble?
Enter your answer as a reduced fraction, like this: 3/14
Answer:
The theoretical probability of drawing a red marble is 1/3.
Step-by-step explanation:
1. Add all of the marbles together to get total marbles. 16 + 12 + 8 = 36.
2. Create a fraction, with numerator being favorable outcomes and denominator being total possible outcomes. In this case it would be 12/36.
3. Since it is asking for a reduced fraction, simplify 12/36 to 1/3.
