Answer:
95% confidence intervals about the population mean is
(51.7656 , 60.2344)
Step-by-step explanation:
Step(i):-
Given random sample of size 'n' =17
Given mean of the sample 'x⁻' = 56
Given standard deviation of sample 's' = 10
95% confidence intervals about the population mean is determined by
[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]
Degrees of freedom
ν = n-1 = 17-1 =16
t₀.₀₅ = 1.7459 (from t-table)
Step(ii):-
95% confidence intervals about the population mean is determined by
[tex](x^{-} - t_{0.05} \frac{s}{\sqrt{n} } ,x^{-} + t_{0.05} \frac{s}{\sqrt{n} } )[/tex]
[tex](56 - 1.7459 \frac{10}{\sqrt{17} } ,56 + 1.7459 \frac{10}{\sqrt{17} } )[/tex]
( 56 - 4.2344 , 56 + 4.2344)
(51.7656 , 60.2344)
Conclusion:-
95% confidence intervals about the population mean is
(51.7656 , 60.2344)
Of 380 randomly selected medical students, 21 said that they planned to work in a rural community. Find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community.
Answer:
[tex]0.0553 - 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0323[/tex]
[tex]0.0553 + 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0783[/tex]
Step-by-step explanation:
The info given is:
[tex] X= 21[/tex] number of students who said that they planned to work in a rural community
[tex] n= 380[/tex] represent the sample size selected
[tex]\hat p =\frac{21}{380}= 0.0553[/tex] the estimated proportion of students who said that they planned to work in a rural community
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
Replpacing we got:
[tex]0.0553 - 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0323[/tex]
[tex]0.0553 + 1.96\sqrt{\frac{0.0553(1-0.0553)}{380}}=0.0783[/tex]
A mean for estimation is the minimum-maximum variation estimate's C.I. The % of pupils planning to work in a rural community alters between 0.0323 and 0.0783.
Confidence interval:
Let's [tex]p^{}[/tex] represent the sampling fraction of the people who promised to work in a rural area.
Sample size:
[tex]n = 380[/tex]
x: the large number the pupils expected to work in a rural setting
[tex]p^{} = \frac{x}{n} \\\\p^{} = \frac{21}{ 380} = 0.0553\\\\(1- \alpha)\ \ 100\%[/tex]confidence for true proportion:
[tex]( p^{}\ \pm Z_{\frac{\alpha}{2}} \times \sqrt{p^{} \times \frac{(1-p^{})}{n}} ) \\\\[/tex]
For [tex]95\%[/tex]confidence interval:
[tex]\to 1 - \alpha = 0.95[/tex]
When:
[tex]\to \alpha = 0.05[/tex]
Calculating the value of Z by using the table:
[tex]\to Z_{0.025} = 1.96[/tex]
When the [tex]95\%[/tex] of the confidence interval:
[tex]\to (0.0553 \pm Z_{0.025} \times \sqrt{(0.0553 \times \frac{(1- 0.0553)}{380}})\\\\\to (0.0553 - Z_{0.025} \times \sqrt{(0.0553 \times \frac{(1- 0.0553)}{380})},0.0553 + Z_{0.025} \times \sqrt{(0.0553 \times \frac{(1- 0.0553)}{380}))}\\\\[/tex]
by solving the value we get:
[tex]\to ( 0.0323 , 0.0783 )[/tex]
We are [tex]95\%[/tex] sure that the true proportion of students planning to work in a rural community is between [tex]0.0323[/tex] and [tex]0.0783[/tex]. That is we are [tex]95\%[/tex] sure that the percentage of students planning to work in a rural community is between [tex]3.23\%[/tex] and [tex]7.83\%[/tex].Find out more about the Confidence interval here:
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Find a formula for the general term an of the sequence, assuming that the pattern of the first few terms continues. (Assume that n begins with 1.) −3, 2, − 4 3 , 8 9 , − 16 27 , ...
Answer:
The general term is
Sn = -(-2)ⁿ.3¹⁻ⁿ
step by step Explanation:
we were told to find a general term of the above sequence, what should come to mind is that the terms will follow an order....
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
If a varies inversely with b, and a=12 when b=1/3, find the equation that relates a and b
Answer:
a = 4 /b
or ab = 4
Step-by-step explanation:
An inverse relation is given by
a = k/b where k is the constant
Rewriting
ab = k
12 * 1/3 = k
4 = k
a = 4 /b
or ab = 4
What is the value of x?
45
m
(2x-5)
Answer:
if m is supposed to be the equals (=) sign then x = 25
Step-by-step explanation:
45 = (2x-5)
+5 +5
50 = (2x)
÷2 ÷2
25 = x
Answer: 70
Step-by-step explanation:
How do you find the surface area of a triangle? A square?
Answer:
The area formula of a triangle is (base * height) / 2 and the area of a square is s² where s is the length of one side.
The accompanying data represent the total travel tax (in dollars) for a 3-day business trip in 8 randomly selected cities. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outliers.
67.85 78.62 70.28 84.03 79.28 87.72 101.54 97.28
1. Determine a point estimate for the population mean travel tax.
2. Construct and interpret a 95% confidence interval for the mean tax paid for a three-day business trip.
Filling the missing boxes.
The lower bound is $_______and the upper bound is $_______. One can be______% confident that all cities have a travel tax between these values.
The lower bound is $______and the upper bound is $______. The travel tax is between these values for______% of all cities.
The lower bound is $_____and the upper bound is $______. There is a_______% probability that the mean travel tax for all cities is between these values.
The lower bound is $_______and the upper bound is______. One can be______% confident that the mean travel tax for all cities is between these values.
3. What would you recommend to a researcher who wants to increase the precision of the interval, but does not have access to additional data?
A. The researcher could decrease the level of confidence.
B. The researcher could decrease the sample standard deviation.
C. The researcher could increase the level of confidence.
D. The researcher could increase the sample mean.
Answer:
1. Point estimate M (sample mean): 83.33
2. The lower bound is $73.36 and the upper bound is $93.30. One can be______% confident that the mean travel tax for all cities is between these values.
3. A. The researcher could decrease the level of confidence.
Step-by-step explanation:
A point esimate for the population mean travel tax can be done with the sample mean.
We can calculate the sample mean as:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{8}(67.85+78.62+70.28+84.03+79.28+87.72+101.54+97.28)\\\\\\M=\dfrac{666.6}{8}\\\\\\M=83.33\\\\\\[/tex]
2. We have to calculate a 95% confidence interval for the mean.
The sample mean is M=83.33.
The sample size is N=8.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
We calculate the sample standard deviation as:
[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{7}((67.85-83.33)^2+(78.62-83.33)^2+(70.28-83.33)^2+. . . +(97.28-83.33)^2)}\\\\\\s=\sqrt{\dfrac{994.49}{7}}\\\\\\s=\sqrt{142.07}=11.92\\\\\\[/tex]
The standard error is:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{11.92}{\sqrt{8}}=\dfrac{11.92}{2.828}=4.214[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=8-1=7[/tex]
The t-value for a 95% confidence interval and 7 degrees of freedom is t=2.36.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.36 \cdot 4.214=9.97[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 83.33-9.97=73.36\\\\UL=M+t \cdot s_M = 83.33+9.97=93.30[/tex]
The 95% confidence interval for the mean travel tax is (73.36, 93.30).
We can be 95% confident that the true mean travel tax is within this interval.
3.. If we have no access to additional data, we can not decrease the standard deviation or increase the sample size.
The only way to have a narrower confidence interval is decreasing its level of confidence. With the same sample information, the lower the confidence, the narrower is the interval.
What is the horizontal asymptote of the function f (x) = StartFraction (x minus 2) Over (x minus 3) squared EndFraction?
The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.
What is an asymptote?An asymptote is a line that is approached by a curve but never touches it. In other words, an asymptote is a line where the graph of a function converges.
What is the horizontal asymptote?Because a horizontal asymptote is a horizontal line, its equation is of the form y = k. The horizontal asymptote of a rational function is at y = 0, which is the x-axis if the degree of the numerator is smaller than the degree of the denominator.
How to solve this problem?Here, the function is f(x) = (x-2)/(x-3)². Here the degree of the numerator of this rational function is 1 and the degree of the denominator is 2. Since 1<2, the horizontal asymptote is at y = 0 which is the x-axis.
The horizontal asymptote of the function f(x) = (x-2)/(x-3)² is at y = 0 which is the x-axis.
Learn more about horizontal asymptotes here -
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Answer:
c
Step-by-step explanation:
Solve these equations using elimination not substitution? 8x + 3y = 13 3x + 2y = 11 15 Points!
Answer:
x = -1, y = 7
Step-by-step explanation:
8x + 3y = 13
3x + 2y = 11
Multiply the first equation by -2 and the second equation by 3. Then add them.
-16x - 6y = -26
(+) 9x + 6y = 33
--------------------------
-7x = 7
x = -1
Now substitute x = -1 in the first original equation and solve for y.
8x + 3y = 13
8(-1) + 3y = 13
-8 + 3y = 13
3y = 21
y = 7
Answer: x = -1, y = 7
The critical value t* gets larger as the confidence level increases. True or false?
Answer:
We can find the critical value [tex]t_{\alpha/2}[/tex]
And for this case if the confidence increase the critical value increase so then this statement is True
Step-by-step explanation:
For a confidence level given c, we can find the significance level like this:
[tex] \alpha=1 -c[/tex]
And with the degrees of freedom given by:
[tex] df=n-1[/tex]
We can find the critical value [tex]t_{\alpha/2}[/tex]
And for this case if the confidence increase the critical value increase so then this statement is True
Please help ?!!! Solve the three equations in the table using any method of your choice. List the method you used.
Equation
x^2-4=-12
-9x^2+4x-10=0
x^2+8x=-17
With solutions and method
Step-by-step explanation:
[tex]x = \frac{ - b \frac{ + }{ - } \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
The quadratic formula is honestly the most straightforward way of solving here.
Your other options are completing the square (which is the same thing as the quadratic formula but it's good to know that method if you have to take Integral Calculus at some point) or maybe factoring by grouping if it's appropriate. But the quadratic formula will work for you in all three equations:
1) a=1, b=0, c=8
This reduces pretty quickly into x=8i,-8i due to the negative under the radical. (Actually we didn't even really need the formula here.)
2) a=-9, b=4, c=-10
This reduces into x=(-4+i√(344))/-18, (-4-i√(344))/-18 and doesn't go any further because 344 isn't a perfect square.
3) a=1, b=8, c=17
This reduces to x=(-4+i), (-4-i)
So those are the answers for each.
Please Refer to the screenshot. Hope this helps!
Average rate of change from G from x=1 to x=4 is
Answer:
3
Step-by-step explanation:
minus the variable, 4-1 is 3.
What is the value of the 7 in the number 0.873?
Write your answer as a fraction.
Answer: 7/100
Step-by-step explanation:
In this question, ignore the 8 and the 3 and focus on the 7. Isolate it and you will get 0.07. 0.07 in fraction from is 7/100.
The place value of 7 in the decimal number 0.873 is in the hundredth place thus it will be 7/100 or 0.07.
What is a number system?The number system is a way to represent or express numbers.
A decimal number is a very common number that we use frequently.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
Given the decimal,
0.873
8 → Tenth place (Fraction value 8/10)
7 → Hundredth place(Fraction value 7/100)
3 → Thousandth place (Fraction value 3/1000)
Since 7 is at hundredth place thus it will be 7/100.
Hence "The place value of 7 in the decimal number 0.873 is in the hundredth place thus it will be 7/100 or 0.07".
For more about the number system,
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Will give brainliest, someone please help
━━━━━━━☆☆━━━━━━━
▹ Answer
Area = 9
▹ Step-by-Step Explanation
A = b * h ÷ 2
A = 9 * 2 ÷ 2
A = 9
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
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WILL MARK BRAINIEST IF CORRECT!!!! Select the correct answer. This table represents a function. Is this statement true or false?
Answer:
true
Step-by-step explanation:
doesn't over lap each other
Find the surface area of this composite solid.
Answer:
B
Step-by-step explanation:
area of top on triangle=1/2×4×3=6m²
area of four top triangles=6×4=24 m²
area of bottom square=4×4=16 m²
area of four side rectangles=4×(4×5)=80 m²
Total area= 24+16+80=120m²
A human resources representative claims that the proportion of employees earning more than $50,000 is less than 40%. To test this claim, a random sample of 700 employees is taken and 305 employees are determined to earn more than $50,000.The following is the setup for this hypothesis test:{H0:p=0.40Ha:p<0.40Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places.
Answer:
The statistic for this case would be:
[tex] z=\frac{\hat p -p_o}{\sqrt{\frac{\hat p(1-\hat p)}{n}}}[/tex]
And replacing we got:
[tex] z= \frac{0.436-0.4}{\sqrt{\frac{0.436*(1-0.436)}{700}}}= 1.92[/tex]
Step-by-step explanation:
For this case we have the following info:
[tex] n =700[/tex] represent the sample size
[tex] X= 305[/tex] represent the number of employees that earn more than 50000
[tex]\hat p=\frac{305}{700}= 0.436[/tex]
We want to test the following hypothesis:
Nul hyp. [tex] p \leq 0.4[/tex]
Alternative hyp : [tex] p>0.4[/tex]
The statistic for this case would be:
[tex] z=\frac{\hat p -p_o}{\sqrt{\frac{\hat p(1-\hat p)}{n}}}[/tex]
And replacing we got:
[tex] z= \frac{0.436-0.4}{\sqrt{\frac{0.436*(1-0.436)}{700}}}= 1.92[/tex]
And the p value would be given by:
[tex] p_v = P(z>1.922)= 0.0274[/tex]
Mount Whitney is 3072 m tall convert the height to kilometers
Answer:
3.072km
Step-by-step explanation:
[tex]3072m*(\frac{1km}{1000m} )=3.072km[/tex]
Suppose that the function g is defined, for all real numbers, as follows.
How is copying line segment similar to copying an angle?
Answer:
In terms of construction, copying a line segment and an angle requires a fixed compass width as a basic tool
Step-by-step explanation:
The basic similarity is in both constructions, or copies is that we are going to use the same compass width in each case as the basic tool to copy a line segment or an angle.
hope this helpes
be sure to give brainliest
Answer:
An angle is form by two rays and the two line segment share a common points and we utilize a straightedge for drawing the comparative figure on paper.
At that point, utilize the straightedge and the compass used to copy this type of figure precisely. To duplicate the given figure, we should copy line as well as angle.
The line of segment are basically formed by adjusting the compass and makes it equal to the line segment length and then copy each point in the figure.
linear equation: y = 5x + 6
quadratic equation: y = x^2 +7x - 18
Show all work to solving your system of equations algebraically.
Answer:
(4, 26)
(-6, -24)
Step-by-step explanation:
Step 1: Substitution
5x + 6 = x² + 7x - 18
Step 2: Move everything to one side
0 = x² + 2x - 24
Step 3: Factor
(x - 4)(x + 6) = 0
Step 4: Find roots
x = 4, -6
Step 5: Plug in x to find y
y = 5(4) + 6
y = 20 + 6
y = 26
y = 5(-6) + 6
y = -30 + 6
y = -24
Use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following equation. y = x squared + x + 6 a. (0.5, -5.75) c. (-0.5, 6) b. (-0.5, 5.75) d. (0.5, 5.75) Please select the best answer from the choices provided A B C D
Answer:
B. (-0.5, 5.75)
Step-by-step explanation:
Use a graphing calc and analyze the graph for the minimum value (vertex).
246,000 in scientific notation
Answer:
246000 in scientific notation is 2.46e5, or 2.46 x 10^5
Step-by-step explanation:
246000, move the decimal place 5 places to the left.
2.4x10^5
Answer:
2.46 × 10⁵
Step-by-step explanation:
The decimal point is after the first non-zero digit.
⇒ 2.46
Multiply the number with base 10 and an exponent which will equal to 246,000.
⇒ 10⁵
Maurice shot 2 under par, or -2, on each of the first 4 holes of golf. What is his score with respect to par after the fourth hole?
Answer: -8
Step-by-step explanation: If he scored -2 four times then his score would be -8 (-2×4).
I NEED HELP PLEASE, THANKS! :)
Write 18(cos169° + isin169°) in rectangular form. Round numerical entries in the answer to two decimal places. (Show work)
Answer:
z = -17.67 + i3.43
Step-by-step explanation:
Let us apply the formula z = r(cos Ф + i sin Ф), given 18(cos169° + isin169°) -
z = 18( cos169 + isin169 ),
z = r(cos Ф + i sin Ф)
Now we can solve this question in the form z = a + bi, in this case where a = 18 cos169, and b = 18 sin169. This is as a = r cos Ф and b = r sin Ф -
sin169 is positive, while cos169 is negative, thus -
a = -17.6692893021...,
b = 3.43456191678...
Rectangular Form, z = -17.67 + i3.43
Hope that helps!
Yesterday in Juneau, Alaska it was -20 degrees and in San Diego, California it was 75 degrees. What was the difference in temperature between these two cities?
Select one:
a. -20 degrees
b. 55 degrees
c. 75 degrees
d. 95 degrees
Answer: d) 95 degrees
Step-by-step explanation:
To find this solution, simply subtract -20 from 75, to get 95. In reality, you would take the absolute value of one temperature - another, but all you need to remember is to always subtract the smaller temperature from the larger.
Answer:
95 degrees(answer d)
Step-by-step explanation:
when you have a negative temp. and a positive temp., you add the two numbers to find the difference.
that means, 20+75=95 degrees(take away the negative sign when adding only.)
That means the difference between the two temperatures is 95 degrees.
A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 290 babies were born, and 261 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective?
Answer:
The 99% confidence interval estimate of the percentage of girls born is between 85.46% and 94.54%.
Usually, babies are equally as likely to be boys or girls. Here, it is desired to increase the probability of conceiving a girl, which is achieved, considering the lower bound of the confidence interval is considerably above 50%.
Step-by-step explanation:
Confidence interval for the proportion:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 290, \pi = \frac{261}{290} = 0.9[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 - 2.575\sqrt{\frac{0.9*0.1}{290}} = 0.8546[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.9 + 2.575\sqrt{\frac{0.9*0.1}{290}} = 0.9454[/tex]
Percentage:
Proportion multplied by 100.
0.8546*100 = 85.46%
0.9454*100 = 94.54%
The 99% confidence interval estimate of the percentage of girls born is between 85.46% and 94.54%.
Based on the result, does the method appear to be effective?
Usually, babies are equally as likely to be boys or girls. Here, it is desired to increase the probability of conceiving a girl, which is achieved, considering the lower bound of the confidence interval is considerably above 50%.
Please help me the venn diagram is wrong too im confused on how to do this :(((
Answer:
probability of chosing a student that has a cat and a dog is 9/25
Step-by-step explanation:
And yes the Venn diagram is wrong because you forgot to subtract 9 from 15 and 16
This makes it
[ 3 ( 6 ( 9 ) 7 ) ]
3 + 6 + 9 + 7 = 25
What is the discrimination of this function !! Please help
Answer:
Option C is correct.
The discriminant of the function is negative since the function doesn't have real roots as evident from the graph.
Step-by-step explanation:
The discriminant of a quadratic equation is the part of the quadratic formula underneath the square root symbol, that is, (b² - 4ac).
The discriminant tells us whether there are two solutions, one solution, or no solutions.
- When the discriminant is positive or greater than zero, that is, (b² - 4ac) > 0, the quadratic function has 2 real distinct roots.
- When the discriminant is equal to zero, that is, (b² - 4ac) = 0, the quadratic function has 1 repeated root.
- When the discriminant is negative or lesser than zero, that is, (b² - 4ac) < 0, the quadratic function has no real roots.
For this question, the graph of the quadratic function shows that it doesn't have real roots (this is evident because the graph doesn't cross the x-axis), hence, the duscriminant of this quadratic function has to bee negative.
Hope this Helps!!!
Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L), or go straight (S). Consider observing the direction for each of three successive vehicles.
A) List all outcomes in the event A that all three vehicles go in the same direction.
B) List all outcomes in the event B that all three vehicles take different directions.C) List all outcomes in the event C that exactly two of the three vehicles turn right.D) List all outcomes in the event D that exactly two vehicles go in the same direction.E) List outcomes in D'.F) List outcomes in C ∪ D.G) List outcomes in C ∩ D.
Answer:
A) A = {RRR, LLL, SSS}
B) B = {LRS. LSR, RLS, RSL, SLR, SRL}
C) C = {RRL, RRS, RSR, RLR, LRR, SRR}
D) D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}
E) D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}
F) C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}
G) C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}
Step-by-step explanation:
A) All vehicles must go right, left or straight ahead (three possibilities):
A = {RRR, LLL, SSS}
B) One vehicle must go right, one must go left, and the remaining one must go straight ahead (six possibilities):
B = {LRS. LSR, RLS, RSL, SLR, SRL}
C) There are three ways that exactly two vehicles go right (1 and 3, 2 and 3, 1 and 2), there are then two options for the remaining vehicle (left and straight) for a total of six possibilities:
C = {RRL, RRS, RSR, RLR, LRR, SRR}
D) Follow the same reasoning from the previous item, but multiply the number of possibilities by 3 (for each direction in which both cars can go: right, left or straight):
D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}
E) D' is the set containing all possibilities not present in set D. D' is comprised by the possibilities of all vehicles going in the same direction, or each vehicle in a different direction:
D' ={RRR, LLL, SSS, LRS. LSR, RLS, RSL, SLR, SRL}
F) The outcomes in C ∪ D is the union of elements from set C and D (neglecting repeated values), which happens to be all values in set D.
C ∪ D = {RRL, RRS, RSR, RLR, LRR, SRR. LLR, LLS, LSL, LRL, RLL, SLL, SSL, SSR, SLS, SRS, LSS, RSS}
G) The outcomes in C ∩ D is the list of values present in both sets C and D, which happens to be all values in set C:
C ∩ D = {RRL, RRS, RSR, RLR, LRR, SRR}
Kimberly is a program director for the channel KID. She tracked the cartoons shown on the channel for a week. The probability that the show had animals in it was 0.7. The probability that the show aired more than 10 times was 0.4. The probability that the show had animals in it and aired more than 10 times was 0.2. Which equation shows the correct use of the addition rule to determine the probability that a randomly selected show had animals in it or aired more than 10 times?
Options
0.7+0.2−0.4=0.5 0.7+0.2=0.9 0.7+0.4=1.1 0.4+0.2=0.6 0.7+0.4−0.2=0.9Answer:
[tex](E)0.7+0.4-0.2=0.9[/tex]
Step-by-step explanation:
In probability theory
[tex]P$(A or B)=P(A)+P(B)$-$P(A and B)[/tex]
Let the event that the show had animals in it = A
P(A)=0.7
Let the event that the show aired more than 10 times =B
P(B)=0.4
P(A and B)= 0.2
[tex]P$(A or B)$=0.7+0.4-0.2=0.9[/tex]
Therefore, the equation which shows the correct use of the addition rule to determine the probability that a randomly selected show had animals in it or aired more than 10 times is:
[tex]0.7+0.4-0.2=0.9[/tex]
The correct option is E.