Answer:
a) 3.6%
Step-by-step explanation:
The given question mixed up, below is the correct question:
The bumper car ride at the state fair has 2 red cars, 4 green cars, and 2 blue cars. Garth is first in line for the ride and is assigned a car at random. Patty is next in line and is randomly assigned a car. Find the probability that both events A and B occur. Express your answer as a percent. If necessary, round your answer to the nearest tenth.
Calculation:
Given that the state fair has 2 red cars, 4 green cars and 2 blue cars.
There are therefore 2+4+2 = 8 cars in total.
Probability that Events A occurs P(A) = [tex]\frac{2}{8}[/tex] = 4
Probability that Events B occurs P(B) = [tex]\frac{1}{7}[/tex]
Probability that Events A and B occur P(A ∩ B) = [tex]\frac{2}{8}[/tex] × [tex]\frac{1}{7}[/tex] = [tex]\frac{2}{56}[/tex] = 0.0357 = 3.57% ≈ 3.6%
Therefore, the probability that both events A and B occur is 3.6%
Final answer:
The probability that both Garth and Patty will drive a red bumper car is found by multiplying the probability of Garth picking a red car (1/4) by the probability of Patty picking a red car after Garth (1/7), resulting in 1/28 or approximately 3.6%.
Explanation:
To solve the problem, we need to calculate the probability that both events A and B happen, which involves Garth and Patty both getting a red bumper car. Initially, there are 2 red cars, 4 green cars, and 2 blue cars, totaling 8 cars.
Event A: Garth picks a red car. The probability of this happening is the number of red cars over the total number of cars. So P(A) = 2/8 = 1/4.
After Garth picks a red car, there is 1 red car, 4 green cars, and 2 blue cars left, totaling 7 cars.
Event B: Patty picks a red car after Garth has already picked one. The probability of this happening is the number of remaining red cars over the total number of remaining cars. So P(B after A) = 1/7.
The probability that both A and B occur is the product of the probability of A and the probability of B given A has occurred. So P(A and B) = P(A) × P(B after A) = (1/4) × (1/7).
P(A and B) = 1/28. To express this as a percent, we multiply by 100%: (1/28) × 100% ≈ 3.6%.
Therefore, the probability that both Garth and Patty will drive a red bumper car is approximately 3.6%, which corresponds to option d.
The population of a city (in millions) at time t (in years) is P(t)=2.6 e 0.005t , where t=0 is the year 2000. When will the population double from its size at t=0 ?
Answer:
year 2139
Step-by-step explanation:
The population will double when the factor e^(.005t) is 2.
e^(.005t) = 2
.005t = ln(2)
t = ln(2)/0.005 = 138.6
The population will be double its size at t=0 when t=138.6. That is the population will be about 5.2 million in the year 2139.
The population will double by the year 2139 from its value of 2.6 million in year 2000.
Population function :
[tex]P(t) = 2.6 {e}^{0.005t} [/tex]
Population size at t = 0
[tex]P(0) = 2.6 {e}^{0.005(0)} = 2.6(1) = 2.6[/tex]
Population at t = 2.6 million.
For the population to double ;
2.6 × 2 = 5.2 million :
[tex]5.2 = 2.6 {e}^{0.005t} [/tex]
We solve for t
[tex] \frac{5.2}{2.6} = {e}^{0.005t} [/tex]
[tex]2 = {e}^{0.005t} [/tex]
Take the In of both sides
[tex] ln(2) = 0.005t[/tex]
[tex]t \: = ln(2) \div 0.005 = 138.629[/tex]
The population will double after 139 years
Therefore, the population will double by the 2139 (Year 2000 + 139 years) = year 2139.
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HVAC technician average salary = $28/hour with a one-year Tech school certification costing an average of $7,500. What would your pay be for your first year of work? Assume you work a 40 hour week for 50 weeks.
Answer:
56,000
Step-by-step explanation:
In your first year of work, you would make $56,000.
The pay rate is $28 per hour and a work week has 40 hours for the HVAC technician.
In a week, you will make:
= Number of hours in week x Amount per hour
= 40 x 28
= $1,120
In a year, assuming there are 50 weeks, the HVAC technician would make:
= Amount per week x Number of weeks in year
= 1,120 x 50
= $56,000
In conclusion, you would make $56,000 a year as an HVAC technician.
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Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of points scored during a basketball game. (b) The amount of rain in City Upper B during April.
Answer:
a) Discrete, because the number of point scored during basket ball is countable.
For instance, the amount of point scored in a basketball could be 75, 103, 63 etc. The numbers are countable
b) Continuous, because the amounts of rainfall is a random variable that is uncountable.
For instance, the amount of rainfall in City Upper B during April could be 0.10 inches of rain per hour, 0.30 inches of rain per hour. This numbers are not countable, they are rather approximated or rounded off.
Step-by-step explanation:
A random variable is considered discrete if its possible values are countable while a random variable is considered to be continuous if it's possible values are not countable.
Lucia hit a golf ball 240 feet. How many yards did she hit the ball?
A) 80 yards
B) 60 yards
C) 120 yards
D) 300 yards
Answer:
a
Step-by-step explanation:
a yard is 3 feet.24/3 equals 8 .then 80!
A trade magazine routinely checks the drive-through service times of fast-food restaurants. Upper A 95% confidence interval that results from examining 745 customers in one fast-food chain's drive-through has a lower bound of 177.6 seconds and an upper bound of 181.0 seconds. What does this mean?
Answer:
-A person can be 95% confident that the mean drive through service time lies between 177.6 seconds and 181.0 seconds.
Step-by-step explanation:
- Confidence level is the degree of certainty we have on a particular statistic.
-The 95% confidence interval means that we are 95% confident that the mean drive through service time is lies between 177.6 seconds and 181.0 minutes.
Cars arrive randomly at a tollbooth at a rate of 20 cars per 10 minutes during rush hour. What is the probability that exactly five cars will arrive over a five-minute interval during rush hour?
Answer:
3.78% probability that exactly five cars will arrive over a five-minute interval during rush hour
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given time interval.
20 cars per 10 minutes
So for 5 minutes, [tex]\mu = 10[/tex]
What is the probability that exactly five cars will arrive over a five-minute interval during rush hour?
This is P(X = 5).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 5) = \frac{e^{-10}*(10)^{5}}{(5)!} = 0.0378[/tex]
3.78% probability that exactly five cars will arrive over a five-minute interval during rush hour
The probability that exactly five cars will arrive over a five-minute interval during rush hour is approximately 0.0378 or 3.78%.
Firstly, the arrival rate is given as 20 cars per 10 minutes. Thus, the arrival rate per minute, λ, is 20 cars / 10 minutes = 2 cars per minute. To find the arrival rate for a 5-minute interval, we multiply this rate by 5 minutes: λ = 2 cars/minute * 5 minutes = 10 cars.
The Poisson probability formula is:
P(X = k) = (λ^k * e^(-λ)) / k!
where λ is the average number of cars in the interval, k is the number of cars, and e is the base of the natural logarithm (approximately equal to 2.71828).
In this problem, we need to find the probability of exactly 5 cars arriving in a 5-minute interval. Thus, λ = 10 and k = 5:
P(X = 5) = (10^5 * e^(-10)) / 5!
P(X = 5) = (100000 * e^(-10)) / 120
P(X = 5) ≈ (100000 / 148.4132) / 120
P(X = 5) ≈ 0.0378
Therefore, the probability that exactly five cars will arrive over a five-minute interval during rush hour is approximately 0.0378 or 3.78%.
evaluate tan( – 33pi/4)
Answer:??
Step-by-step explanation:
Answer: dont have an answer
Step-by-step explanation:
sorry
A publisher reports that 53%53% of their readers own a particular make of car. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 250250 found that 44%44% of the readers owned a particular make of car. Determine the P-value of the test statistic. Round your answer to four decimal places.
Answer:
[tex]z=\frac{0.44 -0.53}{\sqrt{\frac{0.53(1-0.53)}{250}}}=-2.85[/tex]
[tex]p_v =2*P(z<-2.85)=0.0044[/tex]
Step-by-step explanation:
Data given and notation
n=250 represent the random sample taken
[tex]\hat p=0.44[/tex] estimated proportion of of the readers owned a particular make of car.
[tex]p_o=0.53[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true porportion is equal to 0.53.:
Null hypothesis:[tex]p=0.53[/tex]
Alternative hypothesis:[tex]p \neq 0.53[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.44 -0.53}{\sqrt{\frac{0.53(1-0.53)}{250}}}=-2.85[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z<-2.85)=0.0044[/tex]
Help me please I'm in 6th grade
Answer:
1271.7 cm3
Step-by-step explanation:
Answer:
1,271.7cm
Step-by-step explanation:
V=π*r^2 * (h/3)
V= 3.14 * 9^2 * (15/3)
V= 3.14 * 81 * 5 =1271.7
The radius of a certain wheel is 7 inches. Which of the following is closet to the circumference of the wheel?
A. 10.99,
B. 21.98,
C. 14.21,
D. 43.96
A couple plans to have three children. Each child is equally likely to be a girl or boy, with gender independent of that of the other children. a. Construct a sample space for the genders of the children, using B for boy and G for girl. b. Find the probability that all 3 of the children are boys. c. Answer part b if, in reality, for a given child, the chance of a boy is 0.51.
Answer:
a) X={BBB;BBG:BGG:GGG}
b) P(BBB)=0.125
c) P(BBB)=0.133
Step-by-step explanation:
The sample space states all the possible values that the random variable can take. In this case, the order does not matter, so the possible combinations for the random variable are:
X={BBB;BBG:BGG:GGG}
The probability p of having a boy is p=0.5, as it is equally likely to have a girl or a boy.
The probability that all 3 children are boys can be calculated multiplying 3 times the probability of having a boy. That is:
[tex]P(X=BBB)=p\cdot p\cdot \cdot p =p^3=0.5^3=0.125[/tex]
In the case that the chance of having a boy is p'=0.51, the probabiltity of having 3 boys become:
[tex]P(X=BBB)=p'^3=0.51^3=0.133[/tex]
Can someone help me with this question pleaseeee:(
Answer:
try y=3/4x+2
Step-by-step explanation:
2 because it is the y intercept
3/4 because it is the slope
Answer:
The slope for this is 3/4. y=3/4x+2
Carla has a list of all 720 students in her middle school. She writes the name of each student on a slip of paper and puts each slip in a box. Then she pulls out 30 names from the box to decide who she will survey about the upcoming school election. How many students are in Carla's Sample?
Answer:
Step-by-step explanation:
Given that,
Clara has a list of 720 names
She decided to survey 30 names from the sample.
It is very straight forward, there are 30 names in Clara sample
But this sample can be use to generalize the overall population of 720 students if they are given equal chances of being selected maybe by taking a survey or picking their names randomly from a box
If it not a biased sample then we can use the survey to generalized the overall population
So, there are 720 names in Clara's sample
Determine whether the function is even, odd, or neither. Then determine whether the function's graph is symmetric with respect to the y-axis, the origin, or neither. f(x)equals=4 x squared plus x Superscript 4 Baseline plus 3
The function f(x) = 4x2 + x4 + 3 is even because the substitution of (-x) for x results in the original function. It's not odd because replacing (-x) for x doesn't give the negative of the original function. Hence, as an even function, its graph is symmetric with respect to the y-axis.
Explanation:The function f(x) = 4x2 + x4 + 3 can be tested for symmetry. If a function is even, its graph is symmetric with respect to the y-axis. If a function is odd, its graph is symmetric with respect to the origin.
To test if a function is even, we substitute (-x) for x in the function and simplify. If the result is the original function, then the function is even. For the given function, f(-x) = 4(-x)2 + (-x)4 + 3 = 4x2 + x4 + 3. So, the function is even.
To test if a function is odd, we also substitute (-x) for x in the function and simplify. If the result is the negative of the original function, then the function is odd. In our case, f(-x) is not the negative of f(x), so the function is not odd.
Therefore, the function is even and its graph is symmetric with respect to the y-axis.
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a sweater is marked 30% off during an end of the season sale. if the sweater was orginally 56.00, how much was the sweater on sale for
Answer:
39.20000
Step-by-step explanation:
Sweater costs 56.00
To calculate the discounted price of the sweater
56 * (30/100) = 16.8
We used (30/100) to find out the 30 percent of the sweater which will be on discount/reduced.
56-16.8=39.2 is the discounted price
Then we subtract the amount of discount from the original price of sweater to find out the discounted price.
Given that M=(2 0 6 3 7), then the order of the matrix M is
Answer:
63720
Step-by-step explanation:
yes
The National Institute of Standards and Technology (NIST) supplies "standard materials" whose physical properties are supposed to be known. For example, you can buy from NIST an iron rod whose electrical conductivity is supposed to be 10.1 at 293 kelvin. (The units for conductivity are microsiemens per centimeter. Distilled water has conductivity 0.5.) Of course, no measurement is exactly correct. NIST knows the variability of its measurements very well, so it is quite realistic to assume that the population of all measurements of the same rod has the Normal distribution with mean μequal to the true conductivity and standard deviation σ = 0.1. Here are six measurements on the same standard iron rod, which is supposed to have conductivity 10.1.
10.07 9.89 10.04 10.16 10.21 10.11
--> NIST wants to give the buyer of this iron rod a 90% confidence interval for its true conductivity. What is this interval? (Round your answers to three decimal places.)
ANSWER : __________ to ___________ microsiemens per centimeter
Answer:
[tex]10.08-1.64\frac{0.1}{\sqrt{6}}=10.013[/tex]
[tex]10.08+1.64\frac{0.1}{\sqrt{6}}=10.147[/tex]
So on this case the 90% confidence interval would be given by (10.013;10.147)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma =0.1[/tex] represent the population standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (1)
In order to calculate the mean and the sample deviation we can use the following formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
The mean calculated for this case is [tex]\bar X=10.08[/tex]
Since the Confidence is 0.90 or 90%, the value of [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that [tex]z_{\alpha/2}=1.64[/tex]
Now we have everything in order to replace into formula (1):
[tex]10.08-1.64\frac{0.1}{\sqrt{6}}=10.013[/tex]
[tex]10.08+1.64\frac{0.1}{\sqrt{6}}=10.147[/tex]
So on this case the 90% confidence interval would be given by (10.013;10.147)
what is the distance between 120 and -150 on a number line
Answer:
[tex]270[/tex]
Step-by-step explanation:
[tex]120 - ( - 150) \\ 120 + 150 \\ = 270[/tex]
The distance between 120 and -150 on a number line is calculated by subtracting the smaller number from the larger number. Given that -150 is negative, the subtraction turns into addition, leading to a distance of 270.
Explanation:To find the distance between 120 and -150 on a number line, you need to take the following steps:
Identify the two points on the number line. In this case, they are 120 and -150.Subtract the smaller number from the larger one. Since 120 is greater than -150, you subtract -150 from 120.However, since -150 is a negative number, when you subtract it, it becomes addition. So the calculation becomes 120 + 150.The result will be the distance between the two numbers, which is 270.Therefore, the distance between 120 and -150 on a number line is 270
.
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A random sample of 35 bags yielded a confidence interval for the number of calories per bag of 128.2 to 139.8 calories. Is there evidence that the nutrition label does not provide an accurate measure of calories in the bags of potato chips?
Answer:
As Null hypothesis is not satisfied so there is no evident that nutrition label doesn't provide accurate measure of calories.
Answer:
Yes
Step-by-step explanation:
Complete question is:
The nutrition label on a bag of potato chips says that a one ounce(28g) serving of potato chips has 130 calories and contains 10 grams of fats with 3 grams of saturated fats. A random sample of 35 bags yielded a confidence interval for the number of calories per bag of 128.2 to 139.8 calories. Is there evidence that the nutrition label does not provide an accurate measure of calories in the bags of potato chips?
The calories stated in nutriton label (130) is close to the lower bound of confidence interval range which is 128.2. So this can be an evidence that nutrition lable may not provide an accurate measure of calories in bags.
which statement best describes the interquartile range of set of weights
120 115 135 105 80 160
Answer:
The IQR is 30
Step-by-step explanation:
Answer: the difference between the second and fifth element of the set after it has been ordered from least to greatest (D)
Step-by-step explanation: I just finished the quiz and got It correct
match the numbers with the correct label. i will MARK YOU BRAINLIEST if your right, only answer if you know what your doing!!! :))
Answer:
a = 1/7, b = 0.2, c = 3/9
Step-by-step explanation:
[tex]0.2=\frac{2}{10} = \frac{1}{5}[/tex]
[tex]\frac{1}{7}[/tex]
[tex]\frac{3}{9}=\frac{1}{3}[/tex]
[tex]\frac{1}{5} > \frac{1}{7}[/tex] placing it farther along the number line, making 0.2 the red label (b)
[tex]\frac{1}{7}[/tex] is the smallest fraction that you are given, so it will be closest to 0, making it the blue label (a)
[tex]\frac{1}{3} > \frac{1}{4}[/tex] so [tex]\frac{3}{9}[/tex] is the green label (c)
A machine fills 64-ounce jugs with detergent. Assume the distribution of the amount of detergent in these jugs is Normal. Under standard circumstances, the mean amount should be 64 ounces with a standard deviation of 0.4 ounces. A quality control inspector regularly checks the amount poured into the jugs to see if the machine needs an adjustment or not, which is needed when the machine either overflows or underfills the jugs. If the machine is running on target, what proportion of jugs receives more than 65 ounces of detergent
Answer:
The proportion of jugs which receive more than 65 ounces of detergent is 0.0062 or 0.62%
Step-by-step explanation:
Mean amount of detergent = u = 64
Standard deviation = [tex]\sigma[/tex] = 0.4
We need to find the proportion of jugs with over 65 ounces of detergent. Since the population is Normally Distributed and we have the value of population standard deviation, we will use the concept of z-score to solve this problem.
First we will convert 65 to its equivalent z-score, then using the z-table we will desired proportion. The formula to calculate the z-score is:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
x = 65 converted to z score will be:
[tex]z=\frac{65-64}{0.4}=2.5[/tex]
Therefore, the probability of detergent being more than 65 ounces is equivalent to probability of z-score being over 2.5
i.e.
P(X > 65) = P(z > 2.5)
From the z-table and using the property of symmetry:
P(z > 2.5) = 1 - P(z < 2.5)
= 1 - 0.9938
= 0.0062
Therefore,
P(X > 65) = P(z > 2.5) = 0.0062
So, the proportion of jugs which receive more than 65 ounces of detergent is 0.0062 or 0.62%
To find the proportion of jugs that receive more than 65 ounces of detergent when the machine is running on target, we can use the properties of the normal distribution. The proportion is about 0.62%.
Explanation:To find the proportion of jugs that receive more than 65 ounces of detergent when the machine is running on target, we can use the properties of the normal distribution. Since the mean amount is 64 ounces and the standard deviation is 0.4 ounces, we can calculate the Z-score for 65 ounces using the formula Z = (X - μ) / σ, where X is the value of interest, μ is the mean, and σ is the standard deviation.
Plugging in the values, we get Z = (65 - 64) / 0.4 = 2.5. Now, we can look up the cumulative probability for a Z-score of 2.5, which represents the proportion of jugs that receive less than or equal to 65 ounces. Subtracting this proportion from 1 gives us the proportion of jugs that receive more than 65 ounces of detergent when the machine is running on target.
Using a Z-table or a calculator, we find that the cumulative probability for a Z-score of 2.5 is approximately 0.9938. Subtracting this from 1, we find that the proportion of jugs that receive more than 65 ounces of detergent when the machine is running on target is about 0.0062 or about 0.62%.
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plz help!!!!
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p∗=73%. You would like to be 90% confident that your esimate is within 4% of the true population proportion. How large of a sample size is required
Answer:
Ans: n = [1.645/0.02]^2*0.13*0.87 = 766 when rounded up
Step-by-step explanation:
please please Work out the value of (2.5 × 10−2) ÷ (3.8 × 103) Give your answer in standard form correct to 3 significant figures.
Answer:
The answer is 115/1957 and in decimal form is 0.0558634
Step-by-step explanation:
A market survey shows that half the owners of Sorey State Boogie Boards became disenchanted with the product and switched to C&T Super Professional Boards the next surf season, while the other half remained loyal to Sorey State. On the other hand, three quarters of the C&T Boogie Board users remained loyal to C&T, while the rest switched to Sorey State. Set these data up as a Markov transition matrix.
(Let 1 = Sorey State, and 2 = C&T.)
Answer:
[tex]\left[\begin{array}{ccc}\dfrac{1}{2} &\dfrac{1}{2}\\\\\dfrac{1}{4}&\dfrac{3}{4}\end{array}\right][/tex]
Step-by-step explanation:
Let 1 = Sorey State, and 2 = C&T
Half the owners of Sorey State Boogie Boards became disenchanted with the product and switched to C&T Super Professional Boards the next surf season.
This means half moved from State 1 to State 2.Three quarters of the C&T Boogie Board users remained loyal to C&T, while the rest switched to Sorey State.
The rest [tex](1-\frac{3}{4}= \frac{1}{4})[/tex] moved from State 2 to State 1.The Markov Transition Matrix is presented below:
[tex]\left\begin{array}{ccc}\\\\\\$Sorey State&1\\\\C\&T&2\end{array}\right\left[\begin{array}{ccc}$Sorey State&C\&T\\1&2\\------&------\\\dfrac{1}{2} &\dfrac{1}{2}\\\\\dfrac{1}{4}&\dfrac{3}{4}\end{array}\right][/tex]
The above is presented for clarity sake. The transition matrix is:
[tex]\left[\begin{array}{ccc}\dfrac{1}{2} &\dfrac{1}{2}\\\\\dfrac{1}{4}&\dfrac{3}{4}\end{array}\right][/tex]
The Markov transition matrix, based on the given question, would look as follows: The top row represents the switch from Sorey State to C&T (0.5) and C&T to Sorey State (0.25). The bottom row represents the loyal customers who stick with their Sorey State (0.5) and C&T (0.75) boards. This matrix represents the probability of customers transitioning between these two brands in one surf season.
Explanation:
To properly answer this question, we need to convert these figures into a Markov transition matrix. In a Markov transition model, each consumer either stays with the brand they have (represented by the numbers on the diagonals) or switches to the other brand (represented by the numbers not on the diagonals).
Given the problem, set it up as follows:
Half, or 0.5, of the Sorey State Boogie Boards customers transitioned to C&T, this means that 0.5 of those customers stayed with Sorey State.Alternatively, one quarter, or 0.25, of the C&T customers transitioned to Sorey State, meaning that 0.75 of them remained with C&T.As a matrix, this looks as follows:
[Sorey State, C&T Boards]
[0.5, 0.25]
[ 0.5, 0.75]
This is your completed Markov transition matrix, which represents the probability of customers transitioning between these two brands, from one surf season to the next.
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How can you use a point on the graph off-1(x) =
9X to determine a point on the graph of f(x) =
logox?
Answer: switch the x- and y- coordinates
And the 2nd part is c, e , f
The point on the graph -1(x) =9X to determine a point on the graph of f(x) =logox is (-1, -9).
How to know if a point lies in the graph of a function?All the points (and only those points) which lie on the graph of the function satisfy its equation.
Thus, if a point lies on the graph of a function, then it must also satisfy the function.
We are given that;
-1(x) =9X
Now,
To use a point on the graph of one function to determine a point on the graph of another function, you need to find the corresponding x-value on the first graph. Then, you can use that x-value to find the corresponding y-value on the second graph.
In this case, you have a point on the graph of the function f(x) = 9x. To find the corresponding point on the graph of the function g(x) = log(x), you need to find the x-value that corresponds to -1 on the graph of f(x) = 9x.
To do this, you can set f(x) = 9x equal to -1 and solve for x:
9x = -1 x = -1/9
The point (-1, -9) on the graph of f(x) = 9x corresponds to the point (-1/9, log(-1/9)) on the graph of g(x) = log(x). However, note that the logarithm function is not defined for negative values of x, so the point (-1/9, log(-1/9)) is not a valid point on the graph of g(x) = log(x).
Therefore, by the graph of function the point will be (-1, -9).
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Solve the system of linear equations using elimination.
−9x − 10y = 17
−10x − 10y = 10
Answer:
you are to subtract the equation
Answer:
(7,-8)
Step-by-step explanation:
given: f(x)= x^2 -x and g(x)= x+2 find f(-1)
In a survey conducted by the Gallup Organization, 1100 adult Americans were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for the mean number of hours worked had a lower bound of 42.7 and an upper bound of 44.5. Provide two recommendations for decreasing the margin of error of the interval.
Answer:
1) Increase the sample size
2) Decrease the confidence level
Step-by-step explanation:
The 95% confidence interval built for a sample size of 1100 adult Americans on how much they worked in previous week is:
42.7 to 44.5
We have to provide 2 recommendations on how to decrease the margin of Error. Margin of error is calculated as:
[tex]M.E=z_{\frac{\alpha}{2} } \times \frac{\sigma}{\sqrt{n}}[/tex]
Here,
[tex]z_{\frac{\alpha}{2} }[/tex] is the critical z-value which depends on the confidence level. Higher the confidence level, higher will be the value of critical z and vice versa.
[tex]\sigma[/tex] is the population standard deviation, which will be a constant term and n is the sample size. Since n is in the denominator, increasing the value of n will decrease the value of Margin of Error.
Therefore, the 2 recommendations to decrease the Margin of error for the given case are:
Increase the sample size and make it more than 1100Decrease the confidence level and make it lesser than 95%.The two recommendations should be that the sample size should be increased and the confidence interval should be reduced.
Suggestions for reducing the margin of error:Since a 95% confidence interval for the mean number of hours worked had a lower bound of 42.7 and an upper bound of 44.5.
We know that margin of error = z value × population / √n
So for reducing the margin of error of the interval, sample size should be increased and the confidence interval should be reduced.
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4. Each item produced by a certain manufacturer is, independently, of acceptable quality with probability 0.95. Suppose that we want to approximate the probability that at most 10 of the next 150 items produced are unacceptable. a) Approach this using the normal approximation to the binomial distribution. Make sure to provide a z-score and a probability with four decimal places. b) Use either R or the Excel BINOM.DIST function to find the exact probability.
Answer:
Step-by-step explanation:
This one is really hard I cannot