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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A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If 40 different applicants are randomly selected, find the probability that their mean is above 215.
Answer:
[tex]P(\bar X>215)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
If we apply this formula to our probability we got this: for the value of 215
[tex] z = \frac{215-200}{\frac{50}{\sqrt{40}}}= 1.897[/tex]
And we can find this probability using the complement rule and with the normal standard distribution or excel we got:
[tex] P(z >1.897) = 1-P(z<1.897) =1- 0.971= 0.029[/tex]
Step-by-step explanation:
Let X the random variable that represent the ratings of applicants from a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(200,50)[/tex]
Where [tex]\mu=200[/tex] and [tex]\sigma=50[/tex]
We select a sample size of n =40. We are interested on this probability
[tex]P(\bar X>215)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
If we apply this formula to our probability we got this: for the value of 215
[tex] z = \frac{215-200}{\frac{50}{\sqrt{40}}}= 1.897[/tex]
And we can find this probability using the complement rule and with the normal standard distribution or excel we got:
[tex] P(z >1.897) = 1-P(z<1.897) =1- 0.971= 0.029[/tex]
A rectangle has an area of K + 19k + 60 square inches. If the value of k and the dimensions of the rectangle are all natural
numbers, which statement about the rectangle could be true?
The length of the rectangle is k-5 inches.
The width of the rectangle is k + 4 inches.
The length of the rectangle is k-20 inches.
The width of the rectangle is k + 10 inches.
Step-by-step explanation:
By definition, the area of a rectangle is given by:
A = w * lA=w∗l
Where,
w: width of the rectangle
l: length of the rectangle
We then have the following expression for the area:
A = k ^ 2 + 19k + 60A=k
2
+19k+60
What we must do is factorize the expression following the following steps:
1) Find two numbers that are equal to 19
2) Find two multiplied numbers equal to 60
We have then:
A = (k + 15) (k + 4)A=(k+15)(k+4)
Therefore, the width of the rectangle is:
w = (k + 4)w=(k+4)
Answer:
Thats correct! The answer is B. (2nd option.) I took edge.
Step-by-step explanation:
PLEASE HELP ASAP!!!
When would you use a line graph?
A. if the data is given as data pairs
B. if the data is numerical
C. to compare categories
D. to compare change over time
You can also choose more than one
Answer:
d AND C
Step-by-step explanation:
The school held there talent quest and this year they had 1,204 people in attendance. Last year the attendance was only 860. What was the percentage increase from last year?
Answer:
28.57℅
Step-by-step explanation:
If last year attendance was 860 and the attendance increases to 1204:
Attendance increment = 1204-860
= 344
%increase = increment/current attendance × 100%
% increase = 344/1204 × 100
℅ increase = 34400/1204
% increase = 28.57%
Therefore the percentage increase from last year is 28.57℅
An experiment consists of selecting a letter at random from the letters in the word IRRESISTIBLE and observing the outcomes. What is the appropriate sample space for this experiment
Sample space for the experiment is {B, E, I, L , R , S, T } .
Hence option D is correct.
Given, that the word IRRESISTIBLE .
An experiment consist of selecting a letter at random from the letters in the given word.
The number of distinct letters in the word is 7 i.e I is 3 times in the word but consider it as single letter.
Therefore the appropriate sample space for the experiment is {B, E, I, L , R , S, T } .
Thus the option D is correct.
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The sample space for an experiment consists of all possible outcomes or events that can occur. In this case, the experiment involves selecting a letter at random from the letters in the word "IRRESISTIBLE."
The appropriate sample space for this experiment would be the set of all individual letters that can be selected from the word. Therefore, the sample space is:
Sample space = {I, R, E, S, T, I, B, L}
Each element of the sample space represents a possible outcome of the experiment, which is selecting a specific letter from the word "IRRESISTIBLE."
It is important to note that the sample space only includes the individual letters as outcomes, and it does not consider the order or repetition of the letters in the word.
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The mean of the sample is 24.444 squares with a standard deviation of 2.45 squares. Single-ply toilet paper requires 26 squares to absorb one-quarter cup of water. Josh would like to carry out a test to determine if there is convincing evidence that the mean number of squares of Fluffy that are needed to absorb one-quarter cup of water is fewer than 26 squares. What is the appropriate test statistic and P-value of this test?
Answer:
t = -2.69 , p = 0.0078
Step-by-step explanation:
We have the following data:
Sample Mean = x = 24.444
Sample Standard Deviation = s = 2.45
Sample size = n = 18
Josh wants to test that mean number is lesser than 26. So our test value is 26 i.e.
u = 26
Since Josh wants to test that mean would be fewer than 26, so this would be a left tailed test with a less than sign in Alternate Hypothesis. Therefore, the hypothesis would be:
[tex]H_{o}: u\geq 26\\H_{a}: u<26[/tex]
Since, we do not know the value of Population standard deviation, and we have the value of sample standard deviation, we will use One-Sample t-test for the population mean.
The formula to calculate the test-statistic would be:
[tex]t=\frac{x-u}{\frac{s}{\sqrt{n}}}[/tex]
Substituting the values in this formula gives us:
[tex]t=\frac{24.444-26}{\frac{2.45}{\sqrt{18}}}\\t=-2.69[/tex]
This means, the test statistic would be -2.69
Since, the sample size is 18, the degrees of freedom would be:
Degrees of freedom = df = n - 1 = 17
To find the p-value we need to check the p-value against test statistic of 2.69, with 17 degrees of freedom and One-tailed test. This value comes out to be:
p-value = 0.0078
Therefore, the correct answer would be:
t = -2.69 , p = 0.0078
Match each
Match each investment characteristic to the level of risk involved.
growth
savings
speculation
high risk because returns are not guaranteed, but time frames are set
moderate risk because expectations of returns are reasonable and average
low risk because of steady interest without fluctuation in value
High Risk because returns are not guaranteed, but time frames are set
—Speculation
Moderate Disk because expectations of returns are reasonable and average
—Growth
Low Risk because of steady Interest without fluctuation in value
—Savings
In investment terms, growth corresponds to high risk as returns aren't guaranteed, savings relate to low risk due to steady interest income, and speculation signifies moderate risk as it has reasonable return expectations.
Explanation:The types of investment can be associated with different levels of risk as follows:
Growth is correlated with high risk because the returns are not guaranteed, but time frames are set. For example, investing in a start-up tech firm may have great potential for growth, but also carries a significant risk if the company does not succeed. Savings are associated with low risk due to steady interest without fluctuation in value. This might be a savings account or a fixed-rate bond, where the earnings are steady and dependable, and there is little risk of losing your initial investment. Speculation presents a moderate risk because expectations of returns are reasonable and average. This could be investments in commodities, real estate or foreign exchange, where there is some risk involved but also the potential for significant gains. Learn more about Investment Risk here:
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What is the median of the data set?
87, 98, 106, 82, 111, 120
Answer:
The median is 102
Step-by-step explanation:
Median = a measure of central tendency. It represents the value for which 50% of observations a lower and 50% are higher. Put simply, it is the value at the center of the sorted observations.
Therefore, the answer 102 is correct.
(I need to be granted one more brainliest to level up so if my answer helped, it would be very much appreciated to award that to me, no obligations though!)
A triangular prism was sliced parallel to its base. What is the shape of the cross section shown in the figure?
Answer:
it would be a triangle
Step-by-step explanation:
five rock songs and six hip-hop songs on a disk jockeys playlist for a radio show. If the disc jockey shuffle the songs randomly, what is the possibility that all hip-hop song are played consecutively
Answer 39916800
Step-by-step explanation:
The probability that all hip-hop songs are played consecutively is 0.18%.
To calculate the probability that all hip-hop songs are played consecutively, to consider the total number of possible song arrangements and the number of arrangements where all hip-hop songs are consecutive.
The total number of song arrangements calculated using the concept of permutations. Since there are a total of 11 songs on the playlist, the number of possible arrangements is 11!.
Now, let's calculate the number of arrangements where all hip-hop songs are played consecutively treat the 6 hip-hop songs as a single unit or block. This means 6! ways to arrange the hip-hop songs within that block.
Since we have 5 rock songs remaining, we can arrange them in 5! ways.
Therefore, the total number of arrangements where all hip-hop songs are played consecutively is 6! ×5!.
To calculate the probability, we divide the number of favorable outcomes (where all hip-hop songs are played consecutively) by the total number of possible outcomes:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = (6! × 5!) / 11!
Calculating the numerical value:
Probability = (720 × 120) / 39,916,800
Probability ≈ 0.00180
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A sheet of paper contains 18 square feet. The top and bottom margins are 9inches and the side margins are 6 inches. What are the dimensions of the pagethat has the largest printed area?
Answer:
The dimensions of the page are
3.46 ft by 5.20 ft
Step-by-step explanation:
Let
x---> the length of the sheet of paper in feet
y ---> the width of the sheet of paper in feet
[tex]A=xy[/tex]
[tex]A=18\ ft^2[/tex]
so
[tex]18=xy[/tex]
[tex]y=\frac{18}{x}[/tex] -----> equation A
Remember that
[tex]1\ ft=12\ in[/tex]
Convert the margins into feet
[tex]9\ in=9\12=0.75\ ft[/tex]
[tex]6\ in=6\12=0.50\ ft[/tex]
so
we know that
The area of the largest printed area is given by
[tex]A=(y-0.75-0.75)(x-0.50-0.50)[/tex]
[tex]A=(y-1.50)(x-1)[/tex]
[tex]A=xy-y-1.50x+1.50[/tex]
substitute equation A in the above expression
[tex]A=x(\frac{18}{x})-\frac{18}{x}-1.50x+1.50\\[/tex]
[tex]A=18-\frac{18}{x}-1.50x+1.50[/tex]
[tex]A=19.50-\frac{18}{x}-1.50x[/tex]
Now we have an output (A) in terms of only one variable (x),
so
we differentiate:
[tex]\frac{dA}{dx}=\frac{18}{x^2}-1.50[/tex]
equate to zero
[tex]\frac{18}{x^2}=1.50[/tex]
[tex]x^2=12\\x=3.46\ ft[/tex]
Find the value of y
[tex]18=(3.46)y\\y=5.20\ ft[/tex]
therefore
The dimensions of the page are
3.46 ft by 5.20 ft
The required dimensions are,
[tex]x+18=3\sqrt{3}+18\\ y+12=2\sqrt{3}+12[/tex]
Area of the rectangle:The formula of the area of the rectangle is [tex]A=l \times b[/tex]
Let [tex]A[/tex] be the area of the paper then,
[tex]A=(x+18)(y+12)...(1)[/tex]
And the printed area is [tex]xy=18...(2)[/tex]
Now, from the equation (1) and (2) we get,
[tex]A=(x+18)(\frac{18}{x}+12)\\ A=234+12x+\frac{324}{x} ..(3)[/tex]
Now, differentiating equation (3)
[tex]\frac{dA}{dx}=12-\frac{324}{x^2} \\\frac{dA}{dx}=0\\12-\frac{324}{x^2} =0\\x=3\sqrt{3}[/tex]
Substituting the obtained value of [tex]x[/tex] into the equation (2)
[tex]x+18=3\sqrt{3}+18\\ y+12=2\sqrt{3}+12[/tex]
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Distribute 5000 among three friends in ratio of 1:2:3.What will be the greatest share?
Answer:
2500
Step-by-step explanation:
Find out how much 1 part is. Add all the parts together
1+2+3=6
find how much of 5000 is 1 part
5000/6=833.3 recurring
833.3 is 1 part
then multiple the parts
8.333.3 x 1
8.333.3 x 2
8.333.3 x 3
8.333.3 r : 1.666.6 r : 2500
The value of the greatest share is 2500.
Important information:
Total amount = 5000Given ratio = 1:2:3We need to find the greatest share.
Ratio:Let 5000 is divided in three shares whose values are [tex]x, 2x[/tex] and [tex]3x[/tex].
[tex]x+2x+3x=5000[/tex]
[tex]6x=5000[/tex]
[tex]x=\dfrac{5000}{6}[/tex]
[tex]x=\dfrac{2500}{3}[/tex]
The value of greatest share is [tex]3x[/tex].
[tex]3x=3\times \dfrac{2500}{3}[/tex]
[tex]3x=2500[/tex]
Therefore, the value of greatest share is 2500.
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Imagine you are studying a population of finches on one of the Galåpagos Islands. You have been recording many of the birds' physical traits, including the length of both wings. You observe that for 80% of individuals measured, the length of the left wing is not significantly different from the length of the right wing (in other words, they are symmetrical). But for about 20% of birds measured, the wing lengths are asymmetrical. This distribution is true from generation to generation. Suddenly, a rare 5-day windstorm takes over the island. After the storm, you spend the next several days netting each bird on the island that survived the storm. You discover that 85% of the birds with symmetrical wings survived the storm, whereas only 5% of the birds with asymmetrical wings did. Propose a hypothesis to explain this observation.
Answer:
The distribution of symmetrical to asymmetrical will change so that close to 100% of birds will have symmetrical wingspans.
Answer:
Refer below.
Step-by-step explanation:
The appropriation of symmetrical to asymmetrical will change so near 100% of flying creatures will have symmetrical wingspans.
What is the sum of the remote interior angles?
What is the measure of ∠A?
What is the measure of ∠B?
Answer:the sum of the remote interior angles is 95 degrees.
measure of a:85
measure of B:95
Step-by-step explanation:
i just took this
Answer: 95
Step-by-step explanation:
A fish has a triangular tooth with the height that is 2 centimeters longer than the base. If the are of the tooth is 12 square centimeters, find its base and height
Answer:Fishes have a triangular teeth with a height that is 1 centimeter longer than the base. If the area of one tooth is 15 square centimeters, find its base and height. The triangle shows the base to be x and the height to be x+1.
Step-by-step explanation:
Answer:
Fishes have a triangular teeth with a height that is 1 centimeter longer than the base. If the area of one tooth is 15 square centimeters, find its base and height. The triangle shows the base to be x and the height to be x+1.
Step-by-step explanation:
Typing errors in a text are either nonword errors (as when "the" is typed as "teh") or word errors that result in a real but incorrect word. Spell‑checking software will catch nonword errors but not word errors. Human proofreaders catch 70 % of word errors. You ask a fellow student to proofread an essay in which you have deliberately made 10 word errors. (a) If X is the number of word errors missed, what is the distribution of X ? Select an answer choice. X is binomial with n = 10 and p = 0.7 X is binomial with n = 10 and p = 0.3 X is approximately Normal with μ = 3 and σ = 1.45 X is Normal with μ = 7 and σ = 1.45 If Y is the number of word errors caught, what is the distribution of Y ? Select an answer choice. Y is Normal with μ = 7 and σ = 1.45 Y is approximately Normal with μ = 3 and σ = 1.45 Y is binomial with n = 10 and p = 0.3 Y is binomial with n = 10 and p = 0.7 (b) What is the mean number of errors caught? (Enter your answer as a whole number.) mean of errors caught = What is the mean number of errors missed? (Enter your answer as a whole number.) mean of errors missed = (c) What is the standard deviation of the number of errors caught? (Enter your answer rounded to four decimal places.) standard deviation of the number of errors caught = What is the standard deviation of the number of errors missed? (Enter your answer rounded to four decimal places.) standard deviation of the number of errors missed =
Answer:
a) X is binomial with n = 10 and p = 0.3
Y is binomial with n = 10 and p = 0.7
b) The mean number of errors caught is 7.
The mean number of errors missed is 3.
c) The standard deviation of the number of errors caught is 1.4491.
The standard deviation of the number of errors missed is 1.4491.
Step-by-step explanation:
For each typing error, there are only two possible outcomes. Either it is caught, or it is not. The probability of a typing error being caught is independent of other errors. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
10 word errors.
This means that [tex]n = 10[/tex]
(a) If X is the number of word errors missed, what is the distribution of X ?
Human proofreaders catch 70 % of word errors. This means that they miss 30% of errors.
So for X, p = 0.3.
The answer is:
X is binomial with n = 10 and p = 0.3.
If Y is the number of word errors caught, what is the distribution of Y ?
Human proofreaders catch 70 % of word errors.
So for Y, p = 0.7.
The answer is:
Y is binomial with n = 10 and p = 0.7
(b) What is the mean number of errors caught?
[tex]E(Y) = np = 10*0.7 = 7[/tex]
The mean number of errors caught is 7.
What is the mean number of errors missed?
[tex]E(X) = np = 10*0.3 = 3[/tex]
The mean number of errors missed is 3.
(c) What is the standard deviation of the number of errors caught?
[tex]\sqrt{V(Y)} = \sqrt{np(1-p)} = \sqrt{10*0.7*0.3} = 1.4491[/tex]
The standard deviation of the number of errors caught is 1.4491.
What is the standard deviation of the number of errors missed?
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10*0.3*0.7} = 1.4491[/tex]
The standard deviation of the number of errors missed is 1.4491.
(a). X follows a binomial distribution with n = 10 and p = 0.3, while Y follows a binomial distribution with n = 10 and p = 0.7.
(b) The mean number of errors caught is 7 and the mean number of errors missed is 3,
(c) Both with a standard deviation of approximately 1.4491.
Let's analyze the given problem step by step.
Part (a): Distribution of X and Y
X represents the number of word errors missed.
Since 70% of word errors are caught, 30% of word errors are missed.
Therefore, X follows a binomial distribution with n = 10 (total errors) and p = 0.3 (probability of missing an error).
Thus, X is binomial with n = 10 and p = 0.3.Y represents the number of word errors caught.
Since 70% of word errors are caught, Y follows a binomial distribution with n = 10 and p = 0.7 (probability of catching an error).
Thus, Y is binomial with n = 10 and p = 0.7.Part (b): Mean Number of Errors Caught and Missed
Mean of errors caught: The mean of a binomial distribution is given by µ = np. For Y (caught errors), µ = 10 × 0.7 = 7. Thus, the mean number of errors caught is 7.Mean of errors missed: For X (missed errors), µ = 10 × 0.3 = 3. Thus, the mean number of errors missed is 3.Part (c): Standard Deviation of the Number of Errors Caught and Missed
Standard deviation of errors caught:
The standard deviation of a binomial distribution is given by σ = √(np(1-p)). For Y (caught errors), σ = √(10 × 0.7 × 0.3) ≈ 1.4491.Thus, the standard deviation of the number of errors caught is approximately 1.4491.
Standard deviation of errors missed: For X (missed errors), σ = √(10 × 0.3 × 0.7) ≈ 1.4491. Thus, the standard deviation of the number of errors missed is approximately 1.4491.
The line plot shows the heights of the flowers in a neighborhood garden. Part A How many flowers are in the garden? A. 5 B. 7 C. 18 D. 20 Part B How many more flowers have a height that is 7 1 4 714 inches or greater than a height that is 7 7 inches or less? A. 1 B. 2 C. 3 D. 4
Answer:
it's 20
Step-by-step explanation:
I just had the same question and I got it right it's 20.
There are 20 flowers in the garden and there are 4 flowers that have a height that is 7 1/4 inches or greater
Part A: The number of flowers in the gardenFrom the complete question, there are 20 points in the line plot.
Each point represents a flower
Hence, there are 20 flowers in the garden
Part B: Flowers whose heights are 7 1/4 or greaterUsing the same line plot in (a), there are 4 points in the line plot where the flower height is either 7 1/4 or more
Hence, there are 4 flowers that have a height that is 7 1/4 inches or greater
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Men’s heights are normally distributed with mean 69.5 inches and a standard deviation of 2.4 inches.
Women’s heights are normally distributed with mean 63.8 inches and a standard deviation of 2.6 inches
The Gulfstream 100 is an executive jet that seats six and it has a doorway height of 51.6 inches.
a. What percentage of adult men can fit through the door without bending?
b. what percentage of adult women can fit through the door without bending?
c. Does the door design with a height of 51.6 inches appear to be adequate? Why didn’t engineers design a larger door?
d. What doorway height would allow 60% of men to fit without bending?
Answer:
a. The percentage of adult men that will fit through the door without bending is 0.
b. The percentage of adult women that will fit through the door without bending is 0.
c. No, it is not adequate. There must be another technical reasons to not use a larger door.
d. The doorway height that would allow 60% of men to fit without bending is 70.1 inches.
Step-by-step explanation:
a. To fit throught the door, the height has to be under 51.6. To calculate this proportion, we have to calculate the z-score for X=51.6 for the distribution of men's height N(μ=69.5, σ=2.4).
We can calculate the z-score as:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{51.6-69.5}{2.4}=\dfrac{-17.9}{2.4}=-7.4583[/tex]
[tex]P(X<51.6)=P(z<-7.4583)=0[/tex]
The percentage of adult men that will fit through the door without bending is 0.
b. To fit throught the door, the height has to be under 51.6. To calculate this proportion, we have to calculate the z-score for X=51.6 for the distribution of women's height N(μ=63.8, σ=2.6).
We can calculate the z-score as:
[tex]z=\dfrac{X-\mu}{\sigma}=\dfrac{51.6-63.8}{2.6}=\dfrac{-12.2}{2.6}=-4.6923[/tex]
[tex]P(X<51.6)=P(z<-4.6923)=0[/tex]
The percentage of adult women that will fit through the door without bending is 0.
c. No, it is not adequate. There must be another technical reasons to not use a larger door.
d. We can calculate this finding a z-value z1 for which P(z<z1)=0.60.
Looking in a standard normal distribution table, the value for z1 is z1=0.25335.
Then, transforming to our adult men's height distribution, we have:
[tex]X=\mu+z\sigma=69.5+0.25335*2.4=69.5+0.6=70.1[/tex]
The doorway height that would allow 60% of men to fit without bending is 70.1 inches.
The following definitions are used: a relation on a set A is defined to be irreflexive if, and only if, for every x A, x R x; asymmetric if, and only if, for every x, y A if x R y then y R x; intransitive if, and only if, for every x, y, z A, if x R y and y R z then x R z. The following relation is defined on the set A = {0, 1, 2, 3}. Determine whether the relation is irreflexive, asymmetric, intransitive, or none of these. (Select all that apply.) R2 = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)}
The relation R2 = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)} is not irreflexive, asymmetric, or intransitive.
Explanation:To determine whether the relation R2 = {(0, 0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)} is irreflexive, asymmetric, or intransitive, we will analyze each property.
Irreflexive: Since every element in the relation has the form (x, x) where x is an element of A, and all such pairs exist in R2, the relation is not irreflexive.Asymmetric: Since the relation contains (x, y) and (y, x) pairs for some x, y in A, it violates the definition of an asymmetric relation. Therefore, R2 is not asymmetric.Intransitive: The relation R2 does not violate the transitive property. For example, (0,1) and (1,2) are in R2, and it also contains (0,2), satisfying the transitive property. Therefore, R2 is not intransitive.Therefore, the relation R2 is none of the given properties (irreflexive, asymmetric, or intransitive).
A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample in the following cases?
Answer: a) 15, b) 1.
Step-by-step explanation:
A researcher studying public opinion of proposed social security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more Americans does the researcher need to sample in the following cases?
(a) 10% of all adult Americans support the changes
Here, [tex]np>5\ and\ n(1-p)>5[/tex]
And , [tex]p=0.10[/tex]
So, consider the equality, to find the value of 'n'.
[tex]np=5\\\\n\times 0.10=5\\\\n=\dfrac{5}{0.10}\\\\n=50[/tex]
So, there are [tex]50-35=15[/tex] more adult Americans needed.
(b) 15% of all adult Americans supports the changes
Here, [tex]p=0.15[/tex]
So, again we get that
[tex]np=5\\\\n\times 0.15=5\\\\n=\dfrac{5}{0.15}\\\\n=33.33\\\\n\approx 34[/tex]
So, there are [tex]35-34=1[/tex] more adult Americans needed.
Hence, a) 15, b) 1.
Which statements about functions g(x) = x2 - 4x + 3 and f(x) = x2 - 4x are true? Select all that apply.
A. The vertex of the graph of function g is above the vertex of the graph of function f.
B. The graphs have the same axis of symmetry.
c. Function f has a maximum value and function g has a minimum value.
Answer:
A and B
Step-by-step explanation:
We are given that
[tex]g(x)=x^2-4x+3[/tex]
[tex]g(x)=(x^2-2\times x\times 2+4)-4+3=(x-2)^2-1[/tex]
Compare with it
[tex]y=(x-h)^2+k[/tex]
Where vertex=(h,k)
We get
Vertex of g=(2,-1)
[tex]f(x)=x^2-4x=(x^2-2\times x\times 2+4)-4=(x-2)^2-4[/tex]
Vertex of f=(2,-4)
Equation of axis of symmetry=x-coordinate of vertex
Axis of symmetry of g
x=2
Axis of symmetry of f
x=2
Differentiate w.r.t x
[tex]g'(x)=2x-4=0[/tex]
[tex]2x-4=0\implies 2x=4[/tex]
[tex]x=\frac{4}{2}=2[/tex]
[tex]f'(x)=2x-4[/tex]
[tex]2x-4=0\implies 2x=4[/tex]
[tex]x=\frac{4}{2}=2[/tex]
[tex]g''(x)=2>0[/tex]
[tex]f''(x)=2>0[/tex]
f and g have both minima at x=2
Hence, option A and B are true.
solve for y 6=2(y+2)
Answer:
y=1
Step-by-step explanation:
6=2(y+2)
Divide each side by 2
6/2=2/2(y+2)
3 = y+2
Subtract 2 from each side
3-2 = y+2-2
1 = y
Answer:
y = 1
Step-by-step explanation:
6 = 2 ( y + 2 )
6 = 2y + 4
subtract four from both sides
2 = 2y
divide by 2 on both sides
y = 1
A car is traveling at a speed of 120 kilometers per hour. What is the car's speed in miles per hour? How many miles will the car travel in 4 hours?
Answer:
The car's speed is 74.5444 mi/hr. It travels 298.2576 miles in 4 hours.
Step-by-step explanation:
If we want to know the speed in mi/hr, we must convert the km to mi. We can convert from kilometers to miles as follows.
mi = km * 0.62137
Then, if the car is moving at 120 km / hr, we have that the car is moving at
120*0.62137 mi /hr, which is 74.5644 mi/hr. If we want to know how many miles the car travels in four hours, we multiply the speed times the total time. Hence
total distance = 74.5444 mi/hr * 4 hr = 298.2576 miles.
what two integers are between the square root of 62
Answer:
The two integers the square root of 62 falls between are 7, and 8.
Step-by-step explanation:
the square root of 62 is 7.874.... so the numbers that it is between are 7 and 8 because its more than 7 but less than 8
The 62 will be in between of square root of 7 and 8.
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.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
The square root of relevant numbers are given below,
2² = 4 , 3² = 9 , 4² = 16 ,5² = 25 , 6² = 36, 7² = 49,8² = 64 ,9² = 81
Now the number 61 is lying in between 49 and 64
So,
"The 62 will be in between of square root of 7 and 8".
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On the morning of November 9, 1994-the day after the electoral landslide that had returned Republicans to power in both branches of Congress-several key races were still in doubt. The most prominent was the Washington contest involving Democrat Tom Foley, the reigning speaker of the house. An Associated Press story showed how narrow the margin had become (120): With 99 percent of precincts reporting, Foley trailed Republican challenger George Nethercutt by just 2,174 votes, or 50.6 percent to 49.4 percent. About 14,000 absentee ballots remained uncounted, making the race too close to call. Let p = P(Absentee voter prefers Foley). How small could p have been and still have given Foley a 20% chance of overcoming Nethercutt's lead and winning the election?
Answer:
p = 0.574197
Step-by-step explanation:
There are 14000 ballots left.
The lead is 2174, so he needs to lead at least 2175 in these 14000 ballots.
He does so if he gets at least 8088 votes.
If P(x >= 8088) = 0.20, then the corresponding z score to this is, by table/technology,
z = 0.841621234
Now, as
z = (x - u) / s
and
u= n p
s = sqrt(n p(1-p))
Then
0.841621234 = (8088 - 14000*p) / sqrt(14000p(1-p))
Solving for p here,
p = 0.574197
One quart is approximately equal to 0.95 liter. To convert quarts to liters, which operation should you use? Why?
A..Addition; there is about 0.95 liter in 1 quart. Add when converting smaller units to larger units.
B...Division; there is about 0.95 liter in 1 quart. Divide when converting smaller units to larger units.
c...Multiplication; there is about 0.95 liter in 1 quart. Multiply when converting larger units to smaller units.
D......Subtraction; there is about 0.95 liter in 1 quart. Subtract when converting larger units to smaller units.
Answer:
c...Multiplication; there is about 0.95 liter in 1 quart. Multiply when converting larger units to smaller units.
Step-by-step explanation:
1 quart : 0.95 litre
X quarts : ?
X/1 = ?/0.95
? = 0.95 × X
The ratio of forks to knives in Isabella’s kitchen drawer is 4 to 5. There are
16 forks in the drawer. How many knives are there?
Answer:
20 knives
Step-by-step explanation:
the ratio of fork to knives is [tex]\frac{4}{5}[/tex] and their are 16 forks, so we put the ratio of fork and knives equal to number of fork and knives so its:
[tex]\frac{4}{5}[/tex] = [tex]\frac{16}{x}[/tex] We cross multiply
80 = 4x Divide both side by 4
x = 20
we can check too
16/20 if we simplify, its give us 4/5
There are 20 knives in Isabella's kitchen.
The ratio of forks to knives in Isabella’s kitchen drawer is 4 to 5.
Given that there are 16 forks in the drawer, we can set up a proportion to find the number of knives:
4/5 = 16/X
Cross multiply to get: 4X = 80
Divide by 4 to find X = 20
Therefore, there are 20 knives in Isabella's kitchen drawer.
a large college class has 160 students. All 160 students attend the lectures together, but the students are divided into 4 groups, each of 40 students, forfor lab sections administered by different eaching assistants. The professor wants to conduct a survey about how satisfied the students are with the course, and he belives that the lab section a student is in might affett the students overall satisfaction ith course. (a) suwhat type of study is this? (b) suggest a sampling stragey for carrying out the study
Answer: Please see answer in explanatory column
Step-by-step explanation:
STEP 1 - Since the survey is not an experimental one which occurs in a laboratory with a control and interference with sample.
Then the professor will use an observational study is in which he will observe the behavior of the students in a systematic manner without interfering with the students behavior so as to know how satisfied the students are with the course. After getting to know how satisfied the students are for his course he would record the behavior that he or she observes and rate accordingly
STEP 2:The sampling strategy the Professor can use in carrying out the research is a Stratified sampling which occurs when the population to be observed is divided into groups known as strata which contains similar cases grouped together, then a second sampling, mostly a random sampling where the professor will randomly sample few students from the different strata to get his observations. for example, the students divided in 4 groups of 40 students represents each strata placed in common according to the different teaching assistant, then the professor can then randomly sample few students from each strata from a class of the 120 students.
This study is an observational study. A possible sampling strategy for this study could be stratified sampling.
Explanation:(a) This study is an observational study since the researcher is not manipulating any variables or assigning participants to groups. The researcher is simply observing and collecting data on the students' satisfaction with the course.
(b) A possible sampling strategy for this study could be stratified sampling. The researcher could divide the 160 students into four strata based on their lab sections and then randomly select a certain number of students from each stratum to participate in the survey. This ensures that each lab section is represented in the sample.
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A study conducted by the Pew Research Center reported that 58% of cell phone owners used their phones inside a store for guidance on purchasing decisions. A sample of 15 cell phone owners is studied. What is the probability that 10 or more of them used their phones for guidance on purchasing decisions? Round your answer to 2 decimal places
Final answer:
The student is asked to calculate the probability that 10 or more out of 15 cell phone owners use their phones for help with purchasing decisions, with a 58% chance each. The calculation is done using the binomial probability formula and the answer is rounded to two decimal places.
Explanation:
The student seeks to determine the probability that 10 or more cell phone owners out of a sample of 15 use their phones for guidance on purchasing decisions, given that 58% of cell phone owners do so. This question can be addressed using the binomial probability formula:
[tex]P(X ≥ k) = Σ (nCk * p^k * (1-p)^(n-k))[/tex]
n is the sample size (15 in this case),k is the number of successes (10, 11, 12, 13, 14, or 15 in this case),p is the probability of success on a single trial (0.58), andnCk is the combination of n items taken k at a time.To find the total probability of 10 or more successes, we sum the probabilities of having 10, 11, 12, 13, 14, or 15 successes. Each of these probabilities is found by plugging the appropriate numbers into the binomial formula. In practice, to simplify the calculation, one might use statistical software or a binomial probability calculator.
After calculating these probabilities and summing them up, we round the answer to two decimal places as per the instruction given in the question.
lists the amount of U.S. cash per capita in circulation as of June 30 in the given year. Use linear approximation to estimate the amount, C(2010), of cash per capita in circulation in the year 2010.
Answer:
C(2010) = $1312 using linear approximation.
Step-by-step explanation:
The full complete question is attached to this solution.
The full table is given as
Year | 1970 | 1980 | 1990 | 2000
Cash |$180 |$262 |$564 | $938
we are told to use linear approximation to obtain C(2010)
Linear approximation, Mathematically, results in
C(2010) = C(2000) + C'(t) [t]
where t = years since 2010 = (Year - 2000)
Linear approximation gives C'(t) as the rate of change of C with time
C'(t) = (ΔC/Δt)
We will be using the latest year for this approximation.
ΔC = C(2000) - C(1990) = 938 - 564 = $374
Δt = 2000 - 1990 = 10
C'(t) = (374/10) = $37.4 per year.
C(2010) = C(2000) + C'(t) [t]
t = 2010 - 2000 = 10
C(2000) = $938
C'(t) = $37.4 per year
C(2010) = 938 + (37.4)(10) = $1312
Hope this Helps!!!
The amount, C(2010), of cash per capita in circulation in the year 2010 = $1312.
The full table is given as
Year | 1970 | 1980 | 1990 | 2000
Cash |$180 |$262 |$564 | $938
we are told to use linear approximation to obtain C(2010)
Linear approximation, Mathematically, results in
C(2010) = C(2000) + C'(t) [t]
where t = years since 2010 = (Year - 2000)
Linear approximation gives C'(t) as the rate of change of C with time
C'(t) = (ΔC/Δt)
We will be using the latest year for this approximation.
ΔC = C(2000) - C(1990) = 938 - 564 = $374
Δt = 2000 - 1990 = 10
C'(t) = (374/10) = $37.4 per year.
C(2010) = C(2000) + C'(t) [t]
t = 2010 - 2000 = 10
C(2000) = $938
C'(t) = $37.4 per year
C(2010) = 938 + (37.4)(10) = $1312.
Complete question: