Answer:
a) [tex]H_{0}: p = 0.66\\H_A: p > 0.66[/tex]
b) P-value = 0.2650
c) No, this programme will not be recommended as there is no real improvement over the national average.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 240
p = 66% = 0.66
Alpha, α = 0.05
Number of students admitted to law school , x = 163
a) First, we design the null and the alternate hypothesis
[tex]H_{0}: p = 0.66\\H_A: p > 0.66[/tex]
This is a one-tailed(right) test.
Formula:
[tex]\hat{p} = \dfrac{x}{n} = \dfrac{163}{240} = 0.6792[/tex]
[tex]z = \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
Putting the values, we get,
[tex]z = \displaystyle\frac{0.6792-0.66}{\sqrt{\frac{0.66(1-0.66)}{240}}} = 0.6279[/tex]
b) Now, we calculate the p-value from the table.
P-value = 0.2650
c) Since the p-value is greater than the significance level, we fail to reject the null hypothesis and accept the null hypothesis.
Thus, there is no real improvement over the national average.
No, this programme will not be recommended as there is no real improvement over the national average.
Finding the average rate of change of g(z) =4x^2_5 between the points( -2,11) and (2,11
Answer:
The average rate of change of g(z) =4x^2_5 between the points( -2,11) and (2,11) is 0.
Step-by-step explanation:
Given a function y, the average rate of change S of [tex]y=g(z)[/tex] in an interval [tex](z_{s}, z_{f})[/tex] will be given by the following equation:
[tex]S = \frac{g(z_{f}) - g(z_{s})}{z_{f} - z_{s}}[/tex]
In this problem, we have that:
[tex]g(z) = 4z^{2} - 5[/tex]
Between the points( -2,11) and (2,11).
So [tex]z_{f} = 2, z_{s} = -2[/tex]
[tex]g(z_{f}) = g(2) = 4*(2)^{2} - 5 = 11[/tex]
[tex]g(z_{s}) = g(-2) = 4*(-2)^{2} - 5 = 11[/tex]
So
[tex]S = \frac{g(z_{f}) - g(z_{s})}{z_{f} - z_{s}} = \frac{11 - 11}{2 - (-2)} = \frac{0}{4} = 0[/tex]
The average rate of change of g(z) =4x^2_5 between the points( -2,11) and (2,11) is 0.
What are the solutions to the inequality (x-3)(x+5) <_ 0
(x-3)(x-5)<_0
If any individual factor on the left side of the equation is equal to 00, the entire expression will be equal to 00.
x−3=0x-3=0
x+5=0x+5=0
Set the first factor equal to 00 and solve.
x=3x=3
Set the next factor equal to 00 and solve.
x=−5x=-5
Consolidate the solutions.
x=3,−5x=3,-5
Use each root to create test intervals.
x<−5x<-5
−5<x<3-5<x<3
x>3x>3
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
x<−5x<-5 False
−5<x<3-5<x<3 True
x>3x>3 False
The solution consists of all of the true intervals.
−5<x<3-5<x<3
The result can be shown in multiple forms.
Inequality Form:
−5<x<3-5<x<3
Interval Notation:
(−5,3)
use gcf to factor the expression 40x+24y-56
every 55 students there were 2 professor's
How many professors for 1650 students
Answer:
60 professors
Step-by-step explanation:
for every 55 students there were 2 professors
for 1650 students, there will be (1650 x 2) / 55 =3300/55 = 60 professors
Final answer:
To find the number of professors needed for 1650 students when the ratio is 2 professors for every 55 students, you calculate 2 / 55 = x / 1650, resulting in x = 60. Therefore, 60 professors are needed for 1650 students.
Explanation:
The question asks how many professors would be needed for 1650 students if there is a ratio of 2 professors for every 55 students. To solve this, you can set up a proportion where the number of students is directly proportional to the number of professors. The proportion can be expressed as 2 professors / 55 students = x professors / 1650 students. Solving for x involves cross-multiplying and dividing.
Step 1: Cross-multiply to get 2 × 1650 = 55 × x.
Step 2: Simplify the equation: 3300 = 55x.
Step 3: Divide both sides by 55 to solve for x: x = 3300 / 55.
Step 4: Calculate the result: x = 60. Thus, you would need 60 professors for 1650 students.
A deer population grows at a rate of four percent per year. How many years will it take for the population to double?
Answer:
It is going to take 17.65 years for the population to double.
Step-by-step explanation:
The population of the deer is after t years is given by the following equation
[tex]P(t) = P_{0}(1 + r)^{t}[/tex]
In which [tex]P_{0}[/tex] is the initial population and r is the decimal growth rate.
A deer population grows at a rate of four percent per year. This means that [tex]r = 0.04[/tex]
How many years will it take for the population to double?
This is t when [tex]P(t) = 2P_{0}[/tex]
[tex]P(t) = P_{0}(1.04)^{t}[/tex]
[tex]2P_{0} = P_{0}(1.04)^{t}[/tex]
[tex](1.04)^{t} = 2[/tex]
Here, we apply the log 10 to both sides of the equation.
It is important to note the following property of logarithms.
[tex]\log{a^{t}} = t\log{a}[/tex]
[tex]\log{(1.04)^{t}} = \log{2}[/tex]
[tex]t\log{1.04} = 0.3[/tex]
[tex]0.017t = 0.3[/tex]
[tex]t = \frac{0.3}{0.017}[/tex]
[tex]t = 17.65[/tex]
It is going to take 17.65 years for the population to double.
Answer:it will take approximately 18 years
Step-by-step explanation:
A deer population grows at a rate of four percent per year. The growth rate is exponential. We would apply the formula for exponential growth which is expressed as
A = P(1 + r/n)^ nt
Where
A represents the population after t years.
n represents the period of growth
t represents the number of years.
P represents the initial population.
r represents rate of growth.
From the information given,
A = 2P
P = P
r = 4% = 4/100 = 0.04
n = 1
Therefore
2P = P(1 + r/n)^ nt
2P/P = (1 + 0.04/1)^1 × t
2 = (1.04)^t
Taking log of both sides to base 10
Log 2 = log1.04^t = tlog1.04
0.3010 = t × 0.017
t = 0.3010/0.017 = 17.7 years
How many people have to be in a room in order that the probability that at least two of them celebrate their birthday on the same day is at least 0.06? (Ignore leap years, and assume that all outcomes are equally likely.)
Answer:
At least 8 people are needed in the room
Step-by-step explanation:
The probability of n people celebrating their birthday in different days is
1*364/365*363/365*....*(365-(n-1))/365
(for the first person any of the 365 days is suitable, for the second person only 364 persons is suitable, for the third only 364 and so on)
At least two people celebratig their birthday on the same day is the complementary event, thus its probability is
1- 364/365*....*(365-n+1)/365
Lets compute the probabilities for each value of n:
for n = 2: 1-364/365 = 0.00273for n = 3: 1-364/365*363/365 = 0.008for n = 4: 1-364/365*363/365*362/365 = 0.016for n = 5: 1-364/365*363/365*362/365*361/365 = 0.027for n = 6: 1-364/365*363/365*362/365*361/365*360/365 = 0.04for n = 7: 1-364/365*363/365*362/365*361/365*360/365*359/365 = 0.056for n = 8: 1-365/365*363/365*362/365*361/365*360/365*359/365*358/365 = 0.074 > 0.06We need at least 8 people in the room.
*8. Consider a LTI system with unit impulse response, h(t) = e-3tu(t). Using direct integration technique for finding convolution, find its zero-state response due to an input, x(t) = u(t) (which is called unit step response of the system). Also, from your answer above, write down its response due to an input of the form, x(t) = 2δ(t) – 4u(t). [Hint: Use principle of superposition]
Answer:
Step-by-step explanation:
Check the attachment for solution
A banner is hung for a party. The
distance from a point on the bottom edge of
the banner to the floor can be determined by
using the function f(x) = 0.25x 2 − x + 9.5,
where x is the distance, in feet, of the point
from the left end of the banner. How high
above the floor is the lowest point on the
bottom edge of the banner? Explain.
Answer:
8.5 feetExplanation:
The function that can determine the distance from a point on the bottom edge of the banner to the floor is:
[tex]f(x)=0.25x^2-x+9.5[/tex]
That function is a quadratic function which means that it is a parabola. Given that the coefficient of the quadratic term (0.25) is positive, the parabola open upwards, and the vertex is the lowest point of the parabola and it represents how high above the floor is the lowest point on the bottom edge of the banner.
So, you need to find the vertex of the parabola.
I will complete squares to find the form A(x -h)² + k, where h and k are the coordinates of the vertex (h, k).
[tex]f(x)=0.25x^2-x+9.5\\ \\ 4(f(x))=4(0.25x^2-x+9.5)\\ \\ 4f(x)=x^2-4x+38\\ \\ 4f(x)-38=x^2-4x\\ \\ 4f(x)-38+4=x^2-4x+4\\ \\ 4f(x)-34=(x-2)^2\\ \\ 4f(x)=(x-2)^2+34\\ \\ f(x)=(1/4)(x-2)^2+8.5[/tex]
Hence, the vertex (h,k) is (2, 8.5), meaning that the lowest point on the bottom edge of the banner is at 2 feet from the left edge of the banner and 8.5 feet above the floor.
The lowest point on the bottom edge of the banner which results in a height of 8.5 feet above the floor.
To find the height above the floor of the lowest point on the bottom edge of the banner using the function f(x) = 0.25x^2 - x + 9.5, we need to determine the vertex of this quadratic function. The vertex form of a quadratic function f(x) = ax^2 + bx + c gives the minimum or maximum value of the function.
Here, the coefficient a is positive (0.25), indicating that the parabola opens upwards and thus has a minimum point. The x-coordinate of the vertex can be found using the formula x = -b / (2a).
Identify the coefficients: a = 0.25 and b = -1.Calculate the x-coordinate of the vertex: x = -(-1) / (2 * 0.25) = 2 feet.Substitute x = 2 back into the function to find the minimum height:
f(2) = 0.25(2)^2 - 2 + 9.5 = 1 - 2 + 9.5 = 8.5 feet.
Therefore, the lowest point on the bottom edge of the banner is 8.5 feet above the floor.
A model for the basal metabolism rate, in kcal/h, of a young man is given by the formula below, where t is the time in hours measured from 5:00 AM. What is the total basal metabolism of this man over a 24 hour period?R(t)=80-0.18cos πt/1224∫ R(t) dt=____?0
Answer:
1920 k calories is the basal metabolism.
Step-by-step explanation:
Formula to get the total basal metabolism has been given by the formula
R(t) = [tex]80-0.18cos\frac{\pi t}{12}[/tex]
Where t = time
Now to calculate the total basal metabolism we will integrate the function with respect to time from 0 to 24 hours.
[tex]\int_{0}^{24}R(t)=\int_{0}^{24}(80-0.18cos\frac{\pi t}{12})dt[/tex]
= [tex][80t-{0.18}\times \frac{sin\frac{\pi t}{12}}{\frac{\pi}{12}}]_{0}^{24}[/tex]
= [tex][(80-0)24-\frac{0.18\times 12}{\pi}(sin2\pi - sin0)][/tex]
= [(80-0)24-(sin2\pi - sin0)]
= 80×24
= 1920 k calories
Therefore, 1920 k calories is the total basal metabolism of the young man.
The World Health Organization wishes to estimate the mean density of people per square kilometer. They collect data on 56 countries. State the individual, variable, population, sample, parameter, and statistic:_____________.
Individual: A single country.
Variable: The mean density of people per square kilometer of all countries.
Population: Set of all countries.
Sample: Set of the 56 countries on which data is collected.
Parameter: The mean density of people per square kilometer calculated from the population.
Statistic: The mean density of people per square kilometer calculated from the sample.
Explanation:Individual: Individuals are the objects described by a set of data.
Variable: Variables are characteristics of individuals.
Population: Population is all individuals of interest.
Sample: Sample is a subset of the population.
Parameter: Parameter is a characteristic of a population.
Statistics: Statistic is a characteristic of a sample.
The individual is the country, the variable is the density of people per square kilometer, the population is all the countries in the world, the sample is the 56 countries, the parameter is the true mean density of all countries, and the statistic is the estimated mean density from the 56 sampled countries.
Explanation:In the example given, the individual is each of the 56 countries from which the World Health Organization collects data. The variable is the density of people per square kilometer in each of these countries. The population consists of all the countries in the world. The sample includes the 56 countries for which data was collected. The parameter is the true mean density of people per square kilometer for all countries. Finally, the statistic is the estimated mean density of people per square kilometer based on the data from the sample of 56 countries.
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We run a linear regression and the slope estimate is 0.5 with estimated standard error of 0.2. What is the largest value of for which we would NOT reject the null hypothesis that ?
Answer: (0.1, 0.9) We cannot reject the null hypothesis.
Step-by-step explanation:
First, calculate with the negative. Next, with the positive.
B1 - 2 x SE(B1)
0.5 - 2 x 0.2 = 0.1
B1 + 2 x SE(B1)
0.5 + 2 x 0.2 = 0.9
Final answer:
The student's question about hypothesis testing in linear regression focuses on whether to reject the null hypothesis based on a slope estimate, its standard error, and the p-value. Since the p-value exceeds the significance level, the null hypothesis is not rejected, indicating insufficient evidence of a nonzero slope at the 5 percent level.
Explanation:
The student is asking about hypothesis testing in the context of linear regression. Specifically, the question pertains to whether the null hypothesis, which posits no effect (i.e., a slope of zero), should be rejected based on a given slope estimate, its standard error, and a provided p-value. In hypothesis testing, if the p-value is greater than the chosen level of significance (alpha), you do not reject the null hypothesis.
In the provided scenario, if the p-value is indeed 0.2150 and the level of significance (alpha) is set to 5 percent (0.05), the decision would be not to reject the null hypothesis. This is because the p-value is greater than the alpha level (0.2150 > 0.05). The conclusion is that there is insufficient evidence at the 5 percent significance level to suggest that the true slope is different from zero.
Suppose that 20% of adults practices a gluten-free diet, 15% of adults practice a dairy-free diet, and 8% of adults practice both of these diets. One adult is selected at random.
a. Given a random individual practices a glute-free diet, what is the probability they practice a dairy-free diet?
b. Are events "practices a gluten-free diet" and "practices a dairy-free diet" independent?
c. Given a random individual practices a dairy-free diet, what is the probability they do not practice a gluten free diet?
Answer:
a. 0.4
b. Not independent events
c. 0.47
Step-by-step explanation:
Let A= Practices Gluten free diet
B= Practices Dairy free diet
A and B= Practices Both diets
P(A)=0.20
P(B)=0.15
P(A and B)=0.08
a.
[tex]P(B/A)=\frac{P(A and B)}{P(A)}[/tex]
[tex]P(B/A)=\frac{0.08}{2}[/tex]
[tex]P(B/A)=0.40[/tex]
b.
The two events are independent if P(B/A) =P(B) or P(A/B)=P(A)
As, P(B/A) ≠P(B)
0.4≠0.15
So, the event gluten free diet and dairy free diet are dependent events.
c.
[tex]P(A'/B)=\frac{P(A' and B)}{P(B)}[/tex]
[tex]P(A'and B)= P(B)-P(A and B)[/tex]
[tex]P(A' and B)=0.15-0.08=0.07[/tex]
[tex]P(A'/B)=\frac{P(A' and B)}{P(B)}[/tex]
[tex]P(A'/B)=\frac{0.07}{0.15}[/tex]
[tex]P(A'/B)=0.47[/tex]
Answer:
a. 0.4
b. Not independent
c. 0.47
Step-by-step explanation:
If sinФ = 1/6 . what are the values of cosФ and tanФ? Show steps
sinФ = 1/6
sinФ = opposite/hypotenuse
cosФ = adjacent/hypotenuse
tanФ = opposite/adjacent
SOHCAHTOA
1^(2)+b^(2)=6^(2)
1+b^(2)=36
b^(2)=35
[tex]\sqrt{35}[/tex]
cosФ = [tex]\sqrt{35}[/tex]/6
tanФ = 1/[tex]\sqrt{35}[/tex] = [tex]\sqrt{35}[/tex]/35
Answer:
Cos ø = √35/6
Tan ø = √35/35
Step-by-step explanation:
Sin ø = opposite/hypothenus
Sin ø = 1/6
Pythagoras theorem says
Hyp² = Opp² + Adj²
6² = 1² + A²
A² = 35
A = √35
Hence, cos ø = √35/6
tan ø = 1/√35 = √35/35
The following sample data represent the gasoline mileages (in miles per gallon) determined for cars in a particular weight class:
25.1 29.0 34.5 35.7 37.9 34.9 24.3 26.6 27.3 32.0 30.0 34.5 35.3 33.5 36.6 34.8 16.2 13.1 24.5 33.6 28.0 33.9 30.7 32.0 37.7 21.1 31.2 35.6 34.4 25.2 35.9 18.3 29.4 29.5 34.8 29.4 26.4 38.8 36.0 28.7 23.4 35.3 33.7 38.1 28.6 34.2 34.8 39.2 39.9 36.8
1. Using 10 mpg as the lower limit of the first class interval, construct a histogram with intervals of width 5 mpg. What is the midpoint of the cell with the largest number of observations (the mode).
2. Is the histogram skewed to the left or right or symmetric?
Answer:
1) Explanation and figure attached below.
2) For this case we see that most of the values are on the right part of the distribution so then we can conclude that the distribution is skewed to the left. The mean seems to be < Median< Mode for this case.
Step-by-step explanation:
Part 1
If we order the data from the smallest to the largest we got:
13.1 , 16.2 ,18.3 , 21.1 , 23.4 , 24.3 , 24.5
25.1 , 25.2 , 26.4 , 26.6 ,27.3 ,28 , 28.6 ,
28.7 , 29 , 29.4 , 29.4 , 29.5 , 30 , 30.7
31.2 , 32 , 32 , 33.5 , 33.6 , 33.7 , 33.9
34.2 , 34.4 , 34.5 , 34.5 , 34.8 , 34.8
34.8 , 34.9 , 35.3 , 35.3 , 35.6 , 35.7
35.9 , 36 , 36.6 , 36.8 , 37.7 , 37.9
38.1 , 38.8 , 39.2 , 39.9
For this case if we use 10 mpg as the lower limit and with a width of 5 mpg for the intervals we have the following table:
Interval Frequency Midpoint
[10-15) 1 12.5
[15-20) 2 17.5
[20,25) 4 22.5
[25-30) 12 27.5
[30-35) 17 32.5
[35-40) 14 37.5
Total 50
So the histogram is on the figure attached. The midpoint for the class interval with the largest number of observations is 32.5.
Part 2
For this case we see that most of the values are on the right part of the distribution so then we can conclude that the distribution is skewed to the left. The mean seems to be < Median< Mode for this case.
Final answer:
To construct the histogram, determine the class intervals and count the number of observations in each interval. The midpoint of the cell with the largest number of observations is approximately 37.45 mpg.
Explanation:
To construct a histogram with intervals of width 5 mpg, we start by determining the class intervals. Given that the lower limit of the first interval is 10 mpg, the class intervals can be calculated as follows: 10-14.9, 15-19.9, 20-24.9, 25-29.9, 30-34.9, 35-39.9. Next, we count the number of observations falling into each interval:
10-14.9: 3
15-19.9: 6
20-24.9: 5
25-29.9: 7
30-34.9: 9
35-39.9: 10
The cell with the largest number of observations is the one corresponding to the interval 35-39.9 mpg. To calculate the midpoint of this interval, we take the average of the lower and upper limits: (35 + 39.9) / 2 = 37.45. Therefore, the midpoint of the cell with the largest number of observations (the mode) is approximately 37.45 mpg.
The following are the number of birth per year per 1,000 population for 20 countries: 34, 24, 10, 15, 22, 15, 17, 22, 10, 17, 25, 32, 15, 20, 31, 18, 37, 12, 15, 18.The mean birth per year per 1,000 population is:A.22.3B.19.5C.22.45D.None of the aboveThe median birth per year per 1,000 population isA.15B.18C.22D.None of the aboveThe mode birth per year per 1,000 population isA.15B.18C.22D.None of the aboveThe range birth per year per 1,000 population isA.15B.18C.28D.None of the above
Answer:
A. D = None of the above
B. B = 18
C. A = 15
D. D = None of the above
Step-by-step explanation:
Rearranging the population from the highest to the lowest.
10, 10, 12, 15, 15, 15, 15, 17, 17, 18, 18, 20, 22, 22, 24, 25, 31, 32, 34, 37
Mean = (summation of all the 20 samples)/ no of samples
Mean per year per 1000 population = 409/20
= 20.45
Median = the middle value (for odd numbered samples)
= the sum of the middle value ÷ 2 ( for even numbered samples)
Median birth per year per 1000 population = (18 + 18)/2
= 18
Mode = the sample that has the number of frequency
Mode per year per 1000 population = 15 (frequency = 4)
Range = highest value sample - lowest value sample
Range per year per 1000 population = 37 - 10
= 27
"Use the following information to answer the question. The mean age of lead actresses from the top ten grossing movies of 2010 was 29.6 years with a standard deviation of 6.35 years. Assume the distribution of the actresses' ages is approximately unimodal and symmetric.
In 1993, actress Anna Paquin won an academy award in for the movie ""The Piano."" She was 11-years-old. Finish the statement: ""According to the Empirical Rule, the ages of nearly all lead actresses will be between______________and_____________ years. Anna Paquin was this range when she won the academy award."""
a) 10.6; 48.7; within
b) 23.3: 36.0; within
c) 16.9: 42.3; not within
d) 10.6: 48.7; not within
Answer:
a) 10.6; 48.7; within
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 29.6
Standard deviation = 6.35
"According to the Empirical Rule, the ages of nearly all lead actresses will be between______________and_____________ years.
Nearly all(99.7%) will be within 3 standard deviations from the mean.
So from 29.6 - 3*6.35 = 10.6 years to 29.6 + 3*6.35 = 48.7 years.
Anna was 11-years old, so she was within this range.
So the correct answer is
a) 10.6; 48.7; within
The ages of nearly all lead actresses will be between 16.9 and 42.3 years according to the Empirical Rule. Anna Paquin's age falls within this range when she won the academy award.
Explanation:According to the Empirical Rule, for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations, and approximately 99.7% falls within three standard deviations. Since the mean age is 29.6 years and the standard deviation is 6.35 years, we can calculate the range as follows:
One standard deviation: 29.6 ± 6.35 = 23.25 to 35.95
Two standard deviations: 29.6 ± (2 × 6.35) = 16.9 to 42.3
Three standard deviations: 29.6 ± (3 × 6.35) = 10.55 to 48.65
Since Anna Paquin was 11 years old when she won the academy award, her age falls within the range of two standard deviations, which is 16.9 to 42.3 years. Therefore, the correct answer is option c) 16.9: 42.3; not within.
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Ann and Bill play rock-paper-scissors. Each has a strategy of choosing uniformly at random out of rock, paper, and scissors every round (making independent selections each round). Each round can end in a win, loss, or a tie for each player.
a. What is the probability Ann wins the first round. (Remember that a tie is a possibility)
Prob=
b. What is the probability that Ann's first win happens in round #5?
Prob=
C. What is the probability that Ann's first win comes after round #5?
Prob=
Answer:
a) 1/3
b) 0.0658436214
Step-by-step explanation:
Part a
Ann wins first round = (P , R) + (S , P) + (R , S) = 3 possibilities of win
Total outcomes = Wins + Losses + Ties = 9 possibilities
Hence,
P (Ann wins first round) = 3/9 = 1/3
Part b
Ann losses or ties first 4 rounds and wins 5th round
P(Ann loosing or tie in any round) = 6/9 = 2/3
Hence,
P(Ann wins 5th round only) = (2/3)^4 * (1/3) = 0.0658436214
Part c
Final answer:
In rock-paper-scissors, Ann has a 1/3 probability of winning the first round. The probability of Ann's first win in round #5 is (2/3)^4 × (1/3), and the probability of Ann's first win coming after round #5 is 1 - (2/3)^5.
Explanation:
To answer these questions, we will calculate the probabilities based on the uniform random choices made by Ann and Bill in the game of rock-paper-scissors.
Probability Ann wins the first round: Each player has 3 choices, resulting in 9 possible outcomes. There are 3 ways Ann can win (rock beats scissors, paper beats rock, scissors beats paper), so the probability is 3/9 or 1/3.
Probability Ann's first win happens in round #5: We need 4 consecutive non-wins (losses or ties) and a win in the 5th round. The probability of a non-win per round is 2/3, making the probability of four non-wins (2/3)^4. The probability Ann wins the 5th round is 1/3. Therefore, the probability of this scenario is (2/3)^4 × (1/3).
Probability that Ann's first win comes after round #5: This is the probability of Ann not winning in the first 5 rounds. As each round is independent, we raise the non-winning probability to the power of 5, (2/3)^5, and subtract from 1 to get the desired probability.
Two students each use a random number generator to pick an integer between 1 and 7.
(a) What is the probability that they pick the same number?
(b) What is the probability that they pick different numbers?
Answer:
a) 14.29% probability that they pick the same number.
b) 85.71% probability that they pick the different numbers.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
The outcomes in this problem is as follows:
(Student A Number, Student B Number)
(1,1), (2,1), (3,1), (4,1), (5,1), (6,1), (7,1)
(1,2), (2,2), (3,2), (4,2), (5,2), (6,2), (7,2)
(1,3), (2,3), (3,3), (4,3), (5,3), (6,3), (7,3)
(1,4), (2,4), (3,4), (4,4), (5,4), (6,4), (7,4)
(1,5), (2,5), (3,5), (4,5), (5,5), (6,5), (7,5)
(1,6), (2,6), (3,6), (4,6), (5,6), (6,6), (7,6)
(1,7), (2,7), (3,7), (4,7), (5,7), (6,7), (7,7)
So there are 49 total outcomes.
(a) What is the probability that they pick the same number?
There are 7 possible outcomes in which they pick the same number:
(1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7)
So there is a 7/49 = 0.1429 = 14.29% probability that they pick the same number
(b) What is the probability that they pick different numbers?
There are 49-7 = 42 possible outcomes in which they pick different numbers.
So there is a 42/49 = 0.8571 = 85.71% probability that they pick the different numbers.
A sum is invested at 4% continuous interest. This means that its value grows exponentially with k equaling the decimal rate of interest. Find, to the nearest tenth of a year, the time required for the investment to double in value.
Answer:
T = 72/4 = 18years
T = 20years (to the nearest tenth)
Step-by-step explanation:
Using the rule of 72, which is used to estimate the number of years for a given investment to double at a given interest rate.
Doubling time = 72/interest rate
T = 72/r
Rate r (in percentage) = 4%
Time T (in years)
T = 72/4 = 18years
T = 20years (to the nearest tenth)
Which of the following statement is true about k-NN algorithm?
k-NN performs much better if all of the data have the same scale
k-NN works well with a small number of input variables (p), but struggles when the number of inputs is very large
k-NN makes no assumptions about the functional form of the problem being solved
A) 1 and 2
B) 1 and 3
C) Only 1
D) All of the above
In this exercise we have to use the knowledge of algorithm to write the correct alternative that best matches, thus we can say that:
Letter D
The computational complicatedness of K-NN increases as the extent or bulk of some dimension of the training basic document file increase and the treasure gets considerably unhurried as the number of examples and free variables increase.
Also, K-NN happen a non-parametric machine intelligence treasure and as such form no assuming possession about the working form of the question at hand.
The invention everything better accompanying information in visible form of the same scale, therefore standard the information in visible form superior to applying the invention happen urged.
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All the statements provided about k-NN (scale importance, efficiency with small input variables, and no assumptions about the functional form of the problem) are true.
Explanation:The question asks which of the given statements is true about the k-NN (k-Nearest Neighbors) algorithm. The correct answer would be 'D) All of the above.' This is because all three statements accurately describe different aspects of how the k-NN algorithm works:
k-NN performs much better if all of the data have the same scale. Applying a suitable scaling method is important as it ensures all features contribute equally. k-NN works well with a small number of input variables (p), but struggles when the number of inputs grows large. This is due to the 'curse of dimensionality,' as the volume of the input space increases exponentially with the number of dimensions, impacting performance and accuracy. k-NN makes no assumptions about the functional form of the problem being solved. This is a key strength of k-NN; it's a non-parametric method that doesn’t make explicit assumptions about the functional form of the data.Learn more about k-NN algorithm here:
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Determine if the statement is true or false.
Different sequences of row operations can lead to different reduced echelon forms for the same matrix.
True False
Justify your answer.
Answer:
False
Step-by-step explanation:
There are two concepts:
1. Row Echelon Form: There can be more than two row echelon forms of a single matrix, so different sequences of row operations can lead to different row echelon forms of a single matrix.
2. Reduced Row Echelon Form: It's unique for each matrix, so different sequences of row operations always lead to the same reduced row echelon form for the same matrix.
MVA Harper industries has $900 million of common equity on its balance sheet; its stock price is $80 per share; and its market value added (MVA) is $50 million. How many common shares are currently outstanding?
Answer:
11,875,000 common shares outstanding
Step-by-step explanation:
The number of common shares outstanding of Harper industries is determined by the company's common equity added to its MVA and then divided by the stock price per share.
If common equity is $900 million, MVA is $50 million and the price per share is $50, the number of shares outstanding is:
[tex]n=\frac{900,000,000+50,000,000}{80}\\n=11,875,000[/tex]
Answer:
N = 11,875,000
Therefore, the number of common shares that are currently outstanding is 11,875,000
Step-by-step explanation:
Oustanding shares can be defined as the company's stock currently held by all its shareholders, it also including share blocks held by institutional investors and restricted shares owned by the company’s officers and insiders. The outstanding common shares can be defined mathematically with the equation below.
MVA = (P ×N) - BV .....1
Where;
MVA = market value added
P = price per share
N = Number of outstanding shares
BV = balance sheet value of common equity
From equation 1, we can make N the subject of formula.
N = (MVA + BV)/P .....2
Since;
MVA = $50,000,000
BV = $900,000,000
P = $80
Substituting into equation 2
N = (50,000,000 + 900,000,000)/80
N = 11,875,000
Therefore, the number of common shares that are currently outstanding is 11,875,000
A summary measure that is computed to describe a population characteristic from a sample is called a: A) statistic. B) census. C) parameter
Answer:
A. Statistic
Step-by-step explanation:
Usually whole population is difficult to cover so the part of population is considered to assess the aspects of population. The statistic is the quantity which summarizes the sample. The problem illustrate that summary measure is calculated from sample to describe a population. As the summary measure is computed from sample then it is a statistic.
if a pound of almonds costs $8, how many ounces can be bought for $4.60?
The number of ounces that can be bought for $4.60 will be 9.2 ounces.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Conversion means to convert the same thing into different units.
If a pound of almonds costs $8.
We know that in one pound, there are 16 ounces. Then the cost of each ounce will be
⇒ 8 / 16
⇒ $0.5 per ounce
Then the number of ounces that can be bought for $4.60 will be
⇒ 4.6 / 0.5
⇒ 9.2 ounces
The number of ounces that can be bought for $4.60 will be 9.2 ounces.
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In a box of 25 external hard disks, there are 2 defectives. An inspector examines 5 of these hard disks. Find the probability that there is at least 1 defective hard disk among the 5.
Answer:
0.3667 or 36.67%
Step-by-step explanation:
The probability of getting at least 1 defective hard disk among the 5 (P(X>0)) is equal to 100% minus the probability of getting none defectives (1-P(X=0)).
If 23 out of 25 hard disks are non-defective, the probability is:
[tex]P(X>0) = 1 -P(X=0)\\P(X>0) = 1 -\frac{23}{25}*\frac{22}{24} *\frac{21}{23} *\frac{20}{22} *\frac{19}{21}\\ P(X>0) = 0.3667=36.67\%[/tex]
The probability that there is at least 1 defective hard disk is 0.3667 or 36.67%.
Assume that you are on a cross-country flight at an altitude of 4,500 feet pressure altitude and your course is 275 degrees. The outside air temperature is 10 degrees Celsius, your indicated airspeed is 115 knots, the wind direction is 210 degrees, the wind velocity is 15 knots, and you passed your last checkpoint at 0942. If you have 218 nautical miles remaining, at what time will you arrive at your destination?
First you need to find your True Air Speed (TAS). I used the formula:
[tex]TAS=IAS\sqrt{\frac{\rho_0}{\rho}}\\[/tex]
where [tex]\rho_0[/tex] is the density at mean sea level at 15°C which is 1.225 kg/m^3 and [tex]\rho[/tex] is the density of the air in which the airplane is flying. In this case with the given altitude and air temperature is about: 1.073 kg/m^3.
So TAS is equal to: 123 kt in this case.
To get the time of arrival you need to get your ground speed. For that you need to compensate for the wind speed and direction. With the drift angle you can get your ground speed.
In this case you get ground speed of 115 kt which means to travel 218 nautical miles you need 1 h and 53 min which means you will arrive at: 1135.
If we get the 100 from number 1 each year for ten years and invest each payment in an account that earns 8% how much will be there at the end? (1448.66)
Answer:
$1,448.66
Step-by-step explanation:
The future value of an annuity with yearly deposits 'P' at an interest rate of 'r' invested for 'n' years is determined by:
[tex]FV = P[\frac{(1+r)^n-1}{r}][/tex]
For P = $100, r = 0.08 and n = 10 years:
[tex]FV = 100[\frac{(1+0.08)^{10}-1}{0.08}]\\FV=\$1,448.66[/tex]
The amount at the end of the ten years is $1,448.66
LetAandBbe two events in a sample space for which P(A)=2/3,P(B)=1/6, and P(A∩B)=1/9. What is P(A∪B)?
Answer:
13/18
Step-by-step explanation:
P(A∪B)=P(A)+P(B)−P(A∩B)
P(A∪B)=2/3 + 1/6 − 1/9 = 13/18
Consider the concentration, C, in mg/liter, of a drug in the blood as a function of x, of the amount, in mg, of the drug given and t, the time in hours since the injection. For 0 < = x < = 4 mg and t > = 0 hours, we have C = f(x, t) = te^-t(5-x). Find f(1, 2).Interpret in terms of drug concentration. a. The change in concentration of a 1 mg dose in the blood 2 hours after injection. b. The amount of a 1 mg dose in the blood 2 hours after injection. c. The concentration of a 1 mg dose in the blood 2 hours after injection. d. The concentration of a 2 mg dose in the blood 1 hour after injection. e. The change in concentration of a 2 mg dose in the blood 1 hour after injection.
Answer:
c. the concentration of 1 mg dose in the blood 2 hours after injection.
Step-by-step explanation:
We have, C = f(x, t) = t*e^-t(5-x)
then
C = f(1, 2) = 2*e^-2(5-1)
C = 2*e^-2(4)
C = 2*e^-8 OR C = 2/e^8
The concentration of a drug in blood depends on the dose and the time since administration. The given function allows calculating these concentrations, resulting in a concentration of a 1 mg dose 2 hours after injection of 8e^-2 mg/liter and a 2 mg dose 1 hour after injection of 3e^-1 mg/liter. The change in concentration cannot be determined without the previous concentration information.
Explanation:To find the concentration of the drug, we need to plug the values of x and t into the given function C = f(x, t) = te^-t(5-x). For f(1,2), we replace x with 1 and t with 2. Therefore, C = 2e^-2(5-1) = 2e^-2*4 = 2*4*e^-2 = 8e^-2.
a. The change in concentration of a 1 mg dose in the blood 2 hours after injection. To find the change in concentration, we would need the previous concentration. However, as this information is not provided, we cannot determine the change in concentration for this case.
b. The amount of a 1 mg dose in the blood 2 hours after injection. The amount of the dose remains constant at 1 mg; what changes is its concentration due to distribution and elimination processes.
c. The concentration of a 1 mg dose in the blood 2 hours after injection. With the values provided, we already calculated this to be C = 8e^-2 mg/liter.
d. The concentration of a 2 mg dose in the blood 1 hour after injection. Plain the value of x = 2 and t = 1 into the equation, we get C = 1e^-1(5-2) = 3e^-1 mg/liter.
e. The change in concentration of a 2 mg dose in the blood 1 hour after injection. Similar to part a, without previous concentration information, it is not possible to determine the change in this case.
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A computer password consists of eight characters. How many different passwords are possible if each character may be any lowercase letter or digit? How many different passwords are possible if each character may be any lowercase letter or digit, and at least one character must be a digit? A computer system requires that passwords contain at least one digit. If eight characters are generated at random, and each is equally likely to be any of the 26 letters or 10 digits, what is the probability that a valid password will be generated?
Answer:
1. 2,821,109,907,456 passwords
2. 2,612,282,842,880 passwords
3. 0.93
Step-by-step explanation:
Number of lower case letters = 26
Number of digits = 10
Total Characters = 26 + 10 = 36
Length of password = 8
1. Each character can be chosen from 36 objects (26 lowercase letters and 10 digits).
Since there's no restriction on repetition of characters, there are
(26+10)^8 different passwords
= 36^8
= 2,821,109,907,456 passwords
2.
For atleast one character to be a must be a digit means 1 character or 2 character or 3 characters... and so on
So we calculate by looking at no character being a digit
and then subtract the result from the total(36^8).
No character being a digit = All the characters are only letters
I.e. 26^8
Atleast one character being a digit = 36^8 - 26^8
= 2,821,109,907,456 - 208,827,064,576
= 2,612,282,842,880 passwords
3.
Probability = Number of possible outcomes/Number of Total outcomes
Number of possible outcomes = Number of Atleast 1 digit = 36^8 - 26^8 (as in question 2)
Total outcomes = 36^8
Probability = (36^8 - 26^8) / 36^8
= 2,612,282,842,880 / 2,821,109,907,456
= 0.92597698373108952
= 0.93 (approximated)
From the probability, the number of different passwords that are possible if each character may be any lowercase letter or digit is 2,821,109,907,456 passwords
How to calculate the probabilityThe following information can be deduced:
Number of lower case letters = 26Number of digits = 10Total Characters = 26 + 10 = 36Length of password = 8The number of different passwords are possible if each character may be any lowercase letter or digit will be:
= (26+10)⁸ different passwords
= 2,821,109,907,456 passwords
The number of different passwords that are possible if each character may be any lowercase letter or digit, and at least one character must be a digit will be:
= 36⁸ - 26⁸
= 2,612,282,842,880 passwords
Lastly, the probability that a valid password will be generated will be:
= (36⁸ - 26⁸) / 36⁸
= 0.93
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