Answer:
In this question, we shall be accepting the null hypothesis H0 since the critical value is greater than the test statistic value
Step-by-step explanation:
Here in this question, we want to make a conclusion about the null hypothesis H0.
To make or give the correct conclusion about the null hypothesis in this case, we shall need to compare the absolute value of the test statistic used against the value of the critical value.
Hence, we draw a conclusion if the test statistic is larger or smaller than the critical value.
From the value given in the question, we can see that the test statistic given as 1.68 is lesser in value compared to the critical value given as 1.96.
In this kind of case, the conclusion that we shall be drawing is that we will accept the null hypothesis H0 and reject the alternative hypothesis
A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of ounces and a standard deviation of ounce. You randomly select cans and carefully measure the contents. The sample mean of the cans is ounces. Does the machine need to be reset? Explain your reasoning. ▼ Yes No , it is ▼ very unlikely likely that you would have randomly sampled cans with a mean equal to ounces, because it ▼ lies does not lie within the range of a usual event, namely within ▼ 1 standard deviation 2 standard deviations 3 standard deviations of the mean of the sample means.
Complete question is;
A machine used to fill gallon-sized paint cans is regulated so that the amount of paint dispensed has a mean of 128 ounces and a standard deviation of 0.20 ounce. You randomly select 35 cans and carefully measure the contents. The sample mean of the cans is 127.9 ounces. Does the machine need to be? reset? Explain your reasoning.
(yes/no)?, it is (very unlikely/ likely) that you would have randomly sampled 35 cans with a mean equal to 127.9 ?ounces, because it (lies/ does not lie) within the range of a usual? event, namely within (1 standard deviation, 2 standard deviations 3 standard deviations) of the mean of the sample means.
Answer:
Yes, we should reset the machine because it is unusual to have a mean equal to 127.9 from a random sample of 35 as the mean of 127.9 doesn't fall within range of a usual event with 2 standard deviations of the mean of the sample means.
Step-by-step explanation:
We are given;
Mean: μ = 128
Standard deviation; σ = 0.2
n = 35
Now, formula for standard error of mean is given as;
se = σ/√n
se = 0.2/√35
se = 0.0338
Normally, the range of values should be within 2 standard deviations of mean. In this case, normal range of values will be;
μ ± 2se = 128 ± 0.0338
This gives; 127.9662, 128.0338
So, Yes, we should reset the machine because it is unusual to have a mean equal to 127.9 from a random sample of 35 as the mean of 127.9 doesn't fall within range of a usual event with 2 standard deviations of the mean of the sample means.
Arbitron Media Research Inc. conducted a study of the iPod listening habits of men and women. One facet of the study involved the mean listening time. It was discovered that the mean listening time for a sample of 13 men was 35 minutes per day. The standard deviation was 8 minutes per day. The mean listening time for a sample of 11 women was also 35 minutes, but the standard deviation of the sample was 18 minutes. Use a two-tailed test and at 0.10 significance level, can we conclude that there is a difference in the variation in the listening times for men and women?
Answer:
Since the critical f-value of the test statistic is less than the f value of 2.9130, we will fail to reject the null hypothesis and conclude that there's no sufficient evidence to support the claim that there is a difference in the variation in the listening times for men and women
Step-by-step explanation:
We are given;
Sample size for men; n1 = 13
Sample size for women; n2 = 11
standard deviation for men; s1 = 8 minutes
Standard deviation for women; s2 = 18 minutes.
Significance level; α = 0.1
Let's state the hypothesis;
Null hypothesis;H0: (μ1)² = (μ2)²
Alternative hypothesis;Ha: (μ1)² ≠ (μ2)²
The value of the test statistic would be;
F = (s1)²/(s2)²
F = 8²/18² = 0.1975
Now, degree of freedom for n1 is;
DF1 = n1 - 1
DF1 = 13 - 1
DF1 = 12
Also, degree of freedom for n2 is;
DF2 = 11 - 1
DF2 = 10
Now, since it's two tailed, we will make use of α/2 for the F-distribution table.
Thus, α/2 = 0.1/2 = 0.05
So,from the f-table attached, at df1 = 12 and df2 = 10,the F-Critical value is;
F_α/2 = 2.9130
Since,the critical f-value of the test statistic is less than 2.9130, we will fail to reject the null hypothesis and conclude that there's no sufficient evidence to support the claim that there is a difference in the variation in the listening times for men and women
The Freeman family is barbecuing veggie burgers, corn cobs, and mushroom caps in their local park. If 3 8 of the items barbecued are veggie burgers, and 1 3 of the items barbecued are corn cobs, what fraction of barbecued items are mushroom caps?
Answer:
The answer is below
Step-by-step explanation:
The Freeman family barbecued veggie burgers, corn cobs, and mushroom caps. 3/8 of the items barbecued are veggie burgers, and 1/3 of the items barbecued are corn cobs.
Let the total number of berbecued items be x. Therefore:
x = barbecued veggie burgers + barbecued corn cobs + barbecued mushroom caps
Barbecued veggie burgers = (3/8)x, barbecued corn cobs = (1/3)x, Let barbecued mushroom caps be y
Substituting:
x = (3/8)x + (1/3)x + y
Multiply through by 24
24x = 9x + 8x + 24y
24x = 17x + 24y
24y = 24x - 17x
24y = 7x
y = (7/24)x
barbecued mushroom caps = (7/24) of items
7/24 of the items barbecued are mushroom caps
Using fractions, it is found that the fraction of barbecued items that are mushroom caps is of [tex]\frac{7}{24}[/tex].
---------------------------
The total proportion of all products is 100% = 1.The fraction corresponding to veggie burgers is [tex]\frac{3}{8}[/tex].The fraction corresponding to corn cobs is [tex]\frac{1}{3}[/tex].The fraction corresponding to mushroom caps is x.---------------------------
Thus:
[tex]\frac{3}{8} + \frac{1}{3} + x = 1[/tex]
Solving for x, we find the fraction of mushroom caps.The least common multiple of 3 and 8 is 24.Then:
[tex]\frac{3\times3 + 8\times1 + 24x}{24} = 1[/tex]
[tex]\frac{17 + 24x}{24} = 1[/tex]
[tex]17 + 24x = 24[/tex]
[tex]24x = 7[/tex]
[tex]x = \frac{7}{24}[/tex]
The fraction of barbecued items that are mushroom caps is of [tex]\frac{7}{24}[/tex].
A similar problem is given at https://brainly.com/question/4231000
Find the Value of X 1. Solve for X algebraically. 2. Using complete sentences, describe your method for finding X.
The value of x using complete sentences is 40 degrees.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees. A right-angle triangle is a triangle that has a side opposite to the right angle the largest side and is referred to as the hypotenuse. The angle of a right angle is always 90 degrees.
We are given that;
The measure of angles 75,50 and 85
Now,
In triangle 1
50+75+y=180
y=180-125
y=55
In triangle 2
55+85+x=180
140+x=180
x=40
Therefore, by angle sum properties of triangle answer will be 40 degrees.
Learn more about the triangles;
https://brainly.com/question/2773823
#SPJ3
please Factor 12n - 18.
Answer:
[tex]\large \boxed{6(2n-3)}[/tex]
Step-by-step explanation:
[tex]12n-18[/tex]
Factor out 6 from each term.
[tex]6(2n)+6(-3)[/tex]
Take 6 as a common factor.
[tex]6(2n-3)[/tex]
Answer:
[tex] \boxed{3(4n - 6)}[/tex]Step-by-step explanation:
[tex] \mathsf{12n - 18}[/tex]
In such expression, the factor which is present in all terms of the expression is taken out as common and each term of the expression should be divided by the common factor to get another factor
Factor out 3 from the expression
[tex] \mathsf{ = 3(4n - 6)}[/tex]
Hope I helped!
Best regards!
) A jar contains 4 white balls and 6 black balls. A ball is chosen at random, and its color noted. The ball is then replaced, along with 3 more balls of the same color. Then, another ball is drawn at random from the jar. (a) Find the chance that the second ball drawn is white. (b) Given that the second ball drawn is white, what is the probability that the first ball drawn is black
Answer:
The answer is "[tex]\bold{\frac{2}{5}\ \ and \ \ \frac{6}{13}}[/tex]".
Step-by-step explanation:
You have 4/10 opportunities to choose a white ball, and there'll be 7 white balls and 6 black balls out of 13, and so the second time they choose a white one is 7/13, as well as the second time they choose a black, 6/13. people will also have a 4/10 chance.
There are 6/10 chances which users pick its black ball and 4 white balls would still be picked, but 9 black balls and out 13 balls and thus, its second and third time you select the white one is 4/13 but you are likely to pick a black for the second time is 9/13.
Taking the diagram of the next tree. The very first draw is marked with a and the second draw is marked with b.
[tex]\to P(a) = \frac{4}{10}\ \ \ \ \ \ \ \ \ P(b) = \frac{6}{10}\\\\\to P(\frac{a2}{a1}) = \frac{7}{13} \ \ \ \ \ \ \ \ \ \ P(\frac{a}{b}) = \frac{4}{13}\\\\\to P(\frac{b2}{a1}) = \frac{6}{13} \ \ \ \ \ \ \ \ \ \ P(\frac{b2}{b1}) = \frac{9}{13}[/tex]
Calculating the second drawn ball is white:
[tex]\to P(b2)=P(a)P(\frac{a2}{b1})+P(b)P(\frac{a}{b})\\[/tex]
[tex]=\frac{4}{10}\frac{7}{13}+\frac{6}{10}\frac{4}{13}\\\\=\frac{28}{130}+\frac{24}{130}\\\\=\frac{28+24}{130}\\\\=\frac{52}{130}\\\\=\frac{2}{5}\\\\[/tex]
In point b:
[tex]\to P(\frac{b}{a1})= \frac{P(B)P(\frac{a}{b})}{P(a)P(\frac{a2}{b1})+P(b)P(\frac{a}{b})\\}[/tex]
[tex]=\frac{\frac{6}{10} \frac{4}{13}}{\frac{52}{130}}\\\\=\frac{\frac{24}{130}}{\frac{52}{130}}\\\\=\frac{24}{130} \times \frac{130}{52}\\\\=\frac{24}{52}\\\\=\frac{6}{13}\\[/tex]
Next, the students at the Pearson Cooking Academy are assigned a take-home written exam to assess their knowledge of all things culinary. Historically, students scores on this exam had a N(68, 36) distribution. However, these days, there is an company called Charred Egg that offers to help students on tasks whether or not the exercises are for homework or for exams. In a cohort of 19 students, what is the probability that their average score will be at least 70?
Answer:
The probability is [tex]P( \= X \ge 70 ) = 0.07311[/tex]
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 68[/tex]
The standard deviation is [tex]\sigma = \sqrt{36} = 6[/tex]
The sample size is [tex]n = 19[/tex]
Generally the standard error of the mean is mathematically represented as
[tex]\sigma_{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma_{\= x } = \frac{6 }{\sqrt{19} }[/tex]
=> [tex]\sigma_{\= x } = 1.3765[/tex]
Generally the probability that their average score will be at least 70 is mathematically represented as
[tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 1 - P(\frac{ \= X - \mu }{\sigma_{\= x}} < \frac{70 - 68}{ 1.3765} )[/tex]
Generally [tex]\frac{ \= X - \mu }{\sigma_{\= x}} = z(The \ z-score \ of \ \= X )[/tex]
So
[tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 1 - P(Z <1.453 )[/tex]
From the z-table
[tex]P(Z <1.453 ) = 0.92689[/tex]
=> [tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 1 - 0.92689[/tex]
=> [tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 0.07311[/tex]
=> [tex]P( \= X \ge 70 ) = 0.07311[/tex]
If c o v (x comma space y )space equals space 1260, s subscript x squared equals 1600, and s subscript y squared equals 1225 , then the coefficient of determination is:
Complete Question
The complete question is shown on the first uploaded image
Answer:
The coefficient is [tex]r =0.81[/tex]
Step-by-step explanation:
From the question we are told that
[tex]cov(x, y )= 1260[/tex]
[tex]s_x^2 = 1600[/tex]
[tex]s_y^2 = 1225[/tex]
Generally the coefficient of determination is mathematically represented as
[tex]r = [ \frac{cov(x,y)}{ \sqrt{s_x^2} * \sqrt{s_y^2} } ]^2[/tex]
substituting values
[tex]r = [ \frac{ 1260}{ \sqrt{1600} * \sqrt{1225} } ]^2[/tex]
[tex]r =0.81[/tex]
What is the midpoint of the segment below?
A.
(0, 0)
B.
(-1, 1)
C.
(0.5, 0.5)
D.
(0.5, -0.5)
Answer:
B(-1,1) so you can find that when you calculation for the basic principles
Find an equation in slope-intercept form of the line that has slope –9 and passes through point A(-9,-1)
Answer:
y = -9x - 82
Step-by-step explanation:
Line with slope m=-9 passing through A(x1, y1) =A(-9,-1)
y-y1 = m(x-x1)
Substitute values
y-(-1) = -9(x-(-9)
y+1 = -9x -81
y = -9x - 82
The data given below consists of the number of children with food allergies at a sample of elementary schools: 3, 9, 5, 5, 14, 10, 5, 11, 9, 6, 1, 8, 10, 7, 9, 13, 18, 9, 8, 11, 9, 7, 6, 14, 12. Find the z-score corresponding to the median of school allergies. You may use your calculator to find the mean and standard deviation.
Answer:
z -score = 0.0459
Step-by-step explanation:
Given that:
the number of children with food allergies at a sample of elementary schools: 3, 9, 5, 5, 14, 10, 5, 11, 9, 6, 1, 8, 10, 7, 9, 13, 18, 9, 8, 11, 9, 7, 6, 14, 12.
The objective is to find the z- score , but before we can do that , we need to determine the mean and the standard deviation of the sample.
Mean = sum of the sample/ total number of the sample
Mean = (3+9+ 5+ 5+ 14+ 10+ 5+ 11+ 9+ 6+ 1+ 8+ 10+ 7+ 9+13+ 18+ 9+ 8+11+ 9+ 7+ 6+ 14+ 12)/25
Mean = 219/25
Mean = 8.76
Standard deviation = [tex]\sqrt{\dfrac {\sum (x_i - \mu)^2}{N}}[/tex]
Mean (in order )= 1, 3,5,5,5,6,6,7,7,8,8,9,9,9,9,9,10,10,11,11,12,13,14,14,18)
Standard deviation = [tex]\sqrt{\dfrac { (8.76 - 1)^2}{25} + \dfrac { (8.76 - 3)^2}{25} +\dfrac { (8.76 - 5)^2}{25} +...+ \dfrac { (8.76 - 18)^2}{25} }[/tex]
Standard deviation = 5.2174
The standard z score formula is:
[tex]z = \dfrac{X- \mu}{\sigma}[/tex]
where X = median (13th observation ) = 9
[tex]z = \dfrac{9- 8.76}{5.2174}[/tex]
[tex]z = \dfrac{0.24}{5.2174}[/tex]
z -score = 0.0459
the sum of two numbers is twenty-four. The second number is equal to twice the first number.
Answer:
The two numbers are: 8 and 16.
Step-by-step explanation:
Let the two unknown numbers be a and b.
The sum of the two number is 24. In other words:
[tex]a+b=24[/tex]
The second number is equal to twice the first number. In other words:
[tex]a=2b[/tex]
This is a system of equations. Solve by substitution:
[tex]a+b=24\\a=2b\\\\2b+b=24\\3b=24\\b=8\\a=2b\\a=2(8)=16[/tex]
Angle A corresponds to angle____
B
C
E
D
none of the above
Answer:
Angle E.
Step-by-step explanation:
Hope this helps!
Solving a word problem with three unknowns using a linear...
Rachel, Trey, and Deshaun sent a total of 98 text messages during the weekend. Trey sent 4 times as many messages as Deshaun. Rachel sent 10 fewer
messages than Deshaun. How many messages did they each send?
Number of text messages Rachel sent:
221
Х
?
Answer:If Rachel texted 221 text messages, then Deshaun texted 231 text messages, and Trey texted 924 text messages.
Step-by-step explanation:
221+10=231, 321 times 4 equal 924
A state lottery randomly chooses balls numbered from through without replacement. You choose numbers and purchase a lottery ticket. The random variable represents the number of matches on your ticket to the numbers drawn in the lottery. Determine whether this experiment is binomial. If so, identify a success, specify the values n, p, and q and list the possible values of the random variable x. Is the experiment binomial? A. Yes, there are a fixed number of trials and the trials are independent of each other. B. No, because the probability of success is different for each trial. C. No, there are more than two outcomes for each trial. D. Yes, the probability of success is the same for each trial.
Answer:
B. No, because the probability of success is different for each trial.
The experiment is not binomial.
Step-by-step explanation:
The trials are not independent because they are chosen without replacement.
There are successes and failures but the trials are dependent.
So it is not binomial.
When the balls are not replaced the probability of success becomes different for each ball.
Suppose we have 10 balls and we pick out 1 so the p1 = 1/10
but when we again pick out another without replacement the p2= 1/9
This explains why it is not binomial. In binomial the n is fixed.
Identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represents the decimal Letter C represents the decimal
[tex]10[/tex] divisions between $15.59$ and $15.6$ so each division is $\frac{15.60-15.59}{10}=0.001$
A is 5 division from $15.59$, so, A is $15.59+5\times 0.001=15.595$
similarly, C is 4 division behind $15.59$ so it is $15.590-4\times0.001=15.586$
and B is $15.601$
Find the probability that when a couple has four children, at least one of them is a boy. (Assume that boys and girls are equally likely.)
Answer:
The probability that at least, one of the four children the couple has is a boy is 0.8.
Step-by-step explanation:
Given that boys and girls are equally likely, we want to find the probability of having at least, one boy, from four children..
Note that it is possible to have the following for 4 children:
1. 4 boys, 0 girls
2. 3 boys, 1 girl
3. 2 boys, 2 girls
4. 1 boy, 3 girls
5. 0 boys, 4 girls.
To have at least, one boy, out of the 5 options, only 4 is possible.
1. 4 boys, 0 girls.........YES
2. 3 boys, 1 girl ...........YES
3. 2 boys, 2 girls.........YES
4. 1 boy, 3 girls.............YES
5. 0 boys, 4 girls..........NO
The probability is therefore,
(Probability of event = 4) ÷ (Total possible outcome = 5)
P = 4/5 = 0.8
In a cumulative relative frequency curve, the interval with the highest proportion of measurements is the interval with the:_______
a. flattest slope.
b. steepest slope
c. backward slope.
d. negative slope.
Answer:
b. steepest slope
Step-by-step explanation:
The cumulative relative frequency curve also known as Ogive is used for reading the median, upper quartile, lower quartile from the curve and calculating the semi-interquartile range when needed.
From the cumulative relative frequency curve, the interval with the highest proportion of measurements is the interval with the steepest slope. This is because the cumulative relative frequency curve always have a positive slope, and given that the interval has the highest proportion, then the slope will be steepest.
What is the solution of the linear equation? LaTeX: 5k\:+\:3.8\:=\:3k\:+\:95 k + 3.8 = 3 k + 9 Group of answer choices 26 6.4 .065 2.6
Answer:
[tex]k = 2.6[/tex]
Step-by-step explanation:
Given
[tex]5k + 3.8 = 3k + 9[/tex]
Required
Solve
[tex]5k + 3.8 = 3k + 9[/tex]
Collect like terms
[tex]5k -3k+ 3.8 = 3k -3k + 9[/tex]
[tex]2k+ 3.8 = 9[/tex]
Subtract 3.8 from both sides
[tex]2k+ 3.8 - 3.8= 9 - 3.8[/tex]
[tex]2k= 9 - 3.8[/tex]
[tex]2k = 5.2[/tex]
Divide through by 2
[tex]k = 5.2/2[/tex]
[tex]k = 2.6[/tex]
Evaluate b h for b = 12 and h = 2 . Type a numerical answer in the space provided. If necessary, use the / key to represent a fraction bar. Do not type spaces in your answer.
Answer:63
Step-by-step explanation:
Evaluate. log (down)2 256 . Write a conclusion statement.
[tex] \Large{ \boxed{ \bf{ \color{blue}{Solution:}}}}[/tex]
By using the fact that,
When,
[tex] \large{ \sf{ {a}^{x} =b}}[/tex]
Then, With logarithm base a of a number b:
[tex] \large{ \sf{ log_{a}(b) = x}}[/tex]
☃️So, Let's solve ths question....
To FinD:
[tex] \large{ \sf{log_{2}(256) }}[/tex]
Let it be x,
[tex] \large{ \sf{ \longrightarrow{ log_{2}(256) = x}}}[/tex]
Proceeding further,
[tex] \large{ \sf{ \longrightarrow \: {2}^{x} = 256}}[/tex]
[tex] \large{ \sf{ \longrightarrow \: {2}^{x} = {2}^{8} }}[/tex]
Then, We have same base 2, So
[tex] \large{ \sf{ \longrightarrow \: x = 8}}[/tex]
Or,
➙ log₂(256) = log₁₀(256) / log₁₀(2)
➙ log₂(256) = 2.40823996531 / 0.301029995664
➙ log₂(256) = 8
☕️ Hence, solved !!
━━━━━━━━━━━━━━━━━━━━
Answer:
256
Step-by-step explanation:
log 256 can most easily be found by rewriting 256 as a power of 2:
2
2^5 * 2^3 = 32*8 = 256, so 2^ (5 + 3) = 2^8.
Then we have:
log 256
2 2 = 256
Alternatively, write:
log (down)2 256 = log (down)2 2^8 = 2*8 = 256
Note that your "log (down)^2 and the function y = 2^x are inverse functions that effectively cancel one another.
22/25of a number is what percentage of that number?
Answer:
88%.
Step-by-step explanation:
Multiply the fraction by 100:
(22/25) * 100
= 22 * 4
= 88%.
4x + 1 -5x =2x +4(x-5)
Answer:
x = 3
Step-by-step explanation:
To answer for x first distribute the 4 in the parenthesis
4x + 1 - 5x = 2x +4x - 20
Next add or subtract the x's
-x + 1 = 6x - 20
Now subtract 6x and 1 on both sides to get x on the left and the rest on the right
-7x = -21
Lastly, divide -7 on both sides
x = 3
In the figure, ∆BAT ≅ ∆CAT. Which statement is not true by CPCTC? ∠BTA ≅ ∠CTA ∠BAT ≅ ∠CAT
Answer:
The two choices are true by CPCTC. Are there other choices that were not posted?
The blue dot is at what value on the number line?
Answer:
-19
Step-by-step explanation:
By looking at the 2 numbers provided, -10 and -4, you can work out that there is a gap of 6 numbers as(-4) - (-10) = 6
There are 2 intervals between -10 and -4, so each interval is
6/2 = 3
a gap of 3
This means the number to the left of -4 is -7, then -10 which works.
From there, you count how many intervals there is between -10 and the ?
There are 3 intervals, so you have to decrease -10 by -3x3 or -9
Therefore the ? is -19
Another way is to just count it directly
The number directly left of -10 is going to be -13, then -16 and finally -19
The following argument is an instance of one of the five inference forms MP, MT, HS, DS, Conj. Identify the form.
[(P ≡ T) • (H • N)] ⊃ (T ⊃ ~S)
(T ⊃ ~S) ⊃ [(H ∨ E) ∨ R]
[(P ≡ T) • (H • N)] ⊃ [(H ∨ E) ∨ R]
a. MP
b. DS
c. MT
d. Conj
e. HS
Answer:
e. HS
Step-by-step explanation:
The argument:
[(P ≡ T) • (H • N)] ⊃ (T ⊃ ~S)
(T ⊃ ~S) ⊃ [(H ∨ E) ∨ R]
[(P ≡ T) • (H • N)] ⊃ [(H ∨ E) ∨ R]
is an instance of one of hypothetical syllogism (HS).
Hypothetical syllogism contains conditional statements for its premises.
Let
p = [(P ≡ T) • (H • N)]
q = (T ⊃ ~S)
r = [(H ∨ E) ∨ R]
The this can be interpreted as:
p ⊃ q
q ⊃ r
p ⊃ r
This interprets that:
If p then q
but if q then r
therefore if p then r
Thus, in logic HS is a valid argument form:
p → q
q → r
∴ p → r
Note that ⊃ symbol is used to symbolize implication relationships. This is used in conditional statements which are represented in the if...then... form. For example p ⊃ q means: if p then q. So the type of Hypothetical syllogism used in this is conditional syllogism.
There are three parts of syllogism:
major premise
minor premise
conclusion
An example is:
If ABC is hardworking, then ABC will go to a good college.
Major premise: ABC is hardworking.
Minor premise: Because ABC is hardworking , ABC will score well.
Conclusion: ABC will go to a good college.
Example of Hypothetical syllogism:
If AB is a CD, then EF is a GH
if WX is a YZ, then AB is a CD
therefore if WX is a YZ, then EF is a GH
This can be understood with the help of an example:
If you study the topic, then you will understand the topic.
If you understand the topic, then you will pass the quiz.
Therefore, if you study the topic, then you will pass the quiz.
PART A: Suppose at another time you would like to use the same pancake recipe. You have plenty of all the ingredients except that you only have 3 eggs. Convert the recipe to use exactly 3 eggs. Blueberry Pancakes Recipe, makes 6 servings 2 cups flour 2 tablespoons baking powder 1 teaspoon salt 2 eggs 1 1/2 cups milk 1 1/4 cups blueberries Convert the recipe to use exactly 3 eggs. Hint: You may want to make use of the conversion factor 3/2. PART B: Suppose you would like to make pancakes according to the given recipe: Blueberry Pancakes Recipe, makes 6 servings 2 cups flour 2 tablespoons baking powder 1 teaspoon salt 2 eggs 1 1/2 cups milk 1 1/4 cups blueberries Convert the amount of each ingredient of the recipe to make 15 servings. Round any decimal answers to two places. Hint: You may want to make use of the conversion factor 15/6.
Answer:
see the attachment
Step-by-step explanation:
The repetitive scaling is best handled by a spreadsheet.
Part A
We know the scale factor is 3/2, so we can multiply the number of servings and everything else by 3/2. The scaled recipe will make 9 servings.
__
Part B
Since 15 = 6 + 9, we could arrive at this recipe by adding the Part A recipe to the original recipe. Instead, our spreadsheet uses the suggested 15/6 multiplier.
The formula used is shown in the spreadsheet attachment. It is filled to the right and down to cover all of the recipes and ingredients.
4 Points] Under the HMM generative model, what is p(z1 = z2 = z3), the probability that the same die is used for the first three rolls? b. [4 Points] Suppose that we observe the first two rolls. What is p(z1 = 1 | x1 = 2, x2 = 4), the probability that the casino used the fair die in the first roll?
Answer:
Step-by-step explanation:
We first examine a simple hidden Markov model (HMM). We observe a sequence of rolls of a four-sided die at an "occasionally dishonest casino", where at time t the observed outcome x_t Element {1, 2, 3, 4}. At each of these times, the casino can be in one of two states z_t Element {1, 2}. When z_t = 1 the casino uses a fair die, while when z_t = 2 the die is biased so that rolling a 1 is more likely. In particular: p (x_t = 1 | z_t = 1) = p (x_t = 2 | z_t = 1) = p (x_t = 3 | z_t = 2) = p (x_t = 4 | z_t = 1) = 0.25, p (X_t = 1 | z_t = 2) = 0.7, p (X_t = 2 | z_t = 2) = p (X_t = 3 | z_t = 2) = p (X_t = 4 | z_t = 2) = 0.1. Assume that the casino has an equal probability of starting in either state at time t = 1, so that p (z1 = 1) = p (z1 = 2) = 0.5. The casino usually uses the same die for multiple iterations, but occasionally switches states according to the following probabilities: p (z_t + 1 = 1 | z_t = 1) = 0.8, p (z_t = 2) = 0.9. The other transition probabilities you will need are the complements of these. a. Under the HMM generative model, what is p (z1 = z2 = z3), the probability that the same die is used for the first three rolls? b. Suppose that we observe the first two rolls. What is p (z1 = 1 | x1 = 2, x2 = 4), the probability that the casino used the fair die in the first roll? c. Using the backward algorithm, compute the probability that we observe the sequence x1 = 2, x2 = 3, x3 = 3, x4 = 3 and x5 = 1. Show your work (i.e., show each of your belief for based on time). Consider the final distribution at time t = 6 for both p (z_t = 1) = p (z_t = 2) = 1.
ANSWER:
Let say we have that the first state of the die is state 1. Therefore the probability of this is p(z1=1)=0.5.
Also the probability that the same die is used(i.e. casino would be in the same state) is p(z2=1|z1=1)=0.8.
Again, suppose the first state of the die is state 2. So, p(z1=2)=0.5 and p(z2=2|z1=2)=0.9.
Other transition probabilities can be written as
p(zt+1=2|zt=1)=1-p(zt+1=1|zt=1)=.2
p(zt+1=1|zt=2)=1-p(zt+1=2|zt=2)=.1
p(z3=1|z1=1) = [p(z3=1|z2=2)*p(z2=2|z1=1)]+[p(z3=1|z2=1)*p(z2=1|z1=1)] = 0.1*0.2+0.8*0.8 = 0.66
p(z3=2|z1=2) = [p(z3=2|z2=2)*p(z2=2|z1=2)]+[p(z3=2|z2=1)*p(z2=1|z1=2)] = 0.9*0.9+0.2*0.1 = 0.83
With this, the total probability that the same die is used for the first three rolls (i.e. casino would be in the same state) is given thus;
{p(z1=1)*p(z3=1|z1=1)}*{p(z1=2)*p(z3=2|z1=2)}
= 0.5*0.66+0.5*0.83 = 0.745
Prob = 0.745
1
1
A baseball weighs approximately
3
pound. A golf ball weighs about pound.
10
What expression can be used to find the combined weight of a baseball and a golf ball?
Answer:
6 pounds 10 ounces
Step-by-step explanation:
I take this to mean "a baseball weighs approximately 3 pounds and a golf ball three pounds ten ounces."
Adding these two weights together, we get 6 pounds 10 ounces.
If each interior angle of a regular polygon measures 160°, how many sides does it have?
Answer:
18
Step-by-step explanation:
Each exterior angle is the supplement of the adjacent interior angle, so is ...
180° -160° = 20°
The total of all n of these exterior angles is 360°, so we have ...
n(20°) = 360°
n = 18 . . . . . . . . . divide by 20°
The polygon is an 18-gon. It has 18 sides.
Answer:
18 Sides
Step-by-step explanation:
Each interior angle = 160°
Each exterior angle = 180° - 160° = 20°
The sum of the exterior angles = 360°
Hence the number of exterior angles =360°/20°
= 18
The polygon has 18 sides (since it has 18 exterior angles).
Hope this helps.
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