Answer:
The operation:
(a,b) is equal to the rest of the division of a by b.
Now, if we have:
(a + kb,b) = (a,b) + (k*b,b)
But if we have that k and b are integers, then:
(k*b)/b = k
So b divides k*b into a whole number, this means that (k*b,b) = 0
then:
(a + kb,b) = (a,b) + (k*b,b) = (a,b) + 0 = (a,b)
A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.9 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.6. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes.Required:a. Assume that you are a motorist entering the traffic system and receive a radio report of a traffic delay. What is the probability that for the next 60 minutes (two time periods) the system will be in the delay state?b. What is the probability that in the long run the traffic will not be in the delay state?c. An important assumption of the Markov process model presented here has been the constant or stationary transition probabilities as the system operates in the future. Do you believe this assumption should be questioned for this traffic problem? Explain.
Answer:
a) 0.36
b) 0.3
c) Yes
Step-by-step explanation:
Given:
Probability of no traffic delay in one period, given no traffic delay in the preceding period = P(No_Delay) = 0.9
Probability of finding a traffic delay in one period, given a delay in the preceding period = P(Delay) = 0.6
Period considered = 30 minutes
a)
Let A be the probability that for the next 60 minutes (two time periods) the system will be in the delay state:
As the Probability of finding a traffic delay in one period, given a delay in the preceding period is 0.6 and one period is considered as 30 minutes.
So probability that for the next two time periods i.e. 30*2 = 60 minutes, the system in Delay is
P(A) = P(Delay) * P(Delay) = 0.6 * 0.6 = 0.36
b)
Let B be the probability that in the long run the traffic will not be in the delay state.
This statement means that the traffic will not be in Delay state but be in No_Delay state in long run.
Let C be the probability of one period in Delay state given that preceding period in No-delay state :
P(C) = 1 - P(No_Delay)
= 1 - 0.9
P(C) = 0.1
Now using P(C) and P(Delay) we can compute P(B) as:
P(B) = 1 - (P(Delay) + P(C))
= 1 - ( 0.6 + 0.10 )
= 1 - 0.7
P(B) = 0.3
c)
Yes this assumption should be questioned for this traffic problem because it implies that traffic will be in Delay state for the 30 minutes and just after 30 minutes, it will be in No_Delay state. However, traffic does not work like this in general and it makes this scenario unrealistic. Markov process model can be improved if probabilities are modeled as a function of time instead of being presented as constant (for 30 mins).
Can I have help with 43 and 44 I need to see how to do them thanks.
Answer:
see explanation
Step-by-step explanation:
(43)
3[tex]x^{5}[/tex] - 75x³ ← factor out 3x³ from each term
= 3x³(x² - 25) ← this is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , thus
x² - 25 = x² - 5² = (x - 5)(x + 5)
Thus
3[tex]x^{5}[/tex] - 75x³ = 3x³(x - 5)(x + 5)
(44)
81c² + 72c + 16 ← is a perfect square of the form
(ac + b)² = a²c² + 2abc + b²
Compare coefficients of like terms
a² = 81 ⇒ a = [tex]\sqrt{81}[/tex] = 9
b² = 16 ⇒ b = [tex]\sqrt{16}[/tex] = 4
and 2ab = 2 × 9 × 4 = 72
Thus
81c² + 72c + 16 = (9c + 4)²
1. 3x^5 -75x³
=3x³(x²-25)
=3x³(x²-5²)
=3x³(x-5)(x+5)
2. 81c²+72c+16
=81c²+36c+36c+16
=9c(9c+4)+4(9c+4)
=(9c+4)(9c+4)
=(9c+4)²
Please help me with this
Answer:
Median; 60
Step-by-step explanation:
For a data plot as shown in the question above, one easier measure of center that can be used for the data set represented is the median.
From the dot plot, we can easily pinpoint the exact median, which can be used as a measure of center.
There are 11 data points represented on the dot plot by 11 dots. The median, that is the median value of the data set, would be the 6th value represented by the 6th dot on the dot plot.
Thus, the middle value is 60.
60 is the median of the data set.
Suppose you have a bag with the following in it: 5 one dollar bills, 4 fives, 3 tens, 5 twenties, and 3 fifties. Assuming the experiment requires drawing one bill from the bag at random, complete the probability distribution for this experiment.
Required:
What is the probability of drawing 9 dollars or less in a single draw?
Answer:
(a) Probility Distribution
Outcome probability
$1 5/15 = 1/3
$5 4/15
$10 3/15 = 1/5
$20 5/15 = 1/3
(b) P($9 or less) = 3/5
Step-by-step explanation:
(a) Probility Distribution
Outcome probability
$1 5/15 = 1/3
$5 4/15
$10 3/15 = 1/5
$20 5/15 = 1/3
Any other denomination
0
(b)
ways to draw $9 or less in a single draw
P($1) = 1/3
P($5) = 4/15
P($9 or less) = P($1) + P($5) = 1/3 + 4/15 = 9/15 = 3/5
The margin of error ________ (increases or decreases) with an increased sample size and ________ (increases or decreases) with an increase in confidence level.
With such a larger sample size, the margin of error lowers (grows or decreases), whereas, at a higher confidence level, it increases (increases or declines).
The margin of error:
A margin of error increases as the confidence level rises, resulting in a larger interval. A margin of error is reduced as confidence is increased, resulting in a narrower interval.By increasing sample size and confidence level, the margin of error lowers and grows.
Margin of error [tex](E) = Z_c * {\frac{\sigma}{\sqrt{n}}}[/tex]
Here [tex]Z_c[/tex] denotes the confidence level's critical value.Whenever it comes to sample size, n is the number of people who take part in the study.As a result, the margin of error lowers as the sample size grows, and the margin of error increases as the confidence level grows.Find out more about the margin of error here:
brainly.com/question/10501147
Find the surface area of the triangular prism.
Answer:
169 [tex]cm^{2}[/tex]
Step-by-step explanation:
Surface area (SA) = 2B + PH
SA = 2 ([tex]\frac{1}{2}[/tex] x 9 x 6) + (7+7+9) 5
= 2 (27) + (23) 5
= 54 + 115
SA = 169 [tex]cm^{2}[/tex]
A chemical company makes two brands
of antifreeze. The first brand is 30% pure
antifreeze, and the second brand i$ 80% pure
antifreeze. In order to obtain 80 gallons of a
mixture that contains 70o£ pure antifreeze, hov
mabry gallons of each band ot antifneze must
bo used?
Answer:
16 bags for the first(30% pure) and 64 bags of the second(80% pure)
Step-by-step explanation:
If they are mixed in a ratio of x bags to y bags
(0.3x+0.8y)/(x+y) = 0.7
0.3x + 0.8y = 0.7(x+y)
Multiply both sides with 10
3x + 8y = 7(x+y)
4x = y ——(1)
x + y = 80 ——(2)
Solve simultaneously
x + 4x = 80
5x = 80
x = 16 bags
y = 4x = 64 bags
1) At AJ Welding Company they employ 253 people, 108 employees receive 2 weeks of paid 1) _______ vacation each year. Find the ratio of those who receive 2 weeks of paid vacation to those whose paid vacation is not 2 weeks.
Answer:
108 : 145
Step-by-step explanation:
253 - 108 = 145
Ratio of those who receive 2 weeks of paid vacation is 108
Ratio of those paid vacation is not 2 weeks is 145
108 : 145
Please answer this correctly without making mistakes
Answer:
1/8
Step-by-step explanation:
3/8-1/8-1/8=1/8
One number is twice another. The sum of their reciprocals is 3/2 . Find the numbers.
Answer:
The two numbers are 1 and 2.
Step-by-step explanation:
Let the two numbers be a and b.
One number is twice another, so let's let b=2a.
Their reciprocals are 3/2. Thus:
[tex]\frac{1}{a}+\frac{1}{b} =\frac{3}{2}[/tex]
Substitute and solve for a:
[tex]\frac{1}{a}+\frac{1}{2a} =\frac{3}{2}\\[/tex]
Combine the fractions by forming a common denominator by multiplying the left term by 2:
[tex]\frac{2}{2a} +\frac{1}{2a}=\frac{3}{2}[/tex]
Combine and cross-multiply:
[tex]3/2a=3/2\\6a=6\\a=1\\b=2(1)=2[/tex]
Thus, the two numbers are 1 and 2.
The distance that Sarah travels varies directly to how long she drives. She travels 440 miles in 8 hours. Write the equation that relates the distance, d, to the time, t. How many miles can Sarah travel in 6 hours?
Answer:
330
Step-by-step explanation:
If d = distance, t = time, and s = speed, then the relationship between the 3 is s * t = d.
Solve for speed by dividing the distance over the time, s = d/t. Then, plug in the speed which in this case is 55 mph and then multiply by the time of 6 hours.
What is the 25th term in the following arithmetic sequence? -7, -2, 3, 8, ...
Answer:
108.
Step-by-step explanation:
-7, -2, 3, 8 is an arithmetic sequence with a1 (first term) = -7 and common difference (d) = 5.
The 24th term = a1 + (24 - 1)d
= -7 + 23 * 5
= -7 + 115
= 108.
Type the correct answer in each box. Use numerals instead of words,
The domain of this function is {-12, -6, 3, 15).
y = -32 +7
Complete the table based on the given domain.
y
6
0
5
15
15
Reset
Next
Answer:
x = -6,3,15,-12; y = 11,5,-3,15
Step-by-step explanation:
Domain is the x value, so plugged in the x values into the equation and got the y values or range.
Answer:
x: y:
-6 11
3 5
15 -3
-12 15
NEED HELP ASAP
Which point represents the center of the circle shown below?
Answer:
Point O represents the center of the circle
Step-by-step explanation:
HOPE IT HELPS. PLEASE MARK IT AS BRAINLIEST
Students who score within 14 points of the number 88 will pass a particular test. Write this statement using absolute value notation and use the variable x for the score.
Answer:
|88-x| ≤ 14
Step-by-step explanation:
their score has to be within 14 points of 88.
if their score is above 88, the number will be negative, but the absolute value makes the number positive. if that number is still within 14 of 88, they pass.
if their score is below 88, the number will be negative, and the absolute value keeps the number positive. if that number is still within 14 of 88, they pass.
Closing prices of two stocks are recorded for 50 trading days. The sample standard deviation of stock X is 4.665 and the sample standard deviation of stock Y is 8.427. The sample covariance is $35.826.
Calculate the sample correlation coefficient. (Round your answer to 4 decimal places.)
Answer:
The sample correlation coefficient r = 0.9113
Step-by-step explanation:
In this question, we are interested in calculating the sample correlation coefficient.
From the question, we are given;
We are given that,
The sample standard deviation of stock X = 4.665
The sample standard deviation of stock Y = 8.427
The sample covariance = 35.826
Mathematically, the Pearson correlation coefficient "r", it is given as;
r = (co-variance of X and Y)/(standard deviation of X * Standard deviation of Y)
Inputing these values, we have;
r = (35.826)/(4.665 * 8.427) = 0.9113
A test is being conducted to test the difference between two population means using data that are gathered from a matched pairs experiment. If the paired differences are normal, then the distribution used for testing is the:
Answer:
Student t-distribution.
Step-by-step explanation:
In this scenario, a test is being conducted to test the difference between two population "means" using data that are gathered from a matched pairs experiment. If the paired differences are normal, then the distribution used for testing is the student t-distribution.
In Statistics and probability, a student t-distribution can be defined as the probability distribution which can be used to estimate population parameters when the population variance is not known (unknown) and the sample population is relatively small. The student t-distribution is a statistical distribution which was published in 1908 by William Sealy Gosset.
A student t-distribution has a similar curve with the normal distribution curve, except that it is fatter and a little bit shorter.
The lengths of pregnancies in a small rural village are normally distributed with a mean of 265 days and a standard deviation of 14 days. In what range would we expect to find the middle 50% of most lengths of pregnancies
Answer:
the middle 50% of most lengths of pregnancies ranges between 255.62 days and 274.38 days
Step-by-step explanation:
Given that :
Mean = 265
standard deviation = 14
The formula for calculating the z score is [tex]z = \dfrac{x -\mu}{\sigma}[/tex]
x = μ + σz
At middle of 50% i.e 0.50
The critical value for [tex]z_{\alpha/2} = z_{0.50/2}[/tex]
From standard normal table
[tex]z_{0.25}=[/tex] + 0.67 or -0.67
So; when z = -0.67
x = μ + σz
x = 265 + 14(-0.67)
x = 265 -9.38
x = 255.62
when z = +0.67
x = μ + σz
x = 265 + 14 (0.67)
x = 265 + 9.38
x = 274.38
the middle 50% of most lengths of pregnancies ranges between 255.62 days and 274.38 days
20 points!
Please help.
A machine that produces ball bearings has initially been set so that the true average diameter of the bearings it produces is 0.500 in. A bearing is acceptable if its diameter is within 0.004 in. of this target value. Suppose, however, that the setting has changed during the course of production, so that the bearings have normally distributed diameters with a mean 0.499 in. and standard deviation 0.002 in. What percentage of bearings will now not be acceptable
Answer:
the percentage of bearings that will not be acceptable = 7.3%
Step-by-step explanation:
Given that:
Mean = 0.499
standard deviation = 0.002
if the true average diameter of the bearings it produces is 0.500 in and bearing is acceptable if its diameter is within 0.004 in.
Then the ball bearing acceptable range = (0.500 - 0.004, 0.500 + 0.004 )
= ( 0.496 , 0.504)
If x represents the diameter of the bearing , then the probability for the z value for the random variable x with a mean and standard deviation can be computed as follows:
[tex]P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - \mu}{\sigma} \leq \dfrac{X -\mu}{\sigma} \leq \dfrac{0.504 - \mu}{\sigma})[/tex]
[tex]P(0.496\leq X \leq 0.504) = (\dfrac{0.496 - 0.499}{0.002} \leq \dfrac{X -0.499}{0.002} \leq \dfrac{0.504 - 0.499}{0.002})[/tex]
[tex]P(0.496\leq X \leq 0.504) = (\dfrac{-0.003}{0.002} \leq Z \leq \dfrac{0.005}{0.002})[/tex]
[tex]P(0.496\leq X \leq 0.504) = (-1.5 \leq Z \leq 2.5)[/tex]
[tex]P(0.496\leq X \leq 0.504) = P (-1.5 \leq Z \leq 2.5)[/tex]
[tex]P(0.496\leq X \leq 0.504) = P(Z \leq 2.5) - P(Z \leq -1.5)[/tex]
From the standard normal tables
[tex]P(0.496\leq X \leq 0.504) = 0.9938-0.0668[/tex]
[tex]P(0.496\leq X \leq 0.504) = 0.927[/tex]
By applying the concept of probability of a complement , the percentage of bearings will now not be acceptable
P(not be acceptable) = 1 - P(acceptable)
P(not be acceptable) = 1 - 0.927
P(not be acceptable) = 0.073
Thus, the percentage of bearings that will not be acceptable = 7.3%
How do I solve these equations:
sin(2θ) + sin θ = 0
sin(2θ) = sqrt 3 cos θ
for intervals 0=< θ < 2pi
Answer:
Step-by-step explanation:
Given that
sin(2θ)+sinθ=0
We know that
sin(2θ)=2 sinθ x cosθ
Therefore
2 sinθ x cosθ + sinθ=0
sinθ(2 cosθ+1)=0
sinθ= 0
θ=0
2 cosθ+1=0
cosθ= - 1/2
θ=120°
_______________________________________________________
[tex]sin 2\theta=\sqrt{3cos\theta}[/tex]
By squaring both sides
[tex]sin^2 2\theta={3cos\theta}[/tex]
4 sin²θ x cos²θ=3 cosθ
4 sin²θ x cos²θ - 3 cosθ=0
cos θ = 0
θ= 90°
4 sin²θ=3
θ=60°
16.50 and pays 20.00 in cash the change due is
Answer:
Change due is 3.50
Step-by-step explanation:
20.00-16.50 is 3.50
Answer: $3.50
Step-by-step explanation:
You subtract 20 from 16.50.
The entire graph of the function h is shown below write the domain and range of h using interval notation.
you can only see values of [tex] x[/tex] Ranging from $-3$ to $3$ and they're included, so domain is $[-3,3]$
and $y$ values ranging from $-2$ to $4$ but $-2$ is not included so range is $(-2,4]$
I really need help i will rate you branliest
Work Shown:
A = P*(1+r)^t
A = 21450*(1+(-0.08))^5
A = 21450*(1-0.08)^5
A = 21450*(0.92)^5
A = 21450*0.6590815232
A = 14137.29867264
A = 14,137.30
Notice how I used a negative r value to indicate depreciation rather than growth.
Determine whether the statement (p∧(p⟶q))⟶q is a tautology one time by using truth table and the other time without using truth table
It is.........................................................
One way to prove this without a truth table is to use a conditional proof. We assume the portion p ^ (p --> q). If that's true, then so is p and p-->q
Using p and p-->q, the modus ponens rule allows us to derive q. It says that if p is true and p --> q, then q must be true as well.
Since we arrive at q, we have found the conclusion we're after. The assumption (p ^ (p-->q)) leads to q, and therefore the entire statement (p ^ (p-->q)) --> q is true for any combination of p,q.
i need help quick!!!
Answer: A,C, and D
Step-by-step explanation:
Answer:
the answer to this question may be option B, C and D
A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 80 indicated they like the taste. At 95% confidence, test to determine if at least 22% of the population will like the new soft drink.
Required:
Determine the p-value.
Answer: p-value of the test = 0.167
Step-by-step explanation:
Given that,
sample size n = 400
sample success X = 80
confidence = 95%
significance level = 1 - (95/100) = 0.05
This is the left tailed test .
The null and alternative hypothesis is
H₀ : p = 0.22
Hₐ : p < 0.22
P = x/n = 80/400 = 0.2
Standard deviation of proportion α = √{ (p ( 1 - p ) / n }
α = √ { ( 0.22 ( 1 - 0.22 ) / 400 }
α = √ { 0.1716 / 400 }
α = √0.000429
α = 0.0207
Test statistic
z = (p - p₀) / α
z = ( 0.2 - 0.22 ) / 0.0207
z = - 0.02 / 0.0207
z = - 0.9661
fail to reject null hypothesis.
P-value Approach
P-value = 0.167
As P-value >= 0.05, fail to reject null hypothesis.
Since test is left tailed so p-value of the test is 0.167. Since p-value is greater than 0.05 so we fail to reject the null hypothesis.
Please Show Work
Need Help
Answer:
The distance is 87.5 miles
Step-by-step explanation:
We can use a ratio to solve
1 in 3.5 inches
----------- = ----------------
25 miles x miles
Using cross products
1x = 3.5 * 25
x =87.5
The distance is 87.5 miles
━━━━━━━☆☆━━━━━━━
▹ Answer
87.5 miles
▹ Step-by-Step Explanation
[tex]\frac{1}{25} * \frac{3.5}{x} \\\\1 * 3.5 = 3.5\\25 * 3.5 = 87.5 \\\\Actual Distance = 87.5 miles[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft. For a group of 1013 adults, the mean of those who do not worry about identify theft is closest to ________.
Answer: 669
Step-by-step explanation:
Given, In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft.
i.e. The proportion of adults said that they worry about identity theft. (p) = 0.66
Sample size : n= 1013
Then , Mean for the sampling distribution of sample proportion = np
= (1013) × (0.66)
= 668.58 ≈ 669 [Round to the nearest whole number]
Hence, the mean of those who do not worry about identify theft is closest to 669 .
An honest die is rolled. If the roll comes out even (2, 4, or 6), you will win $1; if the roll comes out odd (1,3, or 5), you will lose $1, Suppose that in one evening you play this game n=2500 times in a row.
(a) Estimate the probability that by the end of the evening you will not have lost any money.
(b) Estimate the probability that the number of "even rolls" (roll a 2, 4, or 6) will fall between 1250 and 1300.
(c) Estimate the probability that you will win $100 or more.
Answer:
(a) 50%
(b) 47.5%
(c) 2.5%
Step-by-step explanation:
According to the honest coin principle, if the random variable X denotes the number of heads in n tosses of an honest coin (n ≥ 30), then X has an approximately normal distribution with mean, [tex]\mu=\frac{n}{2}[/tex] and standard deviation, [tex]\sigma=\frac{\sqrt{n}}{2}[/tex].
Here the number of tosses is, n = 2500.
Since n is too large, i.e. n = 2500 > 30, the random variable X follows a normal distribution.
The mean and standard deviation are:
[tex]\mu=\frac{n}{2}=\frac{2500}{2}=1250\\\\\sigma=\frac{\sqrt{n}}{2}=\frac{\sqrt{2500}}{2}=25[/tex]
(a)
To not lose any money the even rolls has to be 1250 or more.
Since, μ = 1250 it implies that the 50th percentile is also 1250.
Thus, the probability that by the end of the evening you will not have lost any money is 50%.
(b)
If the number of "even rolls" is 1250, it implies that the percentile of 1250 is 50th.
Then for number of "even rolls" as 1300,
1300 = 1250 + 2 × 25
= μ + 2σ
Then P (μ + 2σ) for a normally distributed data is 0.975.
⇒ 1300 is at the 97.5th percentile.
Then the area between 1250 and 1300 is:
Area = 97.5% - 50%
= 47.5%
Thus, the probability that the number of "even rolls" will fall between 1250 and 1300 is 47.5%.
(c)
To win $100 or more the number of even rolls has to at least 1300.
From part (b) we now 1300 is the 97.5th percentile.
Then the probability that you will win $100 or more is:
P (Win $100 or more) = 100% - 97.5%
= 2.5%.
Thus, the probability that you will win $100 or more is 2.5%.
