A die is rolled three times and a curious pattern emerges. On the first roll, the number is greater than 3. On the second roll, the under is greater than 4, and on the third roll, the number is greater than 5. If all three rolls are independent, what is the probability that this occurs?
Therefore, the probability of the curious pattern occurring is 1/36.
What is probability?Probability theory is an important branch of mathematics that is used to model and analyze random phenomena, such as the outcomes of games of chance, the behavior of particles in physics, or the performance of complex systems in engineering. It has many practical applications in fields such as statistics, finance, economics, and computer science.
Here,
The probability of rolling a number greater than 3 on a fair die is 3/6 = 1/2, since there are three numbers (4, 5, 6) that satisfy this condition out of the six possible outcomes.
Similarly, the probability of rolling a number greater than 4 on a fair die is 2/6 = 1/3, and the probability of rolling a number greater than 5 is 1/6.
Since each roll is independent, we can multiply these probabilities together to get the probability that all three conditions are satisfied:
P = (1/2) × (1/3) × (1/6)
= 1/36
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Please help! I will give Brainliest!
Who is correct?
90% of people marry there 7th grade love. since u have read this, u will be told good news tonight. if u don't pass this on nine comments your worst week starts now this isn't fake. apparently if u copy and paste this on ten comments in the next ten minutes you will have the best day of your life tomorrow. you will either get kissed or asked out in the next 53 minutes someone will say I love you
Step-by-step explanation:
Are this two triangles similar?
Yes
No
If the two triangles are similar,find the length of side AC.
They are not similar,so I can’t find the length
10
6
8
======================================================
Explanation:
Focus on triangle ABC. Let's find the missing angle
A+B+C = 180
113+B+22 = 180
B+135 = 180
B = 180-135
B = 45
Between the triangles, have two pairs of angles that are congruent
A = D = 113
B = E = 45
Which is enough to prove the triangles are similar through the angle angle (AA) similarity theorem. This must mean that C = F = 22
Since we have A pair with D, and B pair with E, this means that \(\triangle ABC \sim \triangle DE F\)
The order of the letters is important so we know how the angles pair up. The first letters pair up together, the second letters pair up, and so on.
Consequently, this means sides BC and EF pair up and AC and DF pair up
We can then say...
BC/EF = AC/DF
18/12 = x/4
18*4 = 12*x
72 = 12x
12x = 72
x = 72/12
x = 6
AC = 6
SERIOUS MATH HELP PLEAZE
SHOW WORK OR AN EXPLANATION
HELPPPPPPPPPPPP
Answer:
The correct answer is B.
Step by step explanation:
Domain of \(x^2-4 : \left [ {{Solution : - \infty} <x<\infty}} \atop {Interval Notation: (-\infty, \infty})}} \right]\)
Range of \(x^2-4:\)\(x^2-4 : \left [ {{Solution : f(x)\geq -4}} \atop {Interval Notation: [-4, \infty})}} \right]\)
Axis interception points of \(x^2-4 :\) X Intercepts: \((2,0), (-2,0)\), Y Intercepts: \((0,-4)\)
Vertex of \(x^2-4:\) Minimum \((0,-4)\)
Hope this helps. If so, may I get brainliest and a thanks?
Thank you, Have a good day!
"A line passes through the points (12, -1) and (4, -5). Which points lie on the same line?"
Multiple Choice Question
(-5, 4)
(0, -7)
(6, -3)
(-4, 5)
(2, -6)
(16, 1)
The points (-5, 4), (6, -3), (-4, 5), (2, -6), and (16, 1) all lie on the same line as the points (12, -1) and (4, -5).
to check which points lie on the same line as the points (12, -1) and (4, -5), we can first find the slope of the line passing through these two points. the slope of a line passing through two points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1)/(x2 - x1)
using the points (12, -1) and (4, -5), we have:
slope = (-5 - (-1))/(4 - 12) = -4/8 = -1/2
so the slope of the line passing through these two points is -1/2. now we can check which points have the same slope when connected to one of the points (12, -1) or (4, -5) using the slope-intercept form of a line:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line.
for example, using the point (12, -1), we have:
y - (-1) = (-1/2)(x - 12)
simplifying this equation, we get:
y = (-1/2)x + 5
now we can check which points satisfy this equation:
(-5, 4): 4 = (-1/2)(-5) + 5, so this point lies on the line
(0, -7): -7 = (-1/2)(0) + 5, so this point does not lie on the line
(6, -3): -3 = (-1/2)(6) + 5, so this point lies on the line
(-4, 5): 5 = (-1/2)(-4) + 5, so this point lies on the line
(2, -6): -6 = (-1/2)(2) + 5, so this point lies on the line
(16, 1): 1 = (-1/2)(16) + 5, so this point lies on the line
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how do i write this equation in function notation.
=−2/5+1
Answer:
f(x) = −2/5x + 1
Step-by-step explanation:
when putting an equation in function notation first you must make sure the equation is in slope-intercept form and then you must rewrite the equation but instead of putting y you will replace it with f(x), or g(x), whichever one you are given directions to put it as.
Hope This Helps!
Plz Mark Brainliest!
Expand (3x + 1)(x + 2) using the box method of by foiling. Show or explain
your steps.
Find the approximate height of the cylinder. Use 3.14 for π.
Volume = 146.952 cm3 A cylinder is shown. The diameter is labeled six centimeters.
Answer: The height is 5.2 cm.
Step-by-step explanation:
146.952 = n r^2 h
146.952= 3.14 * 9 *h
146.952= 28.26 h divide both sides by 28.26
h = 5.2
In a box there are chips numbered from 1 to 15. If a chip is randomly removed, what is the probability that the number drawn is a multiple of 2 or 3. (
The probability that the number drawn is a multiple of 2 or 3 is 8/15 or 0.53.
This can be easily found by finding the number of multiples of 2 and 3 between 1 and 15 and adding them together. The multiples of three go from 3 to 15 and therefore there are 5 such numbers. The multiples of two go from 2 to 14 and hence there are 7 such numbers. Therefore, when we add these two numbers together, we get 12.
This is the total number of multiples of 2 or 3 between 1 and 15. We divide this by the total number of elements in the box, which is 15, to get the probability that the number drawn is a multiple of 2 or 3. This comes out to be 8/15 or 0.53.
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(brainliest) is this a linear function?
a jar contains 4 red, 7 white and 10 blue marbles. a child selects two marbles at random from the jar. find the probability that the first is red and the second is white.
The probability that the first is red and the second is white is 4/21 or 0.190476.
The total number of marbles in the jar is 4 red, 7 white and 10 blue. This means there is a total of 21 marbles.
The probability of selecting a red marble first is 4/21 (4 out of 21 marbles are red).
The probability of selecting a white marble second is 7/20 (7 out of the remaining 20 marbles are white).
The probability of selecting a red marble first and a white marble second is 4/21 x 7/20 = 28/420 = 4/60 = 0.190476
The probability of selecting two marbles at random from the jar is calculated by multiplying the individual probabilities of selecting each marble. The probability of selecting the first marble is 4/21 (4 out of 21 marbles are red) and the probability of selecting the second marble is 7/20 (7 out of the remaining 20 marbles are white). Thus, the probability of selecting a red marble first and a white marble second is 4/21 x 7/20 = 28/420 = 4/60 = 0.190476.
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One year, the population of a city was 330,000. Several years later it was
270,600. Find the percent decrease.
HELP ASAP
Answer:
18%
Step-by-step explanation:
Express the ending population as a percentage of the starting population:
270000 divided by 330000=0.82
0.82 *100=82
subtract from the 100% we started with to get the percent decrease:
100% - 82% = 18
:)
why would you choose a mortgage over other methods of credit?
Answer: The only reason would be the benefits of a mortgage plan. which includes, helping you to maintain your credit score, money available to you when need for curtain life decisions, and there are many tax benefits that come with a mortgage plan! Hope this helps! best of luck!
assume a simple model with only two countries: the united states and germany, and two goods: beer and motorcycles. suppose that the opportunity cost for the united states to produce 1 beer is 3 motorcycles and the opportunity cost for germany to produce 1 beer is 1/2 motorcycles. which of the following statements is true
The statement opportunity cost for Germany to produce 1 beer is 1/2 motorcycles is true.
The German economy would be better off if it produced beer and traded motorcycles with the US.
Germans would benefit from specializing in producing beer and engaging in trade with the United States since their opportunity cost is lower (1/2 is less than 3).
A country is said to be having a comparative advantage in producing a good if it can produce it at a lower opportunity cost. Germany has a lower opportunity cost in producing beer so it has a comparative advantage in making beer.
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answer the following, Round final answer to 4 decimal places. a.) Which of the following is the correct wording for the randon variable? r×= the percentage of all people in favor of a new building project rv= the number of people who are in favor of a new building project r N= the number of people polled r×= the number of people out of 10 who are in favor of a new building project b.) What is the probability that exactly 4 of them favor the new building project? c.) What is the probabilitv that less than 4 of them favor the new building project? d.) What is the probabilitv that more than 4 of them favor the new building project? e.) What is the probabilitv that exactly 6 of them favor the new building project? f.) What is the probability that at least 6 of them favor the new building project? 8.) What is the probabilitv that at most 6 of them favor the new building project?
In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.
a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.
b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.
c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.
d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).
e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.
f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).
g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).
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the point S (-1,-3) is reflected across the line y=-2
Answer:
a reflection of ΔRST across the line y = –x
Step-by-step explanation:
A reflection across the line y = –x transforms point (x, y) into (-y, -x)
After reflecting ΔRST across the line y = –x we get:
R (-1, 3) -> (-3, 1)
S (3,-2) -> (2, -3)
T (1, -4) -> (4, -1)
where S is at the desired vertex
Step-by-step explanation:
======================================================
Explanation:
Refer to the diagram below.
The point S(-1,-3) is exactly 1 unit below the line y = -2.
Move up 1 unit to go from S to a point on the line, and directly above S.
Then move another unit up to arrive at S ' (-1, -1) which is the result of reflecting point S(-1,-3) over the line y = -2.
Both S and S' are the same distance away from the mirror line y = -2.
Will mark Brainliest for the correct answer. Also, it wouldn’t hurt to explain your thought process when going through these problems but is not required to get Brainliest.
Answer:
Step-by-step explanation:
2a) p * \((3p^{3} )^{2}\)
\(p^{1}\) * \(9p^{2*3}\)
\(p^{1}\) * \(9p^{6}\)
\(9p^{6+1}\)
\(9p^{7}\)
2b) ( \((-3x)^{2}\) * \(x^{3}\) *\(y^{5}\) ) / \(y^{6}\)
\(9x^{2}\) *\(x^{3}\) / \(y^{1}\)
\(9x^{2+3}\) / y
\(9x^{5}\) /y
Solve the following absolute value equation
Answer:
\( |x - 8| + 1 = 11\)
\( |x - 8| = 10\)
x - 8 = 10 or x - 8 = -10
x = 18 or x = -2
\(|x-8|+1 = 11\)
Move 1 to the right side:\(|x-8| = 10\)
Apply absolute rule: if |w| = a, a > 0 then w = a OR w = - a\(x-8 = -10\) OR \(x-8 = 10\)
Add 8 to both sides.\(x=-2\) OR \(x = 18\)
help meeeeee 1/2 X (6 X 4)+3 + 2
6x4=24
24x1/2=12
12+3=15
15+2=17
17 is the answer
LAST CHANCE FOR TONS OF POINTS!!!!!!! AND BRAINLIEST!!!
A boat can travel 28 miles up a river in the same amount of time it takes to travel 36 miles down the same river. If the current is traveling at 2 miles per hour, what is the speed of the boat in still water?
Answer:
6
Step-by-step explanation:
Prepare a report answering the following three questions about the Stokes approximation and Oseen approximation.
[1] Briefly describe the two approximations.
[2] Interpret the difference between the results of the two approximations in terms of fluid dynamics.
[3] Give your opinion on the significance of the difference between the two approximations.
The Stokes approximation and Oseen approximation are methods used to determine the motion of fluid particles in a fluid dynamics problem.
The Stokes approximation applies to slow-moving fluid particles, where viscous forces are dominant, while the Oseen approximation applies to higher velocities, where convective forces are dominant..Oseen approximation: In this approximation, the equations governing the motion of fluid particles account for the convective forces in addition to the viscous forces.
This approximation is valid at moderate Reynolds numbers and is used when the viscous forces are still strong but not as dominant as in the Stokes approximation. The velocity of the fluid decreases less rapidly than in the Stokes approximation, and the approximation is valid for Reynolds numbers greater than one .The difference between the results of the two approximations lies in their range of applicability and the accuracy of their results.
The significance of the difference between the two approximations lies in their application to real-world problems. In fluid dynamics, it is essential to have accurate approximations to predict the behavior of fluid particles accurately. Therefore, choosing the appropriate approximation for the specific problem is critical. knowing the range of applicability of each approximation can help in determining the parameters for the problem.
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What is the slope of the line with an equation of 5x - 3y = -12
Answer: \(m=\frac{5}{3} =1.67\)
Step-by-step explanation:
Original equation: \(5x-3y=-12\)Subtract 5x from both sides of the equation: \(-3y=-5x-12\)Divide both sides of the equation by -1: \(3y=5x+12\)Divide both sides of the equation by 3 to get y on the left, leaving the equation in \(y=mx+b\) form: \(y=\frac{5}{3}x+4\)Evaluate. Slope is equal to m in this form, so the slope is \(m=\frac{5}{3}\).Hope this helps!
An amusement park sells 2 kinds of tickets.
Tickets for children cost $1.50. Adult tickets
cost $4. On a certain day, 278 people entered
the park. On that same day the admission fees
collected totaled $792. How many children
were admitted on that day? How many adults
were admitted?
Please help!!
The 100-meter dash times in the girls track meet were normally distributed with a mean of 13 seconds and a standard deviation of 0.3 seconds. What is the probability that a runner finished between 12.4 and 14 seconds?
Answer:
The probability is 0.97682
Step-by-step explanation:
We start by finding the z-values of the runner times given.
Mathematically;
z-score = (x-mean)/SD
From the question, mean = 13 seconds and SD = 0.3 seconds
So for 12.4 seconds, we have;
z = (12.4-13)/0.3 = -0.6/0.3 = -2
For 14 seconds, we have;
z = (14-13)/0.3= 1/0.3 = 3.33
So the probability we want to calculate is;
P(-2<z<3.33)
We can find this using the standard normal distribution table
Mathematically;
P(-2<z<3.33) = P(z<3.33) - P(z < -2)
Using the standard normal distribution table, the value of this is;
P(-2<z<3.33) = 0.97682
Question 2 (1 point) A sample of 13 children has a mean IQ of 112 and a standard deviation of 15. Is it likely that this could be a random sample from a population whose mean is known to be 113.5? Yes, it is likely that a random sample mean could deviate that much from a population mean. No, a random sample mean could not deviate that much from a population mean. No, the calculations are incorrect. The question cannot be answered on the basis of the information given.
Yes, it is likely that a random sample mean could deviate that much from a population mean.
To test whether the sample mean of 112 is significantly different from the population mean of 113.5, we can use a one-sample t-test. With 12 degrees of freedom (n-1), the critical value for a two-tailed test at a 5% significance level is ±2.179.
Using the formula t = (\(\bar{X}\) - μ) / (s / √n), where \(\bar{X}\) is the sample mean, μ is the population mean, s is the standard deviation, and n is the sample size, we get: t = (112 - 113.5) / (15 / √13) = -1.01
Since |-1.01| < 2.179, we fail to reject the null hypothesis that the sample mean is not significantly different from the population mean. Therefore, it is likely that this sample could be a random sample from a population with a mean of 113.5.
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By some estimates __________ of employee learning occurs via on the job training.
a. 60-70 percent
b. 20-30 percent
c. 40-50 percent
d. 80-90 percent
By some estimates 80-90 percent of employee learning occurs via on the job training.
What does on the job training mean?
This is the term that is used to refer to the training that people would receive based on the fact that it is preparing them to have the competent skills that are useful for a particular job. It is one of the ways that employers help to get their employees ready for the task at hand.
It has been reported from available data that on the job training is a great component of employee learning.
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(a) Find the value of the test statistic. (Round to three or more decimal places.)
(b) Find the p-value. (Round to three or more decimal places.)?
(c) Can we conclude that the proportion of women with anemia in the first country is less than the proportion of women with anemia in the second country?
O Yes O No
(a) The value of the test statistic is -1.097. (b) The p-value is 2099. (c) No, we cannot conclude that the proportion of women with anemia in the first country is less than the proportion of women with anemia in the second country
To perform the hypothesis test, we will compare the proportions of women with anemia in the two countries. Let's denote the proportion of women with anemia in the first country as p1 and the proportion in the second country as p₂.
Null hypothesis: p₁ >= p₂
(The proportion of women with anemia in the first country is greater than or equal to the proportion in the second country.)
Alternative hypothesis: p₁ < p₂
(The proportion of women with anemia in the first country is less than the proportion in the second country.)
(a) To find the test statistic, we can use the formula for the test statistic for two independent proportions:
Test Statistic
\(= \frac{(p_1 - p_2)}{\sqrt{(\frac{p \times (1 - p)}{n1}) + (\frac{p \times (1 - p)}{n_2})}}\)
where
p = (x₁ + x₂) / (n₁ + n₂)
In this case,
x₁ = 489,
n₁ = 2100,
x₂ = 463, and
n₂ = 1900.
Calculating the test statistic:
p₁ = 489 / 2100
≈ 0.232857
p₂ = 463 / 1900
≈ 0.243684
p = (489 + 463) / (2100 + 1900)
≈ 0.238706
Test Statistic
\(= \frac{(0.232857 - 0.243684)}{\sqrt{\frac{0.238706 \times (1 - 0.238706)}{2100} + \frac{0.238706 \times (1 - 0.238706)}{1900}}}\)
Calculating this value:
Test Statistic ≈ -1.097
(b) To find the p-value, we need to use the test statistic and the degrees of freedom. Since this is a one-tailed test, the degrees of freedom can be approximated by the smaller of (n₁ - 1) and (n₂ - 1).
In this case, the degrees of freedom would be
= (2100 - 1)
= 2099.
Using the test statistic and degrees of freedom, we can find the p-value using a t-distribution table or statistical software. The p-value represents the probability of observing a test statistic as extreme as the one calculated (or even more extreme) under the null hypothesis.
(c) To make a conclusion, we compare the p-value to the significance level (0.05 in this case). If the p-value is less than the significance level, we reject the null hypothesis in favor of the alternative hypothesis. Otherwise, we fail to reject the null hypothesis.
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Complete Question:
A researcher studied iron-deficiency anemia in women in each of two developing countries. Differences in the dietary habits between the two countries led the researcher to believe that anemia is less prevalent among women in the first country than among women in the second country. A random sample of 2100 women from the first country yielded 489 women with anemia, and an independently chosen, random sample of 1900 women from the second country yielded 463 women with anemia. Based on the study can we conclude, at the 0.05 level of significance, that the proportion p, of women with anemia in the first country is less than the proportion P2 of women with anemia in the second country? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the parts below. (If necessary, consult a list of formulas.)
(a) Find the value of the test statistic. (Round to three or more decimal places.)
(b) Find the p-value.?
(c) Can we conclude that the proportion of women with anemia in the first country is less than the proportion of women with anemia in the second country?
(i) Yes
(ii) No
the within-groups estimate of variance is the estimate of the variance of the population of individuals based on the variation among the:
Group of answer choices
Scores in each of the actual groups studied
Mean of the groups minus the mean of the scores of the actual groups
Equal to the between-groups estimate of population variance
Means of the groups studied
The within-group estimate of variance is the estimate of the variance of the population of individuals based on the variation among the scores in each of the actual groups studied.
The within-groups estimate of variance is the estimate of the variance of the population of individuals based on the variation among the:
Scores in each of the actual groups studied.
This estimate represents the variation within each group and helps in understanding the population's variance by looking at individual differences within the groups.
The estimated within-group variance is the sum of the within-group variances for each group in the model. Effectively, this is the sum of the variance of each value (j) from its group (i) divided by the sample size minus one.
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what is the value of (2+6i)^(2) ?
i=imaginary and the 2 by itself in parenthesis is sqaure
Answer:
(2 + 6i)²
(2 + 6i)(2 + 6i)
2 + 12i + 12i -36
24i - 34
Why is Earth's outer core hotter than Earth's oceanic crust?
Earth's oceanic crust is denser than Earth's outer core is.
Earth's oceanic crust has lava flowing from the mantle.
Earth's outer core has a composition of solid iron and nickel.
O Earth's outer core is deeper within Earth than oceanic crust is.
Answer:
D earrhs outer cors is deeper within eafth than aceanic crust is
Answer:
d
Step-by-step explanation: