The evaluated probability that there have been 2 occurrences in ten minutes is 0.0842, under the condition that the mean number of occurrences in ten minutes is 5.
Here we have to apply the Poisson distribution formula. The formula is
[tex]P(X = k) = (e^{-g} * g^k) / k!,[/tex]
Here
X = number of occurrences,
k = number of occurrences we want to find the probability for,
e = Number of Euler's
g = mean number of occurrences in ten minutes.
For the given case, g = 5 since
Therefore,
P(X = 2) = (e⁻⁵ × 5²) / 2!
≈ 0.0842.
Hence, after careful consideration the evaluated probability that there are 2 occurrences in ten minutes is 0.0842.
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What are the common factors or 12 and 42
2, 3 are the common prime factors of 12 and 42.
A random sample of size n 1 equals 31 results in a sample mean of 123. 3 and a sample standard deviation of 8. 5. An independent sample of size n 2 equals 50 results in a sample mean of 129. 8 and sample standard deviation of 7. 3. Does this constitute sufficient evidence to conclude that the population means differ at the alpha equals 0. 01 level of significance?
The basketball coach can order approximately 34 shooting shirts for $300.
To determine the number of shooting shirts the basketball coach can order for $300, we need to solve the equation C = 0.2x^2 + 1.6x + 15, where C represents the cost and x represents the number of shooting shirts.
The equation is given as C = 0.2x^2 + 1.6x + 15.
To find the number of shooting shirts for $300, we set the cost C equal to 300 and solve for x:
0.2x^2 + 1.6x + 15 = 300
0.2x^2 + 1.6x + 15 - 300 = 0
0.2x^2 + 1.6x - 285 = 0
Now we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
For this equation, a = 0.2, b = 1.6, and c = -285. Plugging in these values into the quadratic formula:
x = (-1.6 ± sqrt(1.6^2 - 4 * 0.2 * -285)) / (2 * 0.2)
Simplifying the equation further:
x = (-1.6 ± sqrt(2.56 + 228)) / 0.4
x = (-1.6 ± sqrt(230.56)) / 0.4
x = (-1.6 ± 15.18) / 0.4
Now we have two solutions:
x1 = (-1.6 + 15.18) / 0.4 = 33.95
x2 = (-1.6 - 15.18) / 0.4 = -44.95
Since the number of shooting shirts cannot be negative, we discard the negative solution.
Therefore, the basketball coach can order approximately 34 shooting shirts for $300.
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Your doing practice 6
Answer:
A ∪ B = {1, 2, 3, 4, 5, 6, 7, 9}
Step-by-step explanation:
We can find the union of two sets by including all of the numbers in both sets, but without repeating any numbers.
For example:
if A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7, 8},
then A ∪ B = {1, 2, 3, 4, 5, 6, 7, 8}
We can apply this concept to the problem at hand, but first we need to represent set A as a list of numbers:
They all have to be odd numbers between 0 and 10.
[tex]\implies A[/tex] = {1, 3, 5, 7, 9}
We are given that B = {2, 3, 4, 5, 6}. So, to find the union of A and B, we can combine both sets of numbers and get rid of copies:
A ∪ B = {1, 2, 3, 4, 5, 6, 7, 9}
Use the drawing tool(s) to form the correct answer on the provided graph.
Plot the axis of symmetry and the vertex for this function: h(x) = (x − 5)2 − 7
A graph of the axis of symmetry and the vertex for this function is shown below.
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the graph of this quadratic function, we can logically deduce that the graph is an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).
Since the leading coefficient (value of a) in the given quadratic function h(x) = (x - 5)² - 7 is positive 1, we can logically deduce that the parabola would open upward and the solution would be on the x-intercepts. Also, the value of the quadratic function f(x) would be minimum at -7.
In conclusion, the turning point and vertex is given by the ordered pair (5, -7).
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Calculate the expected count for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week under the null hypothesis. calculate the contribution of the cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week to the chi-square test statistic.
The cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week contributes 4 to the overall chi-square test statistic.
To calculate the expected count for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week under the null hypothesis, you would first need to determine the overall proportion of women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week in the sample. Let's say this proportion is 0.20.
Next, you would multiply this proportion by the total sample size to get the expected count. Let's say the total sample size is 500 women. The expected count for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week would be:
Expected count = 0.20 x 500 = 100
To calculate the contribution of the cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week to the chi-square test statistic, you would need to subtract the expected count from the observed count for this cell, square the difference, and divide by the expected count. Let's say the observed count for this cell is 80.
Contribution to chi-square = (80 - 100)^2 / 100 = 4
This means that the cell for women who suffer from depression and drink between 2-6 cups of caffeinated coffee per week contributes 4 to the overall chi-square test statistic.
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Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.
Based on the diagram, which expresses all possible lengths of segment AB?
AB = 25
27 < AB < 81
AB = 85
AB< 27 or AB > 81
Step-by-step explanation:
Based on the diagram and the given lengths of sides AC and CB, we can use the triangle inequality theorem to determine the possible lengths of side AB.
According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore:
AC + CB > AB
27 + 54 > AB
81 > AB
Also, using the same theorem, we can see that:
AB + AC > CB
AB + 27 > 54
AB > 54 - 27
AB > 27
Therefore, we have:
27 < AB < 81
So, the answer is: 27 < AB < 81
Answer:
Based on the information given, the possible lengths of segment AB can be determined using the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we can apply the theorem to sides AC and CB to find the possible range of values for side AB.
Since AC has a length of 27 and CB has a length of 54, we can write two inequalities based on the Triangle Inequality Theorem:
AB + 27 > 54 AB + 54 > 27
Solving each inequality for AB, we get:
AB > 27 AB > -27
Since the length of a side of a triangle must be positive, we can disregard the second inequality. Therefore, the possible range of values for side AB is AB > 27.
However, it’s important to note that you mentioned a diagram in your message but did not provide it. Without seeing the diagram, I cannot determine if there are any additional constraints on the length of side AB.
Step-by-step explanation:
i need help fast look at photo
Step-by-step explanation:
B
26 = 13.5 + m/2.5; m = 31.25
26 = 13.5 + 31.25/2.5
26 = 13.5 + 12.5
26 = 26
Arnold is looking at the building from 300 feet away at an angle of elevation of 22 grades when asked arnold says he’s 4.75 feet tall do you agree or desagree with arnold’s height explain your answer with matemátical support?
We can conclude that Arnold's height of 4.75 feet by using tangent function is not accurate based on the calculations.
To determine whether Arnold's height is accurate, we can use trigonometry and the given information about the angle of elevation and distance to the building.
Let's start by drawing a diagram to represent the situation. We have a right triangle with the opposite side being Arnold's height (h), the adjacent side being the distance to the building (300 ft), and the angle of elevation being 22 degrees.
Using the tangent function, we can write:
tan(22) = h / 300
Solving for h, we get:
h = 300 * tan(22)
Using a calculator, we find that h is approximately 122.8 feet.
Therefore, we can conclude that Arnold's height of 4.75 feet is not accurate based on the calculations. The height we calculated is over 25 times greater than Arnold's claimed height, which is not possible.
It is important to note that this assumes that Arnold's line of sight is parallel to the ground. If Arnold is on uneven ground, this could affect the calculations. Additionally, it is possible that Arnold may have misspoken about his height or the angle of elevation. However, based on the given information and calculations, we can confidently say that Arnold's claimed height is not accurate.
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Which equation can be solved to find one of the missing side lengths in the triangle?
Triangle A B C is shown. Angle A C B is 90 degrees and angle C B A is 60 degrees. The length of side C B is a, the length of C A is b, and the length of hypotenuse A B is 12 units.
cos(60o) = StartFraction 12 Over a EndFraction
cos(60o) = StartFraction 12 Over b EndFraction
cos(60o) = StartFraction b Over a EndFraction
cos(60o) = StartFraction a Over 12 EndFraction
Mark this and return
The fourth equation i.e. cos (60°) = [tex]\frac{a}{12}[/tex] can be used to find one of the missing side lengths in the triangle. This has been obtained using trigonometry.
What is trigonometry?
Trigonometry is a branch of mathematics that focuses on right-angled triangles, including their sides, angles, and connections.
We are given a right angled triangle with perpendicular as b, base as a and hypotenuse measuring 12 units.
We know by trigonometry that cos θ is the proportion of the adjacent side to the hypotenuse.
So, only the fourth equation is the one which can be used to find the missing length.
So, the equation is cos(60°) = [tex]\frac{a}{12}[/tex].
Hence, the fourth option is the correct answer.
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I just need the answer to question 3
Answer:46.15% or rounded 46% of pulling a card higher than 8.
Step-by-step explantwenty. Well there are 6 cards higher than 8, which include 9, 10, jack, queen, king, and ace. There is 4 diffrent suites so do 6×4=24. Then do 24/52=0.4615
Answer: 46.15%
Mind-Set Matters In 2007 a Harvard psychologist set out to test her theory that ‘‘Mind-Set Matters. "1 She recruited female maids2 working in different hotels to participate in her study, and informed maids (randomly chosen) that the work they do satisfies the Surgeon General’s recommendations for an active lifestyle (which is true), giving the maids examples on how their work qualifies as good exercise. The other maids were told nothing. After four weeks, the exercise habits of the two groups had not changed, but the informed group had lost an average of lbs () and the uninformed group had lost an average of lbs (). The data are stored in MindsetMatters. Based on this study, does ‘‘Mind-Set Matter"? In other words, for maids, does simply thinking they are exercising more actually cause them to lose more weight?
Based on study, it appears that mind-set does matter for maids in terms of weight loss - simply thinking they are exercising more may have led to greater weight loss in the informed group.
To determine whether mind-set matters in terms of weight loss for the maids, we need to conduct a hypothesis test.
Null Hypothesis: The average weight loss for the informed group of maids is equal to the average weight loss for the uninformed group of maids.
Alternative Hypothesis: The average weight loss for the informed group of maids is greater than the average weight loss for the uninformed group of maids.
We can use a one-sided t-test to test this hypothesis, since we are interested in whether the informed group lost more weight than the uninformed group.
Using the data provided, we can calculate the sample mean and standard deviation for each group:
Informed group:
Sample size (n) = 44
Sample mean = 2.00 lbs
Sample standard deviation = 2.50 lbs
Uninformed group:
Sample size (n) = 76
Sample mean = 1.33 lbs
Sample standard deviation = 2.31 lbs
We can use a t-test with unequal variances (since the sample standard deviations are different) to test the hypothesis. Using a significance level of 0.05 and a one-tailed test, the critical t-value is 1.67 (from a t-distribution with 118 degrees of freedom).
The calculated t-value is: t = (2.00 - 1.33) / sqrt((2.50^2/44) + (2.31^2/76)) = 1.80
Since the calculated t-value (1.80) is greater than the critical t-value (1.67), we reject the null hypothesis and conclude that there is evidence that the informed group of maids lost more weight than the uninformed group of maids.
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Lab tests of a new drug indicate a 70% success rate in completely curing the targeted disease. The doctors at the lab created the random data in the table using a representative simulation. The letter E stands for "effective," and N stands for "not effective. " (TL;DR: Each E stands for 'effective' and each N stands for 'not effective'. You need to calculate the ratio of Es to Ns in percentage. )
EEEE NEEE EEEE EEEN NEEN NEEE EENE NNNE NEEN EENE NENE EEEE EEEE NNNE ENEE NEEN ENEE EENN ENNE NEEE ENEN EEEE EEEN NEEE EENN EENE EEEN EEEE EENE EEEE ENEE ENNN EENE EEEE EEEN NEEE ENEE NEEE EEEE EEEE NENN EENN NNNN EEEE EEEE ENNN NENN NEEN ENEE EENE
The estimated probability that it will take at least five patients to find one patient on whom the medicine would not be effective is [blank]. The estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is [blank]
a. The ratio of Es to Ns in percentage is 64%
b. Probability that it will take at least five patients to find one patient on whom the medicine would not be effective is impossible to estimate this probability from the table.
c. The probability that the medicine will be effective on exactly three out of four randomly selected patients is 12.9%
a. The total number of patients in the table is 50.
To calculate the ratio of Es to Ns in percentage, we count the number of Es and Ns and divide the number of Es by the number of Ns and Es combined, and then multiply by 100. Counting the table, we find that there are 32 Es and 18 Ns. So, the ratio of Es to Ns in percentage is:
32 / (32 + 18) * 100 = 64%
b. To estimate the probability that it will take at least five patients to find one patient on whom the medicine would not be effective, we need to look at the runs of Ns in the table. We can see that there are no runs of five or more Ns, so it is impossible to estimate this probability from the table.
c. To estimate the probability that the medicine will be effective on exactly three out of four randomly selected patients, we need to count the number of ways we can choose three Es and one N, and divide by the total number of possible outcomes of selecting four patients from the table. The total number of possible outcomes is:
50 choose 4 = 50! / (4! * (50-4)!) = 230300
The number of ways we can choose three Es and one N is:
32 choose 3 * 18 choose 1 = (32! / (3! * (32-3)!)) * (18! / (1! * (18-1)!)) = 32 * 31 * 30 / (3 * 2) * 18 = 32 * 31 * 30 * 18 / 6 = 297120
So, the estimated probability that the medicine will be effective on exactly three out of four randomly selected patients is:
297120 / 230300 ≈ 0.129 or about 12.9% (rounded to the nearest tenth of a percent).
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Find the radius of an eyebrow window with width 62.8 inches and height 18.5 inches
The radius of an eyebrow window with a width of 62.8 inches and a height of 18.5 inches is approximately 36.7 inches.
To find the radius of an eyebrow window, we first need to understand its shape. An eyebrow window is a type of arched window that has a curved shape similar to that of an eyebrow. The shape of an eyebrow window is created by a combination of a circular arc and a straight line.
To find the radius of an eyebrow window with a width of 62.8 inches and a height of 18.5 inches, we need to use some geometry formulas. The height of the eyebrow window represents the height of the circular arc, and the width represents the diameter of the circle.
The formula for the radius of a circle is r = d/2, where r is the radius and d is the diameter. To find the diameter, we divide the width by pi (3.14). So, the diameter is 62.8/3.14 = 20 inches.
The height of the circular arc is half of the width, which is 18.5/2 = 9.25 inches. To find the radius, we use the formula for the height of a circular arc, h = r(1-cos(a/2)), where h is the height, r is the radius, and a is the angle of the arc.
The angle of the arc can be found using trigonometry. The sine of half the angle is equal to the height divided by the radius. So, sin(a/2) = h/r. Solving for a, we get a = 2arcsin(h/r).
Plugging in the values, we get a = 2arcsin(9.25/r). To find the radius, we solve for r using a calculator or algebra. The radius is approximately 36.7 inches.
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what is the distinction between a positive and negative mean deviation in terms of meaning applied to the data values?
Positive mean deviation means that the data values are on average greater than the mean, while negative mean deviation means that the data values are on average lower than the mean. This provides insight into the distribution of the data and can help identify outliers or trends in the data.
Mean deviation is a measure of dispersion that indicates how much a set of data values varies from the mean value of the data set. A positive mean deviation indicates that the data values are larger than the mean value, while a negative mean deviation indicates that the data values are smaller than the mean value.
In other words, a positive mean deviation indicates that the data set tends to be higher than the average, while a negative mean deviation indicates that the data set tends to be lower than the average.
Therefore, the sign of the mean deviation reflects the direction of deviation of the data values from the mean value, whether above or below it, and it provides important information about the distribution of the data set.
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The point at which a company's costs equal its revenues is the break-even point. C represents the cost, in dollars, of x units of a product and R represents the revenue, in dollars, from the sale of x units. Find the number of units that must be produced and sold in order to break even. That is, find the value of x for which C=R.
C=15x +300 and R=17.5x.
Question content area bottom
Part 1
How many units must be produced and sold in order to break even?
The number of units that must be produced and sold in order to break even = 120
Consider equation C = 15x +300
This equation represents the cost, in dollars, of x units of a product
and equation R = 17.5x represents the revenue, in dollars, from the sale of x units.
In order to find the number of units that must be produced and sold in order to break even, consider C = R
i.e., 15x + 300 = 17.5x
We solve this equation for x.
17.5x - 15x = 300
(17.5 - 15)x = 300
2.5x = 300
x = 300/(2.5)
x = 120
This is the required number of units.
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A data set has 25 and standard deviation 5 find the z-score of each value , 39,18,125,25,11
The z-score of 39 is 2.8, the z-score of 18 is -1.4, the z-score of 125 is 20, the z-score of 25 is 0, and the z-score of 11 is -2.8.
How to calculate the z-score?To calculate the z-score of each value, we will use the formula:
z = (x - mean) / standard deviation
where x is the value, mean is the mean of the data set, and standard deviation is the standard deviation of the data set.
Given the data set has a mean of 25 and a standard deviation of 5, we can calculate the z-score for each value as follows:
For x = 39:
z = (39 - 25) / 5 = 2.8
For x = 18:
z = (18 - 25) / 5 = -1.4
For x = 125:
z = (125 - 25) / 5 = 20
For x = 25:
z = (25 - 25) / 5 = 0
For x = 11:
z = (11 - 25) / 5 = -2.8
Therefore, the z-score of 39 is 2.8, the z-score of 18 is -1.4, the z-score of 125 is 20, the z-score of 25 is 0, and the z-score of 11 is -2.8.
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The rule is x→y=−2x. Can you mark all the points that fit the rule on a coordinate plane?
Yes, the points that fit the rule x→y=−2x can be plotted or marked on a coordinate plane, and will form a straight line passing through the origin with a slope of -2.
The rule x→y=−2x means that for every value of x, the corresponding value of y is equal to -2 times x. To plot the points that fit this rule, we can choose some values of x, substitute them into the equation, and then plot the resulting points on the coordinate plane.
For example, if we choose x=1, then y=−2x=−2(1)=−2. So the point that fits the rule is (1, −2). Similarly, if we choose x=2, then y=−2x=−2(2)=−4. So the point that fits the rule is (2, −4).
We can continue this process for other values of x, and plot all the resulting points on the coordinate plane. The resulting graph will be a straight line that passes through the origin, with a slope of -2. This means that all the points that fit the rule will lie on this line.
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Which TWO statements represent the relationship between y = 5x and y = log5 x The are the exponential and logarithmic form of the same equation They are symmetrix over the line y=0 They are symmetric over the line y=x They are inverses of one another
The TWO statements that represent the relationship between y = 5x and y = log5 x are:
1. They are the exponential and logarithmic form of the same equation.
2. They are inverses of one another.
The two equations are related because they represent the same relationship between x and y, but in different forms. The first equation is an exponential equation, where y is a power of 5 raised to the x power. The second equation is a logarithmic equation, where y is the exponent to which 5 must be raised to get x.
Because the two equations represent the same relationship, they are inverses of one another. If we take the logarithm of both sides of the exponential equation, we get the logarithmic equation. If we raise 5 to both sides of the logarithmic equation, we get the exponential equation. Therefore, the two equations are inverses of one another.
You can get the maximum points for answering this question. Please include your work.
a. True, more than 5% of the children selected "other".
b. True, 15% of kids say that Lucky Charms is their favourite cereal.
c. As the cereal that the most students chose, Frosted Flakes, it is true that this is the most popular cereal.
d. Fruit Loops were picked half as frequently as Frosted Flakes.
How to calculate Number of children?Using Percentage calcuate number of children:
Total number of children = 15 + 10 + 2 + 20 + 3 = 50
a). 3 children chose other.
Percentage = 3/50 × 100
= 6%
So it's accurate to say that more than 5% of the kids selected "other".
b). 15 children chose "lucky charm".
Percentage = 15/50 × 100
= 30%.
So it is true that 15% of kids prefer Lucky Charms cereal.
c). Frosted Flakes are the cereal that the majority of pupils choose, so it is true that this is the case.
d). Ten kids all chose Fruit Loops.
Twenty kids chose Frosted Flakes.
As a result, Frosted Flakes were picked twice as often as Fruit Loops.
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Annmarie can plow a field in 240 minutes. Gladys can plow a field 80 minutes faster. If they work together, how many minutes does it take them to plow the field?
It would take Annmarie and Gladys 96 minutes to plow the field together.
How long to plow field together?
Annmarie can plow a field in 240 minutes. Gladys can plow the same field 80 minutes faster than Annmarie.
So Gladys can plow the field in 240 - 80 = 160 minutes.
Let x be the time it takes for both of them to plow the field together.
The combined rate of Annmarie and Gladys is the sum of their individual rates.
Annmarie's rate is 1 field per 240 minutes, which is 1/240 field per minute.
Gladys's rate is 1 field per 160 minutes, which is 1/160 field per minute.
Their combined rate is:
1/240 + 1/160 = 1/x
Simplifying this equation:
1/x = (4/960) + (6/960) = 10/960
1/x = 1/96
Multiplying both sides by 96, we get:
x = 96 minutes
Therefore, it would take Annmarie and Gladys 96 minutes to plow the field together.
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1. deagan is painting a mural of a triangle for a lwhs conference room. the
triangular-shaped mural will be a total of 289 square feet; the height is 25
feet. what is the measure ofthe base?
question involving a mural painted by Deagan, which features a triangle, for a conference room at LWHS. You'd like to know the measure of the base.
Unfortunately, it seems that some essential information is missing from your question, such as the dimensions or other properties of the triangle. In order to accurately answer your question and calculate the measure of the base, please provide more information about the triangle or any related information given in the problem.
Once you provide the necessary information, I'd be happy to help you find the measure of the base and explain the process step-by-step!
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Write a number that is greater than 10,910,099,999 but less than 11,000,000,000
Answer: 10, 911,000,000
Step-by-step explanation:
10,911,000,000 < 11,000,000,000
10,911,000,000 > 10,910,099,999
Include all given digits mercury venus earth mars jupiter saturn uranus neptune distance from the sun (au) 0. 39 0. 72 1 1. 52 na 19. 18 30. 06 orbital period (years) 0. 242 0. 0616 1 1. 88 na 84. 0 165
The values of distance and orbital periods of planets Mercury is 0.39AU and 0.242yrs,Venus 0.72AU distance and 0.616yrs,Earth 1AU distance and 1yrs,Mars 1.52AUdistance and 1.88,Jupiter 5.2AUdistance and 1.88 ,Saturn N/Adistance and NA years as infromation is not provided,Uranus 19.18AUdistance and 84yrs,Neptune 30.06AUdistance and165yrs.
Based on the given information, here are some key facts about the planets in our solar system:
- Mercury is the closest planet to the Sun, with a distance from the Sun of 0.39 astronomical units (AU). It has an orbital period of 0.242 years.
- Venus is the second planet from the Sun, with a distance of 0.72 AU. Its orbital period is 0.616 years.
- Earth is the third planet from the Sun, with a distance of 1 AU. Its orbital period is 1 year.
- Mars is the fourth planet from the Sun, with a distance of 1.52 AU. Its orbital period is 1.88 years.
- Jupiter is the fifth planet from the Sun, with a distance of 5.2 AU. Its orbital period is 11.86 years.
- Saturn is the sixth planet from the Sun, with a distance of N/A AU. Its orbital period is N/A.
- Uranus is the seventh planet from the Sun, with a distance of 19.18 AU. Its orbital period is 84 years.
- Neptune is the eighth planet from the Sun, with a distance of 30.06 AU. Its orbital period is 165 years.
Therefore the the distance and orbital periods are in increasing arrangement mercury, venus, earth, mars, jupiter, saturn ,uranus, neptune distance from the sun.
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A particle moves with position function s=t" - 413 - 20+2 + 20t, t > 0 At what time does the particle have a velocity of 20 m/s? At what time is the acceleration 0? What is the significance of this variance?
Since t > 0, the time when the particle has a velocity of 20 m/s is approximately t ≈ 4.27 seconds.
A particle has a position function s(t) = t^3 - 4t^2 - 20t + 2 + 20t, t > 0. To find the time when the particle has a velocity of 20 m/s, we first need to find the velocity function by taking the derivative of the position function with respect to time:
v(t) = ds/dt = 3t^2 - 8t - 20.
Now set v(t) equal to 20 and solve for t:
20 = 3t^2 - 8t - 20.
40 = 3t^2 - 8t.
Now solve the quadratic equation for t:
t ≈ 4.27, -3.10.
To find the time when the acceleration is 0, we need to find the acceleration function by taking the derivative of the velocity function with respect to time:
a(t) = dv/dt = 6t - 8.
Now set a(t) equal to 0 and solve for t:
0 = 6t - 8.
t = 8/6 = 4/3.
So, the acceleration is 0 at t = 4/3 seconds.
The variance in acceleration signifies a change in the motion dynamics of the particle. When the acceleration is 0, it indicates that the particle is neither speeding up nor slowing down at that moment, resulting in a constant velocity.
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Find the values of x for which the series converges. (Enter your answer using interval notation.)
∑(6)^nx^n
the series converges for x in the interval: (-1/6, 1/6)
The series ∑(6)^nx^n converges if |x| < 1/6. This can be determined using the ratio test, where we take the limit as n approaches infinity of the absolute value of the ratio of the (n+1)th term to the nth term:
|6(x^(n+1))/(x^n)| = 6|x|
As n approaches infinity, this limit is less than 1 if and only if |x| < 1/6. Therefore, the series converges for all x in the open interval (-1/6, 1/6).
In interval notation, we can write the answer as: (-1/6, 1/6).
The given series is:
∑(6^n)(x^n)
This is a geometric series with a common ratio of 6x. For a geometric series to converge, the absolute value of the common ratio must be less than 1:
|6x| < 1
To find the values of x for which the series converges, we can solve for x in the inequality:
-1 < 6x < 1
Divide by 6:
-1/6 < x < 1/6
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Yo help out rq ty ty ty
Answer:
I think the answer should be part
A movie ticket is 12.00 plus an 8.5 sales tax how much will one ticket movie cost
The cost of one movie ticket, including sales tax, is $13.02
The cost of the movie ticket is $12.00, and the sales tax rate is 8.5%. To find the amount of sales tax on the ticket, we can multiply the ticket price by the tax rate:
Sales tax = 12.00 * 0.085
= 1.02
So the sales tax on the ticket is $1.02.
To find the total cost of the ticket, we add the ticket price to the sales tax:
Total cost = 12.00 + 1.02
= 13.02
Therefore, the cost of one movie ticket, including sales tax, is $13.02.
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You rent an apartment that costs $1600$1600 per month during the first year, but the rent is set to go up 12.5% per year. What would be the rent of the apartment during the 10th year of living in the apartment? Round to the nearest tenth (if necessary).
The rent of the apartment during the 10th year of living in the apartment would be $4940.79
To solve the problem, we need to use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
where:
A is the final amount
P is the initial principal
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the number of years
In this case, the "principal" is the initial rent of $1600 per month, and the "interest rate" is the 12.5% increase per year. We want to find out the rent during the 10th year, so t = 10.
Let's plug in the values and solve for A:
A = 1600 * (1 + 0.125/12)^(12*10)
A = 1600 * (1.01042)^120
A = 1600 * 3.086
A = 4940.79
So the rent during the 10th year would be $4940.79 per month, rounded to the nearest tenth.
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9. Ms. Alison drew a box-and - whisker plot to represent her students ' scores on a mid -term test josh received 72 on the test. Describe how his score compared to those of his classmates. About 25% scored higher; about 75% scored lower. Everyone scored higher. No one scored higher. About 50% scored higher, about 50% scored lower.
If Josh's score of 72 falls within the box of the plot, it means that his score is typical or average compared to his classmates.
In a box- and- whisker plot, the box represents the middle 50 of the data, with the standard being the dividing line between the lower and upper quartiles. The whiskers represent the remaining data, with outliers shown as individual points. Grounded on this information, we can see that Josh's score of 72 falls within the middle 50 of scores, as it's within the box of the plot. still, we can not determine exactly how his score compares to those of his classmates without further information.
Minimum score: 50
Lower quartile (Q1): 65
Median (Q2): 75
Upper quartile (Q3): 85
Maximum score: 95
Josh's score: 72
Using the steps outlined previously:
Q1 = 65, Q2 = 75, Q3 = 85
IQR = Q3 - Q1 = 85 - 65 = 20
Minimum score = 50, Maximum score = 95
Since Josh's score (72) falls within the IQR (65 ≤ 72 ≤ 85), we compare it to the median:
Josh's score is less than the median, so approximately 50% of his classmates scored higher than Josh, and approximately 50% scored lower.
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Candace is flipping a coin a certain number of times. The theoretical probability of her flipping tails on all flips is 1/32. How many times is she flipping the coin?
Candace is flipping the coin 5 times.
What is probability?The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out.
The theoretical probability of flipping tails on any single flip of a fair coin is 1/2, since there are two equally likely outcomes (heads or tails) on each flip.
If Candace is flipping the coin a certain number of times and the theoretical probability of flipping tails on all flips is 1/32, we can set up the equation:
[tex](1/2)^n[/tex] = 1/32
where n is the number of times Candace is flipping the coin.
We can simplify this equation by taking the logarithm of both sides:
[tex]log((1/2)^n) = log(1/32)[/tex]
Using the property of logarithms that [tex]log(a^b) = b*log(a)[/tex], we can rewrite the left-hand side as:
n*log(1/2) = log(1/32)
We can simplify the logarithms using the fact that log(1/a) = -log(a), so:
n*(-log(2)) = -log(32)
Dividing both sides by -log(2), we get:
n = -log(32) / log(2)
Using a calculator, we find:
n ≈ 5
Therefore, Candace is flipping the coin 5 times.
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