(a) Solving initial value problem, P(t) = (1/k) [(kPo + M)e^(kt) - M]
(b)To keep P(t) constant and equal to Po, k must be negative and M must be positive.
(a) To solve the initial value problem:
dP/dt = kP + M, P(0) = Po
We can rewrite the differential equation as:
dP/(kP + M) = dt
Integrating both sides, we get:
(1/k) ln|kP + M| = t + C
where C is a constant of integration. Solving for P, we get:
P(t) = (1/k) (e^(k(t+C)) - M/k)
To find the value of C, we use the initial condition P(0) = Po:
Po = (1/k) (e^(kC) - M/k)
Solving for C, we get:
C = (1/k) ln(kPo + M) - (1/k) ln|kPo|
Substituting this back into the expression for P(t), we get:
P(t) = (1/k) [(kPo + M)e^(kt) - M]
(b) To determine the conditions under which P(t) remains constant and equal to Po, we set P(t) = Po and solve for k and M:
Po = (1/k) [(kPo + M)e^(kt) - M]
Simplifying and rearranging, we get:
(k - 1)e^(kt) = M/Po
If k = 1, then we get 0 = M/Po, which is impossible unless M = 0 (i.e., there is no migration). Therefore, we assume k ≠ 1.
Taking the natural logarithm of both sides, we get:
kt + ln(k - 1) = ln(M/Po)
Solving for k, we get:
k = [ln(M/Po) - ln(k - 1)]/t
To keep P(t) constant and equal to Po, k must be negative (i.e., P(t) is decreasing) and M must be positive (i.e., there is net migration into the population). Physically, this makes sense because if the migration rate is positive, then more individuals are entering the population than leaving, which will tend to increase the population size. Conversely, if the growth rate k is negative, then the population is decreasing in the absence of migration, so the positive migration rate can counteract this decrease and maintain a constant population size.
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find the conditional expectation of alpha x poisson and gamma distribution law of iterated expectation
The conditional expectation of αX given Y=y is (αλy / β + αλ)^α * e^(-(β+αλ)/βy) and the Law of Iterated Expectation gives E[αX] = (αλ / β + αλ)^α * (β / (β+αλ))^α * (Γ(α) / β).
Let X be a Poisson random variable with parameter λ and Y be a Gamma random variable with parameters α and β. We want to find the conditional expectation of αX given Y=y and then apply the Law of Iterated Expectation to find E[αX].
The conditional probability density function of αX given Y=y is:
fX|Y(x|y) = P(X=x|Y=y) = P(X=x,Y=y) / P(Y=y)
Since X and Y are independent, we have:
P(X=x,Y=y) = P(X=x)P(Y=y)
Therefore, the conditional probability density function of αX given Y=y is:
fX|Y(x|y) = (λ^x/x!) * (β^α / Γ(α)) * y^(α-1) * e^(-βy) / (λ^y * e^(-λ) * β^α / Γ(α))
fX|Y(x|y) = (λ^x / x!) * (y^α * e^(-βy)) / (Γ(α) * λ^y * β^α)
Now we can calculate the conditional expectation of αX given Y=y:
E[αX|Y=y] = ∑ x=0^∞ αx * fX|Y(x|y)
E[αX|Y=y] = ∑ x=0^∞ αx * (λ^x / x!) * (y^α * e^(-βy)) / (Γ(α) * λ^y * β^α)
E[αX|Y=y] = (αλy / β + αλ)^α * e^(-(β+αλ)/βy)
Now we can apply the Law of Iterated Expectation to find E[αX]:
E[αX] = E[E[αX|Y]]
E[αX] = E[(αλY / β + αλ)^α * e^(-(β+αλ)/βY)]
Since Y is a continuous random variable, we need to integrate over all possible values of Y:
E[αX] = ∫ 0^∞ (αλy / β + αλ)^α * e^(-(β+αλ)/βy) * (β^α / Γ(α)) * y^(α-1) * e^(-βy) dy
E[αX] = (αλ / β + αλ)^α * (β / (β+αλ))^α * (Γ(α) / β)
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The ages of people visiting a senior center one afternoon are recorded in the line plot.
A line plot titled Ages At Senior Center. The horizontal line is numbered in units of 5 from 60 to 115. There is one dot above 80 and 100. There are two dots above 70 and 85. There are three dots above 75.
Does the data contain an outlier? If so, explain its meaning in this situation.
No, there is no outlier. This means that the people were all the same age.
No, there is no outlier. This means that the people are all around the mean age.
Yes, there is an outlier at 100. This means that one person's age was 100, which is 15 years older than the next closest age.
Yes, there is an outlier of 100. This means that the average person at the center is 100 years old.
Hurrrry up
No, there is no outlier. this means that the people are all the same age
No, there isn't an outlier. This indicates that everyone is roughly the same age.
What is an Outlier?
An outlier in a data graph or dataset you're dealing with is a data point that is disproportionately high or low compared to the closest data point and the rest of the nearby coexisting values.
Extreme values that significantly deviate from the dataset for graph's normal distribution are known as outliers.
How to Spot the Outlier?
Data points in a dataset must be fewer than Q1 - 1.5xIQR in order to qualify as low outliers.
As a result, a data point cannot be regarded as a low outlier unless it falls below the first quartile by more than 1.5 times the interquartile range.
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calculating area and circumference or perimeter of a 2d shape. use your measurements to calculate the area and circumference of the circle and to calculate the area and perimeter of the rectangle.
The area and perimeter of 2D shape of Rectangle is 6.8448cm and 11.04cm repectively. The area and perimeter of 2D shape of circle is 5.0761cm and 8.0028cm respectively.
2D shape of Rectangle with dimensions of Length is3.72 cm and Width is 1.84 cm. we can find the area of rectangle with formula Area = length x width and the formula of perimeter is Perimeter = 2(length + width).
Area = length x width = 3.72 cm x 1.84 cm = 6.8448 square cm (rounded to four decimal places)
Perimeter = 2(length + width) = 2(3.72 cm + 1.84 cm) = 11.04 cm
2D shape of Circle with dimension of diameter of 2.54 cm. we can find the area with formula Area = πr^2 and circumference with formula Circumference = 2πr
Radius = diameter / 2 = 2.54 cm / 2 = 1.27 cm
Area = πr^2 = π(1.27 cm)^2 = 5.0761 square cm (rounded to four decimal places)
Circumference = 2πr = 2π(1.27 cm) = 8.0028 cm (rounded to four decimal places)
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____The given question is incomplete, the complete question is given below:
Calculating area and circumference or perimeter of a 2D shape. Use your measurements to calculate the area and circumference of the circle and to calculate the area and perimeter of the rectangle. Rectangle Length: 3.72 cm Width: 1.84 cm Circle : 2.54 cm Diameter of circle
The image of triangle ABC after a 180° rotation around
the origin is:
A'(-1, 2)
B'(-4, 2)
C'
Answer:If A is at point (x,y), then A' would be at point (-x,-y). Same goes for points B and C.
Step-by-step explanation:
a distribution table for the scores on an exam is shown below. the second row says that 10% of the students scored between 60 and 70. fill in the blanks in the height column. do not include units.
The median for the distribution table is falls within the range of 60-70 points.
Understanding the concept of median is crucial in analyzing data and making statistical inferences.
From the given distribution table, we can see that the percentage of students scoring between 0-60 points is 15%, between 60-70 points is 10%, between 70-80 points is 25%, between 80-90 points is 30%, and between 90-100 points is 20%. To calculate the cumulative percentage, we can add up the percentages from left to right.
For instance, the cumulative percentage of students scoring between 0-70 points is
=> 15% + 10% = 25%.
Similarly, the cumulative percentage of students scoring between 0-80 points is
=> 15% + 10% + 25% = 50%.
We can repeat this process to find the cumulative percentage for each score range.
Once we have the cumulative percentages, we can find the median score. In this case, since the total percentage is 100%, the median score would be the point at which the cumulative percentage reaches 50%. We can use the height column to calculate this value.
Starting from the lowest score range, we can add the heights until the cumulative percentage exceeds 50%. The point where this happens is the median score.
Moving on to the next score range, the cumulative percentage for scores between 0-70 points is 25%, which is greater than 50%. Therefore, the median score falls within the range of 60-70 points.
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Complete Question:
A distribution table for the scores on an exam is shown below. The second row says that 10% of the students scored between 60 and 70. Fill in the blanks in the height column. Do not include units.
Points (Width) % 0-60 60-70 70-80 80-90 90-100
(Area) Height=Area/Width (% per point) 15 10 25 30 20
What is the median score?
You have $4,500 to invest. Which plan would generate the most interest after three years?
A. 5.0% compounded semi-annually
B. 4.9% compounded quarterly
C. 4.8% compounded monthly
D. 5.1% compounded yearly
The plan which generate the most interest after three years is 5.0% compounded semi-annually, the correct option is A
How to calculate compound interest's amount?If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:
[tex]CI = P\left(1 +\dfrac{R}{100}\right)^T - P[/tex]
The final amount becomes:
[tex]A = CI + P\\A = P\left(1 +\dfrac{R}{100}\right)^T[/tex]
Given that;
The amount of investment= $4,500
Now,
The amount with rate of 5.0% compounded semi-annually;
The final balance is ₹5,218.62.
The total compound interest is ₹718.62.
The amount with rate of 4.9% compounded quarterly;
The final balance is ₹5,207.94.
The total compound interest is ₹707.94.
The amount with rate of 4.8% compounded monthly;
The final balance is ₹5,195.49.
The total compound interest is ₹695.49.
The amount with rate of 5.1% compounded yearly;
The final balance is ₹5,209.31.
The total compound interest is ₹709.31.
Therefore, maximum compound interest will be of 5% semi annually.
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what is accounting and how to maintain our business accounting?
Answer:
accounting is a systematic and detailed recording of all the financial transactions that further help owners, investors, suppliers, etc. in making the right business decision.
Step-by-step explanation:
Ravi collected 3 parcels, A, B and C. Parcel A is the heaviest and Parcel B is the lightest. The mass of Parcel B is 3/8kg. The difference in the mass between Parcel A and Parcel C is 1/5kg. Find the total mass of the 3 parcels.
Answer:
2 5/8 kg
Step-by-step explanation:
To find the total mass of the 3 parcels, we need to determine the mass of Parcel A and Parcel C.Since Parcel B is the lightest, with a mass of 3/8 kg, and the difference in mass between Parcel A and Parcel C is 1/5 kg, we can say that Parcel A weighs 3/8 + 1/5 = 4/8 = 1/2 kg more than Parcel C.Let's call the mass of Parcel C "x". Then, Parcel A weighs x + 1/2 kg.The total mass of the 3 parcels can be found by adding the masses of all 3 parcels:x + x + 1/2 + 3/8 = 3x + 9/83x = 3 - 9/83x = 27/8 - 9/83x = 18/8x = 6/8 = 3/4 kgSo, the mass of Parcel C is 3/4 kg, the mass of Parcel A is 3/4 + 1/2 = 1 1/4 kg, and the total mass of the 3 parcels is 3/4 + 1 1/4 + 3/8 = 2 5/8 kg.In conclusion, the total mass of the 3 parcels is 2 5/8 kg.
sample of size n will be selected from population with population proportion p. Which of the following must be true for the sampling distribution of the sample proportion to be approximately normal? a. Both np and n(1 P) are at least 10.b. n is greater than 30 c. p is greater than 0.5. d. The mean is equal to np e. the variance is equal to np(1-p)
True sampling distribution sample which is proportion to be approximately normal is "Both np and n(1 P) are at least 10".
For the sampling distribution of the sample proportion to be approximately normal, the sample size must be sufficiently large, and the sample proportion must be neither too small nor too large.
Specifically, the sample size multiplied by the sample proportion (np) and the sample size multiplied by one minus the sample proportion (n(1-P)) must both be at least 10. This is known as the "success-failure" condition.
Option b is not entirely accurate, as a sample size greater than 30 is a rule of thumb for the Central Limit Theorem to apply, but it is not a strict requirement for normality.
Option c is incorrect as a sample proportion greater than 0.5 means the distribution is skewed towards one end and not normal.
Option d and e are the mean and variance of the binomial distribution and are not directly related to normality.
The correct answer is option a. Both np and n(1-P) are at least 10.
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Suppose you have a bag with 10 black and 10 red balls, with the balls of each color numbered 1 to 10 . Suppose you pick two balls (without replacement) uniformly at random from the bag. (i) Show that the probability that you pick a ball of each color is 10/19. (ii) Show that the probability that you pick a ball of each color, with the number on the red ball being one less than the number on the black ball, is 9/190.
The probability of picking one ball of each color is 10/19. The probability of picking a red ball with a number one less than the number on the black ball is 9/190.
(I) To figure the probability of picking one repudiate and one red ball, we can separate it into two cases: first, picking a debase and afterward a red ball, and second, picking a red ball and afterward a renounce.
The probability of picking a torpedo on the principal draw is 10/20 (since there are 10 renounces and 20 all out balls), and the probability of then picking a red ball on the subsequent draw is 10/19 (since there are currently 9 red balls avoided with regards to a sum of 19 balls). So the probability of picking a repudiate first and afterward a red ball is (10/20) * (10/19) = 1/19.
Essentially, the probability of picking a red ball first and afterward a torpedo is (10/20) * (10/19) = 1/19.
Hence, the probability of picking one chunk of each tone is the amount of these two probabilities: 1/19 + 1/19 = 2/19.
Notwithstanding, we want to isolate by 2 to represent the way that we might have picked the balls in the contrary request nevertheless have one chunk of each tone. So the last probability is (2/19)/2 = 10/19.
Consequently, the probability of picking one wad of each tone is 10/19.
(ii) To figure the probability of picking a red ball with a main not exactly the number on the debase, we can initially fix the renounce that we pick. There are 10 decisions for the renounce. The main red ball with a main not exactly the torpedo is the red ball with the following most minimal number, so there is just a single decision for the red ball.
In this manner, the probability of picking a debase and afterward a red ball with the number on the red ball one not exactly the number on the repudiate is (10/20) * (1/19) = 1/190.
We really want to duplicate this by 9, since there are 9 sets of contiguous numbers (1 and 2, 2 and 3, ..., 9 and 10) for which the condition is fulfilled. So the last likelihood is 9/190.
Thusly, the probability of picking one chunk of each tone, with the number on the red ball being one not exactly the number on the debase, is 9/190.
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The pH level, P, of a liquid can be determined from the hydronium ion (H3O+) concentration, c, using the equation P = –log(c). If the pH level of orange juice is 3.5, what is the hydronium ion concentration? (2 points) 1.25 x 105 3.16 x 103 5.44 x 10–1 3.16 x 10–4
The hydronium ion concentration in orange juice with pH 3.5 is 3.16 × 10⁻⁴
What is hydronium ion concentration?The hydronium ion is an important factor when dealing with chemical reactions that occur in aqueous solutions. Its concentration relative to hydroxide is a direct measure of the pH of a solution. It can be formed when an acid is present in water or simply in pure water.
Given that, the pH level, P, of a liquid can be determined from the hydronium ion (H3O+) concentration, c, using the equation P = –log(c). we need to determine the hydronium ion concentration in orange juice with pH level of 3.5
Therefore,
P = -log(c)
P = 3.5
Therefore,
3.5 = -log(c)
log(c) = -3.5
(10)⁻³⁵/₁₀ = c
c = 0.000316227766
c = 3.16 × 10⁻⁴
Hence, the hydronium ion concentration in orange juice with pH 3.5 is 3.16 × 10⁻⁴
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which choices are equivalent to the product below? check all that apply. √6•√3
Answer:
Step-by-step explanation:
[tex]\sqrt{6} * \sqrt{3}\\ \sqrt{18}, 18=9*2, \\ \sqrt{9*2}, \\ \sqrt{9*2} = \sqrt{9} * \sqrt{2}, \sqrt{9}=3\\ 3 \sqrt{2}[/tex]
B.
Calculate the pixel size for a fast spin echo sequence with the following parameters: FOV 30cm, TR 600, TE 10, 320 x 320 matrix, 4 NEX, 3 mm slice thickness, 3 ETL.
0.94 mm x 0.94 mm
FOV ÷ Matrix = pixel size
FOV ÷ phase matrix = phase dimension pixel
FOV ÷ frequency matrix = frequency pixel
Convert 30cm to 300 mm before calculating.
300 ÷ 320 = 0.94mm (phase dimension)
300 ÷ 320 = 0.94mm (frequency dimension)
Pixel size for fast spin echo is 0.94mm x 0.94mm. FOV 30cm, TR 600, TE 10, 320x320 matrix, 4NEX, 3mm slice thickness, 3ETL.
To calculate the pixel size, we first need to convert the FOV from 30cm to 300mm. We can then divide the FOV by the matrix size (320 x 320) to get the pixel size. This will give the same value for both the phase dimension and frequency dimension pixels. So the pixel size for the fast spin echo sequence is 0.94mm x 0.94mm.
The other parameters for the sequence are TR 600, TE 10, 4NEX, 3mm slice thickness and 3ETL. These parameters will determine the type of sequence and the overall image quality. With these parameters, the fast spin echo sequence should produce a high quality image with good resolution.
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Please help me with all asap I’ll mark brainly
The number of solution of each of the equations -2x + 4 = 4 - 2x, 5 - 3x = -5 - 3x and 2 + 3x = 2 + 2x are infinite solution, no solution and one solution respectively.
What is the number of solutions of each equation?Given the equations in the question;
a) -2x + 4 = 4 - 2x
b) 5 - 3x = -5 - 3x
c) 2 + 3x = 2 + 2x
To determine the number of solutions of each equation, solve for x.
a)
-2x + 4 = 4 - 2x
Solve for x
-2x + 2x + 4 - 4 = 4 - 4 - 2x + 2x
-2x + 2x = 4 - 4
0 = 0
Hence, the equation has infinite solutions.
b)
5 - 3x = -5 - 3x
Solve for x
5 - 5 - 3x + 3x = -5 - 5 - 3x + 3x
- 3x + 3x = -5 - 5
0 = -10
Hence, the equation has no solution.
c)
2 + 3x = 2 + 2x
Solve for x
2 - 2 + 3x - 2x = 2 - 2 + 2x - 2x
3x - 2x = 2 - 2
x = 0
Hence, the equation has one solution.
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The vertex from of a function is g(x)=(x-3)2+9 how does the graph of g(c) compare to the graph of the function f(x)=x2
The function g(x) is a quadratic function in vertex form. Its vertex is at (3, 9), and it opens upwards because the coefficient of the squared term is positive.
The function f(x) is also a quadratic function, but in standard form. It opens upwards because the coefficient of the squared term is positive.
Since both functions have a minimum value at the vertex, the graphs of g(x) and f(x) will be similar in shape. However, the vertex of f(x) is at (0,0), so it is shifted to the left of g(x). Also, the y-intercept of f(x) is (0,0), while the y-intercept of g(x) is (0,18).
In summary, the graph of g(x) is the graph of f(x) shifted 3 units to the right and 9 units up.
The plant manager of a company that makes pillows claims that only 8 percent of the pillows made have a stitching defect. The quality control director thought that the percent might be different from 8 percent and selected a random sample of pillows to test. The director tested the hypotheses H : p=0.08 versus Hp +0.08 at the significance level of a = 0.05. The p- value of the test was 0.03. Assuming all conditions for inference were met, which of the following is the correct conclusion? The p-value is less than a, and the null hypothesis is rejected. There is convincing evidence to suggest the true proportion of stitching defects is less than 0.08. Subm B The p-value is less than a, and the null hypothesis is rejected. There is convincing evidence to suggest the true proportion of stitching defects is not 0.08. The p-value is less than o, and the null hypothesis is rejected. There is convincing evidence to suggest the true proportion of stitching defects is greater than 0.08 The p-value is less than , and the null hypothesis is not rejected. There is convincing evidence to suggest the true proportion of stitching defects is not 008 The p-value is less than a, and the null hypothesis is not rejected. There is not convincing evidence to suggest the true proportion of stitching defects is not 0.08
The correct statement regarding the test of the hypothesis is given as follows:
B. The p-value is less than the significance level, and the null hypothesis is rejected. There is convincing evidence to suggest the true proportion of stitching defects is not 0.08.
What is the relation between the p-value and the conclusion of the test hypothesis?Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected, meaning that the research study is not statistically significant.If it is less, it is rejected, meaning that the research study is statistically significant.
The parameters for this problem are given as follows:
Hence the null hypothesis is rejected, as 0.03 < 0.05, and the conclusion is that the proportion is different of 0.08, which is the test made for this problem.
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What’s the answer for these questions
The difference in the production levels will be 3x + 8.
The amount that Jackson spent more will be 5.20 - p.
How to calculate the valueAn equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
Based on the information, a company has two manufacturing plants that had levels of 5x + 11 and 2x - 4.
The difference in the production levels will be:
= 5x + 11 - 2x - 3
= 3x + 8
The amount that Jackson spent more will be:
= 7.65 + 5p - 2.45 - 4p
= 5.20 - p.
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Tamara is painting a rectangular picture that is 6 inches wide by 4 3/4 inches long. What is the area of the picture
Now we can find the area:
Area = length x width
Area = (19/4) x 6
Area = 114/4
Area = 28.5
Therefore, the area of the picture is 28.5 square inches.
What does the mathematical concept of "area" mean?The area of a planar figure is the region that its perimeter includes. The quantity of unit squares that completely encircle the surface of a closed figure is its area. Square units like cm2 and m2 are used to measure area.
The area of a rectangle is found by multiplying its length by its width. In this case, the width is 6 inches and the length is 4 3/4 inches. We can convert the length to an improper fraction to make it easier to multiply:
4 3/4 = 19/4
Now we can find the area:
Area = length x width
Area = (19/4) x 6
Area = 114/4
Area = 28.5
Therefore, the area of the picture is 28.5 square inches.
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The area of the rectangular picture painted by Tamara is 28.5 in.²
What is a rectangle?
The internal angles of a rectangle, which has four sides, are all precisely 90 degrees. The two sides come together at a straight angle at each corner or vertex. The rectangle differs from a square because its two opposite sides are of equal length. Rectangles are flat, two-dimensional shapes. The diagonals of the rectangle's symmetrical shape are of equal length. The rectangle will be split into two right-angle triangles by a diagonal.
The region covered by a two-dimensional plane is known as its area. It has a square unit of measurement. As a result, the rectangle's area is the space enclosed by its exterior lines. It is the same as the length times the width calculation.
Given,
The width of the rectangular picture = 6 inches
The length of the rectangular picture = 4 3/4 inches = 19/4 inches
The area of the picture = Area of the rectangle = Length * breadth
= 19/4 * 6 = 57/2 = 28.5 in.²
Therefore the area of the rectangular picture painted by Tamara is
28.5 in.²
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Find the values at the 25th and 75th percentiles for the data set
22 20 3 20 16 10 20 5 7 11 11 8 17 12 4 18 5 16 6 16
The solution is, the value at the 75th percentiles for the data set is 17.
What is percentile?In statistics, a k-th percentile is a score below which a given percentage k of scores in its frequency distribution falls or a score at or below which a given percentage falls.
here, we have,
The 75th percentile of the data is the value which is greater than 75% of the data. Arranging the values first in ascending order:
given that,
3 4 5 5 6 7 8 10 11 11 12 16 16 16 17 18 20 20 20 22
The data has 20 elements, so 75% of the data consists of .75(20) = 15.
The 75th percentile must be the 15th element.
Therefore, 17.
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The probability of guessing right on a 4-option multiple choice item is 1/4 or 0.25. If a quiz has 10 questions. Determine the mean = (exact answer, no rounding) variance = (exact answer, no rounding) standard deviation = und to one decimal place) imal place)
The probability of getting more than 5 questions right in the quiz is
0.00011445.
ProbabilityProbability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are.
the probability of guessing right on a 4-option multiple choice item is= 1/4
= 0.25
A quiz contains 10 questions.
now, the probability of getting 5 right answers as below,
Required Probability = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
so, this is the probability to come right answers,
Required Probability = (1/4)^6 (3/4)^4 + (1/4)^7 (3/4)^3 + (1/4)^8 (3/4)^2 + (1/4)^9 (3/4)^1 + (1/4)^10
Required Probability = 0.000077 + 0.000025 + 0.0000086 + 0.0000029 + 0.00000095
after adding all values we get the required probability,
Required Probability = 0.00011445.
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the complete and correct question is ,
the probability of guessing right on a 4-option multiple choice item is 1/4 or 0.25. a quiz contains 10 questions. find the probability of getting more than 5 right.
Refer to Example 2.7. Suppose that we record the birthday for each of n randomly selected persons.
a) Give an expression for the probability that none share the same birthday.
b) What is the smallest value of n so that the probability is at least .5 that at least two people share a birthday?
The distribution used to obtain the critical value in this situation is the Student's t-distribution.
What is critical value?Critical value is a statistical value used to determine whether a hypothesis test result is statistically significant or not. It is the value that is compared to the test statistic to determine whether the null hypothesis should be rejected or not. The critical value is determined by the level of significance chosen for the study, the sampling distribution of the test statistic, and the degrees of freedom.
The Student's t-distribution is a symmetric probability distribution that is used when the population standard deviation is unknown. It is used in situations where there is a small sample size (less than 30) and the sample is drawn from a normally distributed population. In this case, the owner is interested in developing a 90% confidence interval estimate, so the critical value will be obtained from the Student's t-distribution.
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What is the error of improved Euler's method?
The error of Improved Euler's Method is that it underestimates the true solution of the differential equation, leading to an inaccurate result.
Improved Euler's Method is used to approximate the solution to a differential equation. The method begins by using the initial value of the function, as well as its derivative at that point. The derivative is then multiplied by a step size, h, and added to the initial value to obtain an estimate of the function at the next point. This estimate is used to calculate the derivative at the new point, which is then multiplied by the same step size and added to the initial value to obtain the next estimate. This process is repeated until the desired solution is obtained. The error of Improved Euler's Method is that it underestimates the true solution of the differential equation, leading to an inaccurate result.
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Here's a box plot that summarizes the number of history questions on Ms. Jones's homework
assignments.
–
|||||||||
+H
024 6 8 10 12 14 16 18 20
Number of questions
Find the median of the data.
questions
Answer:
I will tell you the answer
Step-by-step explanation:
Answer:
the median is 11 questions.
Step-by-step explanation:
khan academy :)
Given ab 12 ac 6 prove c is the midpoint
Answer:
yes
Step-by-step explanation:
Given ab 12 ac 6 prove c is the midpoint is true because the midpoint of 12 is 6.
Determine whether the scenario involves independent or dependent events. Then find the probability.
Your sock drawer has two white socks, six brown socks, and four black socks. You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. You leave the house with a white sock on your left foot and a brown sock on your right. P (white, brown WITHOUT replacing)
-Independent; 1/11
-Dependent; 1/12
-Dependent; 1/11
-Independent; 1/12
The second sock picked is dependent on the first. The probability of picking a white sock for the left foot and a brown sock for the right foot without replacing the first sock is 1/12.
To calculate the probability of picking a white sock for the left foot and a brown sock for the right foot without replacing the first sock, we first need to count the total number of possible outcomes. There are 8 socks in the drawer: 2 white, 6 brown, and 4 black. Since we are picking two socks without replacing the first, the total number of possible outcomes is 8C2 = 28.
Next, we need to count the number of favourable outcomes. In this case, there is only one favourable outcome: picking a white sock for the left foot and a brown sock for the right foot.
Therefore, the probability of picking a white sock for the left foot and a brown sock for the right foot without replacing the first sock is 1/28.
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A bag contains 6 black marbles, 14 white marbles, and 5 grey marbles.
You pick one without looking. What is the probability that the marble will be
either white OR black? Answer as a fraction or whole number in lowest
form.
The set of whole numbers is equal to the set of natural numbers.
• A. True
B. False
Answer:
False
Step-by-step explanation:
This statement is false.
The set of whole numbers include the set of Natural numbers "N" = {1, 2, 3, 4, 5, 6, ...}, the set of the negatives of the natural numbers: {-1, -2, -3, -4,...}, and the zero: {0}
We see then that the set of Natural numbers is a subset of the set of whole numbers Z = {... -4,-3,-2,-1, 0,1, 2, 3, 4, 5, ...}
Answer: i think False
Step-by-step explanation: why not pick false…..
Hope this helps^^
Please help, solve this
The value of f( -10 ) in the piecewise function is 150.
What is the value of f( -10 )?A piecewise function is simply a function which has different definitions of values for different intervals.
Given the piecewise function;
t² - 5t; t ≤ -10
f(t) = { t + 19; -10 < t < -2
t³/( t + 9 ); t ≥ -2
To solve for f( -10 ), we check the interval where -10 falls into.
Since -10 is less than or equal to -10, it falls in the interval of t ≤ -10.
Hence;
f(t) = t² - 5t
Replace t with -10 and simplify.
f( -10 ) = ( -10 )² - 5( -10 )
f( -10 ) = 100 + 50
f( -10 ) = 150
Therefore, the value of f( -10 ) is 150.
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Illustrate with a diagram a consumer in equilibrium with indifference curves and a budget constraint. Measure units of X on the horizontal axis and units of Y on the vertical axis. Provide intuitive and mathematical explanations for what must be true in equilibrium.
What is the slope of the budget line if the slope of the budget line equals the slope of the indifference curve when consumer equilibrium is taken into account on an indifference curve/budget line diagram
A client selects a group of items where an indifference curve is perpendicular to the price range line in order to optimize utility. The fee ratio of the two things is the same as the client's marginal charge of substitution (absolutely the cost of the slope of the indifference curve) at the utility-maximizing solution. The marginal charge of substitution is the indifference curve's slope (MRS). The MRS is the price at which a client will often trade one fact for another.
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Listed below are the balances and annual percentage rates for Jimmy's credit cards. If Jimmy makes the same payment each month to pay off his entire credit card debt in the next 12 months, how much will he have paid in interest in the 12 month period?(Hint, find out how much interest Jimmy pays to each card over the 12 months seperately, and then add them together.)
A, B, and C's interest rates are 49.96, 296.32 and 102.96, respectively. Since the total interest is $449.24.
What is meant by APR?The annual percentage rate (APR) on a credit card indicates that the interest you pay over a year is generally equivalent to your balance.
The balances and annual percentage rates for Jimmy's credit cards are shown below.
If Jimmy pays the same amount each month, he will be free of his credit card debt in a year.
We know that the formula
[tex]$P V=\frac{P M T\left[1-\left(1+\frac{r}{12}\right)^{12 n}\right]}{\frac{r}{12}}$[/tex]
Where, PV be present value
PMT be monthly payment
r be interest rate
n be time
For credit card A, we have
[tex]$\begin{aligned} 563 & =\frac{{PMT}\left[1-\left(1+\frac{0.16}{12}\right)^{12}\right]}{\frac{0.16}{12}} \\ \text { PMT } & =51.08\end{aligned}$[/tex]
Total payment will be, 51.08 × 12 = 612.96
The interest charge will be, 612.96 − 563 = 49.96
For credit card B, we have
[tex]$\begin{aligned} & 2525=\frac{{PMT}\left[1-\left(1+\frac{0.21}{12}\right)^{12}\right]}{\frac{0.21}{12}} \\ & \mathrm{PMT}=235.11\end{aligned}$[/tex]
Total payment will be, 235.11 × 12 = 2821.32
The interest charge will be, 2821.32 − 2525 = 296.32
For credit card C, we have
[tex]$\begin{aligned} 972 & =\frac{\text { PMT }\left[1-\left(1+\frac{0.19}{12}\right)^{12}\right]}{\frac{0.19}{12}} \\ \text { PMT } & =89.58\end{aligned}$[/tex]
Total payment will be, 89.58 × 12 = 1074.96
The interest charge will be, 1075.96 − 972 = 102.96
Total interest = 102.96 + 296.32 + 49.96
Total interest = 449.24
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