The expected number of problems to be resolved today is 10, the standard deviation is 1.3693, the probability that 10 problems can be resolved today is 0.2146, the probability that 10 or 11 problems can be resolved today is 0.3246, and the probability that more than 8 problems can be resolved today is 0.816.
To answer these questions, we will use the binomial distribution since we are dealing with a fixed number of independent trials (the 13 cases reported) with only two possible outcomes (resolved or not resolved).
Let's start with the first question:
Expected number of problems resolved today:
E(X) = n * p = 13 * 0.75 = 9.75
So we would expect about 9.75 problems to be resolved today, but since we cannot have a fraction of a problem, we should round this to 10.
Now let's move on to the second question:
Standard deviation:
σ = sqrt(np(1-p)) = sqrt(13 * 0.75 * 0.25) = 1.3693 (rounded to 4 decimal places).
For the third question:
Probability that 10 of the problems can be resolved today:
P(X=10) = (13 choose 10) * (0.75)^10 * (1-0.75)^(13-10) = 0.2146 (rounded to 4 decimal places).
For the fourth question:
Probability that 10 or 11 of the problems can be resolved today:
[tex]P(X=10 or X=11) = P(X=10) + P(X=11) = (13 choose 10) * (0.75)^10 * (1-0.75)^(13-10) + (13 choose 11) * (0.75)^11 * (1-0.75)^(13-11) = 0.3246 (rounded to 4 decimal places).[/tex]
For the fifth question:
Probability that more than 8 of the problems can be resolved today:
P(X>8) = 1 - P(X<=8) = 1 - (P(X=0) + P(X=1) + ... + P(X=8))
[tex]= 1 - ∑(13 choose i) * (0.75)^i * (1-0.75)^(13-i), for i=0 to 8.[/tex]
= 1 - 0.0003 - 0.0033 - 0.0191 - 0.0672 - 0.1562 - 0.2529 - 0.2897 - 0.2072 - 0.0881
= 0.816 (rounded to 4 decimal places).
Therefore, the probability more than 8 of the problems can be resolved today is 0.816 (rounded to 4 decimal places).
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Formes y equation, decide whenever the línea it represents is parallel to p, perpendicular p, or neither of these
Y= -3x + 10
Y-5 = -1/3 (x+2)
Y= 1;3x
-3 + y = 1
Answer: I got you fam
Step-by-step explanation:
Y=-3x+10 is NEITHER
Y-5=-1/3(x+2) is perpendicular to P
Y=1;3x is NEITHER
-3+y=1 is parallel to P
I NEED HELP what is 1/4 x 20 =
21
The solution of the fractions 1 / 4 × 20 / 21 is 5 / 21.
How to solve fractions?A fraction is number with numerator and denominator. Therefore, let's multiply the fractions.
1 / 4 × 20 / 21 = 20 / 84
Hence, let's reduce the fraction by dividing the numerator and denominator by 4.
20 / 84 ÷ 4 / 4
20 / 84 ÷ 4 / 4 = 5 / 21
Therefore, the fraction is 5 / 21.
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PLEASE HELP ITS URGENT I INCLUDED THE PROBLEM IN IMAGE I WROTE IT DOWN!!!
Answer:
The answer would be D. [tex]\frac{5\sqrt{11} }{11}[/tex]
In order to gain more insight on-employee’s preferences, twenty-three (23) employees from the Private Sector were asked about automobile of their preference. Five (5) of them dislike all the three brands. Eight (8) preferred both LEXUS and MERCEDES. Another eight (8) of them preferred both MERCEDES and AMAROK. Four (4) of them preferred all three brands. Four (4) prefer MERCEDES only. The remainder preferred AMAROK only.
i. How many of the twenty-three (23) employees prefer LEXUS only? ii. How many of the twenty-three (23) employees prefer AMAROK only? iii. From the total of one hundred and seventy-five (175) employees from both Public and Private Sector, how employees disliked all the three brands? iv. What is the percentage increase in the number of employees who preferred all three brands? v. Compute the percentage decrease in the proportion of employees that prefer all three brands?
Since we do not have information on a previous survey, we cannot calculate this percentage
i. To find the number of employees who prefer LEXUS only, we need to subtract the number of employees who preferred both LEXUS and MERCEDES, and the number of employees who preferred all three brands, from the total number of employees who prefer LEXUS:
LEXUS only = Total number of LEXUS preference - (Number of employees who prefer both LEXUS and MERCEDES) - (Number of employees who prefer all three brands)
LEXUS only = (8 + 4) - 8 - 4
LEXUS only = 8
Therefore, 8 employees prefer LEXUS only.
ii. To find the number of employees who prefer AMAROK only, we need to subtract the number of employees who preferred both MERCEDES and AMAROK, and the number of employees who preferred all three brands, from the total number of employees who prefer AMAROK:
AMAROK only = Total number of AMAROK preference - (Number of employees who prefer both MERCEDES and AMAROK) - (Number of employees who prefer all three brands)
AMAROK only = (8 + 4) - 4 - 4
AMAROK only = 4
Therefore, 4 employees prefer AMAROK only.
iii. We are given that 5 employees dislike all three brands. Since this information is only from the Private Sector, we cannot determine the number of employees who dislike all three brands in the total of 175 employees from both Public and Private Sectors.
iv. The percentage increase in the number of employees who preferred all three brands is the difference between the number of employees who preferred all three brands in the current survey and the number of employees who preferred all three brands in a previous survey, divided by the number of employees who preferred all three brands in the previous survey, multiplied by 100%. Since we do not have information on a previous survey, we cannot calculate this percentage.
v. The proportion of employees who preferred all three brands in the current survey is 4/23 or approximately 0.174. To compute the percentage decrease in the proportion of employees who preferred all three brands, we need to compare this proportion with the proportion of employees who preferred all three brands in a previous survey. Since we do not have information on a previous survey, we cannot calculate this percentage.
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write an expression for the apparent nth term (an) of the sequence. (assume that n begins with 1.) 2, 9, 28, 65, 126,
Therefore, the apparent nth term of the expression is: aⁿ = 5n² - 3n - 2.
The given sequence is not an arithmetic or geometric sequence. However, we can notice that the sequence of differences between consecutive terms is an arithmetic sequence.
The sequence of differences is: 7, 19, 37, 61,...
To find the nth term of this sequence, we can use the formula for the nth term of an arithmetic sequence:
dn = a1 + (n-1) * d
where dn is the nth term of the sequence of differences, a1 is the first term of the sequence of differences, d is the common difference of the sequence of differences, and n is the index of the term we want to find.
So, we have:
dn = 7 + (n-1) * 12
Simplifying this expression, we get:
dn = 5n - 3
Now, we can use this formula to find the nth term of the original sequence. Let's call the nth term an:
an = an-1 + dn-1
where an-1 is the (n-1)th term of the original sequence and dn-1 is the (n-1)th term of the sequence of differences.
We know that a1 = 2 and d1 = 7, so we can use the above formula to find the next terms:
a2 = a1 + d1 = 2 + 7 = 9
a3 = a2 + d2 = 9 + 19 = 28
a4 = a3 + d3 = 28 + 37 = 65
a5 = a4 + d4 = 65 + 61 = 126
Therefore, the apparent nth term of the sequence is: aⁿ = 5n² - 3n - 2.
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PLS HELP ASAP 100 POINTS
Find the measure of ∠YOZ by answering the questions.
1. Find the measure of ∠WOV. Which angle relationship did you use? (3 points)
2. Now find the measure of ∠YOZ. Which angle relationship did you use?
3. Check your answer by using another strategy to find the measure of ∠YOZ. Describe your strategy, and show that it gives the same measure for ∠YOZ. (4 points)
The measure of ∠WOV is 60°. You would use complementary angles that are adjacent (∠WOV, and ∠XOW)
How to explain the angleThe measure of ∠YOZ is 60°. You would use the vertical angles that are non-adjacent (∠WOV, and ∠YOZ). These two angles are congruent so they would have the same measure. These angles combined also create supplementary angles
Another way to find the measure of ∠YOZ would be to make/write an equation and solve for x. For example, (3x+30)°=60°. x would equal 10 because 10x3=30+30=60°
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I need help with answering the screenshot
The function that is represented by the graph is -|x - 1| + 8.
Option A is the correct answer.
We have,
The graph of the function - |x - 1| + 8 can be obtained by applying a series of transformations to the graph of the absolute value function, y = |x|.
First, the expression x - 1 inside the absolute value brackets shifts the entire graph of y = |x| one unit to the right.
This means that the "V" shape of the absolute value function is centered at x = 1 instead of x = 0.
Next, the negative sign in front of the absolute value reflects the graph of y = |x| across the x-axis.
This means that the "V" shape is now pointing downwards instead of upwards.
Finally, the entire graph is shifted vertically upward by 8 units due to the constant term + 8.
This means that the lowest point of the "V" shape is at y = 8 instead of
y = 0.
Thus,
The function that is represented by the graph is -|x - 1| + 8.
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Concentric circles are coplanar circles that have the same
Concentric circles are coplanar circles that have the same A. center.
What are concentric circles ?Concentric circles, a set of coplanar circles sharing the same center point, derive their name from the Latin word "concentricus," which translates to "having a common center."
Varied radii differentiate each concentric circle. If one circle has a smaller radius than another's, it is considered nested inside or simply, inside. Radius denotes the distance between the center point and edge of the circle perimeter.
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Options for this question include:
A. Center
B. Diameter
C. Circumference
D. Radius
Help me please and thank you so much!!!
The volume of the figure is given as follows:
V = 132 ft³.
How to calculate the volume?The volume of a triangular prism is given as half the multiplication of the dimensions of the triangle, as follows:
V = 0.5 x l x w x h.
The dimensions of the triangle in this problem are given as follows:
3 ft, 8 ft and 11 ft.
Hence the volume of the prism is given as follows:
V = 0.5 x 3 x 8 x 11
V = 132 ft³.
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You must study for your test in one of three periods, t = 0, 1, 2. The instantaneous utility cost of studying at t = 0 is 8, at t = 1 is 10, and at t = 2 is 12. You are a naive quasi-hyperbolic discounter with β = 0.75 and δ = 1.
a) In which period will you study? [1 mark]
b) You like to reward yourself with a chocolate cake when you finish study. Your instantaneous utility from eating this cake is equal to 6. Discuss whether binding the unpleasant task to a pleasant task overcome procrastination in this example? [1 mark]
c) After completing this unit you learn about your present bias and become a sophisticated quasi-hyperbolic discounter. Does being sophisticated change the period in which you study? (Assume that there is no cake.)
Since the utility cost is lowest at t=0, you will conduct your research during period 0 as a quasi-hyperbolic discounter. Procrastination may be beaten if the painful job was linked to an enjoyable task.
a) As a naive quasi-hyperbolic discounter, you must choose the period to study based on your discount factors (β = 0.75, δ = 1) and the utility costs. To determine this, you must compare the present value of the utility costs of studying in each period:
At t = 0: Utility cost = 8 (since you're studying now, no discounting is applied)
At t = 1: Utility cost = 10 x β = 10 x 0.75 = 7.5
At t = 2: Utility cost = 12 x β x δ = 12 x 0.75 x 1 = 9
Since the utility cost is lowest at t=0 (8), you will study during period 0.
b) By binding the unpleasant task (studying) with the pleasant task (eating chocolate cake with utility of 6), it may help overcome procrastination if the combined utility is less than the utility cost of studying in later periods. In this case:
At t = 0: Combined utility cost = 8 - 6 = 2
Since the combined utility cost at t=0 (2) is lower than the utility costs of studying in periods 1 and 2 (7.5 and 9), binding these tasks could help overcome procrastination.
c) As a sophisticated quasi-hyperbolic discounter, you're now aware of your present bias. However, since there is no cake involved, the utility costs remain the same as in part (a):
At t = 0: Utility cost = 8
At t = 1: Utility cost = 7.5
At t = 2: Utility cost = 9
Even though you're now sophisticated, the period in which you study does not change. You will still study during period 0, as it has the lowest utility cost.
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What is 011.4583 as a fraction?
Answer:
11.4583 = 114583 / 10000
Step-by-step explanation:
triangle xyz is shown. what transformation on xyz results in a similar but not congruent to xyz
The transformation that would result in a similar shape to XYZ but one that is not congruent is D. a dilation centered at the origin with a scale factor of x.
Why does a dilation produce non - congruent shapes ?When a triangle undergoes dilation, there is an alteration to its size while still conserving its shape. In scenarios where the scale factor of the triangular dilation happens to exceed 1, it leads to a bigger triangle than the original.
However, if this factor falls below 1, then the resulting triangle will be smaller compared to its original. The similarity between these triangles exists because they harbour identical shapes, but their incongruency emerges from their diverse magnitudes post-dilation.
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Options for this question are:
A. a translation 3 units to the right
B. a reflection across the line y = - 2x + 3
C. a rotation 90° clockwise around the origin
D. a dilation centered at the origin with a scale factor of x.
14. section 7.3; problem 2: interpretation a. we are 90% certain that the difference in percentages of men and women experiencing food cravings fall within in the specified interval. b. we are 90% certain that the percentages of men and women experiencing food cravings both fall within in the specified interval. c. 90% of men and women feel that the difference report experiencing food cravings a percentage of the time, specified within the given interval. d. the specified interval represents 90% of the data for men and women having food cravings.
The correct interpretation is option (a). It states that we are 90% certain that the difference in percentages of men and women experiencing food cravings falls within the specified interval.
Your question is asking for the correct interpretation of a 90% confidence interval for the difference in percentages of men and women experiencing food cravings. Here are the interpretations of each statement:
a. We are 90% certain that the difference in percentages of men and women experiencing food cravings falls within the specified interval.
b. We are 90% certain that the percentages of men and women experiencing food cravings both fall within the specified interval.
c. 90% of men and women feel that the difference report experiencing food cravings a percentage of the time, specified within the given interval.
d. The specified interval represents 90% of the data for men and women having food cravings.
This interpretation accurately reflects the confidence interval for the difference in percentages between the two groups.
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Find the value of x.
The value of x is 116°
Given that a circle, with two congruent chords, FG and DE we need to find the central angle x,
Here we will use the properties of circle,
Since, the chords are equal, so, the measure of the arc intercepted by them will be equal,
arc DE = arc FG = 116°
Also, we know that the central angle is equal to the measure of the arc intercepted by it,
Therefore, x = m arc DE
x = 116°
Hence, the value of x is 116°
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pls answer this anyone
The values of angles in the diagram are ∠DAE = 53⁰, ∠DAE = 48⁰, ∠ACB = 102⁰, ∠ABC = 56⁰.
What is the value of the marked angles?
The value of angles is calculated as follows;
∠DAE = 90 - 37 (complementary angles add up to 90⁰ )
∠DAE = 53⁰
∠DBE = 90 - 42 (complementary angles add up to 90⁰ )
∠DAE = 48⁰
∠ACB = 180 - 78 (sum of angles on a straight line )
∠ACB = 102⁰
∠ABC = 180 - (22 + 102) (sum of angles in a triangle )
∠ABC = 56⁰
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Consider the following system of equations:
y = −x + 2
y = 3x + 1
Which description best describes the solution to the system of equations?
a
Line y = −x + 2 intersects line y = 3x + 1.
b
Lines y = −x + 2 and y = 3x + 1 intersect the x-axis.
c
Lines y = −x + 2 and y = 3x + 1 intersect the y-axis.
d
Line y = −x + 2 intersects the origin.
Answer:
Step-by-step explanation:To solve the system of equations, we can set the two expressions for y equal to each other:
−x + 2 = 3x + 1
Solving for x, we get:
4x = 1
x = 1/4
Substituting this value of x into either of the original equations, we get:
y = −(1/4) + 2
y = 7/4
Therefore, the solution to the system of equations is the point (1/4, 7/4), which is the point of intersection of the two lines.
So the correct description of the solution to the system of equations is:
a
Line y = −x + 2 intersects line y = 3x + 1.
A restaurant serves 10 different entrees, 6 of which contain meat. What is the ratio of vegetarian to non-vegetarian items?
Answer:
4/6 which is 2:3
Explanation:
the vegterian is 10-6=4
the non vegterian or eat meat is 6
and their ratio is 4/6
2:3
Find the value of x in the
following parallelogram.
3x-12
4x-24
x = [ ? ]
Answer:
[tex]3x - 12 = 4x - 24[/tex]
[tex]x = 12[/tex]
To find the value of x in the given parallelogram, set up an equation using the given sides and solve for x. The value of x is 12.
Explanation:To find the value of x in the given parallelogram, we need to use the properties of a parallelogram. In a parallelogram, opposite sides are equal in length. So, we can set up an equation using the given sides:
3x - 12 = 4x - 24
Now, we can solve the equation to find the value of x:
3x - 4x = -24 + 12
-x = -12
x = 12
Therefore, the value of x is 12.
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karen, who turns eighty years old this year, has just learned about blood pressure problems in the elderly and is interested in how her blood pressure comoares to those of her peers. She has uncovered an article in a scientific Journal that reports that the mean systolic blood pressure measurement for women over seventy-five is 134.1 mmHg, with a standard deviation of 5.7 mmHg. Assume that the article reported correct information. Complete the following statements about the distribution of systolic blood pressure measurements for women over seventy-five. х (a) According to Chebyshev's theorem, at least 36% of the measurements lie between___mmHg and ___ mmHg. (Round your answer to 1 decimal place.) (b) According to Chebyshev's theorem, at least (Choose one) 36% measurements lie between 122.7 mmHg an of the 56% 75% 84% 89%
(a) According to Chebyshev's theorem, at least 36% of the measurements lie between 122.7 mmHg and 145.5 mmHg. (b) According to Chebyshev's theorem, at least 56% measurements lie between 122.7 mmHg and 147.2. So, the correct option is 56%.
(a) Using Chebyshev's theorem to find how much data falls within a certain number of standard deviations from the mean.
Using k = 2, to capture at least 75% of the data (which is 1 - 1/2^2 = 0.75).
Using k = 2, we can say that at least 75% of the data falls within the range of 134.1 - 2(5.7) = 122.7 mmHg and 134.1 + 2(5.7) = 145.5 mmHg.
The percentage of data that falls outside of this range is (1 - 0.75)/2 = 0.125, or 12.5%.
Therefore, at least 12.5% of the data falls in each, below 122.7 mmHg and above 145.5 mmHg. This means that at least 36% of the data falls within the range of 122.7 mmHg and 145.5 mmHg.
(b) We can use Chebyshev's theorem again, this time with k = 2.5, since we want to capture at least 56% of the data (which is 1 - 1/2.5^2 = 0.64).
Using the same calculations as in part (a), we find that at least 64% of the data falls within the range of 121.0 mmHg and 147.2 mmHg.
Therefore, we can say that at least 56% of the data falls within this range, since 56% is less than 64%.
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For a lottery, the probability of a winning ticket is 0. 10. What is the probability the 20th ticket purchased is the second winning ticket? O 0. 015 O 0. 090 O 0. 257 O 0. 29
The probability that the 20th ticket purchased is the second winning ticket is 0.10
Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.
The probability of a winning ticket is = 0. 10
Thus,
This means there is a 10% chance of winning with each ticket purchased.
The likelihood that the 20th ticket will be the second winning ticket is the same as the chance that any other ticket will be the second winning ticket, which is 0.10. This is because each ticket purchase is autonomous and has no bearing on the results of other tickets. Therefore, the probability of the 20th ticket purchased being the second winning ticket is also 0.10 or 10%
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find the newton raphson method formula for finding the square root of a real number r from the equation x^2-r=0 is
a. xi+1= xi/2
b.xi+1= 3xi/2
c.xi+1= 1/2 (xi+ r/xi)
d.xi+1=1/2(3xi - r/xi)
Option (c) is the correct formula for the Newton-Raphson method to find the square root of a real number r from the equation [tex]x^2 - r = 0[/tex]
The Newton-Raphson method is an iterative method for finding the root of a function. To use this method to find the square root of a real number r from the equation [tex]x^2 - r = 0[/tex], we first define a function [tex]f(x) = x^2 - r[/tex]. The root of this function is the square root of r.
The Newton-Raphson method starts with an initial guess x0 for the root and then iteratively improves the guess using the formula:
[tex]xi+1 = xi - f(xi)/f'(xi)[/tex]
where f'(x) is the derivative of f(x). In this case,[tex]f(x) = x^2 - r[/tex], so f'(x) = 2x.
Substituting these values, we get:
[tex]xi+1 = xi - (xi^2 - r)/(2xi)[/tex]
Simplifying, we get:
[tex]xi+1 = xi - (xi/2 - r/2xi)[/tex]
[tex]xi+1 = 1/2(xi + r/xi)[/tex]
Therefore, the formula for the Newton-Raphson method to find the square root of a real number r from the equation [tex]x^2 - r = 0[/tex] is:
[tex]xi+1 = 1/2(xi + r/xi)[/tex]
Option (c) is the correct formula for the Newton-Raphson method to find the square root of a real number r from the equation[tex]x^2 - r = 0[/tex]. This formula involves taking the average of the current guess xi and r/xi as the next guess. This method is efficient and converges quickly to the square root of r.
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Manatees are one creature found in coastal waterways. To study this creature, a random sample of 12 manatees were selected, the sample manatees were released before their weights (in pounds) were carefully recorded: 956, 1012, 954, 988, 973, 1048, 1075, 1064, 856, 1026, 1031, 1064. Assuming the underlying distribution of manatee weights is normal.
1(5 points). Find a 95% confidence interval for the true mean weight.
2(5 points). In a similar study 10 years ago, researchers concluded that the true mean weight of manatees was approximately 1000 pounds. Implement a hypothesis test to verify if there is any evidence to suggest the true mean weight is less than 1000 pounds now. Solve the hypothesis using PP-value method. Let α=0.05.
Confidence interval for the true mean weight is (964, 1043.8)
P-value= 0.5836≥0.5 then conclude that null hypothesis is rejected.
What is null hypothesis?
The assertion that there is no link between the two sets of data or variables under investigation is known as the null hypothesis. The word "null" refers to the idea that any empirically observed difference is entirely attributable to chance and that no underlying causal link exists.
Given,
Data= 956, 1012, 954, 988, 973, 1048, 1075, 1064, 856, 1026, 1031, 1064
n=12
Mean = sum(x)/n=sum(x)/12= 12047/12= 1003.9167
We get the standard deviation from the given data by using formula
Std. deviation= 62.7976
C=95%= 0.95
α= 1-0.95=0.05
Critical value= 2.201
The 95% confidence interval for the true mean value is=
=(1003.9167±2.201*62.7976/√12)
= (1003.9167±39.9)
= (964, 1043.8)
2)The null and alternative hypothesis,
H0:μ=1000
Hα: μ<1000
The statistic is (t)= (1003.9167-1000)/ 62.7976/√12
=0.216
The P-value from online calculator
P-value= 0.5836≥0.5
Then conclude that null hypothesis is rejected.
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Zahra is a company specializing in high-end cosmetics. Its signature nail polish color is Soft Lilac. On a certain day, the company's factory had 5300 bottles of nail polish, and 1400 of those bottles were Soft Lilac. On that day, the inventory manager took a sample of 14 bottles of nail polish in the factory. She found that 3 of those bottles were Soft Lilac. For the inventory manager's sample, find and write with proper notation the population proportion and sample proportion of bottles that were Soft Lilac. Write the proportions as decimals (not percentages) rounded to two decimal places.
The population proportion (P) can be found by dividing the number of Soft Lilac bottles by the total number of bottles in the factory:
P = 1400 Soft Lilac bottles / 5300 total bottles
P ≈ 0.26 (rounded to two decimal places)
The sample proportion (p) can be found by dividing the number of Soft Lilac bottles in the sample by the total number of bottles in the sample:
p = 3 Soft Lilac bottles / 14 total bottles in the sample
p ≈ 0.21 (rounded to two decimal places)
So, the population proportion (P) of Soft Lilac bottles in Zahra's factory is approximately 0.26, and the sample proportion (p) of Soft Lilac bottles in the inventory manager's sample is approximately 0.21.
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5. 10 points Suppose that X (20,25) with mean 20 and variance 25. Please show all steps to find (a) P(19.6 < X < 20.4). (b) a so that P(x > a) 0.5517. (c) a so that P(X
a. A result between -0.08 and 0.08 has a probability of around 0.1562.
b. Using the standard normal distribution table the value of a is 19.4.
c. After using z-score to find the value of a, we got 28.2.
(a) To find P(19.6 < X < 20.4), we need to standardize the values and use the standard normal distribution table:
z1 = (19.6 - 20) / √(25) = -0.4 / 5 = -0.08
z2 = (20.4 - 20) / √(25) = 0.4 / 5 = 0.08
Using the standard normal distribution table, the probability of a value falling between -0.08 and 0.08 is approximately 0.1562. Therefore:
P(19.6 < X < 20.4) = 0.1562
(b) To find the value of a such that P(X > a) = 0.5517, we need to use the standard normal distribution table to find the z-score that corresponds to a cumulative probability of 0.5517:
P(X > a) = 1 - P(X ≤ a) = 0.5517
P(X ≤ a) = 1 - 0.5517 = 0.4483
Using the standard normal distribution table, the z-score that corresponds to a cumulative probability of 0.4483 is approximately -0.12. We can use this z-score to solve for a:
z = (a - μ) / σ
-0.12 = (a - 20) / 5
-0.6 = a - 20
a = 19.4
Therefore, a = 19.4.
(c) To find the value of a such that P(X > a) = 0.05, we need to use the standard normal distribution table to find the z-score that corresponds to a cumulative probability of 0.95:
P(X > a) = 0.05
P(X ≤ a) = 1 - 0.05 = 0.95
Using the standard normal distribution table, the z-score that corresponds to a cumulative probability of 0.95 is approximately 1.64. We can use this z-score to solve for a:
z = (a - μ) / σ
1.64 = (a - 20) / 5
8.2 = a - 20
a = 28.2
Therefore, a = 28.2.
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2. [10 marks] Solve the Cauchy problem 2ux + y = cos x = U.2,0) = sina
The solution of the Cauchy problem is y = (sina - 1/(2u - 1))e^(ux)cos(sqrt(1 - u^2)x) + (1/(2u - 1))cos(x).
To solve the Cauchy problem 2ux + y = cos x, we first need to find the general solution of the corresponding homogeneous equation 2ux + y = 0.
The characteristic equation is r^2 - 2ur + 1 = 0, which has roots r = u ± sqrt(u^2 - 1).
Case 1: u^2 < 1
In this case, the roots are complex conjugates, so the general solution of the homogeneous equation is
y = c₁e^(ux)cos(sqrt(1 - u^2)x) + c₂e^(ux)sin(sqrt(1 - u^2)x).
Case 2: u^2 > 1
In this case, the roots are real and distinct, so the general solution of the homogeneous equation is
y = c₁e^(r1x) + c₂e^(r2x),
where r1 = u + sqrt(u^2 - 1) and r2 = u - sqrt(u^2 - 1).
Case 3: u^2 = 1
In this case, the root is r = u, so the general solution of the homogeneous equation is
y = c₁e^(ux) + c₂xe^(ux).
Now, we can find the particular solution of the non-homogeneous equation using the method of undetermined coefficients.
Assuming a particular solution of the form y = Asin(x) + Bcos(x), we have
2uB - Asin(x) - Bcos(x) = cos(x).
Matching coefficients, we get A = 0 and 2uB - B = 1, so B = 1/(2u - 1).
Therefore, the particular solution is y = (1/(2u - 1))cos(x).
The general solution to the Cauchy problem is then
y = c₁e^(ux)cos(sqrt(1 - u^2)x) + c₂e^(ux)sin(sqrt(1 - u^2)x) + (1/(2u - 1))cos(x).
To determine the constants c₁ and c₂, we use the initial condition y(2,0) = sina.
Substituting x = 0, we get
c₁ + (1/(2u - 1)) = sina.
Substituting x = pi/2sqrt(1 - u^2), we get
c₂sqrt(1 - u^2) = 0.
Since sqrt(1 - u^2) ≠ 0, we have c₂ = 0.
Therefore, c₁ = sina - 1/(2u - 1), and the solution of the Cauchy problem is
y = (sina - 1/(2u - 1))e^(ux)cos(sqrt(1 - u^2)x) + (1/(2u - 1))cos(x).
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10-5+7-2-9+2-5+12-3+7-3+9-10-6+8-2+60-20 if u solve this u will get the same amount of points
Answer: 50
Step-by-step explanation:
Answer:
50?
Step-by-step explanation:
10-5 equals 5
5+7 equals 12
12-2 equals 10
10-9 equals 1
1+2 equals 3
3-5 equals -2
-2+12 equals 10
10-3 equals 7
7+7 equals 14
14-3 equals 11
11+9 equals 20
20-10 equals 10
10-6 equals 4
4+8 equals 12
12-2 equals 10
10+60 equals 70
70-20 equals 50
If there are 280 6th graders and 200 7th graders, then how many more 7th graders are involved in the yearbook?
Using proportions, it is found that 8 more seventh graders are involved in the yearbook.
What is a proportion?
A proportion is a fraction of a total amount.
Researching the problem on the internet, it is found that 10% of the 6th graders and 18% of the 7th graders are on the yearbook, hence:
0.1 x 280 = 28 6th graders.
0.18 x 200 = 36 7th graders.
36 - 28 = 8
8 more seventh graders are involved in the yearbook.
Use the method of Cholesky factorization to solve the system of equations: - X1 – 2x2 + 2x3 = 4 -2x1 +522 - 3x3 = -7 2.01 - 3x2 + 6x3 = 10
The solution to the system of equations is :
x1 = 3, x2 = -1, and x3 = 2.
To use the method of Cholesky factorization to solve this system of equations, we need to first write the system in matrix form as AX = B, where:
A = 1 -2 2
-2 5 -3
2 -3 6
X = x1
x2
x3
B = 4
-7
10
Next, we need to perform Cholesky factorization on matrix A. This involves finding a lower triangular matrix L such that A = LL^T, where L^T is the transpose of L. To do this, we use the following algorithm:
1. Set L11 = sqrt(A11).
2. For i = 2 to n, do the following:
a. Set Lii = sqrt(Aii - sum(Lik^2, k=1 to i-1)).
b. For j = i+1 to n, set Lij = (Aij - sum(Lik*Ljk, k=1 to i-1)) / Lii.
Applying this algorithm to matrix A, we get:
L = 1 0 0
-2 1 0
2 -1 1
Now we can solve for X by first solving L*Y = B for Y using forward substitution, and then solving L^T*X = Y for X using backward substitution. The solutions for Y and X are:
Y = 4
1
3
X = 3
-1
2
Therefore, the solution to the system of equations is x1 = 3, x2 = -1, and x3 = 2.
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A submarine is exploring the ocean floor and begins to ascend to the surface. The depth of the submarine in the water can be modeled by the function `d=500t-4,500` where t is the time (in minutes) since the submarine began to ascend
For the depth function of submarine in water is, d = 500t - 4,500, where t is the time (in minutes), the intercepts say x-intercept and y-intercept values are -4500 and 9 respectively.
The x-intercept is the point where a line cross or meet the x-axis, and the y-intercept is the point where a line cross or meet the y-axis. For y-intercept we are setting x to zero and for x-intercept we are setting y = 0 and determining their corresponding values. We have a submarine is exploring the ocean floor and begins to ascend to the surface.
The depth of submarine in the water can be modeled by equation, d = 500t - 4,500, where t is the time (in minutes). We have to determine the x and y intercept values. As we know, equation of line in slope intercept form is y = mx + b
where, b--> y-intercept
m --> slope
In this case b = - 4500, m = 500
So, y-intercept= -4500 for t = 0. Now, for x-intercept that for t value, plug d = 0, 0 = 500t - 4500
=> 500 t = 4500
=> t = 9
So, x-intercept = 9
Hence, required value is 9.
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Complete question:
A submarine is exploring the ocean floor and begins to ascend to the surface. The depth of the submarine in the water can be modeled by the function `d=500t-4,500` where t is the time (in minutes) since the submarine began to ascend. Find the intercepts of the graph of the equation:
x-intercept:
y-intercept:
A diver leaps off of cliff, modeled by the equation y =-16x^{2}-8x+120. When will the diver reach a height of 72 feet
The diver reaches a height of 72 feet after 1.5 seconds.
Given that, a diver leaps off of cliff, modeled by the equation,
y = -16x²- 8x +120.
We need to time taken by the diver to reach a height of 72 ft.
72 = -16x²- 8x + 120.
-16x²- 8x + 48 = 0
2x² + x - 6 = 0
Factorizing,
2x² + 4x -3x - 6 = 0
2x(x+2) -3(x+2) = 0
(2x-3)(x+2) = 0
x = -2, x = 1.5
Since, time cannot be negative so neglecting x = -2
Hence, the diver reaches a height of 72 feet after 1.5 seconds.
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