The side lengths that form a right triangle are: (Choice C) 5, 6, 8
In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This is known as the Pythagorean Theorem.
For choice A:
2² + 3² = 4²
4 + 9 ≠ 16
Therefore, (2, 3, 4) does not form a right triangle.
For choice B:
8² + 3² ≠ 17²
64 + 9 ≠ 289
Therefore, (8, 3, 17) does not form a right triangle.
For choice C:
5² + 6² = 8²
25 + 36 = 64
Therefore, (5, 6, 8) forms a right triangle.
Thus, the side lengths that form a right triangle are (5, 6, 8).
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1
First try was incorrect
One of the top companies trading on the Stock Exchange is Quect
Company. Last week, by Wednesday Quect Company's stock had
decreased 4 11/50points. By Friday it was down an additional 4 1/50
The requreid total decrease in Quect Company's stock was 8 6/25 points.
To find the total decrease in Quect Company's stock, we need to add the decrease by Wednesday to the decrease by Friday.
The decrease by Wednesday was 4 11/50 points. We can write this as a mixed number:
4 11/50 = 4 + 11/50
The decrease by Friday was 4 1/50 points, which can also be written as:
4 1/50 = 4 + 1/50
Adding these two values together, we get:
(4 + 11/50) + (4 + 1/50) = 8 + 12/50 = 8 + 6/25
Therefore, the total decrease in Quect Company's stock was 8 6/25 points.
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the intelligence quotient (iq) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. what is the probability we could select a sample of 40 adults and find the mean of this sample is between 95 and 105?
The probability of selecting a sample of 40 adults and finding the mean of this sample to be between 95 and 105 is approximately 0.932 or 93.2%.
We can use the central limit theorem and assume that the sample mean follows a normal distribution with a mean of 100 and a standard deviation of 15/sqrt(40) = 2.37.
To find the probability of selecting a sample with a mean between 95 and 105, we can standardize the values using the formula:
z = (x - μ) / (σ / sqrt(n))
where x is the sample mean (which is between 95 and 105), μ is the population mean (which is 100), σ is the population standard deviation (which is 15), and n is the sample size (which is 40).
For a sample mean of 95:
z = (95 - 100) / (15 / sqrt(40)) = -1.77
For a sample mean of 105:
z = (105 - 100) / (15 / sqrt(40)) = 1.77
Using a standard normal distribution table (or a calculator), we can find the probability that z is between -1.77 and 1.77, which is approximately 0.932.
Therefore, the probability of selecting a sample of 40 adults and finding the mean of this sample to be between 95 and 105 is approximately 0.932 or 93.2%.
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Find all intervals on which f is increasing. If you find more than one, present a comma-separated list
of intervals.
∫85(t^2-17t+72)e^t^2
The function f(t) is increasing on the interval (0, ∞). f is increasing on the interval (0, ∞). To find all intervals on which f(t) is increasing, we first need to find the derivative of the given function f(t) = ∫(85(t^2 - 17t + 72)e^(t^2)).
Step 1: Differentiate the function with respect to t.
f'(t) = 85(2t - 17)e^(t^2) + 85(t^2 - 17t + 72)(2t)e^(t^2)
Step 2: Simplify the expression.
f'(t) = 170t(e^(t^2)) - 85(17)e^(t^2) + 170t(t^2 - 17t + 72)e^(t^2)
Step 3: Find the critical points by setting f'(t) to zero.
170t(e^(t^2)) - 85(17)e^(t^2) + 170t(t^2 - 17t + 72)e^(t^2) = 0
Step 4: Solve for t.
t(170 - 85(17) + 170(t^2 - 17t + 72)) = 0
t = 0 is a critical point.
Step 5: Analyze the intervals around the critical point.
f'(t) is increasing when:
- For t < 0: f'(t) < 0
- For t > 0: f'(t) > 0
Hence, the function f(t) is increasing on the interval (0, ∞). Your answer: f is increasing on the interval (0, ∞).
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Find the radius of circle O if XY=10.
The radius of the circle is 7.25
What is the radius of the circle?The radius of the circle is determined using Pythagoras' theorem as `follows:
The length of the chord, XY = 10
The bisector of XY = 5
Let the radius be r
The length of the third side of the right-angles triangle = r - 2
Using Pythagoras' theorem:
r² = (r - 2)² + 5²
r² = r² - 4r + 4 + 25
r² - r² = - 4r + 29
-4r = -29
r = 29/4
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Determine whether the series is absolutely convergent, conditionally convergent, or divergent and state what tests were used to determine the conclusion.
∑ e^(1/n)/n√n
The series ∑(e¹/ⁿ/n√n) is absolutely convergent, determined using the Ratio Test.
To determine whether the series ∑(e¹/ⁿ/n√n) is absolutely convergent, conditionally convergent, or divergent, we can use the Ratio Test.
1. Take the absolute value of the series: |e¹/ⁿ/n√n|.
2. Compute the ratio of consecutive terms: |(e¹/ⁿ⁺¹)/((n+1)√(n+1)))/(e¹/ⁿ/(n√n))|.
3. Simplify the ratio: (n√n)/(e¹/ⁿ/(n+1))(n+1)√(n+1)).
4. Take the limit as n approaches infinity: lim(n->∞) (n√n)/(e¹/ⁿ/(n+1))(n+1)√(n+1)).
5. Observe that the limit is 0, which is less than 1.
Since the limit is less than 1, the series is absolutely convergent according to the Ratio Test.
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Pr. #3) Find the absolute maximum and absolute minimum values of g on the given interval. Put your answers in the form g(a) = b. g(x) = r + sin x+cost; 1,7
The absolute maximum value of g on the interval [1,7] is g(1) = r + sin(1) + cos(1), and the absolute minimum value is g(π) = r + sin(π) + cos(π) = r - 1.
To find the absolute extrema of g on [1,7], we first find the critical points by taking the derivative of g: g'(x) = cos(x) - sin(x)
Setting g'(x) = 0, we get:
cos(x) = sin(x)
which implies that either x = π/4 + kπ/2 or x = 3π/4 + kπ/2 for some integer k. Since 1 ≤ x ≤ 7, we have only one critical point in [1,7], namely x = π/4.
We now evaluate g at the endpoints of the interval and the critical point:
g(1) = r + sin(1) + cos(1)
g(7) = r + sin(7) + cos(7)
g(π/4) = r + √2
The absolute maximum value is the largest of these three values, which is g(1), and the absolute minimum value is the smallest of these three values, which is g(π/4).
Therefore, the absolute maximum value is g(1) = r + sin(1) + cos(1), and the absolute minimum value is g(π/4) = r + √2.
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Find all critical numbers and use the First Derivative Test to classify each as the location of a local minimum, local maximum or neither. x y- 27+ x-1-3 is a local maximum. *--3 is a local minimum. e
To find the critical numbers, we need to take the derivative of the function.
f(x) = y = 27 + x^(2) - 3x
f'(x) = 2x - 3
To find the critical numbers, we set f'(x) = 0 and solve for x:
2x - 3 = 0
x = 3/2
So, the only critical number is x = 3/2.
To classify each critical point, we can use the First Derivative Test. We evaluate the sign of f'(x) on either side of the critical number:
When x < 3/2:
f'(x) = 2x - 3 < 0
So, the function is decreasing to the left of x = 3/2.
When x > 3/2:
f'(x) = 2x - 3 > 0
So, the function is increasing to the right of x = 3/2.
Therefore, x = 3/2 is a local minimum.
Now, let's check the other two given points:
When x = -3:
f'(-3) = 2(-3) - 3 = -9 < 0
So, the function is decreasing at x = -3. This means that x = -3 is a local maximum.
When x = e:
f'(e) = 2e - 3 > 0
So, the function is increasing at x = e. This means that x = e is neither a local maximum nor a local minimum.
Therefore, the critical numbers and their classifications are:
x = -3 is a local maximum.
x = 3/2 is a local minimum.
x = e is neither a local maximum nor a local minimum.
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please, explain the solution step by step WITHOUT using L'HOSPITAL'S RULE. ( please without differentiation )
First, let's understand what L'Hospital's Rule is. It is a rule used in calculus to evaluate limits of functions. It states that if the limit of a function is of an indeterminate form, such as 0/0 or infinity/infinity, then you can take the derivative of the numerator and denominator and evaluate the limit again. This process can be repeated until the limit can be evaluated without an indeterminate form.
However, there are times when L'Hospital's Rule cannot be used or is not the most efficient method. Here are some steps to solving a limit problem without using L'Hospital's Rule:
1. Simplify the function as much as possible by factoring, canceling out terms, or applying algebraic properties.
2. Look for patterns or special cases that may help simplify the problem. For example, if you have a trigonometric function with an angle that approaches 0, you can use the limit definition of sine or cosine to evaluate the limit.
3. Use basic limit rules, such as the limit of a sum or difference, the limit of a product, or the limit of a quotient. These rules can help you evaluate the limit without using L'Hospital's Rule.
4. Use trigonometric identities or logarithmic or exponential properties to rewrite the function in a simpler form.
5. If all else fails, try to graph the function or use a table of values to estimate the limit.
By following these steps, you can find a solution to a limit problem without relying on L'Hospital's Rule.
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studying the number of visitors to a website during a 24 hour period would most likely involve which of the following type of variable? a. continuous b. qualitative c. discrete d. quantitative
The variable represents the number of visitors to the website, which is a countable value. Studying the number of visitors to a website during a 24-hour period would most likely involve a quantitative type of variable.
This is because the number of visitors can be measured and expressed as numerical values. Quantitative variables can be further classified as either continuous or discrete. In this case, the number of visitors is discrete because it can only take on whole numbers. It cannot be fractional or continuous. It is important to determine the type of variable in research studies as it affects the type of statistical analysis that can be used to analyze the data. By knowing that the number of visitors is a quantitative variable, researchers can choose appropriate statistical tests to analyze the data accurately.
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find the symmetric difference of {1, 3, 5} and {1, 2, 3}.
The symmetric difference of two sets is the set of elements that are in either of the sets, but not in their intersection. In this case, the intersection of {1, 3, 5} and {1, 2, 3} is {1, 3}, so the symmetric difference is the set of elements that are in either {1, 3, 5} or {1, 2, 3}, but not in {1, 3}. This set is {2, 5}, since 2 is in {1, 2, 3} but not in {1, 3, 5}, and 5 is in {1, 3, 5} but not in {1, 2, 3}. Therefore, the symmetric difference of {1, 3, 5} and {1, 2, 3} is {2, 5}.
Step 1: Identify the two sets.
Set A = {1, 3, 5}
Set B = {1, 2, 3}
Step 2: Find the difference between the two sets.
A - B = {5} (elements in A that are not in B)
B - A = {2} (elements in B that are not in A)
Step 3: Combine the two differences to find the symmetric difference.
Symmetric Difference = A - B ∪ B - A
Your answer: The symmetric difference of {1, 3, 5} and {1, 2, 3} is {2, 5}.
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Question 10 of 10
Raymond took out a 25-year loan from his bank for $135,000 at an APR of 3.6%, compounded monthly. If his bank charges a prepayment fee of 6 months' interest on 80% of the balance, what prepayment fee would Raymond be charged for paying off his loan 5 years early?
Raymond would be charged a prepayment fee of approximately $772.44 for paying off his loan 5 years early.
To calculate the prepayment fee, we first need to determine the remaining balance on the loan after 20 years of payments. We can use the formula for the present value of an annuity to calculate this:
P = (A / r) * [1 - (1 + r)⁻ⁿ]
where P is the present value, A is the monthly payment, r is the monthly interest rate, and n is the total number of payments.
We can first calculate the monthly interest rate as 3.6% / 12 = 0.003, and the total number of payments as 25 years * 12 months/year = 300 months. Then, we can calculate the monthly payment using the formula for the present value of an annuity:
A = P * (r / (1 - (1 + r)⁻ⁿ))
where P is the principal, r is the monthly interest rate, and n is the total number of payments.
Plugging in the values, we get:
A = 135,000 * (0.003 / (1 - (1 + 0.003)⁻³⁰⁰))
A ≈ $636.93
After 20 years of payments, the remaining balance on the loan would be the present value of the remaining payments, which we can calculate using the same formula:
P = (636.93 / 0.003) * [1 - (1 + 0.003)⁻²⁴⁰]
P ≈ $80,486.94
The prepayment fee would be 6 months' interest on 80% of the remaining balance:
Fee = 0.5 * 6 * (0.003 * 0.8 * $80,486.94)
Fee ≈ $772.44
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for which of the three intervals do you have the most con dence that it captures the population mean ?
To determine which interval has the most confidence in capturing the population mean, we need to look at the confidence level associated with each interval. A confidence interval is a range of values that we believe contains the true population parameter.
If we have three intervals with different confidence levels, the interval with the highest confidence level would be the one with the most confidence in capturing the population mean. For example, if Interval A has a confidence level of 90%, Interval B has a confidence level of 95%, and Interval C has a confidence level of 99%, then Interval C would have the most confidence in capturing the population mean.
It's important to note that the level of confidence we choose affects the width of the interval. The higher the confidence level, the wider the interval will be. Therefore, we need to balance the desire for a high level of confidence with the need for a narrow interval.
In summary, the interval with the highest confidence level is the one with the most confidence in capturing the population mean. Confidence intervals are a powerful tool in statistics that allows us to estimate population parameters from a sample with a known degree of uncertainty.
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OHM'S LAW In electrical engineering, the resistance of a circuit
P
can be found by the equation I = √√
√, where I is the current in
R
amperes, P is the power in watts, and R is the resistance of
the circuit in ohms. Graph this function for a circuit with a
resistance of 4 ohms.
The graph of the function I = √(P/4) is attached accordingly.
What are the features of the graph ?The equation I = √(P/4) represents an inverse relationship between the variables I ad P, where I is the current and P is the power.
As the power P increases, the current I will increase as well, but at a decreasing rate. T his can be seen in the shape of the graph, which is a curve that starts off steep and gradually levels out as P increases.
Conversely, as the power P decreases, the current I will also decrease, but again at a decreasing rate.
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given circle E with diameter CD and radius EA. AB is tangent to E at A. If AD=16 and EA=17 solve for AC
The value of AC is,
⇒ AC = 37.57
We have to given that;
The circle E with diameter CD and radius EA.
AB is tangent to E at A.
Here, AD = 16 and EA = 17
Hence, We get;
CD = 17 + 17
CD = 34
By using Pythagoras theorem;
AC² = AD² + CD²
AC² = 16² + 34²
AC² = 256 + 1156
AC² = 1412
AC = √1412
AC = 37.57
Thus, The value of AC is,
⇒ AC = 37.57
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Exercise 6. 1. 12. Find the laplace transform of f(t) = { t if t >= 1,0 if t < 1 }
The Laplace transform of f(t) is: L{f(t)} = (1/[tex]s^2[/tex]) - (1/s) * [tex]e^(-s)[/tex]
The Laplace transform of the given function f(t) can be found using the definition:
L{f(t)} = ∫[0,∞) [tex]e^(-st)[/tex]f(t) dt
We can split the integral into two parts based on the domain of f(t):
L{f(t)} = ∫[0,1) [tex]e^(-st)[/tex] * 0 dt + ∫[1,∞) [tex]e^(-st)[/tex] * t dt
= 0 + ∫[1,∞) [tex]e^(-st)[/tex] * t dt
To solve the second integral, we can use integration by parts:
u = t, dv = [tex]e^(-st)[/tex] dt
du/dt = 1, v = (-1/s) [tex]e^(-st)[/tex]
∫[1,∞) [tex]e^(-st)[/tex]* t dt = [-t/s * [tex]e^(-st)[/tex]]_[1,∞) + ∫[1,∞) [tex]e^(-st)/s[/tex] dt
= [-(∞/s * e(-∞)) + (1/s * [tex]e^(-s)[/tex])] + (1/[tex]s^2[/tex] *[tex]e^(-s)[/tex])
Since e(-∞) is equal to zero, we can simplify this expression to:
L{f(t)} = (1/[tex]s^2[/tex]) - (1/s) * [tex]e^(-s)[/tex]
Therefore, the Laplace transform of f(t) is:
L{f(t)} = (1/[tex]s^2[/tex]) - (1/s) * [tex]e^(-s)[/tex]
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researcher studies the mean egg length for a bird population. after taking a random sample of eggs, they obtained a 95 percent confidence interval of (45,60). what is the value of the margin of error?
Answer:95% confidence intervalX shrtaa -1.96 standard divination/ square n=45X shrtaa+1.96 standard sicinTION/sqaue root n=60----------------------2x shrtaa=105 sp x=52.5
Step-by-step explanation:
The margin of error is a measure of the precision of an estimate and represents the maximum distance between the sample mean and the true population mean.
To answer your question about the margin of error for the researcher studying the mean egg length for a bird population: Given the 95 percent confidence interval of (45, 60), we can determine the value of the margin of error.
1. First, find the midpoint of the confidence interval by averaging the two values: (45 + 60) / 2 = 52.5. This midpoint represents the estimated mean egg length.
2. Next, determine the margin of error by subtracting the lower value of the confidence interval from the midpoint: 52.5 - 45 = 7.5.
In conclusion, the value of the margin of error for this 95 percent confidence interval is 7.5 units. This means that the researcher is 95% confident that the true mean egg length for the bird population falls within the interval (45, 60).
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let r be the relation on z defined by x r y if and only if x 3y is even. prove that r is an equivalence relation.
r is reflexive, symmetric, and transitive, we can conclude that r is an equivalence relation.
To prove that r is an equivalence relation, we need to show that it is reflexive, symmetric, and transitive.
1. Reflexive: A relation is reflexive if x r x for all x in Z.
Let x ∈ Z. We need to show that x r x, i.e., x 3x is even.
Since 3x is always even (because 3x = 2 * (3/2 * x) and 2 is a factor of 3x), x 3x is even, which means x r x. Therefore, r is reflexive.
2. Symmetric: A relation is symmetric if x r y implies y r x for all x, y in Z.
Let x, y ∈ Z such that x r y, i.e., x 3y is even.
We need to show that y r x, i.e., y 3x is even.
Since x 3y is even, there exists an integer k such that x 3y = 2k.
Then, y 3x = 3y - x = -(x - 3y) = -2k.
As -2k is also an even number, y 3x is even, which means y r x. Therefore, r is symmetric.
3. Transitive: A relation is transitive if x r y and y r z imply x r z for all x, y, z in Z.
Let x, y, z ∈ Z such that x r y and y r z, i.e., x 3y is even and y 3z is even.
We need to show that x r z, i.e., x 3z is even.
Since x 3y and y 3z are even, there exist integers k and m such that x 3y = 2k and y 3z = 2m.
Adding these two equations, we get x 3y + y 3z = 2k + 2m.
Therefore, x 3z = 2(k + m).
As 2(k + m) is even, x 3z is even, which means x r z. Hence, r is transitive.
Since r is reflexive, symmetric, and transitive, we can conclude that r is an equivalence relation.
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: Seven women and nine men are on the faculty in the Computer Engineering department at a school. How many ways are there to select a committee of five members of the department if at least one woman and at least one man must be on the committee? Displa
If Seven women and nine men are on the faculty in the Computer Engineering department at a school, So there are 4368 ways to select a committee of five members.
To find the number of ways to select a committee of five members from the Computer Engineering department with at least one woman and one man, we can use the principle of inclusion-exclusion.
Similarly, we can find the number of ways to select a committee with only women: C(7,5) = 21
However, we need to subtract the cases where there are no women or no men on the committee, which is simply the number of ways to select five members from the faculty excluding either all women or all men:
C(9,5) + C(7,5) = 126 + 21 = 147
Therefore, the total number of ways to select a committee of five members from the Computer Engineering department with at least one woman and one man is:
C(16,5) - C(9,5) - C(7,5) + C(9,5) + C(7,5) = 4368 - 126 - 21 + 147 = 4368 - 0 = 4368
So there are 4368 ways to select a committee of five members from the Computer Engineering department with at least one woman and one man.
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Z Find the mass of the solid cylinder D = {(r,0,z): 0 5157,05756} with density p(r,0,z) = 1 +5 2 Set up the triple integral using cylindrical coordinates that should be used to find the mass of the solid cylinder as efficiently as possible. Use increasing limits of integration. dz S S S az dr de • DO 0 The mass is (Type an exact answer, using a as needed.)
The mass of the solid cylinder is 260π using the triple integral.
To find the mass of the solid cylinder with density p(r,0,z) = 1 + 5^2, we need to integrate the density over the entire volume of the cylinder. Since we are dealing with a cylinder, cylindrical coordinates are the most efficient choice.
The solid cylinder is defined by 0 ≤ r ≤ 5, 0 ≤ θ ≤ 2π, and 0 ≤ z ≤ 6. So we can set up the triple integral as follows:
∫∫∫ p(r,0,z) r dz dr dθ, with limits of integration:
0 ≤ θ ≤ 2π (full revolution around the z-axis)
0 ≤ r ≤ 5 (radius of the cylinder)
0 ≤ z ≤ 6 (height of the cylinder)
Since the density is constant with respect to θ, we can integrate with respect to θ first:
∫0^2π ∫0^5 ∫0^6 (1 + 5^2) r dz dr dθ
Integrating with respect to z next:
∫0^2π ∫0^5 (1 + 5^2) r(6) dr dθ
Simplifying:
∫0^2π 3(1 + 5^2) r^2 dr dθ
Integrating with respect to r:
∫0^2π 3(1 + 5^2) [(5^3)/3] dθ
Simplifying:
10π(26)
The mass of the solid cylinder is 260π.
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he intelligence quotient (iq) test scores for adults are normally distributed with a population mean of 100 and a population standard deviation of 15. what is the probability we could select a sample of 50 adults and find that the mean of this sample exceeds 104? multiple choice 0.9412 0.9706
To solve this problem, use the formula for the sampling distribution of the mean: standard error of the mean = population standard deviation / square root of sample size standard error of the mean = 15 / √50 = 2.1213. So, the probability of selecting a sample of 50 adults and finding that the mean of this sample exceeds 104 is 0.9706. The correct multiple-choice answer is 0.9706.
Then, we can use the z-score formula to find the probability of getting a sample mean greater than 104:
z = (sample mean - population mean) / standard error of the mean
z = (104 - 100) / 2.1213 = 1.8868
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score of 1.8868 or greater is 0.0302.
Therefore, the probability of selecting a sample of 50 adults and finding that the mean of this sample exceeds 104 is 0.0302, or approximately 0.03. The closest multiple choice answer is 0.0294, so the correct answer is 0.9706.
The concept of the standard error of the mean, z-scores, and the z-table for normal distributions.
1. Calculate the standard error of the mean (SEM):
SEM = Population standard deviation / √(Sample size)
SEM = 15 / √50 ≈ 2.121
2. Calculate the z-score for the sample mean of 104:
z = (Sample mean - Population mean) / SEM
z = (104 - 100) / 2.121 ≈ 1.88
3. Look up the probability for the z-score in a z-table:
For z = 1.88, the probability is 0.9706.
So, the probability of selecting a sample of 50 adults and finding that the mean of this sample exceeds 104 is 0.9706. The correct multiple-choice answer is 0.9706.
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how many standard deviations is each student away from hiir school average? if the student gpa is higher than his school average, enter this as a positive number. if the student gpa is lower than his school average, enter this as a negative number.
Without any specific data about the student's GPA or the school's average, it is impossible to provide a numerical answer to this question.
However, in general, to calculate the number of standard deviations a student's GPA is away from the school's average, we would need to find the difference between the student's GPA and the school's average, and then divide that difference by the standard deviation of the GPA distribution for the entire school population. The resulting number would tell us how many standard deviations the student's GPA is away from the mean.
For example, if the school's average GPA is 3.0 and the standard deviation is 0.5, and a student has a GPA of 3.5, then the student is one standard deviation above the mean (since (3.5 - 3.0) / 0.5 = 1). On the other hand, if the same student had a GPA of 2.5, then they would be one standard deviation below the mean (since (2.5 - 3.0) / 0.5 = -1).
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I need help with 7,8,9,10,11,12
Please help me with the right answers they need to know if the angles are adjacent vertical or neither
Thanks
Answer:
see below
Step-by-step explanation:
7. adjacent
8.vertical
9.vertical
10.neither
11.adjacent
12.neither
Hope this helps :)
among all students, what proportion earn an a and don't attend class regularly? aandnotr - numeric answer type your answer here round to four decimal places.
The corresponding probabilities are: A. P(R) = 0.72 B. P(R') = 0.28 C. P(A ∩ R) = P(R) * P(A | R) = 0.72 * 0.51 = 0.367 D. P(A | R) = 0.51 E. P(A ∩ R') = P(R') * P(A | R') = 0.28 * 0.10 = 0.028 F. P(A' ∩ R) = P(R) * P(A' | R) = 0.72 * 0.49 = 0.352 G. P(A' ∩ R') = P(R') * P(A' | R') = 0.28 * 0.90 = 0.252
(a) The tree diagram with the corresponding probabilities is:
A (0.51) A' (0.49) A (0.10) A' (0.90)
(b) The proportion of students who earn an A and don't attend class regularly is:
P(A ∩ R') = 0.028
(c) The chance that a randomly chosen student will earn an A in the class is:
P(A) = P(A ∩ R) + P(A ∩ R')
= 0.367 + 0.028
= 0.395
(d) Given that a student earned an A, the chance they attend class regularly is:
P(R | A) = P(A ∩ R) / P(A)
= 0.367 / 0.395
≈ 0.9291 (rounded to four decimal places)
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Complete question:
A professor has noticed that students hat attend class regularly, mss no more than two classes per term, generally get better grades. For he class, the overall percent o students who attend regularly s 72% or those who come to class on a regular basis, 51% receive A's. Of those who don't attend regularly, only 10% get A's. (b)Among all students what proportion earn an A and don't attend class regularly?
After a helicopter flies to a height of 500 meters, it starts to descend to a
landing pad that ground distance is 11 meters. What is the measure of the
angle formed with the ground looking up to the helicopter?
Step-by-step explanation:
See image
On the map (right), the length of each east-west block is 1/8 mile and the length of each north-south block is 1/10 mile. Victoria has to walk from the grocery store to the bus stop. Find the shortest walking distance. Then find the straight-line distance ('as the crow flies') between the two locations.
What is the shortest walking distance?
(Round to the nearest hundredth as needed.)
On the map (right), the length of each east-west block is 1/8 mile and the length of each north-south block is 1/10 mile, the straight-line distance between the two locations is approximately 1.41 miles.
To find the shortest walking distance, we can use the Pythagorean theorem, which states that for a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Let's label the distance that Victoria walks east as x and the distance she walks north as y.
Then, from the map, we can see that the length of each east-west block is 1/8 mile and the length of each north-south block is 1/10 mile. So, we have:
x = (5/8) + (3/8) = 1 mile
y = (3/10) + (1/10) + (1/10) = 1/2 mile
Now, we can use the Pythagorean theorem:
distance = sqrt(x^2 + y^2)
distance = sqrt(1^2 + (1/2)^2)
distance ≈ 1.12 miles
Therefore, the shortest walking distance is approximately 1.12 miles.
To find the straight-line distance between the two locations, we can simply use the distance formula:
distance = sqrt((1 - 0)^2 + (1.5 - 0.5)^2)
distance = sqrt(1 + 1^2)
distance ≈ 1.41 miles
Therefore, the straight-line distance between the two locations is approximately 1.41 miles.
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the mean number of travel days per year for salespeople employed by three hardware distributors needs to be estimated with a 0.95 degree of confidence. for a small pilot study, the mean was 150 days and the standard deviation was 18 days. if the population mean is estimated within two days, how many salespeople should be sampled? multiple choice 1,219 1,164 4,948 311
The mean number of travel days per year for salespeople employed by three hardware distributors needs to be estimated with a 0.95 degree of confidence. The correct option to this number is 1,219.
To calculate the sample size needed for a desired level of confidence, we can use the formula:
n = (Z^2 * σ^2 * N) / ((B^2 * (N-1)) + (σ^2))
where:
n = required sample size
Z = Z-score (for a 0.95 degree of confidence, Z = 1.96)
σ = standard deviation (18 days)
N = population size (unknown, but not needed for large populations)
B = margin of error (2 days)
n = (1.96^2 * 18^2) / (2^2)
n = (3.8416 * 324) / 4
n = 1241.7984
Since we cannot have a fraction of a salesperson, we round up to the nearest whole number. Thus, the required sample size is approximately 1,242 salespeople. However, this option is not among the multiple choices provided. The closest option to this number is 1,219.
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If 10 pounds of nails cost $4. 38, what is the cost to the bear test cent of 3. 2 pounds of the same type of nail?
The proportion is solved and cost to the bear test cent of 3.2 pounds is given by A = $ 1.4016
Given data ,
Let the cost to the bear test cent of 3. 2 pounds is A
Now , the proportion is
10 pounds of nails cost $4.38
On simplifying , we get
So , cost of 1 pound is = 0.438
Now , the cost of 3.2 pounds is A = 3.2 x 0.438
A = $ 1.4016
Hence , the cost to the bear test cent of 3.2 pounds is $ 1.4016
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jada and andre want to share a big slice of pizza so that each of them gets the same amount, but andre doesn’t like the crust. the pizza slice is a sector of a circle with a radius of 20 cm and a central angle that measures pi/3 radians. how can andre and jada divide the slice of pizza into 2 equal pieces so that andre doesn’t have to eat any crust?
Jada can take the piece with the crust, and Andre can take the piece without the crust. This way, they will each have an equal portion of the pizza slice, and Andre won't have to eat any crust.
To divide the pizza slice into two equal pieces so that Andre doesn't have to eat any crust, Jada and Andre can follow the following steps;
Firstly, find the area of the pizza slice
The area of the sector of a circle is given by the formula A = (1/2) × r² × θ, where r is radius of the circle and θ is the central angle in radians. In this case, the radius of the pizza slice is 20 cm and the central angle is π/3 radians. Plugging in these values, we can calculate the area of the pizza slice.
A = (1/2) × (20 cm)² × (π/3)
A = (1/2) × 400 cm² × (π/3)
A = 200/3 × π cm²
Now, find half of the area of the pizza slice.
To divide the pizza slice into two equal pieces, Jada and Andre need to find half of the total area of the pizza slice.
Half of the area of the pizza slice = (1/2) × (200/3 × π cm²)
Half of the area of the pizza slice = 100/3 × π cm²
However, Cut along the radius.
Jada and Andre can cut along the radius of the pizza slice, starting from the center of the circle (where the crust is) and extending to the outer edge of the pizza. This will result in two equal pieces, with one piece containing the crust and the other piece not containing any crust.
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A photograph of Earth is enlarged so that the diameter appears 4 times larger.
How much larger does the circumference of Earth appear?
The new circumference appears 4 times larger than the original circumference.
The diameter of Earth is the distance across the widest part of its circular shape. The circumference of Earth is the distance around its circular shape. When a photograph of Earth is enlarged, the diameter appears 4 times larger. This means that the new diameter is 4 times the original diameter. Mathematically, if the original diameter of Earth is represented by "d", then the new diameter after enlargement would be 4d.
Now, we need to find out how much larger the circumference of Earth appears after the enlargement. The formula for the circumference of a circle is C = πd, where "C" represents the circumference and "d" represents the diameter. Since the diameter has become 4d, the new circumference would be:
C = π(4d)
C = 4πd
This means that if the original circumference of Earth is represented by "c", then the new circumference after enlargement would be 4c.
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Jacob owns a small business selling bagels. He knows that in the last week 108 customers paid in cash, 24 customers used a debit card , and 18 customers used a credit card Based on these results, express the probability that the next customer will pay with a debit or credit card as a decimal to the nearest hundreth
Probability helps us to know the chances of an event occurring. The probability that the next customer will pay with a debit or credit card as a percent to the nearest hundredth number is 28%.
What is Probability?Probability helps us to know the chances of an event occurring. The sum of all the probabilities of an event is always equal to 1. The formula for probability is given as,
[tex]\text{Probability}=\dfrac{\text{Desired Outcomes}}{\text{Total Number of outcomes possible}}[/tex]
Given that in the last week 108 customers paid cash, 24 customers used a debit card, and 18 customers used a credit card. Therefore, the total number of customers who came to the business last month is,
Total number of customers = 108 + 24 + 18 = 150
Now, the probability that the next customer will pay with a debit or credit card is,
Probability
= Number of customers who pay with debit or credit card / Total number of customers
= 42 / 150
= 0.28
To convert probability into percentage multiply it by 100%, therefore, the probability can be written as,
Probability = 0.28 × 100%
= 0.28 ≈ 28%
Hence, the probability that the next customer will pay with debit or credit card as a percent to the nearest hundredth number is 28%.
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