The mean of the finishers in the New York City 10-km run is 60 minutes and standard deviation is 9 minutes.
To determine the percentage of finishers who have times between 55 and 75 minutes, we need to find the Z-scores for both of these values as follows:
Z1 = (55 - 60) / 9 = -0.56Z2 = (75 - 60) / 9 = 1.67
Now, we need to find the area under the standard normal distribution curve between these two Z-scores as follows:
P(-0.56 < Z < 1.67) = P(Z < 1.67) - P(Z < -0.56) Using a standard normal distribution table,
we can find the probabilities as:
P(Z < 1.67) = 0.9525P(Z < -0.56) = 0.2881
Therefore , P(-0.56 < Z < 1.67) = P(Z < 1.67) - P(Z < -0.56)= 0.9525 - 0.2881= 0.6644Therefore, the percentage of finishers who have times between 55 and 75 minutes is 66.44%.
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A serving of walnuts is 5/6 of a cup. How many servings are there in a 2 1/2-cup bag of walnuts?
Answer:
3
Step-by-step explanation:
5/2 ÷ 5/6 = 5/2 × 6/5
5/2 × 6/5 = 30/10 or 3
you make a one time deposit of 2000 years that earn 5% simple interest. how much interest would you earn in 2 years ?
Answer:
$2205
Step-by-step explanation:
equation set up
2000 (1.05)^2
For a multistate lottery, the following probability distribution represents the cash prizes of the lottery with their corresponding probabilities. Complete parts (a) through (c) below. P(x) 0.00000000821 0.00000014 200,000 10,000 0.000001746 100 0.000153924 7 0.005426433 4 0.006847638 3 0.01791359 0 0.96965652079 (a) If the grand prize is $16,000,000, find and interpret the expected cash prize. If a ticket costs $1, what is your expected profit from one ticket? The expected cash prize is $ (Round to the nearest cent as needed.)
Your expected profit from one ticket, after accounting for the ticket cost, is $2. This means that, on average, you can expect to make a profit of $2 per ticket if you were to play the lottery multiple times.
To find the expected cash prize, we multiply each cash prize by its corresponding probability and sum up the results.
Expected cash prize = (0.00000000821 * $16,000,000) + (0.00000014 * $1,000,000) + (0.000001746 * $200,000) + (0.000153924 * $10,000) + (0.005426433 * $100) + (0.006847638 * $7) + (0.01791359 * $4) + (0.96965652079 * $3) + (0.01791359 * $0)
Calculating this, we get an expected cash prize of $3.00025908719.
Interpreting the result, we can say that, on average, the expected cash prize for one ticket is approximately $3. This means that if you were to play the lottery multiple times, the average amount you could expect to win per ticket would be around $3.
To calculate the expected profit from one ticket, we subtract the cost of the ticket ($1) from the expected cash prize:
Expected profit = $3 - $1 = $2.
Therefore, your expected profit from one ticket, after accounting for the ticket cost, is $2. This means that, on average, you can expect to make a profit of $2 per ticket if you were to play the lottery multiple times.
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Which equation correctly compares the tens place and ones place in 9,999?
A.
90 ÷ 9 = 10
B.
900 ÷ 9 = 100
C.
9,000 ÷ 90 = 100
D.
900 ÷ 90 = 10
Answer:
I'm pretty sure the answer is A.
Step-by-step explanation:
Since 90 plus 9 = 99 and 99 is the tens and ones place.
So, the answer should be A.
Hope this helps! :)
90 / 9 = 10 compares the tens place and one's place in 9,999. Option A is correct.
Given that,
To determine the equation correctly compare the tens place and one's place in 9,999.
A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.
Here,
In the number 9999,
let the number on the ten places be x times the number on unit place,
90 = x * 9
x = 90 / 9
x = 10
Now,
90 / 9 = 10
Thus, 90 / 9 = 10 compares the tens place and one's place in 9,999. Option A is correct.
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A basket contains 41 heads of lettuce, 9 of which are spoiled. If a sample of 3 is drawn and not replaced, what is the probability that all in the sample are spoiled?
The probability is approximately 0.0079, or 0.79%.
To find the probability that all three heads of lettuce in the sample are spoiled, we need to calculate the ratio of favorable outcomes to the total number of possible outcomes.
The total number of possible outcomes is the number of ways to choose 3 heads of lettuce from the 41 available in the basket without replacement. This can be calculated using the combination formula (nCr):
Total possible outcomes = 41 C 3 = (41!)/(3!(41-3)!) = (414039)/(321) = 412013 = 10,660.
The number of favorable outcomes is the number of ways to choose 3 spoiled heads of lettuce from the 9 spoiled ones in the basket:
Favorable outcomes = 9 C 3 = (9!)/(3!(9-3)!) = (987)/(321) = 84.
Therefore, the probability that all three heads of lettuce in the sample are spoiled is:
Probability = Favorable outcomes / Total possible outcomes = 84 / 10,660 ≈ 0.0079 (rounded to four decimal places).
So, the probability is approximately 0.0079, or 0.79%.
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A random sample of n items is to be taken from a distribution with mean μ and standard deviation o. Use the central limit theorem to determine the smallest number of items n that must be taken in order to satisfy the following relation: P(|Xn-μ<0/4) ≥ 0.99.
The given relation is P (|Xn - μ| / σ < 0.25) ≥ 0.99. We need to determine the smallest value of n that satisfies the given relation using the central limit theorem.
Step 1: We know that the standard normal distribution is used in the central limit theorem to approximate the distribution of the sample means. The standard normal distribution has a mean of zero and a standard deviation of one. We need to standardize the given relation so that we can use the standard normal distribution.
Step 2: We substitute the values from the given relation and simplify as follows: P(|Xn - μ| / σ < 0.25) ≥ 0.99P(|Xn - μ| / (o/√n) < 0.25) ≥ 0.99P((Xn - μ) / (o/√n) < 0.25) ≥ 0.99P(-0.25 < (Xn - μ) / (o/√n) < 0.25) ≥ 0.99P(Z < 0.25√n) - P(Z < -0.25√n) ≥ 0.99where Z is the standard normal random variable.
Step 3: We look up the values of -0.25√n and 0.25√n from the standard normal distribution table and find their difference. We use the absolute value of the difference since we are dealing with probabilities. We get: |P (Z < 0.25√n) - P (Z < -0.25√n) | = 0.99. Since the standard normal distribution is symmetric, we have P (Z < 0.25√n) - P (Z > 0.25√n) = 0.99We can rearrange this as: P (Z < 0.25√n) = 0.995P(Z > 0.25√n) = 0.005
Step 4: We look up the value of 0.995 from the standard normal distribution table and find its corresponding z-score. We get: z = 2.58. Using the z-score formula, we can solve for the value of 0.25√n. We get:2.58 = 0.25√nn = (2.58 / 0.25) ²n ≈ 107.58We round up to the nearest integer to get n = 108. Therefore, the smallest number of items n that must be taken in order to satisfy the given relation is 108.
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Mark hopes to one day earn $10,000. Estimate how
many clients Mark would need.
4,14,14, 14.4.4
Determine if the data set is unimodal, bimodal, multimodal, or has no mode. Identify the models). If any exist
The data set is bimodal with modes at 4 and 14.
To determine the mode(s) and the modality of a data set, we need to identify the values that occur most frequently.
The given data set is: 4, 14, 14, 14, 4
To find the mode(s), we can count the frequency of each value:
4 appears 2 times14 appears 3 times
The mode(s) are the value(s) that appear with the highest frequency. In this case, both 4 and 14 have the same frequency of occurrence, so this data set is bimodal, with modes at 4 and 14.
Therefore, the data set is bimodal with modes at 4 and 14.
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15 POINTS PLSS HELP THIS IS MY 3RD TIME POSTING THIS BC NO ONE WILL HELP ME PLSSS AND NO WRONG ANSWERS PLS I REALLY NEED HELPP
Answer:
to find the equation of the line you use y=mx+b
Step-by-step explanation:
m means the slope and the b is the y intercept of the line. so in this case the b is 5. the m is 6 so the answer is y=6x+5
Write a ratio of squares to circles
Answer:
The ratio should be 2:3
Step-by-step explanation:
Hope this helped!
Answer:
2:3 or 2/3 depending on which form they want the answer in.
Step-by-step explanation:
There are 2 squares and 3 circles.
I REALLY NEED HELP IF YOU CAN PLEASE SHOW WORK SO I CAN UNDERSTAND
Answer:
G
Step-by-step explanation:
The number of total bottles sold on that day is 40
11 + 7 + 18 + 4 = 40
On Tuesday, theoretically, this is what will be sold:
22 bottles of apple juice
14 bottles of cranberry juice
36 bottles of orange juice
8 bottles of pineapple juice
We need to find out what doesn't fit the data.
F: 14 - 8 = 6, not correct answer
G: the number of cranberry juice will be 6 times the number of pineapple juice sold? It's not even twice the amount!
H: 36 + 14 = 50, not correct answer
J: 22 - 8 = 14, not correct.
From this, G is the correct answer as it is not even close to matching the data.
Shamma is working at an addition recovery center. She reads somewhere that one of the differences between casual drug use and addiction is despair or depression. She randomly gives a group of her patients the Beck's Depression Inventory (BDI). She knows from previous research that a group of local patients with Major Depressive Disorder had a mean BDI score of 24.
After analyzing the One Sample T-test from her study she writes:
We conducted a one-tailed, one-sample t-test comparing the sample mean BDI score (28.4) against a population mean of 24, t(14) = 2.25, p = 0.021.
How many people were in Shamma's sample?
Using the information from Shamma's study in Question 21 write a null hypothesis and an alternative hypothesis.
From Shamma's study, there are 14 people in her sample. How many people were in Shamma's sample? Shamma's sample consists of 14 people.
Explanation: We can find the answer in the given text, which is the number of people in Shamma's sample.
The sentence that holds the answer is: "We conducted a one-tailed, one-sample t-test comparing the sample mean BDI score (28.4) against a population mean of 24, t(14) = 2.25, p = 0.021." We see that the value of t is in brackets with a value of 14.
Therefore, there are 14 people in Shamma's sample. Now, let's write the null hypothesis and an alternative hypothesis.
Null Hypothesis, H0: H0: μ = 24, There is no significant difference between the sample mean BDI score and population mean. Alternative Hypothesis, Ha: Ha: μ > 24, There is a significant difference between the sample mean BDI score and population mean.
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The sample mean is greater than the population mean i.e., μ > 24.
There were 15 people in Shamma's sample.
Shamma randomly gives the Beck's Depression Inventory (BDI) to a group of her patients.
After analyzing the One Sample T-test from her study she writes:
We conducted a one-tailed, one-sample t-test comparing the sample mean BDI score (28.4) against a population mean of 24, t(14) = 2.25, p = 0.021.
The value given in the bracket is 14.
As we know that N-1 is used as the degrees of freedom, so the number of people in Shamma's sample is:
[tex]N-1 = 14N = 14 + 1 = 15[/tex]
Thus, the number of people in Shamma's sample is 15.
The null hypothesis for Shamma's study would be:
H0: The sample mean is equal to the population mean i.e., μ = 24.
The alternative hypothesis for Shamma's study would be:
HA: The sample mean is greater than the population mean i.e., μ > 24.
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When approximating S(x)dx using Romberg integration, R9,4 gives an approximation of order: h10 h8 h4 h6
R₄,₄ gives an approximation of order h⁸ when approximating ∫(a to b)f(x)dx using Romberg integration. Therefore second option is the correct answer.
When approximating the integral ∫(a to b) f(x) dx using Romberg integration, the term "R₄,₄" refers to the fourth row and fourth column of the Romberg matrix.
This specific entry represents the approximation obtained using the Romberg method with four iterations. The order of approximation is determined by the highest power of h in the error term of the approximation.
Since R₄,₄ has a subscript of 4, it indicates that the approximation is of order h⁸. This means that the error decreases at a rate of h⁸ as the step size h decreases, providing a more accurate estimation of the integral.
Therefore the correct answer is second option.
The question should be:
When approximating ∫(a to b)f(x)dx using Romberg integration, R₄,₄ gives an approximation of order:
h10
h8
h4
h6
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in the case of a triangle with angle measures of 30°, 60°, and 90° and a hypotenuse length equal to x, what is the perimeter of the triangle in terms of x?
The perimeter of triangle is the sum of the lengths of its three sides. In the case of a triangle with angle measures of 30°, 60°, and 90° and a hypotenuse length equal to x, we can determine the perimeter in terms of x.
Let's consider the sides of the triangle:
The side opposite the 30° angle is x/2, which can be derived using the properties of a 30-60-90 triangle.
The side opposite the 60° angle is x√3/2, which can also be derived using the properties of a 30-60-90 triangle.
The hypotenuse, which is opposite the 90° angle, has a length of x.
To find the perimeter, we add up the lengths of these three sides:
Perimeter = x/2 + x√3/2 + x
Combining like terms, we can simplify the expression:
Perimeter = (x + x√3 + 2x)/2
Perimeter = (3x + x√3)/2
Perimeter = x(3 + √3)/2
Therefore, the perimeter of the triangle in terms of x is 2x + x√3.
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Let u(t) = 2t³i + (t²-1)j-8k. Compute the derivative of the following function. (+19+21) u(t) Select the correct choice below and fill in the answer box(es) to complete your choice. OA. The derivative is the scalar function OB. The derivative is the vector-valued function i+ Di+ k
The correct choice is:
B. The derivative is the vector-valued function i + Di + k
The given function is u(t) = 2t³i + (t²-1)j - 8k, which represents a vector-valued function.
To compute the derivative of (19 + 21)u(t), we need to differentiate each component of the vector function with respect to t.
The scalar function (19 + 21) is a constant multiple, and when we differentiate a constant multiple of a vector function, we can simply differentiate each component of the vector function.
Taking the derivative of each component separately, we get:
d/dt (2t³i) = 6t²i
d/dt ((t²-1)j) = 2tj
d/dt (-8k) = 0
Putting the derivatives of each component together, we have:
(6t²i + 2tj + 0k) = 6t²i + 2tj
Hence, the derivative of the function (19 + 21)u(t) is the vector-valued function 6t²i + 2tj.
Therefore, the correct choice is:
B. The derivative is the vector-valued function i + Di + k
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14. Write the ratio of 2 cups of apple juice to 5 cups of orange juice the 3 different ways.
Answer:
1. 2:5
2. 5:2
3. 2,5
Step-by-step explanation:
Hope you have a great day
Micah has been learning about Scientific Notation in math class and is frustrated because he doesn’t understand why he needs to learn it. While working on his homework with his mother, she told Micah that Scientific Notation can be very useful in certain careers. What do you think she meant?
Answer:
Step-by-step explanation:
What is the image of (-10,-8) after a dilation by a scale factor of 1/2 centered at the
origin?
Answer:
(-5, -4)
Step-by-step explanation:
A dilation at the origin would just result with you multiplying the coordinates by the scale factor.
-10 * 1/2 and -8 * 1/2
Given the following perfect square trinomial, fill in the missing term. (2 points)
9x^2 +___+25
Answer:
30x
Step-by-step explanation:
missing must be 2×3x×5=30x
9x²+30x+25=(3x+5)²
Calculate the range, interquartile range, variance and standard deviation for the data of a set A and set B and answer each of the following question. = Set B= Set A = 1,2,3,4,5,6,7 1.2.3.4.5.6.50 (a) Which measure of dispersion for the data of set A and set B has significant difference? (b) Determine the most appropriate measure of dispersion to be used to measure the distribution of the data of set B
(a) The range has a significant difference between Set A and Set B.
(b) The interquartile range is a more appropriate measure for the data of Set B, considering the presence of outliers.
For Set A:
Range = 7 - 1 = 6
Interquartile Range = Q3 - Q1 = 5 - 2 = 3
Variance = 4.67
Standard Deviation = 2.16
For Set B:
Range = 50 - 1 = 49
Interquartile Range = Q3 - Q1 = 6 - 2 = 4
Variance = 205.14
Standard Deviation = 14.33
(a) The measure of dispersion that has a significant difference between Set A and Set B is the range.
(b) The most appropriate measure of dispersion to be used to measure the distribution of the data of Set B depends on the specific characteristics of the data. However, considering the presence of outliers (such as the value 50), a robust measure like the interquartile range may be more suitable for Set B.
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How many teams have played 20 times or more?
Answer:
3
Step-by-step explanation:
Joel says to Kevin, "Give me $100, and I shall become twice as rich as you."
Kevin replies, "Give me $10, and I shall become six times as rich as you."
How many dollars do Joel and Kevin have together?
4. (15 points) One of the eigenvalues of A = independent eigenvectors corresponding to λ = 2. −1 1 −1 !. is λ = 2. Find two linearly
Two linearly independent eigenvectors corresponding to the eigenvalue λ = 2 are v₁ = [-1, 0, 3] and v₂ = [0, 1, 1].
Given the matrix A = [−1 1 −1], one of the eigenvalues is λ = 2. We need to find two linearly independent eigenvectors corresponding to this eigenvalue.
To find the eigenvectors, we solve the equation (A - λI)v = 0, where A is the matrix, λ is the eigenvalue, I is the identity matrix, and v is the eigenvector.
In this case, the equation becomes:
(A - 2I)v = 0
Substituting the values, we have:
[−1 1 −1] - 2[1 0 0] [x] [0]
[y] = [0]
[z] [0]
Simplifying further:
[−3 1 −1] [x] [0]
[y] = [0]
[z] [0]
This gives us the following system of equations:
-3x + y - z = 0
y = 0
z = 0
From the second equation, we get y = 0. Plugging this into the first equation, we have -3x - z = 0, which simplifies to -3x = z.
Choosing a value for z, let's set z = 3. Then, -3x = 3, and solving for x gives x = -1.
Therefore, one eigenvector corresponding to the eigenvalue λ = 2 is v₁ = [-1, 0, 3].
To find the second linearly independent eigenvector, we can choose a different value for z. Let's set z = 1.
Again, from the equation -3x + y - z = 0, we have -3x + y - 1 = 0. By choosing x = 0, we get y = 1.
Thus, another eigenvector corresponding to λ = 2 is v₂ = [0, 1, 1].
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Find the value of the variables in the image above
Answer:
Step-by-step explanation:
Find the volume of the cone.
please help me.
Answer:
46.08
Step-by-step explanation:
the formula for finding the volume of the cone is: V = π r^2 h/3
Insert the information provided (2 because half the diameter is the radius)
and solve. Hope this helps!
The index rises 4.9% over the course of the day. What is the value of the index at the end of the day? Round your answer to the nearest hundred.
Answer: $70400
Step-by-step explanation:
Attached is the question:
Based on the information given in the question:
Value of Stock X = 5000 × $4.30 = $21500
Value of Stock Y = 2000 × $3.20 = $6400
Value of Stock Z = 8000 × $4.90 = $39200
Total Stock Value = $67100.
Since there's a 4.9% increase in value of index, the value of the index at end of the day will be:
= $67100 × (100% + 4.9%)
= $67100 × 104.9%
= $67100 × 1.049 =
= $70388
= $70400 approximately
Answer:
$70,400
Explanation:
Ap3x
2. Columbia Records unvelled the LP (a vinyl record) in the Waldorf Astoria on June 18, 1948,
In two fomats: 10 inches in diameter and 12 Inches in diameter. If the thickness of one
vinyl record is 0.112 in, then determine the difference in volumes between the 10 inch and
12 inch records.
Graph the function. f(x) = x+2+1 Plot four points on the graph of the function: the leftmost point and three 12 х 5 FO 8 - 5 -2 6 8 ID 12 10 -12
The graph should pass through the points (-5, -2), (6, 8), (12, 10), and (-12, -12), forming a diagonal line from the bottom left to the top right of the graph.
To graph the function f(x) = x + 2 + 1, we will plot four points on the graph.
Given the points: (-5, -2), (6, 8), (12, 10), and (-12, -12).
Plotting the points on a graph:
(-5, -2):
Starting from the origin (0,0), move 5 units to the left along the x-axis and 2 units downward along the y-axis. Plot the point (-5, -2).
(6, 8):
From the origin, move 6 units to the right along the x-axis and 8 units upward along the y-axis. Plot the point (6, 8).
(12, 10):
Move 12 units to the right along the x-axis and 10 units upward along the y-axis from the origin. Plot the point (12, 10).
(-12, -12):
Move 12 units to the left along the x-axis and 12 units downward along the y-axis from the origin. Plot the point (-12, -12).
Connecting the plotted points, we get a straight line. This line represents the graph of the function f(x) = x + 2 + 1.
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Which of the following is an example of a physical property?(55 points)
A. nail rusting
B. camp fire burning
C. Table salt melting
D. silver spoon tarnishing
2. Find measure of arc AB.
Find mAB
A) 68
B) 78
C) 88
D) 98
Answer:
C) 88
Step-by-step explanation:
so we are given a circle, and m<ACB is 44°. We need to find the measure of arc AB
<ACB is an inscribed angle (it is inside the circle), and it intercepts the arc AB
Inscribed angle theorem is a theorem that states the measure of an inscribed angle is half of the measure of the arc it intercepts
which also means that the measure of the intercepted arc is twice the measure of the inscribed angle (this is because of how algebra works)
which means mAB=2m<ACB (inscribed angle theorem)
mAB=2*44° (substitution)
mAB=88° (algebra)
therefore, your answer is C
Hope this helps!