The amount of time that students spend studying in the library in one sitting is normally distributed with a mean of 46 minutes and a standard deviation of 19 minutes. Hence the distribution of X is X ~ N (46, 19).
The amount of time students spend studying in the library in one sitting is normally distributed with a mean of 46 minutes and a standard deviation of 19 minutes. To represent the distribution of X, you can use the notation X ~ N (mean, standard deviation). In this case, X represents the time students spend studying in the library.Here mean =46 and standard deviation = 19Therefore the answer is X ~ N (46, 19)know more about mean and standard deviation here: https://brainly.com/question/26941429
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The orthogonal trajectories of s = 3a sin 0 is, where a is an arbitrary constant O 3 = csin Ота =ccos e O 73 = c cose T=csin e
Hi! To find the orthogonal trajectories of the given curve s = 3a sin θ, we first need to determine its differential equation by eliminating the arbitrary constant, a. The orthogonal trajectories should have slopes that are the negative reciprocal of the original curve's slopes.
1. Differentiate s with respect to θ:
ds/dθ = 3a cos θ
2. Solve for a:
a = (ds/dθ) / (3 cos θ)
3. Substitute the expression for a back into the original equation:
s = 3((ds/dθ) / (3 cos θ)) sin θ
4. Simplify:
s = (ds/dθ) tan θ
5. Find the orthogonal trajectories by taking the negative reciprocal of the original slope:
-1 = -ds/dθ / s
6. Rearrange to find the differential equation for the orthogonal trajectories:
ds/dθ = s
7. Integrate with respect to θ to find the orthogonal trajectories:
s(θ) = c * e^θ, where c is an arbitrary constant.
So, the orthogonal trajectories of the given curve s = 3a sin θ are s(θ) = c * e^θ.
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if bruce and bryce work together for 1 hour and 20 minutes, they will finish a certain job. if bryce and marty work together for 1 hour and 36 minutes, the same job can be finished. if marty and bruce work together, they can complete this job in 2 hours and 40 minutes. how long will it take each of them working alone to finish the job?
Bruce can finish the job alone in 5 hours, Bryce can finish the job alone in 8 hours, and Marty can finish the job alone in 10 hours.
Let's assume the job takes x hours for Bruce to complete alone, y hours for Bryce to complete alone, and z hours for Marty to complete alone.
From the first piece of information, we can create the following equation based on the work completed in 1 hour and 20 minutes (4/3 hours):
1/x + 1/y = 3/4
From the second piece of information, we can create the following equation based on the work completed in 1 hour and 36 minutes (8/5 hours):
1/y + 1/z = 5/8
From the third piece of information, we can create the following equation based on the work completed in 2 hours and 40 minutes (8/3 hours):
1/x + 1/z = 3/8
Solving these equations simultaneously, we can find that x = 5, y = 8, and z = 10.
Therefore, Bruce can finish the job alone in 5 hours, Bryce can finish the job alone in 8 hours, and Marty can finish the job alone in 10 hours.
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Use a graphing calculator to solve this:
The solution to the system of equations is given as follows:
(-1, 0.5).
How to solve the system of equations?The system of equations in the context of this problem is defined as follows:
y = -0.5x.y = 0.75x + 1.25.At the solution, the two systems have the same x-coordinates and y-coordinates, hence the value of x of the solution is obtained as follows:
-0.5x = 0.75x + 1.25.
-1.25x = 1.25
1.25x = -1.25
x = -1.25/1.25
x = -1.
Then the y-coordinate of the solution is given as follows:
y = -0.5(-1)
y = 0.5.
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Question 4 (1 point) In his Ted Talk, James Lyne presents the following statistic(s) in his TedX talk about malware and cybercrime. There are 30,000 new infected websites every day. 8 new internet users join every second. 250,000 new pieces of malware appear every day. All of the above. Question 2 (1 point) Why is traditional supply chain management (SCM) ineffective for e-commerce? It is based on manual processes and separation of functions It is based more on manufacturing, whereas e-commerce is mostly retail distribution E-commerce is gnerally more specialized and is not a good fit for traditional SCM It usually doesn't include e-procurement functions.
All of the above are statistics
Traditional supply chain management (SCM) is ineffective for e-commerce because it is based on manual processes and separation of functions.
4)
We have,
James Lyne mentions that there are:
- 30,000 new infected websites every day
- 8 new internet users join every second
- 250,000 new pieces of malware appear every day.
All the above are statistics.
2)
E-commerce is generally more specialized and requires a more integrated approach to supply chain management. Additionally, traditional SCM is based on manufacturing, whereas e-commerce is mostly retail distribution.
Finally, traditional SCM usually doesn't include e-procurement functions, which are essential for e-commerce supply chain management.
Traditional supply chain management (SCM) is ineffective for e-commerce because it is based on manual processes and separation of functions.
Thus,
All of the above are statistics
Traditional supply chain management (SCM) is ineffective for e-commerce because it is based on manual processes and separation of functions.
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rectangle wxyz is dilated by a scale factor of 3 3 to form rectangle w'x'y'z'. side z'w' measures 99 99. what is the measure of side zw
The measure of side ZW in rectangle WXYZ is 33.
It is mentioned that rectangle WXYZ is dilated by a scale factor of 3 to form rectangle W'X'Y'Z'. Side Z'W' measures 99. We need to find the measure of side ZW.
To find the measure of side ZW, we need to use the scale factor. Since the rectangle was dilated by a scale factor of 3, we can divide the measure of side Z'W' by the scale factor to find the measure of side ZW.
Identify the scale factor, which is 3.
Identify the measure of side Z'W', which is 99.
Divide the measure of side Z'W' by the scale factor: 99 ÷ 3 = 33.
So, the measure of side ZW in rectangle WXYZ is 33.
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Please just do question C(ii).
(a) Consider p(z) = z^3 + 2z^2 – 6z +1 when z € C. Prove that if zo is a root of p(z) then zo is also a root. (b) Prove a generalization of (a): Theorem: For any polynomial with real coefficients, if zo € C is a root, then zo is also a root. (c) Consider g(z) = z^2 – 2z: (i) Find the roots of g(z) and show that they satisfy the conclusion of the theorem in (b).
(ii) Explain why the theorem in (b) does not apply to g(z).
For part (c)(ii), we need to explain why the theorem in (b) does not apply to g(z).
The theorem in (b) states that for any polynomial with real coefficients, if zo € C is a root, then zo is also a root. However, g(z) = z^2 - 2z does not have real coefficients, as the coefficient of the z term is -2, which is not a real number.
Therefore, we cannot apply the theorem in (b) to g(z) since it does not satisfy the condition of having real coefficients. However, we can still find the roots of g(z) and show that they satisfy the conclusion of the theorem in (b) if we consider g(z) as a polynomial with complex coefficients.
To find the roots of g(z), we set g(z) equal to zero and solve for z:
z^2 - 2z = 0
z(z - 2) = 0
So the roots of g(z) are z = 0 and z = 2.
If we consider g(z) as a polynomial with complex coefficients, then we can apply the theorem in (b) and conclude that if z = 0 or z = 2 is a root of g(z), then it is also a root of g(z) with real coefficients. However, we cannot apply the theorem in (b) to g(z) directly since it does not have real coefficients.
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If z is a standard normal variable, find the probability. Round your answer to four decimal places. The probability that z lies between -0.55 and 0.55 O A. 0.9000 OB. -0.9000 O C. -0.4176 OD. 0.4176
The probability that z lies between -0.55 and 0.55 is 0.4176. So, the correct option is option OD. 0.4176.
To find the probability that z lies between -0.55 and 0.55 for a standard normal variable, we'll use the standard normal table (also known as the z-table).
Step 1: Look up the z-score of -0.55 in the z-table. This gives us the area to the left of -0.55, which is 0.2912.
Step 2: Look up the z-score of 0.55 in the z-table. This gives us the area to the left of 0.55, which is 0.7088.
Step 3: Subtract the area to the left of -0.55 from the area to the left of 0.55 to find the probability between the two z-scores: 0.7088 - 0.2912 = 0.4176.
Therefore, the probability that z lies between -0.55 and 0.55 for a standard normal variable is approximately 0.4176 (rounded to four decimal places).
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Suppose that a particular brand of 5 inch candles has an average life of 27 hours with a standard deviation of six hours. If all possible samples of 4 candles were selected in the average life of the samples was determined, what would the mean of the distribution of the sample means be?
5
3
4
27
The mean of the distribution of sample means would be 27 hours, which is the same as the average life of the candles.
This is because the sample means would be expected to be centered around the population mean.
The standard deviation of the distribution of sample means (also known as the standard error of the mean) can be calculated using the formula:
standard deviation of sample means = standard deviation of population / square root of sample size
In this case, the standard deviation of sample means would be:
6 / square root of 4 = 3
So the answer is 3.
So, the mean of the distribution of the sample means would be 3. Your answer: 3.
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Angle 6 is 60°.
What is the
measure of 42?
m42 = [?]°
Answer in degrees.
1/2 = [?]°
8/7
4/3
5/6=60°
Step-by-step explanation:
the intersection angles between a line and 2 parallel lines are the same for each parallel line (otherwise they would not be parallel).
and the intersection angles on one side of a line are the same as in the other side - just left-right mirrored.
so,
angle 2 = angle 4 = angle 6 = angle 8 = 60°
Show that the average degree of a vertex in the triangulation is strictly less than 6
In any planar triangulation, there are always fewer edges than three times the number of vertices, so the average degree of a vertex must be less than 6.
Let V stand for the triangulation's collection of vertices and E for its set of edges. As each edge adds two degrees to the total degree count, the triangulation's total degree count is equal to twice the number of edges. Thus,
Σdeg(v) = 2|E| where deg(v) is the degree of vertex v and |E| is the number of edges in the triangulation.
|E| = (3/2) |T|, number of triangles in the triangulation is |T| .
Furthermore, we know that the sum of the degrees of the vertices is equal to 3 times the number of triangles, since each triangle contributes 3 to the total degree count:
Σdeg(v) = 3|T|
Putting these equations together, we have:
Σdeg(v) = 3|T| = (3/2) * 2|E| = 3|E|
Dividing both sides by the number of vertices, n, we obtain:
(1/n) Σdeg(v) = 3/ n * |E|
Thus, the average degree of a vertex in the triangulation is strictly less than 6, since the average degree of a vertex in the corresponding graph is at most 2 (since each triangle is incident to at most 3 other triangles).
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Assume that adults have 10 scores that are normally distributed with a man of 101.1 and a standard deviation of 17. Find the probablity that a randomly selected adult has an IQ greater than 134.4
The probability that a randomly selected adult from this group has an IQ greater than 134.4 is ?
The probability that a randomly selected adult has an IQ greater than 134.4 is 0.025.
We have,
To solve this problem, we need to standardize the IQ score using the
z-score formula:
z = (x - μ) / σ
where x is the IQ score, μ is the mean, and σ is the standard deviation.
Substituting the values we have:
z = (134.4 - 101.1) / 17
z = 1.96
We can then use a standard normal distribution table or a calculator to find the probability of a z-score being greater than 1.96.
Using a standard normal distribution table, we find that the probability of a z-score being greater than 1.96 is approximately 0.025.
Therefore,
The probability that a randomly selected adult has an IQ greater than 134.4 is 0.025.
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Dakota earned $15.75 in interest in Account A and $28.00 in interest in Account B after 21 months. If the simple interest rate is 3% for Account A and 4% for Account B, which account has the
greater principal? Explain.
The account that has the greater principal is account B.
Which account has the greater principal?
Simple interest is a linear function of the amount invested (the principal), the interest rate and the duration of the investment.
The formula that can be used to determine simple interest is:
Interest = principal x time x interest rate
Principal = interest / (time x interest rate)
Principal in account A = $15.75 / (0.03 x (21/12)) = $300
Principal in account B = $28 / (0.04 x (21/12)) = $400
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Describe all numbers x that are at a distance of 3 from the number 10. Express this using absolute value notation.
The numbers that are at a distance of 3 from the number 10 are 7 and 13.
To describe all numbers x that are at a distance of 3 from the number 10, we can use the absolute value notation. The distance between two numbers is given by the absolute value of their difference. So, the numbers x that are 3 units away from 10 can be expressed as:
| x - 10 | = 3
This means that the absolute value of the difference between x and 10 is equal to 3. To find the values of x that satisfy this equation, we can solve for x as follows:
x - 10 = 3 or x - 10 = -3
Adding 10 to both sides of each equation, we get:
x = 13 or x = 7
Therefore, the numbers that are at a distance of 3 from the number 10 are 7 and 13.
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Ekipler e Ödevler (19) Using Euclidean algorithm, find the multiplicative inverses of 41 and 43 in Z/60Z. How many elements does (Z/60Z)* contain?
(Z/60Z)* contains 128 elements.
To find the multiplicative inverse of 41 in Z/60Z, we need to find an integer x such that 41x ≡ 1 (mod 60). Using the Euclidean algorithm:
60 = 1 × 41 + 19
41 = 2 × 19 + 3
19 = 6 × 3 + 1
Working backwards, we have:
1 = 19 - 6 × 3
= 19 - 6(41 - 2 × 19)
= 13 × 19 - 6 × 41
Therefore, 41 has a multiplicative inverse of 13 in Z/60Z. Similarly, we can find that 43 has a multiplicative inverse of 7 in Z/60Z.
The elements of (Z/60Z)* are the integers in the range [1, 60] that are relatively prime to 60. To count them, we can use the formula for Euler's totient function:
φ(60) = φ(2^2) × φ(3) × φ(5) = 16 × 2 × 4 = 128
Therefore, (Z/60Z)* contains 128 elements.
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(a) How many forks should Kathy plan to
have if she expects there will be 20
guests? Show how you arrived at your
answer.
Answer:
Step-by-step explanation:
Kathy would like to plan for fiver more guests than she expects to come.
So we have to set the table for 25 guests.
Each guest will need 2 forks.
25x2=50 forks
What is the radius of each figure described? a. A sphere with a volume of 500*3. 14/3 cm^3 b. A cylinder with a height of 3 and a volume of 147*3. 14 c. A cone with a height of 12 and a volume of 16*3. 14
The radius of each shape, sphere, cylinder and cone are 5, 7 and 2 cm respectively.
The formula for the volume of sphere is -
V = 4/3πr³, where V refers to volume and r is the radius. So, 500 × 3.14/3 = 4/3πr³
We know that π is 3.1 and both π and 1/3 are common on both side thus will cancel out each other.
r³ = 500/4
r³ = 125
r = [tex] \sqrt[3]{125} [/tex]
r = 5 cm
The volume of cylinder is given by the formula -
V = πr²h
147 × 3.14 = 3.14 × r² × 3
r² = 147/3
r = ✓49
r = 7
The volume of cone is -
V = πr²h/3
16 × 3.14 = 3.14 × r² × 12/3
r² × 12 = 16 × 3
r² = (16 × 3)/12
r² = 4
r = ✓4
r = 2
Hence, the radius of sphere, cylinder and come are 5, 7 and 2 cm.
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In a high school, 250 students take math and 50 students take art. If there are 280 students enrolled in the school and they all take at least one of these courses, how many students take both math and art?
If 50 students take math and 50 students take art. If there are 280 students enrolled in the school and they all take at least one of these courses then 20 students take both math and art
let A be the set of students taking math, and let B be the set of students taking art.
We know that:
|A| = 250
|B| = 50
|A ∪ B| = 280
We want to find |A ∩ B|, the number of students taking both math and art.
Using the formula above, we can solve for |A ∩ B|:
|A ∩ B| = |A| + |B| - |A ∪ B|
|A ∩ B| = 250 + 50 - 280
|A ∩ B| = 20
Therefore, 20 students take both math and art.
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A boy who is flying a kite lets out 300 feet of string which makes an angle of 52 with the ground. Assuming that the string is stretched taut, find, to the nearest foot, how high the kite is above ground.
The height of the kite above the ground is approximately 433.76 feet. Rounded to the nearest foot, the answer is 434 feet.
We can use trigonometry to solve this problem. Let h be the height of the kite above the ground. Then, the opposite side of the triangle formed by the kite string and the ground is h, and the adjacent side is 300 feet. The angle between the ground and the kite string is 52 degrees.
We can use the tangent function to find the value of h:
[tex]tan(52) = h/300[/tex]
Multiplying both sides by 300, we get:
h = 300 t[tex]an(52)[/tex]
Using a calculator, we find:
h ≈ 433.76 feet
Therefore, the height of the kite above the ground is approximately 433.76 feet. Rounded to the nearest foot, the answer is 434 feet.
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Ricardo calculates a line of best fit for a data set with integer x-values 1 through 6. Complete the sentence with the correct word.
Using a line of best fit with the equation y = –3x + 21 to predict the value of y when x = 10 is an example of
To predict the value of y when x=10 is an example of Extrapolation. So, the correct answer is (b) extrapolation.
Extrapolation involves using a mathematical model, such as a line of best fit, to make predictions outside the range of the original data.
In this case, using the equation y = –3x + 21 to predict the value of y when x = 10 is an example of extrapolation because 10 is outside the range of the original x-values.
Using a line of best fit with the equation y = -3x+21 to predict the value of y when x = 10 is an example of extrapolation in statistics.
Extrapolation involves using a mathematical model, such as a line of best fit, to make predictions outside the range of the original data.
Ricardo's next step to construct the circumscribed circle for △XYZ would be to construct the perpendicular bisector of YZ
In this case, constructing the perpendicular bisector of YZ would give Ricardo the center of the circumscribed circle, which is equidistant from the three vertices of the triangle.
Complete Question:
Ricardo calculates a line of best fit for a data set with integer x-values 1 through 6. Complete the sentence with the correct word.
Using a line of best fit with the equation y = –3x + 21 to predict the value of y when x = 10 is an example of
a) correlation
b) extrapolation
c) causation
d) intrapolation
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Mark wanted to buy a new car for $43,500. The salesman told him that with rebate and discounts he could lower the price by 15%. What is the sale price of the car? What is the final cost of the car if Kentucky sales tax of 6% is added ?
The sale price of the car is $36,975 and the final cost of the car including 6% sales tax is $39,193.50.
The sale price of the car after a 15% discount can be calculated as:
Sale Price = Original Price - Discount
Sale Price = $43,500 - 0.15($43,500)
Sale Price = $43,500 - $6,525
Sale Price = $36,975
The final cost of the car including 6% sales tax can be calculated as:
Final Cost = Sale Price + Sales Tax
Final Cost = $36,975 + 0.06($36,975)
Final Cost = $36,975 + $2,218.50
Final Cost = $39,193.50
Therefore, the sale price of the car is $36,975 and the final cost of the car including 6% sales tax is $39,193.50.
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please help! I have faith in you guys!
The probabilities and the expected values are calculated below
Evaluating the probabilities and the expected valuesNext cereal box wll contain blue or yellow
Here, we have
Yellow or blue = 15 + 5 = 20
Total = 50
So, we have
P(Yellow or blue) = 20/50
P(Yellow or blue) = 2/5
Arrival time before 7:30 am
Here, we have
Arrival time before 7:30 am = 7
Total time = 20
So, we have
P(Arrival time before 7:30 am) = 7/20
Team least likely
Convert the probabilities to decimal
So, we have
Nets = 0.67
Rockets = 0.5
Bucks = 0.8
Warriors = 0.375
This means that the team least likely to play in the championship game is 0.375
Section 7 in the game
Here, we have
P(7) = 35/250
In 150 times, we have
n(7) = 35/250 * 150
n(7) = 21
So, the number of times is 21
Expected students to eat chicken nuggets
Here, we have
P(Chicken) = 14/40
In 840 students, we have
n(Chicken) = 14/40 * 840
n(Chicken) = 294
Hence, the expected number of students to eat chicken nuggets is 294
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What is radical form (5x)½
Answer:
[tex] {(5x)}^{ \frac{1}{2} } = \sqrt{5x} [/tex]
The distance of a swinging pendulum from its resting position is given by the function d(t)=
5.5cos(8t), where the distance is in inches and the time is in seconds. Once released, how
long will it take the pendulum to reach its resting position? Round your answer to the near-
est hundredth.
It will take the pendulum approximately 0.20 seconds to reach its resting position.
We have,
The resting position of the pendulum is when d(t) = 0.
So we need to solve the equation:
5.5cos(8t) = 0
We know that cos(0) = 1 and that cos(π) = -1, and that the cosine function has a period of 2π.
Therefore, the first time the pendulum will reach its resting position is at
t = 0, and then it will reach its resting position again at t = π/8.
However, we are interested in the time it takes for the pendulum to go from its starting position to its resting position, which is half of its period.
So the time it takes for the pendulum to reach its resting position is:
t = π/8 / 2
t = π/16
Using a calculator, we can approximate this value to the nearest hundredth:
t = 0.20 seconds
Therefore,
It will take the pendulum approximately 0.20 seconds to reach its resting position.
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Which expression is equivalent to 3218y = 8√3y, if y+0?
O A. 12V/2y²
OB. 46
O c. 4√/15y
O D. 46y
The equivalent expression to 3218y = 8√3y is 4√(15) / 15y when y is not equal to zero. Option C is the correct answer.
To find an equivalent expression to 3218y = 8√3y when y is not equal to zero, we can start by dividing both sides of the equation by 8y, giving us:
3218y / 8y = 8√3y / 8y
Simplifying the right-hand side, we get:
3218 / 8 = √3
Squaring both sides, we get:
(3218 / 8)² = 3
Simplifying the left-hand side, we get:
130071.25 = 3
Dividing both sides by 3, we get:
y = 4√(15) / 15
Therefore, the expression that is equivalent to 3218y = 8√3y when y is not equal to zero is an option (C) 4√(15) / 15y. Option (D) 46y is not equivalent to the original expression because it does not involve the square root of 3. Option (A) 12V / 2y² and option (B) 46 are also not equivalent to the original expression because they involve different values and operations than those in the original expression.
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The following polygons are similar find the scale factor of the small figure to the large figure 1-2
Answer:
1.5 and 4
Step-by-step explanation:
the scale factor is the ratio of corresponding sides, image to original.
1
scale factor = [tex]\frac{DF}{AC}[/tex] = [tex]\frac{21}{14}[/tex] = [tex]\frac{3}{2}[/tex] = 1.5
2
scale factor = [tex]\frac{8}{2}[/tex] = 4
5. A recent investigation into a rare blood disorder
found 3 out of 500 people had genetic markers
for it.
(a) Test at 75% confidence if the percentage of people
with this genetic marker is under 1%.
The null hypothesis and conclude that there is sufficient evidence to support the claim that the percentage of people with genetic markers is less than 1%.
To test whether the percentage of people with genetic markers is less than 1%, we can use a one-tailed hypothesis test with the following null and alternative hypotheses:
H0: p >= 0.01
Ha: p < 0.01
where p is the true proportion of people with the genetic markers.
Using the sample proportion, p-hat = 3/500 = 0.006, and the sample size, n = 500, we can calculate the test statistic z:
z = (p-hat - p) / sqrt(p * (1 - p) / n)
= (0.006 - 0.01) / sqrt(0.01 * 0.99 / 500)
= -1.434
At 75% confidence, the critical value for a one-tailed test is -1.15 (using a standard normal distribution table or calculator). Since our calculated test statistic (-1.434) is less than the critical value (-1.15), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the percentage of people with genetic markers is less than 1%.
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what 2 numbers equal -884
Answer:
-883 - 1
Step-by-step explanation:
Use the range rule of thumb to identify the values that are significantly low, the values that are signficantly high, and the values that are neither significantly low nor significantly high. A test is used to assess readiness for college. In a recent year, the mean test score was 21.6 and the standard deviation was 5.4. Identify the test scores that are significantly low or significantly high. What test scores are significantly low? Select the correct answer below and fill in the answer box(es) to complete your choice. A. Test scores that are between and (Round to one decimal place as needed. Use ascending order.) B. Test scores that are less than (Round to one decimal place as needed.) C. Test scores that are greater than (Round to one decimal place as needed.)
Previous question
Using the range rule of thumb:
A. Test scores that are between 10.8 and 32.4 (rounded to one decimal place) are neither significantly low nor significantly high.
B. Test scores that are less than 10.8 (rounded to one decimal place) are significantly low.
C. Test scores that are greater than 32.4 (rounded to one decimal place) are significantly high.
The range rule of thumb states that we can identify significantly low or high values by looking at data points that are more than two standard deviations away from the mean.
In this case, the mean test score is 21.6 and the standard deviation is 5.4.
To find test scores that are significantly low, we need to subtract two standard deviations from the mean:
21.6 - (2 x 5.4) = 10.8
Therefore, test scores that are significantly low are less than 10.8. The answer is B. Test scores that are less than 10.8.
To find test scores that are significantly high, we need to add two standard deviations to the mean:
21.6 + (2 x 5.4) = 32.4
Therefore, test scores that are significantly high are greater than 32.4. The answer is C. Test scores that are greater than 32.4.
Test scores that are neither significantly low nor significantly high are between 10.8 and 32.4. The answer is A. Test scores that are between 10.8 and 32.4.
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Solve
a. 0.00032x500 / 2,000,000
___ x 10 ^--
b. 15,000 x 0.0000007 / 0.005
___ x 10 ^--
The solution of the a) part is 8 x 10⁻⁸ and the solution to the b) part is 2.1 x 10⁰.
Simplify simply means to make an expression simple.
In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form.
a. To get the solution of 0.00032 x 500 / 2,000,000, follow these steps:
1. Multiply 0.00032 by 500, which equals 0.16.
2. Divide 0.16 by 2,000,000, which equals 8x10⁻⁸.
So, 0.00032x500 / 2,000,000 = 8 x 10⁻⁸.
b. To solve 15,000 x 0.0000007 / 0.005, follow these steps:
1. Multiply 15,000 by 0.0000007, which equals 0.0105.
2. Divide 0.0105 by 0.005, which equals 2.1.
So, 15,000 x 0.0000007 / 0.005 = 2.1 x 10⁰, since 10⁰ equals 1, and 2.1 remains the same.
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Let a, b, c ∈ Z be arbitrary with 3 | a, 3 | b, and c
≡ 2 (mod 3). Prove ax + by ≡ c (mod 3) has no solution.
The solution for the equation ax + by ≡ c (mod 3) does not exist. Hence, it has no solution.
We need to prove that the equation ax + by ≡ c (mod 3) has no solution.
Since 3 | a and 3 | b, we know that a ≡ 0 (mod 3) and b ≡ 0 (mod 3).
Now let's look at the left side of the equation ax + by. Since a and b are both divisible by 3, their product with any integers x and y will also be divisible by 3.
Therefore, ax + by will always be divisible by 3 and can be written as ax + by ≡ 0 (mod 3).
However, we know that c ≡ 2 (mod 3), which means that c is not divisible by 3. Therefore, we can conclude that ax + by can never be congruent to c (mod 3), as their remainders when divided by 3 are different.
In other words, the equation ax + by ≡ c (mod 3) has no solution.
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