The sampling technique used in this scenario is stratified random sampling. Stratified random sampling is a useful technique for obtaining a representative sample from a population with identifiable subgroups, and can improve the validity and generalizability of survey results.
Stratified random sampling involves dividing the population into homogeneous groups, or strata, based on a specific characteristic, and then taking a random sample from each stratum. In this case, the population of gym members was divided into men and women, which are two distinct and easily identifiable strata. A simple random sample was then taken from each stratum to obtain a representative sample of both genders.
The use of stratified random sampling can increase the precision and accuracy of the sample by ensuring that each stratum is represented proportionally in the sample. This technique is commonly used when the population of interest exhibits a significant characteristic that may impact the outcome of the survey. For example, if the survey was investigating the effectiveness of a new exercise program, it would be important to ensure that both men and women were represented equally in the sample, as their physiological differences may impact their response to the program.
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find √49. A. 14 B. 9 C. 7 D. 8
Answer:
C. 7 because 7 x 7 = 49
Does the set of numbers 20,25,15 represent a right triangle ?
Answer:
YES - it is a right triangle, the Pythagorean Theorem is true for its sides.
20^2+15^2=25^2
400+225= 625
Hope this helps! =D
Step-by-step explanation:
What is the area for the triangle shown below?
Step-by-step explanation:
Base...from - 7 to + 4 = 11 units
Height from -4 to +5 = 9 units
Area of a traingle = 1/2 * base * height = 1/2 (11)(9) = 49.5 units^2
if you select three sticks, each of random length (between 0 and 1), what is the probability of being able to form a triangle with them?
The probability of being able to form a triangle with three sticks of random length is 1/2 or 50%.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.
The probability of being able to form a triangle with three sticks of random length can be found using geometric probability.
First, we can assume that the length of the first stick is x, where 0 ≤ x ≤ 1. The second stick can be any length y such that 0 ≤ y ≤ 1. The third stick can be any length z such that 0 ≤ z ≤ 1.
For the three sticks to form a triangle, they must satisfy the triangle inequality, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we have three cases to consider:
x + y > z
x + z > y
y + z > x
We can graph these three inequalities on a coordinate plane, where x and y are the lengths of two sides of the triangle, and the third side is represented by the area below the line.
The area of the triangle formed by the inequalities is 1/2, and the total area of the square representing the possible lengths of the sticks is 1.
Therefore, the probability of the three sticks forming a triangle is the ratio of the area of the triangle to the area of the square:
P(triangle) = area of triangle / area of square = (1/2) / 1 = 1/2
Hence, the probability of being able to form a triangle with three sticks of random length is 1/2 or 50%.
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Joy bought 8 bags of bagels Each bag had 8 bagels. How many bagels did Joy buy?
Find the missing side of each triangle
By Pythagorean theorem, the missing sides of right triangles are listed below:
Case 1: x = 6 cm
Case 2: x = 12 ft
Case 3: x = 4 yd
Case 4: x = 9 in
Case 5: r = 40 mi
Case 6: r = 35 cm
Case 7: x = 15 cm
Case 8: r = 30 in
Case 9: x = 24 km
Case 10: r = 37 km
How to determine the missing length of a right triangle
In this problem we find ten cases of right triangles, whose missing sides can be determine by using Pythagorean theorem:
r² = x² + y²
Where:
r - Hypotenusex, y - LegsNow we proceed to determine the missing side for each case:
Case 1
x = √(10² - 8²)
x = 6 cm
Case 2
x = √(13² - 5²)
x = 12 ft
Case 3
x = √(5² - 3²)
x = 4 yd
Case 4
x = √(15² - 12²)
x = 9 in
Case 5
r = √(32² + 24²)
r = 40 mi
Case 6
r = √(21² + 28²)
r = 35 cm
Case 7
x = √(17² - 8²)
x = 15 cm
Case 8
r = √(24² + 18²)
r = 30 in
Case 9
x = √(26² - 10²)
x = 24 km
Case 10
r = √(35² + 12²)
r = 37 km
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Find T8, T9, and T10 for each of the following sequences: (a) 5,8,11,14....
Answer:
26, 29, 32
Step-by-step explanation:
Each term is 3 more than the previous term.
5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, ...
Find a formula for the number of ways to seat r of n people around a circular table, where seatings are considered the same if every person has the same two neighbors without regard to which side these neighbors are sitting on.
The formula for the number of ways to seat r of n people around a circular table is given by (n-1) choose (r-1), where "choose" denotes a binomial coefficient.
When we arrange the people around a table, we can fix one person's position, for instance, at the top of the table. Then, we can arrange the other (n-1) people in a line, and there are (n-1) choose (r-1) ways to pick r-1 people from the remaining (n-1) to sit with the fixed person. This is because we are essentially choosing r-1 positions in a line to be filled by people, and there are (n-1) positions to choose from.
Since the table is circular, there is only one way to rotate the arrangement, which gives us (n-1) different arrangements for each arrangement of the chosen r people. Therefore, the total number of arrangements is (n-1) choose (r-1).
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what is true about the slope of the line segment between points G and H and the slope of the line segment between points G and I refer to the graph bellow
A. the slope has different signs
B.the slopes are the same because the small triangle and the large triangle are similar
C.the slopes are different because the triangles are different sizes
D.it is not possible to determine the slopes from the gragh
The statement that is true about the slope of both line segments is: "B. the slopes are the same because the small triangle and the large triangle are similar."
What is the Slope of a Line?The Slope of a line is simply the ratio of the vertical distance over the horizontal distance along the line, which is calculated as: m = change in y / change in x or rise / run of the line. Also, note that the corresponding sides of two triangles will have the same slope.
Slope of line segment GH (m) = rise/run = -2/1 = -2
Slope of line segment HI (m) = rise/run = -4/2 = -2
This means that the slope of the hypotenuse of both triangles are the same because they are similar. The answer is: "B. the slopes are the same because the small triangle and the large triangle are similar."
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ind the unit tangent vector t(t) at the point with the given value of the parameter t. r(t) = 5te−t, 10 arctan(t), 10et , t = 0
We need to find the d/dt of the curve, then evaluate at t=0, and finally normalize the result to get the unit tangent vector. The derivative can be found using the chain rule, and after putting t=0, we get the point (0, 0, 10). The magnitude of this vector is 10, so the unit tangent vector is (0, 0, 1).
Explanation:
The unit tangent vector T(t) is defined as the derivative of the position vector r(t), divided by its magnitude. In other words, T(t) = r'(t)/|r'(t)|. To find the derivative of the curve r(t), we need to use the chain rule, as follows:
r'(t) = (5e^(-t) - 5te^(-t), 10/(1+t^2), 10e^t)
Now, we can evaluate r'(t) at t=0 to get the tangent vector at that point:
r'(0) = (5, 10, 10)
The magnitude of r'(0) is given by:
|r'(0)| = sqrt((5)^2 + (10)^2 + (10)^2) = 10sqrt(3)
Therefore, the unit tangent vector at t=0 is:
T(0) = r'(0)/|r'(0)| = (5/sqrt(3), 10/sqrt(3), 10/sqrt(3))
However, this vector can be simplified to:
T(0) = (0, 0, 1)
since the first two components are zero and the third component is equal to 1. This is the final answer for the unit tangent vector at the point where t=0.
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The ordered pairs below represent a relation between x and y
(-3,1) (-2,3) (-1,5) (0,7) (1,9) (2,11)
Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.
The ordered pairs are given as:
(-3,1), (-2,3), (-1,5), (0,7), (1,9), (2,11)
Now, First, look at the values of the abscissas: -3, -2, -1, 0, and 1.
The values form an arithmetic sequence with common difference of 1.
On the other hand the values of the ordinates: 1, 3, 5, 7, and 9 also form an arithmetic sequence with common difference of 2.
Since the coordinates form arithmetic sequences
Hence, From the ordered pair above:
We can see that, as x increases by 1, the value of y increases by 2
The above is a property of a linear function
Hence, the true statement is (c)
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Complete question is,
The ordered pairs below represent a relation between x and y. (-3,1), (-2,3), (-1,5), (0,7), (1,9), (2,11). Could this set of ordered pairs have been generated by a linear function?. A) Yes, because the distance between consecutive x-values is constant. B) No, because the distance between consecutive y-values is different than the distance between consecutive x-values. C) Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it. D) No, because the y-values decrease and then increas
on a wechslet iq test test, if i recieved a score of 125 in what standard deviation would my score fall
The Wechsler IQ test is scored with a mean of 100 and a standard deviation of 15. Therefore, a score of 125 falls 1.67 standard deviations above the mean. This is considered a very high score, as it falls within the top 5% of the population.
The standard deviation range in which your score of 125 on the Wechsler IQ test falls, follow these steps:
1. Identify the mean and standard deviation for the Wechsler IQ test. The mean (average) is 100, and the standard deviation is 15.
2. Calculate the range for each standard deviation:
- 1 standard deviation above the mean: 100 + 15 = 115
- 2 standard deviations above the mean: 100 + (15 * 2) = 130
3. Compare your score (125) to these ranges. Since your score is between 115 and 130, it falls within 1 and 2 standard deviations above the mean.
In conclusion, on a Wechsler IQ test, if you received a score of 125, your score would fall between 1 and 2 standard deviations above the mean.
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20 POINTS
What is the rate of change of the equation f(x) = ¯x² + 6x + 5 for the interval 0≤x≤ 3?
[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ f(x)= x^2+6x+5 \qquad \begin{cases} x_1=0\\ x_2=3 \end{cases}\implies \cfrac{f(3)-f(0)}{3 - 0} \\\\\\ \cfrac{[(3)^2+6(3)+5]~~ - ~~[(0)^2+6(0)+5]}{3}\implies \cfrac{27}{3}\implies \text{\LARGE 9}[/tex]
If a bivariate correlational study fails to use a random sample, it should not cause us to automatically reject the association?
When conducting a bivariate correlational study, it is important to use a random sample to ensure that the results are generalizable to the larger population.
However, if a random sample is not used, it does not necessarily mean that the association should be automatically rejected. There are several reasons why a random sample may not have been used in a correlational study. For example, the researcher may have had limited access to a specific population or may have chosen to use a convenience sample for practical reasons. In these cases, it is important to consider the potential limitations and biases in the sample. Additionally, it is possible to adjust for some of these limitations through statistical techniques such as weighting or stratification. These techniques can help to ensure that the results are more representative of the larger population, even if a random sample was not used. Overall, while a random sample is preferred in bivariate correlational studies, it is not always feasible or practical. As such, it is important to carefully consider the limitations of the sample and to use appropriate statistical techniques to account for any potential biases. Ultimately, the validity of the association should be evaluated based on the strength of the evidence and the quality of the study design, rather than solely on the use of a random sample.
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Which study would produce results that are skewed by bias?
A. A study of standardized test scores of high school students based on data collected across the country.
B. A study of the interest in a town library renovation based on a random survey of 500 residents.
C. A study of the average length of earthworms based on data collected across the world
D. A study of the popularity of a new sneaker conducted by the sneaker manufacturer
The required, D. A study of the popularity of a new sneaker conducted by the sneaker manufacturer is more likely to produce results that are skewed by bias.
This is because the sneaker manufacturer has a vested interest in promoting the new sneaker and may use biased methods to ensure that the study produces favorable results. For example, the manufacturer may selectively sample individuals who are more likely to be interested in the sneaker or use leading questions to bias the responses in favor of the sneaker. In contrast, the other studies listed are less likely to be influenced by bias because they rely on random sampling or objective measurements.
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find integral from 2^(x) t dt (the answer is a function of x).
The integral of 2^(x) t dt is: (2^(x) t^2)/(ln 2) + C where C is the constant of integration.
To evaluate this integral, we can use the power rule of integration, which states that the integral of x^n is (x^(n+1))/(n+1), where n is any real number except for -1. In this case, we have a product of 2^(x) and t, so we use the product rule of integration, which states that the integral of f(x)g(x)dx is f(x)∫g(x)dx + g(x)∫f(x)dx. We let f(x) = 2^(x) and g(x) = t, so that ∫g(x)dx = (t^2)/2, and we have:
∫2^(x) t dt = f(x)∫g(x)dx = 2^(x) (t^2)/2 + C
We then simplify this expression by multiplying the second term by ln 2/ln 2, which gives:
(2^(x) t^2)/(ln 2) + C
This is the final answer.
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suppose there is a 7-approxmiation algorithm for the general traveling salesman problem. then there exists a polynomial time solution for the 3-sat problem. True/False
The statement is true. To understand why, we need to look at the relationship between the traveling salesman problem (TSP) and the 3-satisfiability problem (3-SAT).
The TSP is a well-known NP-hard problem, which means that there is no known algorithm that can solve it in polynomial time. On the other hand, 3-SAT is also an NP-hard problem, but it is known to be solvable in polynomial time by using algorithms such as the Davis-Putnam-Logemann-Loveland (DPLL) algorithm.
Now, if there exists a 7-approximation algorithm for the TSP, it means that we can find a solution that is at most 7 times the optimal solution. This is a significant improvement over not having any polynomial time algorithm at all. In fact, there are many approximation algorithms for the TSP that are used in practice, such as the Christofides algorithm and the Lin-Kernighan heuristic. The connection between the TSP and 3-SAT comes from the fact that we can reduce the TSP to a special case of 3-SAT known as the Hamiltonian cycle problem. This means that if we can solve the TSP using a 7-approximation algorithm, we can also solve the Hamiltonian cycle problem using the same algorithm.
In summary, if there exists a 7-approximation algorithm for the TSP, then there exists a polynomial time solution for the 3-SAT problem. This is because the TSP can be reduced to the Hamiltonian cycle problem, which in turn can be reduced to 3-SAT. However, it is worth noting that the constant factor of 7 in the approximation algorithm for the TSP may be very large, and may not be practical for solving large instances of 3-SAT.
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26. How many 2'/k stamps can be bought for N5.28 (a) 15 (b)105 (c)201 (d)310 (e)1312
Using division operation and unit conversion, the number of 2k stamps that can be bought for N5.28 is 264.
What is division operation?Division operation and multiplication operation are two of the mathematical operations used in unit conversions.
Division operation involves the dividend divided by the divisor, resulting in the quotient.
The total amount spend for stamps = N5.28
N1 = 100k
N5.28 = 528k (N5.28 x 100)
The unit price per stamp = 2k
2k = N0.02 (2 ÷ 100)
The number of stamps = 264 (528 ÷ 2) or (N5.28 ÷ N0.02)
Thus, one can comfortably buy 264 stamps of 2k each with N5.28, based on division operation for unit conversions.
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Kelly spent the following amounts for school lunches last week: $2.09, $1.82, $1.59, $1.73. How much did her lunches cost in all?
The height of a right pyramid with a square base is 4 feet. The length of a side of the base of the pyramid is 6 feet. What is the slant height, s , of the pyramid?
A right pyramid with a square base. The length of a side of the base of the pyramid is 6 feet. A right triangle is created by the height, the slant height s, and half of the base.
A.
5
2
52
feet
B.
52 feet
C.
5 feet
D.
25 feet
* The height of the pyramid is 4 feet.
* The length of a side of the square base is 6 feet.
* We need to find the slant height, s.
Let's draw a diagram:
Height (4 ft)
│ │
│ │
│ │
│ │
│ │
│ s │
│ │
│ │
│ │
│ 3 ft │
└
In the figure, AXYZ AMNL.
Find m/Y.
X
33⁰
Y
m/Y =
L
12
124°
Z
N
8
M
Answer:
Without additional information or a diagram, it is not possible to accurately determine the value of m/Y.
Simple interest on a sum of
money at the end of 5 years is
4/5 of the sum itself. Find the
rate per cent p.a.
Answer:16%
Step-by-step explanation:
Solve for x the options are: 5, 8, 10, and 14
Answer:
D) 5Step-by-step explanation:
[tex]8/10=4/5[/tex] [tex]so[/tex] [tex]20/5x=4/5[/tex]
[tex]5x=25, x=5[/tex]
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Line ST and point V are shown on the graph.
On a coordinate plane, line S T goes through (negative 5, 0) and (5, 2). Point V is at (0, negative 2).
Line VW is to be drawn on the graph such that it is perpendicular to line ST. If the coordinates of point W are (−1, y), what is the value of y?
−7
−5
2
3
Answer:
3
Step-by-step explanation:
y + 2 = -5x
Substituting x = -1, we get:
y + 2 = 5
y = 5 - 2 = 3
Therefore, the value of y is 3. Answer: 3.
determine the domain on which the following graph of f(x) is positive
Step-by-step explanation:
Between x = -5 to x = -1 the graph is positive ( > 0) at -5 and -1 it is EQUAL to zero...so those numbers are not included
(-5,-1)
The domain on which the graph of a function is positive involves finding the x-values for which the function's output is greater than zero. This can be visualized by identifying where on the graph the curve is situated above the x-axis.
Explanation:The domain on which the graph of f(x) is positive is the set of x-values for which the y-values (the outputs of the function) are greater than zero.
So, for each point (x, y) on the graph, if y is larger than zero that means f(x) is positive. To find out where this is the case, simply look at the graph and identify where the curve lies above the x-axis. These will be the x-values that make f(x) positive.
For example, if the plot of the function is above the X-axis between interval a and b, then the domain on which f(x) is positive is the interval (a, b).
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Rational numbers a, b, and c are shown on
the following number line.
a b
0 c
Note that the distance between a and b is the
same as the distance between 0 and c.
Make a true statement by placing the letters
a, b, and c into the equation.
The distances between a and b and between 0 and c are equal, which can be expressed mathematically using Absolute value notation as |b - a| = |c - 0|.
One possible true statement that can be made using the letters a, b, and c from the given number line is:|b - a| = |c - 0|
This statement represents the fact that the distance between a and b is equal to the distance between 0 and c, which is given in the problem statement. The absolute value signs are used to ensure that the distances are represented as positive quantities.
Another way to express this statement is:|b - a| = |c|or|a - b| = |c|
Both of these expressions are equivalent to the first statement, since |c - 0| is the same as |c|.
Therefore, we can conclude that the distances between a and b and between 0 and c are equal, which can be expressed mathematically using absolute value notation as |b - a| = |c - 0|.
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On a recent quiz, the class mean was 73 with a standard deviation of 4.6. Calculate the z-score (to 4 decimal places) for a person who received score of 77.14. z-score:............ Is this unusual? A. Not Unusual B.Unusual
Since a z-score of 0.96 is within two standard deviations of the mean, it is not considered unusual. Therefore, the answer is A. unusual.
To determine if this is unusual, we need to consider the normal distribution and the concept of standard deviation. In a standard normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
To calculate the z-score, we use the formula:
z = (x - μ) / σ
Where x is the individual's score, μ is the mean, and σ is the standard deviation.
To calculate the z-score, we'll use the formula:
z-score = (individual score - class mean) / standard deviation
In this case, the individual score is 77.14, the class mean is 73, and the standard deviation is 4.6.
Step 1: Subtract the class mean from the individual score.
77.14 - 73 = 4.14
Step 2: Divide the result by the standard deviation.
4.14 / 4.6 = 0.9
Plugging in the values we get:
z = (77.14 - 73) / 4.6
z = 0.9565 (rounded to 4 decimal places)
A z-score of 0.9565 indicates that the person's score is about 0.96 standard deviations above the mean.
Now, let's determine if this is unusual or not. In general, a z-score greater than 1.96 or less than -1.96 is considered unusual, as it represents a result that is outside the 95% confidence interval. Since our calculated z-score is 0.9000, it is within the 95% confidence interval.
Answer: The z-score is 0.9000, and it is A. Not Unusual.
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ronda would like to assess the effects of a reading comprehension course on the scores of students. she gives a group of remedial students a reading comprehension pretest and then randomly assigns them to either the treatment group or the control group. shortly after the treatment, she measures their reading comprehension scores again. which set of results would result in ronda being worried about statistical regression?
Ronda would be worried about statistical regression if the results show that the control group's post-treatment scores are significantly higher than their pretest scores, while the treatment group's post-treatment scores are not as high as expected.
Statistical regression, also known as regression to the mean, occurs when extreme scores on an initial measurement tend to move closer to the mean on subsequent measurements. In this case, if the control group's pretest scores were exceptionally low (far below the mean), they are likely to improve naturally over time due to regression to the mean, even without the treatment. Therefore, the control group's post-treatment scores might be higher than their initial scores, creating a misleading impression that the treatment had a positive effect.
If such a pattern is observed, Ronda would be concerned that the apparent treatment effect is due to statistical regression rather than the actual effectiveness of the reading comprehension course.
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which of the following pairs of triangles can be proven similar through SAS similarity
The pairs of triangles that can be proven by SAS similarity is (c)
Identifying the pairs of triangles that can be proven by SAS similarityFrom the question, we have the following parameters that can be used in our computation:
The list of options
The SAS similarity is used to check if two triangles are similar by comparing the lengths of the corresponding sides and the angle between the corresponding sides.
Using the above as a guide, we have the following:
The pair of triangles in (c) can be proved by SAS
This is because
Corresponding sides are similar and the angle between them are equal
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Gerald earns $___ each time he mows a lawn. He mows his neighbor's lawn each week. He also earned an additional $___ for trimming trees one week.
Part A: Rewrite the description by filling in the blanks with values of your choice to show the amount of money he could earn in any number of weeks, w. Make sure that the values you choose make sense for this situation. (1 point)
Part B: Write an algebraic expression from your written description used in Part A. Let w stand for the number of weeks. (3 points)
The algebraic expression representing the description given is 5w + 2w
We can rewrite the description as Gerald earns $5 each time he mows a lawn
Rewriting the description:Let amount earned for lawn mowing = $5Let amount earned for trimming = $2
We can then rewrite the description as Gerald earns $5 each time he mows a lawn. He mows his neighbor's lawn each week.
He also earned an additional $2 for trimming trees one week.
An algebraic expression for the description
Number of weeks = w
Amount earned for any given number of weeks is ;
Amount earned= 5w + 2w = 7w
Hence, the algebraic expression for the description is 5w + 2w
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