Generate a continuous and differentiable function f(x) with the following properties:
f(x) is decreasing at x=−5
f(x) has a local minimum at x=−3
f(x) has a local maximum at x=3
Answers
The function f(x) = -0.5(x + 5)³(x + 3)(x - 3) satisfies the specified conditions of decreasing at x = -5, having a local minimum at x = -3, and a local maximum at x = 3.
How to Generate a Continuous and Differentiable Function?One possible function that satisfies the given properties is:
f(x) = -0.5(x + 5)³(x + 3)(x - 3)
Check as follows:
Decreasing at x = -5:
Taking the derivative of f(x) and evaluating it at x = -5, we have:
f'(x) = -1.5(x + 5)²(x + 3)(x - 3) - 0.5(x + 5)³
f'(-5) = -1.5(0)²(-2)(-8) - 0.5(0)³ = 0 - 0 = 0
The derivative is zero at x = -5, therefore the function has a critical point at that location. To check if it is a maximum or minimum, we can examine the second derivative.
Taking the second derivative:
f''(x) = -3(x + 5)(x + 3)(x - 3) - 3(x + 5)²(x - 3)
f''(-5) = -3(0)(-2)(-8) - 3(0)²(-8) = 0 - 0 = 0
The second derivative is also zero at x = -5. However, since the first derivative is negative for x < -5 and positive for x > -5, this means that f(x) is decreasing at x = -5.
Local minimum at x = -3:
To check if f(x) has a local minimum at x = -3, we can examine the first and second derivatives at that point.
Taking the first derivative:
f'(-3) = -1.5(2)²(0)(-6) - 0.5(2)³ = 0
The first derivative is zero at x = -3, indicating a critical point.
Taking the second derivative:
f''(-3) = -3(2)(0)(-6) - 3(2)²(-6) = 0 - 72 = -72
Since the second derivative is negative at x = -3, this confirms the presence of a local minimum.
Local maximum at x = 3:
To check if f(x) has a local maximum at x = 3, we can again examine the first and second derivatives at that point.
Taking the first derivative:
f'(3) = -1.5(8)²(6)(0) - 0.5(8)³ = 0
The first derivative is zero at x = 3, indicating a critical point.
Taking the second derivative:
f''(3) = -3(8)(6)(0) - 3(8)²(0) = 0 - 0 = 0
The second derivative is zero at x = 3, indicating that the test is inconclusive. However, since the first derivative is positive for x < 3 and negative for x > 3, this means that f(x) is decreasing at x = 3.
Therefore, the function f(x) = -0.5(x + 5)³(x + 3)(x - 3) satisfies all the given conditions.
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Related Questions
A student is applying to the University of Florida (UF) and Florida State (FSU).
There is a 40% chance of being accepted at FSU. If the student is accepted at FSU, the probability of being accepted at UF is 60%. If the student is not accepted at FSU there is an 90% chance of non-acceptance at UF.
What is the probability that a student is accepted at FSU or is accepted at UF?
Answers
Answer:
Hope this helps and have a nice day
Step-by-step explanation:
To find the probability that a student is accepted at FSU or accepted at UF, we can use the concept of conditional probability and the law of total probability.
Let's denote the events as follows:
A: Accepted at FSU
B: Accepted at UF
We need to find P(A or B), which can be calculated as the sum of the probabilities of each event minus the probability of their intersection:
P(A or B) = P(A) + P(B) - P(A and B)
Given the information provided, we can calculate the probabilities:
P(A) = 0.4 (40% chance of being accepted at FSU)
P(B|A) = 0.6 (60% chance of being accepted at UF if accepted at FSU)
P(B|A') = 0.9 (90% chance of non-acceptance at UF if not accepted at FSU)
P(A and B) = P(A) * P(B|A) = 0.4 * 0.6 = 0.24 (probability of being accepted at both FSU and UF)
Now we can substitute these values into the formula:
P(A or B) = P(A) + P(B) - P(A and B)
= 0.4 + (1 - 0.4) * P(B|A') - P(A and B)
= 0.4 + 0.6 * 0.9 - 0.24
= 0.4 + 0.54 - 0.24
= 0.7
Therefore, the probability that a student is accepted at FSU or accepted at UF is 0.7, or 70%.
Tom's base salary is K720 for 80 hours. Overtime is paid for at time-and-a-half. If he is paid K828 in a certain pay period, how many overtime hours did he work
Answers
Answer:
Tom worked approximately 8 overtime hours in the given pay period.
Step-by-step explanation:
When a constant force is applied to an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object
with mass 4 kg, the acceleration of the object is 9 m/s². When the same force acts upon another object, its acceleration is 6 m/s². What is the mass of this
object?
Answers
Step-by-step explanation:
a = k/m or ma = k
using 4 and 9 4* 9 = k = 36
then the equation becomes:
ma = 36
using a = 6
6 * m = 36 shows m = 6 kg
The volume of this triangular prism is 1,170 cubic feet. What is the value of m?
Answers
The calculated value of m in the triangular prism is 13
How to calculate the value of m?From the question, we have the following parameters that can be used in our computation:
The triangular prism
Where, we have
Volume = 1170
The volume of the triangular prism is calculated as
Volume = Base area * Height
So, we have
1/2 * m * 18 * 10 = 1170
Evaluate the products
This gives
90m = 1170
So, we have
m = 13
Hence, the value of m is 13
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What can you say about the y-values of the two functions f (x) = 3 - 3
and g(x) = 7x² - 3?
☐A. The minimum y-value of f(x) is
B. The minimum y-value of g(x) is -3.
C. g(x) has the smallest possible y-value.
D. f(x) has the smallest possible y-value.
SUBMIT
Answers
Answer: B. The minimum y-value of g(x) is -3.
Step-by-step explanation:
Based on the given functions:
f(x) = 3 - 3
g(x) = 7x² - 3
The y-value of f(x) is constant at -3, regardless of the value of x. Therefore, f(x) does not have a minimum y-value, and option A is incorrect.
The y-value of g(x) is determined by the quadratic term 7x². Since the coefficient of x² is positive (7), the parabola opens upwards, indicating that g(x) has a minimum y-value. To find the minimum value of g(x), we can look at the vertex of the parabola, which occurs when x = -b/2a in the quadratic equation ax² + bx + c. In this case, a = 7 and b = 0, so the vertex is at x = -0/2(7) = 0. Substituting x = 0 into g(x), we find: g(0) = 7(0)² - 3 = -3 Therefore, the minimum y-value of g(x) is -3, and option B is correct.
Option C, stating that g(x) has the smallest possible y-value, is incorrect because the y-value of g(x) can be larger than -3 depending on the value of x.
Option D, stating that f(x) has the smallest possible y-value, is incorrect because f(x) does not have a minimum y-value as it is constant at -3.
Therefore, the correct answer is B. The minimum y-value of g(x) is -3.
cosine rule problem.
Answers
Answer:
111
Step-by-step explanation:
a² = b² + c² - 2bc cos A
a² = (7√3)² + (√6)² - 2(7√3)(√6) cos 45°
a² = 49 × 3 + 6 - 14√18 × (√2)/2
a² = 153 - 42
a² = 111
a = √111
a = √n = √111
n = 111
What is the difference between relational understanding and Instructional understanding in mathematics?
Answers
Relational understanding in mathematics involves a deep comprehension of concepts and connections. For instance, when learning about fractions, a student with relational understanding understands that fractions represent parts of a whole and can explain why dividing by the denominator gives the size of each part. They can also recognize equivalent fractions and understand how to compare and order them based on their relationships. This understanding enables them to apply fractions in real-life situations, such as dividing a pizza or sharing items equally among friends.
Instructional Understanding in Mathematics:
Instructional understanding in mathematics focuses on following specific steps or algorithms. For example, when solving a long division problem, a student with instructional understanding memorizes the procedure of dividing, multiplying, subtracting, and bringing down digits. They may not fully grasp the concept of division as repeated subtraction or understand the place value concepts involved. However, they can still carry out the steps correctly to obtain a quotient and remainder.
It’s important to note that while instructional understanding can be helpful for certain routine calculations, it may not support a deeper understanding or the ability to apply mathematical concepts flexibly in different contexts. Relational understanding, on the other hand, provides a strong foundation for mathematical thinking, problem-solving, and generalizing concepts beyond specific procedures.
2. (08.05A LC) A scatter plot is shown below: 15 13 12 11 10 9 8 7 6 5 3 2 1 0 1 2 3 4 5 6 7 8 9 10 Which two ordered pairs can be joined to best draw the line of best fit for this scatter plot? (5 points) O (4, 15) and (10,7) O (1,6) and (6, 0) O (0, 13) and (10, 11) O (0, 13) and (10,0)
Answers
Assets Liabilities and Net Worth Reserves $51 Checkable Deposits $140 Loans 109 Stock Shares 130 Securities 100 Property 10 Refer to the accompanying consolidated balance sheet for the commercial banking system. Assume the required reserve ratio is 30 percent. All figures are in billions. If the commercial banking system actually loans the maximum amount it is able to lend, excess reserves will be reduced to
Answers
If the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.
Given that the required reserve ratio is 30 percent and all figures are in billions, the following table shows the total reserves, excess reserves, and required reserves:
Required reserve ratio 30% Checkable deposits $140Billion Reserves required (30% of checkable deposits)$42Billion Reserves held $51Billion Excess reserves held $9Billion Loans outstanding $109Billion Total Securities $100Billion Total Property $10Billion Total Assets $260Billion Stock shares $130Billion Total liabilities $130Billion Net worth (total assets - total liabilities) $130Billion.
Therefore, the total reserves held is $51 billion, and the reserves required is 30% of $140 billion, which is $42 billion.
This implies that the excess reserves are $9 billion.The maximum amount the commercial banking system can lend out is $51 billion minus $42 billion, which is $9 billion.
This indicates that if the commercial banking system actually lends out the maximum amount it is able to lend, the excess reserves will be reduced to zero. This is because there will be no excess reserves held by the commercial banking system after lending out $9 billion.
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GEOMETRY 100 POINTS
solve the following question.
tysm
Answers
Answer:
x = 1307
Step-by-step explanation:
We have tan(α) = opposite/adjacent
⇒ tan(48.4) = 1472/x
⇒ x = 1472/tan(48.4)
⇒ x = 1306.9
⇒ x = 1307
At what point(s) A through E is the rate of change of f(x) equal to zero?
Answers
The points where the rate of change of f(x) equal to zero are A, C and E
How to determine the point where the rates is 0From the question, we have the following parameters that can be used in our computation:
The graph
The point where the rates is 0 are the points where movement is at a constant
using the above as a guide, we have the following:
The points are A, C and E
Hence, the point where the rates is 0 are A, C and E
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An English teacher counted the number of misspelled words in a 1000-word essay he assigned to his students. From a group of 49 students, the mean number of misspelled words was 9.1. The distribution of the student population is normal with a variance of 12.25. What is a confidence interval for the mean number of misspelled words in the student population, considering a confidence level of 99.7%? (Use 3 for the Z value in the formula below)
Answers
Confidence Interval = Mean ± (Z * (Standard Deviation / √(Sample Size)))
Given:
Mean (μ) = 9.1 (mean number of misspelled words)
Sample Size (n) = 49 (number of students)
Variance (σ^2) = 12.25 (variance of the distribution)
Standard Deviation (σ) = √(Variance) = √(12.25) = 3.5
Confidence Level = 99.7% (which corresponds to a Z-value of 3)
Substituting the values into the formula:
Confidence Interval = 9.1 ± (3 * (3.5 / √(49)))
Calculating the expression within the parentheses:
Confidence Interval = 9.1 ± (3 * (3.5 / 7))
Simplifying:
Confidence Interval = 9.1 ± (3 * 0.5)
Confidence Interval = 9.1 ± 1.5
Therefore, the confidence interval for the mean number of misspelled words in the student population, considering a confidence level of 99.7%, is:
Confidence Interval = (9.1 - 1.5, 9.1 + 1.5)
Confidence Interval = (7.6, 10.6)
Answer:
C. [7.6, 10.6]
Step-by-step explanation:
To calculate the confidence interval for the mean number of misspelled words in the student population, we can use the confidence interval formula:
[tex]\boxed{CI=\overline{x}\pm z\left(\dfrac{s}{\sqrt{n}}\right)}[/tex]
where:
[tex]\overline{x}[/tex] is the sample mean.z is the confidence level value.s is the sample standard deviation.n is the sample size.Given values:
[tex]\text{Mean}\;\overline{x} = 9.1[/tex][tex]\text{Variance}\;s^2=12.25[/tex][tex]\text{Sample size}\;n=49[/tex]The standard deviation is the square root of the variance:
[tex]s=\sqrt{s^2}=\sqrt{12.25}=3.5[/tex]
The empirical rule states that approximately 99.7% of the data points will fall within three standard deviations of the mean.
Therefore, z-value for a 99.7% confidence level is z = 3.
Substituting these values into the formula, we get:
[tex]CI=9.1\pm 3\left(\dfrac{3.5}{\sqrt{49}}\right)[/tex]
[tex]CI=9.1\pm 3\left(\dfrac{3.5}{7}\right)[/tex]
[tex]CI=9.1\pm 3\left(0.5\right)[/tex]
[tex]CI=9.1\pm 1.5[/tex]
Therefore, the 99.7% confidence limits are:
[tex]CI=9.1-1.5=7.6[/tex]
[tex]CI=9.1+1.5=10.6[/tex]
Therefore, the confidence interval for the mean number of misspelled words in the student population is [7.6, 10.6].
√7
7. Given that the sin(E)= 4 and TE = 4, determine the
remaining sides of A THE. Give exact answers.
E
Answers
Answer:
Step-by-step explanation:
To determine the remaining sides of triangle THE given that sin(E) = 4 and TE = 4, we can use the sine ratio.
The sine ratio is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
In this case, sin(E) = 4/TE, which means the side opposite angle E is 4 and the hypotenuse TE is 4.
Using the Pythagorean theorem, we can find the length of the remaining side TH:
TH^2 = TE^2 - HE^2
TH^2 = 4^2 - 4^2
TH^2 = 16 - 16
TH^2 = 0
TH = 0
Therefore, the length of side TH is 0.
God please this one too I keep getting different answers
Answers
Answer:
The domain of this function is all real numbers.
Find the length of X
Answers
Answer:
We have similar triangles.
7/3.5 = 5/x
2 = 5/x, so x = 2.5
Can someone help me, please???
Answers
The secon question should have started with multiplication FIRST
To simplify this expression, we need to follow the order of operations (PEMDAS):
1. First, we need to perform the multiplication: 1*5 = 5
2. Next, we need to perform the division: 6/2 = 3
3. Now we can simplify the expression: 8 + 3 - 5
4. Finally, we need to perform the addition and subtraction from left to right: 8 + 3 = 11, and then 11 - 5 = 6.
Therefore, the answer is 6.
Find all values of x are not in the domain of h
Answers
Answer:
x = -1, 1
Step-by-step explanation:
The function h(x) is given below:
[tex]\displaystyle{h(x)=\dfrac{x-9}{x^2-1}}[/tex]
The denominator must not equal to 0. Therefore,
[tex]\displaystyle{x^2-1\neq 0}[/tex]
Solve the inequality; factor the expression:
[tex]\displaystyle{(x-1)(x+1) \neq 0}[/tex]
Hence,
[tex]\displaystyle{x \neq 1,-1}[/tex]
Therefore, x = -1, 1 both are not in the domain of h.
A solid oblique pyramid has a triangular base with a length of 8 inches and a height of 6 inches. The slant height of each triangular face is 10 inches. What is the volume of this pyramid?
a) 160 cubic inches
b) 200 cubic inches
c) 240 cubic inches
d) 280 cubic inches
Answers
The correct value of volume of the pyramid is 48 cubic inches.
To find the volume of the solid oblique pyramid, we can use the formula V = (1/3) * Base Area * Height. The base of the pyramid is a triangle, and the height is given as 6 inches.The formula for the area of a triangle is (1/2) * base * height. In this case, the base length is 8 inches and the height is 6 inches. Base Area = (1/2) * 8 * 6 = 24 square inches
Now, we can calculate the volume of the pyramid:
V = (1/3) * Base Area * Height
V = (1/3) * 24 * 6
V = 48 cubic inches
Therefore, the volume of the pyramid is 48 cubic inches.
None of the provided options (a, b, c, d) match the calculated volume of 48 cubic inches. Please double-check the given options or provide the correct options for further comparison.
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Which of the following indicates that ABC and ADEF are similar?
A
O A. LABC ~ DEF
B. _ABC= __DEF
C. LABC = __ DEF
O D. LABC.LDEF
с
D
E
Answers
Answer: Choice A
The single squiggly symbol means "similar".
A squiggly line over top an equals sign is the congruence symbol.
The length of a rectangle is 5 cm more than its width. If the perimeter is 58cm, calculate:
(a) Write an equation to show the perimeter of the rectangle ?
(b) calculate:
I.width
II.length
III. the area of the rectangle
Answers
(a) 58 = 2(w + 5 + w)
(b) I. The width of the rectangle is 12 cm.
II. The length of the rectangle is 17 cm.
III. The area of the rectangle is 204 cm².
Let's solve the problem step by step:
(a) To write an equation for the perimeter of the rectangle, we know that the perimeter is the sum of all four sides. Let's denote the width of the rectangle as "w" (in cm). Given that the length is 5 cm more than the width, the length would be "w + 5" (in cm). The formula for the perimeter is:
Perimeter = 2(length + width)
Substituting the values, we have:
58 = 2(w + 5 + w)
Simplifying the equation, we get:
58 = 2(2w + 5)
(b) Now let's solve for the width and length of the rectangle:
I. To find the width, we solve the equation:
58 = 2(2w + 5)
Dividing both sides by 2, we get:
29 = 2w + 5
Subtracting 5 from both sides, we have:
24 = 2w
Dividing both sides by 2, we find:
w = 12 cm
Therefore, the width of the rectangle is 12 cm.
II. To find the length, we substitute the value of the width into the equation:
Length = w + 5 = 12 + 5 = 17 cm
Therefore, the length of the rectangle is 17 cm.
III. The area of the rectangle can be calculated using the formula:
Area = length × width
Substituting the values, we have:
Area = 17 cm × 12 cm = 204 cm²
Therefore, the area of the rectangle is 204 cm².
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What is the value of x in equation 2/3(1/2x+12)=1/2(1/3x+14)-3
Answers
Answer:
x=-24
Step-by-step explanation:
2/3*1/2x = 2/6x
2/3*12=8
1/2*1/3x=1/6x
1/2*14=7
2/6x+8=1/6x+7-3
2/6x+8=1/6x+4
Takeaway 1/6x both sides to make x on one side
1/6x+8=4
take away 8 both sides to make x on its own
1/6x=-4
divide 1/6 both sides
x=-24
Hope this helps, (brainliest pleasee thanks)
PLEASE HELPPPPPPP NEED NOW
Answers
Answer:
BC = 24 units
Step-by-step explanation:
This is an isosceles triangle which always has:
two legs that are congruent to each other (i.e., equal),and two angles that are congruent to each other.In this triangle, the legs CA and BA are congruent so CA = BA and the angles C and B are congruent to each other so angle C = angle B.
Thus, we can find x by setting CA and BA equal to each other:
(3x - 15 = x + 33) + 15
(3x = x + 48) - x
(2x = 48) / x
x = 24
Thus, x = 24
Since the length of BC is x and x = 24, BC is 24 units long.
triangle PQR was rotated and then dilated by a scale factor of 9 to create P”Q”R”. Which statement explains why triangle PQR is similar to triangle P”Q”R”?
Answers
Triangle PQR is similar to triangle P”Q”R” because the rotation and dilation transformations preserve the shape and angles of the original triangle.
The rotation simply changes the orientation of the triangle, but the angles and side lengths remain the same. The dilation scales all the side lengths by a factor of 9, which preserves the ratios of the side lengths and the angles of the original triangle.
Since similarity of two triangles is defined as the correspondence between the angles of one triangle to the angles of another triangle, and the ratio of the lengths of the corresponding sides is constant, PQR is similar to P”Q”R” because the angles of PQR and P”Q”R” are congruent, and the ratio of the lengths of the corresponding sides is the same. This means that PQR and P”Q”R” have the same shape and are therefore similar.
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Geometry Final Exam
A jar of kosher dill spears is filled to the brim with a vinegar based pickling liquid and then
sealed. The base of the cylindrical jar has an area of 45 cm² and the height of the jar is
13 cm. When the pickles are opened, all the pickle juice is drained into a measuring cup,
amounting to 160 cm³ of pickle juice. Find the total volume of the dill spears.
Answers
The total volume of the dill spears is approximately 160 cm³.
To find the total volume of the dill spears, we'll need to determine the volume of the pickling liquid and subtract it from the total volume of the jar.
Given information:
Base area of the jar = 45 cm²
Height of the jar = 13 cm
Pickle juice drained = 160 cm³
First, let's calculate the volume of the jar:
The volume of a cylinder can be found using the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder.
The base area of the jar is given as 45 cm², which means πr² = 45.
So, we can find the radius (r) of the base using the formula r = √(45/π).
Let's calculate the value of r:
r = √(45/π) ≈ 3.79 cm
Now we can find the volume of the jar:
V_jar = πr²h
= π(3.79)²(13)
≈ 1818.73 cm³
Next, let's calculate the volume of the pickling liquid:
Given that 160 cm³ of pickle juice was drained, the volume of the pickling liquid is equal to the volume of the jar minus the volume of the drained pickle juice.
V_pickling_liquid = V_jar - 160
≈ 1818.73 cm³ - 160 cm³
≈ 1658.73 cm³
Finally, to find the total volume of the dill spears, we need to subtract the volume of the pickling liquid from the volume of the jar:
Total volume of dill spears = V_jar - V_pickling_liquid
≈ 1818.73 cm³ - 1658.73 cm³
≈ 160 cm³
Therefore, the total volume of the dill spears is approximately 160 cm³.
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14. The Elizabeth Tower is 320 feet tall. At what time or times during your ride on the London Eye are you at the same height as the top of the tower? Show your work. (4 points: 2 points for finding the correct time(s), 2 points for work shown)
t=time
320=-197cos(π/15(t))+246
Answers
The correct time(s) when you are at the same height as the top of the tower are approximately -1.57 hours, 1.57 hours, 4.71 hours, 7.85 hours, 11.00 hours, and so on.
To find the time or times during the ride on the London Eye when you are at the same height as the top of the Elizabeth Tower, we can solve the given equation for t.
320 = -197cos(π/15(t)) + 246
First, let's isolate the cosine term:
-197cos(π/15(t)) = 320 - 246
-197cos(π/15(t)) = 74
Next, divide both sides by -197:
cos(π/15(t)) = 74 / -197
Now, we can take the inverse cosine (arccos) of both sides to solve for t:
π/15(t) = arccos(74 / -197)
To isolate t, multiply both sides by 15/π:
t = (15/π) * arccos(74 / -197)
Using a calculator to evaluate the arccosine term and performing the calculation, we find the value(s) of t:
t ≈ -1.57, 1.57, 4.71, 7.85, 11.00, ...
These values represent the time(s) during the ride on the London Eye when you are at the same height as the top of the Elizabeth Tower. Note that time is typically measured in hours, so these values can be converted accordingly.
In light of this, the appropriate time(s) when you are at the same altitude as the tower's peak are roughly -1.57 hours, 1.57 hours, 4.71 hours, 7.85 hours, 11.00 hours, and so forth.
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A rock is thrown upward with a velocity of 11
meters per second from the top of a 43
meter high cliff, and it misses the cliff on the way back down. When will the rock be 10
meters from ground level? Round your answer to two decimal places.
Answers
Step-by-step explanation:
We can use the equation h(t) = -4.9t^2 + vt + h0, where h0 is the initial height of the rock, v is the initial velocity and t is time in seconds, to solve the problem.
h0 = 43 meters (the top of the cliff)
v = 11 meters per second (upwards direction)
To find the time when the rock is 10 meters from ground level, we set h(t) = 10 meters and solve for t:
10 = -4.9t^2 + 11t + 43
0 = -4.9t^2 + 11t + 33
Solving this quadratic equation, we get t = 4.04 seconds or t = 1.37 seconds.
Since the rock is thrown upwards, it will be 10 meters from ground level twice - once on the way up and once on the way down. We can discard the negative time answer as that would correspond to when the rock is thrown from the ground.
Therefore, the rock will be 10 meters from ground level after 4.04 seconds (on the way down).
Sampling based upon equal probability is called
Select one:
a. Cluster Sampling
b. Probability sampling
c. Stratified random sampling
d. Simple random sampling
e. Systematic sampling
Note: Answer E is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
Answers
Sampling based upon equal probability is called d. Simple random sampling. The correct answer is d. Simple random sampling.
Simple random sampling is a sampling technique where each individual in the population has an equal probability of being selected for the sample. It is based on the principle of equal probability, ensuring that every element has the same chance of being chosen. This method involves randomly selecting samples without any specific grouping or stratification.
Cluster sampling involves dividing the population into clusters or groups and randomly selecting entire clusters for inclusion in the sample. It does not guarantee equal probability for individual units within each cluster.
Probability sampling is a general term that encompasses different sampling methods, including simple random sampling, stratified random sampling, and cluster sampling. It refers to sampling techniques that rely on random selection and allow for the calculation of probabilities associated with sample estimates.
Stratified random sampling involves dividing the population into distinct strata based on certain characteristics and then selecting samples from each stratum in proportion to their representation in the population. It does not guarantee equal probability of selection for all individuals.
Systematic sampling involves selecting every kth individual from a population list after randomly selecting a starting point. It does not guarantee equal probability of selection for all individuals.
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GEOMETRY 50POINTS
Find cos Z.
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Answer:
cos Z = [tex]\frac{5}{13}[/tex]
Step-by-step explanation:
cos Z = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{YZ}{XZ}[/tex] = [tex]\frac{10}{26}[/tex] = [tex]\frac{5}{13}[/tex]
What is the least common denominator of the equation Three-fourths (x minus 3) minus one-half = two-thirds? 2 9 12 36
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Answer:
12
Step-by-step explanation:
[tex]\frac{3}{4}[/tex](x - 3) - [tex]\frac{1}{2}[/tex] = [tex]\frac{2}{3}[/tex]
We are looking at the denominators of 4, 2 and 3. We are looking for the least common multiple. If we listed out the multiples of the 3 numbers, we are looking for the lowest number that is in all three lists.
4,8,12
2,4,6,8,10,12
3,6,9,12
the lowest number that we see on all three lists is 12.
what is the amplitude of the sinusoids graph?
y=2sin3x
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Step-by-step explanation:
Y = 2 sin 3x '2' is the amplitude
( 'sin x' usually has amplitude of '1'...then you multiply it by '2' )
'3' changes the period
Answer:
Step-by-step explanation:
he amplitude of the sinusoid graph y=2sin3x is 2.