Answer: d
Step-by-step explanation:to s is to heavy and the others are for liquid and size
Answer:
D
Step-by-step explanation:
just makes the most sense
Determine whether the series converges or diverges. summation from n=1 to infinity (1/n^2+1)^1/2
To determine whether the given series converges or diverges, we will use the Comparison Test.
The series we are analyzing is:
Σ(1/(n^2 + 1)^(1/2)) from n=1 to infinity.
First, we can observe that (n^2 + 1) > n^2 for all n, which means that:
1/(n^2 + 1) < 1/n^2 for all n.
Now, taking the square root of both sides:
(1/(n^2 + 1)^(1/2)) < (1/n^2)^(1/2) = 1/n.
We know that the series Σ(1/n) is a harmonic series and it diverges. Since the given series is smaller term-by-term than a divergent series, we can use the Comparison Test to conclude that the given series converges.
Your answer: The series Σ(1/(n^2+1)^(1/2)) from n=1 to infinity converges.
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if an organization wants to test whether a minority of its employees are dissatisfied with their bonus, the alternative hypothesis would be that the true population proportion would be:
Answer: If an organization wants to test whether a minority of its employees are dissatisfied with their bonus, the alternative hypothesis would be that the true population proportion is greater than the null hypothesis proportion.
Specifically, the null hypothesis would be that the proportion of employees who are dissatisfied with their bonus is equal to or less than a certain value (usually 0.5 or 0.1, depending on the context). The alternative hypothesis would be that the proportion of employees who are dissatisfied with their bonus is greater than this value.
For example, if the null hypothesis is that 20% of employees are dissatisfied with their bonus, the alternative hypothesis would be that more than 20% of employees are dissatisfied with their bonus.
The alternative hypothesis is typically the hypothesis of interest, as it represents the hypothesis that the organization wants to investigate and potentially take action on.
Step-by-step explanation:
The alternative hypothesis would be that the true population proportion of dissatisfied employees regarding their bonus is greater than the assumed proportion.
The null hypothesis assumes that the proportion of dissatisfied employees regarding their bonus is equal to the assumed proportion. The alternative hypothesis, in contrast, assumes that the proportion of dissatisfied employees is greater than the assumed proportion. In this case, the organization wants to test whether a minority of its employees are dissatisfied with their bonus, which implies that the assumed proportion is less than 50%. Therefore, the alternative hypothesis states that the true population proportion of dissatisfied employees regarding their bonus is greater than the assumed proportion. By conducting hypothesis testing, the organization can determine whether the evidence supports the null hypothesis or the alternative hypothesis and make decisions accordingly.
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for the transformation rule in the form , replacing which variable with what number will result in the transformation displayed in the graph?
For the function transformation form of f(x), \(g(x) = a f(\frac{1}{b} x - h) + k \), we are replacing variable a by 2, result will in the transformation displayed in the above graph. So, option(d) is right one.
A transformation is an another way to a parent function's graph. There are serval formulas for distinct rules of transformation. If consider transformation function of f(x) is g(x) = f(x - h) + k,
Vertically transformation of function by k units. Horizontal transformation of the function f(x) by h units.g(x) = -f(x), refelction in x-axisg(x) = f(-x), reflection in y-axisg(x) = cf(x) , if c>1, vertical stretch by factor cif c < 1, vertical shrink by factor cWe have a function f(x) = 2cos(x), that is cosine function and g(x) is it's transform function. Here, \(g(x) = a f(\frac{1}{b} x - h) + k \), now see the graph carefully.
Thus, for g(x) in above graph, there are no horizontal and vertical translation. So, h = k = 0. Also, the graphs are not reflected on both axes. However, notice that the graph of g(x) is just the vertical stretched version of f(x). The values of g(x) are twice that of f(x). Therefore, the factor a must be twice, a = 2. Hence, we replace a by 2.
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Complete question:
The above graph of shows f(x) = 2cos(x) and transform g(x). For the transformation rule in the form , g(x) = a f( 1/b x - h) + k
replacing which variable with what number will result in the transformation displayed in the graph?
a) b is replacing by 1/2
b) k is replacing by -1/2
c) h is replacing by -2
d) a is replacing by 2
Find the area of the surface generated when the given curve is revolved about the given axis.y=2x−2, for4≤x≤7; about they-axis (Hint: Integrate with respect toy.) The surface area is square units. (Type an exact answer, usingπas needed.)
To find the surface area generated by revolving the curve y = 2x - 2 about the y-axis, we need to use the formula: S = 2π ∫[a,b] y √(1 + (dy/dx)^2) dx
Where a and b are the limits of integration (in this case, a = 4 and b = 7).
First, we need to find dy/dx:
dy/dx = 2
Next, we can substitute y and dy/dx into the formula and integrate:
S = 2π ∫[4,7] (2x - 2) √(1 + 2^2) dx
S = 2π ∫[4,7] (2x - 2) √5 dx
S = 2π√5 ∫[4,7] (2x - 2) dx
S = 2π√5 [x^2 - 2x] from 4 to 7
S = 2π√5 [(7^2 - 2(7)) - (4^2 - 2(4))]
S = 2π√5 (49 - 14 - 16 + 8)
S = 2π√5 (27)
S = 54π√5
Therefore, the surface area generated by revolving the curve y = 2x - 2 about the y-axis is 54π√5 square units.
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The vertex of a parabola is (-1, -8) and the zeros are (-5, 3) Determine the equation of the parabola in standard and factored form
Answer:
Part A
The equation of the parabola in standard form is f(x) = 0.5·x² + x - 7.5
Part B
The equation of the parabola in factored form is f(x) = 0.5·(x + 5)·(x - 3)
Step-by-step explanation:
The coordinates of the vertex of the parabola, (h, k) = (-1, -8)
The zeros of the parabola = -5, 3
Part A
The quadratic equation representing the parabola can be written as follows;
y = a·(x - h)² + k
The standard form of the equation is f(x) = a·x² + b·x + c
k = c - b²/(4·a)
h = -b/(2·a)
c = k + a·h² = -8 + a
From the zeros of the parabola, we have;
f(-5) = a × (-5)² + b×(-5) + c = 25·a - 5·b + c = 0
f(3) = a × (3)² + b×(3) + c = 9·a + 3·b + c = 0
Therefore, we have;
25·a - 5·b + c = 0...(1)
9·a + 3·b + c = 0...(2)
From which we have;
25·a - 5·b + c = 25·a - 5·b - 8 + a = 26·a - 5·b - 8 = 0
9·a + 3·b + c = 9·a + 3·b - 8 + a = 10·a + 3·b - 8 = 0
We then have;
26·a - 5·b = 8...(3)
10·a + 3·b = 8...(4)
Making 'b', the subject of both equations (3) and (4), equating the values, we find the value of 'a' as follows;
From equation (3), we have;
26·a - 5·b = 8
∴ b = (26·a - 8)/5
From equation (4), we have;
10·a + 3·b = 8
∴ b = (8 - 10·a)/3
From b = b, by transitive property, we have;
(26·a - 8)/5 = (8 - 10·a)/3
3 × (26·a - 8) = 5 × (8 - 10·a)
78·a - 24 = 40 - 50·a
∴ 128·a = 64
a = 64/128 = 1/2 = 0.5
a = 0.5
∴ b = (26·a - 8)/5 = (26 × 0.5 - 8)/5 = (13 - 8)/5 = 1
b = 1
c = -8 + a
∴ c = -8 + 0.5 = -7.5
c = -7.5
The equation of the parabola in standard form is therefore presented as follows;
f(x) = 0.5·x² + x - 7.5
Part B
The equation of the parabola in factored form is given as follows;
With the aid of a graphing calculator, we have;
f(x) = 0.5·x² + x - 7.5 = 0.5×(x² + 2·x - 15) = 0.5·(x + 5)·(x - 3)
The equation of the parabola in factored form is f(x) = 0.5·(x + 5)·(x - 3)
PLEASE ANSWER QUICK!!!!! 25 POINTS
find the probability of exactly one successes in five trials of a binomial experiment in which the probability of success is 5%
The probability of one success in five trials in the binomial experiment with a success probability of 5 % is 20. 4 %.
How to find the probability of success ?The formula for calculating the likelihood of one success in a binomial probability with a 5% chance of success is:
P ( X = 1) = (5 choose 1) x ( 0.05 ) x (0.95 ) ⁴
Solving for this success would give :
= ( 0.05 ) x ( 0. 95 ) ⁴
= 0.05 x 0.8145
= 0.040725
Then we multiply both sides to get :
P(X = 1) = 5 x 0.040725
= 0.203625
= 20. 4 %
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If n=370 and ˆ p (p-hat) =0.47, find the margin of error at a 90% confidence level Give your answer to three decimals
Express the confidence interval 15.2%
1. To find the margin of error at a 90% confidence level if n = 370 and p (p-hat) = 0.47, we use the formula below: margin of error = z_(α/2)* sqrt(ˆp*(1-ˆp)/n), where z_(α/2) is the critical value of z at α/2, α = 1 - 0.90 = 0.10 (since we want a 90% confidence interval), and n = 370.
Substituting these values, we have: α/2 = 0.10/2
= 0.05z_(α/2)
= z_0.05
= 1.645
margin of error = 1.645 * sqrt(0.47 * 0.53 / 370) ≈ 0.055
Therefore, the margin of error is approximately 0.055 at a 90% confidence level.
2. To express the confidence interval 14.2% ± 5.4% as a trilinear inequality, we can write:
14.2% - 5.4% ≤ p ≤ 14.2% + 5.4%or8.8% ≤ p ≤ 19.6%
So the trilinear inequality for the confidence interval 14.2% ± 5.4% is 8.8% ≤ p ≤ 19.6%.
3. To express the confidence interval 85.6% ± 6.4% in interval form in decimal format, we can write:
Lower limit = 85.6% - 6.4% = 79.2%
Upper limit = 85.6% + 6.4% = 92.0%
Therefore, the confidence interval is [0.792, 0.920] in decimal format.
4. To find the margin of error of a poll where 170 people were asked if they liked dogs, and 64% said they did at the 90% confidence level, we use the formula:
margin of error = z_(α/2)* sqrt(p*(1 - p)/n), where n = 170, p = 0.64, and α = 0.10 (since we want a 90% confidence level).
Substituting these values, we have: α/2 = 0.10/2
= 0.05z_(α/2)
= z_0.05
= 1.645
margin of error = 1.645 * sqrt(0.64 * 0.36 / 170) ≈ 0.077
Therefore, the margin of error is approximately 0.077 at the 90% confidence level.
5. To construct a 90% confidence interval for the true population proportion of people who received flu vaccinations this year out of 100 people sampled, 14 received flu vaccinations. We use the formula:
margin of error = z_(α/2)* sqrt(ˆp*(1-ˆp)/n), where n = 100, ˆp = 14/100 = 0.14, and α = 0.10 (since we want a 90% confidence level).
Substituting these values, we have: α/2 = 0.10/2
= 0.05z_(α/2)
= z_0.05
= 1.645
margin of error = 1.645 * sqrt(0.14 * 0.86 / 100) ≈ 0.090
Therefore, the margin of error is approximately 0.090 at the 90% confidence level.
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Find the exponential form of 27^3*9^2*3
Answer:
3¹⁴------------------------
We know that:
27 = 3³ and9 = 3²Substitute and evaluate the given expression:
27³ × 9² × 3 = (3³)³ × (3²)² × 3 = 3⁹ × 3⁴ × 3 = 3⁹⁺⁴⁺¹ =3¹⁴a full-cut round brilliant diamond with a 6.50 mm girdle diameter weighs about
That a full cut round brilliant diamond with a 6.50 mm girdle diameter typically weighs around 1.00 carat.
carat weight is determined by a combination of a diamond's size and density. A diamond's size is measured by its diameter, which is the distance across the widest part of the diamond, known as the girdle. Therefore, a diamond with a larger girdle diameter will generally weigh more than a diamond with a smaller diameter, assuming all other factors are equal.
the weight of a diamond can be estimated based on its girdle diameter, and a full-cut round brilliant diamond with a 6.50 mm girdle diameter typically weighs around 1.00 carat. However, it's important to note that other factors, such as depth, cut, and clarity, can also affect a diamond's weight and value.
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Which of the following identities is FALSE? Multiple Choice Y≡C+1+G+NX YD≡Y−TA+TR BS≡TA−TR−G I−S≡(G−TA+TR)+NX S+TA−TR≡1+G+NX
The false identity among the given options is: S + TA - TR ≡ 1 + G + NX, which suggests that savings plus taxes on households minus transfers received by households is equal to one plus government spending plus net exports.
In the national income accounting framework, the first equation, Y ≡ C + I + G + NX, represents the national income identity, where Y denotes national income, C represents consumption, I represents an investment, G represents government spending, and NX represents net exports.
The second equation, YD ≡ Y - TA + TR, represents the disposable income identity, where YD denotes disposable income, TA represents taxes on households, and TR represents transfers received by households.
The third equation, BS ≡ TA - TR - G, represents the government budget surplus/deficit identity, where BS denotes the government budget surplus/deficit.
The fourth equation, I - S ≡ (G - TA + TR) + NX, represents the saving-investment identity, where I denotes investment and S denotes savings.
The false identity, S + TA - TR ≡ 1 + G + NX, suggests that savings plus taxes on households minus transfers received by households is equal to one plus government spending plus net exports. This equation is not consistent with the principles of national income accounting and economic theory, hence making it false.
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find x
please help i’ll mark the first one or whoever right brainliest
Answer: 86
Step-by-step explanation:
gordon types 1800 words in 25 minutes. word per minute
Answer:
72
Step-by-step explanation:
words per minutes= 1800÷25=72
Triangle ABC has vertices A(0, -1), B(6, 5), and C(-4, 3). Which statement about triangle ABC is true?
The coordinates of the vertices of triangle ΔABC, A(0, -1), B(6, 5), and C(-4, 3), indicates that the triangle ΔABCD is a right triangle with all sides of different length.
What is a right triangle?A right triangle is a triangle that has an interior angle of 90°, and therefore, it has two sides known as the legs that are perpendicular.
The lengths of the sides of the triangle ΔABC can be found using the Pythagorean formula for finding the distance, d, between two points, (x₁, y₁) and (x₂, y₂) on the coordinate plane as follows;
d² = (x₂ - x₁)² + (y₂ - y₁)²
The vertices of the triangle ΔABC are; A(0, -1), B(6, 5), and C(-4, 3), which gives;
\(\overline{AB}^2\) = (6 - 0)²+ (5 - (-1))² = 72, AB = 6·√2
\(\overline{AC}^2\) = (-4 - 0)² + (3 - (-1))² = 32, AC = 4·√2
\(\overline{BC}^2\) = (-4 - 6)² + (3 - 5)² = 104, BC = 2·√(26)
72 + 32 = 104
Therefore; \(\overline{AB}^2\) + \(\overline{AC}^2\) = \(\overline{BC}^2\)
ΔABC is a right triangle
The slopes of the equation of the lines of the sides of the triangle are;
Slope of side AB = (5 - (-1))/(6 - 0) = 1
Slope of side BC = (3 - 5)/(-4 - 6) = 0.2
Slope of side AC = (3 - (-1))/(-4 - 0) = -1
Therefore;
\(\overline{AB}\) ⊥ \(\overline{AC}\)
Which gives;
A true statement about triangle ΔABC is that ΔABC is a right triangle a nd the lengths of the sides of the triangle are differentLearn more about the Pythagorean theorem in mathematics here:
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PEASE HELP ME AAAAA
^.^♡
You have a budget of 300 to order shirts for math club. The equation 10x +12y=300 models the total cost, where x is the number of short-sleeved shirts and y is the number of Ling-sleeved shirts.
/////
a.) Interpret the terms and coefficients in the equation.
____(Write here)_____
///
Graph the equation - on photo>
///
b.) Interpret the intercepts.
___(write here)___
///
c.) Find three possible solutions in the context of the problem.
a) The terms are: 10x, 12y,300
The Coefficients are: 10,12
b) x intercept is (30,0). y intercept is (0,25)
c) The three possible solutions:
(1,24), (8,18) , (6,20)
what are terms and coefficients?
Term could be a single number (positive or negative), a single variable (a letter), or a combination of multiple variables multiplied but never added or removed. Variables with numbers in front of them can be found in some terms. A coefficient is the number that appears in front of a phrase.
10x +12y=300
Terms: 10x, 12y,300
Coefficients: 10,12
Refer to the attachment for graph:
b) The locations on a Cartesian coordinate system known as intercepts are where the graph of an equation or function crosses the x- and y-axes.
From the graph, x intercept is (30,0). y intercept is (0,25)
c) solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
10x +12y=300
Find y when x=1:
10(1)+12y=300
10+12y=300
12y=300-10=290
y= 24.2 ≈ 24
Similarly, the three possible solutions:
(1,24), (8,18) , (6,20)
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feature scaling using techniques like mean normalization can make gradient descent converge faster true false
The statement is True. Mean normalization scales data to have a mean of 0, which allows the gradient descent algorithm to more quickly identify the optimum point.
Mean normalization is a feature scaling technique used to speed up the learning process of gradient descent algorithms. It works by mapping the values of a dataset to a range of [-1, 1], or [0, 1], by subtracting the mean from each data point and dividing by the standard deviation. This scaling process helps to reduce the impact of the outliers and normalize the data, allowing the gradient descent algorithm to more quickly converge on the optimal solution. This results in faster and more accurate models.
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A color printer prints 26 pages in 9 minutes. How many minutes does it take per page?
Answer:
2.80
Step-by-step explanation:
you want to figure out the unit rate (minute per page) by divideing 26 by 9
26 wont go into 9 evenly so you will have decimal
Tammy made a recipe that called for 3/4 teaspoon of salt. If the recipe is cut in half, how much salt is needed?
Answer:
answer is A your welcome
Answer:
If the recipe is cut in half, 3/8 teaspoon of salt is needed.
Step-by-step explanation:
Since the recipe is cut in half, we need to find 1/2 of 3/4. This means we need to multiply 1/2 times 3/4. For the numerator, 1 times 3 equals 3. For the denominator, 2 times 4 equals 8. The fraction is 3/8.
Using the table, find the average rate of change over the following intervals. I will give brainliest!!
Answer:
\(-4\)
Step-by-step explanation:
The formula for average rate of change (AROC) is: \(\frac{f(b)-f(a)}{b-a}\)
\(\frac{f(2)-f(0)}{2-0}\) ⇒ \(\frac{-3-5}{2-0} =-4\)
Which of the following is/are correct? (Select all that apply. You have only one submission for this question.) If u and v are parallel, then either u.v=jul lvl or u. V-lul lvl. The vector projuv is parallel to v If u and v are orthogonal, then u xv = 0. The expression u. (vw) is meaningful and the result is a scalar. Suppose u: O. If u xv=uxw, it follows that vw. If u and v are parallel, then u xv = 0. The expression u u can be negative
The correct statements are If u and v are orthogonal, then u × v = 0. The vector proj_v u is parallel to v. If u and v are parallel, then u × v = 0.
The statement "If u and v are parallel, then either u · v = |u||v|" is incorrect. The correct statement is "If u and v are parallel, then u · v = |u||v|".
The statement "The expression u.(vw) is meaningful and the result is a scalar" is incorrect. The expression u.(vw) is not meaningful because the dot product is only defined for vectors of the same dimension.
The statement "Suppose u: O. If u × v = u × w, it follows that v = w" is incorrect. The correct statement is "Suppose u ≠ 0. If u × v = u × w, it follows that v - w is parallel to u".
Finally, the statement "The expression u · u can be negative" is incorrect. The dot product u · u is always non-negative, and is only equal to zero if and only if u = 0
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for this lesson, you will come up with your own challenging algorithm for other students to trace. it must contain at least 4 if statements, 1 else statement and use at least one and or or boolean condition. note: elif statements will not count - your statements must be if statements. each if statement should use a unique variable name. for this challenge, try reading 3 or 4 of your classmates' code as well. trace their code and predict what it will output, then check the code by running it to see if you got it right, and submit your work for a grade.
By using Python, you will come up with your own challenging algorithm for other students to trace.
What are If else Statements ?If a certain is true, the if/else expression triggers a sequence of instructions to run. Another piece of code may be run if the condition is false.
The if/else statement is a component of Python's "Conditional" Statements, which are used to carry out various operations based on various circumstances.
These conditional statements are available in Python:
If you want a block of code to run only if a certain condition is true, use the if statement.
If the same expression is false, use instead that to provide a set of instructions that should be run.
If the first expression is false, can use else if sentence to establish a comprehensive criterion to test.
To choose which of the several program code should be performed, use the switch.
How to write the code?
num = 100
if num < 20:
print('Less than 20')
if num < 30:
print('Less than 30')
if num < 40:
print('Less than 40')
if num < 50:
print('Less than 50')
if num > 100 or num == 100:
print('More than or equal to 100')
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I need help fast plss
The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°
Finding the measures of the anglesFrom the question, we have the following parameters that can be used in our computation:
The transversal lines and the other lines
So, we have
∠1 = 180 - 53
Evaluate
∠1 = 127°
Also, we have
∠5 = 53°
By vertical angles, we have
∠2 = 53°
∠3 = 127°
Next, we have
∠4 = 127 - 90°
∠4 = 37°
Solving further, we have
∠6 = 90°
By corresponding angles, we have
∠7 = 37°
∠9 = 180 - 90 - 53°
∠9 = 37°
∠10 = 90 + 53°
∠10 = 143°
∠8 = 143°
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please help me find the volume and surface area of this square pyramid.
answer plsss ASAP !!!!!!!!!!!!!!!1!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Point B
Step-by-step explanation:
The square root of 38 is 6.164, and point B is closest to 6.164
32 + (-12 7/8) what is it I mak u brainlyiest or whatever
Answer:
The answ is 20 7/8
Step-by-step explanation:
Answer:
44 7/8
Step-by-step explanation:
Hope this helps!
And just to make sure do you mean twelve and seven eighths?
Determine whether each of the following is a power series. For any that are, state where they are centered. Σ( – η)^n
Yes, Σ( - η)^n is a power series.
It is centered at η = 0. The general form of a power series is Σ(a_n * (x - c)^n), where a_n represents the coefficients, x is variable, and c is the center of the series.
In this case, a_n = 1, x = η, and c = 0.
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Write True and false
A test statistic based on point estimation is used to construct the decision rule which defines the rejection region.
The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.
In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.
The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.
Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.
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False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.
The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.
Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.
While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.
The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.
Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.
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Work out the volume of this sphere 19cm
V=4/3πr3
The answer is V≈28730.91
Answer:
Step-by-step explanation:
I dont know if the radius is 19cm or 9.5cm so ill just do both
19cm
\(V=\frac{4}{3} \pi r^3\\=\frac{4}{3} *\pi *19^3\\=28730.91cm^3\)
9.5cm
\(V=\frac{4}{3} \pi r^3\\=\frac{4}{3} *\pi *9.5^3\\=3591.36cm^3\)
I need help with this
The length of a line segment that has endpoints (-1, 3) and (5, 11) is 10 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
By substituting the given end points into the distance formula, we have the following;
Distance = √[(5 + 1)² + (11 - 3)²]
Distance = √[(6)² + (8)²]
Distance = √[36 + 64]
Distance = √100
Distance = 10 units.
Read more on distance here: brainly.com/question/12470464
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Which one is it?????
April shoots an arrow upward at a speed of 80 ft/sec from a platform of 25 ft. High. The pathway of the arrow can be represented by the equation h = -16t^2 + 80t + 25, where h is the height and t is the time in seconds. What is the maximum height that the arrow reaches
Answer:
125feet
Step-by-step explanation:
Given the equation that modeled the height expressed as h = -16t^2 + 80t + 25, where h is the height and t is the time in seconds.
The arrow reaches the maximum height at dh/dt = 0
dh/dt = -32t + 80
0= -32t+80
32t = 80
t = 80/32
t = 2.5secs
substitute t = 2.5 into the formula;
h = -16t^2 + 80t + 25
h = -16(2.5)^2 + 80(2.5) + 25
h = -16(6.25)+225
h = -100+225
h = 125
Hence the maximum height the arrow reaches is 125feet