define a transformation t:[3->[2by t(x)=ax. find t(u), the image ofuunder the transformation t.
The transformation t is defined as t(x) = ax, where a is a constant.
To find the image of u under the transformation t, we need to substitute u for x in the expression t(x).
The transformation t:[3 ≥ [2 is defined as t(x)=ax, where a is a constant.
This means that for any given value of x in the domain [3,
the transformation t maps it to a corresponding value of ax in the codomain [2.
To find the image of u under the transformation t
t(u) = au.
This means that the image of u under the transformation t is the value of au in the codomain [2.
For example, if u = 4 and a = 2, then t(u) = 2(4) = 8, which is the image of u under the transformation t.
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How
do you solve this for coefficients?
g(x) = { 1₁ -1 - T≤x≤0 осхь п 1 f(x+2TT) = g(x)
The coefficient for the interval -T ≤ x ≤ 0 in the function g(x) is 1. However, the coefficient for the interval 0 ≤ x ≤ 2π depends on the specific form of the function f(x). Without additional information about f(x), we cannot determine its coefficient for that interval.
To solve for the coefficients in the function g(x), we need to consider the conditions given:
g(x) = { 1, -1, -T ≤ x ≤ 0
{ 1, f(x + 2π) = g(x)
We have two pieces to the function g(x), one for the interval -T ≤ x ≤ 0 and another for the interval 0 ≤ x ≤ 2π.
For the interval -T ≤ x ≤ 0, we are given that g(x) = 1, so the coefficient for this interval is 1.
For the interval 0 ≤ x ≤ 2π, we are given that f(x + 2π) = g(x). This means that the function g(x) is equal to the function f(x) shifted by 2π. Since f(x) is not specified, we cannot determine the coefficient for this interval without additional information about f(x).
The coefficient for the interval -T ≤ x ≤ 0 is 1, but the coefficient for the interval 0 ≤ x ≤ 2π depends on the specific form of the function f(x).
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I need help. Find the value of x.
Answer:
11
Step-by-step explanation
sorry
find the perimeter in inches of the polygon. 7 in.24 in. a right triangle is given. one leg is labeled 7 inches. the other leg is labeled 24 inches. the hypotenuse is not labeled. in
The perimeter of the triangle is 56 inches.
The Pythagorean theorem is a fundamental concept in mathematics that relates to the sides of a right triangle. It states that the square of the length of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the lengths of the other two sides
We can use the Pythagorean theorem to find the length of the hypotenuse, which is the missing side of the right triangle:
\(c^2 = a^2 + b^2\)
\(c^2 = 7^2 + 24^2\)
\(c^2 = 625\)
c = 25
So the length of the hypotenuse is 25 inches. The perimeter of the triangle is the sum of the lengths of its three sides:
P = 7 + 24 + 25
P = 56
Therefore, the perimeter of the triangle is 56 inches.
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what is a geometric sequence with a first term of 3/4 and a constant ratio of 4
Answer:
Below
Step-by-step explanation:
A geometric sequence is a sequence where you keep multiplying a term by the ratio to generate the next one.
The first term is 3/4
Let n0 = 3/4
The next term is n1.
To get n1 we must multiply n0 by the ratio 4.
● n1 = n0×4
This formula gives us the second term. We need a general one that can generate all the terms of the sequence.
Let S(n) be a term of this sequence.
To get n we have multiplied n0 (the first term) by 4 (the ratio) one or many times. Precisely, n times.
So:
● S(n )= n0 ×4^n
no is 3/4
● S(n)= (3/4) × 4^n
This formula generates any term from this geometric sequence. If you want to calculate the 77th term then just replace n with 77.
Answer:
Step-by-step explanation:
To find the next term, multiply the previous term by constant ratio
a₁ = 3/4
\(a_{2}=\frac{3}{4}*4=3*1 = 3\\\)
a₃ = a₂ * constant ratio = 3 * 4 = 12
a₄ = a₃ * constant ratio = 12 *4 = 48
Geometric sequence :
3/4, 3,12, 48, 192,.......
Sergio has p paintings in his art collection. He and other local painting collectors agreed to donate a total of 484848 paintings to the local museum. Each of the 121212 collectors will donate the same number of paintings.
The expression for the number of paintings Sergio will have in his art collection after his donation is p - 4
How to calculate the expression?Number of Sergio's paintings = p
Total number of paintings to donate = 48
Number of collectors to donate (including Sergio) = 12
Number of paintings donated by each collector = Total number of paintings to donate ÷ Number of collectors to donate
= 48 ÷ 12
= 4 paintings per collector
Therefore,
Number of paintings Sergio will have in his art collection after his donation = Number of Sergio's paintings - Number of paintings donated by each collector
= p - 4
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Complete question
Sergio has p paintings in his art collection. He and other local painting collectors agreed to donate a total of 48 paintings to the local museum. Each of the 12 collectors will donate the same number of paintings. How many paintings will Sergio have in his art collection after his donation? Write your answer as an expression
in geometry what is n = 1
it takes josh 40 minutes yo walk the dog it takes mike 80% as long to walk the dog how long does it take mike to walk dog
Answer:
32 minutes
Step-by-step explanation:
80% = .80
40 * .80 = 32
Find the volume of the sphere:
A. 452.4 cubic meters
B. 904.8 cubic meters
C. 150.8 cubic meters
D. 36 cubic meters
Work Shown:
r = 6 = radius
V = volume of a sphere of radius r
V = (4/3)*pi*r^3
V = (4/3)*pi*6^3
V = 904.77868423386
V = 904.8
I used my calculator's stored version of pi (instead of something like pi = 3.14)
The units "cubic meters" can be abbreviated to m^3 or \(m^3\)
The volume of the given sphere is 904.8 cubic meters. Thus, option B is the answer.
The volume of a sphere can be calculated using the formula:
V = \(4/3 * \pi * r^3\),
Where V is the volume and r is the radius of the sphere.
\(\pi\) = 3.14
The radius of the sphere (r) = 6m
Plugging in the given radius of 6m into the formula, we get:
V = (4/3) * \(\pi\) * (6^3)
V = 1.333 * \(\pi\) * 216
V = 1.333 * 3.14 * 216
V = 4.1866 * 216
V = 904.8 cubic meters
Therefore, when the radius of the sphere is 6m, the volume of the sphere is 904.8 cubic meters.
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Which linear inequality is represented by the graph?
y > 2x + 2
y ≥ One-halfx + 1
y > 2x + 1
y ≥ One-halfx + 2
Tthe inequality that describes this graph is y ≤ 1/3x - 4/3
How to determine the linear inequality represented by the graph?The graph that completes the question is added as an attachment
From the attached graph, we have the following points
(0, -1.3) and (3, -0.3)
The slope is calculated as:
m = (y2 - y1)/(x2 - x1)
Substitute the known values in the above equation
m = (-0.3 + 1.3)/(3 - 0)
Evaluate
m = 1/3
The equation is then calculated as:
y = m(x - x1) + y1
This gives
y = 1/3(x - 0) - 1.3
Evaluate
y = 1/3x - 4/3
From the graph, we have the following highlights:
The line of the graph is a closed lineThe upper part is shadedThe first highlight above implies, the inequality can be any of ≥ and ≤
While the second highlight above implies, the inequality is ≤
Hence, the inequality that describes this graph is y ≤ 1/3x - 4/3
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Jackie And her friends of their favorite organization. Jackie received four times the votes warren received .there were 200 ballots cast how many votes did Jackie receive
Answer:
800
Step-by-step explanation:
what is the area of the circle to the nearest square foot?
Answer:
G. 113
Step-by-step explanation:
We know that the diameter = 12, so the radius = 6.
area of circle = πr²
= π (6²)
= 36π
= 113.0973355 . . .
≈ 113 ft²
Which of the following expressions is equivalent to 4^−3?
A. 1/-4^-3
B. -4^-3
C. 1/4^3
D. 1/4^-3
Answer:
C
Step-by-step explanation:
Evaluate.
Exact Form:
1 /64
Decimal Form:
0.015625
Cat Behavior A report stated that the average number of times a cat returns to its food bowl during the day is 34. Assuming the variable is normally distributed with a standard deviation of 3 , what is the probability that a cat would return to its dish between 32 and 37 times a day? Round the final answer to four decimal places and intermediate z-value calculations to 2 decimal places. P(32
The probability that a cat would return to its food bowl between 32 and 37 times a day is approximately 0.589.
To find the probability that a cat would return to its food bowl between 32 and 37 times a day, we need to calculate the z-scores corresponding to these values and then find the area under the normal curve between these z-scores. Given: Mean (μ) = 34; Standard Deviation (σ) = 3. Step 1: Calculate the z-scores. For the lower value, 32: z₁ = (32 - 34) / 3 . For the higher value, 37: z₂ = (37 - 34) / 3. Calculating the z-scores: z₁ = -2 / 3 ≈ -0.67; z₂ = 1. Step 2: Calculate the probabilities. Now we need to find the area under the normal curve between these z-scores. This represents the probability that a cat would return to its food bowl between 32 and 37 times a day. Using a standard normal distribution table or calculator, we find the cumulative probabilities associated with the z-scores: P(Z ≤ -0.67) ≈ 0.2514; P(Z ≤ 1) ≈ 0.8413.
Step 3: Calculate the desired probability. To find the probability between the two values, we subtract the lower probability from the higher probability: P(32 ≤ X ≤ 37) = P(Z ≤ 1) - P(Z ≤ -0.67); P(32 ≤ X ≤ 37) ≈ 0.8413 - 0.2514; P(32 ≤ X ≤ 37) ≈ 0.5899. Therefore, the probability that a cat would return to its food bowl between 32 and 37 times a day is approximately 0.589.
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Let A € Rnxn, let c be a scalar and I €R"x" be the identity matrix. Assume that A is diagonalisable. Relate the diagonalisation of A + cI to that of A. Show all mathematical working. What are the eigenvalues and eigenvectors of A +cI in terms of the eigenvalues and eigenvectors of A?
The eigenvalues of (A + cI) are λ + c, where λ is an eigenvalue of A. The eigenvectors of (A + cI) are the same as the eigenvectors of A.
If A is diagonalizable, then A is similar to a diagonal matrix D. That is, there is an invertible matrix P such that P-1AP = D. For A + cI, where I is the identity matrix of the same size as A, we have the following:(A + cI) = A + cI = PDP-1 + cP
-1IP= P(D + cI)P-1Here, D + cI is a diagonal matrix whose diagonal entries are the diagonal entries of D with c added to them. Therefore, A + cI is diagonalizable since it is similar to a diagonal matrix. Furthermore, the eigenvectors of A + cI are the same as the eigenvectors of A, while the eigenvalues of A + cI are the eigenvalues of A, each of which is increased by c.
Eigenvalues and eigenvectors of A + cIIf λ is an eigenvalue of A with corresponding eigenvector v, then we have A v = λ v. Multiplying by (cI + A) on both sides, we get(cI + A) v = c v + λ v = (c + λ) vSo, (c + λ) is an eigenvalue of (A + cI) with corresponding eigenvector v. Conversely, suppose μ is an eigenvalue of (A + cI) with corresponding eigenvector u. We have (A + cI)u = μ u.
Multiplying by P-1 on both sides, we get P-1(A + cI)u = P-1(μ u). That is, P-1A(P-1u) + cP-1u = μP-1u. Letting w = P-1u, we see that A w = (μ - c) w. Thus, μ - c is an eigenvalue of A with corresponding eigenvector w.
Therefore, the eigenvalues of (A + cI) are λ + c, where λ is an eigenvalue of A. The eigenvectors of (A + cI) are the same as the eigenvectors of A.
This can be proved by applying the definition of eigenvectors.
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The diagram shows a right-angled triangle.
Use Pythagoras ' Theorem to work out the length of AC.
Answer:
AC = 15.52 centimeters
Step-by-step explanation:
Step 1) Determine the definition of the Pythagorean Theorem.
According to the Pythagorean Theorem, the square of the length of the hypotenuse of any right triangle equals the sum of each of the legs squared.
Step 2) Apply the theorem to the problem.
In this specific situation, AB and BC are the legs of the right triangle, while AC is the hypotenuse. This means that AB^2 + BC^2 should equal AC^2.
Step 3) Create an equation based on the formula.
The equation should look like this:
AB^2 + BC^2 = AC^2
4^2 + 15^2 = AC^2
16 + 225 = AC^2
241 = AC^2
AC = \(\sqrt{241}\)
AC = 15.52 centimeters
Hope this helps! Comment any questions <3
Nicole measured some distances on a map of Lassen Volcanic National Park. The scale on the map is 34
inch = 2 miles. What is the actual distance from Raker Peak to Hat Mtn?
Responses
A 4 miles4 miles
B 223
miles2 2 3 miles
C 214
miles2 1 4 miles
D 212
miles2 1 2 miles
E 3 miles
Performing a change of scale we will see that the actual distance is 4 miles.
What is the actual distance from Raker Peak to Hat Mtn?We know that the scale is:
3/4 inch = 2 miles.
And the distance that Nicole found on the map is (1 + 1/2) inches.
We can rewrrite the scale as:
1 inch = (4/3)*2 miles
1 inch = (8/3) miles.
Then the actual distance will be:
distance = (1 + 1/2) inches = (1 + 1/2)*(8/3) miles = 4 miles.
The correct option is A.
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What are the integer solutions to the inequality below?
4x+1<5x≤3(x+2)
Answer:
1<x≤3
Step-by-step explanation:
Which expression is equivalent to 2(a+3) when a= 3?
A 2(3)
B 5(3)
C 2(3)+3
D 2(3)+6
Answer:
D
Step-by-step explanation:
2(a+3), a=3
2(3+3)
2(6)
12
A) 2(3)=5 (not equivalent)
B) 5(3)=15 (not equivalent)
C) 2(3)+3=9 (not equivalent)
D) 2(3)+6=12 (equivalent)
Answer:
I believe it'll be D.
Step-by-step explanation:
2(a+3) would be 2(3+3). Following PEMDAS, it'll be 2(6), or in other words 12.
In the answer D, 2(3) would equal 6. And 6 + 6 equals 12.
Sorry if this explanation isn't proper enough.
The answer options are the 4 options given for all the answers, all of those options contain the right answer for part of the problem but need to be put in their correct place.
Part A. When we have two chords that intercept at one of the exterme points of a circle, like this:
Then the relationship between the minor arc and the interior angle of the chords is:
\(y=\frac{1}{2}x\)therefore, if we substitute according to the given circle we have:
\(a=\frac{150}{2}=75\)Therefore, angle a is 85°.
Part B. The angle formed by a tangent and a chord of a circle is half the the arc that is formed:
We have that:
\(y=\frac{1}{2}x\)Now, we substitute:
\(b=\frac{1}{2}(210)=105\)Therefore, "b" is 105°.
Part C. Given the following configuration:
The following relationship holds:
\(ab=cd\)Now, we substitute the values according to the given circle:
\((13)(c)=(16)(11)\)Now, we divide both sides by "c":
\(c=\frac{(16)(11)}{(13)}=13.5\)Therefore, the value of "c" is 13.5
Part D. In the following configuration:
The following relationship holds:
\(x=\frac{1}{2}(x+z)\)Now, we substitute the values:
\(d=\frac{1}{2}(85+75)\)Solving the operations:
\(d=80\)therefore, the angle "d" is 80 degrees.
Which of the following is a factor of xy 3y − 7x − 21?
The factor of xy 3y − 7x − 21 is x − 3.
xy 3y − 7x − 21 = x(y 3y − 7) − 21 = x(y 3y − 7) − 3(7) = (x − 3)(y 3y − 7)
The expression xy 3y − 7x − 21 can be simplified by factoring out the greatest common factor, which in this case is x. We can factor out an x by dividing the entire expression by x. This gives us y 3y − 7 − 21/x. Now, we can look for a common factor between the two terms. In this case, the factor is -3. We can factor out -3 from both terms to get -3/x and y 3y − 7. This can be rewritten as (x − 3)(y 3y − 7). Therefore, the factor of xy 3y − 7x − 21 is x − 3.
To explain further, factoring is the process of breaking down an expression into its factors. A factor is a number, variable, or expression that can be multiplied to produce the original expression. In this case, we are looking for the factors of xy 3y − 7x − 21. To find these factors, we first simplify the expression by factoring out the greatest common factor, which in this case is x. We then look for a common factor between the two terms, which is -3. We factor out -3 and rewrite the expression as
(x − 3)(y 3y − 7). This means that the factor of xy 3y − 7x − 21 is x − 3.
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Help please I need this asap
Answer:
It is a little hard to see. I think that it is 10.
Step-by-step explanation:
They break even where the two lines intersect. If you look at the bottom of the graph and find 10 and then trace that straight up, I think that is where I see the lines crossing.
christina's pizza sells pizza by the slice for lunch. today, they sold 76 slices, including 20 slices of pepperoni pizza. what is the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza?
The experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is approximately 0.263
The experimental probability is found by dividing the number of times the desired outcome occurred by the total number of trials. In this case, the desired outcome is selling a slice of pepperoni pizza as the first slice tomorrow.
Since we only know the number of slices sold today, we don't have any specific information about the number of slices that will be sold tomorrow. However, we can assume that the same types of pizzas will be sold tomorrow, and the probability of selling a slice of pepperoni pizza tomorrow will be the same as the proportion of pepperoni slices sold today.
So, the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is
Experimental probability = Number of pepperoni slices sold today / Total number of slices sold today
Experimental probability = 20 / 76
Experimental probability = 0.263
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alex stocks up for winter . he buys 36 cans of vegetables. He pays 80 cents per can for tomatoes and 40 cents per can for corn, for a total cost of $20.8. How many cans of corn does he buy?
Answer:
Therefore, Alex buys 20 cans of corn.
Step-by-step explanation:
Let's assume Alex buys x cans of tomatoes and y cans of corn.
Given that he buys 36 cans in total, we can write the equation:
x + y = 36 ----(1)
The cost of tomatoes per can is 80 cents, and the cost of corn per can is 40 cents. The total cost is $20.8, which can be expressed as 2080 cents.
The cost of the tomatoes (80 cents per can) multiplied by the number of tomato cans (x) gives the cost of tomatoes, and the cost of corn (40 cents per can) multiplied by the number of corn cans (y) gives the cost of corn. The sum of these costs should equal 2080 cents.
80x + 40y = 2080 ----(2)
Now we have a system of equations (equations (1) and (2)) that we can solve to find the values of x and y.
To solve the system, we can use substitution or elimination. Let's use the substitution method here.
From equation (1), we have:
x = 36 - y
Substituting this value of x into equation (2), we get:
80(36 - y) + 40y = 2080
Expanding and simplifying:
2880 - 80y + 40y = 2080
2880 - 40y = 2080
-40y = 2080 - 2880
-40y = -800
y = (-800) / (-40)
y = 20
Therefore, Alex buys 20 cans of corn.
Answer:
20
Step-by-step explanation:
Let x be the number of cans of corn Alex buys.
Then, the number of cans of tomatoes he buys is 36-x.
The cost of the cans of tomatoes is:
\((36 - x) \times 0.80\)
The cost of the cans of corn is:
\(x \times 0.40\) dollars
The total cost is:
\((36-x) \times 0.80 + x \times 0.40 = 20.8 dollars\)
Simplifying the expression, we get:
28.8 - 0.40x = 20.8
0.40x = 8
x = 20
Therefore, Alex buys 20 cans of corn.
hope it helps...
Brainliest! Fast answer! Correct answer!
Answer:
It would be C i believe
Step-by-step explanation:
a high school senior uses the internet to get in- formation on february temperatures in the town where he’ll be going to college. he finds a web site with some sta- tistics, but they are given in degrees celsius. the conver- sion formula is °f
It reaches a high of 51.8 degrees Fahrenheit. There is a 59.4 degree F range. 12.6 degrees Fahrenheit is the standard deviation. The average temperature is 33.8°F. The median temperature is 35.6 °F. IQR is 60.8 degrees Fahrenheit.
What is statistics?The study of statistics focuses on gathering, organizing, organizing, analyzing, interpreting, and presenting data. It is customary to start with a statistical population or a statistical model to be researched when applying statistics to a scientific, industrial, or social problem. The study of gathering, analyzing, interpreting, presenting, and organizing data in a particular way is the focus of the mathematic branch known as statistics. The process of gathering data, classifying it, presenting it in a way that makes it understandable, and then conducting additional analyses of the data is known as statistics.
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identify the parameters p and n in the following binomial distribution scenario. the probability of winning an arcade game is 0.489 and the probability of losing is 0.511. if you play the arcade game 15 times, we want to know the probability of winning more than 8 times. (consider winning as a success in the binomial distribution.)
Here the parameters, p =0.489 and n=15, and the probability of winning more than 8 times is 0.17946
while you playing an arcade game, there are two possible outcomes: win or lose, which is related to the binomial distribution, such as :
P= \(C_{n,k}\) \(p^{n}\) \(q^{n-k}\)
where C is the combination, p is the probability of success and the q is the complement of the p (q=1-p) .Here we are given that the probability of winning an arcade game is 0.489 and the probability of losing is 0.511. So p= 0.489, since the number of the trial are 15, we need to find the probability for more than 8 times, which means
P(X>8)= P(X=9)+P(X=10)+P(X=11)+P(X=12)+P(X=13)+P(X=14)+P(X=15) P(X>8)=P(X>=8)- P(X=8)
= 0.34328- 0.16382
=0.17946
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Assertion: The sides of a triangle are in the ratio of 3: 4: 5 and its perimeter is 144cm. The area of the triangle is 864cm²
Reason: Perimeter of a triangle = a + b + c, where a,b,c are sides of a triangle.
Answer: Below
Step-by-step explanation: The three sides of the triangle are in the ratio of 3:4:5. There is some factor, x, for which we can add the three sides to arrive at the perimeter of the triangle:
3x + 4x + 5x = 144 cm
12x = 144 cm
x = 12 cm
The three sides are 36, 48 and 60 cm. We know that a 3:4:5 triangle has a right angle. We also know that if we square and then add the two sides adjacent to the right angle, that it will be equal to the square of the hypothenuse. We find that 36^2 + 48^2 does indeed equal 60^2 (both are 3600). The 36 and 48 cm sides are therefore the base and height of this triangle. Area is (1/2)bh, so A = (1/2)*(36)*(48). Area = 864cm^2
Fatima is taking a test that is 45 minutes long.
She finishes the test at 10:50 a.m.
What time did she start the test?
Answer:10:05
Step-by-step explanation:
subtract 45 from 50!
Answer:
She started the test at 10:05 am
Step-by-step explanation:
Take the end time and subtract the time of the test
10:50-45 = 10:05
She started the test at 10:05 am
When conducting a significance test in practice, how should you choose the alpha level? A.Use a larger alpha when the consequences of mistakenly rejecting the null hypothesis are more serious. B.Always use alpha-0.05 since it's the most appropriate for every situation.C. Always use alpha-0.05 since it's the most commonly used one.D.Use a smaller alpha when the consequences of mistakenly rejecting the null hypothesis are more serious
Always use alpha=0.05 since it's the most commonly used one. Use a smaller alpha when the consequences of mistakenly rejecting the null hypothesis are more serious.
A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory's veracity. It is sometimes referred to as just "the null," and its symbol is H0.
When the repercussions of incorrectly rejecting the null hypothesis are more severe, use a smaller alpha. Generally speaking, you should reject the null hypothesis less frequently when there is a greater risk of doing so, which happens as you lower the significance level.
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