The equilibrium tuition price p and the consumers' and producers' surpluses at this tuition level is 11400
Find the equilibrium tuition price p and the consumers' and producers' surpluses at this tuition levelFrom the question, we have the following parameters that can be used in our computation:
q = 20,000 − 2p
q = 8,500 + 0.5p
The equilibrium tuition price p and the consumers' and producers' surpluses at this tuition level is when q = q
So, we have
20,000 − 2p = 8,500 + 0.5p
Evaluate the like terms
2.5p = 28500
Divide by 2.5
p = 28500/2.5
Evaluate
p = 11400
Hence, the equilibrium tuition price p is 11400
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3. A vehicle starting from rest (v(0) = m/s) at position x = 0 is subjected to the following acceleration, a(t):
A. Use your knowledge of derivatives and or integrals to plot the velocity and clearly indicate the maximum velocity on your graph
B. Given your results of part (a), use your knowledge of derivatives and or integrals to plot the position x (t), and clearly indicate the total distance traveled on your graph
Part A: The maximum velocity occurs at t = 0. We can plug this value into the velocity function to find the maximum velocity:
v_max = 0² = 0
Part B: The time at which the vehicle comes to rest is T = 0.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range.
The first step is to integrate the acceleration function to obtain the velocity function. Then, we can integrate the velocity function to obtain the position function.
Let's assume that the acceleration function is given by:
a(t) = 2t, where t is time in seconds.
Part A:
To find the velocity function, we integrate the acceleration function with respect to time:
v(t) = ∫a(t)dt = ∫2tdt = t² + C
where C is the constant of integration. We can find C by using the initial condition v(0) = 0.
v(0) = C = 0
Therefore, the velocity function is given by:
v(t) = t²
To find the maximum velocity, we can take the derivative of the velocity function and set it equal to zero:
dv/dt = 2t = 0
t = 0
Therefore, the maximum velocity occurs at t = 0. We can plug this value into the velocity function to find the maximum velocity:
v_max = 0² = 0
So, the maximum velocity is 0 m/s.
Part B:
To find the position function, we integrate the velocity function with respect to time:
x(t) = ∫v(t)dt = ∫t²dt = (1/3)t³ + C
where C is the constant of integration. We can find C by using the initial condition x(0) = 0.
x(0) = C = 0
Therefore, the position function is given by:
x(t) = (1/3)t³
To find the total distance traveled, we can find the area under the velocity graph. Since the velocity is always positive, the total distance traveled is the same as the total displacement. Therefore, we can find the displacement by finding the area under the velocity graph from t = 0 to t = T, where T is the time at which the vehicle comes to rest.
v(T) = 0
T² = 0
T = 0
Therefore, the time at which the vehicle comes to rest is T = 0.
The displacement is given by:
x_displacement = ∫v(t)dt from t=0 to t=T = ∫0 dt = 0
Therefore, the total distance traveled is 0 meters.
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Three fair coins are tossed. How many different outcomes will
there be?
Answer:
just 2 outcomes
Step-by-step explanation:
no matter how often you throw it, there are only two sides available
Music streaming services are the most popular way to listen to music. Data gathered over the last 12 months show Apple Music was used by an average of 1.81 million households with a sample standard deviation of 0.47 million family units. Over the same 12 months Spotify was used by an average of 2.21 million families with a sample standard deviation of 0.32 million. Assume the population standard deviations are not the same. Using a significance level of 0.02, test the hypothesis of no difference in the mean number of households picking either service.
a. Compute the test statistic.
b. Compute the p-value.
1. What is Maxwell's filing status?
a. Single
b. Married filing jointly
c. Head of household
d. Dependent
Maxwell's filing status can be described as: b. Married filing jointly.
What is a filing status?A filing status is a category that defines your tax-filing status based on your marital status and family situation. The filing status determines tax rate and standard deduction, as well as the eligibility for certain credits, deductions, and exemptions.
Maxwell can be described as married filing jointly because he and his spouse combined their income, deductions, and credits on one tax return. This status generally results in lower tax rates and a larger standard deduction compared to filing separately.
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A hard drive has enough storage space left for 7 1/2 hours of TV programmes. How many programmes each lasting 5/6 of an hour can be recorded on the hard drive?
Answer:
9
Step-by-step explanation:
7 1/2 divided by 5/6 would equal 9.
first step: convert the mixed number into an improper fraction.
7 1/2 = 15/2
2nd step: change the operation. (KCF)
keep the first term - change the operation - flip the second term
so, 15/2 x 6/5 =.
15x6=90
2x5=10
90/10 = 9
hope it helps!
Two numbers to have a hcf of 4 one of the numbers is between 10 and 20 and the other is between 20 and 40 what are the two numbers find all possible answers
To find all possible answers, we can start by listing all the numbers between 10 and 20, and all the numbers between 20 and 40, and then check which pairs of numbers have a highest common factor of 4.
Numbers between 10 and 20: 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
Numbers between 20 and 40: 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40
To have a highest common factor of 4, both numbers must be divisible by 4. Therefore, we can eliminate any numbers in these lists that are not divisible by 4.
Numbers between 10 and 20 that are divisible by 4: 12, 16, 20
Numbers between 20 and 40 that are divisible by 4: 20, 24, 28, 32, 36, 40
Now we can check which pairs of these numbers have a highest common factor of 4.
some possible answers are:
12 and 20
12 and 24
12 and 28
12 and 32
12 and 40
16 and 20
16 and 24
16 and 28
16 and 32
16 and 40
20 and 24
20 and 28
20 and 32
20 and 36
20 and 40
there are more answers, all you have to do is to pair 2 numbers.
if you do not want to include 20 and 40 make sure to not chose them.
Hope this could help.
Y can represent the distance Frog B hopped as y=x+ 8/3 x. Now rewrite the equation using the distributive property.
The rewritten expression of y = x + 8/3x using the distributive property is y = x(1 + 8/3)
Rewriting the equation using the distributive property.From the question, we have the following parameters that can be used in our computation:
Y can represent the distance Frog B hopped as y=x+ 8/3 x.
This means that
y = x + 8/3x
Factor out x from the equation
So, we have
y = x(1 + 8/3)
The above equation has been rewritten using the distributive property.
Hence, the rewritten expression using the distributive property is y = x(1 + 8/3)
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What is the surface area of the cylinder? Approximate using π = 3.14 and round to the nearest square meter.
A. 99 square meters
B. 122 square meters
C. 160 square meters
D. 553 square meters
The surface area of the cylinder to the nearest square meter include the following: C. 160 square meters.
How to calculate surface area of a cylinder?In Mathematics and Geometry, the surface area (SA) of a cylinder can be calculated by using this mathematical equation (formula):
SA = 2πrh + 2πr²
Where:
h represents the height.r represents the radius.By substituting the given parameters into the formula for the surface area (SA) of a cylinder, we have the following;
Surface area = 2πrh + 2πr²
Surface area = 2(3.14)(2.8)(6.3) + 2(3.14)(2.8²)
Surface area = 160 square meters.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
What is 5a^2b + 15ab^2 factories fully
Answer:
[tex]5 {a}^{2} b + 15a {b}^{2} = [/tex]
[tex]5ab(a + 3b)[/tex]
Can you write equation in conic form?
The equation x = 1/16y² - 1/8y + 17/16 in conic form is (y - 1)² = 16(x - 1)
Writing the equation in conic form?From the question, we have the following parameters that can be used in our computation:
x = 1/16y² - 1/8y + 17/16
Multply through the equation by 16
S, we have
16x = y² - 2y + 17
Rewrite as
16x - 17 = y² - 2y
Add the square of half the coefficient of y to both sides
So, we have
16x - 17 + 1 = y² - 2y + 1
Evaluate and express as perfect squares
16x - 16 = (y - 1)²
Factor out 16
16(x - 1) = (y - 1)²
Rewrite as
(y - 1)² = 16(x - 1)
The above equation is an equation of a parabola whose inverse has been calculated
Hence, the conic equation is (y - 1)² = 16(x - 1)
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At the store, 60% of the customers are parents and 40% of the customers are not. The average age of the parents is 52 years old. The average age of those not parents is 20 years old.
The average age of all the customers in the store, given the percentages that are parents and not, is 39.2 years.
How to find the average age ?To answer this question, we will use a weighted average formula. Since the percentage of parents and non-parents is given, we can use these percentages as weights.
Weighted Average Age = (Weight for Parents x Average Age of Parents) + (Weight for Non-Parents x Average Age of Non-Parents)
Parents:
Percentage (weight) = 60% = 0.60
Average age = 52 years
Non-Parents:
Percentage (weight) = 40% = 0.40
Average age = 20 years
Weighted Average Age = (0.60 x 52) + (0.40 x 20)
Weighted Average Age = 39.2 years
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The full question is:
At the store, 60% of the customers are parents and 40% of the customers are not. The average age of the parents is 52 years old. The average age of those not parents is 20 years old.
What is the average age of all the customers at the store?
Find the mean, median and mode of the data set. If there is no mode, enter the words "no mode". 72, 65, 68, 68, 73, 45, 68, 71
Answer:
Step-by-step explanation:
72+65+68+68+73+45+68+71 = 530
530/8 because there are 8 numbers
mean: 66.25
for the median, you line the numbers up from small to big and find the center number. But since there are 2 of them (68 and 68) , add 68+68 and divide by 2 which is still 68!
45,65,68,68,68,71,72,73
the mode is 68 because it is the most occurring number.
ok yea
PLEASE HELP ON QUESTION!(if answer and explanation is correct I'll rate you five stars a thanks and maybe even brainly. Also your very smart!)
What is value of x in this equation:
4x+15=33-2x
Answer: Simplifying
4x + 15 = 33 + -2x
Reorder the terms:
15 + 4x = 33 + -2x
Solving
15 + 4x = 33 + -2x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '2x' to each side of the equation.
15 + 4x + 2x = 33 + -2x + 2x
Combine like terms: 4x + 2x = 6x
15 + 6x = 33 + -2x + 2x
Combine like terms: -2x + 2x = 0
15 + 6x = 33 + 0
15 + 6x = 33
Add '-15' to each side of the equation.
15 + -15 + 6x = 33 + -15
Combine like terms: 15 + -15 = 0
0 + 6x = 33 + -15
6x = 33 + -15
Combine like terms: 33 + -15 = 18
6x = 18Divide each side by '6'.
x = 3
Simplifying
x = 3
so X=3 is your answer
Mackenzie answered 72 questions correctly on her multiple choice math final that had a total of 160 problems. What percentage of questions did Mackenzie answer correctly on the final exam?
Answer:
45%
Step-by-step explanation:
72/160 = 0.45
0.45 x 100 = 45%
raph the image of △BCD after a dilation with a scale factor of
1/3, centered at the origin.
Therefore, The dilated image's vertices are as follows:B'(2 , 3) C'(3 , 3) D'(1 , 3)
dilated image definition ?It is not necessary for the dilation's center to be inside the form. It might be the polygon's vertices. The preimage is still a square in this case, but the center of the dilatation is at the top-left vertex, which is shared by both of the dilated pictures (one smaller and one larger).
To get the vertices of the dilated image, multiply each vertex's coordinate by a factor of three.
B(6,9)⇒B'(1/3×6,1/3×9) = B'(2 , 3)
C(9,9)⇒C'(1/3×9 , 1/3×9) = C'(3 , 3)
D(3,9)⇒D'(1/3×3 ,1/3×9) = D'(1 , 3)
The dilated image's vertices are as follows:
B'(2 , 3) C'(3 , 3) D'(1 , 3)
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find the gcf of 8a^3b^2 and 12ab^4
Answer:
To find the greatest common factor (GCF) of 8a^3b^2 and 12ab^4, we need to factor each term into its prime factors and then find the common factors.
8a^3b^2 can be written as:
8a^3b^2 = 2^3 * 2 * a * a * a * b * b
12ab^4 can be written as:
12ab^4 = 2^2 * 3 * a * b * b * b * b
The common factors are 2, a, and b^2.
Therefore, the GCF of 8a^3b^2 and 12ab^4 is:
2 * a * b^2 = 2ab^2
Which of these is an accurate way to measure the volume of a rectangular prism
A. Fill it with water and then weigh the water.
B.Trace each face of the prism on centimeter grid paper, and then count the number of squares it comprises.
C. Measure the length and the width, and then multiply the two values.
D. pack it with unit cubes, leaving no gaps or overlaps, and count the number of unit cubes.
The correct option is (D) if unit cubes are packed into a rectangular prism without any gaps or overlaps, the volume of the prism can be calculated by counting the number of unit cubes.
What is a rectangular prism?A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases.
It also goes by the name cuboid.
Six faces, each with a rectangle shape and twelve edges, make up a rectangular prism.
It is referred to as a prism because of the length of its cross-section.
There are 6 faces, 8 vertices, and 12 edges on a rectangular prism.
A rectangular prism's volume can be determined by packing unit cubes into it without any gaps or overlaps, then counting the number of unit cubes.
A rectangular prism's surface area is equal to the sum of the areas of each of its faces.
It can be calculated using the formula 2(lw+ wh+ hl).
Therefore, the correct option is (D) if unit cubes are packed into a rectangular prism without any gaps or overlaps, the volume of the prism can be calculated by counting the number of unit cubes.
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a truck costs $30,000 and has an estimated life of 5 years with a residual value of $10,000. Prepare a depreciation schedule using the declining-balance method at twice the straight-line rate
The depreciation schedule for this truck using the declining-balance method at twice the straight-line rate are $24,000, $33,600, $39.744, $43,502 and $45,248
To create the depreciation schedule, we'll start with the cost of the asset and subtract the depreciation for each year. The depreciation for each year is calculated by multiplying the declining-balance rate by the book value of the asset at the beginning of the year.
The book value is simply the cost of the asset minus the accumulated depreciation. So in year 1, the book value is $30,000, and the depreciation is $8,000 (the declining-balance rate) times $30,000, which is $24,000. This means that the accumulated depreciation at the end of year 1 is $24,000.
To calculate the book value at the end of year 1, we simply subtract the accumulated depreciation ($24,000) from the cost of the asset ($30,000), which gives us $6,000.
=> $30000 - $6000 = $24000
This process is continued for the next five years that can be illustrated through the table.
Year Cost Depreciation Accumulated Depreciation Book Value
1 30,000 24,000 24,000 6,000
2 6,000 9,600 33,600 -3,600
3 -3,600 6,144 39,744 -9,744
4 -9,744 3,758 43,502 -13,502
5 -13,502 1,746 45,248 -15,248
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100 Points! Algebra question. Find each value if f(x)=5/x+2and g(x)=-2x+3. Only looking for an answer to question B. Please show as much work as possible. Photo attached. Thank you!
Therefore, the value of f(m-2) is 5/(m-2) + 2, and the value of function g(1/2) is 2.
What is function?In mathematics, a function is a rule or correspondence between two sets, where each input value from the first set (called the domain) corresponds to exactly one output value in the second set (called the range). A function is often represented by a formula, equation, or graph.
Here,
1. To find f(m-2), we substitute (m-2) for x in the expression for f(x):
f(m-2) = 5/(m-2) + 2
So the value of f(m-2) is 5/(m-2) + 2.
2. To find g(1/2), we substitute 1/2 for x in the expression for g(x):
g(1/2) = -2(1/2) + 3
So the value of g(1/2) is -1 + 3, which simplifies to 2.
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Based on the information in the table, what
was the approximate value of this item in
1980?
Answer:
B) 4,700
Step-by-step explanation:
6000 - 4000 = 2000
2000 in 15 year, find how much for each year
2000/ 15 = 133.3333333
133.3333333 estimated = 133
133 approximately for each year
1975 to 1980 is five years
133 x 5 = 665
4000 + 665 = 4665
4665 rounded the the nearest hundred
4700
solve for f
f/40 = 10/f
Answer:
Step-by-step explanation:
To solve for f, we can cross-multiply the equation:
f/40 = 10/f
Multiplying both sides by 40f gives:
f^2 = 400
Taking the square root of both sides yields:
f = ±20
Therefore, the solutions for f are f = 20 and f = -20. However, since f represents a physical quantity (presumably a frequency), we take only the positive value:
f = 20
find an equivalent expression to 2-4(x+1)-18
Answer:
Sure. Here are the steps on how to find an equivalent expression to 2-4(x+1)-18:
1. Expand the parentheses:
```
2-4(x+1)-18 = 2-4x-4-18
```
2. Combine like terms:
```
2-4x-4-18 = -4x-14
```
Therefore, the equivalent expression to 2-4(x+1)-18 is -4x-14.
2 - 4(x + 1) - 18 can be simplified as follows:
= 2 - 4x - 4 - 18 [distribute -4]
= -20 - 4x [combine like terms]
Therefore, an equivalent expression to 2-4(x+1)-18 is -20 - 4x.
The sales tax for an item was 11.70 and it cost 390 before tax.
Find the sales tax rate. Write your answer as a percentage.
The sales tax rate for the item is 3%.
How to find the sales tax rate?To find the sales tax rate, we can divide the sales tax amount by the original cost of the item, and then multiply by 100 to express the result as a percentage.
Given:
Sales tax amount = $11.70
Original cost of item = $390
Sales tax rate = (Sales tax amount / Original cost of item) x 100
Plugging in the given values:
Sales tax rate = (11.70 / 390) x 100
Calculating:
Sales tax rate = 0.03 x 100
Final result:
Sales tax rate = 3%
So, the sales tax rate for the item is 3%.
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PLEASE HELP!!!!!!!!!!!!!!!!!!!!!!
Find the probability of drawing a green, then yellow, with replacement.
A bag has 4 green blocks, 6 red blocks, 7 blue and 3 yellow.
The probability of drawing a green block followed by a yellow block with replacement is 0.03, or 3%.
What is probability?The probability of an event is calculated by dividing the total number of possible outcomes by the number of possible outcomes.
The likelihood of drawing a green block on the main draw is:
P(green) = (number of green blocks) / (total number of blocks)
P(green) = 4 / (4 + 6 + 7 + 3)
P(green) = 4 / 20
P(green) = 0.2
Since the blocks are replaced after each draw, the probability of drawing a yellow block on the second draw is still:
P(yellow) = (number of yellow blocks) / (total number of blocks)
P(yellow) = 3 / (4 + 6 + 7 + 3)
P(yellow) = 3 / 20
P(yellow) = 0.15
To find the probability of both events happening, we multiply the probabilities:
P(green, then yellow) = P(green) * P(yellow)
P(green, then yellow) = 0.2 * 0.15
P(green, then yellow) = 0.03
As a result, replacing a yellow block with a green one has a chance of 0.03, or 3%, being drawn.
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Working alone, Lisa can pick forty bushels of apples in 13 hours. One day her friend Cody helped and it only took them 4.8 hours to do it together. Find out how long it would take Cody to do it alone.
it would take Cody 40 bushels / 5.26 bushels per hour = 7.61 hours to pick 40 bushels of apples alone.
How to find Lisa's individual work?To begin, let's determine Lisa's individual work rate, or the amount of work she can complete in an hour.
The work formula states that the amount of work completed is equal to the product of the work rate and the amount of time spent working. Lisa's work rate is 40 bushels divided by 13 hours equals 3.08 bushels per hour.
Let C represent Cody's work rate, and let t represent the amount of time it takes him to pick 40 bushels on his own.
At the point when Lisa and Cody cooperate, they pick 40 bushels, so we can compose:
Lisa's work + Cody's work = Total work
3.08 bushels/hour * 4.8 hours + C * 4.8 hours = 40 bushels
14.78 + 4.8C = 40
4.8C = 25.22
C = 5.26 bushels per hour
Consequently, it would take Cody 40 bushels/5.26 bushels each hour = 7.61 hours to pick 40 bushels of apples alone.
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What is the length of the diagonal from P to Q ?
Step-by-step explanation:
Use a modified Pythagorean theorem for 3 -D
diagonal = sqrt ( 9^2 + 12^2 + 8^2 ) = sqrt(289) = 17 units
Help pls! Average winter temperatures in 45 states were recorded and divided by geographical region.
Choose True or False.
A: The mean of Region 2 is 5.8 greater than the mean of Region 1.
B: The data of Region 2 has greater variability than the data of Region 3 because the data are clustered around a greater average temperature
C: The difference of the means of Region 2 and Region 3 is about twice the MAD of Region 3
D: The average of the means of the three regions is closest to the mean of Region 3
pls show work
The correct answer is a. True, b. False, c. True, d. True
How to find the mean of regions?The mean of Region 1 is 31+ (32+33+34)×3+35×4+36/15 = 33.6°CThe mean of Region 2 is 36+ 37+ 2x38+ (39+41)x3 +40x4+42/15 = 39.4°C
(The mean = all temperature of region divided by the number of states )
So, 39.4- 33.6 = 5.8 True
The data of Region 2 is more concentrated, So its variability is weaker than Region 3.So False (variability is comparing the density)
The mean of Region 3 is (32+ 2x (34+35+37+38)+ 36x3+ 39+ 40] ÷15 = 33.8°CThe difference is 39.4 - 33.8= 5.6
The MAD of Region 3 is (32 - 33.8) +2 x (34 -33.8) + 2x (35 - 33.8) + 4x (36-33.8) + 2x (37-33.8) + 2x (38-33.8) + (39-33.8) + (40-33.8) ÷ 15 = 2.64
2-64 × 2 = 5.28, so true
The average of mean is 33.6+ 39.4+ 33.8/3 = 35.633.8 is closest to 35.6, so true.
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if L(x) =sinx-cosx, then dxy=? A. cosx+sinx B. cosx-sinx C. sin²x+cosx D. none
Answer: To find d(L(x))/dx, we need to differentiate L(x) with respect to x using the derivative rules.
d(L(x))/dx = d/dx (sinx - cosx)
= cosx + sinx
Therefore, the correct answer is option A, cosx+sinx.
Step-by-step explanation:
XYZ Software employed three different salespeople last year. Person 1
earned $4700 in the first quarter, Person 2 earned $19,800 in the first quarter,
and Person 3 earned $6500 in the first quarter. What are the maximum FUTA
deductions for the first quarter?
OA. $291.40
OB. $1227.60
C. $403.00
D. $1128.40
The maximum FUTA deductions for the first quarter is $1092.Because none of the given options correspond to this result, the correct answer is not listed.
The Federal Unemployment Tax Act (FUTA) tax rate is 6% on the first $7,000 paid to each employee in a calendar year. Therefore, the maximum FUTA deduction for each employee is $420 ($7,000 x 0.06).
Person 1 earned $4700, so the FUTA deduction for Person 1 is $282 ($4700 x 0.06).
Person 2 earned $19,800, but only the first $7,000 is subject to FUTA. Therefore, the FUTA deduction for Person 2 is $420.
Person 3 earned $6500, so the FUTA deduction for Person 3 is $390 ($6500 x 0.06).
The total FUTA deduction for the first quarter is the sum of the FUTA deductions for each employee:
$282 + $420 + $390 = $1092
Therefore, the maximum FUTA deductions for the first quarter is $1092.Because none of the given options correspond to this result, the correct answer is not listed.
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Let sin (30°)
degrees, for cos(B) = 1/2.
=
Enter the angle measure (B), in degrees