write tan41π36 in terms of the tangent of a positive acute angle.
Answers
Tangent of a positive acute angle is tan(41π/36) = tan(π/12).
Let's discuss it further below.
To write tan(41π/36) in terms of the tangent of a positive acute angle, follow these steps:
1. First, we need to find an equivalent angle within the range of 0 to π/2 or 0 to 90 degrees. To do that, we can subtract multiples of π (180 degrees) from the given angle until it falls within this range.
2. Observe that 41π/36 is slightly more than π (180 degrees) because 41/36 > 1. So, subtract π from the angle:
tan(41π/36 - π) = tan(41π/36 - 36π/36) = tan(5π/36)
3. Now the angle is 5π/36, which is a positive acute angle within the desired range (0 to π/2). So, tan(41π/36) can be written as tan(5π/36) in terms of the tangent of a positive acute angle.
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Related Questions
Find an equation of the line tangent to the curve y=1/2(ln(sin^2(x))) at the point (pi/4 , -1/2ln2)
Answers
Given:
Equation of Curve is:
\(y=\frac{1}{2}\ln (\sin ^2x)\)To find: Equation of tangent to the curve at point
\((\frac{\pi}{4},\frac{-1\ln 2}{2})\)Equation of tangent to the curve is given by:
\(y-y_1=m(x-x_1)\)where, m is slope of line.
Now, m is derivative of y with respect to x at given point.
Hence,
\(\begin{gathered} m=\frac{1}{2}\text{ }\times\frac{2\sin x\cos x}{\sin^2x} \\ m=\frac{\cos \text{ x}}{\sin \text{ x}} \\ m=\cot \text{ x} \end{gathered}\)At given point, the slope m is:
\(\begin{gathered} m=\cot (\frac{\pi}{4}) \\ m=1 \end{gathered}\)Therefore,the equation of tangent to the curve is given as:
\(\begin{gathered} y-y_1=1(x-x_1) \\ y-(\frac{-1(\ln \text{ 2))}}{2})=x-\frac{\pi}{4} \\ \frac{2y+\ln \text{ 2}}{2}=\frac{4x-\pi}{4} \\ 2y+\ln 2=\frac{4x-\pi}{2} \end{gathered}\)\(\begin{gathered} 4y+2\ln 2=4x-\pi \\ 4y=4x-\pi-2\ln 2 \end{gathered}\)Thus the required equation of tangent to the curve is
\(4y=4x-\pi-2\ln 2\)The critical value, or z*, that is used to construct a confidence interval for a proportion depends upon? A. the confidence level. B. the sample size.C. the confidence level and the sample size. D. the sample size and the sample proportion. E. the confidence level, the sample size, and the sample proportion.
Answers
The critical value that is used to construct a confidence interval for a proportion depends upon C. the confidence level and the sample size.
The critical value used to construct the confidence interval for proportion depends on:
1) The sample size:
The probability changes as the sample size changes as the distribution of the test statistics is dependent on sample size, thus the critical value will depend on sample size.
2) The confidence level:
The critical value is always calculated by using the confidence level, so it is dependent on it.
The sample proportion is the observed value which is used to perform the test, but not to construct the critical value.
Thus the correct option is:
Option C: The confidence level and sample size.
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The model shows the area (in square units) of each part of a rectangle. Use the model to find missing values that complete
the expression.
?
12
?
16
12+16=+D
Explain your reasoning.
Answers
Using the given model, we can complete the expression
12 + 16 = 4 × (4 + 3).
What are the area of a rectangle and a square?
The area of a rectangle having length "l" and breadth "b" is
Area of a Rectangle = l × b.
The area of a square with side "a",
Area of a square = side².
Let the given expression be 12 + 16 = x × (y + x)
For the given figure the area of the square which is displayed in pink portion can be expressed as
Area = y²
16 = y²
Taking square root on both sides, we get
y = 4.
Now for the red part, we get the length of the rectangle i.e., y = 4.
Area of a rectangle = length * breadth
12 = 4 * x
x = 3.
Hence, the expression would look like
12 + 16 = 4 × (4 + 3)
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The academic planner of a university thinks that at least 39% of the entire student body attends summer school. Which of the following is the correct set of hypotheses to test his belief?
a. H0: p ≤ 0.39
Ha: p > 0.39
b. H0: p > 0.39
Ha: p ≤ 0.39
c. H0: p ≥ 0.39
Ha: p < 0.39
d. H0: p < 0.39
Ha: p ≥ 0.39
Answers
The correct set of hypotheses to test the academic planner's belief that at least 39% of the entire student body attends summer school is option a.
This is because the null hypothesis (H0) always includes the equal sign, so in this case, it states that the proportion of students attending summer school (p) is less than or equal to 0.39. The alternative hypothesis (Ha) states that the proportion is greater than 0.39, which aligns with the academic planner's belief. Therefore, the correct set of hypotheses to test this belief is:
H0: p ≤ 0.39
Ha: p > 0.39
It is important to note that hypothesis testing involves collecting data and analyzing it to either reject or fail to reject the null hypothesis based on the level of significance and the calculated p-value.
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Odell has the same number of quarters, dimes, and nickels. He has $4. How many of each coin does he have?
Answers
Answer:
10 dim 10 nickel and 10 quarter
Step-by-step explanation:
10 dim=100
10 nickel=50
10 quarter=250
2x + 2 = x + 3 Please help asap
Answers
During the past five months, Elle
spent $3.25 on candy, $12.09 on
cupcakes, and $9.88 on chips. ABOUT
how much did Elle spend?
Answers
A bag contains 1 blue, 2 green, 3 yellow, and 3 red marbles, as shown.
What is the probability of drawing a red marble out of the bag without looking?
19
29
Answers
Answer:
1/3 or 33%
Step-by-step explanation:
5x + 55= 2x+ 100
Please answer.
Answers
Answer:
x = 15
Step-by-step explanation:
Given
5x + 55 = 2x + 100 ( subtract 2x from, both sides )
3x + 55 = 100 ( subtract 55 from both sides )
3x = 45 ( divide both sides by 3 )
x = 15
Subtract 2x from Both sides and subtract 55 from both sides so that’ll be 3x=45 divide both sides by 3 and get 15
What is the description method of sinigang?
(Description method set)
Answers
Answer:
Sinigang is a sour soup native to the Philippines. This recipe uses pork as the main ingredient. Other proteins and seafood can also be used.
Step-by-step explanation:
someone help please
Answers
Steps to finding the line in the diagram with the format 'ax + by = c
1. Find the slope
To find the slope, we need any two points on the line --> (0,4) and (3,0)\(Slope = \frac{y2-y1}{x2-x1} =\frac{4-0}{0-3} =-\frac{4}{3}\)
2. Set up, with any one point on the line and the slope, in point-slope form
\((y-y0)=m(x-x0)\\(y-4)=-\frac{4}{3} (x-0)\\y-4 = -\frac{4}{3} x\\\frac{4}{3}x+y = 4\)
Answer: \(\frac{4}{3}x+y = 4\)
Hope that helps!
Answer:
\(\sf 4x+3y=12\)
Step-by-step explanation:
Choose two points on the line:
Let \(\sf (x_1,y_1)=(0,4)\)
Let \(\sf (x_2,y_2)=(3,0)\)
Use the slope formula to find the slope of the line:
\(\sf slope(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{0-4}{3-0}=-\dfrac43\)
Use the point-slope formula to find the equation of the line:
\(\sf y-y_1=m(x-x_1)\)
Substitute values into the formula:
\(\sf y-4=-\dfrac43(x-0)\)
Expand the brackets:
\(\sf y-4=-\dfrac43x\)
Add 4 to both sides:
\(\sf y=-\dfrac43x+4\)
Rearrange into the form \(ax+by=c\)
Multiply both sides by 3
\(\sf 3y=-4x+12\)
Add 4x to both sides:
\(\sf 4x+3y=12\)
What can we say about the relationship between the correlation r and the slope m of the least-squares line for the same set of data?(Note: In the activities that are just about lines, the slope is written using the letter m in y=mx+b. The readings use the letter b for the slope in y = a + b*x. These slopes are the same slope—it's just whatever is multiplied by x is the slope, and represents the change in y for each 1-unit change in x—but in different contexts people usee different letters in the general form of the equation of a line.)Group of answer choicesr and m have the same sign (+ or −).Both r and m always have values between −1 and 1.The slope m is always equal to the square of the correlation r. m is always larger than r.m is always larger than r.r is always larger than m.
Answers
The correlation and the slope always have the same sign (+ or −), meaning that if the correlation is positive, the slope will also be positive and vice versa.
The slope and the correlation are two important measures in statistics. The slope of a line represents the change in the dependent variable (y) for every 1 unit change in the independent variable (x).
In the case of the least-squares line, the slope (m) and the correlation (r) have a relationship.
It is important to note that the slope of the line is always equal to the correlation times the ratio of the standard deviation of the dependent variable to the standard deviation of the independent variable.
This can be represented mathematically as:
=> m = r * (SDy/SDx).
Therefore, the correlation (r) always has a value between −1 and 1, indicating the strength of the relationship between the variables. If r is close to 1, the relationship between the variables is strong and positive.
On the other hand, if r is close to −1, the relationship between the variables is strong and negative.
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a schematic diagram that uses symbols to represent the parts of a system is a(n) ____.
Answers
A schematic diagram that uses symbols to represent the parts of a system is called a schematic or a circuit diagram.
A schematic diagram is a type of diagram that represents a system or process using symbols, lines, and other graphical elements. The purpose of a schematic diagram is to convey information about a system or process in a clear and concise manner, making it easier to understand and analyze.
Schematic diagrams are commonly used in fields such as electrical engineering, mechanical engineering, and process engineering. They may be used to depict a wide range of systems or processes, including electronic circuits, hydraulic systems, HVAC systems, and manufacturing processes, among others.
In a schematic diagram, symbols are used to represent various components or elements of the system or process being depicted. For example, in an electrical circuit schematic, symbols might be used to represent resistors, capacitors, diodes, and other electronic components. Lines and other graphical elements are used to show the connections and interactions between the different components.
Schematic diagrams are an important tool in the design, analysis, and troubleshooting of systems and processes. They allow engineers and other professionals to quickly and easily understand the workings of complex systems, identify potential problems, and develop solutions.
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Suppose a normal distribution has a mean of 266 and a standard deviation of
12. What is P(x >= 242)
Answers
If we standarize the variable x, we get:
\(z=\frac{x-\mu}{\sigma}=\frac{x-266}{12}\)doing this inside the probability, we get the following:
\(\begin{gathered} P(x\ge242)=P(\frac{x-\mu}{\sigma}\ge\frac{242-266}{12})=P(z\ge-2) \\ By\text{ the property of the complement, we have:} \\ P(z\ge-2)=1-P(z<-2)=1-0.0228=0.9772 \\ \Rightarrow P(x\ge242)=0.97 \end{gathered}\)therefore, the probability is 0.97
Find the partial derivatives of the function f(x,y)=4x+8y−3x−5y fx(x,y) fy(x,y)= Note: You can earn partial credit on this problem.
Answers
The partial derivatives of the function f(x,y) = 4x + 8y - 3x - 5y are fx(x,y) = 1 and fy(x,y) = 3.
To find the partial derivatives of the function f(x,y) = 4x + 8y - 3x - 5y, we need to find the derivative of the function with respect to each variable separately.
To find the partial derivative with respect to x, we treat y as a constant and differentiate with respect to x. The derivative of 4x with respect to x is 4, and the derivative of -3x with respect to x is -3. So, the partial derivative of f(x,y) with respect to x, denoted as fx(x,y), is 4 - 3 = 1.
To find the partial derivative with respect to y, we treat x as a constant and differentiate with respect to y. The derivative of 8y with respect to y is 8, and the derivative of -5y with respect to y is -5. So, the partial derivative of f(x,y) with respect to y, denoted as fy(x,y), is 8 - 5 = 3.
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the micro devices company earned 3,632,859,678 dollars this year .2,459,632,852 dollars were earned last year .which is the best estemate of how many more dollars were earned this year and last year
Answers
Answer 1,173,226,826
Explanation
Take the 3,632,859,678 dollars and subtract it with your 2,459,632,852 dollars and it will come out to 1,173,226,826 dollars
What is the solution to the linear equation?
4b + 6 = 2 – b + 4
b = –2
b = 0
b = 4
b = 6
Answers
Answer:
b = 0
Step-by-step explanation:
4b + 6 = 2 - b + 4
4b + b = 2 + 4 - 6
5b = 6 - 6
5b = 0
b = 0 / 5
b = 0
Answer:
The answer is B.
Step-by-step explanation:
b=0
in a survey of 2480 golfers, 15% said they were left-handed. the survey's margin of error was 3%. construct a confidence interval for the proportion of left-handed golfers.
Answers
The confidence interval for the proportion of left-handed golfers is of:
(0.12, 0.18).
How to obtain a confidence interval?A confidence interval is calculated as the sample mean plus/minus the margin of error, hence the bounds of the confidence interval are given as follows:
Lower bound: sample mean - margin of error.Upper bound: sample mean + margin of error.In the context of this problem, these parameters are given as follows:
Sample mean: 15% as a percentage, 0.15 as a proportion.Margin of error: 3% as a percentage, 0.03 as a proportion.Hence the lower bound of the confidence interval for the proportion of left-handed golfers is:
0.15 - 0.03 = 0.12.
The upper bound of the confidence interval for the proportion of left-handed golfers is:
0.15 + 0.03 = 0.18.
Then the interval is:
(0.12, 0.18).
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Given ƒ(x) = −x − 1, find ƒ(0).
Answers
The value of f(0) is '-1'.
Let's see the step-by-step solution:
Step 1:
For f = -x -1
substitute the x with 0
So, f(0) = -0-1
Step 2:
Simplifying it: -0-1: -1
Thus, the value of f(0)= -1
HELP I NEED HELP ASAP
Answers
Answer:
constant... I think... sorry if it's wrong... just trying to help ;-;
Step-by-step explanation:
Hope this helped! Good luck! :)
Answer:
linear
Step-by-step explanation:
if you put it into an equation, it would be y = 5 + 2x, which is a linear (straight line) equation
The first two steps in determining the solution set of the system of equations, y = -x2 + 4x + 12 and y=-3x + 24,
algebraically are shown in the table.
Step
Equation
Step 1 |-x2 + 4x+12 --3x+24
Step 2
x? - 7x+12-0
Which represents the solution(s) of this system of equations?
(3, 15)
(4.36)
(3, 15) and (4, 12)
(-3, 33) and (-4, 36)
Answers
Answer:
C. (3,15) and (4, 12)
Step-by-step explanation:
Given the system of linear equations
y = -x² + 4x + 12 and y=-3x + 24
Since both equations represents the variable y, we will equate both of the equations together.
Step 1: Equating both equations together we have;
-x² + 4x + 12 = -3x + 24
-x²+3x+4x+12-24 = 0
-x²+7x-12 = 0
x² -7x+12 = 0
x²-4x-3x+12 = 0
x(x-4)-3(x-4)= 0
x-3(x-4) = 0
x = 3 and 4
Step 2: substitute x = 3 and 4 into any of the equations to get the value of y. Using equation 2
when x = 3, y = -3(3)+24
y = -9+24
y = 15
when x = 4, y = -3(4)+24
y = -12+24
y = 12
The solutions yo the system of equations are (3,15) and (4, 12)
Answer:
c
Step-by-step explanation:
or (3, 15) and (4, 12)
The zeroes of t' are - 3. 1, and 4 so the local extrema are located at these points. Choose the correct answer below. O A. True. The zeros of f' are local extrema so long as the denominator is nonzero at those points. OB. False. The zeros of f' are the inflection points of f. OC. True The zeros off' are the local extrema off. OD. False. A zero off' is a critical point and is a local extremum so long as f'(x) changes sigh Take, for example, the function f(x)=(x + 3)º(x-1)*(x-4)
Answers
The correct answer is: OC. True. The zeros of f' are the local extrema of f.
By the first derivative test, if f'(x) changes sign from positive to negative at a critical point, then there is a local maximum at that point. If f'(x) changes sign from negative to positive at a critical point, then there is a local minimum at that point.
In this case, the zeros of f' are -3, 1, and 4, which are the critical points of f. Therefore, by the first derivative test, there are local extrema of f at these points.
Option A is incorrect because the denominator of f' is not relevant in determining the local extrema of f. Option B is incorrect because the zeros of f' are not necessarily inflection points. Option D is incorrect because a zero of f' is not necessarily a local extremum unless f'(x) changes sign at that point.
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A theme park charges $52 for a day pass and $110 for a weekly pass. Last month 4,432 day passes were sold and 979 weekly passes were sold. How much money did they make on daily and weekly passes last month
Answers
The theme park made $230,464 on daily passes and $107,690 on weekly passes, for a total of $338,154.
How to calculate the amount of money made by a theme park on daily and weekly passes based?To calculate the amount of money made on daily passes, we need to multiply the number of day passes sold by the price per day pass:
Money made on daily passes = 4,432 x $52 = $230,464
To calculate the amount of money made on weekly passes, we need to multiply the number of weekly passes sold by the price per weekly pass:
Money made on weekly passes = 979 x $110 = $107,690
Therefore, the total amount of money made on both daily and weekly passes last month is:
$230,464 + $107,690 = $338,154
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What is the best number?: Five million, three hundred eighteen thousand and eight or 73 because it is a binary ____?____?Select one:a. 73 because it is a binary palindromeb. Five million, three hundred eighteen thousand and eight because it is a binary palindromec. All of the aboved. None of the above
Answers
The binary representation of 5,318,008 is 10100010010010101111000, whereas the binary representation of 73 is 1001001.
We notice that 73 is a binary palindrome while 5,318,008 is not, therefore we conclude that the best number is 73 and the answer is a.
How do I find the measure qrs help????
I’m very confused thanks guys
Answers
Answer:
I do not know good luck my bro
Step-by-step explanation:
Answer:
∠QRS = 72°
Step-by-step explanation:
∠R + ∠Q = 180° (supplementary angles)
18x + 12x = 180
30x = 180
x = 6
∠R = 12x = 72° ∠Q = 18x = 108°
Each histogram represents a set of data with a median of 29.5. Which set of data most likely has a mean that is closest to 29.5?
A graph shows the horizontal axis numbered 9 to 48. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 33 then a downward trend from 33 to 45.
A graph shows the horizontal axis numbered 15 to 48. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 30 then a downward trend from 30 to 45.
A graph shows the horizontal axis numbered 12 to 56. The vertical axis is numbered 2 to 8. The graph shows an upward trend from 1 to 32 then a downward trend from 32 to 56.
A graph shows the horizontal axis numbered 15 to 54. The vertical axis is numbered 1 to 5. The graph shows an upward trend from 1 to 24, a downward trend from 24 to 27, an upward trend from 27 to 30, a downward trend from 30 to 39, an upward trend from 39 to 45, a downward trend from 45 to 48, then an upward trend from 48 to 51.
Answers
To determine which set of data most likely has a mean closest to 29.5, we need to analyze the shape and position of the histograms in relation to the value 29.5.
Looking at the histograms described:
The first histogram ranges from 9 to 48, and the upward trend starts from 1 and ends at 33, followed by a downward trend. This histogram suggests that there may be values lower than 29.5, which would bring the mean below 29.5.
The second histogram ranges from 15 to 48, with an upward trend from 1 to 30 and then a downward trend. Similar to the first histogram, it suggests the possibility of values lower than 29.5, indicating a mean below 29.5.
The third histogram ranges from 12 to 56, and the upward trend starts from 1 and ends at 32, followed by a downward trend. This histogram covers a wider range but still suggests the possibility of values below 29.5, indicating a mean below 29.5.
The fourth histogram ranges from 15 to 54 and exhibits multiple trends. While it has fluctuations, it covers a wider range and includes both upward and downward trends. This histogram suggests the possibility of values above and below 29.5, potentially resulting in a mean closer to 29.5.
Based on the descriptions, the fourth histogram, with its more varied trends and wider range, is most likely to have a mean closest to 29.5.
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please help me find what to plot for this (no decimals )
Answers
Answer:
(0, 6), (4, 5)
Step-by-step explanation:
graph (0, 6) first, then from those points go down -1 and over 4 to get (4, 5)
helppppppppppp me pleaseeee
Answers
tis the season for the slope formula
Answers
Answer:
65
Step-by-step explanation:because
10. (8 pts) A tank contains 200 gallons of water, in which 0.3 kg of salt has been dissolved. A brine solution containing 0.4 kg of salt per gallon is pumped into the tank at a rate of 5 gallons per minute, and the well stirred mixture is pumped out of the tank at the same rate. How many kg of salt will be in the tank after 10 minutes?
Answers
After 10 minutes, there will be 130 kg of salt in the tank.
The initial amount of salt in the tank is 0.3 kg. We need to find the amount of salt in the tank after 10 minutes of adding and removing brine solution.
During each minute, 5 gallons of brine solution with 0.4 kg of salt per gallon is added to the tank. So, the amount of salt added per minute is:
0.4 kg/gallon x 5 gallons/minute = 2 kg/minute
At the same time, 5 gallons of the mixture containing salt is removed from the tank. So, the amount of salt removed per minute is:
(0.3 kg + amount of salt added) / 200 gallons x 5 gallons/minute = (0.3 + 2t) / 200 kg/minute
where t is the number of minutes.
The change in the amount of salt in the tank after 1 minute is the difference between the amount of salt added and the amount of salt removed:
2 kg/minute - (0.3 + 2t) / 200 kg/minute = (400 - 3 - 4t) / 200 kg/minute
After 10 minutes, the amount of salt in the tank will be:
0.3 kg + integral from t=0 to t=10 of [(400 - 3 - 4t) / 200] dt
= 0.3 kg + [200t - 2\(t^2\) - 3t] evaluated from t=0 to t=10
= 0.3 kg + [200(10) - 2\((10)^2\) - 3(10)] - [200(0) - 2\((0)^2\) - 3(0)]
= 0.3 kg + 160 - 30
= 130 kg
Therefore, after 10 minutes, there will be 130 kg of salt in the tank.
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