Evaluate each expression. Write your answer in exact form.
cot (-150°)
Answers
The value of the cotangent function at cot (-150°) in exact form is -√3.
To evaluate the expression cot (-150°), we need to find the cotangent of -150 degrees.
The cotangent function is defined as the ratio of the adjacent side to the opposite side of a right triangle. In a unit circle, the cotangent is the reciprocal of the tangent.
To find the cotangent of -150°, we can consider its reference angle, which is 30°. The reference angle is the positive acute angle between the terminal side of the angle and the x-axis.
In the first quadrant, the cotangent is positive. However, in the third quadrant where -150° lies, the cotangent is negative. So, we need to find the negative value of the cotangent of 30°, which is -√3.
Therefore, the exact value of cot (-150°) is -√3.
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Related Questions
The most important condition for making an inference about a population mean from a significance test is that the data contain no outliers. the data come from a random sample. the sample size is at least 30. the sample size is less than 10% of the population size. the population distribution is exactly Normal.
Answers
The most important condition for making an inference about a population mean from a significance test is that option (b) the data come from a random sample
A random sample is essential to ensure that the sample is representative of the population and that the statistical inference is valid. Other conditions, such as the absence of outliers, sample size, or population distribution, may also affect the validity of the inference, but they are not as crucial as the random sampling condition.
In practice, it is recommended to check for outliers, assess the sample size and the population distribution, and ensure other assumptions of the statistical test are met, such as the normality of the sampling distribution or the equal variance assumption, depending on the test used. However, the random sampling condition remains the most fundamental requirement.
Therefore, the correct option is (b) the data come from a random sample
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Things that are equivalent to 5 : 2
Answers
Answer:
2/5
Step-by-step explanation:
Answer:
10 : 4, 15 : 6, 20 : 8,
Step-by-step explanation:
increase the first number by 5 then add two to the second number
a deparment store paid $56.46 for a cookware set. overhead expense is 25% of the regular selling price and profit is 13% of the regular selling price. during a clearance sale, the wet was sold at a markdown of 35%. what was the operating profit or loss on the sale?
Answers
the operating profit or loss on the sale is $0.
Let's begin by calculating the regular selling price of the cookware set. To calculate this, we need to first determine the overhead expense and profit.Overhead expense is 25% of the regular selling price:Let "x" be the regular selling price.
Then, 25% of x is 0.25x. So, overhead expense = 0.25x.Profit is 13% of the regular selling price:Again, let "x" be the regular selling price. Then, 13% of x is 0.13x. So, profit = 0.13x.Now, we can set up an equation using the information given in the problem. The department store paid $56.46 for the cookware set, which is 65% (100% - 35%) of the regular selling price. So,0.65x = $56.46
Solving for "x", we get,x = $86.86Now that we know the regular selling price, we can calculate the overhead expense and profit.Overhead expense = 0.25x = 0.25($86.86) = $21.72Profit = 0.13x = 0.13($86.86) = $11.31
During the clearance sale, the set was sold at a markdown of 35%, which means it was sold for 65% of the regular selling price.65% of $86.86 = $56.46This is the same price that the department store paid for the cookware set, so they did not make any profit or incur any loss on the sale.
To calculate the operating profit or loss on the sale, we need to compare the selling price during the clearance sale to the cost of the cookware set.Cost of cookware set = $56.46Regular selling price = $86.86Selling price during clearance sale = 65% of regular selling price = 0.65($86.86) = $56.46
The selling price during the clearance sale is the same as the cost of the cookware set. Therefore, the department store did not make any profit or incur any loss on the sale. This means that the operating profit or loss on the sale is $0.
The department store paid $56.46 for the cookware set. During the clearance sale, the cookware set was sold at a markdown of 35%. This means that the selling price during the clearance sale was $56.46. Since the selling price was the same as the cost, the department store did not make any profit or incur any loss on the sale. Therefore, the operating profit or loss on the sale is $0.
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let be the solution of the equation y'' 6y' 9y=0 satisfying the conditions y(0)=0 and y'(0)=1. find the value of the function f(x)=ln[y(x)/x] at x=1
Answers
The value of f(x) at x = 1 is approximately -3.0986.
How to find the differential equations ?The given differential equation is a second-order homogeneous linear differential equation with constant coefficients. The characteristic equation is \(r^2\) + 6r + 9 = 0, which can be factored as \((r + 3)^2 = 0\). Thus, the roots are repeated and equal to -3.
The general solution of the differential equation is \(y(x) = (c1 + c2 x) e^(-3x)\), where c1 and c2 are constants to be determined by the initial conditions.
Using the first initial condition y(0) = 0, we get c1 = 0.
Using the second initial condition y'(0) = 1, we get c2 = 1/3.
Therefore, the particular solution to the differential equation with the given initial conditions is y(x) = \((1/3)x e^(-3x)\).
Now, we need to find the value of \(f(x) = ln[y(x)/x]\) at x = 1.
\(f(x) = ln[y(x)/x] = ln[(1/3)x e^(-3x) / x] = ln[(1/3) e^(-3x)]\)
\(f(1) = ln[(1/3) e^(-3)] = ln(1/3) - 3 = -3.0986 (approx)\)
Therefore, the value of f(x) at x = 1 is approximately -3.0986.
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denclue is founded on a solid mathematical model for finding density attractors in the dataset under analysis
Answers
DenClue is founded on a solid mathematical model for finding density attractors in the dataset under analysis.
DenClue (Density-based Clustering) is a clustering algorithm that aims to identify dense regions in a dataset, known as density attractors. The algorithm is based on a solid mathematical model that enables the detection of these density attractors.
The mathematical model used in DenClue is rooted in the concept of density estimation. It employs a kernel density estimation technique, where each data point contributes to the estimation of the underlying density function. The density function describes the distribution of data points in the dataset.
By analyzing the density function, DenClue identifies regions with high density as density attractors. These attractors represent clusters or groups of data points that are tightly packed together, indicating significant patterns or structures within the dataset.
The mathematical model utilized in DenClue ensures that the algorithm is based on rigorous mathematical principles and statistical analysis. This foundation allows for accurate and reliable identification of density attractors, leading to effective clustering of the dataset.
Overall, the solid mathematical model underlying DenClue provides a robust framework for density-based clustering, facilitating the exploration and understanding of complex datasets by revealing meaningful patterns and structures through the identification of density attractors.
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If a hypothesis test has a type I error probability of 0.05, what does this mean?
a. If the null hypothesis is true, we don't reject it 5% of the time.
b. If the null hypothesis is false, we reject it 5% of the time.
c. If the null hypothesis is true, we reject it 5% of the time.
d. If the null hypothesis is false, we don't reject it 5% of the time.
Answers
Option c is correct
c. If the null hypothesis is true, we reject it 5% of the time.
Null hypothesis :
The null hypothesis and the alternative hypothesis are types of conjectures used in statistical tests, which are formal methods of reaching conclusions or making decisions on the basis of data. The hypotheses are conjectures about a statistical model of the population, which are based on a sample of the population. The tests are core elements of statistical inference, heavily used in the interpretation of scientific experimental data, to separate scientific claims from statistical noise.
"The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength of the evidence against the null hypothesis. Usually, the null hypothesis is a statement of 'no effect' or 'no difference'."It is often symbolized as H0.
The statement that is being tested against the null hypothesis is the alternative hypothesis. Symbols include H1 and Ha.
Statistical significance test: "Very roughly, the procedure for deciding goes like this: Take a random sample from the population. If the sample data are consistent with the null hypothesis, then do not reject the null hypothesis; if the sample data are inconsistent with the null hypothesis, then reject the null hypothesis and conclude that the alternative hypothesis is true."
given that
If a hypothesis test has a type I error probability of 0.05
When we reject the null hypothesis in hypothesis testing even though it is true, this is known as a Type 1 error.
Given: The Type I error probability for a hypothesis test is 0.05.
It has the numerical value 5%.
therefore, option c is correct
c. If the null hypothesis is true, we reject it 5% of the time.
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A manufacturer determines that the number of toys it can sell is given by the formula
T=-4p2+160p-305, where p is the price of the toys in dollars.
At what price will the manufacturer sell the maximum number of toys and what is the maximum
number of toys that can be sold?
Answers
Answer:
The price where the manufacture sells the maximum number of toys is $20
Step-by-step explanation:
The given equation for that represents the number of toys the manufacturer can sell is given as follows;
T = -4·p² + 160·p - 305
Where;
p = The price of the toys in dollars
At the point where the manufacture sells the maxim number of toys on the graph of the equation T = -4·p² + 160·p - 305, which is the top of the graph, the slope = 0
Therefore, at the maximum point;
The slope = 0 = dT/dp = d(-4·p² + 160·p - 305)/dp = -8·p + 160
∴ -8·p + 160 = 0
160 = 8·p
8·p = 160
p = 160/8 = 20
The price where the manufacture sells the maximum number of toys is = p = 20 dollars
(1) tyler ate x fruit snacks, and han ate 3/4 less than that. write an expression for the number of fruit snacks han ate. (2) mai skated x miles, and clare skated 3/5 farther than that. write an expression for the distance clare skated
Answers
(1) Han ate: x(1 - 3/4) = x/4. (2) Clare skated: x(1 + 3/5) = 8/5x.
What is algebraic expression ?
An algebraic expression is a mathematical phrase that can include numbers, variables, and operations. It represents a value or a set of values, but it does not provide a specific numerical result until the variables are replaced with specific numbers.
(1) Let's say x is the number of fruit snacks Tyler ate.
Han ate 3/4 less than that, so the expression for the number of fruit snacks Han ate would be x - (3/4)x = x(1 - 3/4) = x/4.
(2) Let's say x is the number of miles Mai skated.
Clare skated 3/5 farther than that, so the expression for the distance Clare skated would be x + (3/5)x = x(1 + 3/5) = 8/5x.
(1) Han ate: x(1 - 3/4) = x/4. (2) Clare skated: x(1 + 3/5) = 8/5x.
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(n + 18)
(2n)
What is the value of n
Answers
Answer: if this is what you wanted ,I think that n=0 and /or n= -18
Step-by-step explanation:
In an equation equal to 0 you can say that if it is a product like that : A x B =0 so A or / and B can be equal to 0 so you have to search when A=0 and when B=0 separately then you know when n is equal to 0 so the values of n . I’m sorry if it is not what you needed as an answer.
What are the solutions of the quadratic equation below?
x²-4x-6=0
Answers
Answer: x=2±√10 or x=5.16227766
Step-by-step explanation:
40 ahletes are surveyed it is found that 30 athletes play tennis and 10 play gold 5 play both. what is the probability an athlete plays golf or tennis but not both?
Answers
The probability an athlete plays golf or tennis but not both = 0.75
Probability:The ratio of favorable outcomes to all possible outcomes of an event is known as probability.
The formula to calculate the probability of an event is given by
Probability(E) = Favorable Outcomes/Total Outcomes
Here we have 40 athletes,
Number of athletes who plays both tennis and golf = 5
Number of athletes who plays tennis = 30
=> Number of athletes who plays only tennis = 30 - 5 = 25
Number of athletes who plays golf = 10
Number of athletes who plays only golf = 10 - 5 = 5
From the above calculations,
Number of athletes who plays tennis or golf but not both = 25 + 5 = 30
Probability that athletes play golf or tennis but not both = 30/40 = 0.75
Therefore,
The probability an athlete plays golf or tennis but not both = 0.75
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a rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a​ single-strand electric fence. with m of wire at your​ disposal, what is the largest area you can​ enclose, and what are its​ dimensions?
Answers
To find the largest area you can enclose with a single-strand electric fence and m units of wire at your disposal, you need to optimize the dimensions of the rectangular plot.
Let's denote the length of the rectangular plot as L and the width as W. The perimeter of the plot can be calculated as P = L + 2W.
Since one side of the plot is already bounded by the river, we have L + W = m. Rearranging this equation, we get L = m - W.
To find the largest area, we need to maximize the function A = L * W. Substituting the value of L, we have A = (m - W) * W.
Expanding the equation, we have A = mW - W^2.
To find the maximum value of A, we take the derivative of A with respect to W and set it equal to zero: dA/dW = 0.
Differentiating, we get m - 2W = 0. Solving for W, we have W = m/2.
Substituting this value back into the equation for L, we have L = m/2.
Therefore, the dimensions of the largest area are L = m/2 and W = m/2.
To find the area, we substitute these values into the equation for A: A = (m/2) * (m/2) = m^2/4.
In conclusion, the largest area that can be enclosed is m^2/4, with dimensions L = m/2 and W = m/2.
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which shape has 4 square
Answers
Answer:
it is indeed the square
Step-by-step explanation:
Answer:
ummmm a triangle?
Step-by-step explanation:
LIke i dont know, kinda reminds me of my x never knew how to- never mind. Like just put traingle or whatever
a storage shed is to be built in the shape of a box with a square base. it is to have a volume of 729 cubic feet. the concrete for the base costs $5 per square foot, the material for the roof costs $6 per square foot, and the material for the sides costs $5.50 per square foot. find the dimensions of the most economical shed.
Answers
There is no minimum value for the side length x, and thus it is not possible to determine the dimensions of the most economical shed.
To find the dimensions of the most economical shed, we need to consider the cost of each component (base, roof, and sides) based on the given cost per square foot. Let's denote the side length of the square base as x.
The volume of the shed is given as 729 cubic feet, and since the base is square, the height of the shed is also x.
The cost of the base would be the area of the base (x * x) multiplied by the cost per square foot, which is 5 * x².
The cost of the roof would be the area of the base (x * x) multiplied by the cost per square foot, which is 6 * x².
The cost of the sides would be the sum of the areas of all four sides (2 * x * x) multiplied by the cost per square foot, which is 4 * 5.5 * x².
To find the most economical shed, we need to minimize the total cost, which is the sum of the costs of the base, roof, and sides.
Total Cost = Cost of Base + Cost of Roof + Cost of Sides
= 5 * x² + 6 * x² + 4 * 5.5 * x²
= 11 * x² + 22 * x²
= 33 * x²
To minimize the total cost, we need to minimize x², which means finding the minimum value of x.
Taking the derivative of the total cost function with respect to x and setting it to zero, we can find the critical points:
d(Total Cost)/dx = 66 * x = 0
From this, we can see that x = 0 is not a valid solution. Therefore, we can divide both sides by 66 to find:
x = 0
Since the side length cannot be zero, we can conclude that the minimum value of x is not achievable.
Hence, there is no minimum value for the side length x, and thus we cannot determine the dimensions of the most economical shed based on the given volume and cost information.
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Look at the imagien BUT QUICKLY help
Answers
This is because a triangle angles add up to 180 the square means a 90 degree angle so 90+35=125
180-125=55
63+n=55. 63-55 =n. N=8 but it’s a negative because it just makes sense
board sum (-4)+1=x+(-4)
Answers
x=1
i gues dont know
hav nice day✌
Simplify the expression (−1 3/4)^2 - √ [127−2(3)]
Answers
On simplifying the expression (−1 3/4)²- √ [127−2(3)] we get -127/16
Simplifying an expression:
To simplify the expression, we need to follow the order of operations, which is PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, we simplify the exponent by squaring -1 3/4 to get 49/16. Then, we simplify the expression under the square root by subtracting 2 times 3 from 127 to get 121, and we take the square root of 121 to get 11.
Here we have
(−1 3/4)²- √ [127−2(3)]
The above expression can be simplified as follows
=> (−1 3/4)²- √ [127−2(3)]
Convert the mixed fraction into an improper fraction
=> 1 3/4 = 7/4 [ ∵ 4 × 1 + 3 = 7 ]
So given expression can be
=> (−7/4)²- √ [127−2(3)]
=> (49/16) - √ [121]
=> (49/16) - 11
=> (49 - 176 /16)
=> -127/16
Therefore,
On simplifying the expression (−1 3/4)²- √ [127−2(3)] we get -127/16
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MR. Reyes want wants to set aside an are at the beach for a family reunion. He wants to have at least 150 square feet. he finds a rectangular space that measures 9 3/4 feet by 14 2/3 feet will this large enough.
Answers
Answer:
No
Step-by-step explanation:
1. Since you are finding the area you would want to do the length times width.
9 3/4 x 14 2/3 =143 or (39/4) feet x ( 44/ 3 ) feet= 143 square feet
2. Conclusion: 143 square feet is less than 150 square feet, so the rectangular space would not be large enough.
Which angle is coterminal with a 110° angle?
O A. An angle measuring 460°
O B. An angle measuring -110°
C. An angle measuring 290°
O D. An angle measuring 470°
Answers
Answer:
D. An angle measuring 470*
Step-by-step explanation:In this question
The coterminal angle for 110° is 470°.
What are coterminal angles?"Coterminal angles are two (or more) angles that have their initial and terminal sides in the same positions. However, the angle measures differ either because one angle is measured clockwise and the other is measured counterclockwise".
For the given situation,
The angle is 110°.
The coterminal angles can be determined by adding or subtracting 360° to the given angle.
For 110° = \(360+110\)
⇒ \(470\)°
Hence we can conclude that the coterminal angle for 110° is 470°.
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Write the explicit formula for the sequence:
Answers
The explicit rule for the sequence is f(n) = 6 - 4(n - 1)
Finding the explicit rule for the sequenceFrom the question, we have the following parameters that can be used in our computation:
a1 = 6
a(n) = a(n - 1) - 4
In the above sequence, we can see that -4 is added to the previous term to get the new term
This means that
First term, a = 6
Common difference, d = -4
The nth term is then represented as
f(n) = a + (n - 1) * d
Substitute the known values in the above equation, so, we have the following representation
f(n) = 6 - 4(n - 1)
Hence, the explicit rule isf(n) = 6 - 4(n - 1)
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Please help, will mark brainliest!!! :D
btw, you can just answer in A B C D; A is upper left, B is upper right, C is lower left, D is lower right.
THANK YOUUUUUUUUUUUUU
Answers
Answer:
D because that the only that make sense
Step-by-step explanation:
What is the slope of a line that passes through the points shown in this table?
XY
00
13
26
Please enter your answer in the blank provided below (Example answer: 42)
Answers
The slope of a line that passes through the points is 3
What is a slopeA slope is defined as the ratio of rise to run of a line. It is expressed according to the formula below;
Slope = rise/run
Slope = y₂-y₁/x₂-x₁
Using the coordinate points (1, 3) and. (2, 6), the slope is expressed as:
Slope = 6-3/2-1
Slope = 3/1
Slope = 3
Hence the slope of a line that passes through the points is 3
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Fill in the blank with the correct response.
What is the scale factor?
3
S
R
ARST - AMNO
5.5 T
6
N
M
X
O
Answers
The scale factor of the dilation of the triangles is 2
What is the scale factor of the dilation?From the question, we have the following parameters that can be used in our computation:
The similar triangles
The scale factor of the dilation is the division of the corresponding sides
So, we have
Scale factor = 6/3
When evaluated, we have
scale factor = 2
Hence the scale factor is 2
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What is the mean absolute percent error of the following forecasts? Period Actual Demand Forecas 1 800 720
2 700 720
3 1800 720 4 300 720
5 750 720 A. 0 B. 0.4528 C.-0.1377 D. 150 E. 0.4337 F. 260.23 F. 1.1137 H. 326
Answers
The Mean Absolute Percent Error (MAPE) is a metric used to assess the accuracy of forecasts MAPE = 0.535 or 53.5%
1. Calculate the absolute errors (|Actual Demand - Forecast|)
2. Find the percentage errors (|Absolute Error / Actual Demand|)
3. Calculate the average of the percentage errors
For the given data, we have the following:
Period 1:\( |800 - 720| = 80\); Percentage Error = \(80 / 800 = 0.1\)
Period 3:\( |1800 - 720| = 1080\); Percentage Error =\( 1080 / 1800 = 0.6\)
Period 4:\( |300 - 720| = 420\); Percentage Error = \(420 / 300 = 1.4\)
Period 5: \(|750 - 720| = 30\); Percentage Error = \(30 / 750 = 0.04\)
Now, find the average percentage error:
\((0.1 + 0.6 + 1.4 + 0.04) / 4 = 2.14 / 4 = 0.535\)
\(MAPE = 0.535 or 53.5%\)
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A recipe called for the ratio of sugar to flour to be 10: 1. If you used 90 ounce of sugar, how
many ounces of flour would you need to use?
Answers
Answer:9 ounces of flours
Step-by-step explanation:90:9 ratio or sugar to flour
A company makes 130 bags.
49 of the bags have buttons but no zips.
32 of the bags have zips but no buttons.
39 of the bags have neither zips nor buttons.
A bag is selected at random.
What is the probability that the bag has buttons?
Answers
130-49 = 81
Answer 81/130
The probability that the bag has buttons is 0.38.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes.
Given that, a company makes 130 bags.
Here, the number of favorable outcomes = 49 and the total number of outcomes =130
Now, probability of an event = 49/130
= 0.38
Therefore, the probability that the bag has buttons is 0.38.
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please help im going to cry. anyway..
what would i write for the equations
Answers
Answer:
Equation 1: 2y + x = 81
Equation 2: 2y = 81 - x
Step-by-step explanation:
I used the word problem. Good luck.
Ruth buys 19 identical tickets for £280.25.
Estimate the cost of one ticket.
Answers
Answer:
The cost of one ticket is $14.75
Step-by-step explanation:
To find the cost of one ticket we need to divide 280.25 by 19
=$14.75
plz mark me as brainliest
Answer:
The cost of one ticket is $14.75
Step-by-step explanation:
The cost of one ticket is $14.75
To find the cost of one ticket we need to divide 280.25 by 19
=$14.75
please mark as brainliest
What is the answer and how do you get it?
Answers
Answer:
it would D, when you simplify both expressions, they get the same result which is 1024y^6
Match each interval with its corresponding average rate of change for q(x) = (x + 3)2. 1. -6 ≤ x ≤ 0 -1 2. -3 ≤ x ≤ -2 -3 3. -6 ≤ x ≤ -3 -4 4. -6 ≤ x ≤ -4 0 5. -4 ≤ x ≤ -3 3 6. -3 ≤ x ≤ 0 1