The correct answer is B. power of the test
The probability that a test correctly rejects a false null hypothesis is referred to as the power of the test. It is a statistical measure that helps us to determine the effectiveness of a test in detecting a real difference or effect when it exists. The power of the test is generally represented by the Greek letter beta (β) and is calculated as 1-β.
A test with a high power value is more likely to correctly reject a false null hypothesis, which means it is better at detecting the real difference or effect when it exists. On the other hand, a test with a low power is more likely to fail to reject a false null hypothesis, which means it is not as effective in detecting the real difference or effect. The p-value and significance level are also statistical measures used in hypothesis testing, but they are not directly related to the power of the test.
P-value refers to the probability of observing a test statistic as extreme or more extreme as the one observed, given that the null hypothesis is true. Significance level refers to the threshold of p-value beyond which the null hypothesis will be rejected.
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Given f (x) = 4x + 3 – 2, what is f –1(x)?
f –1(x) = log4(x – 3) + 2
f –1(x) = log4(x + 3) – 2
f –1(x) = log4(x – 2) + 3
f –1(x) = log4(x + 2) – 3
The inverse function of f(x) = 4^(x + 3) -2 is f-1(x) = log₄(x + 2) - 3
How to determine the inverse function?The function is given as:
f(x) = 4^(x + 3) -2
Rewrite as:
y = 4^(x + 3) -2
Swap x and y
x = 4^(y + 3) -2
Add 2 to both sides
x + 2 = 4^(y + 3) -2 + 2
This gives
x + 2 = 4^(y + 3)
Take the logarithm of both sides
log(x + 2)= log(4)^(y + 3)
Apply the base rule of logarithm
log(x + 2)= (y + 3)log(4)
Divide both sides by log(4)
log(x + 2)/log(4) = y + 3
Apply the change of base rule of logarithm
log₄(x + 2) = y + 3
Subtract 3 from both sides
log₄(x + 2) - 3 = y + 3 - 3
Evaluate the difference
log₄(x + 2) - 3 = y
Rewrite as:
y = log₄(x + 2) - 3
Rewrite as:
f-1(x) = log₄(x + 2) - 3
Hence, the inverse function of f(x) = 4^(x + 3) -2 is f-1(x) = log₄(x + 2) - 3
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help please I really need it
A retailer buys a table costing £95 and sells it for £114 what is the name percentage change
Answer:
20% increase
Step-by-step explanation:
To find the percent increase, use this formula
New value - original value
----------------------------------------
original value
114-95
-----------
95
19
---- = .2
95
.2 is 20%, so it is a20% increase
Can someone answer this for me
The linear equation graphed is given by:
y - 5 = 3(x - 1).
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In point-slope form, considering a point [tex](x_0, y_0)[/tex], the equation is:
[tex]y - y_0 = m(x - x_0)[/tex]
The line goes through points (0,2) and (1,5), hence the slope is:
m = (5 - 2)/(1 - 0) = 3.
Since the line goes through point (1,5), the equation is:
y - 5 = 3(x - 1).
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Why is it important for the world to have an order of operations
Answer:
Well a sovial reason is that no one would no what order yo do it in, which would cause arguments
Answer:
without the order of operations, maths literally doesn't work.
Step-by-step explanation:
like whilst some equations don't rely on a particular order for solving, if you for example, don't solve brackets first, then try to multiply them by something else basically the equation breaks and you get the wrong answer. So... kids remember your BODMAS :)
3. Consider the equation 2x² + 4y² + 8x - 16y + F = 0. Find all values of F such that the graph of the equation is a) an ellipse b) a point - ellipse
The equation 2•x² + 4•y² + 8•x - 16•y + F = 0, at a value of F is the graph of an ellipse when we have;
a. A value of F that results in the equation of an ellipse is; F = 23
b. A point on the ellipse is ((-2), 2.5)
Which method can be used to find the value of F that gives the graph of an ellipse?The equation of an ellipse can be presented as follows;
[tex] \frac{(x - h) ^{2} }{ {a}^{2} } + \frac{(y - k) ^{2} }{ {b}^{2} } = 1[/tex]
The given equation can be presented as follows;
2•x² + 4•y² + 8•x - 16•y + F = 0
Collecting like terms, gives;
2•(x² + 4•x) + 4•y² - 16•y + F = 0
Adding a constant value to both sides, we get;
2•(x² + 4•x + 4) + 4•y² - 16•y + 16 + F = 24
2•(x + 2)•(x + 2) + (2•y - 4)•(2•y - 4) + F = 24
2•(x + 2)² + 4•(y - 2)² + F = 24
2•(x + 2)² + 4•(y - 2)² + F - 23 = 24 - 23 = 1
When F = 23, we have;
2•(x + 2)² + 4•(y - 2)² + 23 - 23 = 1
2•(x + 2)² + 4•(y - 2)² = 1Which gives;
[tex] \mathbf{\frac{(x + 2) ^{2} }{ \left( {\frac{1}{ \sqrt{2} }} \right)^{2}} + \frac{(y - 2) ^{2} }{ \left( {\frac{1}{ 2} } \right)^{2}} } = 1[/tex]
Where;
a = 1/(√2)b = 1/2b) A point on the ellipse can be found as follows;
2•(x + 2)² + 4•(y - 2)² = 1When x = -2
2•((-2) + 2)² + 4•(y - 2)² = 1
0 + 4•(y - 2)² = 1
y - 2 = √(1/4) = 1/2
y = 2 + 1/2 = 2.5A point on the ellipse is therefore;
((-2) , 2.5)When y = 2
2•(x + 2)² + 4•(2 - 2)² = 1
2•(x + 2)² + 0 = 1
2•(x + 2)² = 1
(x + 2)² = 1/2
x + 2 = √(1/2)
x = √(1/2) - 2
Another point on the ellipse is therefore;
((√(1/2) - 2), 0)
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Identify the correct trigonometry formula to solve for x
The correct trigonometry formula to solve for x in the right angled triangle is sin(62°) = 18 / x
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Hence:
sin(62°) = 18 / x
The correct trigonometry formula to solve for x in the right angled triangle is sin(62°) = 18 / x
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Complete this activity.
If the first element of the following pairs of numbers is a measure of hours and the second element is a measure of distance in miles, write an equation for D.
B = {(t, D ): (1, 50), (2, 100), (3, 150), . . .}
D =
t /2
50 t
50/ t
Answer:
D = 50t
Step-by-step explanation:
we see, with every additional hour the distance increases by 50.
that means in general that the number of hours are multiplied by 50 to get the distance.
in other words, this just calculates for a vehicle going constantly 50 miles per hour the distance it is traveling.
y varies indirectly as the square of x. if y=8 when x=4, find y when x=8
Given that, y varies indirectly as the square of x, the value of y when x equal 8 is 2.
What is the value of y when x equal 8?
Indirect variation is expressed as;
y ∝ 1/x
Given that;
y ∝ 1/x²
y = k/x²
Where k is the proportionality constant.
Given that;
y₁ = 8x₁ = 4x₂ = 8y₂ = ?First, we determine the proportionality constant.
y = k/x²
8 = k/4²
8 = k/16
k = 128
Now, we find y when x = 8
y = k/x²
y = 128 / 8²
y = 128 / 64
y = 2
Given that, y varies indirectly as the square of x, the value of y when x equal 8 is 2.
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A company's year-end data shows the following amounts. Current assets $65,000 Current liabilities $25,000 Net income $7,500 Net sales $125,000 Total assets $150,000 Based on this information, what is the company's current ratio?
The company's current ratio is 2.6.
What is the current ratio?
Current ratio is an example of a liquidity ratio. Liquidity ratios are financial ratios measure a firm's ability to honour its short terms obligations.
Current ratio = current asset /current liability
$65,000 / 25,000 = 2.6
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Find u. v.
U V=
(8, 2)
= (-6, 3)
U =
V =
Answer:
-42
Step-by-step explanation:
Assuming you want the dot product,
(8)(-6)+(2)(3)= -42
Find the ratio of 700m to 2 km
Answer:
7 : 20
Step-by-step explanation:
2km = 2000m
Then the ratio of 700m to 2 km is :
700 / 2000
Then the ratio in simplest form is :
7 / 20
The day you were born your Grandparents started to save money for your future education. They decided to deposit $3,000 at the end of each year, for eighteen years, in a savings account that pays 7.5% per year, compounded annually.
On your 19th birthday you get admission into university for a four-year degree course. You calculate that you require approximately $35,000, for your fees, books and living expenses for each year. Assuming you keep the money in the bank accruing the same interest, and withdraw $ 35,000, at the beginning of each year.
a) Calculate the total value of this investment at the end of the term?
b) Determine the total interest earned?
Will your inheritance last you for the full tenure of your four years at the university?
The total value of the investment is $107,032.16.
The total interest earned is $53,032.16
The inheritance would last the tenure of the university.
What is the total value of the investment?The formula that can be used to determine the future value of the 18-year annuity is: annuity factor x amount deposited yearly
Annuity factor = {[(1+r)^n] - 1} / r
Where:
r = interest rate n = number of years$3000 x [(1.075^18 - 1) / 0.075] = $107,032.16
Amount deposited in the course of 18 years = (3000 x 18) = 54,000
Interest earned = 107,032.16 - 54,000 = $53,032.16
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a right triangle has side lengths of 6, 10, and x. find x if it is the hypotenuse
X= root 6^2 + 10^2
X=2 root 34
So, x is 11.66 to 2d.p
(root means square root)
Hope this helps!
Answer:
x = 11.66
Step-by-step explanation:
Hello!
We can use the Pythagorean theorem to solve for the hypotenuse.
Pythagorean Theorem: [tex]a^2 + b^2 = c^2[/tex]
a = legb = legc = hypotenusePlug the values of 6 and 10 into the formula to solve.
Find the Hypotenuse[tex]a^2 + b^2 = c^2[/tex][tex]6^2 + 10^2 = c^2[/tex][tex]36 +100 = c^2[/tex][tex]136 = c^2[/tex][tex]c = \sqrt{136[/tex][tex]c \approx 11.66[/tex]The hypotenuse is approximately 11.66.
if x was 4, what is the value of 4x + 3
Answer:
19
Step-by-step explanation:
4(4)+3
16+3=19
Answer:
19
Step-by-step explanation:
4x+3
4(4)+3
16+3
19
hope it helps
the ammount of time between interest payments is know as
The amount of time between interest payments is know as period.
What is period?Period is the time between when interests are paid. Period can vary depending on the terms of the investment. Periods can be yearly, quarterly, semi-annually, biweekly or weekly.
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Which of the following is the most accurate statement about Spatial Relations?
A- Children understand the spatial world watching movies about animals all over the world.
B- Children Need to know, use and be able to read spatial terms before they can demonstrate spatial awareness.
C-Spatial terms such as above, below, behind, and under are used to describe objects in space from different perspectives and are important for children to understand and express as they understand spatial relations.
Option C. The correct statement about spatial relationshipo is that Spatial terms such as above, below, behind, and under are used to describe objects in space.
What are spatial relationship?These are the types of relationships that are used to relate objects to the location of somethings else. It makes use of words like under, above etc.
It is one of the knowledge that children need in the preoperational stage to learn how to use logical operations.
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what’s the equation of this line?
Answer:
Step-by-step explanation:
Hello : let A(0,-6) B(8,-8)
the slope is : (YB - YA)/(XB -XA)
(-8+6)/(8-0) = -2/8=-1/4
an equation is : y=ax+b a is a slope
y = (-1/4)x +b
the line through point A (0;-6) : -6 = (-1/4)(0)+b
b = -6 the equation is : y =(-1/)4x-6
(SAT prep) Find the value of x in each case of the following exercises:
The value of x from the figure is 70°
How to determine the valueIt is important to note that alternate angles are equal and angles in a triangle sum up to 180°
We then have that,
x + 50 + 60 = 180 °
x + 110 = 180°
Make 'x' subject
x = 180 - 110
x = 70 °
Thus, the value of x from the figure is 70°
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The sum of the roots of the quadratic equation x^2 + 1=0 is equal to
Answer:
x² + 1 = 0
a = 1
b = 0
c = 1
[tex]x1.2 = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
[tex]x1.2 = \frac{ - 0 ±\sqrt{ {0}^{2} - (4.1.1) } }{2.1} [/tex]
[tex]x1.2 = \frac{0± \sqrt{0 - 4} }{2} [/tex]
[tex]x1.2 = \frac{± \sqrt{ - 4} }{2} [/tex]
There is no real solution because the discriminant is negative
Note.
Formula diskriminan
√b² - 4ac.
if the diskrimanan is negatif, so the quadratic equatoin dont have solution
A rock is dropped from a height of 100 feet. Calculate the time between when the rock was dropped and when it landed. If we choose "down" as positive and ignore air friction, the function is h (t) = 36t2 - 64
t= 3.56 seconds
t= 1.78 seconds
t= 1.33 seconds
t= 8 seconds
The time it takes between when the rock was dropped and when it landed is 1.33 seconds.
What is the time it takes for the rock to land?The time it takes the rock to land on the ground from where it is dropped can be determined by using the function given.
The height of the function when it hits the ground will be zero, so the function can be written as:
[tex]\mathbf{h(t) =36t^2 -64}[/tex]
[tex]\mathbf{0 =36t^2 -64}[/tex]
64 = 36t²
[tex]\mathbf{t^2 = \dfrac{64}{36}}[/tex]
t² =1.778
[tex]t = \sqrt{1.778}[/tex]
t = 1.333 seconds
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A tennis ball can in the shape of a right circular cylinder holds six tennis balls snugly. If the radius of a tennis ball is 3.4 cm, what percentage of the can is not occupied by tennis balls?
The percentage of the can that is not occupied by tennis balls is 33.33%.
PercentageGiven:
Radius of cylinder=3.4cm
First step
Height of cylinder=3.4×2×6
Height of cylinder=40.8 cm
Second step
Volume of cylinder=(3.4)^2×40.8
Volume of cylinder=471.648
Volume of tennis=6×4/3×(3.4)^3
Volume of tennis=314.432
Third step
Percentage=471.648-314.432/471.648×100
Percentage=33.33%
Therefore the percentage of the can that is not occupied by tennis balls is 33.33%.
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A polynomial function g(x) has a positive leading coefficient. Certain values of g(x) are given in the following table. x –4 –1 0 1 5 8 12 g(x) 0 3 1 2 0 –3 0 If every x-intercept of g(x) is shown in the table and each has a multiplicity of one, what is the end behavior of g(x)?
Using the Factor Theorem and limits, the end behavior of g(x) is that the function decreases to the left and increases to the right.
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
Considering the table, the roots are given as follows:
[tex]x_1 = -4, x_2 = 5, x_3 = 12[/tex]
Hence the function is:
f(x) = a(x + 4)(x - 5)(x - 12).
f(x) = a(x² - x - 20)(x - 12)
f(x) = a(x³ - 13x² - 32x + 240).
When x = 0, y = 1, hence the leading coefficient is found as follows:
240a = 1
a = 0.004167
Then:
f(x) = 0.004167(x³ - 13x² - 32x + 240).
The end behavior is given by the limits of f(x) as x goes to infinity, hence:
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} 0.004167 x^3 = -\infty[/tex].[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} 0.004167 x^3 = \infty[/tex].Hence the end behavior is that the function decreases to the left and increases to the right.
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Curves defined using parametric equations have an orientation
true or false?
Answer:
True
Step-by-step explanation:
So this problem is asking whether Parametric because have an orientation and the short answer to that is that this is true. Parametric curves do have an orientation and we'll just do a little demonstration to share. Why? So let's take these very standard privatization of the unit circle where X is he going to cause of tea and why is equal to sign of tea now? The final part of defining the characterization is defining that the main range of tea on will take t to go from zero to two pi Andi, In this case, this is the this parts of circle going in this direction in the counter clockwise direction. And this is because as X as he goes from zero to play over two x decreases and signed increases on it sets us off on this direction as if that's one orientation off this curve of the circle. But we can alter this curve to get a different orientation. So if we were to take the Parametric equation given by X is equal to the co sign a minus T and why is equal to the sign of minus T in this case? Well again, take the domain to be from 0 to 2 pi. But because of the mind, the sign when it the mind sign doesn't actually affect X, it doesn't effect for co sign Well, it does affect the sign of minus T. So as T increases, the X value still decreases. But the Y value initially decreases as well, so this sets the arrows off on the clockwise direction. So this is another orientation off the same curve. So we've got two very different characterizations that describe the same physical curve. But because of the differences, the curve is constructed in opposite direction, and that is what the orientation defines. So it's very important to make sure that when you're drawing and describing the curve, you're parametric equations are in the correct orientation because otherwise you may encounter some difficulties later on. Because you'll be working with equation start that are, in fact, wrong
Thank you,
Eddie.
To calculate the area of this shape, you would identify the known figures and add their individual areas together.
However, the half circle is unlike the other known figures in this unknown shape in that it TAKES AWAY from the total area. How should you handle its area when
calculating the total area of the unknown figure?
When calculating the total area of this unknown figure, you should use (π - r²)/4 for the area of both the semicircle (half circle) and the larger square.
How to determine the total area?By critically observing this unknown figure, we can logically deduce that it comprises a semicircle, squares, a rectangle and a triangle. Thus, its total area should be calculated by adding the area of each of the geometric figures together.
Total area = A₁ + A₂ + A₃ + A₄
However, you should take note that the diameter of the semicircle (half circle) is equal to the side length of the larger square.
Area of a semicircle = πr²/4
Thus, the total area of both the semicircle (half circle) and the larger square is given by:
Area = πr²/4 - d²
Note: d = 2r
Area = πr²/4 - (2r)²
Area = πr²/4 - 4r²
Area = (π - r²)/4 sq. units.
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The hospital in patient admission rate for employees of the ramsey
The computation shows that the the hospital in-patient admission rate for the employees of the Prendergast Corporation is 104.5 admissions per 1000 employees.
How to calculate the value?The in-patient admission rate for Ramsey Manufacturing company = 100 admissions per 1000 employees.
It is given that the in-patient rate of Prendergast will be 10% higher than Ramsey's.
So, in-patient rate of Prendergast:
= 100 + 10% of 100
= 110 admissions
Now, it is also given that out of total in-patients, 5% are for tonsillectomies (which are not in-patient).
So, in-patient admission rate for Prendergast:
= 110 - 5% of 110
= 110 - 5.5
= 104.5 admissions per 1000 employees
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Complete question:
The hospital in-patient admission rate for employees of the Ramsey Manufacturing Company is 100 admissions per 1000 employees per year.
The Prendergast Corporation has older employees and is told that its hospital in-patient admission rate will be 10% higher than Ramsey’s. At the same time, however, all tonsillectomies will be done in the hospital’s outpatient department instead of requiring the patient to be admitted as an in-patient. Given that 5% of all in-patient admissions are for tonsillectomies, what is the hospital in-patient admission rate for the employees of the Prendergast Corporation?
A. 110.0 B. 115.0 C. 109.5 D. 100.0 E. 104.5 F. 117.0
I can't find the answer for 46.3 divided by 1.5 Help!
The solution to the problem when [tex]46.3[/tex] divided by [tex]1.5[/tex] the result of the division is [tex]30.8666667[/tex] in decimal form.
When a large number is distributed into small numbers of equal parts is called division.
The number [tex]1.5[/tex] is not a factor of [tex]46.3[/tex] , on dividing them the remainder is not zero.
Therefore, first convert [tex]1.5[/tex] it into a whole number by multiplying it [tex]10[/tex] so it becomes [tex]15[/tex] .
Then convert [tex]46.3[/tex] it into a whole number by multiplying it by [tex]10[/tex] so it becomes [tex]463[/tex]
Here, [tex]\dfrac{463 \times 10}{15 \times 10}[/tex] which results in [tex]\dfrac{463}{15}[/tex].
Now, divide [tex]\dfrac{463}{15}[/tex] , the result will be [tex]30.8666667[/tex].
The solution to the problem when [tex]46.3[/tex] divided by [tex]1.5[/tex] the result is [tex]30.8666667[/tex].
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IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
If the radius of the circle is 5 m and angle subtended by arc LKM is 70° then the length of the arc LNM is 25.29 m.
Given that the radius of the circle is 5 m and angle subtended by arc LKM is 70°.
From the figure given we can estimate that the length of arc LNM can be circumference of circle subtracted by length of arc LKM.
Circulference of the circle is basically the length of whole arc of the circle. It is also know as perimeter of the circle. The formula of calculating circumference of a circle is 2πr in which r is the radius.
So,
length of arc LNM=Circumference of circle-length of arc LKM.
We know that length of an arc =Θr
in which Θ is the angle in radian.
length of arc=70*π[tex]/180*5[/tex]
=70π[tex]/36[/tex]
Circumference of circle=2π*5
=10π
Length of arc LNM=10π-70π[tex]/36[/tex]
=(360π-70π)[tex]/36[/tex]
=290π[tex]/36[/tex]
Put π=3.14
=290*3.14[tex]/36[/tex]
=910.6[tex]/36[/tex]
=25.29m
Hence the length of arc LNM is 25.29 m.
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Identify the coordinates of the vertices after the transformation
Answer:
A' is (-2,-1)
B' is (3,0)
C' is (2,4)
Step-by-step explanation:
Write the expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression.
csc ß- sin ß
Choose the correct answer below.
OA. 1
B. cos ßcot B
OC. sin²B
OD. 1-sin² B
OE. sin² ßtan² ß
OF. cos B
...
Using trigonometric identities, the simplified expression, without quotients, is given as follows:
A. [tex]\cos{\beta}\cot{\beta}[/tex]
Which trigonometric identities are used to solve this question?The cosecant of an angle is given by one divided by the sine of the angle, hence:
[tex]\csc{\beta} = \frac{1}{\sin{\beta}}[/tex]
The sine and the cosine of an angle are related as follows:
[tex]\sin^2{\beta} + \cos^2{\beta} = 1[/tex]
[tex]\cos^2{\beta} = 1 - \sin^2{\beta}[/tex]
The cotangent of an angle is:
[tex]\cot{\theta} = \frac{\cos{\theta}}{\sin{\theta}}[/tex]
Which is the simplified expression?The expression given is:
[tex]\csc{\beta} - \sin{\beta}[/tex]
Simplifying the cosecant:
[tex]\csc{\beta} - \sin{\beta} = \frac{1}{\sin{\beta}} - \sin{\beta} = \frac{1 - \sin^{2}\beta}{\sin{beta}}[/tex]
Then, applying the last two identities in the subsection above to remove the quotient, the simplified expression will be found as follows:
[tex]\frac{1 - \sin^{2}\beta}{\sin{beta}} = \frac{\cos^2{\beta}}{\sin{\beta}} = \frac{\cos{\beta}}{\sin{\beta}} \times \cos{\beta} = \cos{\beta}\cot{\beta}[/tex]
Hence option A is correct.
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