[tex]\\ \rm\Rrightarrow \dfrac{1-cos^2\theta}{cos^2\theta}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{sin^2\theta}{cos^2\theta}[/tex]
[tex]\\ \rm\Rrightarrow tan^2\theta[/tex]
Option C
Answer:
Trigonometric identities
[tex]\large \begin{aligned}\cos^2 \theta + \sin^2 \theta & = 1\\\implies \quad \quad \sin^2 \theta & = 1 - \cos^2 \theta\\\\\tan \theta=\dfrac{\sin \theta}{\cos \theta} \end{aligned}[/tex]
Therefore, using the identities, the given expression can be simplified as follows:
[tex]\large\begin{aligned}\implies \dfrac{1- \cos^2 \theta}{\cos^2 \theta} & = \dfrac{\sin^2 \theta}{\cos^2 \theta}\\\\& = \tan^2 \theta\end{aligned}[/tex]
Wey wey drops a pencil in her cup and notices that it only fits diagonally. the pencil is 9 centimeters long and the cup is 7 centimeters tall. what is the diameter of the cup?
please help asap
Answer:
5.656854249 cm
Step-by-step explanation:
Use the Pythagorean theorem to solve this (assuming that the bottom of the cup is a right angle). [tex]a^{2} +b^{2} =c^{2}[/tex]. a and b are sides, and c is the hypotenuse.
The length of the pencil would be the hypotenuse (c), and how tall the cup is (7 cm) would be one of the sides (a). The diameter of the cup, would be the other side (b).
Plug this into the Pythagorean theorem to get the equation: [tex]7^{2} +b^{2} =9^{2}[/tex]. From here, we can find the diameter of the cup by isolating b - remove everything from the left side, but remember, what you do to one side you must do to the other.
First, solve all of the exponents: [tex]49+b^{2}=81[/tex]
Second, subtract 49 from both sides: [tex]b^{2}=32[/tex] This cancels out the 49 on the left.
Lastly, square root both sides: [tex]x=5.656854249[/tex] This cancels out the exponent on the left.
In conclusion, the diameter of the cup is 5.656854249 centimeters.
Help me please please please please
Answer: 3ln4 + 3lna
Step-by-step explanation:
[tex]\ln (4a)^{3}\\=3 \ln 4a\\=3(\ln 4+\ln a)\\=\boxed{3\ln 4+3\ln a}[/tex]
What is the quotient? startfraction t 3 over t 4 endfraction divided by (t squared 7 t 12)
A fraction is a way to describe a part of a whole. The quotient of the fraction is 1/(t+4)².
What is a Fraction?A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.
The quotient of [tex]\dfrac{\dfrac{t+3}{t+4}}{t^2+7t+12}[/tex] can be found by factorizing the denominator of the fraction. Therefore, the factors of the denominator are,
t² + 7t + 12
= t² + 4t + 3t + 12
= t(t+4) +3(t+4)
= (t+4)(t+3)
Now, quotient will be,
[tex]\dfrac{\dfrac{t+3}{t+4}}{t^2+7t+12}\\\\\\=\dfrac{\dfrac{t+3}{t+4}}{(t+4)(t+3)}\\\\\\=\dfrac{(t+3)}{(t+4)(t+3)(t+4)}\\\\\\= \dfrac1{(t+4)^2}[/tex]
Hence, the quotient of the fraction is 1/(t+4)².
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Can someone help me PLEASE I've been trying to get someone to help me for hours Come on I'm offering 20 points?!?!?!?
AND means multiply, so if probability is dependent on two things happening, then we will multiply the individual probabilities together.
1. P(A and 1) = 1/4 x 1/6 = 1/24
2. P(C and 2) = 1/4 x 2/6 = 2/24 = 1/12
3. P(B and 3) = 2/4 x 1/6 = 2/24 = 1/12
4. P(A and 4) = 1/4 x 2/6 = 2/24 = 1/12
5. P(C and 3) = 1/4 x 1/6 = 1/24
6. P(B and 2) = 2/4 x 2/6 = 4/24 = 1/6
7. P(a consonant and an odd #) = 3/4 x 2/6 = 6/24 = 1/4
8. P(a consonant and a prime #) = 3/4 x 3/6 = 9/24 = 3/8
9. P(a vowel and a 5) = 1/4 x 0/6 = 0
10. P(a vowel and a number less than 3) = 1/4 x 3/6 = 3/24 = 1/8
11. P(B and 1) = 2/4 x 1/6 = 2/24 = 1/12
Experimental probability is based on something that has already happened, or data that has already been collected.
12. P(1) = 3/30 = 1/10
13. P(2) = 8/30 = 4/15
14. P(3) = 7/30
15. P(4) = 5/30 = 1/6
16. P(5) = 3/30 = 1/10
17. P(6) = 4/30 = 2/15
Hope this helps!
If you draw four cards at random from a standard deck of 52 cards, what is the probability that all 4 cards have distinct characters (letters or numbers)
There are [tex]\binom{52}4[/tex] ways of drawing a 4-card hand, where
[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]
is the so-called binomial coefficient.
There are 13 different card values, of which we want the hand to represent 4 values, so there are [tex]\binom{13}4[/tex] ways of meeting this requirement.
For each card value, there are 4 choices of suit, of which we only pick 1, so there are [tex]\binom41[/tex] ways of picking a card of any given value. We draw 4 cards from the deck, so there are [tex]\binom41^4[/tex] possible hands in which each card has a different value.
Then there are [tex]\binom{13}4 \binom41^4[/tex] total hands in which all 4 cards have distinct values, and the probability of drawing such a hand is
[tex]\dfrac{\dbinom{13}4 \dbinom41^4}{\dbinom{52}4} = \boxed{\dfrac{2816}{4165}} \approx 0.6761[/tex]
It takes Mario and Jessica 15 minutes to set up 5 tables. If Mario and Jessica work at a constant rate, which best describes a possible constant of proportionality?
Answer:
3 minutes per table
Step-by-step explanation:
15 minutes = 5 tables
to get how much it will be per table, divided both sides by 5
since 5 / x = 1 and x would be 5
15 / 5 minutes = 5 / 5 tables
3 minutes = 1 table
Find the volume of the rectangular prism below
V = L * W * H
Answer:
40[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
V = L × W × H
V = 1.5 × 6 × 4.5
V = 40.5 or 40[tex]\frac{1}{2}[/tex]
Answer:
40 1/2ft
Step-by-step explanation:
H(4 1/2 )x W(1 1/2) = 6.75
HW(6.75)x L(6) = 40.5
Which number(s) below belong to the solution set of the equation? Check all
that apply.
X+ 6 = 45
A. 45
B. 39
C. 35
D. 3
E. 51
F.0
What are all the partial products for 5×1,234?
The partial products of 5 * 1234 are 5 * 1000, 5 *200, 5 * 30 and 5 * 4
How to determine the partial products?The product expression is given as:
5 * 1234
Express 1234 as the sum of numbers
5 * (1000 + 200 + 30 + 4)
Expand
5 * 1000 + 5 *200 + 5 * 30 + 5 * 4
Hence, the partial products of 5 * 1234 are 5 * 1000, 5 *200, 5 * 30 and 5 * 4
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1. How many ways can Grant arrange 3 of his 10 plants on a window ledge?
2. A parade organizer received 8 entries for floats. How many ways can he arrange 4 floats out of the 8 entries?
3. Express 4! in expanded form.
4. The number of ways 15 members of a 24-member club can be arranged. ( use permutation notation). PLEASE HELP ME!! and thankyou
The number of ways that Grant can arrange 3 of the 10 plants is 120 ways and the number of ways that 4 floats out of 8 can be arranged is 70 ways.
How can these combination problems be solved?Grant can arrange 3 out of 10 plants in the following number of ways:
= 10!/ ((10! - 3!)3!)
= ( 10 x 9 x 8) / (3 x 2)
= 120 ways
The parade organizer can arrange 4 floats out of 8 as:
= 8!/((8! - 4!)4!)
= (8 x 7 x 6 x 5) / (4 x 3 x 2)
= 70 ways
When 4! is written in expanded form, it comes out as:
= (4 x 3 x 2)
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Using a trial and improvement method, find x correct to 1 decimal place.
3x² - x = 30
Answer:
x = 10/3
x = -3
Step-by-step explanation:
3x² - x = 30
3x² - x - 30 = 0
multiply 3 and -30 which =
-90
what are 2 numbers that when multiplied make
-90
and that when added make
-1
(-1 is the number in -x in the equation)
they are the numbers 9 and 10
namely -10 and +9
3(x-10/3)(x+9/3)=0
divide both sides by 3
(x-10/3)(x+9/3)=0
then split factors being multiplied
(x-10/3)=0
(x+9/3)=0
x = 10/3
x = - 9/3 = -3
How do i add and subtract
Answer:
take the dots and either put them together or rake them away
Step-by-step explanation:
Example: .....+..=....... five dots plus two dots equals seven dots.
......-...=... six dots minus three dots equals three since you are taking away three
i hope u found this helpful.
help please I will give you the brianliest
Answer:
66
Step-by-step explanation:
A=12×11/2=66
Hope this helps:)
Sequence A: 4;9;16;25;36; ... ; ...
a) write the next two numbers
b) describe how sequence A is being formed
Answer:
49,64
Step-by-step explanation:
Every time the number changes there is an addition of two. for instance, from 4 to 9 the was an addition of 5 and from 9 to 16 there was an addition of 7. Thats how it works
Urgent Question, 50 points and will mark brainliest.
Part A
Describe a relationship that can be modeled by the function represented by the graph, and explain how the function models the relationship.
Part B
Identify and interpret the key features of the function in the context of the situation you described in part A.
A key feature is there is a constant y-value level between x values from 0 to 15 and there is a parabolic curve from x-values of 15 to 65. The vertex is at (3, 45)
How to get the relationship between graphs?A) This is a parabolic graph and from the graph, we see that, the y-values remain the same from x-values of 0 to 15. Thereafter the x-values increases with a corresponding decrease in y-values until the vertex point before increase in x-values with corresponding increase in y-values.
A relationship could be: Battery percentage remains at the mark of 40 for the first 15 minutes of use. Thereafter, it begins to decrease parabolically until 45 minutes when it it is almost at 0 level and is charged before it starts to increase in a parabolic manner again for another 20 minutes when it increases linearly.
B) A key feature is there is a constant y-value level between x values from 0 to 15 and there is a parabolic curve from x-values of 15 to 65. The vertex is at (3, 45)
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Charlotte is buying milk. She can get 64 oz. for $3.00 or 80 oz. for $4.50. Which is the better deal, 64 oz. or 80 oz.?
Answer:
80 oz
Step-by-step explanation:
Examine the steps used to solve the equation.
2
-3y += 2y-4
3
2
1.
3 = 5y-4
2
14=5y
3
14
(²) ¹/4 = (3) 5y
5
Intro
3.
Evaluate the steps used to solve the equation, and
then describe each step.
What is the solution to the equation?
Answer:
step1:add 3y to both sides
step2:add 4 to both sides
step3:multiply both sides by(1/5)
14/15
Step-by-step explanation:
Make f the subject of
m² = 3 ef
Answer:
below
Step-by-step explanation:
f. =. m²
------
3e
hope makes sense dive both sides by 3e to get f alone
−4(4x-6)= 3(-7x-1)
How do I solve this step by step when trying to solve for x?
[tex]-4(4x-6)=3(-7x-1)[/tex]
[tex]-16x+24=3\left(-7x-1\right) [/tex]
[tex]-16x+24=-21x-3 [/tex]
[tex]-16x+24+21x=-3 [/tex]
[tex]5x+24=-3 [/tex]
[tex]5x=-3-24 [/tex]
[tex]5x=-27 [/tex]
[tex]x=\frac{-27}{5} [/tex]
[tex]x=-\frac{27}{5} [/tex]
Explanation:
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I can write a system of linear equations and inequalities from context.
One smartphone plan costs $40 per month and an
extra $3.50 per gigabyte of data used each month.
Another smartphone plan costs $75 per month and
$0.50 per gigabyte of data used each month.
Let c represent the cost of a phone plan, m represent
number of months, and g represent the number of
gigabytes of data used each month. Write a system of
two linear equations that could be used to determine
the number of gigabytes used in a month so that the
two phone plans cost the same amount.
Equation 1:
Equation 2:
An equation is formed of two equal expressions. The number of gigabytes that is used in a month so that the two phone plans cost the same amount is 11.6667 Gigabyte.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Let c represent the cost of a phone plan, m represent the number of months, and g represent the number of gigabytes of data used each month.
Equation1: C = 40m + 3.5mg = (40+3.5g)m
Equation2: C = 75m + 0.5mg = (75+0.5g)m
Equating C,
(40+3.5g)m = (75+0.5g)m
40 + 3.5g = 75 + 0.5g
3g = 35
g = 11.6667 gigabyte of data per month
Hence, the number of gigabytes that is used in a month so that the two phone plans cost the same amount is 11.6667 Gigabyte.
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Segment BD is a median. Solve for x. Round to the nearest tenth, if necessary. (Image not necessarily to scale.)
Answer: 10
Step-by-step explanation:
By definition, the point at which a median intersects the side of the triangle opposite from the vertex from which it is drawn is the midpoint of that side.
Decide whether quadrilateral ABCD with vertices 4(-3,0), B(-4,1), C(-1.4), and D(0,3) is a rectangle, rhombus, square, or parallelogram.
Answer: rectangle
Step-by-step explanation:
The options imply the figure is a parallelogram. Furthermore, we can tell that not all the sides are congruent, so we can rule out the possibility that it is a rhombus or a square.
To determine if it is a rectangle, we can use the slope formula to determine if there is a pair of perpendicular sides. If this is the case, then this will be a parallelogram with a right angle, making it a rectangle.
[tex]m_{\overline{AB}}=\frac{1-0}{-4-(-3)}=-1\\m_{\overline{BC}}=\frac{4-1}{-1-(-4)}=1\\\therefore \overline{AB} \perp \overline{BC}[/tex]
So, the most specific classification is a rectangle
A website offers a free trial membership for an online streaming service from a list of 25 channels. Another website is also offering a free trial, but you chose from a list of 30 different channels. If you can only pick one from each service, how many outcome pairs can you have
There are 750 many outcome pairs you can have
How to determine the number of outcome pairs?The given parameters are:
Website 1 = 25
Website 2 = 30
The number of outcome pairs is calculated as:
Outcome = Website 1 * Website 2
So, we have:
Outcome = 25 * 30
Evaluate the product
Outcome = 750
Hence, there are 750 many outcome pairs you can have
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Find the circumerference
Circumference = diameter x PI
Circumference = 8 in x Pi
Circumference = 8PI in. (Exact)
Or as a decimal answer: 25.12 in.
Answer:
25.1 in (nearest tenth)
Step-by-step explanation:
Formula
Circumference = πd (where d is the diameter)
From inspection of the diagram:
Diameter (d) = 8 in⇒ Circumference = 8π
= 25.1 in (nearest tenth)
If x and y are supplementary angles, then x is _____ obtuse.
answer choices - always, sometimes, or never.
Answer:
sometimes
Step-by-step explanation:
a supplementary angle is "either of two angles whose sum is 180°".
So, x or y could be any degree, (less than 180 of course) and either one could be obtuse (>90) or acute (<90).
The Bloomington Bank has a height of 163 meters. Molly is making a scale model of this building using a scale of 125 meters: 1 meter. To the nearest tenth of a meter, what will be the height of the scale model?
The height of the scale model 1.304 scale units.
What is unit conversion?Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
Given:
The Bloomington Bank has a height of 163 meters.
Molly is making a scale model of this building using a scale of 125 meters.
125 meters = 1 scale unit
1 meter = 1/125 scale unit
So, for 163 meters = 1/125* 163
= 1.304 scale units.
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Find the function to which the given series converges within its interval of convergence. Use exact values. 1 3 x 9 x 2 2 ! 27 x 3 3 ! 81 x 4 4 ! 243 x 5 5 !
It looks like the series could be
[tex]\displaystyle 1 + 3x + \frac{9x^2}{2!} + \frac{27x^3}{3!} + \cdots = \sum_{n=0}^\infty \frac{3^nx^n}{n!} = \sum_{n=0}^\infty \frac{(3x)^n}{n!}[/tex]
Recall that
[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{x^n}{n!}[/tex]
It follows that the given series is the power series expansion for [tex]\boxed{e^{3x}}[/tex].
Pettit printing company has a total market value of $100 million, consisting of 1 million shares selling for $50 per share and $50 million of 10 percent perpetual bonds now selling at par. the company's ebit is $13.24 million, and its tax rate is 15 percent. pettit can change its capital structure by either increasing its debt to 70 percent (base on market value) or decrease it to 30 percent. if its decides to increase its use of leverage, it must call its old bonds and issue new ones with a 12 percent coupon. if it decides to decrease its leverage, it will call in its old bonds and replace them with new 8 percent coupon bonds. the company wills ell or repurchase stock at the new equilibrium price to complete the capital structure change. the firm pays out all earnings as dividends; hence; its stock is a zero growth stock. its current cost of equity, rs; is 14 percent. if it increases leverage rs will be 16 percent. if it decreases leverage, rs will be 13 percent. what is the firm's wacc and total corporate value under each capital structure?
The weighted average cost of capital for the firm will be 11.25%.
How to calculate the WACC?The weighted average cost of capital is the calculation of the cost of capital for a firm where each category of capital is weighted.
Here, the weighted average cost of capital will be:
= 0.5(10%)(1 - 15%) + 0.5(14%)
= 0.5(0.1)(0.85) + 0.5(0.14)
= 11.25%
The corporate value at 70% debt when WACC is 11.94% will be:
= (EBIT)(1 - T)/WACC
= (13.24)(1 - 0.15)/0.1194
= $94.26 million
The corporate value at 30% debt when WACC is 11.14% will be:
= (EBIT)(1 - T)/WACC
= (13.24)(1 - 0.15)/0.1114
= $101.02 million
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solve the proportion
Answer:
The answer would be 5.
Step-by-step explanation:
To solve proportions, you multiply the denominator (6) by the numerator (15). 15 times 6 is equal to 90. You then divide 90 by the denominator (18) to get an answer of 5. I hope this helps you! Have a great day! :)
The archway of the main entrance of a university is modeled by the quadratic equation y = -x2 6x. the university is hanging a banner at the main entrance at an angle defined by the equation 4y = 21 − x. at what points should the banner be attached to the archway?
The banner attached to the archway will be at (1, 5) and (5.25, 3.938).
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
The archway of the main entrance of a university is modeled by the quadratic equation
y = -x² + 6x ....1
The university is hanging a banner at the main entrance at an angle defined by the equation
4y = 21 − x ....2
Then the banner attached to the archway will be
From equations 1 and 2, we have
4(-x² + 6x) = 21 - x
-4x² + 24x = 21 - x
4x² - 25x + 21 = 0
4x² - 21x - 4x + 21 = 0
x(4x - 21) - 1(4x - 21) = 0
(4x - 21)(x - 1) = 0
x = 5.25, 1
Then the value of y will be
When x = 5.25, then we have
y = -(5.25)² + 6(5.25)
y = 3.938
When x = 1, then we have
y = -(1)² + 6(1)
y = 5
The banner attached to the archway will be at (1, 5) and (5.25, 3.938).
The graph is given below.
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