find the exact value of 2sin30 cos30
Answers
Answer:
[tex]\frac{\sqrt{3}}{2}[/tex]
Step-by-step explanation:
Let's take a look at the unit circle below.
Remmeber that cos represents the x-value and that sin represents the y-value.
We see that:
[tex]sin(30)= \frac{1}{2}\\\text{and}\\ cos(30) = \frac{\sqrt{3}}{2}[/tex]
Now we just multiply all the together and we get:
[tex]2*\frac{1}{2}*\frac{\sqrt{3}}{2} =\frac{\sqrt{3}}{2}[/tex]
Related Questions
How does your Web browser get a file from the Internet? Your computer sends a request
for the file to a Web server, and the Web server sends back a response. For one
particular Web server, the time X (in seconds) after the start of an hour at which a
randomly selected request is received has the uniform distribution shown in the figure. in
Answers
The probability that the request is received by this server within the first 5 minutes (300 seconds) after the hour is 0.0833 or 8.33%.
How does your Web browser get a file from the Internet?Your computer sends a request for the file to a Web server, and the Web server sends back a response.
For one particular Web server, the time X (in seconds) after the start of an hour at which a randomly selected request is received has the uniform distribution shown in the figure.
The probability of finding value less than the X is,
[tex]P(X < x)=\dfrac{x-a}{b-a}[/tex]
Here, a and b are two bonds of uniform distribution.
The probability distribution of X can be modeled by a uniform density curve on the interval from 0 to 3600 seconds, as shown in the given figure.
The probability that the request is received by this server within the first 5 minutes (300 seconds) after the hour has to be found out. Thus,
[tex]P(X < x)=\dfrac{300-0}{3600-0}\\P(X < x)=0.0833\\P(X < x)=8.33\%[/tex]
Thus, the probability that the request is received by this server within the first 5 minutes (300 seconds) after the hour is 0.0833 or 8.33%.
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What is the correct answer?
Answers
Answer:
B
Step-by-step explanation:
When multiplying exponents with the same base, you add the powers together.
In B, that is exactly what they are showing when they do:
[tex]2^{\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}}[/tex]
You are calculating how many seats there are at Wrigley
Field in Chicago, Illinois. You count that there are 1,487 rows
Each row has 28 seats.
How many seats are there in the whole field?
Answers
Answer:
41,636
Step-by-step explanation:
Easy, on each row, there are 28 seats, and we know there's 1487 rows in total.
Hence, number of rows multiplied by number of seats counted
1487 × 28
=41,636
(Dang, that's alot of seats then)
Calculate the perimeter of the figure shown below.
5 ft
15 ft
10 ft
18 ft
Answers
Answer:
its c
Step-by-step explanation:
think about it for a second
Which algebraic expression is equivalent to this expression?
9(3x - 12) + 9x
A.
36x - 12
B.
18x + 108
C.
36x - 108
D.
18x - 108
Answers
Use the Distributive Property, which states the following:-
[tex]\bigstar{\bf{a(b+c)=ab+ac}[/tex]
where
we distribute a by multiplying it times b and c
In this case, we should distribute 9:-
9(3x-12)+9x
27x-108+9x
Combine Like Terms:-
[tex]\longrightarrow\sf{36x-108}[/tex]
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)
Answer:
C. 36x + 108
Step-by-step explanation:
Our expression :
9(3x - 12) + 9xExpanding :
#1) Open the bracket applying the distributive property.
9(3x - 12) + 9x9(3x) - 9(12) + 9x27x - 108 + 9x#2) Combine like terms.
27x + 9x - 10836x + 108The option with this answer is C.The range of the function f(x) = x + 5 is {7, 9}. What is the function’s domain? A. {2, 4} B. {-2, -4} C. {12, 14} D. {-12, -14} E. {0, 5}
Answers
Answer:
The answer is A. {2,4}
Step-by-step explanation:
I took the test on edmentum. 100%
A family of 6 is going to the fair. They have a coupon for $2.50 off each ticket. If they pay $96 for all their tickets, and each ticket costs the same amount, how much does a ticket, t, cost without the coupon?
Answers
Answer:
6x=46.50
Step-by-step explanation:
What is the radius of the sphere? Use 3.14 for 7 and round your answer to the nearest
tenth.
O 4.7 m
O 3.4 m
O 6.2 m
O 2.8 m
Answers
Answer:
its 3.4 m
Step-by-step explanation:
i had the same test
Answer:
2.8
Step-by-step explanation:
r=(3V4π)⅓=
(3·91.94·π)⅓≈2.79947
I tried other answer, got it wrong, this one is right.
Which expression has a value of -22?
−5 × 2 − 12
8 − (−3) +33 ÷ (−3)
−3 + (−2) − (−8) −1
−6 × 2 − (−15)
Answers
Answer:
(-5)*2 - 12
Step-by-step explanation:
First multiply (-5) and 2. Then (-10) and (-12) have same signs ie. neagtive .
If two integers have same sign, add and the result will have the sign of the both integers.
(-5)*2 - 12 = -10 - 12
= -22
Factor completely 9x3 + 36x2 - x - 4.
(3x + 4)(3x – 4)(x + 1)
(3x + 1)(3x - 1)(x + 4)
(9x2 - 1)(x + 4)
-
(3x + 1)(3x – 1)(x – 4)
-
Answers
The correct answer is: (3x + 1)(3x - 1)(x + 4)
a listing for a home for sale is shown as follows: “3/2/1 house for sale. price 140000” what does “3/2/1” mean
Answers
Answer:
A
Step-by-step explanation:
Usually when purchasing a house you refer to the bedroom then the bathroom then potentially your garden width/height or you garage
can someone help me with this
Answers
Answer:
B. across the y-axis
Step-by-step explanation:
The line of reflection is the perpendicular bisector of the segment between the orginal point and its image. If you plot the two points, you see that the y-axis is that bisector.
The point was reflected across the y-axis.
__
Additional comments
Changing the sign of the x-coordinate means a point that was some distance on one side of the y-axis is now that same distance on the other side. That is, the y-axis is the line of reflection when the sign of x changes.
Similarly, the x-axis is the line of reflection when the sign of y changes.
(x, y) ⇒ (-x, y) . . . . reflection across the y-axis
(x, y) ⇒ (x, -y) . . . . reflection across the x-axis
__
Changing the signs of both coordinates (in either order) is effectively a reflection across the origin. There are other names for this reflection, too.
(x, y) ⇒ (-x, -y) . . . . reflection across both axes, across the orign, rotation 180°
Tallulah's family took a road trip to the Grand Canyon. Tallulah slept for the last 129 miles of the trip. If the total length of the trip was 300 miles, what percentage of the total trip had they traveled when Tallulah fell asleep?
Answers
When Tallulah fell asleep, the family had already traveled 57% of the total trip.
A percentage is a way of expressing a number as a fraction of 100. It is often used to describe proportions, ratios, or rates. For example, if 20 out of 100 people in a room are wearing red shirts, we can say that 20% of the people are wearing red shirts.
If Tallulah slept for the last 129 miles of the trip, it means that the family had already traveled 300 - 129 = 171 miles before she fell asleep.
To calculate the percentage of the total trip that they had traveled when Tallulah fell asleep, we can use the following formula:
Percentage = (Part ÷ Whole) x 100
Where "Part" is the number of miles the family had traveled before Tallulah fell asleep (171 miles) and "Whole" is the total length of the trip (300 miles).
Percentage = (171 ÷ 300) x 100
Percentage = 0.57 x 100
Percentage = 57%
Therefore, when Tallulah fell asleep, the family had already traveled 57% of the total trip.
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Helppp
For triangle ABC below, find missing side length BC and both missing angle measures
Answers
Answer:
3
Step-by-step explanation:
use the pythagoreum therory
Expand & simplify
4
(
x
+
5
)
+
5
(
x
−
5
)
Answers
4(x+5) + 5(x-5)
The first step is to distribute (PEMDAS --> parenthesis)
4x + 20 + 5x - 25 Now combine like terms
9x - 5
Thus, the answer is 9x-5
A triangular prism is 15 yards long and has a triangular face with a base of 12.9 yards and a height of 10.3 yards. what is the volume of the triangular prism?
Answers
Answer:
Step-by-step explanation:
Area of the base = 1/2 * B * h
B: 12.9
h = 10.3
Area of the face = 1/2 * 12.9 * 10.3
Area of the face = 66.435
Volume = Triangle * height
Triangle = 66.435 yd^2
Height = 15 yd
Volume = 66.435 * 15
volume = 996.525
I think this should be rounded to one decimal place: 996.5
A 5-year project will require an investment of $100 million. this comprises of plant andmachinery worth $80 million and a net working capital of $20 million. the entire outlay willbe incurred at the project’s commencement.financing for the project has been arranged as follows:80,000 new common shares are issued, the market price of which is $500 per share. theseshares will offer a dividend of $4 per share in year 1, which is expected to grow at a rate of 9%per year for an indefinite tenure.remaining funds are borrowed by issuing 5-year, 9% semi-annual bonds, each bond having aface value of $1,000. these bonds now have a market value of $1,150 each.at the end of 5 years, fixed assets will fetch a net salvage value of $30 million, whereas the networking capital will be liquidated at its book value.the project is expected to increase revenues of the firm by $120 million per year. expenses,other than depreciation, interest and tax, will amount to $80 million per year. the firm is subjectto a tax rate of 30%plant and machinery will be depreciated at the rate of 25% per year as per the written-downvalue method.you are required to:1. compute the cost of equity for this project (2 marks)2. compute the relevant cost of debt for this project. (2 marks)3. compute the wacc (4 marks)4. determine the initial cash flow for the project. (1 mark)5. determine the earnings before taxes for years 1 through 5 (2 marks)6. compute the ocf for years 1 through 5 (3 marks)
Answers
Answer:
1. The cost of equity can be derived from the share price, which is the present value of the expected dividend one year from now(using the present value of growing perpetuity) as shown below:
share price=D1/(r-g)
share price=$500
D1=expected dividend one year from now=$4
r=cost of equity=unknown
g=constant growth rate=9%
$500=$4/(r-9%)
$500*(r-9%)=$4
r-9%=$4/$500
r=($4/$500)+9%
r=9.8
the Cost of Equity for the project is 9.8%
2. Compute the relevant cost of debt for this project is 5.53%
Market Value= 1,150
Face Value= 1,000
Term= 5 years, 10 semi-annual periods
Coupon Rate= 9%, 4.5% semi-annual rate
Tax Rate= 30%
N=10(semiannual coupons in 5 years)
PMT=45(semiannual coupon=face value*coupon rate/2=$1000*9%/2=$45)
PV=-1150(current market price)
FV=1000(face value of the bond is $1,000)
CPT(press compute)
I/Y=2.762766%(semiannual yield)
annual yield=2.762766%*2
annual yield=5.53%
3. The weighted average cost of capital is the sum of equity and the after-tax cost of debt multiplied by their respective market value weights
WACC=(cost of equity*weight of equity)+(after-tax cost of debt*weight of debt)
cost of equity=9.80%
the market value of equity raised=shares issued*market price of the share
the market value of equity raised=80,000*$500
the market value of equity raised=$40 million
weight of equity=market value of equity/total amount raised
weight of equity=$40 million/$100 million
weight of equity=40.00%
weight of debt=1-weight of equity
weight of debt=1-40.00%
weight of debt=60.00%
after-tax cost of debt=bond yield*(1-tax rate)
the after-tax cost of debt=5.53%*(1-30% )
the after-tax cost of debt=3.87%
WACC=(9.80%*40.00%)+(3.87%*60.00%)
WACC= 6.2426% or 6.24%
Therefore the WACC is 6.2426% or 6.24% rounded off to 2decimal place
4. Determine the initial cash flow for the project =$100 million
The initial cash outlay is the sum of the plant and machinery and net working capital investment required to commence the project
Plant and machinery= $80 million
Networking capital = $20 million
Total Initial Cash Flow= $100 million
5. Determine the earnings before taxes for years 1 through 5
Year
1 2 3 4 5
Revenue
120,000,000 120,000,000 120,000,000 120,000,000 120,000,000
Expenses
(80,000,000) (80,000,000) (80,000,000) (80,000,000) (80,000,000)
Depreciation (20,000,000) (15,000,000) (11,250,000) (8,437,500) (6,328,125)
EBT
20,000,000 25,000,000 28,750,000 31,562,500 33,671,875
Step-by-step explanation:
5. Depreciation schedule:
Year 1 = 80 × 25% = 20
Year 2 = (80-20) × 25% = 15
Year 3 = (80-20-15) × 25% = 11.25
Year 4 = (80-20-15-11.25) × 25% = 8.4375
Year 5 = (80-20-15-11.25-8.4375) × 25% = 6.328125
EBT = revenue - Expenses - depreciation
Year 1 = 120 - 80 - 20 = 20 Million
Year 2 = 120-80- 15 = 25 Million
Year 3 = 120-80- 11.25 = 28.75 Million
Year 4 = 120-80- 8.4375 = 31.5625 Million
Year 5 = 120-80- 6.328125 = 33.671875Million
The cost of equity of the project through the use of Gordan's formula will be 9.87%.
How to compute the cost of equity?It should be noted that the price of stock is computed thus:
= Previous dividend + Growth / Cost of equity - Growth
Po = Do + g/Ke - g
500 = 4 + 9%/Ke - 9%
500 = 4 + (0.09 × 4) / Ke - 9%
500 = 4.36/Ke - 9%
500(Ke - 9%) = 4.36
500Ke = 4.36 + 45
500Ke = 49.36
Ke = 49.36/500
Ke = 9.87%
The cost of debt will be:
= Interest rate (1 - Tax rate)
= 9% × (1 - 30%)
= 9% × 0.7
= 6.30%
The amount of the cost of debt will be:
= $1000 × 6.30%
= $63.00
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You received an $40,000 bonus, which was 18% of your salary. What is the percentage of your salary is this bonus?
Answers
Answer:
salary: $40,000÷18% = $ 222. 222 22
222 222 22÷40,000×100%
= 555.56%
Find the value if x. PLS HELP ASAP
Answers
Answer: 90°
Step-by-step explanation:
(x°+90°)=180°(being the sum of angles of the triangle)
or, x°= 180°-90°
or x°= 90°
I need 16,18, and 20 answered thank you
Answers
16:
4b(5b-3)-2(b²-7b-4)
= 20b²-12b-2b²+14b+8
=18b²+2b+8
18:
3m(3m+6)-3(m²+4m+1)
= 9m²+18m-3m²-12m-3
=6m²+6m-3
20:
4x(3x+2)-3x×2x
=12x²+8x-6x²
=6x²+8x
Tony bought a printer on sale for 45. The original price was 60 . What is the percent decrease of the price of the load ?
Answers
Answer:
25%
Step-by-step explanation:
STEP 1:
Find the difference between the two values
e.g 60-45=15
STEP 2
Divide the difference by the original value
e.g 15/60=1/4
STEP 3
Convert 1/4 into a percentage
e.g 1/4=0.25=25%
PLS HELP OFFERING BRAINLIEST+20 POINTS! I RLLLLLLLLLYYYYYYY NEED HELP!
Answers
Answer:
c and d
Step-by-step explanation:
hope it helps bud
A line passes through the point (-9, -3) and has a slope of 2.
Write an equation in slope-intercept form for this line.
Answers
Answer:
Step-by-step explanation:
hello :
note :
Use the point-slope formula.
y - y_1 = m(x - x_1) when : x_1= -9 y_1= -3
m= 2 (the slope)
an equation in the point-slope form is : y +3 = 2(x+9)
means : y+3 =2x +18
an equation in slope-intercept id : y=2x+15
(Can somebody please help me!) (NO links!)
What do I put!
Answers
Answer:
x = 16angle = 48°Step-by-step explanation:
The marked angles have a sum of 90°. This lets you find the unknown angle and the value of x.
42° +3x° = 90°
3x° = 48° . . . . . . . . . subtract 42°. This is the value of the unknown angle
x = 16 . . . . . . divide by 3°
__
The value of x is 16.
The measure of the missing angle is 48.
WILL GIVE BRAINLIEST
What causes wind?
Question 3 options:
There is an increase in temperature and an increase in density.
An area of high pressure pushes toward an area of low pressure.
An area of low pressure pushes toward an area of high pressure.
Answers
An area of high pressure pushes toward an area of low pressure causing wind
I attached a diagram that can hopefully help you visualize the situation
Hope that helps!
Find the area of a circle with a radius of 21 inches. Use 22/7
for pi.
Answers
Answer:
Area of circle=πr^2
Step-by-step explanation:
Area of circle=πr^2
=22/7*21^2
=22/7*441
=9702/7
=1386 sq.inch
Maria wrote the equation log (startfraction x over 2 endfraction) log (startfraction 20 over x squared endfraction) = log 8 what is the solution to maria’s equation?
Answers
The solution to maria’s equation [tex]\rm log\frac{x}{2} +log\frac{20}{x^{2} } = log8[/tex] by using the properties of the logarithm is 5/4.
What is a logarithm?A logarithm is the exponentiation inverse function that can be expressed by the exponent or power to which a base must be raised to yield a number.
It is given that
[tex]\rm log\frac{x}{2} +log\frac{20}{x^{2} } = log8[/tex]
Using properties of a logarithm, we get
[tex]\rm log x + log y=logxy[/tex]
[tex]\rm log[\frac{x}{2} \times\frac{20}{x^{2} }] = log8\\\rm log[\frac{10}{x}] = log8[/tex]
on comparing
10/x = 8
x = 10/8
x = 5/4
Hence, the solution to maria’s equation [tex]\rm log\frac{x}{2} +log\frac{20}{x^{2} } = log8[/tex] is 5/4.
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Answer:
C
Step-by-step explanation:
C) 5/4
Three metallic tanks have the capacities of 447 litres, 577 litresand 669 litres. Find the capacity of the largest container that can fill the tanks an exact number of times, leaving a remainder of 7 litres, 5 litres and 9 litres respectively. (3 marks)
Answers
Answer:
44 litres
Step-by-step explanation:
We subtract the remainders from the amounts.
447 - 7 = 440
577 - 5 = 572
669 - 9 = 660
Now we need the GCF of 440, 572, 660
440 = 2³ × 5 × 11
572 = 2² × 11 × 13
660 = 2² × 3 × 5 × 11
GCF = 2² × 11 = 44
The greatest common factor is 44.
Answer: 44
Check:
447/44 = 10 reminder 7
577/44 = 13 remainder 5
669/44 = 15 remainder 9
17. Which of the following transformations does NOT preserve congruence?
(x,y) - (y + 2,-x-1)
(x,y) - (x-3, y-2)
(x,y) -- (0.5x + 1,0.5y-2)
(x,y) - (-y-3,x+5)
Answers
(x,y) - (y + 2,-x-1) is the transformation that DOES NOT maintain congruence.
what is transformation ?An item in one space is mapped to another using a function known as a transformation in mathematics. A geometric shape or other mathematical object is altered by this method by shifting its location, direction, or size. Geometric qualities including symmetry, congruence, and resemblance are studied using transformations. Objects are frequently transformed through translations (moving), rotations (turning), reflections (flipping), and dilations (resizing an object). In other branches of mathematics and science, including physics, calculus, and linear algebra, transformations are also employed.
given
(x,y) - (y + 2,-x-1) is the transformation that DOES NOT maintain congruence.
In other branches of mathematics and science, including physics, calculus, and linear algebra, transformations are also employed.
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Find y.
B
C
Зу
A
8 D
м
2
4
15
10
Answers
Answer:
y=4
Step-by-step explanation:
The question is asking what is the value of y:
Since all lengths have a dash on them they are all equal :
So 3y = y+8
3y = y + 8
First we subtract y from both sides:
3y-y = y+8-y
2y = 8
Divide both sides by 2:
2y÷2 = 8÷2
y = 4
