Using equivalent angles, we have that the measures are given as follows:
[tex]\sin{120^\circ} = \frac{\sqrt{3}}{2}[/tex][tex]\cos{120^\circ} = -\frac{1}{2}[/tex][tex]\tan{120^\circ} = -\sqrt{3}[/tex]What are equivalent angles?Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
120º is in the second quadrant, hence the equivalent on the first quadrant is:
180º - 120º = 60º.
The sine on the second quadrant is positive, hence:
[tex]\sin{120^\circ} = \sin{60^{\circ}} = \frac{\sqrt{3}}{2}[/tex]
The cosine on the second quadrant is negative, hence:
[tex]\cos{120^\circ} = \cos{60^{\circ}} = -\frac{1}{2}[/tex]
The tangent is given by the sine divided by the cosine, hence:
[tex]\tan{120^\circ} = \frac{\sin{120^\circ}}{\cos{120^\circ}} = -\sqrt{3}[/tex]
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Which of the following will form the composite function G(F(x)) shown
below?
G(F(x)) = x² + 4
OA. F(x) = x + 4 and G(x) = x²
OB. F(x)= x and G(x) = x²
O C. F(x)=x² and G(x) = 4
OD. F(x) = x² and G(x) = x + 4
The composite function G(F(x)) = x² + 4 is formed with these following original functions:
D. F(x) = x² and G(x) = x + 4.
How to find the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given as follows:
[tex](f \circ g)(x) = f(g(x))[/tex]
For g of f(x), we have that:
[tex](g \circ f)(x) = g(f(x))[/tex]
For this problem, we have that:
G(F(x)) = x² + 4.
Which is possible with option D, as:
[tex]G(F(x)) = G(x^2) = x^2 + 4[/tex]
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average person burns approximately 221 calories per half-hour while bicycling. If a person does 2 hours of bicycling per day then how many calories will they burn in a week if they work out 5 days a week?
Total Assets
Sales
Task 3: Preparing a Cash Flow Statement
Nikea Inc.'s income statement for the year 2013 is shown below:
During the year, the balances for the sales account, cost of goods sold, and gross profit
increased. This information is provided to you. Prepare the cash flow for operating activities,
using both the direct method and the indirect method.
Accounts
Nikea's income statement for the year 2013 is shown below.
Cost of Goods Sold
Gross Profit
Operating Expenses
Deprecation
Styles
Net Income
934,000 Total Liability & Stockholders Equity
Type your response here:
Amount ($)
600,000
14
(400,000)
200,000
(30,000)
(20,000)
150,000
934,000
4
Editin
The preparation of the Cash Flow Statement for Nikea Inc. for the year ended December 31, 2013, is as follows:
Direct Method:
Nikea Inc.
Cash Flow StatementCash received from customers $600,000
Cash paid to suppliers of goods (400,000)
Cash paid to vendors of servides (30,000)
Cash from operating activities $170,000
Indirect Method:
Nikea Inc.
Cash Flow StatementFor the year ended December 31, 2013
Net income $150,000
Add non-cash expenses:
Depreciation 20,000
Cash from operating activities $170,000
What is the difference between the direct method and the indirect method of Cash Flow Statement?The direct method of preparing the Cash Flow Statement starts with the operating income and adds the non-cash expenses to obtain the cash flow from operating activities.
On the other hand, the indirect method reconciles the accounts receivable and payable to extract the exact cash flows received from customers or paid to suppliers of goods and services.
Both methods of determining the cash flow from operating activities yield the same result.
Data and Calculations:Nikea’s income statement for the year 2013
Sales $600,000
Cost of Goods Sold (400,000)
Gross Profit 200,000
Operating Expenses (30,000)
Deprecation (20,000)
Net Income 150,000
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Find the difference between Simple interest and compound interest on 1200 for one year at 10% per annum
Answer:
the difference between them is zero cause on first year simple interest and compound interest are equal
If a cylinder has a height of 12 feet and a radius of 4 feet, what is its surface area (in square feet)? What is its volume (in cubic feet)? (Round your answers to two decimal places.)
The volume of the cylinder is 602.88 ft³.
The surface area of the cylinder is 301.44 ft²
How to find the volume and surface area of a cylinder?volume of a cylinder = πr²h
volume of a cylinder = 3.14 × 4² × 12
volume of a cylinder = 3.14 × 16 × 12
volume of a cylinder = 602.88 ft³
Surface are of a cylinder = 2πr(r + h)
Surface are of a cylinder = 2 × 3.14 × 4(4 + 8)
Surface are of a cylinder = 25.12(12)
Surface are of a cylinder = 301.44 ft²
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Determine the output voltage of the op-amp circuit shown below:
The output voltage of the op-amp circuit shown is -5v.
What is voltage?It should be noted that voltage is the electric potential difference between two points l.
In this case, the output voltage will be:
= -5 × i
where I = 1.
Voltage = -5 × 1
= -5v
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does this represent two quantities that are proportional
Answer:
from looking at this we can see
1*4=4
2*4=8
3*4=12
6*4=24
a
Hope This Helps!!!
there was 506 tickets sold for the school play they were either student tickets or adult tickets there was 56 more student tickets sold than adult tickets sold how many adult tickets were sold
Answer:
A = 228 tickets
Step-by-step explanation:
We need to set up a system of equation to find the number of adult tickets sold, where A represents the adult tickets and S represents the student tickets.
Because the number of adult and student tickets together equals 506, we have A + S = 506.
Because there are 56 more student tickets than adult tickets we have A + 56 = S
And the way the system is already set up allows us to use substitution.
Thus, we have:
[tex]A + S=506\\A+56 = S\\\\A+A+56 =506\\2A+56=506\\2A=456\\\\A=228\\228+56=S\\278=S[/tex]
The number of student tickets was not necessary to find in this problem, but I found anyway just in case you wanted check the work or wanted to prove the validity of the values.
Solve the following system of equations
y= -½/x-2
Answer:
Wolfram|Alpha is capable of solving a wide variety of systems of equations. It can solve systems of linear equations or systems involving nonlinear equations, and it can search specifically for integer solutions or solutions over another domain. Additionally, it can solve systems involving inequalities and more general constraints.
Step-by-step explanation:
Choose the correct product of (6x - 2)(6 x + 2).
The correct product of (6x - 2)(6 x + 2) is 36x^2 - 4
How to determine the product?The expression is given as:
(6x - 2)(6 x + 2).
The above expression is a difference of two squares.
And this is represented as
(a - b)(a + b)= a^2 - b^2
So, we have
(6x - 2)(6 x + 2) = (6x)^2 - 2^2
Evaluate
(6x - 2)(6 x + 2) = 36x^2 - 4
Hence, the correct product of (6x - 2)(6 x + 2) is 36x^2 - 4
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Zoya asked the students of her class their baseball scores and recorded the scores in the table shown below:
Baseball Scores
Score Number of Students
0 1
1 2
2 5
3 3
4 6
5 7
6 9
Based on the table, what is the mean baseball score?
2.5
2.9
3.5
4.1
Option D, 4.1 is the correct answer. The mean baseball score is 4.1 given the table of values of baseball scores and score number of students. This can be obtained by using the formula for mean.
Calculate mean for the data:Mean can be obtained by the formula,
Mean = [tex]\frac{sum\ of\ observations}{total\ number\ of\ observations}[/tex]
Sum of basketball scores = 0×1 + 1×2 + 2×5 + 3×3 + 4×6 + 5×7 + 6×9
= 0 + 2 + 10 + 9 + 24 + 35 + 54
total number of basketball scores = 1 + 2 + 5 + 3 + 6 + 7 + 9 = 33
Mean = [tex]\frac{0+2+10+9+24+35+54}{33}[/tex] = 4.06 ≈ 4.1
Hence the mean baseball score is 4.1 given the table of values of baseball scores and score number of students. Option D, 4.1 is the correct answer.
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The amount of detergent dispensed into bottles of liquid laundry detergent bottles for a particular brand is normally distributed with a mean of 84.5 ounces with a standard deviation of 1.1 ounces. If seventeen bottles are randomly chosen from the factory, what is the probability that the mean fill is more than 84.8 ounces
The probability that the mean fill is more than 84.8 ounces is 0.39358
How to determine the probability that the mean fill is more than 84.8 ounces?From the question, the given parameters about the distribution are
Mean value of the set of data = 84.5Standard deviation value of the set of data = 1.1The actual data value = 84.8The z-score of the data value is calculated using the following formula
z = (x - mean value)/standard deviation
Substitute the given parameters in the above equation
z = (84.8 - 84.5)/1.1
Evaluate the difference of 84.8 and 84.5
z = 0.3/1.1
Evaluate the quotient of 0.3 and 1.1
z = 0.27
The probability that the mean fill is more than 84.8 ounces is then calculated as:
P(x > 84.8) = P(z > 0.27)
From the z table of probabilities, we have;
P(x > 84.8) = 0.39358
Hence, the probability that the mean fill is more than 84.8 ounces is 0.39358
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Need an detailed step by step answer and solution again
Answer:
12u²
Step-by-step explanation:
area of a regular quadrilateral is always base x vertical height.
the base here is clearly 4 (just count the squares)
draw an imaginary line connecting the bottom right corner to the line before the top right corner (the line should be vertical)
count the squares here too and you get 3.
so the area = 3 x 4,
the area is 12u²
Luther High School's basketball coach won a record 33 out of 42 games how many games must the team win in the next 28 games for the coach to maintain to the ratio of wins to losses?
Using proportions, they must win 22 games to maintain to the ratio of wins to losses.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
Considering the next 28 games, we have that:
The team will have won 33 + x games.The team will have played 42 + 28 = 70 games.To keep the same proportion, we have that:
[tex]\frac{33}{42} = \frac{33 + x}{70}[/tex]
Applying cross multiplication:
42(33 + x) = 33 x 70
Simplifying by 14:
3(33 + x) = 33 x 5
3x = 33 x 5 - 33 x 3
3x = 33 x 2
3x = 66
x = 66/3
x = 22.
They must win 22 games to maintain to the ratio of wins to losses.
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Karen wants to advertise how many chocolate chips are in each Big Chip cookie at her bakery. She randomly selects a sample of 101 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 12.9 and a standard deviation of 3.2. What is the 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies? Enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
The 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is (12.4,13.3).
Given that a sample of 101 cookies and per cookie in the sample has a mean of 12.9 and a standard deviation of 3.2.
From the given information,
Let n=101 represents the size of the sample.
Let [tex]\bar{x}[/tex]= 12.9 represents the mean of the sample.
Let s= 3.2 represents the standard deviation of the sample.
Degrees of freedom:
df = n-1
df= 101-1
df= 100
The critical value of t at 0.2 level of significance with 100 degrees of freedom is,
[tex]\begin{aligned}t_{cric}&=t_{(\frac{\alpha}{2}, n-1)}\\ &=t_{(0.2,100)}\\ &=1.2900\end[/tex]
The 80% confidence interval for the number of chocolate chips per cookie for Big chip cookies is computed as follows:
[tex]\begin{aligned}CI_{80\%}&=\bar{x}\pm t_{(\frac{\alpha}{2},n-1)}\left(\frac{s}{\sqrt{n}}\right)\\ &=12.9\pm 1.2900\left(\frac{3.2}{\sqrt{101}}\right)\\ &=12.9\pm 1.2900\times 0.3184\\ &=12.9\pm 0.410736\\ &=12.489264,13.310736\end[/tex]
Hence, the 80% confidence interval for the number of chocolate chips per cookie for Big Chip cookies when the mean is 12.9 and standard deviation is 3.2 is (12.4,13.3).
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The set of all three-digit binary numbers
The set of all three-digit binary numbers as required in the task content includes; 100,101,110,111.
What is the set of all three-digit binary numbers?A binary number by definition is one which is made of a combination of numbers 0 and 1.
On this note, it follows that the three digits binary numbers in discuss include; 100,101,110,111.
Binary numbers are most often used in computer programs to represent data.
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50 POINTS!!!!!!!!!!!!!!!!!!!!!!!! SOLVE THIS QUICKLY WITH AN EXPLANATION
Answer:
x = 30 degrees
Step-by-step explanation:
angles MNO, LNM, and KNL make a straight line: 105+45+y = 180 --> y = 30 degrees
KNL = 30 degrees
angle KLN is 90 degrees, a triangle is equal to 180 degrees
2x+30+90 = 180
2x = 60
x = 30 degrees
Multiply 3.4x and 1.2x.
4.08x2
4.6x2
4.08x
4.6x
Answer: 4.08x2
Step-by-step explanation:
Answer:
4.08x2
Step-by-step explanation:
1376x13 please solve this equation and show work
The value of 1376 * 13 is 17888
How to solve the expression?The expression is given as:
1376 * 13
Express 1376 as 1300 + 76
(1300 + 76) * 13
Expand
1300 * 13 + 76 * 13
Evaluate the product
16900 + 988
Evaluate the sum
17888
Hence, the value of 1376 * 13 is 17888
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When the sum of a number and 3 is subtracted from 10 the result is 5 solve om algebraic equation?
Answer:
y = 2
Step-by-step explanation:
Algebraic Equation is an equation where alphabets are used to represent numbers.
Solving the above question,
Let the number = y
Therefore,
Sum of the number = y + 3
If it's subtracted from 10 it becomes
10 - ( y + 3 )
The result : 10 - y - 3 = 5
- y = 5 - 10 + 3
- y = -2
Therefore,
y = 2
– 42 – 54 + 96 =
what is the answer
Answer:
Answer:the answer is zero
Answer:the answer is zero Step-by-step explanation:
Answer:the answer is zero Step-by-step explanation:when we add -42 and -54 the answer we get is -96. -96and +96 cut each other and then the answer is zero
[tex] - 42 - 54 + 96 = 0[/tex]
suppose the equation z^2+4z+20+iz(A+1)=0 where A is constant has complex conjugate root if one of the root of this quadratic is z=B+2i where B is real constant find possible value of A ? please help me I need your help
If one of the roots is [tex]w=B+2i[/tex], then the other root is its conjugate [tex]\bar w=B-2i[/tex]. So we can factorize the quadratic to
[tex]z^2 + 4z + 20 + iz (A+1) = (z-(B+2i)) (z-(B-2i))[/tex]
Expand the right side and collect all the coefficients.
[tex]z^2 + (4+(A+1)i) z + 20 = z^2 - 2B z + B^2+4[/tex]
From the [tex]z[/tex] and constant terms, we have
[tex]\begin{cases}4 + (A+1)i = -2B \\ 20 = B^2 + 4 \end{cases}[/tex]
From the second equation we get
[tex]B^2 = 16 \implies B = \pm4[/tex]
Then
[tex]4+(A+1)i = \pm8[/tex]
[tex](A+1)i = 4 \text{ or } (A+1)i = -12[/tex]
Since [tex]\frac1i=-i[/tex], we have
[tex]-\dfrac{A+1}i = 4 \text{ or } -\dfrac{A+1}i = -12[/tex]
[tex]A+1 = -4i \text{ or } A+1 = 12i[/tex]
[tex]\boxed{A = -1 - 4i \text{ or } A = -1 + 12i}[/tex]
ION 10
answered
out of 1.00
Flag
n
What is the likelihood of Jada investing with Bank JNC if the following holds under the following conditions?
..
there is a 75% chance Jada will invest if the economic conditions remain stable;
there is a 25% chance investing if economic conditions suffer a decline;
there is a 55% chance of investing if the economic conditions improve.
the chance the economic conditions remaining stable (S), declining (D) and improving (1) are 0.20, 0.40
and 0.40, respectively.
Select one:
O.a. 0.135
O b. 0.103
OC. 0.400
O d. 0.470
Answer:
a
Step-by-step explanation:
For csc 330:
a) state value of the ratio exactly
b) find one equivalent expression
c) draw a diagram to illustarte.
The value of the ratio based on the angle illustrated is 1:12.
How to illustrate the information?From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:
= 360° - 330°
= 30°
The equivalent expression based on the angle will be:
= 30/360
= 1/12
= 1:12
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Simplify:
x² + 3x + 2 /x² - 4x - 5
x² + 7x + 12 / x²-3x - 28
[tex]\\ \rm\Rrightarrow \dfrac{x^2+3x+2}{x^2-4x-5}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x^2+2x+x+2}{x^2-5x+x-5}[/tex]
[tex]\\ \rm\Rrightarrow {(x+2)(x+1)}{(x-5)(x+1)}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x+2}{x-5}[/tex]
And
[tex]\\ \rm\Rrightarrow \dfrac{x^2+7x+12}{x^2-3x-28}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x^2+4x+3x+12}{x^2-7x+4x-28}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{(x+4)(x+3)}{(x-7)(x+4)}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{x+3}{x-7}[/tex]
Find the distance between points H(8, 2) and K(6, 10). Round your answer to the nearest tenth
Step-by-step explanation:
when you mark such points on a coordinate grid, and mark also the coordinate differences in x and y direction as soft lines, you notice that these coordinate difference lines and the direct connection between the 2 points create a right-angled triangle.
so, Pythagoras applies :
c² = a² + b²
with c being the Hypotenuse (the baseline opposite of the 90° angle, which is the direct connection between the 2 points). a and b are the legs (coordinate differences).
so,
distance² = (8 - 6)² + (2 - 10)² = 2² + (-8)² = 4 + 64 = 68
distance = sqrt(68) = 8.246211251... ≈ 8.2
Plug in different values of h and k to answer the following questions. What happens when h is positive? What happens when h is negative? What happens when k is positive? What happens when k is negative?
A logarithmic function is the inverse of an exponential function.
What is a logarithmic function?A logarithmic function is the inverse of an exponential function.
Now we have the function;
f(x) = log(x) and the translated function f(x) = log (x-h) + k.
When h is positive, the asymptote moves upwards by the stated amountWhen h is negative , the asymptote moves downwards by the stated amountSimilarly;
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Missing parts;
Use the graphing calculator to graph the parent function.
f(x) = log(x)
Add the translated function.
f(x) = log (x-h) + k
Plug in different values of h and k to answer the following questions.
What happens when h is positive?
What happens when h is negative?
What happens when k is positive?
What happens when k is negative?
Answer:
When h is positive: horizontal shift to the right
When h is negative: horizontal shift to the left
When k is positive: vertical shift up
When k is negative: vertical shift down
Step-by-step explanation:
got it right on Edge
Find an equation for the plane that contains the line
v=(-3,4,5)+t(3,2,4)
and is perpendicular to the plane
2x+y-3z+4=0
(Use symbolic notation and fractions where needed.)
The equation for the plane that contains the line and is perpendicular to the plane 2 · x + y - 3 · z = - 4 is - 10 · x + 17 · y - z = 76.
How to find the equation of a plane that contains a line and is perpendicular to another plane
From the equation of the plane 2 · x + y - 3 · z = - 4 we know that its normal vector is (2, 1, - 3). Hence, we have found two direction vectors and already know a point, which are part of this parametric equation:
(x, y, z) = (- 3, 4, 5) + t · (3, 2, 4) + u · (2, 1, - 3) (1)
The normal vector of the plane is equal to the cross product of the direction vectors of (1):
[tex]\vec n = (3, 2, 4) \,\times\,(2, 1, -3)[/tex]
[tex]\vec n = \left|\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\3&2&4\\2&1&-3\end{array}\right|[/tex]
[tex]\vec n = (-6-4,8+9, 3-4)[/tex]
[tex]\vec n = (-10, 17, -1)[/tex]
Since the plane contains the point (x, y, z) = (- 3, 4, 5), then we find that the independent constant of the equation of the plane is:
- 10 · x + 17 · y - z = k
- 10 · (- 3) + 17 · 4 - 5 = k
30 + 51 - 5 = k
k = 76
The equation for the plane that contains the line and is perpendicular to the plane 2 · x + y - 3 · z = - 4 is - 10 · x + 17 · y - z = 76.
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Set B and the universal set U are defined as follows.
U={f,g,h,p,q,r}
B={g,q,r}
Find the following sets.
Write your answer in roster form or as Ø.
(a) B' U U =
(b) B ∩ Ø =
Answer:
(a) B' U U = { f,g,h,p,q,r}
(b) B ∩ U = {g,q,r}
Step-by-step explanation:
Greetings !
(a) B/c B'= {X: X∈U and X∉B}
thus,B'= {f,h,p}
B' U U= {f,h,p} U {f,g,h,p,q,r}
= {f,g,h,p,q,r}
(b) B ∩ U= {g,q,r}
What is the midpoint of the line segment graphed below?
Answer:
(4, 7/2)
Step-by-step explanation:
midpoint = x values/2, y values/2