the graph represents a function with the form f(x)=asin(bx+c) which values of a,b, and c are possible

Answer:

4

Step-by-step explanation:

44-12=32 divide then 4

A sketch is made with the principal angle θ and the related acute angle α. The measure of the related acute angle α is approximately 40.6179 degrees. The measure of the angle θ is approximately 220.6179 degrees. The length of the terminal arm from (0, 0) to (6, -5) is approximately 8.60 units.

a) To sketch the principal angle θ in standard position, we start by drawing the positive x-axis and the positive y-axis. Then, we locate the point P(6, -5) on the terminal arm. We draw a straight line connecting the origin (0, 0) and point P. Label the angle as θ and mark the related acute angle as α.

b) To determine the measure of the related acute angle α, we can use the tangent function. We calculate α = tan^(-1)(|y / x|) = tan^(-1)(|-5 / 6|) ≈ 40.6179 degrees.

c) To determine the measure of the angle θ, we consider that the given point P(6, -5) is in the fourth quadrant. Hence, θ = 180 degrees + α ≈ 220.6179 degrees.

d) To find the length r of the terminal arm from (0, 0) to (6, -5), we use the distance formula. We calculate r = sqrt((6 - 0)^2 + (-5 - 0)^2) = sqrt(36 + 25) ≈ 8.60 units.

In summary, a sketch is made with the principal angle θ and the related acute angle α. The measure of the related acute angle α is approximately 40.6179 degrees. The measure of the angle θ is approximately 220.6179 degrees. The length of the terminal arm from (0, 0) to (6, -5) is approximately 8.60 units.

Know more about Terminal  here:

https://brainly.com/question/32155158

#SPJ11

Given:

a.) The chance of Kenny being selected is 1/29.

From the given, we can say that the total population is 29.

Since it's been given that Kenny and Tara are both memb

Two events A and B are mutually exclusive if they cannot occur together, that is, P(A∩B) = 0.P(A∩B) = 0.42

P(A∩B) ≠ 0

Therefore, A and B are not mutually exclusive.

1. Probability of A or B or both occurring P(A∪B) = P(A) + P(B) - P(A∩B)0.42 = 0.4 + 0.3 - P(A∩B)

P(A∩B) = 0.28

Therefore, probability of either A or B or both occurring is P(A∪B) = 0.28

2. Probability of both A and B occurring

P(A∩B) = P(A) + P(B) - P(A∪B)P(A∩B) = 0.4 + 0.3 - 0.28 = 0.42

Therefore, the probability of both A and B occurring is P(A∩B) = 0.42

3. Probability of A occurring but not B P(A) - P(A∩B) = 0.4 - 0.42 = 0.14

Therefore, probability of A occurring but not B is P(A) - P(A∩B) = 0.14

4. Probability of both A and B occurring when C occurs, if A, B and C are statistically independent

P(A∩B|C) = P(A|C)P(B|C)

A, B and C are statistically independent.

Hence, P(A|C) = P(A), P(B|C) = P(B)

P(A∩B|C) = P(A) × P(B) = 0.4 × 0.3 = 0.12

Therefore, probability of both A and B occurring when C occurs is P(A∩B|C) = 0.12

5. Two events A and B are statistically independent if the occurrence of one does not affect the probability of the occurrence of the other.

That is, P(A∩B) = P(A)P(B).

P(A∩B) = 0.42P(A)P(B) = 0.4 × 0.3 = 0.12

P(A∩B) ≠ P(A)P(B)

Therefore, A and B are not statistically independent.

6. Two events A and B are mutually exclusive if they cannot occur together, that is, P(A∩B) = 0.P(A∩B) = 0.42

P(A∩B) ≠ 0

Therefore, A and B are not mutually exclusive.

To know more about probability, visit:

https://brainly.com/question/31828911

#SPJ11

Answer:

----------------------

According to the diagram we have:

1) Angles w and 138° form a linear pair, hence:

2) Angles 19°, x and w form a right angle, hence:

Answer: (2,1) (0,-3)

(-5,2) (0,-1) (5,-4)

(0,-4) (2,-2)

(-1,0)

(-3,1) (-2,-4)

(0,3)

Step-by-step explanation:

Answer: The answer is C on edge

Step-by-step explanation:

Answer: from generation 19 to 20.

Step-by-step explanation:

The greatest percentage increase will occur  from generation 19 to 20 as the exponential power will be highest.

What is exponential growth?

Exponential growth happens once the larger in size you're the quicker you grow that causes you to even larger in size. it's the expansion characterised by interest, or growth. it's known as exponential growth as a result of it will solely be delineate mathematically by inserting time within the exponent or power of the bottom. Population then is adequate to the population at the current times some discretional range to the facility of the expansion rate times the time. The discretional range is sometimes two then the expansion rates is given because the reciprocal of the doubling time.

Main body:

initial population = 25

Total generation = 20

growth rate = 0.2

General formula of exponential function = aˣ

here a = 25 and x = 0.2

⇒25⁰°²

= 1.9

hence total population = 25+2 = 27

So it is clear that in 19 to 20 generation , growth will be highest.

To know more about exponential growth , visit:

https://brainly.com/question/11975096

#SPJ4

Answer:

1. B

2. E

3. D

4. B

5. C

6. B

7. E

8. D

9. D

10.D

11. E

Answer:

0

Step-by-step explanation:

Both M and m equal 81

The resultant value of the difference of Median and Mean will be 0.

The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.

The median is the middle value when a data set is ordered from least to greatest.

The mode is the number that occurs most often in a data set.

Given is the test scores of 8 students are shown in the table.

We can write the data in the order least to greatest as -

67, 75, 75, 75, 87, 87, 91, 91

Mean = 648/8 = 81

Median = (75 + 87)/2 = 81

So, we can write (Median- Mean) as 81 - 81 = 0

Therefore, the resultant value of the difference of Median and Mean will be 0.

To solve more questions on statistics, visit the link below-

brainly.com/question/12730221

#SPJ2

Answer:

x5

Step-by-step explanation:

Answer:

He got 49 - 42 = 7 wrong. 7 out of 49 can be written as 7/49 which simplifies to 1/7.

Answer:

7/49=1/7

Step-by-step explanation:

Wrong questions: 49-42=7

7/49=1/7.

Answer:

Four equivalent ratios:

1) 5:15

2)1:3

3) 10:30

4) 20:60

Step-by-step explanation:

The fraction of a day that can be attributed to 8 hours 20 minutes is   25/72 of a day.

In math, a fraction is a way of representing a part of a whole or a ratio between two numbers. It is written as a numerator and a denominator separated by a horizontal line called a fraction bar.

One hour is equal to 60 minutes, then we can say that 8 hours is equivalent to( 8*60) minutes. Then we can say that (480 minutes + 20 minutes) = 500 minutes.

since we know that 1 day is 24 hours = 24(60), then we can form this inform of a ratio as ;

500:( 24(60))

= 500: 1440

= 50/ 144

= 25/72 of a day.

Learn more about fraction at:

https://brainly.com/question/78672

#SPJ1

Given data;

The given length of one leg is a=6 cm.

The given hypotenuse is c=10 cm.

The expression for the pythagoras theorem is,

Substitute the given values in the above expr

Answer:

1. 3

2. 4

3. 0

4. 2

Step-by-step explanation:

Hope that helps

Answer:

1. is 3 2. is 4 3. is 0 4. is 2

The correct option is a) (-7, 3) which is the midpoint of the segment.

To find the midpoint of a segment, we need to use the midpoint formula:

Midpoint = ( \((x1 + x2)/2 , (y1 + y2)/2\) )

The midpoint of a segment is the point that lies exactly halfway between the two endpoints of the segment.

It is calculated using the midpoint formula, which involves finding the average of the x-coordinates and y-coordinates of the endpoints.

Using the coordinates given in the diagram, we can substitute them into the formula:

Midpoint = ( (-9 + 5)/2 , (3 + 3)/2 )

Midpoint = ( (-4)/2 , 6/2 )

Midpoint = ( -2 , 3 )

However, it means that if we were to draw a line segment connecting (-9, 3) and (5, 3), the midpoint would be exactly in the middle of that line.

To know more about segment refer here:

https://brainly.com/question/17410964#

#SPJ11

The particular solution of the differential equation in the integral form is

yp(x) = -2[G(x)]f(x) = -2G(x) ∫ f(t) dt + C

For finding a particular solution yp(x) of the given differential equation using the integral form, we can follow these steps:

yp(x) = G(x)f(x) ........... (1)

Given the differential equation is y" + 2y' + y = f(x)

Substituting yp(x) = G(x)f(x) into the differential equation, we get:

y" + 2y' + y = f(x)

By differentiating the expression for yp(x) twice, we gety

p'(x) = G'(x)f(x) + G(x)f'(x)

yp''(x) = G''(x)f(x) + 2G'(x)f'(x) + G(x)f''(x)

Substituting these values in the differential equation:

y''(x) + 2y'(x) + y(x) = yp''(x) + 2yp'(x) + yp(x) = [G''(x) + 2G'(x) + G(x)]f(x) + [2G'(x) + G(x)f''(x)]

When we compare the coefficient of f(x) on both sides of the equation. It is given that the function G(x) satisfies the equation G''(x) + 2G'(x) + G(x) = 0

Now,

[2G'(x) + G(x)]f''(x) + [G''(x) + 2G'(x) + G(x)]f(x) = f(x)

Substituting the given value of the differential equation, f(x) = fx) and simplifying the above expression, we get

[2G'(x) + G(x)]fx) = f(x)

Comparing the above expression with the given equation, we can obtain G(x) as

G(x) = -2G'(x)

Substituting this value in equation (1), we get

yp(x) = G(x)f(x) = -2G'(x)f(x)

So the required particular solution yp(x) of the given differential equation in integral form yp(x)-G(x, t)f(t) dt y" + 2y' + y = fx) is given as

yp(x) = -2[G(x)]f(x) = -2G(x) ∫ f(t) dt + C

where G(x) satisfies the equation G''(x) + 2G'(x) + G(x) = 0 and C is a constant of integration.

To know more about the "differential equation": https://brainly.com/question/18760518

#SPJ11

Answer:

the price per soda is $2.70

Step-by-step explanation:

$5.40/2 = 2.7

$13.50/5 = 2.7

$24.30/9 = 2.7

$27.00/10 = 2.7

so I came to the conclusion the price per soda is 2.7

Polynomial equation has y=cos(x), y=sin(x), and y=eˣ as solutions.

We can consider these functions as roots of a polynomial. Let's use the terms given to construct a polynomial equation:

Let P(y) be the polynomial, and let's denote the roots as y1 = cos(x), y2 = sin(x), and y3 = eˣ.

According to Vieta's formulas, for a cubic polynomial with roots y1, y2, and y3, we have:

P(y) = (y - y1)(y - y2)(y - y3)

Now, substitute the given roots:

P(y) = (y - cos(x))(y - sin(x))(y - eˣ)

This polynomial equation has y=cos(x), y=sin(x), and y=eˣ as solutions.

Learn more about polynomial equation.

brainly.com/question/25958000

#SPJ11

Answer: 582

Step-by-step explanation:

18+156=174

174+120=294

294+288=582

The shadow lengthens at a rate of 8.32 ft/sec when the woman is 35 ft from the base of the pole.

To calculate the rate at which the shadow lengthens, we can use similar triangles. Let's denote the length of the shadow as \(\(s\)\) and the distance of the woman from the pole as . According to the problem, the height of the pole is 13 ft and the height of the woman is 6.25 ft.

We can set up a proportion between the similar triangles:

\(\(\frac{{s + 13}}{x} = \frac{13}{6.25}\)\)

To solve for \(\(s\)\), we can cross-multiply and simplify:

\(\(6.25 \cdot (s + 13) = 13 \cdot x\) \\\(6.25s + 81.25 = 13x\)\)

Now, we differentiate both sides with respect to time \((\(t\))\):

\(\(\frac{d}{dt}(6.25s + 81.25) = \frac{d}{dt}(13x)\)\\\\\(6.25 \cdot \frac{ds}{dt} = 13 \cdot \frac{dx}{dt}\)\)

We are given that \(\(\frac{dx}{dt}\)\) (the rate at which the woman is approaching the pole) is 4 ft/sec. Substituting this value, we can solve for \(\(\frac{ds}{dt}\)\):

\(\(6.25 \cdot \frac{ds}{dt} = 13 \cdot 4\) \\\(\frac{ds}{dt} = \frac{13 \cdot 4}{6.25}\) \\\(\frac{ds}{dt} = \frac{52}{6.25}\) \\\(\frac{ds}{dt} \approx 8.32\) ft/sec\)

Therefore, the shadow lengthens at a rate of approximately 8.32 ft/sec when the woman is 35 ft from the base of the pole.

To learn more about similarity of triangles, refer here-

brainly.com/question/14285697#

#SPJ11

Answer:

c = -4

Step-by-step explanation:

If f(x) = 2x^3 - x + c and f(2) = 10, plug in 2 for the x values in the function and make the function output 10.

10 = 2(2^3) - 2 + c    Now, we only have to deal with one variable, that is c.

10 = 2(8) - 2 + c

10 = 16 - 2 + c

10 = 14 + c

-4 = c    After simplifying, we get that c is -4.

To check this, plug in 2 for x, and -4 for c in the function. If the function produces 10 as the result, the halleluja!

f(2) = 2(2^3) - 2 - 4

f(2) = 2(8) - 2 - 4

f(2) = 16 - 2 - 4

f(2) = 10

\(\\ \tt\hookrightarrow 2x^3-x+c=10\)

\(\\ \tt\hookrightarrow 2(2)^3-2+c=10\)

\(\\ \tt\hookrightarrow 2(8)-2+c=10\)

\(\\ \tt\hookrightarrow 16-2+c=10\)

\(\\ \tt\hookrightarrow 14+c=10\)

\(\\ \tt\hookrightarrow c=-4\)

The  periods that you can use for an n period moving average is 3.

The term n period moving average is the type of average that an investor can use to determine the trends in investments and the equities market. This type of average helps the traders to be able to understand the moving trends in the market and also to be able to make forecasts.

The period of the moving average spans across the times that the stock would last. This is determined by the equities market. Hence we can say that number of periods that you can be able to substitute for n to obtain the period moving average is 3.

Learn more about moving average:https://brainly.com/question/15572913

#SPJ1

Total stockholders’ equity 7,800,000

Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000

Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000

Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000

Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000

To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.

The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.

Calculations:Opening balance of common stock = $100,000

Opening balance of additional paid-in capital = $4,100,000

Opening balance of retained earnings = $3,000,000

Net Income for the year ended December 31, 2012 = $800,000

Retained earnings (Opening Balance) = $3,000,000

Add: Net Income for the year ended December 31, 2012 = $800,000

Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000

Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000

Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000

Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
To learn more about : equity

https://brainly.com/question/27821130

#SPJ8

Answer:

y=9

Step-by-step explanation:

12/y=4/3

3×12/y=3×4/3

36/y=4

y×36/y= 4×y

36=4y

36/4=4y/4

9=y

Only the statement "One machine is considerably more unreliable than the rest." is valid for the data.

Total number of correct cuts = 42 + 55 + 13 + 24 + 17 = 151

Total number of cuts = 100 + 100 + 100 + 100 + 100 = 500

Percentage of correct cuts = (151/500) * 100 = 30.2%

This statement is not valid, as only 30.2% of the cuts are the correct length.

One machine is considerably more unreliable than the rest."

By examining the number of correct cuts for each machine, we can see that Machine 3 has only 13 correct cuts, while the other machines have more than 17. This statement is valid.

3. When a machine misses the correct length, it tends to cut too long."

We need to compare the number of cuts that are too long (1.26-1.27 feet) with those that are too short (1.23-1.24 feet) across all machines:

Total number of cuts too long = 4 + 2 + 3 + 6 + 4 = 19

Total number of cuts too short = 980 + 72 + 67 = 1119

This statement is not valid, as the machines tend to cut too short rather than too long.

4. "Machine 5 will cut every batch the correct length at least 92% of the time."

To check this statement, we need to find the percentage of correct cuts for Machine 5:

Percentage of correct cuts for Machine 5 = (17/100) * 100 = 17%

This statement is not valid, as Machine 5 only cuts the correct length 17% of the time, which is less than 92%.

only the statement "One machine is considerably more unreliable than the rest." is valid for the data.

Read more on valid statements here:https://brainly.com/question/28335524

#SPJ1

The equation e(xy) = e(x)e(y) holds true and can be proven by utilizing the properties of exponential functions.

To prove the equation e(xy) = e(x)e(y), we start with the left-hand side (LHS) of the equation, which is e(xy). The exponential function e(x) can be defined as the infinite series: e(x) = 1 + x/1! + x^2/2! + x^3/3! + ...

Now, substituting xy for x in the exponential function, we have e(xy) = 1 + (xy)/1! + (xy)^2/2! + (xy)^3/3! + ...

Next, let's consider the right-hand side (RHS) of the equation, which is e(x)e(y). Using the definition of the exponential function, we have e(x)e(y) = (1 + x/1! + x^2/2! + x^3/3! + ...)(1 + y/1! + y^2/2! + y^3/3! + ...).

Expanding this expression, we obtain e(x)e(y) = 1 + (x+y)/1! + (x^2+2xy+y^2)/2! + (x^3+3x^2y+3xy^2+y^3)/3! + ...

Comparing the expressions for e(xy) and e(x)e(y), we can see that both are equal. Therefore, the equation e(xy) = e(x)e(y) is proven.

For more questions like Function click the link below:

https://brainly.com/question/16008229

#SPJ11