find the perimeter of this figure

it is made up of semicircles and quarter circles

Answer:

  D. [tex]f^{-1}(x)=\log_2{(x-6)}[/tex]

Step-by-step explanation:

Solve x = f(y) for y:

  x = 2^y +6

  x -6 = 2^y . . . . subtract 6

  log2(x -6) = y . . . . take the log base 2 . . . . matches choice D

Answer:

The answer is D

Step-by-step explanation:

In order to find out the inverse of the function, you have to express a new function where the independent variable must be "y" instead of "x".

So, you have to reorganize the base function and then free the variable "x".

[tex]f(x)=2^x+6\\f(x)=y\\y=2^x+6\\2^x=y-6\\log_2(2^x)=log_2(y-6)\\x*log_2(2)=log_2(y-6)\\log_2(2)=1\\x=log_2(y-6)\\[/tex]

Then, we recall "y" as "x" and [tex]x=f^-^1(x)[/tex]

Finally, the answer is:

[tex]f^-^1(x)=log_2(x-6)[/tex]

bank b for the loan and bank a for the savings account.

The answer is:

They will be 10 miles apart after 3 hours.

To calculate how long after they start will they be 10 miles apart, we need to assume that after 1 one hour, they were at the same distance (5 miles), then, calculate the time when they are 10 miles apart, knowing that Paul increased its speed two times, running first at 5mph and then, at 10 mph.

The time that will pass to be 10 miles apart can be calculated using the following equation:

[tex]TotalTime=TimeToReach5miles+TimeToBe10milesApart[/tex]

Calculating the time to reach 5 miles for both Larry and Paul, at a speed of 5 mph, we have:

[tex]x=xo+v*t\\\\5miles=0+5mph*t\\\\t=\frac{5miles}{5mph}=1hour[/tex]

We have that to reach a distance of 5 miles, they needed 1 hour. We need to remember that at this time, they were at the same distance.

If we want to know how many time will it take for them to be 10 miles apart with Paul increasing its speed to 10mph, we need to assume that after that time, the distance reached by Paul will be the distance reached by Larry plus 10 miles.

So, for the second moment (Paul increasing his speed) we have:

For Larry:

[tex]x_{L}=5miles+5mph*t[/tex]

Therefore, the distance of Paul will be equal to the distance of Larry plus 10 miles.

For Paul:

[tex]x{L}+10miles=xo+10mph*t\\\\5miles+5mph*t+10miles=5miles+10mph*t\\\\5miles+10miles-5miles=10mph*t-5mph*t\\\\10miles=5mph*t\\\\t=\frac{10miles}{5mph}=2hours[/tex]

Then, there will take 2 hours to Paul to be 10 miles apart from Larry after both were at 5 miles and Paul increased his speed to 10 mph.

Hence, calculating the total time, we have:

[tex]TotalTime=TimeToReach5miles+TimeToBe10milesApart[/tex]

[tex]TotalTime=1hour+2hours=3hours[/tex]

Have a nice day!

Answer:

1. P(A) = 0.6826

2. P(B) = 0.13591

Step-by-step explanation:

the first graph is given just as an example to show the percentage distribution values for bell shaped curve

Answer:

68.3%, 33.3%

Step-by-step explanation:

PLATO answer!! pls mark brainliest :)))

The net of a cylinder is best described by a circle and one rectangle.

A cylinder is a three-dimensional solid, the most basics of curvilinear shapes which is considered as a prism with circle as its base.

A cylinder has a base radius and the height from its base to top .

Formula of surface area of cylinder is =  2πr(r + h)

Formula of Volume of cylinder is = [tex]\pi r^{2} h[/tex]

The net of the cylinder should have one side open such that it can be inserted within the cylinder.

As the top of the cylinder is circle, thus the net should have one circular top . Also the body of the cylinder is in the form of a rectangle which ensures the net should have also one rectangular body.

Therefore the net of a cylinder is best described by a circle and one rectangle.

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The net of a cylinder is comprised of 'one rectangle and two circles', which represent the lateral surface and the two equal-sized circular bases of the cylinder, respectively.

The net of a cylinder consists of two equal-sized circles and one rectangle that wraps around to form the curved surface. The two circles represent the top and bottom (or base) of the cylinder, and they are identical in size because the top and the bottom of a cylinder have the same cross-sectional area. The rectangle represents the lateral surface area of the cylinder, which, if 'unrolled', resembles a rectangle whose length is equal to the circumference of the circles (the perimeter of the base) and whose height is equal to that of the cylinder. The correct option that describes the net of a cylinder is thus 'one rectangle, two circles'.

For this case we have that by definition, the slope-intersection equation of a line is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

[tex]m = \frac {y2-y1} {x2-x1} = \frac {-1 - (- 7)} {2-0} = \frac {-1 + 7} {2} = \frac {6} { 2} = 3[/tex]

Thus, the equation is:

[tex]y = 3x + b[/tex]

Substituting a point we find b:[tex]-7 = 0 + b\\b = -7[/tex]

Finally the equation is:

[tex]y = 3x-7[/tex]

ANswer:

The missing value is 3

Answer:

The value of missing is 3

Step-by-step explanation:

* To form an equation of a line from two points on the line, you

  must find the slope of the line at first

- The form of the equation is y = mx + c, where m is the slope of the

 line and c is the y-intercept

- The rule of the slope of a line passes through point (x1 , y1) and (x2 , y2)

  is m = (y2 - y1)/(x2 - x1)

* Lets solve the problem

∵ (0 , -7) and (2 , -1) are tow points on the line

- Let (0 , -7) is the point (x1 , y1) and (2 , -1) is the point (x2 , y2)

∴ m = (-1 - -7)/(2 - 0) = (-1 + 7)/2 = 6/2 = 3

- Lets write the equation

∴ y = 3x + c

- c is the y-intercept means the line intersect the y-axis at point (0 , c)

∵ Point (0 , -7) on the line

∴ The line intersect the y-axis at point (0 , -7)

∴ The y-intercept is -7

∴ The equation of the line is y = 3x - 7

* The value of missing is 3

Answer:

1. Range =30

2. Variance =137.6

3. Standard deviation=11.7303

Step-by-step explanation:

This question requires you to find the range, variance and standard deviation of sample data set.

Given the data as; 127 150 121 120 140 128

Arrange the data in ascending order;

sample set S={120, 121, 127, 128, 140, 150}

number of elements, n=6

1. Range = Maximum (S) - Minimum (S) = 150- 120 = 30

⇒Find the mean of the data set

[tex]mean= \frac{120+121+127+128+140+150}{6} = 786/6 = 131[/tex]

2. Variance is the measure of how far a set of data is spread out.Standard deviation is the square-root of variance.To find variance you need to follow the steps below;

Finding the deviations from the mean and their squares

Deviations             Squares of deviations

120-131= -11               -11²=   121

121-131= -10                -10² =100

127-131= -4                  -4² = 16

128-131= -3                   -3= 9

140-131= 9                    9²=  81

150-131= 19                19²=  361

Finding the sum of the squares of the deviations from the mean

[tex]=121+100+16+9+81+361=688[/tex]

Finding the variance

Variance, S²=(sum of squares of deviations from mean)/ n-1

[tex]=\frac{688}{n-1} =\frac{688}{6-1} =\frac{688}{5} =137.6[/tex]

Finding standard deviation

Standard deviation , s , is the square-root of the variance 

[tex]s=\sqrt{137.6} =11.73[/tex]

Final Answer:

- Range: 30 mmHg
- Variance: 137.6 (mmHg)²
- Standard Deviation: Approximately 11.73 mmHg
- Ideal Standard Deviation: 0 mmHg

Explanation:

To find the range, variance, and standard deviation for the given blood pressure readings, we can follow these steps:
1. **Range:**
  - The range is the difference between the highest and lowest values in the data set.
  - Highest reading = 150 mmHg
  - Lowest reading = 120 mmHg
  - Range = Highest reading - Lowest reading = 150 - 120 = 30 mmHg

2. **Variance:**
  - Variance measures the average degree to which each reading differs from the mean of the readings. Because we are dealing with a sample of the population, not the entire population, we'll use the sample variance formula.
  - First, compute the mean of the readings.
  - Mean (average) blood pressure reading = (127 + 150 + 121 + 120 + 140 + 128) / 6
  - Mean = 786 / 6 = 131 mmHg
  - Now, we'll calculate the square of the differences between each reading and the mean, sum those, and divide by (n-1), where n is the number of readings.
  - Differences squared: (127-131)², (150-131)², (121-131)², (120-131)², (140-131)², (128-131)²
  - = (-4)², (19)², (-10)², (-11)², (9)², (-3)²
  - = 16, 361, 100, 121, 81, 9
  - Sum of squared differences = 16 + 361 + 100 + 121 + 81 + 9 = 688
  - Sample variance = 688 / (6 - 1) = 688 / 5 = 137.6 (mmHg)²

3. **Standard Deviation:**
  - The standard deviation is the square root of the variance and provides a measure of the average distance from the mean.
  - Standard deviation = √variance = √137.6 ≈ 11.73 mmHg

4. **Ideal Standard Deviation:**
  - If the subject's blood pressure remains constant, and the measurement technique is applied correctly and without any error, the ideal standard deviation should be zero because all measurements would be the same, resulting in no variability.

In summary:
- Range: 30 mmHg
- Variance: 137.6 (mmHg)²
- Standard Deviation: Approximately 11.73 mmHg
- Ideal Standard Deviation: 0 mmHg

1962 - 2003 = 41 years

In 2003 it’s value increased to = $435,000

$435,000 / 41 years

Per year’s value = $10,609.7561

B. 1950 - 1960 = 12 years

$60,000 / 12 years = $5000

Value of the house @ 1950 = $5000

Using proportions, it is found that:

Item a:

From an initial value of $60,000, the house increased in value by $375,000, as 435000 - 60000 = 375000.

The percent increase is given by:

[tex]\frac{375000}{60000} \times 100\% = 625\%[/tex]

In 2003 - 1962 = 41 years, hence:

[tex]r = \frac{625}{41} = 15.24[/tex]

The annual rate of increase in the value of the house was of 15.24%.

Item b:

The value increases 15.24% a year, hence, in t years after 1962, considering an initial value of $60,000, the value is:

[tex]V(t) = 60000(1.1524)^t[/tex]

1950 is 12 years before 1950, hence the value is V(-12), that is:

[tex]V(-12) = 60000(1.1524)^{-12} = \frac{60000}{(1.1524)^{12}} = 4029[/tex]

In 1950, the house was valued at $4,029.

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Answer:

either of ...

• quadrant 1 only

• quadrant 1 and 4 only

Step-by-step explanation:

Time since the storm started is always positive. The values of x are positive in quadrants 1 and 4.

Temperatures in a blizzard are not always terribly cold. Some of the coldest snowstorms on record have temperatures in the range of +5 °F to +18 °F. These values are negative temperatures on the Celsius scale, so the quadrant used for plotting them will depend on the temperature scale you choose.

While temperatures in Alaska can be well below zero (on either the F or C temperature scales), the air usually has to warm up to the range indicated above before it can snow. US temperatures are generally reported using the Fahrenheit scale, but weather records are often kept using the Celsius scale.

I would be inclined to choose "Quadrant 1 and 4 only", but arguments can be made for "1 only" and "4 only" as suggested above.

Answer:Answer:

either of ...

• quadrant 1 only

• quadrant 1 and 4 only

Step-by-step explanation:

Time since the storm started is always positive. The values of x are positive in quadrants 1 and 4.

Temperatures in a blizzard are not always terribly cold. Some of the coldest snowstorms on record have temperatures in the range of +5 °F to +18 °F. These values are negative temperatures on the Celsius scale, so the quadrant used for plotting them will depend on the temperature scale you choose.

While temperatures in Alaska can be well below zero (on either the F or C temperature scales), the air usually has to warm up to the range indicated above before it can snow. US temperatures are generally reported using the Fahrenheit scale, but weather records are often kept using the Celsius scale.

I would be inclined to choose "Quadrant 1 and 4 only", but arguments can be made for "1 only" and "4 only" as suggested above.

Step-by-step explanation:

The expression (5x + 2) + (5x + 2) + (5x + 2) simplifies to 15x + 6 by combining like terms; three 5x's give 15x, and three 2's give 6 when added together.

The expression (5x + 2) + (5x + 2) + (5x + 2) is given by adding three identical binomials. To find an equivalent expression, you can use the distributive property of multiplication over addition, which in this case can also be seen as simply combining like terms.

Step-by-step, here's how you simplify the expression:

So, (5x + 2) + (5x + 2) + (5x + 2) is equivalent to 15x + 6 for all values of x.

namely, how many times does 2/7 go into 7/8?

[tex]\bf \cfrac{7}{8}\div\cfrac{2}{7}\implies \cfrac{7}{8}\cdot \cfrac{7}{2}\implies \cfrac{49}{16}\implies 3\frac{1}{16}\impliedby \textit{3 whole times}[/tex]

A 7/8 inch long string can be cut into 3 pieces of length 2/7 inch each.

This is an example of fraction division, which is related to Mathematics. To find out, how many pieces of string that are 2/7 of an inch long can be cut from a piece of string that is 7/8 of an inch long, you would have to divide the whole length of the string (7/8 inch) by the length of each piece (2/7 inch).

When you divide fractions, you actually multiply by the reciprocal of the second fraction. The reciprocal of a fraction is simply, flipping the numerator and denominator. So, the reciprocal of 2/7 would be 7/2.

Now simply multiply the two fractions, (7/8) times (7/2) which equals 49/16 or roughly 3.06. However, since you can't cut a string into a .06 piece, the answer would be 3 pieces.

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The expression that represents the statement is (56 - 14) ÷ 8.

To represent the given statement, "Subtract 14 from 56 and divide the result by 8," we need to follow these steps:

Step 1: Subtract 14 from 56: 56 - 14 = 42

Step 2: Divide the result by 8: 42 ÷ 8 = 5.25

So, the expression that represents the statement is (56 - 14) ÷ 8.

The correct answer is: (56 - 14) ÷ 8.

The complete question is here:

Which expression represents the statement shown? Subtract 14 from 56 and divide the result by 8. (56/ 8)-14 (14-56)/ 8 14-(56/ 8) (56-14)/ 8.  

[tex]

3x^2y^5\cdot(4xy^2)^3 = 3x^2y^5\cdot(64x^3y^6) = \boxed{192x^5y^{11}}

[/tex]

The answer is x=17. Since it says that the plot point is the answer to square root 4.1^2 = 16.81 which is closest to 17.

Hope this helps and hope you have a great day and brainiest is always appreciated

Answer:

  D.  37.22%

Step-by-step explanation:

One of my favorite probability z-table websites calculates the fraction as 0.3722 = 37.22%.

___

Your graphing calculator or spreadsheet can probably do the same for you.

Using the concepts of the normal distribution and z-scores, you calculate the z-scores for $25,000 and $40,000. Then, looking up these z-scores in a standard normal distribution table, and subtracting these, you get the percentage 37.17%, making the closest answer option D: 37.22%.

This question requires understanding of both normal distribution and z-scores. A Z-score measures how many standard deviations an element is from the mean. To solve this, we calculate the z-scores for $25,000 and $40,000, respectively, using the formula: z = (X - μ) / σ where X is the value, μ is the mean, and σ is the standard deviation.

Then, look up these z-scores in a standard normal distribution table (also known as a Z table). The values corresponding to -1.35 and -0.10 are 0.0885 and 0.4602, respectively. Substract these to find the percentage of homeowners with incomes between $25,000 and $40,000. That is, (0.4602 - 0.0885) * 100 = 37.17%. The closest answer is then option D: 37.22%

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the answer in decimal form is .25 but in fraction form is 1/4

The value of cos(75°)cos(15°) is 0.25.

To solve the expression cos(75°)cos(15°), we use the identity cos(a)cos(b) = 0.5[cos(a+b) + cos(a-b)]. Applying this identity, we have:

cos(75°)cos(15°) = 0.5[cos(75°+15°) + cos(75°-15°)].

Using the values of cos(90°) = 0 and cos(60°) = 0.5, we can simplify the expression:

cos(75°)cos(15°) = 0.5[cos(90°) + cos(60°)] = 0.5[0 + 0.5] = 0.25.

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Answer: first option

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

The Standard form of the equation of the line is:

[tex]Ax + By = C[/tex]

Where A is a positive integer, and B, and C are integers.

You can observe in the graph that the line intersects the y-axis at [tex]y=-2[/tex], then, "b" is:

[tex]b=-2[/tex]

Find the slope of the line with this formula:

 [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Choose two points of the line and substitute values.

Points:(-3,0) and  (3,-4)

Then:

 [tex]m=\frac{-4-0}{3-(-3)}=-\frac{2}{3}[/tex]

Substituting values into  [tex]y=mx+b[/tex], you get the equation of the line in Slope-intercept form:

 [tex]y=-\frac{2}{3}x+2[/tex]

To write it in Standard form, make the addition indicated:

[tex]y=\frac{-2x+6}{3}[/tex]

Multiply both sides of the equation by 3:

[tex]3(y)=(3)(\frac{-2x+6}{3})[/tex]

[tex]3y=-2x+6[/tex]

And finally add 2x to both sides:

[tex]2x+3y=-2x+6+2x[/tex]

[tex]2x+3y=6[/tex]

Answer:x=4 , y=-1

Step-by-step explanation:

X-y=5

X+y=3

If 1 and 2 are added then y will be eliminated

(1)+(2) gives : 2x=8 then x=4

Now substitute this value of x into either of the 2 equations and solve for y.

Let x=4 in (1) =4-y=5 = y=-2

Answer:

in this problem we do a comparison case t i.e if 1/12 he writes 1/6 of page what about 1 page

     1/12minute  =   1/6

      ?    ×    1          then we cross multiply

(1*1/12)    ÷  1/6     =1/12*6  =  1/2 minute

Answer:

  y = -(1/3)x -2

Step-by-step explanation:

For each horizontal "run" of 3 units, the "rise" of the line is -1 unit. Hence the slope is ...

   rise/run = -1/3

The y-intercept is where the line crosses the y-axis, at y = -2. So, the slope-intercept form of the equation of the line is ...

  y = (slope)·x + (y-intercept)

  y = -1/3x -2

Answer:

Step-by-step explanation:

A) Let x represent acres of pumpkins, and y represent acres of corn. Here are the constraints:

  x ≥ 2y . . . . . pumpkin acres are at least twice corn acres

  x - y ≤ 10 . . . . the difference in acreage will not exceed 10

  12 ≤ x ≤ 18 . . . . pumpkin acres will be between 12 and 18

  0 ≤ y . . . . . the number of corn acres is non-negative

__

B) If we assume the objective is to maximize profit, the profit function we want to maximize is ...

  P = 360x +225y

__

C) see below for a graph

__

D) The profit for an acre of pumpkins is the highest, so the farmer should maximize that acreage. The constraint on the number of acres of pumpkins comes from the requirement that it not exceed 18 acres. Then additional profit is maximized by maximizing acres of corn, which can be at most half the number of acres of pumpkins, hence 9 acres.

So profit is maximized for 18 acres of pumpkins and 9 acres of corn.

Maximum profit is $360·18 +$225·9 = $8505.

[tex]\displaystyle\bf\\m \overset{\frown}{HE}=360-m \overset{\frown}{HL}-m \overset{\frown}{EV}-m \overset{\frown}{VL}\\m\overset{\frown}{HE}=360^o-40^o-130^o-110^o=360^o-280^o=80^o\\\\m\widehat{EYH}=m\widehat{EYV}=\frac{m \overset{\frown}{EV}-m\overset{\frown}{HE}}{2}=\frac{130^o-80}{2}=\frac{50^o}{2}=\boxed{\bf25^o}[/tex]

Answer:

T= 200+45m

Step-by-step explanation:

m= months

T=total money

Answer:

  No

Step-by-step explanation:

The volume of a cube is the cube of the edge length, so the edge length of the cube-shaped block is ...

  edge length = ∛(64 cm³) = 4 cm

Then the smallest cross-section will be a square of edge length 4 cm, so will have an area of (4 cm)² = 16 cm².

The 16 cm² shape will not fit through an 8 cm² hole.

Using given area of the square hole, we find its side length to be approx. 2.83 cm. Calculating the side length of the block using its volume, we get 4 cm. As the block is larger than the hole, it won't fit.

The problem involves geometry, specifically the concepts of area and volume. The area of a square is given by the formula, A = s^2, where s is the side of the square. In this case, the area of the square hole is 8 sq cm, which means the side length of the square hole (s) is the square root of 8, or about 2.83 cm.

The volume of a cube is given by the formula V = s^3, where s is the side length of the cube. The volume of the cube block is 64 cubic cm, which means the side length of the block (s) is the cube root of 64, or 4 cm.

Therefore, since the side length of the block (4 cm) is greater than the side length of the square hole (2.83 cm), the block will not fit through the hole.

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Answer:

Step-by-step explanation:

Givens

Cyclist A

r = r_a - 3

t = 5 hours.

d = ?

Cyclist B

r = r _a

t = 5 hours - 1/2 hour = 4.5 hours.

d = d - 31.5

Formula

(r - 3)*5 + 5*r = d

r*4.5 = d - 31.5

Explanation

The rate of A is 3 less than the rate of B. Together, they bicycle the entire distance (d). That's the first equation

The second equation is a lot harder. That equation has to do with the one starting off from B. His useful cycling time is 4 1/2 hours because he starts off 1/2 hour later.

He travels d - 31.5 which A travels 31.5

Solution

The total distance is the same. We will use that fact to solve for r first.

(r - 3)*5 + 5r = d

4.5r + 31.5 = d

Remove the brackets in the top equation.

5r - 15 + 5r = d

10r - 15 = 4.5r + 31.5             Add 15 to both sides

10r -15+15 = 4.5r + 31.5+15

10r = 4.5r + 46.5                   Subtract 4.5 r from both sides.

10r-4.5r = 46.5

5.5r = 46.5

r = 8.45 mph

====================

4.5r + 31.5 = d

4.5*8.45 + 31.5 = d

d = 69.53 miles

====================

If this proves to be incorrect, and you have choices, please list them.

Answer:

  (-x +5) -5/(3x)

Step-by-step explanation:

Divide term by term.

  = (3x^2)/(-3x) +(-15x)/(-3x) +(5)/(-3x)

  = -x +5 -5/(3x)

Answer:

20

Step-by-step explanation:

9/15 = 3/5

3*4=12

5*4=20

Answer:

20 shots

Step-by-step explanation:

First round

basket = 9

Total shots = 15

Percentage = 9/15 x 100 = 60%

Second round

baskets = 12

Total = x

(12/x) x 100 = 60%

12/x = 0.6

x = 12 ÷ 0.6

x = 20

Answer:2006

Step-by-step explanation:

[tex]A = 118e^{0.024t}[/tex]

When A = 140:

[tex]140 = 118e^{0.024t}[/tex]

[tex]\frac{140}{118} = e^{0.024t}[/tex]

[tex]ln(\frac{140}{118}) = 0.024t[/tex]

[tex]\frac{1}{0.024} ln(\frac{140}{118}) = t[/tex]

Plugging into a calculator, t is approximately 7.12.  Since t represents years since 1998, we round up to the nearest whole number: t=8.  So the population of the city will reach 140 thousand in the year 2006.

The population of the city reach 140 thousand will be after 7.123 years.

Let a be the initial value and x be the power of the exponent function and b be the increasing factor.

The exponent is given as

y = a(b)ˣ

The equation models the number of inhabitants in a specific city, in thousands, t years after 1998 is given below.

[tex]\rm A = 118 \times e^{0.024 \times t}[/tex]

The number of years when the population becomes 140 thousands is given as,

[tex]\rm 140 = 118 \times e^{0.024 \times t}[/tex]

Take natural log on both sides, then we have

0.024 t = ln (140 / 118)

0.024 t = 0.170957

t = 7.123 years

The population of the city reach 140 thousand will be after 7.123 years.

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Answer:

The exact value of 2 sin(120°) cos(120°) is -√3/2

Step-by-step explanation:

* Lets revise the trigonometry functions of the double angle

# sin(2x) = 2 sin(x) cos(x)

# cos(2x) = cos²(x) - sin²(x) OR

  cos(2x) = 2 cos²(x) - 1 OR

  cos(2x) = 1 - 2 sin²(x)

# tan(2x) = 2 tan(x)/(1 - tan²(x))

* Now lets solve the problem

∵ 2 sin(120°) cos(120°)

- Put sin(120°) = sin(2×60°)

∵ sin(2x) = 2 sin(x) cos(x)

∴ sin(120°) = 2 sin(60°) cos(60°)

∵ sin(60°) = √3/2 and cos(60°) = 1/2

∴ sin(120°) = 2 (√3/2) (1/2) = √3/2

∴ sin(120°) = √3/2 ⇒ (1)

- Put cos(120°) = cos(2×60°)

∵ cos(2x) = cos²(x) - sin²(x)

∴ cos(120°) = cos²(60°) - sin²(60°)

∵ cos(60°) = 1/2 and sin(60°) = √3/2

∴ cos(120°) = (1/2)² - (√3/2)² = 1/4 - 3/4 = -2/4 = -1/2

∴ cos(120°) = -1/2 ⇒ (2)

- Substitute (1) and (2) in the expression 2 sin(120) cos(120)

∴ 2 sin(120°) cos(120°) = 2 (√3/2) (-1/2) = -√3/2

* The exact value of 2 sin(120°) cos(120°) is -√3/2

Answer:

C 1/2

Step-by-step explanation:

There are 4 suits, 2 suits are  red (hearts and diamonds) while 2 are black (clubs and spades)

Since 13 cards are in each suit, 26 cards are red ( 2 * 13)  

There are 52 total cards

P (red) = red cards/ total cards

           = 26 / 52

           = 1/2