What is the radius of a circle with a circumference of 64 feet?

Cofunction equivalent to [tex]$\sin (5 \pi / 12)=\cos (1 \pi / 12)$[/tex].

You use the formula for the sine of a sum:

[tex]$$\sin (a+b)=\sin a \cos b+\cos a \sin b$$[/tex]

Think of a pie divided into twelve slices. Three of them form one quarter, two more form one sixth of the pie. So, thinking of the "pie" as [tex]$\pi$[/tex]:

[tex]\frac{5 \pi}{12}=\frac{\pi}{4}+\frac{\pi}{6}[/tex]

With that in mind, put [tex]$a=\frac{\pi}{4}, b=\frac{\pi}{6}$[/tex] into the sine formula given above:

[tex]$$\sin \left(\frac{5 \pi}{12}\right)=\sin \left(\frac{\pi}{4}\right) \cos \left(\frac{\pi}{6}\right)+\cos \left(\frac{\pi}{4}\right) \sin \left(\frac{\pi}{6}\right)$$[/tex]

Plug in the familiar values [tex]$\sin \left(\frac{\pi}{4}\right)=\cos \left(\frac{\pi}{4}\right)=\frac{\sqrt{2}}{2}, \cos \left(\frac{\pi}{6}\right)=\frac{\sqrt{3}}{2}$[/tex], [tex]$\sin \left(\frac{\pi}{6}\right)=\frac{1}{2}$[/tex], and you get the answer given above. And, yes, putting that expression into a calculator gives [tex]$0.9659$[/tex] (four significant digits).

The cofunction of an angle θ is the trigonometric complement of an angle. It shows the relationship between trignometric functions:

List the cofunction formula for [tex]$\sin$[/tex]

[tex]$$\sin (\theta)=\cos (\pi / 2-\theta)$$[/tex]

Plug in [tex]$\theta=5 \pi / 12$[/tex] for our cofunction formula:

[tex]$$\sin (5 \pi / 12)=\cos (\pi / 2-5 \pi / 12)$$[/tex]

Determine common denominator in radians

We use a common denominator of [tex]$(12 \div 2)=6$[/tex]

[tex]$\sin (5 \pi / 12)=\cos (6 \pi / 12-(5 \pi / 12))$[/tex]

[tex]$\sin (5 \pi / 12)=\cos (1 \pi / 12)$[/tex]

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The equivalent expressions of the given expressions are

The expressions are given as

The distributive property stated that

a(b + c)= ab + ac

Using the above as a guide, the equivalent expressions are

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A reasonable domain for this function is [0, 18)

The domain of a function is a value of the independent variable of the function for which it exists.

Given the equation below:

M(x)= -40x+720

Since the function represents the The amount of money remaining in the budget for marketing  then the function f(x) must be greater than zero;

−40x + 720 > 0

-40x> -720
x < 720/40
x < 18

This shows that a reasonable domain for this function is [0, 18)

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Answer:

The number is -2

Step-by-step explanation:

First let's turn this into an equation

5 times a number (we'll use x) + 34 = 24

5x+34= 24

Now to start solving the problem

First thing's first, let's carry over the 34 to the other side by subtracting 34 from both sides. This helps us try to get x by itself

5x+34 = 24

     -34     -34

5x = -10

Now we just divide both sides by 5 to get rid of it entirely from the x

5x = -10

/5      /5

x = -2

Your number should be -2

We can also check by plugging -2 back into the equation for x

5 (-2) +34 = 24

-10 +34 = 24

24 = 24

Since they are both equal, -2 is really your answer

I hope this helps :)

The balance in Larry's savings account at the end of these 8 years is 1698 dollars and 84 cents

The given parameters are

Principal, P = 1287

Rate, R= 4%

Time, T = 8

The balance in dollars and cents in Larry's savings account at the end of these 8 years

Balance = P * PRT

This gives

Balance = 1287 + 1287 * 4% * 8

Evaluate

Balance = 1698.84

Hence, the balance in Larry's savings account at the end of these 8 years is 1698 dollars and 84 cents

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Answer:

7

Step-by-step explanation:

subtracting a negative is the same as just adding the number, so five minus negative seven is just five plus seven

Answer:

71.815<701.815

Step-by-step explanation:

Step-by-step explanation:

f(x) = 3x² - 2x + 8 , x = 3

f(3) = 3.3² - 2.3 + 8

= 27 - 6 + 8

= 29

Answer:

81/730

Step-by-step explanation:

The chance of picking a day forecasted to have no rain is 45/365.

There is a 90% chance it actually rains on this day, so the probability is

[tex](45/365)(0.9)=81/730[/tex]

Answer:

the answer is A

that is 828263

Answe

G=1.5

Step-by-step explanation:

Answer:

  see attached

Step-by-step explanation:

You want a Venn diagram that represents the flavor preferences of 135 students.

The diagram you show is a good start. It usually works best to start by filling in the center spot, where all three circles overlap. You have correctly identified the number liking all three flavors as 15.

Working outward, the next step is to fill in the numbers for those who like two flavors. These numbers already include the number who like all three. This means ...

  caramel + vanilla (only) = (caramel + vanilla) (28) - (caramel +vanilla +chocolate (15)

  caramel + vanilla (only) = 28 -15 = 13

Similar computations are done for the other "likes 2 only" spots on the diagram:

  chocolate + caramel (only) = 31 -15 = 16

  chocolate + vanilla (only) = 22 -15 = 7

In like fashion, the numbers for one flavor only need to subtract out the numbers already inside the circle for that flavor.

  chocolate (only) = 63 -16 -15 -7 = 25

Finally, the number of students having no preference is found by subtracting the numbers inside the parts of the circles from the total number of students:

  no preference = 135 -111 = 24

The attachment shows the completed diagram.

Answer:

q = 6

Step-by-step explanation:

|q - 8| = 14

The negatives within an absolute value turn positive so it's really:

q + 8 = 14

q = 6

The x-intercept is 0.4 and the y-intercept is 1.2.

Given that, an amusement park charges $70 for admission before 6 P.M. and $25 for admission after 6 P.M. On Saturday, the park took in a total of $28,000.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let x represent the admissions sold before 6 P.M., and let y represent the admissions sold after 6 P.M.

According to the question, we get the equation as 70x+25y=28,000

The graph of the obtained equation is given below.

The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis.

From the graph, the x-intercept is 0.4 and the y-intercept is 1.2.

Therefore, the x-intercept is 0.4 and the y-intercept is 1.2.

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The required distance is 16.40 km.

This problem can be solved if we know the concept of speed, time and distance.

We know the speed=[tex]\frac{distance}{time}[/tex]

To solve the problem let us assume that the total distance between the workplace and home is x km.

Given that his speed while going from home to work is 45 mph and while returning is 35 mph.

Time for the complete journey is [tex]\frac{5}{6}hr[/tex].

Now according to question;

   [tex]\frac{x}{45}+\frac{x}{35}=\frac{5}{6}[/tex]

⇒[tex]\frac{7x+9x}{315}=\frac{5}{6}[/tex]

⇒[tex]16x=\frac{5*315}{6}[/tex]

⇒ [tex]x=\frac{5*315}{6*16}[/tex]

∴ [tex]x=16.40\ km[/tex]

So, the required distance is 16.40 km.

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Answer: as a decimal 1.6

as a fraction 8/5 hope this helps

Step-by-step explanation:

Answer:

In decimal

[tex] - 2.8[/tex]

As fraction

[tex] \frac{ - 14}{5} [/tex]

And as mixed fraction

[tex] - 2 \frac{4}{5} [/tex]

Step-by-step explanation:

Greetings !

Given expression

[tex]f(x) = \frac{x - 8}{x + 11} [/tex]

Thus, plug in -6 in the variable x and solve

[tex]f( - 6) = \frac{ - 6 - 8}{ - 6 + 11} [/tex]

solve -6-8 = -14

solve -6+11 = 5

[tex] = \frac{ - 14}{5} [/tex]

Apply fraction rule

[tex] \frac{ - a}{b} = - \frac{a}{b} [/tex]

Thus

[tex] = - \frac{14}{5} [/tex]

Convert iimproper fraction to mixed fraction .

[tex] \frac{14}{5} = 2 \: \: remainder \: \: 4[/tex]

[tex]convert \: to \: mixed \: number \\ quotient \frac{remainder}{divisor} [/tex]

whereas

[tex] \frac{14}{5} = 2 \frac{4}{5} [/tex]

[tex] = - 2 \frac{4}{5} [/tex]

Hope it helps !!!

The time that it will take the ball to hit the ground in 4 seconds.

To solve this problem you need the function;

h(t) = -16t² + v₀t + h₀

where;

t = time

v₀ is the initial velocity, which in our case is 0

h₀ is initial height, which in our case is 121 ft

h(t) = 0 since we want to know when the ball will hit the ground.

Thus;

0 = -16t² + 121

And we can solve for t;

If we rearrange the terms we see that this is a difference of 2 squares

0 = 121 - 16t²

0 = (11 - 4t)(11 + 4t)

Setting each factor = 0 gives;

11 - 4t = 0       11 + 4t = 0

t = 11/4       or      t = -11/44

The second solution is discarded as time cannot be negative.

Thus, the ball will hit the ground in 4 seconds.

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Answer:

Se hunde mas rapido en agua salada.

Step-by-step explanation:

None of the options is correct. 813 divided by 13 equals 62.538461, whose approximate value is 62

13 times 813 equals 62.538461.

813/13 produces a non-terminating, repeating decimal as a consequence.

The repeating pattern seen above, 538461, is referred to as repetend and is shown with an overline and vinculum.

Another typical parenthetical remark is this one: 813/13 = 62.(538461): However, it's likely that you may see the reptend marked with an ellipsis in daily use: 813 / 13 = 62.538461… .

Decimal 813 divided by 13 equals 62.538461.

In a fraction, 813 is equal to 813/13.

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Answer: 12 cm^2

Step-by-step explanation:

BC ==> Base of triangle

Divide the triangle in two parts:

BC/2=BC'

6/2=BC'

BC'=3

Distance formula: a^2+b^2=c^2

c^2-a^2=b^2

5^2-3^2=b^2

25-9=b^2

b^2=16

b=4 ==> height of triangle

Area of triangle=A. b=base. h=height

A=1/2 * b * h=

A=1/2 * 6 * 4

A=1/2 * 24

A=12 cm^2

Answer:

$3285.47

Step-by-step explanation:

We know the value decreased by a factor of 2500/28000 after 5 years.

This means the value decreased by a factor of (2500/28000)⅕ per year.

Therefore, after 3 years, the value is

[tex]28000(2500/28000)^{3/5} \approx 3285.47[/tex]

Answer:

8

Step-by-step explanation:

shirts = 10, price per shirt = $9

shirts = 25, price per shirt = $8.40

Linear equation be:

y = mx + b

x = 10 , 25

y = 9 , 8.40

9 = 10m + b  

8.4 = 25m + b

9 = 10 m + b  b = 9 - 10m

8.4 = 25m + b 8.4 = 25m + 9 - 10m

8.4 - 9 = 15m m = -0.6/15 = -0.04

m = - 0.04

b = 9 - 10m = 9 - 10(-0.04) = 9+0.4 = 9.4

b = 9.4

The linear equation =

y = mx + b

y = -0.04x + 9.4

Hope this helped xx ?<3

Answer:

The police will catch the thief in 5 minutes.

Step-by-step explanation:

Distance between thief and police after 2 minutes = 100 m

Implies, thief covers total 100 + 50t m

The police runs with the following patterns 60,65,70...

This is an Arithmetic Progression with a = 60, d = 5 & number of terms = t

t/2 (2 × 60+ (t − 1) ×5)= 50t + 100

t× (120 + 5t −5)= 100t + 200

​(−3+13)÷2= 5

So, the police will catch the thief in 5 minutes.

Answer:

y = 3x - 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 2) and (x₂, y₂ ) = (1, - 4) ← 2 points on the line

m = [tex]\frac{-4-2}{1-3}[/tex] = [tex]\frac{-6}{-2}[/tex] = 3

the line crosses the y- axis at (0, - 7 ) ⇒ c = - 7

y = 3x - 7 ← equation of line

Answer:

0

Step-by-step explanation:

To find the slope of a line, you have to use the slope formula: [tex]\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

So, plug in the numbers: [tex]\frac{-7-(-7)}{-2-1}[/tex]

Simplifying it becomes: [tex]\frac{-7+7}{-2+-1}[/tex]. It then becomes [tex]\frac{0}{-3}[/tex].

Finally, dividing 0 by -3 gets you 0.

Answer: -19

Step-by-step explanation:

n=number

6n+1=-113

6n=-114

n=-19

Answer:

C. & D.

Step-by-step explanation:

I believe it is C & D because, They both are in the same order just switched around, combine like like terms on both sides of the equation then if they are identical then they're equivalent.

Answer:

21.6 miles

Step-by-step explanation:

59-15.5-21.9= 21.6

or

21.6+15.5+21.9= 59