What is the exact volume of the cylinder?



Enter your answer, in terms of π , in the box.

Step 1: Convert [tex]\frac{5\pi }{12}[/tex], which is in radians into degrees. To convert it multiply by [tex]\frac{180}{\pi }[/tex]

[tex]\frac{5\pi }{12} =\frac{180}{\pi }[/tex]

900/12

75

Step 2: 75 degrees isn't on the unit circle but 45 degrees and 30 degrees is. Since 45 + 30 = 75 you can use the cosine of 45 and 30 to find the exact value

cos45 = [tex]\frac{\sqrt{2} }{2}[/tex]

cos30 =[tex]\frac{\sqrt{3} }{2}[/tex]

Step 3: Add the cos45 and cos30 to get cos5pi/12

[tex]\frac{\sqrt{2} }{2} +\frac{\sqrt{3} }{2} = \frac{\sqrt{2}+\sqrt{3}}{2}[/tex]

Hope this helped!

Answer:

C. 48,5 cm²

Step-by-step explanation:

The area is 8×4 + 3×3 + 5×3/2 = 32+9+15/2 = 41+7,5 = 48,5 cm²

Answer: It can not be a mixed number because if you divide -27 by 50 you get -0.54, so then if you turn -0.54 in fraction form it would be -27/50, so the fraction would stay the way it is. -27/50 is not an improper fraction. To be improper, the numerator must be greater than the denominator!

* Hopefully this helps:) Mark me the brainliest:)!!!

James will have $32,270.13 after 6 years

Answer:

[tex]y=20000(1.083)^6[/tex]

Step-by-step explanation:

Let y represents the amount James have after 6 years,

Given,

Principal amount, P = $ 20,000,

Compound rate of interest per year, r = 8.3 %,

Thus, the amount after x years would be,

[tex]A=P(1+\frac{r}{100})^x[/tex]

[tex]=20,000(1+\frac{8.3}{100})^x[/tex]

[tex]=20000(1.083)^x[/tex]

Therefore, the amount after 6 years would be,

[tex]y=20000(1.083)^6[/tex]

Which is the correct equation that represents the amount, James will have after 6 years.

ANSWER

a. 16

b. 1

c. 64

d. 64

EXPLANATION

We want to simplify the following exponential expressions

a.

[tex] {2}^{4} [/tex]

This implies that

[tex] {2}^{4} = 2 \times 2 \times 2 \times 2[/tex]

[tex] {2}^{4} = 16[/tex]

b. Any non-zero number exponent zero is 1.

This implies that,

[tex] {3}^{0} = 1[/tex]

c. The given exponentiial expression is,

[tex] {4}^{6} \times {4}^{ - 3} [/tex]

The bases are the same so we add the exponents.

[tex] {4}^{6} \times {4}^{ - 3} = {4}^{6 + - 3} [/tex]

This simplifies to,

[tex]{4}^{6} \times {4}^{ - 3} = {4}^{3} [/tex]

[tex]{4}^{6} \times {4}^{ - 3} = 4 \times 4 \times 4 = 64[/tex]

d. We want to simplify:

[tex] { ({2}^{3}) }^{2} [/tex]

This is the same as

[tex]{ ({2}^{3}) }{ ({2}^{3}) }[/tex]

We add the exponents now to get:

[tex]{2}^{3 + 3} = {2}^{6} = 64[/tex]

Answer:

13/6

Step-by-step explanation:

-6 1/3 + 5 5/6

1. You can reduce the first equation to 2

-6 1/3, becomes -2 x 1/1. This is because 3 goes into itself 1 time, and it goes into 6, -2 times. Your new equation: -2 + 5 5/6

2. Multiply the 5's in 5 5/6 by each other to get...

25/6

Your new equation: -2 + 25/6

3. Multiply 6 by -2 to get -12

4. Now add the numerators(remember -12 is basically, -12/1) together to get your answers

-12 + 25/6 = 13/6

Hello There!

If we add -6 1/3 and 5 5/6 together, we will get a sum of -1/2

STEP 1 First, I like to convert mixed numbers into improper fractions because they are easier to work with. So, I would change -6 1/3 to -19/3. Then, I would change 5 and 5/6 to 35/6.

STEP 2 Applying the fraction formula for addition. (-19x6) + (35x3) and then i would put this over 6x3

STEP 3   -114+105

                      18

STEP 4

-9/18 = -1/2

Answer:

You had it correctly chosen, (9, infinity)

Step-by-step explanation:

Good job =)

ANSWER

[9,∞)

EXPLANATION

The given radical function is ;

[tex]f(x) = \sqrt{x - 9} [/tex]

This function is defined if and only if the expression under the radical sign is greater than or equal to zero.

[tex]x - 9 \geqslant 0[/tex]

[tex]x \geqslant 9[/tex]

Or

In interval notation, we have

[9,∞)

Answer:

25.5%

Step-by-step explanation:

% error = | estimate - actual | / actual × 100%

% error = | 59 - 47 | / 47 × 100%

% error ≈ 25.5%

Answer:

20.3%

Step-by-step explanation:

The formula for percent error is the experimental value minus the theoretical value divided by the theoretical value all times 100.

Experimental - Theoretical

------------------------------------------ x 100

         Theoretical

−12

------- ×100

59

=−0.20339×100

=−20.339

=20.339%

=20.3% error

Answer: 3/5=0.60

Step-by-step explanation:

The p(a/b) is 3/5 = 0.6

The Bayes theorem predicts the likelihood that an event connected to any condition would occur. Use the concept of the conditional probability formula, P(Ei|A)=P(Ei∩A)P(A), to demonstrate the Bayes theorem (A). The Bayes' Theorem describes the likelihood that an event connected to any condition would occur.

Given

P(a) = P(student in karate ) = 3

P(b) =P(student in chess) = 5

P(a|b) = 3/5 = 0.60

To know more about Bayes theorem refer to :

https://brainly.com/question/14989160

#SPJ2

Answer:

Shravan's age is 40 years old

Gaurav’s age is 30 years old

Step-by-step explanation:

Let

x-----> Shravan's age

y-----> Gaurav’s age

we know that

x=y+10 -----> equation A

(1/7)(x-5)=(1/5)(y-5) ----> equation B

substitute equation A in equation B and solve for y

(1/7)(y+10-5)=(1/5)(y-5)

(1/7)(y+5)=(1/5)(y-5)

5(y+5)=7(y-5)

5y+25=7y-35

7y-5y=25+35

2y=60

y=30 years

Find the value of x

x=y+10  ----> x=30+10=40 years

therefore

Shravan's age is 40 years old

Gaurav’s age is 30 years old

Answer:

24649-17424=7225 UNITS

Step-by-step explanation:

This step implies that Lara was using the Pythagoras theorem to find the missing length of the right triangle.

a²+b²=c², taking a and b to be the  two lengths adjoined by the right angle and c the hypotenuse.

Laura's step represents the step above.

157²=24649

132²=17424

157²-132²=c²

24649-17424=7225

Answer:

$0.75 tax

Step-by-step explanation:

1. Find total cost of meal: $10.50 + $1.50 + $0.50 = $12.50

2. Find tax of meal: $12.50 * 6% = 12.5 * 0.06 = $0.75

Answer: x÷(2÷5y)

Step-by-step explanation: this is because you have to first do the quotient of 2 and try then the answer will be divided by 5

Answer:

The quotient of x and the quotient of 2 and 5y.

Expression:

x/(2/5y)

Explanation:

The quotient means to divide the numbers. The “and” after quotient is what the number is dividing with. So, x us dividing with the division of 2 and 5y.

Answer:

2 2/5

Step-by-step explanation:

-1 3/5 ÷ -2/3

Change the mixed number to an improper fraction

-1 3/5 =  - (5*1 +3)/5 = -8/5

-8/5÷-2/3

Copy dot flip

-8/5 * -3/2

24/10

Divide top and bottom by 2

12/5

Change to a mixed number

12/5 = 2 2/5

The conjugate of the complex number 2 - 8i is 2 + 8i, found by changing the sign of the imaginary part from negative to positive.

The conjugate of a complex number is found by changing the sign of the imaginary part.

For a complex number with a real part of 2 and an imaginary part of -8i, the complex number is represented as 2 - 8i. To find its conjugate, we change the sign of the imaginary part, resulting in 2 + 8i.

The general form of a complex number is a + bi, where a is the real part and bi is the imaginary part.

The conjugate is then written as a - bi. Therefore, if we have the complex number z = 2 - 8i, the conjugate, denoted as [tex]\( \overline{z} \)[/tex], is 2 + 8i.

The complement of A would be the elements in U that are not in A.

A is 2, 4, 6, 8

Remove those numbers from U for the complement.

The complement would be {1, 3, 5, 7, 9, 10}

Answer: The complement is 1, 3, 5, 7, 9, 10

I hope that this helps! :3

Answer:

The answer B

Step-by-step explanation:

Answer: The graph is attached.

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.

You can solve for "y":

[tex]2y<5x-10\\\\y<\frac{5}{2}x-\frac{10}{2}\\\\y<\frac{5}{2}x-5[/tex]

You need to rewrite the expression:

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

You can identify that the slope of this line is:

[tex]m=\frac{5}{2}[/tex]

And the y-intercept is:

[tex]b=-5[/tex]

Substitute [tex]y=0[/tex] and solve for "x" to know the x-intercept:

[tex]0=\frac{5}{2}x-5\\\\5*2=5x\\\\x=2[/tex]

Now you know that the line passes through the points (0,-5) and (2,0).

Since the inequality is "<", you know that the line must be dashed and the shaded region must be below the line [tex]y=\frac{5}{2}x-5[/tex].

Knowing this, you can graph it (Observe the graph attached)

Answer:

A)

15 hours

B)

108 hours

C)

2074.29 miles

Step-by-step explanation:

Under the assumption the earth is a perfect circle, then in one complete rotation about its axis ( 24 hours) the Earth will cover 360 degrees or 2π radians.

A)

In every 24 hours the earth rotates through 360 degrees ( a complete rotation). We are required to determine the length of time it will take the Earth to rotate through 225 degrees. Let x be the duration it takes the earth to rotate through 225 degrees, then the following proportions hold;

(24/360) = (x/225)

solving for x;

x = (24/360) * 225 = 15 hours

B)

In 24 hours the earth rotates through an angle of 2π radians (a complete rotation) . We are required to determine the length of time it will take the Earth to rotate through 9π radians. Let x be the duration it takes the earth to rotate through 9π radians, then the following proportions hold;

(24/2π radians) = (x/9π radians)

Solving for x;

x = (24/2π radians)*9π radians = 108 hours

C)

If the diameter of the earth is 7920 miles, then in a day or 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle;

circumference = 2*π*R = π*D

                         = 7920*3.142

                         = 24891.43 miles

Therefore a point on the equator covers a distance of 24891.43 miles in 24 hours. This will imply that the speed of the earth is approximately;

(24891.43miles)/(24 hours) = 1037.14 miles/hr

The distance covered by the point in 2 hours will thus be;

1037.14 * 2 = 2074.29 miles

Answer:

-13 < 16

Step-by-step explanation:

(4 is x, -5 is y)

-5 - 8 < 4(4)

-13 < 16

It is true and is a solution

Answer:

The ordered pair is not a solution to the inequality because -13 < -16 is false.

Step-by-step explanation:

Step 1: Plug x and y into the inequality

-5 - 8 < -4(4)

Step 2: Simplify the inequality

-13 < -16

Step 3: Interpret and conclude

The ordered pair is not a solution to the inequality because -13 < -16 is false.

ANSWER

B. 10

EXPLANATION

We need to find the value of x first.

It was given that the perimeter of triangle XYZ is 24.

This means that:

XY+YZ+XZ=24

we substitute the expression in terms of x to get;

[tex](5x - 1) + (13 - x) = 24[/tex]

This implies that

[tex]5x - x = 24 - 13 + 1[/tex]

[tex]4x = 12[/tex]

Divide both sides by 4 to get;

[tex]x = 3[/tex]

|WY|=|ZX|=13-3=10

Answer:

WY = 10 units

Step-by-step explanation:

From the figure we can see a rectangle WXYZ.

Diagonals of rectangle are equal.

It is given that, Perimeter of triangle XYZ = 24

XY + YZ = 5x - 1 and XZ = 13 - x

To find the value of x

Perimeter of ΔXYZ = XY + YZ + XZ

24 = 5x - 1 + 13 - x

4x + 12 = 24

4x = 12

x = 12/4 = 3

x = 3

To find the value of WY

We have WY = XZ

XZ = 13 - x

 = 13 - 3 = 10

Therefore WY = XZ = 10 units

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Answer:

Step-by-step explanation:

the zeroes of a function basically mean when y = 0, so basically the x-intercept(s)

in this case, the zeroes are 3 and 6

Answer:

A. x = 3 and x = 6

Step-by-step explanation:

Zeros occur when the function crosses the x - axis. In this case, the quadratic function crosses the function when x = 3 and x = 6.

Answer: Option b

b. x greater or equal than 1.8

Step-by-step explanation:

In this problem we have the following inequality:

[tex]2x\leq 3(x-0.6)[/tex]

To solve it we must group the x on one side and the constants on the other side

[tex]2x\leq 3(x-0.6)[/tex]

Apply distributive property on the right side of the inequality

[tex]2x\leq 3x-3*0.6[/tex]

[tex]2x\leq 3x-1.8[/tex]

Subtract 3x on both sides of the inequality

[tex]2x-3x\leq 3x-3x-1.8[/tex]

[tex]-x\leq-1.8[/tex]

Multiply by -1 both sides of the inequality

[tex]x\geq 1.8[/tex]

The answer is the option b

Answer:

the answer is option B

Step-by-step explanation:

Hello There!

The value of the number "5" in the number 15,406 would be the value of 5,000

This result represents the total area under the curve y = x^2 + 4 between x = -3 and x = 2.

The area under the curve y = x^2 + 4 on the interval [-3,2] can be found using definite integration. The definite integral of a function gives us the net area between the function and the x-axis across the specified interval. To compute the area, we set up the integral from -3 to 2 of the function x^2 + 4.

To solve this, we integrate the function with respect to x:

This result represents the total area under the curve y = x^2 + 4 between x = -3 and x = 2.

Answer:

Kristen would be 7.5 yo and Nicole would be 24.5 years old

Step-by-step explanation:

let x= kristen's age

3x+2= nicole's age

(3x+2)+x=32

4x+2=32

4x=30

x=7.5

3(7.5)+2= 24.5

Answer:

y = - 3x + 16

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 )

y = [tex]\frac{1}{3}[/tex] x + 8 ← is in slope- intercept form

with slope m = [tex]\frac{1}{3}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3, so

y = - 3x + c ← is the partial equation of the perpendicular line

To find c substitute (6, - 2) into the partial equation

- 2 = - 18 + c ⇒ c = - 2 + 18 = 16

y = - 3x + 16 ← equation of perpendicular line

Answer:

[tex](x-3)^{2} +(y+2)^{2}=9[/tex]

Step-by-step explanation:

we know that

the equation of a circle into center radius form is equal to

[tex](x-h)^{2} +(y-k)^{2}=r^{2}[/tex]

In this problem we have

center ( 3,-2)

radius r=3 units

substitute

[tex](x-3)^{2} +(y+2)^{2}=3^{2}[/tex]

[tex](x-3)^{2} +(y+2)^{2}=9[/tex]

Answer: A on edg

Step-by-step explanation:

For this case we must find an expression equivalent to:

[tex](x ^ {\frac{1}{4}} * y ^ {16}) ^ {\frac {1} {2}}[/tex]

By definition of power properties we have to:

[tex](a ^ n) ^ m = a ^ {n * m}[/tex]

Then, rewriting the expression:

[tex](x ^ {\frac {1 * 1} {4 * 2}} * y ^ {\frac {16 * 1} {2}}) =\\x ^ {\frac {1} {8}} * y ^ {\frac {16} {2}}) =\\x ^ {\frac {1} {8}} * y ^ {8}[/tex]

Answer:

Option B