What are the steps in order to figure out this answer?

The integral to calculate the volume of the solid generated by revolving the region R about the y-axis is: ∫π/2 0 (π/2) (3 - \(y^2\)) dy

∫π/2 0 (π/2) (3 - \(y^2\)) dy

1. The region R is bounded in the first quadrant, so the integral limits are from 0 to π/2.

2. The integrand is the area of the cross-section of the solid generated by revolving the region R about the y-axis. The area of this cross-section is the difference between the outer radius (x=√3) and the inner radius (x2+y2=3). Therefore, the integrand is 3 - y^2.

3. The integral to calculate the volume of the solid generated by revolving the region R about the y-axis is: ∫π/2 0 (π/2) (3 - \(y^2\)) dy

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Answer:

W = 8cm

L = 19cm

Step-by-step explanation:

The first step to solving these problems is always writing the information that is given into 2 equations.

Piece of info #1: Length is 5cm less than 3 times the width

Piece of info #2: Perimeter (of the rectangle, which has 4 sides) is 54cm

Turing these into equations...

Equation 1) L = 3*W - 5

Equation 2a) L+L+W+W = 54

Let's simplify that second equation:

Equation 2b) 2L+2W = 54

Now, we just solve the system of two equations by substitution. Take the known value of L from equation 1 and substitute it in for the value of L in equation 2b:

2*(3*W-5)+2W = 54

Now we solve for W:

6W - 10 + 2W = 54

8W - 10 = 54

8W = 64

W = 64/8

W = 8 cm

Now that we know W, we can substitute its value into either equation 1 or equation 2 to find L. Here, I'll randomly choose equation 1.

Equation 1) L = 3*W - 5

L = 3*8 - 5

L = 24-5

L = 19 cm

To calculate your bi-weekly paycheck, follow these steps:

Step 1: Calculate the gross earnings:

Multiply the number of hours worked per week by the hourly rate.

20 hours/week * $9.00/hour = $180.00/week

Step 2: Calculate the total earnings for two weeks:

Multiply the weekly earnings by the number of weeks in a bi-weekly pay period.

$180.00/week * 2 weeks = $360.00

Step 3: Calculate the deductions:

Calculate each deduction separately and subtract them from the gross earnings.

Federal Income Tax: $360.00 * 11.9% = $42.84

State Income Tax: $360.00 * 3.6% = $12.96

F.I.C.A: $360.00 * 7.65% = $27.54

Professional Dues: Amount varies depending on the specific dues.

Total Deductions: $42.84 + $12.96 + $27.54 + Professional Dues

Step 4: Calculate the net earnings:

Subtract the total deductions from the gross earnings.

Net Earnings = Gross Earnings - Total Deductions

Once you have the net earnings, you can determine if it is sufficient to cover your monthly car insurance bill of $200. If your bi-weekly net earnings are greater than or equal to $200, you will be able to pay your car insurance bill.

It is important to note that these calculations are based on the information provided, and actual tax rates and deductions may vary depending on your specific circumstances and location.

Additionally, professional dues may differ depending on your profession. It is recommended to consult with a tax professional or payroll department for precise calculations.

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Answer:

(-∞, -4)

Step-by-step explanation:

11x > 4(1+3x)

11x > 4*1+4*3x  ==> distribute 4 to 1 and 3x using the distribution property

11x > 4 + 12x  ==> simplify

11x-12x > 4 + 12x-12x  ==> isolate x by subtracting 12x on both sides

-x > 4

x < -4  ==> when dividing by a negative number, switch the inequality sign

x < -4 can also be written as -∞ < x < -4

This is because x is greater than -∞ but can never equal -∞.

-∞ < x < -4 ==> (-∞, -4)

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Answer:

Step-by-step explanation:

L = 3W

Perimeter = 2L + 2W = 2(3W) + 2W = 8W

8W = 65.6 cm

W = 8.2 cm

Therefore , the solution of the given problem of function comes out to be f[g(x)] = 3x² - 2 is the formula for the function f[g(x)].

The mathematics programme covers a wide range of topics, including mathematics, numbers, but also their subsets, along with building, construction, and the both real and fictional geographic locations. A work covers the connections between different variable elements that all work together to produce the same result. A utility is made up of several distinctive components that, when combined, produce specific results for each input.

Here,

We must first assess g(x) in order to determine f[g(x)], and then we can use the outcome to determine f[g(x)].

=> g(x) = x² + 1

When we substitute g(x) for f(x), we obtain:

=> f[g(x)] = f(x² + 1)

=> 3(x² + 1) - 5 = 3x² + 3 - 5

=> 3x² - 2

Therefore, f[g(x)] = 3x² - 2 is the formula for the function f[g(x)].

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Classifying the polynomial 5x³ + 4x − 2 by degree gives a degree of

An equation made up of variables, exponents, and coefficients along with operations and the equal sign is known as a polynomial equation.

Sums of terms of the form kxⁿ, where k is any number and n is a positive integer, make up polynomials.

The degree refers to the highest exponents which is a positive integer

examining the function the degree is 3 and referred to as cubic

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Subtracting decimals, just like adding decimals, is similar to subtracting whole numbers. Just like adding decimals, the only difference is that we line up according to the decimal point instead of the last digit

One type of number that has a whole number and a fractional component separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.

Comparable to subtracting whole numbers is the operation of adding and subtracting decimals. The only difference between adding decimals and doing so is that we line up according to the decimal point rather than the last digit.

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The scale ratio is therefore 1:5 miles per inch

The connection between distances on the map and their equivalent distances on the ground is expressed by the scale ratio. Here, one inch on the chart corresponds to five miles on the Earth. We must represent this connection as a fraction using the same units in order to calculate the scale ratio:

5 miles per inch.

By reducing both the numerator and denominator by one inch, we may simplify the following fraction:

1/5 of a mile per inch

The scale ratio is therefore 1:5 miles per inch. This implies that the comparable distance on the ground is 5 units long for every 1 unit of distance indicated on the map (1 inch) (5 miles).

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Answer:

11/20

Step-by-step explanation:

the probability for all = 7+4+9 = 20

the probability that the golf ball is not a type A ball = the probability of type B + the probability of type C

= 7/20 + 4/20

= 11/20

The probability that the selected member is 21 or more is 88%.

The probability that the selected member is 55 or less is 86%.

The probability that the selected member is not in the 21 to 35 age group is 58%.

The basic probability formula of dividing the number of favorable outcomes by the total number of outcomes.

In this case, we are given the percentage of members in each age group, and we need to find the probability of selecting a member with a certain age range.

Here we have

The table shows the age distribution of members of a gym.  

Age -            Under 21      21 -35     36 - 55   Over 55

percentage       12                42            32          14  

a) To find the probability that the selected member is 21 or more,

Add the percentage of members who are 21-35, 36-55, and over 55 since all of these age groups are 21 or more.

Probability (21 or more)

= Percentage (21-35) + Percentage (36-55) + Percentage (Over 55)

= 42% + 32% + 14%

= 88%

b) To find the probability that the selected member is 55 or less,  

Add the percentage of members who are under 21, 21-35, and 36-55 since all of these age groups are 55 or less.

Probability (55 or less)

= Percentage (Under 21) + Percentage (21-35) + Percentage (36-55)

= 12% + 42% + 32%

= 86%

c) To find the probability that the selected member is not in the 21 to 35 age group,

Add the percentage of members who are under 21, 36-55, and over 55 since all of these age groups are not in the 21 to 35 age group.

Probability (not in the 21 to 35 age group)

= Percentage (Under 21) + Percentage (36-55) + Percentage (Over 55)

= 12% + 32% + 14%

= 58%

Therefore,

The probability that the selected member is 21 or more is 88%.

The probability that the selected member is 55 or less is 86%.

The probability that the selected member is not in the 21 to 35 age group is 58%.

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Answer:

3 Customers named vanilla

Step-by-step explanation:

Multiply 25 by the percentage of people who said vanilla

Read the question carefully to make sure it says vanilla. Mine said cookies and cream which represents the answer above.

Answer:

  x = 36

Step-by-step explanation:

Given a tangent segment of length 24, and a secant segment from the same point with an external length of 12 and a total length of (12+x), you want to find the value of x.

The product of lengths from the common point to the two intersections with the circle are the same for both segments. In the case of the tangent, the two intersections with the circle are the same point, so the square of the length is used.

  24² = 12(12 +x)

  2·24 = 12 +x . . . . . . . divide by 12

  36 = x . . . . . . . . . subtract 12

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The equation of the circle with center (0, 5) and a point on the circle (2, 4) is x² + (y - 5)² = 5

In geometry, a circle is a closed two-dimensional shape that is formed by a set of points that are equidistant from a fixed point called the center. The distance between any point on the circle and the center is called the radius.

The equation of a circle with center (h, k) and radius r is given by:

 r²=(x - h)² + (y - k)²  

In this case, the center of the circle is (0, 5) and a point on the circle is (2, 4). The radius of a circle, which is the separation between its centre and any point on the surface, may be calculated using the following formula:

r = √((2 - 0)² + (4 - 5)²) = √(5)

Now we can substitute the values of the center and the radius into the equation of the circle:

(x - 0)² + (y - 5)² = (√(5))²

Simplifying, we get:

x²+ (y - 5)² = 5

As a result, the circle's equation with its centre (0, 5) and a point on it (2, 4) is:

x² + (y - 5)² = 5

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The minimum number of trips the bus will have to make to accommodate everyone is 5.

To find the minimum number of trips the bus needs to make, we divide the total number of people by the capacity of the bus.

1. Divide the total number of people (330) by the capacity of the bus (68):

  330 / 68 = 4.85 (rounded to the nearest whole number)

2. The result is approximately 4.85, which means that 4 trips will not be enough to accommodate everyone.

3. Since we can't have a fraction of a trip, we need to round up to the nearest whole number to ensure that everyone is accommodated.

4. Therefore, the minimum number of trips the bus will have to make is 5, as it will require 5 full trips to transport all 330 people.

It's important to note that on the fifth trip, the bus will not be completely full, as only 10 people will be left to transport. However, this is the minimum number of trips needed to ensure that everyone can go sight-seeing on the bus.

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answer would most likely be C

you take 2pi and divide it by bits stolen from the equation its explained more in the screennshot

Given:

Total money Ravi has to begin with = 119 dollars.

He spent b dollars.

The number of dollars he has left is:

119 - b

Answer:

495

Step-by-step explanation:

using the definition

n\(C_{r}\) = \(\frac{n!}{r!(n-r)!}\)

where n! = n(n - 1)(n - 2) ... × 3 × 2 × 1

then

12\(C_{4}\)

= \(\frac{12!}{4!(12-4)!}\)

= \(\frac{12!}{4!(8!)}\)

cancel 8! on numerator/ denominator

= \(\frac{12(11)(10)(9)}{4!}\)

= \(\frac{11880}{4(3)(2)(1)}\)

= \(\frac{11880}{24}\)

= 495

Answer:

b is increased by 17% : A and E

b is decreased by 17%: H and J

Step-by-step explanation: took the test

The inequalities which satisfy the number line shown is x>2 and x>=2.

We are given that;

The number line showing inequality

Now,

x>2 satisfies the equation by the given number line

x>=2 satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

x<=-3 does not satisfies the equation by the given number line

Therefore, by the number line the answer will be x>2 and x>=2 .

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Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Hello!

\(\large\boxed{(4, -150)}\)

We can solve for the vertex by completing the square. Begin by factoring out 6 from the equation to simplify the process:

6(x² - 8x) - 54 = 0

To complete the square, we must look at the first two terms (x² - 8x).

Remember that squaring a binomial uses the format a² + 2ab + b². We are already given a² and 2ab², so solve for b:

-8 / 2 = -4. This is the value of b.

We can rewrite this as:

(x - 4)²

However, this produces +16 which much be taken into account. Substitute (x - 4)² into the original equation:

6(x - 4)² - 54 = 0

Multiply 16 by the term in the front and subtract to cancel out this term:

6(x - 4)² - 54 - (6 · 16) = 0

Simplify:

6(x - 4)² - 150 = 0

In this form, the vertex is given as:

a(x - h)² + k, where h = x-coordinate and k = y-coordinate of the vertex.

In this instance, h = 4 and k = -150, so the coordinates of the vertex are:

(4, -150)

Answer:

y = 6x²-48x-54 has a vertex at (4,-150)

Step-by-step explanation:

There is no vertex. The solution set to 6x²-48x-54 = 0 is two points, (-1,0) and (9,0).

If you mean y = 6x²-48x-54, that is an up-opening parabola.

Put the equation into vertex form:

y = 6x²-48x-54

 = 6(x²-8x)-54

 = 6(x²-8x+4²)-6·4²-54

 = 6(x-4)² - 150

vertex at (4,-150)

Answer:

A.  22.5

Step-by-step explanation:

you can break. it into two smaller shapes first

Then you find the area of each and add.

The small one: 3x1.5= 4.5

The large one: 6x3= 18

18+4.5=22.5

Answer:

22.5

Step-by-step explanation:

It helps to break up each shape of a composite figure. For this shape break it up into two rectangles and then add them together.

3 · 1.5 = 4.5 (smaller rectangle)

6 · 3 = 18 (larger rectangle)

4.5 + 18 = 22.5

I hope this helps!!!

The equation of the line in fully simplified slope-intercept form is y = x + 7.

We have,

From the graph,

The coordinates of the line are:

(0, 7), (-7, 0), and (-2, 5).

We can use any coordinates the line touches on the graph.

We will use,

(0, 7) and (-7, 0)

The equation can be written in the form y = mx + c

m = (0 - 7) / (-7 - 0)

m = -7/-7

m = 1 ______(1)

And,

(0, 7) = (x, y)

So,

y = mx + c ______(2)

7 = 1 x 0 + c

7 = c

c = 7 ______(3)

Now,

From (1), (2), and (3).

y = x + 7

Thus,

The equation of the line in fully simplified slope-intercept form is y = x + 7.

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Answer:

y=5x+19

Step-by-step explanation:

y+1=-5(x+4)

y+1=-5x-20

Subtract 1 (like terms)

y=-5x-21

Answer:

it's called the difference quotient of a function

Step-by-step explanation:

f(x+h)-f(x)/h is the slope of the secant line of a function