Find the area of the circle with the given radius or diameter. Use pi = 3.14. r = 2

The circumference of a circular rug with a radius of 3 feet is equal to 18.84 feet.

Given the following data:

Mathematically, the circumference of a circle is calculated by using this formula:

Circumference = 2πr

Where:

r is the radius of a circle.

Substituting the given parameters into the formula, we have;

Circumference = 2 × 3.14 × 3

Circumference = 18.84 feet.

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To solve the system of inequalities, we find the values of x that satisfy both conditions: x > 3 and x < -1.

To solve this problem, we need to find the values of x that satisfy the given inequalities:

4x+2 > 14

-21x+1 > 22

For the first inequality, subtracting 2 from both sides gives us:

4x > 12

Dividing both sides by 4, we get:

x > 3

For the second inequality, subtracting 1 from both sides gives us:

-21x > 21

Dividing both sides by -21 (and flipping the inequality sign), we get:

x < -1

Therefore, the values of x that satisfy both inequalities are:

x > 3 and x < -1

Answer:

6 inches.

Step-by-step explanation:

The distance between two cities is around = 600 miles.

Map has a scale of 0.3 inches = 30 miles.

Therefore, on the scale 1 inches = [tex]\frac{30}{0.3}[/tex] miles

                                                      = 100 miles

Since on the map, 100 miles = 1 inches

The distance of 600 miles =  [tex]\frac{600}{100}[/tex]

                                            = 6 inches

The scale distance between cities is 6 inches.

Final answer:

A cone cut with a plane parallel to its base forms a circular cross section, a concept that is part of the study of conic sections.

Explanation:

When a cone is cut with a plane parallel to its base, the cross section or plane section that is created is a circle. This concept falls under the study of conic sections, which also includes other shapes like ellipse, parabola, and hyperbola, all of which are formed by the intersection of a plane with a cone. If the cut is made closer to the apex, the circle will be smaller, and if it's made closer to the base, the circle will be larger, but all such cross sections remain circular as long as the cut is parallel to the base.

Answer:

6.25

Step-by-step explanation:

I go to rsm and this answer worked

The range of sales that will earn at least $40 and at most $50 is represented by the inequalities x >= 40 and x <= 50. Hence, the range of possible sales is x such that 40 <= x <= 50.

The subject of this question is inequalities and the concept of a range of numbers in mathematics. Here, we're looking at a range of sales values that will result in the organizer earning between $40 and $50.

The two inequalities that represent this scenario are: x >= 40 and x <= 50.

To find the range of sales, we look at the values that satisfy both conditions. Therefore, the range of sales is all the sales amounts (x) such that: 40 <= x <= 50. This means that any amount of sales that is greater than or equal to $40 and less than or equal to $50 will meet the criteria.

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Answer:

The height of the liquid in the new cylinder = 4 cm

Step-by-step explanation:

∵ The volume of the liquid = 36π cm³

∵ It poured into a cylinder that has radius 3 cm

∵ The volume of any cylinder = πr²h

∴ The volume of the liquid in the cylinder = π(3)²h = 9πh

- Where h is the height of the liquid inside the cylinder

∴ 9πh = 36π ⇒ divide both sides by π

∴ 9h = 36 ⇒ h = 36/9

∴ h = 4 cm

∴ The height of the liquid in the new cylinder = 4 cm

The height of the liquid in the new cylinder will be 4 cm. The term height is frequently used to describe someone's or something's height.

Height is defined as the vertical distance between an object's top and bottom. It is measured in centimeters, millimeters, meters, and other units.

From the given conditions;

The volume of the liquid is, [tex]\rm V_L=36 \pi \ cm^3[/tex]

The radius of the cylinder is,[tex]\rm r=3 cm[/tex]

The volume of the cylinder is found as;

[tex]\rm V= \pi r^2 h \\\\ \rm V= \pi (3)^2 h \\\\ \rm V=9\pi h[/tex]

The height of the liquid is in the new cylinder is found as;

The volume of cylinder = Volume of liquid

[tex]\rm 9 \pi h= 36 \pi \\\\ \rm h=\frac{36}{9} \\\\ h= 4 \ cm[/tex]

Hence the height of the liquid in the new cylinder will be 4 cm.

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In scientific notation the product is written as  [tex](2.144)\times10^{12}[/tex].

Two scientific notation values are [tex]6.7\times10^6[/tex] and [tex]3.2 \times10^5[/tex].

We have to explain the steps to find the product of these values.

Scientific notation is a widely used floating-point system in which numbers are expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10.

For the product of the above values we multiply coefficients separately like

[tex](6.7\times3.2=21.44)[/tex]

and powers of 10 separately

[tex](10^6\times10^5=10^{11} )[/tex].

So,

[tex]6.7\times10^6 \times 3.2\times10^5=(6.7\times3.2)\times(10^6\times10^5)[/tex].

[tex]6.7\times10^6 \times 3.2\times10^5=(21.44)\times10^{11}[/tex]

Or, in scientific notation form,

[tex]6.7\times10^6 \times 3.2\times10^5=(2.144)\times10^{12}[/tex].

Hence, in scientific notation the product is written as  [tex](2.144)\times10^{12}[/tex].

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Answer:

polynomial x³ -6x² +8x .

Step-by-step explanation:

Given  :  polynomial function in standard form with zeros at 0, 2, and 4.

To find : Which of the following is a polynomial function.

Solution : we have given that

zeros at 0, 2, and 4.

x = 0 .

x = 2

x = 4

(x -0)(x -2) (x -4).

x (x-2)(x-4).

x( x² -4x -2x +8).

x (x² -6x +8).

x³ -6x² +8x .

Therefore, polynomial x³ -6x² +8x .

The probability that the hacker guesses the password on his first try is 0

The password is given as:

Password = 6 digit long

The usable numbers are:

Digits = 0 to 8 i.e. 9 digits

If the digits can be repeated, then the number of passwords is:

Password = 9^6

Evaluate the exponent

Password = 531441

The probability that the hacker guesses the password on his first try is

P = 1/531441

Evaluate

P = 0.00000188167

Approximate

P = 0.0000

Hence, the probability that the hacker guesses the password on his first try is 0

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The probability of guessing the password on the first try is 0.000001881.

To calculate the probability of guessing the password on the first try, we need to determine the number of possible passwords and divide it by the total number of possible guesses. In this case, the password is 6 digits long and each digit can be a number between 0 and 8.

So, there are 9 possible digits for each of the 6 positions, giving us a total of 9^6 = 531441 possible passwords.

The hacker makes random guesses, so there are 9^6 = 531441 possible guesses they can make.

The probability of guessing the password on the first try is therefore 1/531441 = 0.000001881, rounded to four decimal places.

Final answer:

After reflecting the origin (0,0) first across the line y=2, and then across the line x=-3, the final image of the point is at (-6,4).

Explanation:

The reflection of a point in the Cartesian coordinate system can be found using certain rules, depending on the line of reflection.

For the first reflection across L1: y = 2, imagine that every point has to move in a perpendicular motion to this line until it is on the opposite side but the same distance from L1.

The origin (0,0) will move up to (0,4) because it is 2 units away from y=2 and needs to move another 2 units up to be an equal distance on the opposite side of the line.

Next, for the reflection across L2: x = -3, use the same principle, but horizontally.

The point (0,4) is 3 units away from the line x=-3.

Reflecting over this line, you would move (0,4) to the left by 6 units (twice the distance from the line), giving us a final position of (-6,4).

The final position of the point O (0,0) after the two reflections is (-6,4).

Answer:

Te correct option B.

Step-by-step explanation:

The surface area of a cone is

[tex]A=\pi r(r+l)[/tex]

Where, r is the radius and l is slant height.

From the given figure it is noticed that the radius of the cone is 6 and slant height is 15.

The surface area of cone is

[tex]A=\pi \times 6\times (6+15)[/tex]

[tex]A=\pi \times 6\times 21[/tex]

[tex]A=126\pi[/tex]

The area of the cone is 126π units². Therefore option B is correct.

The probability of drawing a red, blue, and a candy that is not yellow from the bag is 1/3, 4/9, and 7/9 respectively.

The question involves the concept of probability in mathematics, with a scenario of drawing candies from a bag. The total number of candies in the bag is 45 (15 red + 20 blue + 10 yellow).

The probability of drawing a red candy is the number of red candies divided by the total number of candies, which is 15/45 or 1/3.

The probability of drawing a blue candy is the number of blue candies divided by the total number of candies, which is 20/45 or 4/9.

If we want to find the probability of drawing something other than a yellow candy, this is essentially the sum of the probabilities of drawing a red or blue candy. This is 35 out of 45 (15 red candies + 20 blue candies), which reduces to 7/9.

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