Find the exact circumference of the circle.

Options:
10π cm
11π cm
12π cm
​

Answer: First, we need to find the coordinates of points P and Q. Since both P and Q lie on the line 3x + 4y + 15 = 0 and are equidistant from the origin, we can set up two equations:

3x + 4y + 15 = 0 (equation of the line)

x^2 + y^2 = 5^2 (equation of the circle with radius 5)

Solving these two equations simultaneously, we get:

x = -3, -12/5

y = -4, 3/5

Since P and Q lie on the same line, we can find the midpoint of PQ as:

(((-3) + (-12/5))/2, ((-4) + (3/5))/2) = (-33/10, -37/10)

Let O be the origin. Then the length of PO is the distance between O and P, which is:

sqrt((-3 - 0)^2 + (-4 - 0)^2) = 5

Similarly, the length of QO is also 5. Thus, we have a right triangle POQ with hypotenuse of length 5 and legs of length 5. Therefore, the area of triangle POQ is:

(1/2) * base * height

= (1/2) * 5 * 5

= 12.5 square units.

Step-by-step explanation:

The area of triangle POQ is approximately 17.32 square units.

We will apply  the formula for the distance between a point and a line to find their coordinates.

The formula for the distance between a point (x0, y0) and a line Ax + By + C = 0 is:

d = |Ax0 + By0 + C| / √t(A^2 + B^2)

Here we have, A = 3, B = 4, and C = 15.

5 = |3x0 + 4y0 + 15| / sqrt(3^2 + 4^2)

Solving for |3x0 + 4y0 + 15|, we get:

|3x0 + 4y0 + 15| = 5 * sqrt(3^2 + 4^2) = 25

This gives us two equations, solving these equations simultaneously, we get two points:

3x0 + 4y0 + 15 = 25

3x0 + 4y0 + 15 = -25

P = (-5, 0)

Q = (5, 0)

PO = √((-5 - 0)^2 + (0 - 0)^2) = 5

QO = √((5 - 0)^2 + (0 - 0)^2) = 5

PQ = √((5 - (-5))^2 + (0 - 0)^2) = 10

Using Heron's formula to find the area of triangle POQ:

s = (5 + 5 + 10) / 2 = 10

Area = √ (s(s-5)(s-5)(s-10)) = √(300)

=17.32

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Based on the information in the table, the statement that is true is: The farther a planet is from the Sun, the slower it moves on its orbital path. Therefore the correct option is option B.

This is implied by the fact that as a planet gets further from the Sun, its orbital period, or the amount of time it takes to complete an orbit around the Sun, lengthens.

A planet's orbital radius increases with distance from the Sun and takes longer to complete. When a planet is farther from the Sun, it travels a greater distance in one orbit, hence its orbital speed must be slower to account for this greater distance. Therefore the correct option is option B.

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Given

(x - 2)² = - 16 ( take the square root of both sides )

x - 2 = ± [tex]\sqrt{-16}[/tex] = ± [tex]\sqrt{16(-1)}[/tex] = ± 4i ( add 2 to both sides )

x = 2 ± 4i

Thus

x = 2 + 4i → (d)

x = 2 - 4i → (g)

Answer:

the distance from the foot of the building to the car is approximately 25.98 meters.

Answer: 1/5

Step-by-step explanation:

The probability that a trip will be to either Nassau or Paris is 0.2 or 20%.

Given, a travel agency is giving away a free trip as part of a grand opening.

The trip will be to one of the ten locations listed. The 10 locations are London, Paris, Rome, Sydney, Athens, Nassau, Hong Kong, Madrid, Tokyo, and Rio De Janeiro.

To find the probability, we need to find how many outcomes are favorable to the event "the trip is to Nassau or Paris" and divide by the total number of possible outcomes.

So, favorable outcomes = 2 (Nassau, Paris)

Total possible outcomes = 10

Probability = (Favorable outcomes)/(Total possible outcomes)= 2/10= 0.2 or 20%.

Therefore, the probability that a trip will be to either Nassau or Paris is 0.2 or 20%.

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Answer:

To find the area of the rectangle, you would do length times width, so it would be (4+√3)(2-√3)

Then the area would be 5.732050808 which would round up to 5.73.

To find the perimeter you would do P=2(l+w), so you would have 2(4+√3)(2-√3)

Then you would get 11.46, which you would round up to 11.5.

All in all:

Area = 5.73

Perimeter = 11.5

Step-by-step explanation:

Therefore , the solution of the given problem of fraction comes out to be 1600 grams of 30% sulfuric acid were created using 1200 grams of 20% sulfuric acid and 400 grams of 60% sulfuric acid.

Any arrangement of components of the same size can be used to depict the whole. Quantity is referred to as "a portion" in a specific measure in Standard English. 8, 3/4. Fractions are included in wholes. In mathematics, numbers are represented by the ratio, and these is the ratio's divisor. These are all examples of basic fractions that might be divided by whole integers. The remainder is a difficult fraction despite the amount itself includes a fraction.

Here,

Assume that 1600 grams of a combination of 30% sulfuric acid and 60% sulfuric acid were created using x grams of 20% sulfuric acid and y grams of 60% sulfuric acid.

Equation 1: 1600 = x plus y (total amount of solution)

Equation 2: 0.3(1600) = 0.2x + 0.6y (total amount of solute)

By condensing Equation 2, we obtain:

=>  0.2x + 0.6y = 480

=>  2x + 6y = 4800

=>  x + 3y = 2400

Formula 3:

=>  x + y = 1600

=>  x + 3y = 2400

=>  2y = 800

=>  y = 400

=>  x + 400 = 1600

=> x = 1200

Thus, 1600 grams of 30% sulfuric acid were created using 1200 grams of 20% sulfuric acid and 400 grams of 60% sulfuric acid.

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Answer:

Add −40 and 18 to get −22.

−12−(−22)

The opposite of −22 is 22. (because of the two negatives it makes a positive)

−12+22

Add −12 and 22 to get 10.

Step-by-step explanation:

The answer of the given question based on the rectangular prism is ,  the height needed to reach the desired volume of 90 ft³ is 3 feet.

Volume is a physical quantity that measures the amount of space that an object or substance occupies. It is usually measured in units like cubic meters (m³) or cubic feet (ft³), and it is expressed as the product of three dimensions: length, width, and height.

Volume is important concept in many fields of science, including physics, chemistry, and engineering. It is used to calculate amount of material needed for certain project or to measure capacity of container

The volume of rectangular prism  the formula is:

V = lwh

In this problem, the length is 6 feet, the width is 5 feet, and the desired volume is 90 ft³. So we can put the values into formula and solve for height:

90 = 6 x 5 x h

90 = 30h

h = 90/30

h = 3

Therefore, the height needed to reach the desired volume of 90 ft³ is 3 feet.

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Answer: the answer is 3ft

Step-by-step explanation:

6x5x3=90! hope this helps

Answer: -9

Step-by-step explanation: When you’re subtracting with negative numbers, the subtraction sign changes to an addition sign. Also, negatives and positives always turn out as negatives.

Therefore, -3 - 6 = -9

The approximate radius of the circle is about 20 inches. So, the correct option is A. 20 in.

What is radius?

The formula for the circumference of a circle is:

C = 2πr

where C is the circumference and r is the radius.

We are given that the circumference is about 124 inches, so we can write:

124 = 2πr

Solving for r, we get:

r = 124/(2π) ≈ 19.73

Therefore, the approximate radius of the circle is about 20 inches. So, the correct option is A. 20 in.

What is circumference of a circle?

The circumference of a circle is the distance around the edge of the circle. It is the same as the perimeter of any other shape, but specifically for circles.

To calculate the circumference of a circle, you can use the formula:

C = 2πr

where C is the circumference, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle (the distance from the center of the circle to any point on the edge).

Alternatively, you can use the formula:

C = πd

where d is the diameter of the circle (the distance across the circle passing through the center).

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Complete question is: 9 The circumference of a circle is about 124 inches. The approximate radius of the circle is about 20 inches. So, the correct option is A. 20 in.

Therefore, the sales price is $151.25. So, the answer is (C) $151.25.

Sale price refers to the price of a product or service that has been reduced from its original or regular price. It is usually offered as a discount or promotion to attract customers and increase sales. The sale price can be expressed as a percentage or a dollar amount off the regular price. For example, a shirt with a regular price of $50 might be put on sale for 20% off, making the sale price $40.

To find the sales price, we need to apply the discount to the original price:

Discount amount = 45% of $275 = 0.45 x $275 = $123.75

[tex]Sales price = Original price - Discount amount[/tex]

[tex]Sales price = $275 - $123.75 = $151.25\[/tex]

Therefore, the sales price is $151.25. So, the answer is (C) $151.25.

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Answer:

(56 3/4 + 1 3/8) + 1 1/5 = 58 + 23/5 = 293/5 or 58.6

Step-by-step explanation:

The sum of (56 3/4 + 1 3/8) + 1 1/5 can be calculated as follows:

First, we need to add the whole numbers:

56 + 1 + 1 = 58

Next, we add the fractions:

3/4 + 3/8 = (6/8) + (3/8) = 9/8

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1:

9/8 ÷ 1/8 = 9

Finally, we add the last fraction:

9 + 1/5 = (45/5) + (1/5) = 46/5

Again, we can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

46/5 ÷ 2/2 = 23/5

The probability of not seeing the ad given that the person purchased the game is 0.388.

Probability is a number between 0 and 1, where 0 represents impossibility and 1 represents certainty.

Let A be the event that a person has seen the advertisement, and B be the event that a person has purchased the game. We want to find the probability of not seeing the ad given that the person purchased the game, i.e. P(A' | B).

From the problem, we know that:

P(A) = 0.24 (24% of the market has seen the ad)

P(B | A) = 0.42 (42% of those who see the ad have purchased the game)

P(B | A') = 0.07 (93% of those who have not seen the ad have not purchased the game)

We can use the law of total probability to find P(B), the probability of purchasing the game:

P(B) = P(B | A) * P(A) + P(B | A') * P(A')

       = 0.42 * 0.24 + 0.07 * 0.76

       = 0.1296 + 0.0532

       = 0.1828

Now, we can use Bayes' theorem:

P(A' | B) = P(B | A') * P(A') / P(B)

Substituting the values we have:

P(A' | B) = 0.93 * 0.76 / 0.1828

             = 0.388

Rounding to three decimal places, the probability of not seeing the ad given that the person purchased the game is 0.388.

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The FAA selects 6 regions from its 32 regions, and then randomly audits 25 departing commercial flights in each

region for compliance with legal fuel and weight requirements. This is an example of stratified random sampling.

Stratified random sampling is a type of probability sampling method that involves dividing the population into smaller

groups, or strata, and then selecting samples from each stratum. This sampling technique is used when the population

is too large to sample as a whole, and it is necessary to divide it into smaller, more manageable groups.

Stratified random sampling is designed to ensure that each stratum within the population is adequately represented in

the sample. This is achieved by selecting a random sample from each stratum, with the size of the sample determined

by the proportion of the population that it represents.

By selecting a sample from each stratum, stratified random sampling allows for a more accurate representation of the

population as a whole.

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The two jacket prices that will make the store exactly $12,000 in revenue are $100 and $60.

To find the two jacket prices that will make the store exactly $12,000 in revenue, follow these steps:
Step 1: Write the expression for the revenue
Revenue = price (p) * number of jackets sold (-2p + 320)
Step 2: Set the revenue equal to the goal ($12,000)
12,000 = p(-2p + 320)
Step 3: Solve the equation for p
[tex]12,000 = -2p^2 + 320p[/tex]
[tex]2p^2 - 320p + 12,000 = 0[/tex]
Step 4: Factor the equation or use the quadratic formula to find two possible values of p
Using the quadratic formula:
p = (-b ± √([tex]b^2[/tex] - 4ac)) / 2a
In this equation, a = 2, b = -320, and c = 12,000.
p = (320 ± √[tex]\sqrt{((-320)^2 - 4(2)(12,000))) / (2*2)}[/tex]
Step 5: Calculate the two possible values of p
p = (320 ± √(102,400 - 96,000)) / 4
p = (320 ± √(6,400)) / 4
p = (320 ± 80) / 4
Step 6: Find the two jacket prices
Price 1: (320 + 80) / 4 = 400 / 4 = $100
Price 2: (320 - 80) / 4 = 240 / 4 = $60.

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Answer:

area: 100km

Explanation:

Answer:

Step-by-step explanation:

S(square) = Area, if it's true ===> 10km * 10 km = 100 km^2
Because u need just (10km)^2

Step-by-step explanation:

Using the rules of PEDMAS :

32  ÷  10 - 8  ÷ 2 - 3 = 5

32 ÷ (10-8)   ÷  2  -3  = 5

32 ÷ 2  ÷  2  -3  = 5  

       With multiple divisions or multiplications go from L to right in order

16  ÷  2  - 3 = 5

  8 - 3 = 5

1/2 x 12 ÷2-2+11 = 13

1/2 x (12 ÷ 2 - 2) + 11 = 13

1/2 x (6-2) + 11 =13

1/2 (4) + 11 = 13

   2 + 11 = 13

Answer: To write the proportional relationship between books and months, we can use the formula:

unit rate = (total books) / (total months)

Let's calculate the total books and months for Estelle's reservations:

Two years ago: 24 books in 4 months

Last year: unknown number of books in 36 months

This year: 18 books in 3 months

To find the total number of books for last year, we can use a proportion:

24 books / 4 months = x books / 36 months

Cross-multiplying, we get:

24 * 36 = 4 * x

x = 24 * 9

x = 216

So Estelle reserved 216 books in 36 months last year.

Now we can calculate the unit rate:

unit rate = (total books) / (total months)

unit rate = (24 + 216 + 18) / (4 + 36 + 3)

unit rate = 258 / 43

unit rate = 6

Therefore, the proportional relationship between books and months is:

books = 6 * months

Step-by-step explanation:

The answer is (D) 5/10.

what is data?

Data refers to any set of observations, measurements, or facts that can be collected, analyzed, and interpreted to gain insights or knowledge about a particular subject or phenomenon. It can be in the form of numbers, text, images, audio, or any other type of information that can be recorded.

To create a line plot, we need to represent each value in the data set with a point on a number line and then connect the points with a line. Here is the line plot for the given data:

 4|              ●

 3|        ●     ●

 2|  ●     ●     ●

 1|  ●  ●  ●  ●  ●

  +-----------------

     1  2  3  4  5  6

Part A:

From the line plot, we can see that the greatest amount of rainfall in a month is 4 inches, and the least amount of rainfall is 1 inch. Therefore, the difference between the greatest and least amounts of rainfall in a month is:

4 - 1 = 3 inches

The answer is not given as one of the options provided.

Part B:

To determine the fraction of the 10 months that had more than 2 inches of rainfall, we count the number of months that had more than 2 inches and divide by the total number of months:

There are 6 months with more than 2 inches of rainfall: 1st, 2nd, 3rd, 7th, 8th, and 10th.

So, the fraction of the 10 months with more than 2 inches of rainfall is:

6/10 = 3/5

Therefore, the answer is (D) 5/10.

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MAD is the mean for the following data for coins in student's pocket here is = 1.42.

Mean can also be referred to as average. The average height of the 9th grade class, for instance, is 150 cm, which denotes the average height of all the students. Significant financial consequences are associated with the statistical concept of mean, which is used in a number of financial contexts and corporate appraisal. The mean, median, and mode are the three statistical indicators of a data set's central-tendency.

Here in the question,

The given data for 7 observations is:

3, 1, 0, 2, 0, 2, 1, 1

Mean = (3 + 1 + 0 + 2 + 0 + 2 + 1 + 1)/7

= 10/7

= 1.42

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Answer:

$701.20

Step-by-step explanation:

1.  If she earns $6 per hour and worked 79 hours, how much, in the form of pay, did she earn?

2.  If she sold $2292 in merchandise, she receives 10% of that as a bonus.  How much is this bonus?

3.  Add the results of (1) and (2) together.  The result will be her total earnings.

Radical can also mean "basic" or "far-reaching," therefore it's possible that the cube root's radical shift involved erasing the cubic functions maths homework.

A function in mathematics is a relationship between a set of possible outputs (the range) and a set of inputs (the domain), with the property that each input is associated to exactly one outcome. A rule or procedure that transforms an input value into an output value is referred to as a function. Typically, the variable x represents the input value, while the object y or f represents the output value (x). A formula or equation that explains the relationship here between values of the input and output is frequently used to express functions.

given

The riddle's solution is: Since it desired a profound transformation!

Expressions using cubic functions can be made simpler by using the cube root, a kind of radical function.

Radical can also mean "basic" or "far-reaching," therefore it's possible that the cube root's radical shift involved erasing the cubic functions maths homework.

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So the distance between X and Z is simply 80 km. Rounded to one decimal place, this is 80.0 km.

Trigonometry is a branch of mathematics that focuses on the relationships between the sides and angles of triangles. It involves the study of trigonometric functions, which relate angles and sides of a right triangle, as well as the application of these functions to various real-world problems such as navigation, physics, and engineering. Trigonometry has a wide range of applications in fields such as science, engineering, architecture, and more.

Here,

First, we need to find the coordinates of each point. Let's assume that X is located at the origin (0,0) on the map. From X, we know that Y is 80 km away on a bearing of 190°. This means that Y is located 80 km to the southwest of X. To find the coordinates of Y, we need to use trigonometry. Let's define angle A as the angle between the positive x-axis and the line XY. Then we can use the cosine and sine functions to find the x and y coordinates of Y:

cos(A) = adjacent/hypotenuse = x/80

sin(A) = opposite/hypotenuse = -y/80 (note the negative sign because Y is southwest of X)

Solving for x and y, we get:

x = 80 cos(A)

y = -80 sin(A)

Now we need to find the coordinates of Z. We know that Z is due south of X, which means it lies on the y-axis. We also know that Z is on a bearing of 140° from Y, which means it forms a 40° angle with the negative y-axis. Let's call this angle B. Using trigonometry again, we can find the distance between Y and Z (which we'll call d) and the coordinates of Z:

cos(B) = adjacent/hypotenuse = x/d

sin(B) = opposite/hypotenuse

= -y/d (again note the negative sign)

We want to find d, so we can rearrange the cosine equation:

d = x/cos(B)

Substituting in the expressions for x and y in terms of A, we get:

d = (80 cos(A))/cos(B)

Finally, we need to eliminate the variables A and B. We know that A + B = 180° because angle AYX + angle BYZ = 180°. Rearranging, we get:

B = 180° - A

Substituting into the expression for d, we get:

d = (80 cos(A))/cos(180°-A)

Simplifying using the cosine difference identity, we get:

d = (80 cos(A))/(-cos(A))

= -80

This negative distance means that Z is actually due north of X, which makes sense because it is "directly south" of X on the map. So the distance between X and Z is simply 80 km.

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As per the probability, to interpret these expected values, we can say that on average, Mark Ross could expect to receive $40,200 if he wins the case and is awarded 60% of the amount requested.

.

To calculate the expected value, we need to multiply the probability of each outcome by the value of that outcome and then add them up. In this case, the outcome is the settlement amount that could be paid to Mark Ross. Let's assume that the amount requested by Mark Ross is $100,000.

The probability that the plaintiff wins and is awarded 60% of the amount requested is 67% * 60% = 40.2%. Therefore, the expected value of the settlement amount is:

Expected Value = 40.2% * $100,000 = $40,200

This means that on average, Mark Ross could expect to receive $40,200 if he wins the case and is awarded 60% of the amount requested.

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The value of m∠NMO is 110°.

What is the area of the shaded sector?

A sector is an area that is enclosed by the arc of the circle that lies between two radii and two radii. A sector's area is a portion of the circle's total area. This region is inversely proportional to the principal angle. This suggests that the sector's area increases with increasing central angle.

Here, we have

Given: In circle M, MN = 6 and the area of the shaded sector = 11π

We have to find the value of m∠NMO.

area of the shaded sector = πr²× m∠NMO/360°

11π = π(6)²× m∠NMO/360°

11 = 36× m∠NMO/360°

11 = m∠NMO/10°

11×10° = m∠NMO

m∠NMO = 110°

Hence, the value of m∠NMO is 110°.

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