Shaded areas
A circle with radius of 3 cm sits inside a 8 cm x 7 cm
rectangle.
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
8 cm

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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The area of each part of the figure and the whole figure is Rectangle A = 15 square units
Triangle B = 6 square units
Rectangle C = 8 square units
Whole figure = 29 square units

To find the area of each part of the figure, we need to use the formula for the area of a rectangle and the area of a triangle.

Let's start with Rectangle A. We can see from the figure that its length is 5 units and its width is 3 units. To find its area, we use the formula A = l x w, where A represents the area, l represents the length, and w represents the width. So, for Rectangle A, we have:

A = 5 x 3 = 15 square units

Next, let's move on to Triangle B. We can see from the figure that the base of the triangle is 4 units and the height is 3 units. To find its area, we use the formula A = (1/2) x b x h, where A represents the area, b represents the base, and h represents the height. So, for Triangle B, we have:

A = (1/2) x 4 x 3 = 6 square units

Finally, let's find the area of Rectangle C. We can see from the figure that its length is 4 units and its width is 2 units. To find its area, we use the same formula as for Rectangle A:

A = 4 x 2 = 8 square units

Now that we have the area of each part, we can add them up to find the whole figure. So, we have:

Whole figure = Rectangle A + Triangle B + Rectangle C
Whole figure = 15 + 6 + 8
Whole figure = 29 square units

Therefore, The area of each part of the figure and the whole figure are as follows:
Rectangle A = 15 square units
Triangle B = 6 square units
Rectangle C = 8 square units
Whole figure = 29 square units

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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

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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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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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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Answer:

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

Answer:

5/2 es mayor que 5/6

Step-by-step explanation:

your welcome :D

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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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 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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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: 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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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: -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 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center is (2.166, 2.634). So, the correct option is B).

To find the 90% confidence interval for the mean number of days per week that Americans who are members of a fitness club go to their fitness center, we can use the formula:

CI = X ± z*(σ/√n)

where X is the sample mean, σ is the sample standard deviation, n is the sample size, and z is the z-score associated with the desired confidence level (90% in this case).

The z-score for a 90% confidence level is 1.645.

Plugging in the values given in the problem, we get:

CI = 2.4 ± 1.645*(2.1/√220)

Solving this equation gives us a confidence interval of (2.166, 2.634) rounded to three decimal places.

Therefore, the correct answer is (2.166, 2.634) and option is B).

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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:

(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

Answer:

41cm

Step-by-step explanation:

If observed closely you can see that perimeter C is the merged factor of both perimeter A and B.

To get the perimeter of C, merge both perimeter A and B together

The height will be 10cm

The bottom will be 6cm seeing as the top of perimeter A is 6cm and there are the same length

The top will be 6+7 = 13cm because perimeter A and B have been merged meaning they will be added

The right side will be 5cm because 5cm is the side of perimeter B

The long bottom will be 7cm because it is the same as perimeter B and they have the same length meaning

10+6+13+5+7 =  41cm(The answer is not squared because we only added the sides not multiplied it)

The truth of ΔABC and ΔDEF is that both triangles i.e. ΔABC and ΔDEF are similar because[tex]\frac{12-6}{4-2} = \frac{27-15}{9-5}[/tex],So the correct option is Option(D).

A three-sided polygon with three corners is termed as triangle.

This is the simplest polygon produced when three non-collinear points are connected by line segments.

Triangles can be classified according to the length of sides and size of the angles. There are several triangles that are as :

Scalene triangle: A triangle without equal sides.

isosceles triangle: A triangle with tow equal and same sides.

ΔABC and ΔDEF are similar because:-  

[tex]\frac{12-6}{4-2} = \frac{27-15}{9-5}[/tex]

[tex]\frac{6}{2} = \frac{12}{4}[/tex]

3 = 3

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The complete question is :-

Absolute value equation for a straight horizontal line with marked points and x-axis intercepts. Therefore, the absolute value equation that has the given solution set is:y + 1 = | x + 3 | .

How to write an absolute value equation that has the following solution set?

To find the absolute value equation that corresponds to the given solution set, we need to determine the axis of symmetry of the V-shaped graph formed by the absolute value function. The axis of symmetry is the vertical line that passes through the vertex of the graph. Since the vertex of the graph is located at the midpoint of the two given points, which is at x = -3, the axis of symmetry is x = -3.

The equation of the absolute value function can be written as:

b + | x - a |  

= y

where a is the x-coordinate of the vertex and b is the y-coordinate of the point where the graph intersects the y-axis. In this case, the y-coordinate of the point where the graph intersects the y-axis is -1, so we have b = -1.

Substituting the value of a and b in the equation above, we get:

| x - (-3) | - 1 = y

Simplifying the equation, we get:

y + 1  = | x + 3 |

Therefore, the absolute value equation that has the given solution set is:

y + 1 = | x + 3 | .

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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:

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:

Answer:

No solutions

Step-by-step explanation:

- 3x - y = 10 ⇒ ( 1 )

3x + y = - 8 ⇒ ( 2 )

( 1 ) + ( 2 )

-3x - y + 3x + y = 10 - 8

Combine like terms.

0 ≠ 2

NO solutions

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.

The probability that a woman with breast cancer will survive after her surgery is less than -1.33 is approximately 0.0918.

Therefore P(X < 6) = 0.0918 or 9.18%.

 To find the probability that a woman with breast cancer will survive after surgery, we need to use the normal distribution formula.

z = (x - μ) / σ

where z =z-score

x=survival time in years,

μ =mean survival time,

and σ= standard deviation of survival time.

Let X be the survival time, then [tex]X ~ N(8, 1.5^2).[/tex]

a) 10+ year survival probability:

I would like to find P(X > 10). Using the formula above, we get:

z = (10 - 8) / 1.5 = 1.33

A standard normal distribution table or calculator tells us that the probability that z is greater than 1.33 is approximately 0.0918.

Therefore P(X > 10) = 0.0918 or 9.18%. b) 5- to 7-year survival probabilities:

b) 5- to 7-year survival probabilities: I would like to find P(5 < X < 7).

Using the formula above, we get: z1 = (5 - 8) / 1.5 = -2

z2 = (7 - 8) / 1.5 = -0.67

From a standard normal distribution table or calculator, we know that the

probability that z is between -2 and -0.67 is approximately 0.1841.

Therefore P(5 < X < 7) = 0.1841 or 18.41%.

c) Probability of survival <6 years:

Find P(X < 6). Using the formula above, we get:

z = (6 - 8) / 1.5 = -1.33

A standard normal distribution table or calculator tells us that the probability that z is less than -1.33 is approximately 0.0918. Therefore P(X < 6) = 0.0918 or 9.18%.  

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