Find the shaded area. Round your answer to the nearest tenth, if necessary.

Use 3.14 for pi.
Area of the Rectangle =


Area of the Circle =


Total Shaded Area =

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:

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

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 sampling technique used in this scenario is stratified random sampling.

This is because Kane grouped the population of licensed nurses in Florida into two distinct strata, namely urban and nonurban areas, based on a specific characteristic (geographical location). Then, he randomly selected 250 nurses from each stratum, resulting in a total sample size of 500 nurses.

The purpose of stratified random sampling is to ensure that the sample is representative of the population by including participants from each stratum in proportion to their representation in the population. This allows for more accurate and precise estimates of population parameters than simple random sampling, especially when there are significant differences between strata.

By stratifying the population and randomly selecting participants from each stratum, Kane can draw more reliable conclusions about the attitudes of licensed nurses toward evidence-based practice in urban and nonurban areas of Florida.

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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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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: 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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Pythagoras theorem is the square of two sides gives the square of third side.

Given,

Height of flagpole= 25 ft

base= 5 ft

Let the broken part be x

The remaining part becomes 25-x

Apply Pythagoras theorem

[tex]5^{2}[/tex] + [tex]x^{2}[/tex] = [tex](25-x)^{2}[/tex]

25 + [tex]x^{2}[/tex] = [tex]25^{2}[/tex] + [tex]x^{2}[/tex] - 2*25*x

25 + [tex]x^{2}[/tex] = 625 + [tex]x^{2}[/tex] - 50x

([tex]x^{2}[/tex] cancels out on both side)

50x = 625- 25

50x = 600

x = 600/50

x = 12

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 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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Answer:

5/2 es mayor que 5/6

Step-by-step explanation:

your welcome :D

They can get 32 portions of 1/8 lb each from a 4-pound block of Parmesan cheese.

To determine how many portions can be made from a 4-pound block of Parmesan cheese at the market, follow these steps:
1. Identify the size of each portion: 1/8 lb
2. Identify the total weight of the cheese block: 4 lb
3. Divide the total weight by the portion size to find the number of portions:

4 lb ÷ 1/8 lb

To do this division, you can multiply 4 by the reciprocal of 1/8 (which is 8/1):
4 × 8/1 = 32.

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The area of the regular polygon is  [tex]49\sqrt3[/tex] square unit.

What is area?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

Here the given triangle ,

Apothem a = [tex]\frac{7\sqrt3}{3}[/tex]

Now side length s = [tex]2\sqrt3 a[/tex]

=> side length s = [tex]2\sqrt3\times \frac{7\sqrt3}{3} = \frac{14\times3}{3}[/tex] = 14

Now area of equilateral triangle A = [tex]\frac{\sqrt3 s^2}{4}[/tex] square unit.

=> A = [tex]\frac{\sqrt3\times14^2}{4}[/tex] = [tex]49\sqrt3[/tex] square unit.

Hence the area of the regular polygon is  [tex]49\sqrt3[/tex] square unit.

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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 :-

The value of the expression m + (7.9) is 10.4. when m= 2.5 and n = 5

from the question, we have the following parameters that can be used in our computation:

m + (7.9)

The expression m + (7.9) means that we need to add the value of m to 7.9.

Substituting m = 2.5, we get:

m + (7.9) = 2.5 + 7.9 = 10.4

Therefore, when m = 2.5, the value of the expression m + (7.9) is 10.4.

Note that the value of n is not used in this expression since it is not included in the expression to be evaluated.

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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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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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There are 90 positive odd integers less than 1000 that can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 by choosing any of the three odd digits as the last digit, and any of the remaining digits for the first and second positions.

To form a positive odd integer, the last digit must be an odd number, i.e., 1, 3, 5. For each of these three possible last digits, we can choose any of the remaining six digits for the first position, and any of the remaining five digits for the second position (since we cannot repeat digits in forming a positive integer).

Therefore, the total number of positive odd integers less than 1000 that can be formed from the digits 0, 1, 2, 3, 4, 5, and 6 is:

3 × 6 × 5 = 90

So there are 90 positive odd integers less than 1000 that can be formed from the given digits.

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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) 70 meters

2) at 3 seconds

3) about 114 meters

[tex]h(3) = - 4.9 ({3}^{2} ) + 29.4(3)+ 70 = 114.1[/tex]

4) about 8 seconds

5)

[tex]h(t) = - 4.9 {t}^{2} + 40.5t + 70[/tex]

Answer:

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

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 circle  is ,  the width of the shaded region is 4 inches, and the answer is (a).

Radius is distance from center of  circle to any point on circle. It is a fixed length and is the same for all points on the circle. The radius is usually denoted by the letter "r".

The radius is an important parameter of a circle and is used in many geometric calculations, like finding the circumference, area, diameter, chord length, and arc length of a circle. The diameter of a circle is twice the radius, and the circumference of a circle is equal to 2π times the radius.

The area of shaded region is equal to area of the outer circle minus area of inner circle. We are given that the area of the shaded region is 56π in², and the radius of the inner circle is 5 in.

Let radius of outer circle be " r ". Then we have:

Area of the shaded region = Area of the outer circle - Area of the inner circle

56π = πr² - π(5²)

56π = π(r² - 25)

r² - 25 = 56

r² = 81

r = 9

So, the radius of the outer circle is 9 inches.

The width of the shaded region is the difference between the radius of the outer circle and the radius of the inner circle:

Width of shaded region = 9 in - 5 in = 4 in

Therefore, the width of the shaded region is 4 inches, and the answer is (a).

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Since, distribution is skewed right even after we remove the outlier (600) from the data set. The median is a good measure regardless of whether the outlier is included.

We have a data set represents the dollar amounts of donations collected at the entrance to a free museum during one hour. The data present in above figure. Now, first we determine the median. As we know, median of a data set is equals to the middle value of data set, so sometimes it is called middle value. It is the value which separates upper and lower halves of data sample or population etc. First we ordered the data values in ascending order. In case odd number of data values, median = middle value and in case of even number of terms, median = mean of two middle terms. Now, here data values in ascending order are 1,5,5,5,5,5,10,10,10,15,600. That is total data values = 11 ( odd) , so median

= 6th value = 5.

So, regardless of whether the outlier is included median is good measure in this situation.

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Answer:

x = 4

Step-by-step explanation:

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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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 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.