find the mean, median, and model 19 , 18 , 13 , 55 , 15 , 16

Answer: The area of the small inner circle is 1/3 of the area of the outer annulus if and only if the ratio of the radii of the circles is 2:1

Step-by-step explanation: The area of the small inner circle is 1/3 of the area of the outer annulus if and only if the ratio of the radii of the circles is 2:1. In that case, the reason is very simple. The inner circle has an area of πr^2, and the outer circle has an area of π(2r)^2 = 4πr^2, where r is the radius of the inner circle.

Answer:  A  8[tex]\pi[/tex]

Step-by-step explanation:

A=[tex]\pi r^{2}[/tex]  so for larger  [tex]16\pi =\pi r^{2}[/tex]   and r=4  therefore d=8

To find the length of square I use the diameter of the larger circle as the diagonal of the square.  Use pythagorean:

[tex]d^{2} =x^{2}+ x^{2} \\8^{2} =2x^{2} \\64/2 = x^{2} \\x=\sqrt{32} =4\sqrt{2}[/tex]     this is the length of the square side which is also the diameter of the inner circle

so the radius is x/2   r=2[tex]\sqrt{2}[/tex]

[tex]A=\pi r^{2} =\pi (2\sqrt{2} )^{2} = \pi (2^{2} *2} )=8\pi[/tex]

The equation of the line trend anchored at point (-8,22) and (3,0) is -2x+6.

A line is a one-dimensional figure, which has length but no width and extends infinitely in both directions.

To calculate the equation of the trend line, we use the formula below.

Formula:

From the question,

Given:

Substitute these values into equation 1

Hence, the equation of the line is -2x+6.

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Answer:  The difference of the medians is approximately 1 times the range

Step-by-step explanation:

Answer: Slope is m = 3, y-intercept is (0,-24)

Step-by-step explanation: I hope this helps!

The best measure of variability for the data, and its value is: D. The range is the best measure of variability, and it equals 9.

In Mathematics and Statistics, a line plot simply refers a type of graph that is used for the graphical representation of data set above a number line, while using crosses, dots, or any other mathematical symbol.

From the data set, we have:

10, 1, 1, 4, 4, 2, 2, 2, 5, 5, 5, 3, 3, 3, 3

For the IQR, we have:

IQR = Third quartile (Q₃) - First quartile (Q₁)

IQR = 5 - 2

IQR = 3

For the range, we have;

Range = maximum - minimum

Range = 10 - 1

Range = 9.

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Answer:

Given information:

To obtain the equation of the regression line for the given data.

The equation of regression line of y on x is given by:

y

−

¯

y

=

b

y

x

(

x

−

¯

x

)

;

w

h

e

r

e

,

y

=

d

e

p

e

n

d

e

n

t

v

a

r

i

a

b

l

e

x

=

i

n

d

e

p

e

n

d

e

n

t

v

a

r

i

a

b

l

e

b

y

x

=

s

l

o

p

e

o

f

r

e

g

r

e

s

s

i

o

n

l

i

n

e

¯

x

=

m

e

a

n

o

f

x

¯

y

=

m

e

a

n

o

f

y

y−y¯=byx(x−x¯);where,y=dependentvariablex=independentvariablebyx=slopeofregressionlinex¯=meanofxy¯=meanofy

The calculations for the equation of regression line is tabulated below:

The regression coefficient of y on x is given by:

b

y

x

=

∑

x

y

−

1

n

∑

x

∑

y

∑

x

2

−

1

n

(

∑

x

)

2

=

1944

−

1

5

×

98

×

69

2580

−

1

5

(

98

)

2

=

591.6

659.2

=

0.898

byx=∑xy−1n∑x∑y∑x2−1n(∑x)2=1944−15×98×692580−15(98)2=591.6659.2=0.898

Mean of x is calculated as:

¯

x

=

1

n

∑

x

=

1

5

×

98

=

19.6

x¯=1n∑x=15×98=19.6

Mean of y is calculated as:

¯

y

=

1

n

∑

y

=

1

5

×

69

=

13.8

y¯=1n∑y=15×69=13.8

The equation of regression line is given as:

y

−

¯

y

=

b

y

x

(

x

−

¯

x

)

y

−

13.8

=

0.898

(

x

−

19.6

)

y

=

0.898

x

−

3.8

y−y¯=byx(x−x¯)y−13.8=0.898(x−19.6)y=0.898x−3.8

Therefore, the required equation of regression line is y = 0.898x - 3.8.

Answer:

Step-by-step explanation:

You want the proportion and its solution that represents the question, "25% of what number is 9?"

The problem statement is telling us the ratio of 9 to w is 25%:

  [tex]\dfrac{9}{w}=\dfrac{25}{100}\\\\9\times100=25\times w\qquad\text{multiply by $100w$}\\\\w=\dfrac{9\times100}{25}=36\qquad\text{divide by 25}[/tex]

The number is 36.

__

Additional comment

We like to write these problems using the exact relation given:

  "25% of w is 9"

  0.25w = 9 . . . . . . . . . . . using math symbols

  w = 9/0.25 = 36 . . . . . . solve this one-step equation

The "cross multiplication" step used above inevitably results in multiplying the variable by a number, then dividing by that number. That seems unnecessary.

Answer:

Step-by-step explanation:

n + 7 = - 12 | -7

n +7 - 7 = -12 - 7

n = -19

7/18

Since we're talking about the number 18, I assume you're referring to the 18 letters of the English alphabet after "r." In that case, there are 7 letters in the alphabet after "r" that are not "s": "t", "u", "v", "w", "x", "y", and "z".

So the probability of choosing a letter other than "s" from these 18 letters is 7/18. Therefore, the answer is:

7/18

The box plot that matches the data-set is given by the following option:

Option B.

A box and whisker plots shows these five features from a data-set, listed as follows:

The parameters for the data-set in this problem are given as follows:

Hence option B gives the box plot for this data-set.

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Answer:

Step-by-step explanation:

Slope= -2

y-intercept= 3

For a sample of 903 voters from Tampa.

a) The percentage of Tampa, FL voters who self-identify as conservative is equals to 41%.

b) The percent of these Tampa, FL voters who identify themselves as conservatives and are in favor of the citizenship option is equals to 6.31%.

Random or probabilistic sampling is a process in which every person in the population has an equal chance of being included in the sample. The sample is the part of the population that represents the characteristics of the population within a certain margin of error. We have a sample of 903, voters from Tampa, Florida. The table above represents valuable information. From Table we have

a) Number of voters who define themselves as conservative = 372

Total number of registered voters = 903

Percentage of votes who define themselves as conservative = [tex] \frac{372}{903}[/tex]

= 0.41196013289 = 41%

b)Number of voters who identify themselves as conservatives and are in favor of the citizenship option = 57

The Percent of voters who identify themselves as conservatives and are in favor of the citizenship =[tex]\frac{57}{903} [/tex]

= 0.0631229235 = 6.31%.

Hence, required value is 6.31%.

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Complete question:

903 randomly sampled registered voters from Tampa, FL were asked if they thought workers who have illegally entered the US should be (i) allowed to keep their jobs and apply for US citizenship, (ii) allowed to keep their jobs as temporary guest workers but not allowed to apply for US citizenship, or (iii) lose their jobs and have to leave the country. The results of the survey by political ideology are shown below.

a) What percent of these Tampa, FL voters identify themselves as conservatives?

b) What percent of these Tampa, FL voters identify themselves as conservatives and are in favor of the citizenship option?

The amount Isabella invested in the 4%, obtained using the percentage interest rates of the three investments and the annual income from the three investments is $25,000

A percentage is the expression of the ratio of two quantities as a fraction of 100.

Let x represent the amount of money Isabella invested at 3% and let 2·x represent the amount of money she invested at 4%, let (x + $500) represent the amount of money Isabella invested at 5%, we get;

The percentage of the interest rates and the her annual income from the three investments after can be used to obtain the following equation.

0.03·x + 0.04×(2·x) + 0.05 × (x + 500) = 2025

0.16·x + 25 = 2025

0.16·x = 2025 - 25 = 2000

x = 2000/0.16 = 12500

x = 12,500

The amount Isabella invested at 3% is, x = $12,500

The amount she invested at 4% = 2 × x = 2 × $12,500 = $25,000

The amount she invested at 4% is $25,000

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Answer:

The answer to 24 times 4 is 96.

Step-by-step explanation:

To solve this, we must multiply the 4 in 24 by the 4 by itself. 4 times 4 is 16. So, the 6 is part of the answer. Place the 1 above the 2 in 24. Now, multiply 2 by 4 and add 1. You then get 9, the final number in the answer. So, the complete answer is 96.

Visual steps:

24

* 4

1

24

* 4

= 6

1

24

* 4

96

In short, the answer is 96.

10. Diameter = 16 cm, Circumference = 50.24 cm
11. Diameter = 26 cm, Circumference = 81.64 cm

12. Radius = 4.5 m, Circumference = 28.26 m

13. Diameter = 11.36 in, Radius = 5.86 in.

10.

When radius is 8 cm

The diameter is 2(8) = 16 cm

Circumference = πd

=3.14×16 = 50.24 cm

11.

Radius = 13 ft

Diameter = 2(13)= 26 feet

Circumference = πd

=3.14×26 = 81.64 square feet.

12.

diameter = 9m

Radius  = 4.5m

Circumference = 3.14×9 = 28.26 m

13.

Circumference = 35.7 inches

Circumference = πd

35.7 = 3.14 d

d=11.36

r = 5.68

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The length of the central angle JKL is 230°, the area of the shaded region is 575π / 9 and the area of the unshaded region is 325π / 9.

In this problem we must find the value of a central angle, in degrees, and the areas of circular sectors. The area of a circular sector is described by following formula:

A = π · (α / 360°) · r²

Where:

m JKL = 360° - 130°

m JKL = 230°

Area of shaded sector

A = π · (230° / 360°) · 10²

A = 575π / 9

Area of unshaded sector

A = π · (130° / 360°) · 10²

A = 325π / 9

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Answer:

∠ Y ≈ 39°

Step-by-step explanation:

using the tangent ratio in the right triangle

tanY = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{XZ}{YZ}[/tex] = [tex]\frac{36}{45}[/tex] = [tex]\frac{4}{5}[/tex] , then

∠ Y = [tex]tan^{-1}[/tex] ( [tex]\frac{4}{5}[/tex] ) ≈ 39° ( to the nearest degree )

Yuri has 42.86% of the original cloth left after cutting a 2 meter length from a 3.5 meter long cloth.

Percentage is a way of expressing a number as a fraction of 100, representing a portion of a whole, where 100% represents the entire amount.

Yuri originally had 3.5 meters of cloth. After cutting 2 meters of cloth, he has 3.5 - 2 = 1.5 meters of cloth left.

To find the percentage of cloth that Yuri has left, we can use the formula:

percentage = (amount left / original amount) x 100%

Plugging in the values we have

percentage = (1.5 / 3.5) x 100%

Divide the numbers

percentage = 0.4286 x 100%

Multiply the numbers

percentage = 42.86%

Therefore, Yuri has 42.86% of the original cloth left.

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The probability that the player A, B, C, and D are assigned to go 1st, 2nd, 3rd, and 4th respectively is 0.0083 up to 4 decimal places.

The probability of a specific batting order for 5 players is given by the formula:

P = 1/n!

where n is the number of players and the "!" symbol represents factorial notation, which means multiplying a series of descending natural numbers.

For 5 players, the number of possible batting orders is:

n! = 5! = 5 x 4 x 3 x 2 x 1 = 120

So the probability of a specific batting order is:

P = 1/120 = 0.0083 up to 4 decimal places.

Therefore, the required probability is 0.0083 up to 4 decimal places.

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The equation to model this situation is Hannah = 1 4/5 * 7 2/3 miles.

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

This means that

Hannah = 1 4/5 * Jamil

So. we have

Hannah = 1 4/5 * 7 2/3 miles.

Evaluate

Hannah = 13 4/5 miles.

Using the above as a guide, we have the following:

The equation is

Hannah = 1 4/5 * 7 2/3 miles.

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The approximate area that the Theater Club will have to paint to fill in this tree is about 14.5314 square feet.

The formula for the area of a circle is A = πr², where A is the area and r is the radius (which is half of the diameter). In this case, the trunk has a diameter of 0.2 feet, so the radius is 0.1 feet. Therefore, the area of the trunk is:

A(trunk) = π(0.1)² = 0.0314 square feet

Next, let's move on to the foliage of the tree. We can break it down into two parts: the triangular shape of the tree's body and the trapezoidal shape of the top. To find the area of the triangular shape, we can use the formula for the area of a triangle, which is:

A(triangle) = 0.5 x base x height

In this case, the base of the triangle is 3 feet (the width of the base of the tree), and the height is 5 feet (the height of the tree). Therefore, the area of the triangular shape is:

A(triangle) = 0.5 x 3 x 5 = 7.5 square feet

To find the area of the trapezoidal shape, we can use the formula for the area of a trapezoid, which is:

A(trapezoid) = 0.5 x (base1 + base2) x height

In this case, base1 is 3 feet (the width of the base of the tree), base2 is 4 feet (the width of the top of the tree), and the height is 2 feet (half of the distance between the base and the top). Therefore, the area of the trapezoidal shape is:

A(trapezoid) = 0.5 x (3 + 4) x 2 = 7 square feet

Finally, to find the total area of the tree, we just need to add up the areas of all the parts:

Total area = A(trunk) + A(triangle) + A(trapezoid) Total area = 0.0314 + 7.5 + 7 Total area = 14.5314 square feet (approx.)

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Answer:

see explanation

Step-by-step explanation:

1

the sum of the exterior angles of a polygon = 360°

sum the exterior angles and equate to 360°

let the unknown exterior angle be ? , then

48° + 35° + 118° + 73° + ? = 360°

274° + ? = 360° ( subtract 274° from both sides )

? = 86°

exterior angle + interior angle = 180° , that is

86° + x = 180° ( subtract 86° from both sides )

x = 94°

2

the sum of the exterior angles of any polygon = 360°

Answer:  D: Add the fractions together on the right side of the equation

Step-by-step explanation:

Applying the alternate interior angles theorem, the value of b in the image given is solved as: 62 degrees.

The alternate interior angles theorem posits that if two angles are alternate interior angles, then they have equal angle measure or are congruent to each other.

Since the diagram shows two parallel lines, then the second unlabeled angle in the triangle formed would be equal to 49.5 degrees, based on the alternate interior angles theorem.

To solve for b, we have the following equation based on the triangle sum theorem:

b = 180 - 68.5 - 49.5

b = 62 degrees.

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The length of the hypotenuse is approximately 4.95 cm.

We have,

Since triangle ABC is a 45-45-90 triangle, we know that the measure of angle B is also 45 degrees.

Therefore, we can use the 45-45-90 Triangle Theorem, which states that in a 45-45-90 triangle, the length of the hypotenuse is √2 times the length of either leg.

In this case,

We know that leg a = 3.5 cm, so we can find the length of the hypotenuse c using the formula:

c = a√2

Substituting the value of a, we get:

c = 3.5√2 ≈ 4.95 cm

Therefore,

The length of the hypotenuse is approximately 4.95 cm.

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The functional notation for the rolls of wristbands would be R (175 , 50) = 25.

Let's denote the number of patients per day as P and the number of wristbands per roll as W.

P = 175 and W = 50

Since there are 7 days in a week, we can represent the total number of wristbands needed per week as follows:

= P x 7

Now, write this equation using function notation:

R (P, W) = (P x 7) / W

R ( 175, 50) = (175 x 7) / 50

R (175, 50) = 1, 225 / 50 = 24.5

R (175, 50) = 25

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Answer:

yes

Step-by-step explanation:

I'm not 100% sure but I think so, sorry if incorrect or too late.

The area of the tile is: Option C: 42.5 cm².

A trapezoid is defined as a four-sided geometric shape with one pair of parallel sides. The two non-parallel sides are usually referred to as the "legs" and the other two sides are the "bases". A trapezoid can be either isosceles or non-isosceles depending on the angles of the legs. A trapezoid can also be equilateral if all four sides have equal lengths.

The formula for the area of a trapezoid is:

Area = ¹/₂ (base 1 + base 2) * height

In this case, we are given the parameters as:

Base 1 is 3 cm

Base 2 is 6 cm

The height is 5 cm.

Plugging these values into the equation, we get:

Area = ¹/₂(6 + 5) + 3) * 5 cm

Area = 42.5 cm². Therefore, the area of the tile is 42.5 cm².

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The reasonable solution for the linear inequalities is to order 200 pounds of apples and 150 pounds of oranges, which satisfies the requirement of having at least 50 more pounds of apples than oranges while keeping the cost under $225.

Let x be the number of pounds of apples and y be the number of pounds of oranges. We can then set up the following system of inequalities:

0.5x + 0.75y < 225 (the total cost of the order must be less than $225)

x > y + 50 (the market needs at least 50 more pounds of apples than oranges)

To find a reasonable solution, we can use trial and error or graph the inequalities to identify the feasible region. However, it is easier to solve the system of inequalities algebraically.

First, we can rewrite the second inequality as x - y > 50. Then, we can plot the boundary line x - y = 50, which is the line that satisfies x - y = 50 exactly.

Next, we can plot the boundary line 0.5x + 0.75y = 225, which is the line that satisfies the total cost of the order being exactly $225. To plot this line, we can solve for y:

0.5x + 0.75y = 225

0.75y = 225 - 0.5x

y = (225 - 0.5x)/0.75

y = 300 - 0.67x

Now we can plot the two boundary lines and shade the feasible region that satisfies both inequalities,

From the feasible region, we can see that the corner point (200, 150) yields the lowest cost, which is $162.50.

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