Comparing Statistical Measures
A 3-column table with 5 rows. Column 1 has entries Mean, median, mode, range, M A D. Column 2 is labeled Noah with entries 87, 85.5, 85, 8, 2.67. Column 3 is labeled Gabriel with entries 87.17, 85, 86, 12, 3.22.

The difference between Noah’s mean and Gabriel’s mean is
.

The ratio of the difference in the mean to Noah’s MAD is
.

The ratio of the difference in the mean to Gabriel’s MAD is
.
Both of these ratios show that the difference in the means is about 5% of the MAD values.

Answer:

15

Step-by-step explanation:

720 divided by 48 equal 15

1. The area of the scale drawing of the park is 146,880 square inches (Option J).

2. The perimeter of the park is 126 feet (Option D).

3. The length of the south side of the park is 40% of the length of the north side (Option F).

1. To find the area of the scale drawing of the park, we need to calculate the area of the trapezium. The formula for the area of a trapezium is (base1 + base2) * height / 2.

Using the scale, the lengths of the bases (parallel sides) in feet would be:

Base1 = 28 inches * 1.5 feet/inch = 42 feet

Base2 = 40 inches * 1.5 feet/inch = 60 feet

Plugging in the values into the formula, we have:

Area = (42 + 60) * 16 / 2 = 1020 square feet

Since the answer options are in square inches, we need to convert the area back to square inches:

Area = 1020 square feet * 144 square inches/square foot = 146880 square inches

Therefore, the area of the scale drawing of the park is 146880 square inches.

2. The perimeter of the park can be calculated by summing up the lengths of all sides.

The lengths of the sides in feet would be:

Side1 = 28 inches * 1.5 feet/inch = 42 feet

Side2 = 40 inches * 1.5 feet/inch = 60 feet

Side3 = 16 inches * 1.5 feet/inch = 24 feet

Adding up all sides, we have:

Perimeter = Side1 + Side2 + Side3 = 42 feet + 60 feet + 24 feet = 126 feet

Therefore, the perimeter of the park is 126 feet.

3. To find the percentage length of the south side compared to the north side, we can calculate:

Percentage = (South Side Length / North Side Length) * 100

Using the scale, the length of the south side in feet would be:

South Side Length = 16 inches * 1.5 feet/inch = 24 feet

The length of the north side is already given as 40 inches * 1.5 feet/inch = 60 feet.

Plugging in the values, we have:

Percentage = (24 feet / 60 feet) * 100 = 40%

Therefore, the length of the south side of the park is 40% of the length of the north side.

Complete Question:

Mikea, an intern with the Parks and Recreation Department, is developing a proposal for the new trapezoidal Springdale Park. The figure below shows her scale drawing of the proposed park with 3 side lengths and the radius of the merry-go-round given in inches. In Mikea's scale drawing, 1 inch represents 1.5 feet.

1. What is the area, in square inches, of the scale drawing of the park? 448 544 H. 640 672 K. 1.088

2. Mikea's proposal includes installing a fence on the perimeter of the park. What is the perimeter, in feet, of the park? A. 84 B. 88 C. 104 D. 126 E 156

3. The length of the south side of the park is what percent of the length of the north side? F. 112% G. 1245 H. 142 J. 1754 K. 250%

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2 x 3 = 3 x 2

Explanation:

The commutative property of multiplication says we can multiply any two numbers in any order we want. The general rule is a x b = b x a, where x represents the multiplication symbol. The 'a' and 'b' can be any two numbers you want.

Choice C shows an example of this. Either side simplifies to 6.

Another example would be 4 x 5 = 5 x 4 where both sides become 20.

Answer:

Step-by-step explanation:

x+60=140

x=140-60

x=80 degree

Answer:

D. 1,2,4......... . .....

Answer:

Step-by-step explanation:

C) 2 and 4

it is a rectangle (from the signs on the picture)

it is a parallelogram (from the interior angles)

Answer:

a: (inf,inf) b: (3,0) c: pos. (inf, 0] neg. (0, inf)

Step-by-step explanation:

a: the graph stretches infinitely left to right.

b: the filled in dot means it includes the number, while empty ones means it does not.

c: brackets mean it also includes the number, so be sure to add that.

-Mr. Willams

Good luck with your homework.

Answer:

The rise divided by the run is the slope of a line. The rise and run are used to estimate the slope of a line from its graph.

To determine the intercepts from a graph,  We put y equal to zero and solve for x to find the x-intercept. Similarly, we put x equal to zero and solve for y to find the y-intercept.

Answer:

1/6

Step-by-step explanation:

hope this helps!!

Answer:

1/6

Step-by-step explanation:

1/2 ÷ 3 → 1/2 ÷ 3/1     *Let's write both as fractions to make things easier

1/2 ÷ 3/1  → 1/2 · 1/3    *Change the division sign into multiplication and turn      3/1 into its reciprocal which is 1/3 (aka just change the numerator into denominator and denominator into numerator)

1/2 · 1/3 = 1/6   *Multiply straight across! So, 1 · 1 = 1 (numerator) over 2 · 3 = 6 (denominator)

The ball will take 5.4s to attain a height of 213ft

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

In this case, we simply input the value of s = 213 and solve the quadratic equation.

s(t) = -16t² + 126t

213 = -16t² + 126t

-16t² + 126t - 213 = 0

t = 5.4s

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The pmf of the sum when rolling these two dice is as follows:

Sum  | Probability
-----|------------
2    | 1/36
3    | 1/18
4    | 1/36
5    | 1/18
6    | 1/18
7    | 1/18
8    | 1/18
9    | 1/18
10   | 1/18
11   | 1/18
12   | 1/36

The pmf (probability mass function) of the sum when rolling two six-sided dice can be calculated by determining the probability of each possible sum.

To find the pmf, we need to consider all the possible outcomes when rolling the two dice. We will calculate the probability for each sum and then normalize the probabilities to add up to 1.

Let's list all the possible sums and their corresponding probabilities:

- The sum can be 2 when both dice show a 1. The probability of this is (1/6) * (1/6) = 1/36.
- The sum can be 3 when one die shows a 1 and the other die shows a 2. There are two possible combinations: (1, 2) and (2, 1). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 3 is 2 * (1/36) = 1/18.
- The sum can be 4 when one die shows a 2 and the other die shows a 2. The probability of this is (1/6) * (1/6) = 1/36.
- The sum can be 5 when one die shows a 2 and the other die shows a 3. There are two possible combinations: (2, 3) and (3, 2). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 5 is 2 * (1/36) = 1/18.
- The sum can be 6 when one die shows a 2 and the other die shows a 4. There are two possible combinations: (2, 4) and (4, 2). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 6 is 2 * (1/36) = 1/18.
- The sum can be 7 when one die shows a 3 and the other die shows a 4. There are two possible combinations: (3, 4) and (4, 3). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 7 is 2 * (1/36) = 1/18.
- The sum can be 8 when one die shows a 3 and the other die shows a 5. There are two possible combinations: (3, 5) and (5, 3). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 8 is 2 * (1/36) = 1/18.
- The sum can be 9 when one die shows a 3 and the other die shows an 8. There are two possible combinations: (3, 8) and (8, 3). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 9 is 2 * (1/36) = 1/18.
- The sum can be 10 when one die shows a 4 and the other die shows a 5. There are two possible combinations: (4, 5) and (5, 4). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 10 is 2 * (1/36) = 1/18.
- The sum can be 11 when one die shows a 4 and the other die shows an 8. There are two possible combinations: (4, 8) and (8, 4). The probability of each combination is (1/6) * (1/6) = 1/36. So, the total probability for a sum of 11 is 2 * (1/36) = 1/18.
- The sum can be 12 when one die shows a 8 and the other die shows an 8. The probability of this is (1/6) * (1/6) = 1/36.

Now, let's add up all the probabilities:
(1/36) + (1/18) + (1/36) + (1/18) + (1/18) + (1/18) + (1/18) + (1/18) + (1/18) + (1/18) + (1/36) = 1/2

Therefore, the pmf of the sum when rolling these two dice is as follows:

Sum  | Probability
-----|------------
2    | 1/36
3    | 1/18
4    | 1/36
5    | 1/18
6    | 1/18
7    | 1/18
8    | 1/18
9    | 1/18
10   | 1/18
11   | 1/18
12   | 1/36

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Answer:

d or c

Step-by-step explanation:

Answer:

2/5

Step-by-step explanation:

Since the formula for grid's are y by x Y=2 X=5 put them as a fraction there you have 2/5 as I think it is

Answer:

The Answer would be ∠W ≅ ∠C

Step-by-step explanation:

Only one that is congruent

The measure of the angle ∠TWM is congruent to the measure of the angle ∠ADC. Therefore, the correct option is B.

Two triangles are said to be congruent if their corresponding sides and angles are equal.

A triangle is a three-sided polygon with three edges and three vertices in geometry.

Given that the triangle ∆MTW is congruent to the triangle ∆CAD.

So, we have

∠MTW ≅ ∠CAD

∠WMT ≅ ∠DCA

∠TWM ≅ ∠ADC

If two triangles are equivalent, the ratio of matching sides will stay constant.

The proportion of the point ∠TWM is harmonious with the proportion of the point ∠ADC.

Therefore, at that point, the right choice is B.

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Answer:

875 \(ft^{2}\)

Step-by-step explanation:

There are more than 1 way to look at this.  I look at the big rectangle starting from the bottom on the graph up until the very last blue section that would not be part of the rectangle.

25 x 30 = 750

Then I looked at the very top blue part and broke that into 2 triangles and I rectangle.

The rectangle would be

20 x 5 = 100

The two triangles together would be

5 x5 = 25

750 + 100 + 25 = 875

The representation that yields the same outcome as the recursive arithmetic sequence is given as follows:

\(a_n = -1 + 4n\)

An arithmetic sequence is a sequence of values in which the difference between consecutive terms is constant and is called common difference d.

The nth term of an arithmetic sequence is given by the explicit formula presented as follows:

\(a_n = a_1 + (n - 1)d\)

The first term of the sequence is given as follows:

\(a_1 = 3\)

From the recursive formula, each term is obtained subtracting the previous term by 4, hence the common difference is given as follows:

d = 4.

Then the explicit formula is:

\(a_n = 3 + 4(n - 1)\)

\(a_n = 3 + 4n - 4\)

\(a_n = -1 + 4n\)

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We have that if we have 30 students, 22 of them will have brown hair. This can be expressed as the relation:

30 students ⇔ 22 students with brown hair

If there are 180 students, we have a certain number of students with brown hair

180 students ⇔ ??

Then, we have the following equivalence

180 students ⇔ ??

30 students ⇔ 22 students with brown hair

If we divide each side of the equivalence we will have the same result:

We want to find the number ??, then we take 22 to the left side of the equation:

Then, we can predict that there will be 132 students with brown hair.

Answer: 132

Answer:

B, D, and E

Step-by-step explanation:

You'll have to distribute each and put them into a full equation again.

A. -3x + 24

B. -3x - 24

C. -3x + 24

D. -3x - 8/3

E. -3x - 24

F. -3x + 24

I bolded the ones that did not equal -3x + 24

so your answer is B, D, and E

Answer:

\({ \tt{ {x}^{2} + 6x + 2 = 0}} \\ { \tt{ {x}^{2} + 6x = - 2 }}\)

- Add the square of the half of the sum on either sides:

\({ \tt{ {x}^{2} + 6x + ( { \frac{6}{2}) }^{2} = - 2 + {( \frac{6}{2}) }^{2} }} \\ \\ { \tt{ {x}^{2} + 6x + 9 = - 2 + 9}} \\ { \tt{ {(x + 3)}^{2} = 7}} \\ { \tt{x + 3 = \sqrt{7} }} \\ { \tt{x = - 3 \pm2.648}} \\ { \tt{x = ( - 3 \pm \sqrt{7} )}}\)

Answer:

60.5・105.1 = 6,358.55

Step-by-step explanation:

To find the Highest Common Factor (H.C.F.) of 567 and 255 using Euclid's division lemma, we can follow these steps:

Step 1: Apply Euclid's division lemma:

Divide the larger number, 567, by the smaller number, 255, and find the remainder.

567 ÷ 255 = 2 remainder 57

Step 2: Apply Euclid's division lemma again:

Now, divide the previous divisor, 255, by the remainder, 57, and find the new remainder.

255 ÷ 57 = 4 remainder 27

Step 3: Repeat the process:

Next, divide the previous divisor, 57, by the remainder, 27, and find the new remainder.

57 ÷ 27 = 2 remainder 3

Step 4: Continue until we obtain a remainder of 0:

Now, divide the previous divisor, 27, by the remainder, 3, and find the new remainder.

27 ÷ 3 = 9 remainder 0

Since we have obtained a remainder of 0, the process ends here.

Step 5: The H.C.F. is the last non-zero remainder:

The H.C.F. of 567 and 255 is the last non-zero remainder obtained in the previous step, which is 3.

Therefore, the H.C.F. of 567 and 255 is 3.

The 21 square root of 98 divided by 7 square root of 21 = 21√98 / 7√21 = 6.4807407

A square root of a number x is a number y such that y2 = x; in other words, a number y who's square and the result of multiplying the number by itself, or y ⋅ y, is x.

Every nonnegative real number x has a unique nonnegative square root, called the principal square root, which is denoted by √where the symbol √ is called the radical sign.

Every positive number x has two square roots: √ which is positive, and -√ which is negative. The two roots can be written more concisely using the ± although the principal square root of a positive number is only one of its two square roots, the designation "the square root" is often used to refer to the principal square root.

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The angles of a triangle with side lengths 5 , 12 and 13 are 90°, 22.63°, 67.38°.

In trigonometry, the law of cosines, also known as the law of cosines or cosine formula, basically relates the length of a triangle to one cosine of its angle. It states that if we know the lengths of two sides of a triangle and the angle between them, we can determine the length of the third side. c² = a²+ b² – 2ab cosγ

where a, b, c are the sides of the triangle and γ is the angle between a and b, see image above.

To find the length of a side of a triangle, take △ABC according to the cosine formula, which can be written as follows.

We have , a = 5 , b = 12 , c= 13

cos α =( 12² + 13² - 5² )/2×12×13= 288/312

=> α = cos⁻¹(0.923 ) = 22.63°

cos β = (5² + 13² - 12² )/2×13×5 = 50/130

=> β = cos⁻¹(5/13) = 67.38°

cos γ = (12² + 5² - 13² )/2×12×5= 0

=> γ = cos⁻¹(0) = 90°

Hence, the required angles are 90°, 22.63°, 67.38°.

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The correct answer is D. f(x) = 11x - 4 and g(x) = (x + 4)/11

To determine which pair of functions are inverses of each other, we need to check if the composition of the functions results in the identity function, which is f(g(x)) = x and g(f(x)) = x.

Let's test each option:

Option A:

f(x) = x/2 + 15

g(x) = 12x - 15

f(g(x)) = (12x - 15)/2 + 15 = 6x - 7.5 + 15 = 6x + 7.5 ≠ x

g(f(x)) = 12(x/2 + 15) - 15 = 6x + 180 - 15 = 6x + 165 ≠ x

Option B:

f(x) = ∛3x

g(x) = (x/3)^3 = x^3/27

f(g(x)) = ∛3(x^3/27) = ∛(x^3/9) = x/∛9 ≠ x

g(f(x)) = (∛3x/3)^3 = (x/3)^3 = x^3/27 = x/27 ≠ x

Option C:

f(x) = 3/x - 10

g(x) = (x + 10)/3

f(g(x)) = 3/((x + 10)/3) - 10 = 9/(x + 10) - 10 = 9/(x + 10) - 10(x + 10)/(x + 10) = (9 - 10(x + 10))/(x + 10) ≠ x

g(f(x)) = (3/x - 10 + 10)/3 = 3/x ≠ x

Option D:

f(x) = 11x - 4

g(x) = (x + 4)/11

f(g(x)) = 11((x + 4)/11) - 4 = x + 4 - 4 = x ≠ x

g(f(x)) = ((11x - 4) + 4)/11 = 11x/11 = x

Based on the calculations, only Option D, where f(x) = 11x - 4 and g(x) = (x + 4)/11, satisfies the condition for being inverses of each other. Therefore, the correct answer is:

D. f(x) = 11x - 4 and g(x) = (x + 4)/11

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Answer:

: If you're anxious, scared or frustrated, take time to feel things around you as you speak to calm down. This can be paper or the surface you're sitting on. It works for me at least. I think this will help. You can also lightly tap on your computer for a rhythm. I hope this helps all of you. I know it's too late but maybe next time it will help. Sorry for the long message.

Step-by-step explanation:

And D should be ur answer.

Answer:

i think is O(-.3.2.1 is it that

The total time it takes the soccer ball to hit the ground, which bounces up at a velocity of 20 feet per second, is 1.535 seconds.

Vertical motion model is the model which is used to find the height of the object which is thrown vertically upward. It can be given as,

\(h(t)=-16t^2+v+t\)

Here, t is time and v is velocity.

Soccer player jumps up and heads the ball while it is 7 feet above It bounces up at a velocity of 20 feet ground. per second.  Thus, the vertical motion model for this situation is,

\(h(t)=-16t^2+20t+7\)

When the ball hit the ground, the value of height (h) become zero. Thus,

\(0=-16t^2+20t+7\\16t^2-20t-7=0\)

On solving this quadratic, the value of x we get,

\(x=1.535,x=-0.285\)

Taking positive side x=1.535 second. Thus, the total time it take the soccer ball to hit the ground which bounces up at a velocity of 20 feet per second, is 1.535 seconds.

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The volume of the remaining portion of the sphere is 2.096 cubic units.

Let's take the volume of the remaining portion of the sphere = V

The volume of the sphere = \(\frac{4}{3}\) * π * \(r^3\)

The volume of the sphere with radius 1  = 4/3 * π

The volume of the cylinder = π * \(r^2\) * h

The volume of the cylinder with height 2 and radius 1 = π * \(r^2\) * h = 2 * π.

The difference between the volume of the sphere and the cylinder is

V = 4/3 * π - 2 * π = 4/3 * π - 2 * π = 2/3 * π.

By taking π = 3.14

V = \(\frac{2}{3}\) * 3.14

V= 2.096.

So, the volume of the remaining portion of the sphere is 2.096 cubic units.

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Answer:

180-130=50

Step-by-step explanation:

done hope you like it

i use the 180 because its a straight line from the x to the 130

Answer:

80.32%

Step-by-step explanation:

The proportion who approved of the mayor :

p = number who approved of the mayor / total respondents = 1640 / 2000 = 0.82

The confidence interval for proportion is given by :

p ± Zcritical * √p(1 - p) / n

Zcritical at 95% = 1.96 (Z standard table distribution)

0.82 ± 1.96 * √0.82(0.18) / 2000

0.82 ± 1.96 * 0.0085906

0.82 ± 0.0168377

(0.8032 ; 0.8368)

Lower boundary = 0.8032

Answer:

See image below

Step-by-step explanation:

Among the three variants of the SPI (Specific, Precise, and Impression) model, the Specific model exhibits the best flexibility, while the Impression model demonstrates the best optimization.

The Specific model excels in flexibility because it focuses on generating highly specific responses. It tends to produce detailed and accurate information based on the given input.

This flexibility allows users to obtain precise answers to their queries, making it particularly useful for tasks requiring specific knowledge, such as providing instructions, explaining concepts, or offering specific recommendations.

The Specific model's ability to generate focused responses enhances its flexibility for various use cases.

On the other hand, the Impression model stands out in optimization. It excels at generating responses that are more creative, imaginative, and subjective.

It has been optimized to prioritize generating impressive or entertaining output. This model is particularly suited for tasks that require engaging and captivating content, such as storytelling, generating ideas, or creative writing.

The Impression model's optimization focuses on generating outputs that leave a lasting impression on the audience, making it the best choice for such scenarios.

In summary, while the Specific model offers the best flexibility by providing specific and detailed information, the Impression model shines in optimization, generating impressive and captivating responses.

The choice between the two depends on the specific requirements of the task at hand, whether it demands precision or creativity.

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