2079 [Optional] Set A Q.No. 20a] In how many different ways can the letters of the word "DETERRANT" be arranged so that the repeated letters do not come together?
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24-gon is the regular polygons has a perimeter that would be closest to circumference of a circle with the same radius

The closer a regular polygon's range of facets is to infinity, the closer its perimeter will be to the circumference of a circle with the identical radius.

Therefore, the answer is the 24-gon, which has greater facets than the octagon and the dodecagon but fewer facets than the 15-gon.

This makes the 24 - gon the most appropriate answer isnce it has more faces

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The regular polygons which has a perimeter that would be closest to the circumference of a circle with same radius is a; 24-gon.

It follows from the task content that the regular polygon which would have a perimeter closest to circumference of a circle with the same radius is to be determined.

By observation, the greater the number of sides of a regular polygon, the greater is its perimeter and the closer is its perimeter to the circumference of a circle with same radius.

Therefore, the answer choice which is correct is; 24-gon.

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Based on the given data, the probabilities of the spinner landing on each color are approximately:

Red: 0.3469

Blue: 0.2449

Green: 0.0816

Yellow: 0.2449

Purple: 0.0816

To calculate the probability of the spinner landing on a specific color, we need to divide the frequency of that color by the total number of spins.

Given the spinner results:

Color Frequency

Red 17

Blue 12

Green 4

Yellow 12

Purple 4

To find the probability of landing on a specific color, we divide the frequency of that color by the total number of spins:

Probability (Red) = Frequency (Red) / Total Spins

= 17 / (17 + 12 + 4 + 12 + 4)

= 17 / 49

= 0.3469 (rounded to four decimal places)

Probability (Blue) = Frequency (Blue) / Total Spins

= 12 / 49

= 0.2449 (rounded to four decimal places)

Probability (Green) = Frequency (Green) / Total Spins

= 4 / 49

= 0.0816 (rounded to four decimal places)

Probability (Yellow) = Frequency (Yellow) / Total Spins

= 12 / 49

= 0.2449 (rounded to four decimal places)

Probability (Purple) = Frequency (Purple) / Total Spins

= 4 / 49

= 0.0816 (rounded to four decimal places)

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The large box weighs 18.75 kg, and the small box weighs 15.75 kg.

We have,

Let's assume the weight of a large box is L kg, and the weight of a small box is S kg.

According to the given information, we can create the following equations:

Equation 1: 3L + 5S = 135 (1st delivery)

Equation 2: 9L + 7S = 279 (2nd delivery)

To solve these equations, we can use a method called "elimination" or "substitution."

Multiply Equation 1 by 3 and Equation 2 by 1, so that the coefficients of L will be the same:

Equation 1: 9L + 15S = 405

Equation 2: 9L + 7S = 279

Now, we can subtract Equation 2 from Equation 1 to eliminate L:

(9L + 15S) - (9L + 7S) = 405 - 279

Simplifying:

8S = 126

Divide both sides of the equation by 8:

S = 126/8 = 15.75

So, the weight of a small box (S) is 15.75 kg.

Now,

substitute the value of S into Equation 1 to find the weight of a large box (L):

3L + 5(15.75) = 135

3L + 78.75 = 135

3L = 135 - 78.75

3L = 56.25

Divide both sides of the equation by 3:

L = 56.25/3 = 18.75

So,

The weight of a large box (L) is 18.75 kg.

Thus,

The large box weighs 18.75 kg, and the small box weighs 15.75 kg.

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Answer: line a is parallel to line b

Step-by-step explanation:

the only 2 lines they're talking abt are line a and line b

Answer:15/17 or 0.88

Step-by-step explanation:

Answer:

113.1 in²

Step-by-step explanation:

A = 2πrh + 2πr²

r = 2 in

h = 7 in

A = 2π(2)(7) + 2π2² = 113.1 in²

There are 1440 minutes in a day (24 hours x 60 minutes = 1440 minutes).

To convert 4320 minutes to days, divide 4320 by 1440:

4320 ÷ 1440 = 3

Therefore, 4320 minutes is equivalent to 3 days.

Answer: 3 days

Step-by-step explanation:

The length of wire is 82.78 foot.

After guiding wire,

It form a right angle triangle which have

One angle is of 65 degree

perpendicular = 75 foot

And we have to find hypotenuse of the triangle which is length of wire.

Since we know that,

The trigonometric ratio sin is the ratio of opposite side of angle and

hypotenuse.

Therefore,

⇒ Sin65 = 75/hypotenuse

⇒ 0.906 = 75/hypotenuse

⇒  hypotenuse = 82.7 foot

Since hypotenuse of triangle represents  length of wire

So, required length of wire is 82.7 foot.

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The actual bridge deck measures 4,320 square feet in size.

First, we need to convert the scaled dimensions to actual dimensions. Since the scale is 60:1, we need to multiply the scaled dimensions by 60 to get the actual dimensions.

The scaled length of the bridge deck is 36 inches, so the actual length is:

36 inches x 60 = 2,160 inches

The scaled width of the bridge deck is 4 4/5, or 24/5, inches. So the actual width is:

24/5 inches x 60 = 288 inches

To find the area of the actual bridge deck in square feet, we need to convert the actual dimensions to feet and then multiply:

Actual length in feet = 2,160 inches ÷ 12 inches/foot = 180 feet

Actual width in feet = 288 inches ÷ 12 inches/foot = 24 feet

Area in square feet = Actual length x Actual width = 180 ft x 24 ft = 4,320 square feet

Therefore, the area of the actual bridge deck in square feet is 4,320 square feet.

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Answer:

2

Step-by-step explanation:

First, we need to arrange the data in order. We can convert the mixed numbers to improper fractions for ease of comparison:

1/3, 2/1, 4/1, 1/1, 7/3, 4/5, 5/2

Now, let's arrange them in ascending order:

1/3, 4/5, 1, 7/3, 2, 5/2, 4

The median is the middle value in the data set. Since we have an odd number of values, the median is the middle value when the data is arranged in order. Therefore, the median is:

median = 2

Therefore, the correct option is C

Answer:

1.5

Step-by-step explanation:

1/3    2    4    1    7    2/3    4/5    5/2

Write the numbers in ascending order.

1/3    2/3    4/5    1    2    5/2    4    7

The median is the middle value if there is an odd number of numbers.

If there is an even number of numbers, the median is the mean of the middle two numbers.

Here, there are 8 values, so we do the mean of the middle 2 values.

median = (1 + 2)/2

median = 1.5

Descriptive Statistics for Variables in the Study

Variable Mean Standard Deviation Skewness Kurtosis

Variable1 10.2 2.1 -0.15 2.8

Variable2 15.3 3.2 0.10 3.2

Variable3 20.1 4.5 -0.05 2.9

Variable4 8.9 1.8 0.30 3.5

Based on Table 1, we can see that all variables have skewness and kurtosis values within the acceptable range of -2 to +2. This suggests that the assumption of normality is not violated, and the variables are normally distributed.

The results of the normality test indicate that the assumption of normality is not violated, and the variables are normally distributed. Therefore, we can proceed with the correlation analysis.

Skewness measures the degree of asymmetry of the distribution, with positive values indicating a right-skewed distribution, negative values indicating a left-skewed distribution, and a value of zero indicating a symmetrical distribution.

Kurtosis measures the degree of peakedness of the distribution, with positive values indicating a more peaked distribution than a normal distribution, negative values indicating a less peaked distribution than a normal distribution, and a value of zero indicating a normal distribution.

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The conic section of the equation 4x² + 9x +4y² - 36y - 125 = 0 is a circle

The given equation is

4x² + 9xy + 4y² - 36y - 125 =0

The above equation is an illustration of a circle equation

The standard form of a circle equation is

(x - a)² + (y - b)² = r²

Where

(a, b) is the center

r is the radius

While the general form of the equation is

ax² + fx + by² + gy + c =0

Where c is a constant

Recall that, we have

4x² + 9x + 4y² - 36y - 125 =0

This is the general form

We can convert to the standard form as follows

Divide through by 4

x² + 2.25x + y² - 9y - 31.25 =0

Next, we complete the square of the x-terms and the y-terms

For the x-terms, we have

x² + 2.25x = x² + 2.25x + (2.25/2)² - (2.25/2)²

x² + 2.25x = (x + 2.25/2)² - (2.25/2)²

For the y-terms, we have

y² - 9y = y² - 9y + (9/2)² - (9/2)²

y² - 9y = (y - 9/2)² - (9/2)²

Substitute the new x and y terms

So, x² + 2.25x + y² - 9y - 31.25 = 0 becomes

(x + 2.25/2)² - (2.25/2)² + (y - 9/2)² - (9/2)²- 31.25 =0

Evaluate the sum of like terms

(x + 2.25/2)² + (y - 9/2)² - 3377/64 = 0

So, we have

(x + 9/8)² + (y - 9/2)² = 3377/64

Using the above as a guide, we can conclude that the conic section of the equation is a circle

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The upper quartile line of the box plot be placed at D

The left and right sides of the box are the lower and upper quartiles.

In the given figure the A represents the minimum value

The point E represents the maximum value

The point B is the lower quartile of the data

The point C is median of the data

The point D is the upper quartile which is 56

Hence, the upper quartile line of the box plot be placed at D

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If owners of a recreation area are filling a small pond with water.  The  total amount of water after 13 minutes is 1016 liters.

Let the total amount of water in the pond = W

Let the total number of minutes that water has been added = T

The equation relating W to T Is:

W = 600 + 32T

Where:

600=  initial amount of water in the pond

32T = additional water added over time

Now let find the  total amount of water in the pond after 13 minutes

Substitute T = 13 into the equation:

W = 600 + 32(13)

W = 600 + 416

W = 1016

Therefore the total amount of water is 1016 liters.

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There are three dots in the greatest height recorded.

We have,

From the table,

We see that,

The greatest height is 75 inches.

The lowest height is 62 inches.

Now,

If we make a line plot with dots above the height as:

*                                      *

*          *        *        *        *

*          *        *        *        *

62     66     68     72     75

Thus,

There are three dots in the greatest height recorded.

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Answer:

Step-by-step explanation:

hoop 132

All the values of a 12-sided die will be represented by two 6-sided die. The probability of rolling a 7 on the 12-sided die is 1/12 and rolling a sum of 7 on the two 6-sided dice will be 1/6.

The 12-sided die which is dodecahedral consists of numbers up to 12. The 6-sided die consists of numbers up to 6. The suggestion of using two 6-sided dice instead of a 12-sided die will make a difference in the probabilities of a specific outcome.

Although, using a pair of 6-sided dice and adding their scores will represent all the values or outcomes you can get in a 12-sided die but still there will be a difference in the probabilities.

If we find the probability of rolling 7 on the 12-sided die, then it will be 1/12.

But, in the case of two 6-sided dice, we will obtain the sum of 7 in 6 outcomes which are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). The total number of outcomes, in this case, is 36.

Therefore, the probability of rolling a sum of 7 on the two 6-sided dice will be 6/36   =  1/6.

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Answer:

9.6 miles per hour

Step-by-step explanation:

The rate is 4/25 miles per minute

To convert to miles per hour, since there are 60 minutes in an hour, multiply:  4/25 x 60

= 240/25

= 9.6 miles per hour

The segment lengths for this problem are given as follows:

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates given by [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Hence the length of segment AB is given as follows:

[tex]AB = \sqrt{(2 - (-5))^2 + (4 - 4)^2} = 7[/tex]

The length of segment AE is given as follows:

[tex]AE = \sqrt{(-5 - (-5))^2 + (4 - (-5))^2} = 9[/tex]

The length of segment BC is given as follows:

[tex]BC = \sqrt{(5-4)^2 + (5 - (-5))^2} = 10.05[/tex]

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The Sanjay method used  to calculate the median is an incorrect formula. The correct value of the median is 7.5 kilometers.

Given:

the distances traveled by the Sanjay on his recent walks - 5, 6, 6, 7, 8, 8, 9, 9

The Median which is calculated by Sanjay = 7 kilometers

We need to find the mistake that Sanjay made in calculating the median

Solution:

We have the following data

5, 6, 6, 7, 8, 8, 9, 9

There are an even number of values, the median is determined by determining the average of the n/2th term and {(n/2) + 1}th term, where:

n = total number of values

= n/2

= 8/2

= 4

= (n/2) + 1

= (8/2) + 1

= 5

The 4th value in the given data = 7

The 5thvalue in the given data = 8

The median is the average of 7 and 8 = (7 + 8)/2 = 7.5

Therefore, the median will be the 7.5

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The weight of the 0.8-meter piece is 19.6 kilograms.

We can use the ratio of length to weight to determine the weight of the 0.8-meter piece.

Let's call the weight of the 2.8-meter piece "W₁" and the weight of the 0.8-meter piece "W₂". Then we have:

W₁/2.8m = 24.5kg/1m

Solving for W₁, we get:

W₁ = (24.5kg/1m) x 2.8m = 68.6kg

Now we can use the same ratio to find W₂:

W₂/0.8m = 24.5kg/1m

Solving for W₂, we get:

W₂ = (24.5kg/1m) x 0.8m = 19.6kg

Therefore, the weight of the 0.8-meter piece is 19.6 kilograms.

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We can match the numbers in Column I with their square roots in Column II as follows:

1. √844 = C. 29.1

2. √900 = H. 30

3. √650 = G. 25.5

4. √784 = E. 28

5. √699 = B. 26.4

6. √805 = D. 28.4

7. √729 = A. 27

To find the square roots of the numbers, we can simply punch the sign into the calculator and insert the figures in it. For instance, to find the square root of 900, we can simply insert the figure into the calculator while inputting the square root sign before it.

To determine if your answer is correct, try squaring the numbers. The output should be the original numbers provided.

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Answer:

Step-by-step explanation:

PEMDAS (order in which to do operations)

P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction

there are no parentheses so skip that

5^2 is an exponent so do that first

3x10 + 3x5^2 + 3 -->    3 x 10 + 3 x 25 + 3

Next, do multiplication/division operations from left to right

3 x 10 + 3 x 25 + 3 -->    30 + 75 + 3

Finally, do the addition operations

30 + 75 + 3 = 108

final answer: 108

The coefficient of a²b² in the expansion of (2a - b)⁴ is 24

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

(2a - b)⁴

When the expression is expanded, we have

(2a-b)⁴ = (2a-b)(2a-b)(2a-b)(2a-b)

So, we have

(2a-b)⁴ = 16a⁴ - 32a³b + 24a²b² - 8ab³ +b⁴

Consider an expression ax where the variable is x

The coefficient of the variable in the expression is a

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

The coefficient of a²b² in the expansion is 24

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Answer:

259.8

Step-by-step explanation:

The apothem of a regular polygon is a segment whose endpoints are the center of the polygon and the midpoint of one side.

Look at the bottom of the drawing. The dimension 17.32 is the distance between two opposite parallel sides of the regular hexagon base. If you draw a segment that is parallel to two opposite sides of the hexagon and passes through the center of the hexagon, it is twice the length of the apothem.

Here,

apothem = 17.32/2 = 8.66

If you divide the hexagon into 6 congruent triangles, each triangle is an equilateral triangle. Then the side of the hexagon measures 10.

A = 1/2 pa

p = perimeter = 6 × side length = 6 × 10

a = apothem = 8.66

A = 1/2 × (6 × 10) × 8.66

A = 259.8

Answer: 9" x 10" x 11" = 990 cubic inches.

990 cubic inches / 5 minutes = 198 cubic inches per minute

22" x 23" x 33" = 16698 cubic inches

16698/198 = 84 and 1/3 minutes

1 hour 24 minutes and 20 seconds

The required measure of side GH is 23.25, and measures of angles G and H are 64.5° and 25.5°.

From the given figure,
The measure of GH is given by, the Pythagorean theorem,
GH = √[10² + 21²]
GH = 23.25

Now applying the trig ratio to determine, angles H and G,
tang=21/10
G = tan⁻¹[21/10]
G = 64.53°

Similarly,
H = 25.5°

Thus, the required measure of side GH is 23.25, and measures of angles G and H are 64.5° and 25.5°.

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