For a rectangle with a perimeter of 20 cm, the width of the rectangle is one-third its length. Use an equation to find the length and width of the rectangle.

Answer:

(a) To find the mean of the data set, sum up all the values and divide by the total number of values.

44 + 44 + 54 + 54 + 65 + 39 + 54 + 44 = 398

Mean = 398 / 8 = 49.75

Rounded to one decimal place, the mean of this data set is 49.8.

(b) To find the median of the data set, i need to arrange the values in ascending order first:

39, 44, 44, 44, 54, 54, 54, 65

The median is the middle value in the sorted data set. In this case, we have 8 values, so the median is the average of the two middle values:

(44 + 54) / 2 = 98 / 2 = 49

Rounded to one decimal place, the median of this data set is 49.0.

(c) To determine the modes of the data set, identify the values that appear most frequently.

In this case, the mode refers to the value(s) that occur(s) with the highest frequency.

From the data set, i see that the value 44 appears three times, while the value 54 also appears three times. Therefore, there are two modes: 44 and 54.

Answer:

468

Step-by-step explanation:

Area of trapezoid=1/2 *h(l1+l2)

=1/2*18*(15+37)

=9*52

=468

The rule for a dilation with center at (0,0) and scale factor k is:

Find the transformed vertices A'. B', C' and D' using this rule:

Similarly, the coordinates of B', C' and D' wil be:

Plot A', B', C' and D' along with A, B, C and D:

Answer:

y=−2x+8

Step-by-step explanation:

https://socratic.org/questions/how-do-you-write-an-equation-of-a-line-with-slope-2-y-intercept-8

Answer:

The answer is -81.

Step-by-step explanation:

Let me know if I got it wrong.

The two numbers required to be solved for in the word problem are:

the greater, x = 47

the smaller, y = 24

let x represent the greater number and the smaller number be y

From the problem it can be deuced that the sum of the two numbers is 71 therefore

x + y = 71

The difference of the two numbers is 23

x - y = 23

the two equations are

x + y = 71

x - y = 23

adding the equations

2x = 94

x = 47

substituting for y

47 - y = 23

y = 47 - 23

y = 24

the two numbers are 47 and 24

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Answer:

the base area is 20,000

2 x 20,000 = 40,000

The given sequence is not a geometric sequence since there is no common ratio between the terms. However, we can still find the sum of the first 9 terms by adding them individually.

First term, a1 = 3

Second term, a2 = -15

Third term, a3 = 75

Sum of the first 9 terms:

3 + (-15) + 75 + 3 + (-15) + 75 + 3 + (-15) + 75

= 204

Therefore, the sum of the first 9 terms of the given sequence is 204.

Probability that the point is in the shaded circular region = 0.79

The area of a square = l²

Each side of the square, l = 8 in

Area of the square = 8²

Area of the square region = 64 in²

The area of the circular region is given by the formula:

Area of the circle = πr²

Radius of the circle, r = 4 in

π = 3.14

Area of the circular region = 3.14 x 4²

Area of the circular region = 3.14 x 16

Area of the circular region = 50.24 in²

The circular region is the shaded region

The square region is the total region

Probability that point is in the shaded region =

(Area of the shaded region)/(Total area)

Probability that point is in the shaded region = 50.24/64

Probability that point is in the shaded region = 0.79

Answer:

C and E

Step-by-step explanation:

23 > 16 and \(23\geq 16\) are both true statements since the quantity of 23 is greater than that of 16.

The polar coordinates of (1, -9) are (9.06, -1.47 radians).

To convert from rectangular coordinates to polar coordinates, we can use the following formulas:

r = √(x² + y²)

θ = tan⁻¹(y/x)

where r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.

In this case, x = 1 and y = -9. Plugging these values into the formulas, we get:

r = √(1² + (-9)²) = √82 ≈ 9.06

θ = tan⁻¹((-9)/1) ≈ -1.47 radians

Therefore, the polar coordinates of (1, -9) are (9.06, -1.47 radians). The distance from the origin to the point is approximately 9.06 units, and the angle between the positive x-axis and the line connecting the origin to the point is approximately -1.47 radians (or approximately -84.26 degrees).

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Answer:

∠ BDC = 29°

Step-by-step explanation:

the sides of a rhombus are congruent, so CD = ED and Δ EDC is therefore isosceles with base angles congruent , then

∠ BCD = ∠ BED = 61°

• the diagonals are perpendicular bisectors of each other , then

∠ CBD = 90°

the sum of the 3 angles in Δ BCD = 180°

∠ BDC + ∠ CBD + ∠ BCD = 180°

∠ BDC + 90° + 61° = 180°

∠ BDC + 151° = 180° ( subtract 151° from both sides )

∠ BDC = 29°

If the triangle on the left had the same area as the circle on the right, it would require more resources and potentially be more unstable than the current configuration.

If the triangle on the left had the same area as the circle on the right, it would mean that the triangle would have to be larger than its current size. This is because the area of a circle is determined by the formula A=πr^2, where r is the radius of the circle.

Therefore, if the area of the circle is equal to the area of the triangle, the radius of the circle would have to be equal to the height of the triangle, and the base of the triangle would need to be wider.

This would result in a larger triangle with a greater surface area than the current triangle. The larger triangle would also have a longer perimeter, which would make it more difficult to enclose and would require more material to construct.

Additionally, the larger triangle would have a higher center of gravity, which could make it more difficult to balance and more prone to tipping over.

Overall, if the triangle on the left had the same area as the circle on the right, it would require more resources and potentially be more unstable than the current configuration.

It is important to consider both the area and the shape of an object when determining its practicality and effectiveness in a given situation.

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

yes

Step-by-step explanation:

Answer:

attached below

Step-by-step explanation:

minus 2 from each side in order to isolate T with the coefficient. To get rid of the coefficient multiply to get 1 which is 5 in this case. Then the answer will be 75

Answer:

22y -15

Step-by-step explanation:

7y-15+ 18y-3y

combine like terms:

22y -15

Answer:

22y-15

Step-by-step explanation:

7y-3y=4y

4y+18y=22y

answer 22y-15

Answer:

g = \(\frac{k}{h^3}\)

Step-by-step explanation:

Given that g varies inversely as h³ then the equation relating them is

g = \(\frac{k}{h^3}\) ← k is the constant of variation

Answer:

Step-by-step explanation:

Answer: area = 697.5 area

Answer:

ab +c=d

Step-by-step explanation:

just took the test

Refer to the images attached. Now I am guessing when it says "use geometry" was to graph it? I wasn't completely sure. I attached how I would normally evaluate that problem and a graph of the piecewise function. It has been a while since I have dealt with integrating piecewise function, please let me know what process you were supposed to use if you figure it out. Hope this helps you a bit, have a good one!

Answer:

Greater than because 0.036 would need .006 to get to .042

Answer:

answer is 2/8 or simplified is still 1/4

Step-by-step explanation:

The position of the image is 42.25 cm in front of the lens. and its height is 5.64 cm and inverted.

We can use the thin lens equation to find the position of the image:

\(1/f = 1/d_o + 1/d_i\)

where f is the focal length of the lens, \(d_o\) is the object distance (distance between object and lens), and \(d_i\) is the image distance (distance between image and lens). We can solve for \(d_i\):

\(1/d_i = 1/f - 1/d_o\)

f = R/2 for a plano-convex lens with radius of curvature R, so in this case

\(f = 13 cm/2 = 6.5 cm\).

Plugging in \(d_o\) = 15 cm and f = 6.5 cm, we get:

\(1/d_i = 1/6.5 - 1/15\\1/d_i = 0.1538\\d_i = 6.5/0.1538\\d_i = 42.25 cm\)

So the position of the image is 42.25 cm in front of the lens.

To find the height of the image, we can use the magnification equation:

\(m = -d_i/d_o\)

where m is the magnification (negative for a virtual image), \(d_i\) is the image distance (which we just found), and \(d_o\) is the object distance (given as 15 cm).

\(m = -42.25/15\\m = -2.82\)

This means that the image is 2.82 times smaller than the object. Since the object is 2.0 cm tall, the height of the image is:

\(h_i = mh_o\\h_i = -2.822.0 cm\\h_i = -5.64 cm\)

The negative sign indicates that the image is inverted (upside down). So the position of the image is 42.25 cm in front of the lens, and its height is 5.64 cm and inverted.

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The probability of randomly picking a school or library-related issue from the ballot is 9/19 or approximately 0.474 (rounded to three decimal places).

To determine the probability of a randomly picked issue being school or library related, you'll need to consider the total number of issues and the number of school and library issues combined.

There are 7 school-related issues, 10 ordinance-related issues, and 2 library-related issues, making a total of 19 issues on the ballot. To find the probability of picking a school or library issue, combine the number of school and library issues: 7 + 2 = 9.

Now, divide the number of school and library issues (9) by the total number of issues (19): 9/19.

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Answer:

Hmm

Step-by-step explanation:

The number that belongs in the green box using sine rule is 13.96.

The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

To calculate the number that belongs in the green box, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

Solve for x

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