The diagram below shows a logo formed by removing a semicircle with diameter AB and a
rhombus DEFG from an isosceles trapezium ABCE where AE = BC.
Find the area of the logo.

The sine, cosine, cosecant, and secant functions have period 2π; the tangent and cotangent functions have period π.

Definition for Period of a Trigonometric Function :

The pause between any function's repetitions is known as the function's period. The duration of one complete cycle is the period of a trigonometric function. Trigonometric functions include three basic types: sin, cos, and tan, which have periods of -2π, 2π, and π respectively.

If a function repeats itself repeatedly at a predetermined frequency, it is said to be periodic. The formula for t is f(x) = f(x + p), where p is a real number that denotes the period of the function. Period is the interval between two occurrences of the wave.

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Since the standard deviation for the population is known, the z-distribution is used as the sampling distribution basis for this hypothesis test.

In this problem, the standard deviation for the population is known, hence the z-distribution is used.

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The length of the rectangle is 26ft.

What is the perimeter of a rectangle?

The perimeter of a rectangle is, P = 96 ft.

The width of the rectangle is, w = 22ft.

As we know the perimeter P of a rectangle is given by the formula, P=2l+2w

Therefore, substituting the values in the equation we get,

P = 2l + 2w

96 = 2l + 2*22

96 = 2l + 44

2l = 96 - 44

2l = 52

l = 52/2

l = 26

Hence, the length of the rectangle is 26ft.

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Answer:

cosF = 0.6

Step-by-step explanation:

cosF = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{EF}{DF}[/tex] = [tex]\frac{6}{10}[/tex] = 0.6

Answer:

Cos F = 0.6

Step-by-step explanation:

    [tex]\sf \boxed{\bf \ Cos \ F = \dfrac{adjacent \ side \ of \ \angle F}{hypotenuse}}[/tex]

                   [tex]\sf =\dfrac{EF}{DF}\\\\=\dfrac{6}{10}\\\\= 0.6[/tex]

Answer: 4:3

Step-by-step explanation:

The side length of the triangle is 48/3 = 16.

The side length of the square is 48/4 = 12.

So, the ratio is 16:12 = 4:3.

Answer:

450 employees work at this company.

Step-by-step explanation:

300 = 2/3 of x
300 × 3 = 2x
900 = 2x
450 = x

The solution to the system of equations is (-1.189, 3.587) and (1.189, 3.587)

The system of equations is given as

y=e^x+e^-x

y=5-x^2

See attachment for the graph of both equations

From the attached graph, the curve intersect at

(-1.189, 3.587) and (1.189, 3.587)

Hence, the solution to the system of equations is (-1.189, 3.587) and (1.189, 3.587)

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The following pairs of lines should be matched with their descriptions as follows:

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.

This ultimately implies that, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

Perpendicular lines can be defined as two (2) lines that intersect or meet each other at an angle of 90° (right angles).

In Mathematics, the condition for perpendicularity of two lines is:

m₁ × m₂ = -1

Given the following equations:

y = 2x/3 + 4 and y = -3x/2 + 9; 2/3 × -3/2 = -1.

y = 4x/5 + 8 and y = 5x/4 + 8; neither parallel nor perpendicular lines.

y = 5x/6 + 8 and y = 5x/6 + 2; 5/6 = 5/6.

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john could be right now 45

What is word problem in math?

A math word problem is a question that is written as one or more sentences and asks students to use their mathematical understanding to solve an issue from "real world."

According to the question:

And

Solution for the above equation:

                                               [tex]x=y-30, y=3 x \quad\\ \quad x=15, y=45[/tex]

steps:

                                                [tex]x=y-30 \\y=3 x[/tex]

Substitute :[tex]$y=3 x$[/tex]

                                               [tex][x=3 x-30][/tex]

                                   [tex]for $$x=3 x-30: \quad x=15[/tex]

For [tex]$y=3 x$[/tex]

Substitute: [tex]$x=15$[/tex]

                                               [tex]y=3 \cdot 15[/tex]

Simplify:

                                               [tex]y=45[/tex]

The solutions to the system of equations are: [tex]$x=15, y=45$[/tex]

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The equation passing through the point ()8, 2 and parallel to 6x - 9y = -7 is y = 6 / 7x - 2 / 7

The equation of the line passes through the point (8, 2) and it is parallel to 6x  - 7y = -7.

The equation of a line can be represented as follows;

y = mx + b

where

m = slope

b = y-intercept

Therefore, parallel line have the same slope.

6x  - 7y = -7

7y = 6x + 7

y = 6 / 7 x + 1

m = 6 / 7

Hence, using (8, 2)

2 = 6 / 7 (8) + b

2 = 16 / 7 + b

b = 2 - 16 / 7

b =  14 - 16/ 7

b = - 2 / 7

Hence, the equation is y = 6 / 7x - 2 / 7

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{12:9}[/tex]

[tex]\huge\textbf{Simplifying:}[/tex]

[tex]\mathsf{12:9}[/tex]

[tex]\mathsf{= 12\div3 : 9 \div 3}[/tex]

[tex]\mathsf{= 4:3}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{4:3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The first step is the parenthesis

The equation is given as:

8(2x+4) = 2(1x+3)

Using PEMDAS, the first step is to open the brackets by multiplication.

So, we have:

16x + 32 = 2x + 6

Hence, the first step is the parenthesis

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Answer:

A

Step-by-step explanation:

there is a common ratio between consecutive terms , that is

9 ÷ - 3 = - 27 ÷ 9 = 81 ÷ - 27 = - 3

this indicates the sequence is geometric.

the recursive formula allows a term in the sequence to be found by multiplying the previous term by the common ratio r , that is

f(n) = - 3f(n - 1) if n > 1 : f(1) = - 3

Answer:

The remaining 15 athletes did not participate in any type of flexibility program

Answer:

53 mph

Step-by-step explanation:

We need to give the answer in terms of miles per hour. This means that we need to find out how many miles Joe needs to travel in one hour. Therefore, this is a ratio problem.

We can set up a proportion where the unknown variable is the number of miles driven in one hour:

[tex]\frac{106}{2} =\frac{x}{1}[/tex]

x is just 106/2, or 53. Therefore, Joe needs to travel 53 mph

168 is  the largest number of stamps that Jenna could be putting on each page

What is the Greatest Common Factor?

The greatest common factor (GCF or GCD or HCF) of a set of whole numbers is the largest positive integer that divides evenly into all numbers with zero remainder. For example, for the set of numbers 18, 30 and 42 the GCF = 6.

So the largest number of stamps that Jenna could be putting on each page

would be gcd of 1008 and 840.

840 = 2 x 2 x 2 x 3 x 5 x 7

1008 = 2 x 2 x 2 x 2 x 3 x 3 x 7.

∴ The Gcd = 2 x 2 x 2 x 3 x 7 = 168.

Hence 168 is  the largest number of stamps that Jenna could be putting on each page

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a. Surface area = 172 cm²

Volume = 112 cm²

b. The surface area would be needed.

c. The volume would be needed.

Surface area = 2(wl+hl+hw).

Volume = (length)(width)(height)

a. l = 7 cm

w = 2 cm

h = 8 cm

Surface area =2(wl+hl+hw) = 2·(2·7+8·7+8·2) = 172 cm²

Volume = (7)(2)(8) = 112 cm²

b. The surface area would be needed.

c. The volume would be needed to find the amount of juice the box will hold.

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Based on the calculations, the ratio of AD to DB ​ is equal to 0.6.

A ratio is a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.

From the graph, we have:

Length of AD = 1.5

Length of DB = 2.5

Ratio = AD/DB

Ratio = 1.5/2.5

Ratio = 0.6.

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Answer:

-4

Step-by-step explanation:

Slope = y/x

1. y=12 x=-3

  12/-3=-4

2. y=8, x=-2

   8/-2 = -4

3. y=4, x=-1

   4/-1 = -4

4. 0/0 = 0

5. y=-4, x=1

   -4/1 = -4

Hope it helps I had this question last year on Acellus.

The correct answer is all of the above.

Why is the range the most convenient measure of variability?

How do you find the range?

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Jasmine will not have enough for the car. The amount more that she needs is $520.

The first step is to convert the fraction that represents the amount needed as a deposit to percentage.

(2/5) x 100 = 40%

Difference in the deposit and the amount Jasmine's father deposited: 40% - 30% = 10%

Amount more that she needs : 10% x 5200 = $520

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The amount of the galleys or the number of galleys.

If given the amount of galleons, you can find the amount of galleys by dividing the number of given galleons by 5.

If given the amount of galleys, you can find the amount of galleons by multiplying the number of given galleys by 5.

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The measure that best describes the data is the median and the measure that might mislead the data is the mode

The mean is calculated as:

[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]

So, we have:

[tex]\bar x = \frac{20* 2 + 50 * 3 + 60 * 6 + 70 * 3 + 80 * 4 + 90 * 4 + 100 * 2 + 130 * 1}{25}[/tex]

This gives

[tex]\bar x = \frac{1770}{25}[/tex]

[tex]\bar x = 70.8[/tex]

So, the mean is 70.8

The median is the middle number, and the position is calculated using

Median = (n + 1)/2 th

This gives

Median = (25 + 1)/2 th

Median = 13th

The 13th element is 70

So, the median is 70

The mode is the data element with the highest frequency.

So, the mode is 60

The line plot has outliers at 20 and 130.

This is so because 20 and 130 are far from other data values

When a dataset has an outlier, the best measure is the median

Hence, the measure that best describes the data is the median.

The measure that might mislead the data is the mode

This is so the highest occurring value does not necessarily represent the dataset

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The approximate area of circle A is π · 8² = 64π ≈ 201.062 square inches.

The approximate area of circle B is π · 4² = 16π ≈ 50.265 square inches.

The approximate area of shaded region 1 is 24² - 64π ≈ 374.938 square inches.

The approximate area of shaded region 2 is 64π - 16π = 48π ≈ 150.796 square inches.

In this situation we have a square whose side length is known and two circles whose radii have to be estimated. By direct inspection we find that the diameter of circle A is two thirds of the length of the square side (l), in inches and the diameter of circle B is the half of the diameter of the former. Now we proceed to find the key dimensions of the figure:

Circle A

Diameter: 16 inches

Radius: 8 inches

Circle B

Diameter: 8 inches

Radius: 4 inches

The approximate area of circle A is π · 8² = 64π ≈ 201.062 square inches.

The approximate area of circle B is π · 4² = 16π ≈ 50.265 square inches.

The approximate area of shaded region 1 is 24² - 64π ≈ 374.938 square inches.

The approximate area of shaded region 2 is 64π - 16π = 48π ≈ 150.796 square inches.

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Answer:

7

Step-by-step explanation:

By the AA Postulate, triangles JKL and MNP are similar. Segment JK corresponds to segment MN, and segment JL corresponds to segment MP.

JK/MN = JL/MP

25/30 = 20/(4x-4)

25(4x-4) = 20*30

100x - 100 = 600

100x = 700

x = 7

Estimate the distance between points G and I with a compass and sketch an arc from point V which bisects the earlier arc U.

To copy an angle we observe the subsequent steps,

1). Mark a working line with the help of a straightedge.

2). Now we set a point S as the vertex of the angle.

3). Create an arc with a radius 'r' (any length ) from vertex S which bisects the working line V.

4). With the exact radius we mark an arc from point E which bisects the line ED and EF at G and H respectively.

5). Mark an arc from point G which bisects line EF at I.

6). Estimate the distance between points G and I with a compass and sketch an arc from point V which bisects the earlier arc U.

7). Now join the points S and U.

Therefore we copy any angle.

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