For my math assessment, I need to apply trigonometry in a real life situation and explain about it. I've been thinking of 1. trigonometry applied in cricket 2. music (sound waves)... but still not quite sure how to. If anyone has knowledge on how I could work on these or any other new ideas that would be relevant, PLEASE help me!!! Thank you!! <3​

Answer:

Yes, the relation is proportional because the ratios are equivalent between each pair of values

Step-by-step explanation:

 Proportional relationships are relationships with equal ratios.

Entries in the respective columns are:

        column 1 (Minutes)              column 2 (Blocks)                 Ratios

                   6                                           3                                    1/2                

                   14                                          7                                    1/2

                   20                                         10                                  1/2

  As the ratio of Blocks and Minutes is same for every row,

   the given table represent a proportional relationship.

  hence, option c is correct.

   Yes, because the ratios are equivalent between each pair of values.

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Answer: Yes, the relation is proportional because the ratios are equivalent between each pair of values :)

The graph of the function has an axis of symmetry at x = 3 will be D. f(x) = x² - 6x - 1. On a coordinate plane, a parabola opens up, it goes through (0, negative 1), has a vertex at (3, negative 10) and goes through (6, 0).

It should be noted that the axis of symettry is the line that divides an object into two equal halves.

Here, the graph of the function has an axis of symmetry at x = 3 is option D. On the coordinate plane, a parabola opens up, it goes through (0, negative 1), has a vertex at (3, negative 10) and goes through (6, 0).

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Answer: D.  f(x) = x² - 6x - 1

Right on Edge 2023 :)

A function assigns the values. The function g(x) can be written as g(x) = -3x + 12.

A function assigns the value of each element of one set to the other specific element of another set.

Given the function f(x)=-x, now since a transformed function g(x) is produced by shifting the function 4 units upwards and vertical stretch by a factor of 3. Therefore, g(x) can be written as,

Vertical Shift by 4 units,

f(x)+4

Vertical stretch by a factor of 3

g(x) = 3(f(x) + 4)

g(x) = -3x + 12

Hence, the function g(x) can be written as g(x) = -3x + 12.

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The Volume and Surface Area of Prism is 294 in² and 114.33 in³.

A large structure built especially in ancient Egypt that usually has a square base and four triangular sides meeting at a point and that contains tombs.

Surface rea of rectangular prism,

= 2( lb +bh +lh)

= 2 ( 7*7 + 7*7+ 7*7)

= 2 ( 49+49+49)

= 2*3*49

= 294 in²

Now, Volume,

= bhl/3

= 7*7*7/3

= 114.33 in³

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Answer:

142 506

Step-by-step explanation:

here the order does not matter

Then

we the number of sets is equal to the number of combinations.

Using the formula :

the number of sets is 30C5

[tex]C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}[/tex]

      [tex]=142506[/tex]

There are 142506 ways in which 5 students can be selected out of 30 students.

The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.

By using the formula:

[tex]\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}[/tex]

where;

[tex]\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}[/tex]

[tex]\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}[/tex]

[tex]\mathbf{^nC_r = 142506}[/tex]

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Answer:

[tex]\huge\boxed{\sf 20z\³ + 24z\² - 5z - 6}[/tex]

Step-by-step explanation:

= (5z + 6)(2z + 1)(2x - 1)

= (5z + 6)[(2z)² - (1)²]

= (5z + 6)(4z² - 1)

Distributing

= 5z (4z² - 1) + 6(4z² - 1)

= 20z³ - 5z + 24z² - 6

Arrange

= 20z³ + 24z² - 5z - 6

[tex]\rule[225]{225}{2}[/tex]

Answer:

y = (- 2/3)x - 3

Step-by-step explanation:

y = mx + c

y = (- 2/3)x + c

- 1 = (- 2/3)(-3) + c

-1 = 2 + c

c = - 3

Therefore,

y = (-2/3)x - 3

Answer:

y = -2/3x - 3

Step-by-step explanation:

y = mx + b

y = y coordinate              → given: - 1

m = slope                        → given: - 2/3

x = x coordinate              → given: - 3

b = y intercept                 → need to find

y = -2/3x + b → -1 = -2/3(-3) + b

-1 = 2 + b

subtract 2 from both sides

-1 - 2 = 2 - 2 + b

-3 = b

y = -2/3x - 3

You buy 3 shirts and 1 pair of pants for $32. Your friend buys 2 shirts and 3 pairs of pants for $40. How much did each item cost?

First let’s define a shirt as X and pants as Y!

In the first scenario, the equation will be 3X + Y =$32

In the second scenario, the equation will be 2X + 3Y = $40  

Now because we have two different variables (X & Y) let’s solve for one of them (Ex: Y) to simplify the equations!

3X + Y= $32—> subtract 3X on both sides of the equation  

-3X.        - 3X

Net result: Y= 32- 3X

Now we can insert this into the second equation 2X + 3Y = $40 in order to solve for X variable  

2X + 3(32-3X) = $40

2X + 96 - 9X = $40 —> simplify the equation  

-7X + 96 = $40 —> substrate 96 from both sides  

-7X = -56 —> divide both sides by -7  

X= 8  

Now reinsert 8= X into 3X + Y = $32

3(8) + Y = $32

24+ Y = $32 —> substract 24 from both sides

y = 8

ANSWER: X= 8, Y= 8

[tex] \huge\underline{\underline{\boxed{\color{blueviolet}{ANSWER}}}}[/tex]

★ 15 trucks can carry 26,850 kg weight

★ We've to find the weight carried by one truck

[tex]\huge \pink {\overline{ \quad \quad \quad \quad \quad \quad \quad\quad \quad}}[/tex]

[tex] \sf{Number \: of \: trucks = 15 }[/tex]

[tex] \sf{Weight \: carried \: by \: one \: truck = \frac{26,850Kg}{15} }[/tex]

[tex] \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:= 1790Kg[/tex]

Therefore , the weight carried by one truck is 1790 kg

Answer:

B. The graph of g(x) is the graph of f(x) vertically stretched by a factor of 5.

Answer:

A

Step-by-step explanation:

these two triangles are similar

therefore corresping sides are proportionate

12/8=9/x

12x=72

x=72/12=6

Answer:

the answer is 6

Step-by-step explanation:

i hope this is helpful

Answer:

$46,819 is the average unemployed salary

The average rate of change of f(x) = -3x² + 1 over each of the given intervals are; -18, 6 nd 38

We are given the function;

f(x) = -3x² + 1

(a) From 2 to 4;

f(2) = -3(2)² + 1

f(2) = -12 + 1

f(2) = -11  (2, -11)

f(4) = -3(4)² + 1

f(4) = -47  (4, -47)

Slope = (-47 - (-11))/(4 - 2)

Slope = -36/2

Slope = -18

(B) From -2 to 0;

f(-2) = -3(-2)² + 1

f(2) = -12 + 1

f(2) = -11  (-2, -11)

f(4) = -3(0)² + 1

f(4) = 1  (0, 1)

Slope = (1 - (-11))/(0 - (-2))

Slope = 12/2

Slope = 6

(C) From 2 to 5;

f(2) = -3(2)² + 1

f(2) = -12 + 1

f(2) = -11  (2, -11)

f(5) = -3(5)² + 1

f(5) = -74  (0, -74)

Slope = ((-74) - 2)/(0 - 2)

Slope = -76/-2

Slope = 38

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Answer:

B

Step-by-step explanation:

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:f(x)= 9280 - 20x [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{1}{16} x + \cfrac{1}{320} y - 29 = 0[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{1}{16} x + \cfrac{1}{320} y = 29[/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{20 x+ y}{320} = 29[/tex]

[tex]\qquad \tt \rightarrow \: 20x + y = 29 \sdot320[/tex]

[tex]\qquad \tt \rightarrow \: y = 9280 - 20x[/tex]

[tex]\qquad \tt \rightarrow \: f(x) = 9280 - 20x[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

x = 90°

2x = 180°

Step-by-step explanation:

angle VTS= angle TSR (alternate angle)

now in ∆TRS,

2x + x + x = 360° (angle sum property of ∆)

4x = 360°

x = 90°

Answer:

y = 47

Step-by-step explanation:

All of the angles in a triangle must add up to 180. The angle marked 3y can help us find the missing angle of the triangle: 180-3y
Then you can make an equation to help solve for y:
50 + (2y-3) + (180-3y) = 180
Combine like terms:
227-y=180
y = 47

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: y=47 \degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \:(2y - 3) + 50 = 3y[/tex]

[tex]\qquad \tt \rightarrow \:2y - 3 + 50 - 3y = 0[/tex]

[tex]\qquad \tt \rightarrow \:2y - 3y + 47 = 0[/tex]

[tex]\qquad \tt \rightarrow \: - y = - 47[/tex]

[tex]\qquad \tt \rightarrow \:y = 47 \degree[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The option second "No, they are not independent because P(student)≈ 0.82 and P(student pirate) ≈ 0.94" is the correct option (B) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have a table given that shows the survey asks teachers and students whether they would like the new school mascot to be a pirate or a moose.

The probability of a person that is a student:

P(student) = (75+15)/110 = 0.83

The probability:

P(student|pirate) = 75/80 = 0.93

The probability of both events is different.

Thus, the option second "No, they are not independent because P(student)≈ 0.82 and P(student pirate) ≈ 0.94" is the correct option (B) is correct.

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Answer:

X = 92 degrees

Step-by-step explanation:

the angles of a triangle all add up to 180 degrees, so 40 plus 180-132 = 88

180-88= 92 so X = 92

The sinusoidal function for the height as a function of time will be h= -15 cos (πt/15)+19 meter

As the Ferris wheel starts with the rider from the bottom position (which is the minimum point in the cycle), we can represent the position of the rider with a negative cosine function.

The general form of the cosine function representing the displacement of the rider is:

f(t) = a cos(bt+c) + d, where:

amplitude = |a| which is the distance that travels above and below the midpoint

period = 2 π/|b| which is the time period i.e. time required to complete one cycle

-c/b is the phase shift.

d = vertical displacement of the function

Given the diameter of the wheel is 30 m, then r = 30/2 = 15 m.

So the distance that travels above and below the midpoint is the radius for which a=15. As we have the negative cosine function, a = -15.

The time period is 0.5min. As it is given the frequency is 2 revolutions per min for which b= 2(2π) rad/min.= 4π/60 rad/sec.= π/15 rad/sec.

The rider starts from the bottom position, so there will be no phase shift, so c=0

Given that the center of the wheel is 19 m above the ground, so d=19m

Therefore the equation will be

height of rider as function of time(t) = h = -15 cos (πt/15)+19 meter

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See attached images for work.

The area of the square is 16 square inches and its perimeter is 16 inches.

What is Area of square ?

A square is a two-dimensional geometric shape with four equal sides and four right angles. The area of a square is the measure of the region enclosed by the square. The area is expressed in square units, such as square inches, square meters, or square feet.

The area of a square is given by the formula:

A = s²

where A is the area and s is the length of a side.

If the side length of the square is 4 inches, the area can be calculated as:

A = 4² = 16 square inches.

The perimeter of a square is given by the formula:

P = 4s

where P is the perimeter and s is the length of a side.

If the side length of the square is 4 inches, the perimeter can be calculated as:

P = 4 x 4 = 16 inches.

Therefore, the area of the square is 16 square inches and its perimeter is 16 inches.

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The numbers should be 2, 2, 5, 9 and 12.

The arithmetic mean is found by adding the numbers and dividing the sum by the number of numbers in the list.

The median is the middle value in a list ordered from smallest to largest. The mode is the most frequently occurring value on the list.

Let us take numbers 2, 2, 5, 9 and 12.

mean = 30/5

mean= 6

range = 10.

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#Step1

It will result -2x-2y=-8

#2

#3

add

Find x

The statements that are true about circle Q are:

The measure of the central angle is 45°.  The measure of the entire circle is 360°.  This makes the ratio of the central angle to the entire circle 45/360 = 9/72 = 1/8

To find the area of the shaded sector, this will be:

A = πr² = π(6²) = 36π

1/8(36π) = 36π/8 = 18π/4 = 9π/2 = 4.5π square units.  This is not 4 square units.

The ratio of the area of the shaded sector to the area of the circle would not be the same as the ratio of the length of the arc to the area of the circle.

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Answer:

1,3,4

Step-by-step explanation:

The shape will have a surface area of 189.25 cm². There are two distinct pieces to the figure: a rectangle and a semicircle.

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.

The figure is divided into two parts one is a rectangle and the second is a semicircle.

Area of figure = Area of rectangle + Area of a semicircle

Area of figure = L × B + (πr²/2)

A = 10 cm × 15 cm + (3.14 ×(5)^2/2)

A= 189.25 cm²

Hence the area of the shape will be 189.25 cm²

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Answer:

[tex]x=10[/tex]

Step-by-step explanation:

Here, we can use an angle rule.

We see that angles [tex](8x+50)[/tex]° and 130° are under a sort of F shape, where lines m and n are the horizontal parts of the letter and where the diagonal line is the vertical part of the letter.

This means we can use the rule:

Corresponding angles are equal.

This means that:

[tex]8x + 50 = 130[/tex]

We can now use this equation we have formed to solve for [tex]x[/tex]:

[tex]8x + 50 = 130\\8x = 80\\x = 10[/tex]

Therefore, our final answer is [tex]x=10[/tex].

The graph is plotted and attached in the attachment. The given equation is a linear equation with the intercept 0.

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as y = mx + c.

Given equation;

y + 2 = (x+2)

Rearrange the equation;

y + 2 = x+ 2

y=x

The standard equation for the straight line is;

y = mx + c

Where c is the intercept and m is the slope

After comparing the given equation with the standard equation we get;

m = 1

c =0

Hence,the graph is plotted and attached in the attachment.

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Answer:

C

Step-by-step explanation:

= The square root of (5^2+2^2)= The square root of 29 ---> C

Using it's concept, it is found that there is a 0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Considering the situation described, the ways that alternate colored balls can be taken with the probabilities given as follows:

Hence the probability that the first three balls are drawn out of the box alternated in colour is given by:

[tex]p = \frac{5}{8} \times \frac{3}{9} \times \frac{5}{11} + \frac{3}{8} \times \frac{5}{10} \times \frac{5}{11} = 0.0689 + 0.0852 = 0.1541[/tex].

0.1541 = 15.41% probability that the first three balls are drawn out of the box alternated in colour.

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