David can you 25/6 meters per hour manually, but using a digging machine he can dig 3 times as fast. how many meters would david be able to dig with the machine in an hour?

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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The choice trigonometric ratio is tangent and the distance is 3. 98 meters.

The given angle is 86

The opposite side is given as 57 meters

The distance is in the adjacent

Thus, trigonometric ratio to use is the tangent

Tangent = opposite/ adjacent

We have,

tan 86 = 57/x

14. 300 = 57/x

x = 57/ 14. 300

x = 3.i 98 meters

Thus, the choice trigonometric ratio is tangent and the distance is 3. 98 meters.

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Answer:

b

Step-by-step explanation:

eq y=x+4 is for x>=2 inclusive

Answer:

$46,819 is the average unemployed salary

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

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°

Step-by-step explanation:

As far as I understand, they can use all 26 letters (alphabet) and all 10 digits (0, 1, ..., 9), and the password looks like this:

letter-letter-letter-letter-letter-letter-number-number (6 letters, 2 numbers).

▪︎ They can reuse the letters, so they can choose the 1st letter out of 26 possible letters, then they still can choose the 2nd letter out of 26 (it's ok if they have both A's for example, they can reuse them) and so on. So each time they can choose one letter out of 26. Thus, it's 26*26*26*26*26*26.

▪︎ The same thing with numbers. Each time they can choose one number out of 10, so it's 10*10.

▪︎ Therefore, the answer is 26*26*26*26*26*26*10*10 = 30,891,577,600. That's almost 31 billion passwords.

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 ❞

Answer:

D. 41

Step-by-step explanation:

To solve, you have to clear "x" from the equation by dividing the other side of the equation by 22:

The only solution for 22x=901 is 41

Answer: x=41

Step-by-step explanation:

Hii!

Do you need to know the solution set of 22x=902? No problem! (:

We just need to divide both sides by 22 to solve for "x".

x=41; this equation has one solution only

--

Hope that this helped! Best wishes.

--

Answer:

I'm not sure what the question is.    I'll offer one simplification that might help.

Step-by-step explanation:

[tex]\sqrt{3} - 3(4*\sqrt{8})[/tex]

One can convert the [tex]\sqrt{8}[/tex] to [tex]\sqrt{2} *\sqrt{4}[/tex] and then that becomes [tex]\sqrt{2} *\2}[/tex]2 or 2[tex]\sqrt{2}[/tex]

[tex]\sqrt{3} - 3(4*\sqrt{2}\sqrt{4})\\[/tex]

[tex]\sqrt{3} - 3(4*2*\sqrt{2})\\[/tex]  See above explanation.

[tex]\sqrt{3} - 24*\sqrt{2})\\[/tex]

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 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:

y = 4x - 17

Step-by-step explanation:

y - 3 = 4(x - 5) ← distribute parenthesis by 4

y - 3 = 4x - 20 ( add 3 to both sides )

y = 4x - 17

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 :)

See attached images for work.

Answer:

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

Answer:

A=30

B=35

C=44

Step-by-step explanation:

Answer:

f(1) = 2

f(n) = 2 × f(n - 1) , n ≥ 2

Step-by-step explanation:

the point of coordinates (1 , 2) is on the graph

Then

f(1) = 2

…………………………

We notice that :

f(2) = 4

f(3) = 8

f(4) = 16

16/8 = 8/4 = 4/2 = 2/1 = 2

________________________

This means the common ratio

of the geo sequence = 2

Hence ,

f(n) = 2 × f(n - 1)

Answer: f(n) = 2 × f(n - 1) , n ≥ 2

Step-by-step explanation:

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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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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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:

C

Step-by-step explanation:

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

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]

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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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Answer:

The team won 144 gold medals

Step-by-step explanation:

A fraction tells us how many parts of a whole we have

144 / 360 translated into words is 144 out of 360

144 is the part and the 360 is the whole (total)

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