On a sunny day, Andrew, who is 1.9 m tall, casts a shadow that is 3.5 m long. A nearby tree casts a shadow that is 28.0 m long. To the nearest tenth of a metre, how tall is the tree?

Based on the calculations, the true statements are:

A. The angular velocity is 10π rad/sec.

E. The angular velocity is 600π rad/min.

Mathematically, angular velocity can be calculated by using this formula:

ω = θ/t

Where:

Note: 1/2 revolution = 0.5 × 2π = π radians.

Substituting the given parameters into the formula, we have;

ω = θ/t

ω = π/0.1

ω = 10π rad/s.

Next, we would convert the time in seconds to minutes:

ω = 10π × 60

ω = 600π rad/min.

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Complete Question:

A golfer’s arm rotates 1/2 of a revolution in 1/10 of a second. If the angular displacement is measured in radians, which statements are true? Check all that apply.

A. The angular velocity is 10π rad/sec.

B. The angular velocity is 10π rad/min.

C. The angular velocity is 60π rad/min.

D. The angular velocity is 600π rad/sec.

E. The angular velocity is 600π rad/min.

Answer:

A,

Step-by-step explanation:

Edge202

Answer:

$0.75, which is

75 cents

Step-by-step explanation:

First add the cost of all the items.

1.25 + .50 + 3.95

= 5.70

To find 10% of 5.70, change the percent to a decimal and multiply.

10% is .10

5.70 × .10 = .57

The tax is 57 cents. This can be written as $0.57



The recursive formula for the geometric sequence is given as follows:

D.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

With a recursive formula, it is given by:

[tex]a_n = a_{n-1} \times q[/tex]

For this problem, the first term and the common ratio are:

[tex]a_1 = 9, q = -\frac{1}{3}[/tex]

Then the recursive formula is:

D.

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The equation of line with the given slope and y-intercept is y = (3/4)x + 4.

Given that;

We use the formula for equation of line to determine the equation.

y = mx + b

Where m is the slope and b is the y-intercept.

We plug in our values

y = mx + b

y = (3/4)x + 4

Therefore, the equation of line with the given slope and y-intercept is y = (3/4)x + 4.

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Answer:

√(3 , √(π , 2

Step-by-step explanation:

ascending order

Answer:

D. Both factors are positive, so the product will be positive.​

Answer: [tex]y+5=-2(x+4)[/tex]

Step-by-step explanation:

See attached image.

The initial age of 10 years and the spaceship speed of 0.60•c, gives the Andrea's age at the end of the trip as 18 years.

The time dilation using the Lorentz transformation formula is presented as follows;

[tex]t' = \frac{t}{ \sqrt{1 - \frac{ {v}^{2} }{ {c}^{2} } } } [/tex]

From the question, we have;

The spaceship's speed, v = 0.6•c

∆t = Rest frame, Courtney's time, change = 10 years

Therefore;

[tex]\delta t' =\delta t \times \sqrt{1 - \frac{ {(0.6 \cdot c)}^{2} }{ {c}^{2} } } = 8[/tex]

The time that elapses as measured by Andrea = 8 years

Andrea's age, A, at the end of the trip is therefore;

A = 10 years + 8 years = 18 years

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The probability of drawing two yellow balls if they're not replaced exists 1/45.

The probability exists in the analysis of the possibilities of happening of an outcome, which exists accepted by the ratio between favorable cases and possible cases.

Number of yellow marbles be 2

Number of pink marbles be 3

Number of blue marbles be 5

Total number of marbles = 2+3+5 = 10

The probability of removing the first yellow ball = 2/10

Since the ball exists not replaced, that indicates there choice be 9 balls left and 1 yellow ball left.

Probability of drawing the second yellow ball = 1/9.

Probability of drawing two yellow balls if they're not replaced

= 2/10 × 1/9

= 2/90

= 1/45

The probability of drawing two yellow balls if they're not replaced exists 1/45.

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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.

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 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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Answer:

circle

Step-by-step explanation:

any point on the circumference of a circle is equidistant from the centre.

Answer:

hi play truth and dare to with me in g met

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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There is a total of 90 handshakes.

There are 5 sets of triplets.

If we select one of the sets, each of the triplets will have one handshake with the other 12 people. So we have 36 handshakes at this point.

Now we only care for the other 4 sets.

We select one set again, each triple on that set will have one handshake with the other 9 people, so for the 3 triplets, we have a total of 27 new handshakes.

For the remaining 3 sets we do the same, this time we add 18 handshakes.

Finally, there are 2 sets of triplets, this time we add 9 new handshakes.

To get the total number of handshakes we need to add them all:

36 + 27 + 18 + 9 = 90

There is a total of 90 handshakes.

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The rotation about 90 degrees clockwise from the origin would give H'( -2, 3) , I' (1 , -1) and J' (-4, 0)

Note that rotation about in clockwise 90 degrees direction when M(h , k) rotated about the origin, the new rotation coordinates would be in the form M' (k , -h)

Coordinates of the preimage were given as;

H ( -3, -2)

I ( 1, 1 )

J ( 0, -4)

The coordinates after a 90 degrees rotation about the origin, would be

For H ( -3, -2)

h = - (-3) = 3

k = -2

H' = ( -2, 3)

For I ( 1, 1)

h = - (1) = -1

k = 1

I' = ( 1, -1)

For J ( 0, -4)

h = - (0) = 0

k = -4

J' = ( -4, 0 )

Thus, the rotation about 90 degrees clockwise from the origin would give H'( -2, 3) , I' (1 , -1) and J' (-4, 0)

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Answer:

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

The xy-value in the solution to the given system of linear equation shows that x = 2 and y = -4.

Whenever two or more linear equations operate simultaneously, we create a System of Linear Equations. These equations must contain one or more similar variables in order to operate together.

When solving a system of linear equations, our objective is to simplify two equations having two variables to a single equation having one variable. Because each equation in the system includes two variables, substituting an expression for a variable is one technique to minimize the number of variables in an equation.

From the given information:

4x + 5y = -12  --- (1)

-2x + 3y = -16 ----- (2)

From equation (1)

4x+5y+(−5y) = −12 + (−5y)       (Add -5y to both sides)

4x = −5y − 12

Divide both sides by 4

[tex]\mathbf{\dfrac{4x}{4}= \dfrac{-5y-12}{4}}[/tex]

[tex]\mathbf{x= \dfrac{-5}{4}y-3}[/tex]

Replacing the value of x in [tex]\mathbf{ \dfrac{-5}{4}y-3}[/tex] into equation (2); we have:

[tex]=\mathbf{-2(\dfrac{-5}{4}y-3)+3y=-16}[/tex]

[tex]\mathbf{\dfrac{11}{2}y+6 =-16}[/tex]

Simplifying both sides of the equation, we have:

[tex]\mathbf{\dfrac{11}{2}y+6-6 =-16-6}[/tex]

[tex]\mathbf{\dfrac{11}{2}y=-22}[/tex]

Cross multiply

11y = -44

y = -4

Replace the value of y = -4 into [tex]\mathbf{x= \dfrac{-5}{4}y-3}[/tex]

[tex]\mathbf{x= \dfrac{-5}{4}(-4)-3}[/tex]

x = 2

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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:

T(1)=1+2(1)+3=6

T(2)=2+2(2)+3=9

T(3)=3+2(3)+3=12

T(100)=100+2(100)+3=303

Multiply by 6

And

Multiply by 3

eq(1)-eq(2)

Then

From Equation 1

[tex] \dfrac{x}{2} + \dfrac{2y}{3} = - 1 [/tex]

[tex] \dfrac{3x + 4y}{6} = - 1[/tex]

[tex]3x + 4y = - 6 [/tex]

From Equation 2

[tex]x - \dfrac{y}{3} = 3 [/tex]

[tex] \dfrac{3x - y}{3} = 3[/tex]

[tex]3x - y = 9[/tex]

By eliminating ;;

For that multiply equation 2 by 4

12x - 4y = 36 _(3)

By taking equation (1) and (3)

3x + 4y = -6

12x - 4y = 36

__________

15x = 30

x = 30/15

x = 2

Putting the value of x in 2

[tex]3(2) - y = 9[/tex]

[tex]6 - y = 9[/tex]

[tex]6 - 9 = y[/tex]

[tex]-3 = y[/tex]

So The value of x = 2 and y = -3

The probability that a student buys coffee OR a muffin before class is 55%

The given parameters are:

P(Coffee) = 30%

P(Muffin) = 40%

P(Tea) = 20%

P(Coffee and Muffin) = 15%

P(Tea and Muffin) = 10%

The probability that a student buys coffee OR a muffin before class is

P(Coffee or Muffin) = P(Coffee) + P(Muffin) - P(Coffee and Muffin)

This gives

P(Coffee or Muffin) = 30% + 40% - 15%

Evaluate

P(Coffee or Muffin) = 55%

Hence, the probability that a student buys coffee OR a muffin before class is 55%

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Answer:

They are parallel.

Step-by-step explanation:

They have the same slope, 7, and different y-intercepts, 4, -1/4, so they are parallel.

The entire interval over which the function, f(x), is positive is (-∞,1).

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Each element of X receives exactly one element of Y when a function from one set to the other is used. The set X is referred to as the function's domain, while the set Y is referred to as the function's codomain.

According to the question,

The function has positive values corresponding to the interval from negative infinity to one.

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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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The principal is 1000

SI = PRT/100

Simple interest = 100

Rate = 5%

Time = 2 years.

SI = PRT/100

100 = (P × 5 × 2)/100

10000 = 10P

P = 10000/10

P = 1000

Let's see

seven eighths means 7/8

So

Forty two eighths