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dangina [55]
1 year ago
7

Margie and Sam collected stamps. Margie collected 4 times as many stamps as sam. together they have 210. how many stamps does ea

ch person have?
Mathematics
1 answer:
Musya8 [376]1 year ago
5 0

Ok, so:

To do this problem, first, we assign variables.

Let x be the smaps that Many collected.

If Margie collegted 4 times as many stamps as Sam, Margie collected 4x stamps.

Then, we know that both of them have 210.

So x + 4x = 210.

Solving the equation:

5x = 210

And x = 42.

Many collected 42 stamps.

Now, we use the last fact to find how many stamps Margie collected.

Margie collected 4x stamps, that is 4(42), which is equal to 168 stamps.

Margie collected 168 stamps.

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Which of the following represents the polar equation r = (cot 2θ)(csc θ) as a rectangular equation?
STALIN [3.7K]

The option that depicts the polar equation r = (cot 2θ)(csc θ) as an equation that is rectangular is: y² = 2x.

<h3>What is a polar equation?</h3>

A polar expression is any equation that describes the correlation between r and θ, where r signifies the anticlockwise angle formed by a point on a curve, the pole, and the positive x-axis, and means the breadth between the origin and a location on a curve.

<h3>What is the solution to the equation above?</h3>

Step 1 - expand the polar equation

r = 2cosθ * cscθ

Step 2  - convert csc and cos to their equivalents in tan and sin

r = 2 * (1/tanθ) * (1/sinθ) * sinθ

r = 2 * (1/tanθ) * sinθ/sinθ

r = 2 * 1/tanθ

r = 2/tanθ, making 2 the subject of the formula, we have

rtanθ = 2



Note that rectangular coordinates of a point will be depicted as (x,y) and it's plolar coordinate will be (r, θ).

This mean

x = r cos θ; and

y = r sinθ

From the above, we can state that:

Since y = r sinθ
⇒ tanθ = y/x

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Thus y * (y/x) = 2

Therefore,

y²/x = 2

y² = 2x

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5 0
2 years ago
ILL GIVE YOU BRAINLIST !! *have to get it right ! *
Marianna [84]

Answer:

-1/2

Step-by-step explanation:

Point L is at (-2,3)

Point M is at (2,1)

We can find the slope using

m =(y2-y1)/(x2-x1)

   = (1-3)/(2 - -2)

    =(1-3)/(2+2)

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3 years ago
Among 420 randomly selected employees at a company, the mean number of hours of overtime worked per month is 10 hours and the st
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To solve for the margin of error:

margin of error = critical value x standard error

To compute for the critical value:
1. compute alpha: α= 1 - (confidence level/100) = 1 - .99 = 0.01
2. Find the critical probability: p = 1 - α/2 = 1 - (0.01/2) = 0.995
3. Look for the z score at the z table, in this case it is 2.58. This is your critical value.

To compute for the standard error, the formula is:
standard error = standard deviation (σ) divided by √n = 1.6 / √420 = 0.0781

Now plug in the following in the formula:

margin of error: 2.58 * 0.0781  = 0.2014 or 0.20

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3 years ago
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