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3 years ago

Write an equation of the line that passes through the given point and is parallel to the graph of the given equation.

1 answer:

7 0

Question 1:

--------------------------------------------------------------------
Find Slope
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Equation: y = 5x - 2
Slope = 5
Slope of parallel line = 5

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Insert slope into the general equation y = mx + c
--------------------------------------------------------------------
y = 5x + c

--------------------------------------------------------------------
Find y-intercept
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At point (2, -1)
y = 5x + c
-1 = 5(2) + c
c = -1 - 10
c = -11

--------------------------------------------------------------------
Insert y-intercept into the equation
--------------------------------------------------------------------
y = 5x + c
y = 5x - 11

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Answer: y = 5x - 11
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Question 2:

--------------------------------------------------------------------
Find Slope
--------------------------------------------------------------------
y = 9x
Slope = 9
Slope of the parallel line = 9

--------------------------------------------------------------------
Insert slope into the equation y = mx + c
--------------------------------------------------------------------
y = 9x + c

--------------------------------------------------------------------
Find y-intercept
--------------------------------------------------------------------
y = 9x + c
At point (0, 5)
5 = 9(0) + c
c = 5

--------------------------------------------------------------------
Insert y-intercept into the equation
--------------------------------------------------------------------
y = 9x + c
y = 9x + 5

--------------------------------------------------------------------
Answer: y = 9x + 5
--------------------------------------------------------------------

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The formula of the volume of a pyramid is 1/3BH, where B represents the area of the base of the pyramid and H represents the hei

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Answer:

It depends on the relation between the heights of both pyramids

Step-by-step explanation:

We know the volume of a pyramid of base b and height h is

$V=\frac{1}{3}bh$

If the volume of the pyramid A is 3 times the volume of the pyramid B, then

$\frac{1}{3}b_ah_a=3*\frac{1}{3}b_bh_b=b_bh_b$

Which means

$b_ah_a=3*b_bh_b$

If we knew both heights are the same, we could conclude that

$b_a=3*b_b$

In which case the base of the pyramid A would be greater than the other base

But if, for example, the height of the pyramid A is 3 times the height of the other height, then

$3*b_a=3*b_b=>b_a=b_b$

Both bases would be the same.

If we choose that

$h_a >3*h_b$

it would mean

$b_a$

In which case the base of the pyramid A would be less than the other base

So the answer entirely depends on the relation between the heights of both pyramids

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3 years ago

6. Suppose that a fair coin is tossed 2 times, and the result of each toss (H or T) is recorded.

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Answer:

a) $S= {HH, HT, TH, TT}$

b) $P(X=0) = (2C0) (0.5)^0 (1-0.5)^{2-0}= 0.25$

$P(X=1) = (2C1) (0.5)^1 (1-0.5)^{2-1}= 0.5$

$P(X=2) = (2C2) (0.5)^2 (1-0.5)^{2-2}= 0.25$

And we have the following table:

X | 0 | 1 | 2

P(X) | 0.25 | 0.5 | 0.25

Step-by-step explanation:

Let's define first some notation

H= represent a head for the coin tossed

T= represent tails for the coin tossed

We are going to toss a coin 2 times so then the size of the sample size is $2^2 = 4$

a. What is the sample space for this chance experiment?

The sampling space on this case is given by:

$S= {HH, HT, TH, TT}$

b. For this chance experiment, give the probability distribution for the random variable of the total number of heads observed.

The possible values for the number of heads are X=0,1,2. If we assume a fair coin then the probability of obtain heads is the same probability of obtain tails and we can find the distribution like this:

$P(X=0) = (2C0) (0.5)^0 (1-0.5)^{2-0}= 0.25$

$P(X=1) = (2C1) (0.5)^1 (1-0.5)^{2-1}= 0.5$

$P(X=2) = (2C2) (0.5)^2 (1-0.5)^{2-2}= 0.25$

And we have the following table:

X | 0 | 1 | 2

P(X) | 0.25 | 0.5 | 0.25

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