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3 years ago

If points (7,a), (-5,2) and (3,6) are collinear, find a.

Mathematics

1 answer:

uysha [10]3 years ago

7 0

Answer:

The value of a is 8

Step-by-step explanation:

If the three lines are collinear, they all lie on the same line

So let us have the equation of a line that passes through the known ends

the slope will be;

m = (6-2)/(3 + 5) = 4/8 = 1/2

The general form is;

y = mx + b

so, we have

y = 1/2x + b

To get b, we use any of the two known points

6 = 3/2 + b

b = 6-3/2

b = (12-3)/2 = 9/2

So the equation of the line is;

y = 1/2x + 9/2

Multiply through by 2

2y = x + 9

So for the point , to get a , we have that

2(a) = 7 + 9

2a = 16

a = 16/2

a = 8

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The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard dev

Vladimir [108]

Answer:

Probability that the average length of a sheet is between 30.25 and 30.35 inches long is 0.0214 .

Step-by-step explanation:

We are given that the population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches.

Also, a sample of four metal sheets is randomly selected from a batch.

Let X bar = Average length of a sheet

The z score probability distribution for average length is given by;

Z = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean = 30.05 inches

$\sigma$ = standard deviation = 0.2 inches

n = sample of sheets = 4

So, Probability that average length of a sheet is between 30.25 and 30.35 inches long is given by = P(30.25 inches < X bar < 30.35 inches)

P(30.25 inches < X bar < 30.35 inches) = P(X bar < 30.35) - P(X bar <= 30.25)

P(X bar < 30.35) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < $\frac{30.35-30.05}{\frac{0.2}{\sqrt{4} } }$ ) = P(Z < 3) = 0.99865

P(X bar <= 30.25) = P( $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ <= $\frac{30.25-30.05}{\frac{0.2}{\sqrt{4} } }$ ) = P(Z <= 2) = 0.97725

Therefore, P(30.25 inches < X bar < 30.35 inches) = 0.99865 - 0.97725

= 0.0214

7 0

3 years ago

20 points.Cynthia has a bag of jellybeans. There are two red jellybeans, one yellow jellybean, and two black jellybeans in her b

solmaris [256]

Answer:

2/5

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Tobias rented a kayak from a sports equipment store.

Ket [755]

Answer:

Step-by-step explanation:

Let x = every day he rented the kayak

Since the store charges $60 for each day, multiply x by 60 like this: 60x

They also have $25 on top of that; 60x + 25

This all has to equal $325; 60x + 25 = 325

To solve for x, subtract 25 from both sides

60x + 25 = 325

- 25 - 25

60x = 300

Divide both sides by 60

60x/60 = 300/60

x = 5

This means Tobias rented the kayak for 5 days

7 0

3 years ago

A toy rocket is launched from a platform that is 48 feet high.

Softa [21]

Answer: then the rocket would be 48 feet in the sky/air.

Step-by-step explanation:

6 0

4 years ago

Two rectangles are similar. One has a length of 11 cm and a width of 10 cm, and the other has a width of 7 cm. Find the length o

s2008m [1.1K]

Answer:

Step-by-step explanation:

If the rectangles are similar to one another, then their sides exist in proportion to one another. Set up a proportion with the larger rectangle on top and the smaller rectangle on bottom:

$\frac{l}{s}:\frac{10}{7}=\frac{11}{x}$

Cross multiply to get

10x = 77 so

x = 7.7

5 0

3 years ago