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3 years ago

Find the probability that a point is chosen randomly inside the rectangle is in each given shape...

Mathematics

1 answer:

Arlecino [84]3 years ago

6 0

By taking the quotients between the areas, we see that:

a) P = 0.275
b) P = 0.85

<h3>How to find the probabilities?</h3>

First we need to find the areas of the 3 shapes.

For the triangle, the area is:

T = 3*5/2 = 7.5

For the blue square, the area is:

S = 3*3 = 9

For the rectangle, the area is:

R = 10*6 = 60

Now, what is the probability that a random point lies on the triangle or in the square?

It is equal to the quotient between the areas of the two shapes and the total area of the rectangle, this is:

P= (7.5 + 9)/60 = 0.275

b) The area of the rectangle that is not the square is:

A = 60 - 9 = 51

Then the probability of not landing on the square is:

P' = 51/60 = 0.85

If you want to learn more about probability:

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Write the digit in the ten thousands place.

navik [9.2K]

What digit is it lets say its 5 the ten thousands place would be 50,000 now the 5 is in the ten thousands place

6 0

3 years ago

The number of fish in a small bay is modeled by the function F defined by F(t)=10 (t3 â 12t2 + 45t +100), where t is measured in

RSB [31]

The graph of the given function is attached showing characteristics of the function.

The correct responses are;

(a) F'(4) = -30 means that on day 4, the number of fish in the bay is decreasing at a rate of 30 fish per day.

(b) Over the interval 0 ≤ t ≤ 8 the absolute minimum number of fish in the bay is; 1,000.

(d) The rate of change of the number of pelicans flying near is; P' = 10·(3·c² - 24·c + 45)

Reasons:

The given function is; f(t) = 10·(t³ - 12·t² + 45·t + 100)

Where;

t = Number of days

0 ≤ t ≤ 8

(a) The derivative of the given function is presented as follows;

F'(t) = 10 × (3·t² - 2×12·t + 45) = 10·(3·t² - 24·t + 45)

Therefore;

F'(4) = 10 × (3 × 4² - 24 × 4 + 45) = -30

Therefore F'(4) = -30 means that on day 4, the number of fish in the bay is decreasing at 30 fish per day.

(b) The absolute minimum is given as follows;

At a minimum or maximum value, F'(t) = 10·(3·t² - 24·t + 45) = 0

Which gives;

3·(t - 5)·(t - 3) = 0

t = 5, or t = 3

At t = 5, we have;

f(5) = 10 × (5³ - 12 × 5² + 45 × 5 + 100) = 1,500

At t = 3, we have;

f(3) = 10 × (3³ - 12 × 3² + 45 × 3 + 100) = 1,540

Therefore, f(5) = 1,500 is a local maximum

However, at x = 0, we have;

f(0) = 10 × (0³ - 12 × 0² + 45 × 0 + 100) = 1000

At x = 8, we have;

f(8) = 10 × (8³ - 12 × 8² + 45 × 8 + 100) = 2,040

Therefore, the absolute minimum is given at t = 8, where f(t) = 1,000

bay is decreasing is between the local maximum at t = 3, and the local

minimum at t = 5, which gives;

The rate of change of the number of fish is decreasing for values of t in the range;

3 ≤ t ≤ 5

(d) P = 10·(t³ - 12·t² + 45·t + 100)

P' = 10·(3·t² - 24·t + 45)

At time t = c, we have;

P' = 10·(3·c² - 24·c + 45)

Based on a similar question online, we have;

(c) The interval over which the rate of change is decreasing

(d) The rate of change of the number of pelicans flying near the bay at t = c

Learn more about differentiation of functions here:

brainly.com/question/1422315

5 0

2 years ago

A building contractor buys 60% of his cement from supplier A and 40% from supplier B. A total of 95% of the bags from A arriv

docker41 [41]

Answer: 0.665.

Step-by-step explanation:

60% of the bags are from supplier A, and 95% of them are undamaged.

40% of the bags are from supplier B, and 75% of them are undamaged.

Then, the number of undamaged bags from supplier A is:

0.6*0.95 = 0.57 or 57%

from B is:

0.4*0.75 = 0.3 or 30%

This means that the percentage of undamaged bags is:

57% + 30% = 87%.

Then, the probability that an undamaged bag is from supplier A is equal to the percentage of undamaged bags that came from supplier A (57%) and the total percentage of undamaged bags (87%) this is:

P = 57%/87% = 0.655 or 65.5%

Then the probability that an undamaged bag comes from supplier A is 0.665.

7 0

3 years ago

Write the equation of a line in slope intercept form of a line that has a slope of 1/2 and contains (-4,1)

Delicious77 [7]

The general form of the line is:
y = mx + c where:
m is the slope
c is the y-intercept

Now, we are given that the slope = 1/2.
The equation now became:
y = (1/2) x + c

Now, we need to get the y-intercept. We are given that (-4 ,1) belongs to the line. Therefore, this point satisfies the equation of the line. Based on this, we will substitute with this point in the equation above and solve for c as follows:
y = (1/2) x + c
1 = (1/2)(-4) + c
1 = -2 + c
c = 1+2
c = 3

Based on the above, the equation of the line is:
y = (1/2) x + 3

6 0

3 years ago

PLS HELP!! WILL MAKE BRAINLIEST!!!!

poizon [28]

Answer:

(86.2,0) is the x-intercept.

Step-by-step explanation:

You can use the slope formula to figure this one out:

Just use two of the points on the table, any of them will work:

$(33,-22)\\(52,-33)$

$\frac{-22-33}{33-52} =\frac{-55}{-19}=\frac{55}{19}$

Now you have the slope of the equation, now using the y-intercept equation you can substitute the variables for point of the table and the new slope.:

$(71,-44)\\y=mx+b\\-44=\frac{55}{19} (71)+b$

Now just solve for b to get the y intercept:

$-44=\frac{55}{19}(71)+b\\-44= \frac{3905}{19} +b\\(-\frac{3905}{19})-44=\frac{3905}{19} +b(-\frac{3905}{19})\\ -\frac{4741}{19}=b$

Now you have the y-intercept so you just have to plug in 0 to the y spot and it will calculate the x-intercept.

$0=\frac{55}{19}x-\frac{4741}{19}\\(+\frac{4741}{19})0=\frac{55}{19}x-\frac{4741}{19}(+\frac{4741}{19})\\\\\frac{4741}{19}=\frac{55}{19}x\\\frac{\frac{4741}{19}}{\frac{55}{19} }= \frac{\frac{55}{19} x}{\frac{55}{19} } \\\frac{431}{5} =x\\or\\86.2=x$

And that's the x-intercept.

5 0

2 years ago

Read 2 more answers