MATHEMATICS HIGH SCHOOL

Suppose you throw a dart at a circular target of radius 10 inches. Assuming that you hit the target and that the coordinates of the outcomes are chosen at random, find the probability that the dart falls (a) within 2 inches of the center. (b) within 2 inches of the rim. (c) within the first quadrant of the target. (d) within the first quadrant and within 2 inches of the rim.

Answers

Answer 1

Answer:

Answer:

a) The probability is 0.04

b) The probability is 0.36

c) The pprobability is 0,25

d) The probability is 0.09

Step-by-step explanation:

Lets calculate areas:

the target has a radius of 10 inces, hence the target area has a area on 10²*π = 100π square inches.

a) A circle of 2 inches of radius has an area of 2²π = 4π square inches, hence the probability of hitting that area is 4π/100π = 1/25 = 0.04

b) If the dart s within 2 inches of the rim, then it is not at distance 8 inches from the center (that is the complementary event). The probability for the dart to be at 8 inches of the center is 8²π/100π = 64/100 = 16/25 = 0.64, thus, the probability that the dart is at distance 2 or less from the rim is 1-0.64 = 0.36.

c) The first quadrant has an area exactly 4 times smaller than the area of the target (each quadrant has equal area), thus the probability for the dart to fall there is 1/4 = 0.25

d) If the dart is within 2 inches from the rim (which has probability 0.36 as we previously computed), then it will be equally likely for the dart to be in either of the 4 quadrants (the area that is within 2 inches from the rim forms a ring and it has equal area restricted on each quadrant). Therefore, the probability for the dice to be in the first qudrant and within 2 inches from the rim is 0.36*1/4 = 0.09.

Related Questions

Sarah solved a quadratic equation. Her work is shown below, with Step 1 missing.What could Sarah have written as the result from Step 1?2(x + 1)2 +6 = 134Step 1(x+1)2 – 64Step 22+1 =18Step 3x = -9 or x = 7 Step 4Khan academy quiz
A sociologists was investigating the ages of grandparents of high school students. From a random sample of 10high school students, the sociologist collected data on the current ages, in years, of the students' maternal grandparents. A. One of the sociologist's research questions was about the mean difference in age without regard to which grandparent is older. The interval constructed in part (a) does not address such a question. Based on the sample of high school students, give the value of the point estimate for the mean difference in age that could be used to address the sociologist's question.
NOT JUST THE ANSWER!! NEED STEP BY STEP ANSWER.6(y+3)=24
A straight line has an equation y= 4x=5 Write down the equation of the straight line that is parallel to y=4x-5 and passes through the point (0,3).
123A5/61/89 011 1213/141516In the figure, plly and "||s. Match each pair of congruent angles with the reason for their congruency.corresponding angles forparallel lines p and q cut bythe transversalrcorresponding angles forparallel lines r and s cut bythe transversal aVertical Angles TheoremLinear Pair Theorem25 2132125210 214213 = 216corresponding angles forparallel lines p and q cut bythe transversal s

The cheerleaders are practicing a dance routine in which all 36 of them need to be in a triangular formation. there will be two more cheerleaders in each row than the previous row. how many rows will be in the formation

Answers

If you start with 1 cheerleader in row A, then you'll have 3 cheerleaders in row B (add on 2), and then 5 cheerleaders for row C (add on another 2), etc etc.

Note how: 1+3+5 = 4+5 = 9 which is a perfect square. Also note that 36 is a perfect square.

Rule: The sum of the first positive n odd numbers is going to be equal to n^2. In the example of adding the first three odd numbers (1,3,5), we have n^2 = 3^2 = 9 as the sum

So as you can see, we'll have n = 6 rows because n^2 = 6^2 = 36 and

1+3+5+7+9+11 = 36

which is the sum of the first six positive odd numbers. So we'll have 1 cheerleader in row A, 3 in row B, 5 in row C, 7 in row D, 9 in row E, 11 in row F to have 6 rows total.

Final answer:

To determine the number of rows in the triangular formation, set up an equation and solve for x. The number of rows is 6.

Explanation:

To determine the number of rows in the triangular formation, we can set up a series of equations.

Let x be the number of rows.

The first row will have 1 cheerleader, the second row will have 3 cheerleaders, the third row will have 5 cheerleaders, and so on.

We can set up the equation: 1 + 3 + 5 + ... + (2x-1) = 36.

This is the sum of an arithmetic sequence with a common difference of 2. Solving for x, we get x = 6.

Therefore, there will be 6 rows in the formation.

Learn more about Number of rows in triangular formation here:

brainly.com/question/32274950

#SPJ12

4 ^sqrt 400/ 4^ sqrt 5

Answers

4^ sqrt(400) / (4^ sqrt(5))
= 4^20/ 4^ sqrt(5)
= 4^ (20- sqrt(5)

The final answer is 4^ (20- sqrt(5)~

When creating a scatterplot, if the points are too close together to see the relationship, how could you adjust your graph?A.
decrease your scale values
B.
increase your scale values
C.
plot more points
D.
plot fewer points

Answers

The correct answer for this question is this one: "B. increase your scale values"

When creating a scatterplot, if the points are too close together to see the relationship, You adjust your graph by increasing your scale values
Hope this helps answer your question and have a nice day ahead.

Answer:

Option: B is correct.

B) Increase your scale values.

Step-by-step explanation:

When creating a scatterplot, if the points are too close together to see the relationship,then we must increase the scale value of our graph .

" Because by doing so the point will seem to be farther and we could see the clear relationship between the points and hence it will not create any confusion regarding the visual of the points and hence easily the inference could be drawn"

Hence, option: B is true.

(B) Increase the scale value)

A total of 60 children signed up for hockey. There were 3 boys for every 1 girl who signed up. How many of the children who signed up for hockey were girls?

Answers

Answer: The answer is 15.

Step-by-step explanation: Given that there are a total of 60 students who signed up for hockey, where there were 3 boys for every 1 girl who signed up. We are to find the number of girls who signed up.

The ratio of the number of boys to the number of girls will be 3 : 1.

Let '3x' and 'x' be the number of boys and number of girls respectively who signed up.

Therefore, we have

$3x+x=60\n\n\Rightarrow 4x=60\n\n\Rightarrow x=15.$

Thus, the number of girls is 15.

60÷(3+1)=15 1*15 = 15 girls 3*15 = 45 boys

Lois is 3 years older than Oscar. The sum of their ages is no more than 20. Write an inequality that can be used to represent this situation, where x represents Oscar’s age.