what is the equation of a parabola with its vertex at the origin and focus at (–6,0)
Since the vertex is at the origin, the equation of the parabola is of the form y^2 = 4px.
The distance from the vertex to the focus is p, so in this case p = 6.
Therefore, the equation of the parabola is y^2 = 24x.
Garrett throws a dart at a circular dart board. The dart board has a radius of 16 inches, and the bull's eye in the center of the dart board has a radius of 6 inches
What is the probability that a dart thrown at random within the dartboard will hit the bull's eye? Round your answer to the nearest tenth, if necessary
The area of the entire dart board is πr^2 = π(16)^2 = 256π square inches.
The area of the bull's eye is πr^2 = π(6)^2 = 36π square inches.
Therefore, the probability of hitting the bull's eye is:
36π / 256π = 0.140625
Rounded to the nearest tenth, the probability is 0.1.
Garrett throws a dart at a circular dart board. The dart board has a radius of 16 inches, and the bull's eye in the center of the dart board has a radius of 6 inches. What is the probability that a dart thrown at random within the dartboard will hit the bull's eye? Round your answer to the nearest tenth, if necessary
A. 37.5%
B. 26.7%
C. 7.1%
D. 14.1%
The area of the entire dart board is πr^2 = π(16)^2 = 256π square inches.
The area of the bull's eye is πr^2 = π(6)^2 = 36π square inches.
Therefore, the probability of hitting the bull's eye is:
36π / 256π ≈ 0.141
Rounded to the nearest tenth, the probability is 14.1%.
Therefore, the correct answer is D. 14.1%.
You roll a standard, six-sided number cube. What is the probability of rolling a prime number or a number greater than 4?
The prime numbers on a standard number cube are {2, 3, 5}. The numbers greater than 4 are {5, 6}. Since 5 is in both sets, we only need to count it once. So, the set of outcomes that satisfy the condition of rolling a prime number or a number greater than 4 is {2, 3, 5, 6}.
The total number of outcomes on a standard number cube is 6, so the probability of rolling a prime number or a number greater than 4 is:
Number of outcomes that satisfy the condition / Total number of possible outcomes
= 4 / 6
= 2 / 3
= 0.667 (rounded to three decimal places)
Therefore, the probability of rolling a prime number or a number greater than 4 is approximately 0.667.
The test scores for a math class are shown below. 81, 85, 82, 93, 85, 84, 95, 87, 88, 91
what are the mean median and mode of date set
To find the mean of the data set, we add up all the numbers and divide by the total number of numbers:
Mean = (81 + 85 + 82 + 93 + 85 + 84 + 95 + 87 + 88 + 91) / 10 = 870 / 10 = 87
So the mean is 87.
To find the median of the data set, we first need to put the numbers in order from least to greatest:
81, 82, 84, 85, 85, 87, 88, 91, 93, 95
There are 10 numbers in the data set, so the median is the average of the 5th and 6th numbers:
Median = (85 + 87) / 2 = 86
So the median is 86.
To find the mode of the data set, we look for the number that appears most frequently. In this case, the number 85 appears twice, and all the other numbers appear only once, so the mode is 85.
So the mean is 87, the median is 86, and the mode is 85.
going back to the first question,
the bot's parabola has a focus at (6,0), should be at (-6,0)
so how about
y^2 = -24x