Two figures that can be transformed into each other by a congruence transformation are said to be congruent. Cougruence transfomations of the plane include translation, rotation, reflection, glides, and the identity map. Every congruent transformation in the plane can be achieved by a maximum of three reflections
f(6) = 1+2+4+8+16+32 = 63
f(7) = 63 + 64 = 127
This is a geometric sequence where r the common ratio = 2.
f(n) = a1 * (r^n - 1) / (r - 1)
here a1 = 1 and r = 2 so
f(n) = (2^n - 1) / (2 -1)
= 2^n - 1.
When n = 64 ( the last square on the chess board)
f(n) = 2^64 - 1 = 2^64 ( I think we can neglect the 1!!)
That is the total number of grains of rice.
In tons of rice this is 2^64 / (25,000 * 2000)
= 3.689349 * 10^11 tons approximately.
So for each person the amount of rice would be 3.689349 * 10^11 / 6 * 10^9
= 61.5 tons approx. (Answer).
Answer:
Yes, point B will lie inside the circle.
Step-by-step explanation:
Let the distance between point C and point A be the radius of our given circle.
We have been given that a circle with center C(4, -2) passes through the point A(1, 3).
Since we know that a point will lie inside circle if the distance between the point and center of circle is less than radius of circle.
Let us find distance between points C and A using distance formula.
Radius of our circle is . Now let us find distance between center of our circle and point B.
We can see that distance of point B from center of our given circle is less than distance between point A and center of circle, therefore point B will lie inside the circle.
Answer:
(x + 3)(2x + 5)
Step-by-step explanation:
Given
2x² + 11x + 15
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × 15 = 30 and sum = + 11
The factors are + 6 and + 5
Use these factors to split the x- term
2x² + 6x + 5x + 15 ( factor the first/second and third/fourth terms )
= 2x(x + 3) + 5(x + 3) ← factor out (x + 3) from each term
= (x + 3)(2x + 5)
Answer:
0.1069 = 10.69%
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation , the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
Between 57 and 69
This is the pvalue of Z when X = 69 subtracted by the pvalue of Z when X = 57. So
X = 69
has a pvalue of 0.9918
X = 57
has a pvalue of 0.8849
0.9918 - 0.8849 = 0.1069 = 10.69%