Find a symmetric matrix A with non-negative eigenvalues and show that A has a symmetric square root R such that R2=A. Then, find two different square roots of the matrix B=[5−3−35].
Find the value of 'c' to make the given quadratic expressions perfect squares. Express the equations in vertex form by completing the square. 1. (a) x2+14x+c, (b) x2−9x+c, (c) x2−67x+c 2. Express the equations in vertex form by completing the square.
Cammy bought a jacket at $43.50. The price was 25% off the regular price. What was the regular price? Jim bought a pair of pants at $16.80. The price was 40% off the regular price. What was the regular price?
A county park system has 19 golf courses of varying difficulty. There are 4 gold courses and twice as many bronze as silver courses. How many selections are possible if a golfer decides to play a round at a silver or gold course? □ possible selection(s).
Select the correct equation for the direct variation between an object's height h and the length of its shadow l, where k is the constant of variation.
A. l=kh
B. h=k
C. l=hk
D. l=h+k
Fifty-four anesthetized wild bears were measured for weights and chest sizes. Is there sufficient evidence of a linear correlation between weights and chest sizes? Can chest size be used to predict weight? Use α=0.05. Correlation Results:
Correlation coeff, r: 0.965434
Critical r: ±0.2680855
P-value (two tailed): 0.000 Determine the null and alternative hypotheses:
H0:ρ=0H1:ρ=0
Find the profit function for a product where revenue is R=580x and cost is C=15,000+40x+x2. Determine the number of units that maximizes profit and the maximum profit. a. P(x)=580x−(15,000+40x+x2)
b. Find x that maximizes P(x)
c. Evaluate P(x) at the optimal x to find the maximum profit.
Identify the sampling method used for a sample of every 49th student from 496 students: A. Convenience, B. Random, C. Systematic, D. Cluster, E. Stratified.
(a) Find area of shaded part of a circle in an 8cm x 8cm square with 4 shaded corners.
(b) Find area of shaded part with no additional information provided.
Find the equation of a quadratic relation transformed from y=(x+6)2+3 with a vertical compression by 21, reflection along the x-axis, and translations 1 unit down and 3 units right.
Beach clean-up volunteers collected 1.5 more pounds per person this year. With 80 volunteers, they removed 360 pounds total. Find the average amount of trash collected per volunteer last year using the equation: 1.5x+80=360.
Find the number of Moons that can fit inside Earth, given that the volume of the Moon is 2.18×1010 cubic km and the volume of Earth is 1.09×1010 cubic km.
The math team divided a set of problems evenly. If each of the 8 teammates got 4 problems, find the total number of math problems in the set. Write a division equation with m to model the story, then solve for m. Division equation: m÷8=4m=32
Find a function g(x) for Juan's weekly earnings, where he earns 7perhourand20 per week making picture frames. Determine the slope and interpret its meaning.