(b) Solve the circuit. That is find all unknown currents, voltages, and resistances. 6. Consider the circuit in Figure 4, where R1 = 5.00×102Ω, R2 = 1.00×103Ω, and VB = 10.0V . (a) Find the equivalent resistance Req of the circuit.
Name Class Date 8-1 1. 3s3t3 Practice Adding and Subtracting Polynomials Form K Find the degree of each monomial. 2. 3n 3. 5xy 4.
[2] iii) Find the equation of the circle. [2] iv) The line y + 5x = 8 cuts the circle at A and again at a second point D. Calculate the coordinates of D. [4] v) Prove that the line AB is perpendicular to the line CD. [3] 5. Find the angle ( and the length x in the triangle shown below. [7] 6.
Give a complete explanation for the "Negative ..._______The negative exponent rule states that when a variable or number is raised to a negative exponent, the expression may be rewritten as one divided the variable or number raised to that positive exponent. A negative exponent indicates “reciprocal”. When a factor is moved from the denominator to the numerator or from the numerator to the denominator, the sign of the exponent changes.9. Give a complete explanation for the "Fraction raised to... ______In the fraction raised to a negative exponent rule, with fractions in the form a over b, a is not equal to zero and b is not equal to zero. A over B with a negative
Then divide each term by GCF to determine what is left inside the parentheses.) Example 2: 18x2y3z5 - 24x5y2z + 30x3y4z2 Solution: 6x2y2z(3yz4 - 4x3 + 5xy2z) 2. Look to see if it is a difference between two perfect squares. (need 4
Set up the matrix equation to solve this system. 2. Given the inequality y < x2 + 2x – 3, is the point (0, -3) part of the solution? Name a point that is part of the solution and one that is not. 3.
Assignment #2 1) Improve the result from problem 4 of the previous assignment by showing that for every e> 0, no matter how small, given n real numbers x1,...,xn where each xi is a real number in the interval [0, 1], there exists an algorithm that runs in linear time and that will output a permutation of the numbers, say y1, ...., yn, such that ∑ ni=2 |yi - yi-1| < 1 + e. (Hint: use buckets of size smaller than 1/n; you might also need the solution to problem 3 from the first assignment!) 2) To evaluate FFT(a0,a1,a2,a3,a4,a5,a6,a7) we apply recursively FFT and obtain FFT( a0,a2,a4,a6) and FFT(a1,a3,a5,a7). Proceeding further with recursion, we obtain FFT(a0,a4) and FFT(a2,a6) as well as FFT(a1,a5) and FFT(a3,a7). Thus, from bottom up, FFT(a0,a1,a2,a3,a4,a5,a6,a7)
TOPIC 8 Chi-Square goodness-of-fit test Problem 12.1 Use a chi-square goodness-of-fit to determine whether the observed frequencies are distributed the same as the expected frequencies (α = .05) Category | fo | fe | 1 | 53 | 68 | 2 | 37 | 42 | 3 | 32 | 33 | 4 | 28 | 22 | 5 | 18 | 10 | 6 | 15 | 8 | Step 1 Ho: The observed frequencies are distributed the same as the expected frequencies Ha: The observed frequencies are not distributed the same as the expected frequencies Step 2 df = k – m – 1 Step 3 α = 0.05 x 2 0.05, 5df = 11.0705 Step 4 Reject Ho if x 2 > 11.0705 Category | fo | fe | | 1 | 53 | 68 | | 2 | 37 | 42 | | 3 | 32 | 33 | | 4 | 28 | 22 | | 5 | 18 | 10 | | 6 | 15 | 8
Use the commutative and associative laws to write at least three expressions equivalent to (3x)y. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 94 3C • b Properties of Real Numbers Use the commutative and associative laws to find equivalent expressions. Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 95 3C Properties of Real Numbers Use the distributive laws to multiply expressions like 8 and x – y. Consider a multiplication problem from arithmetic: To carry out the multiplication, we actually added two products. That is, Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 96 3C Properties of Real Numbers Use the distributive laws to multiply expressions like 8 and x – y. Compute in two ways: Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 97 3C Properties of Real Numbers The Distributive Law of Multiplication over Addition Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. Slide 98 3C Properties of Real Numbers The Distributive Law of Multiplication over
If the sentence is geometric, find the common ratio r. If the sequence is arithmetic, find the common difference d. 3 3 3 3 3 , , , , ,... 2 4 8 16 32 A) arithmetic, d = C) geometric, r = 1 6 1 2 B) neither D) geometric, r = 2 28) 29) Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is geometric, find the common ratio r. If the sequence is arithmetic, find the common difference d. 1 1 1 1 , , , 4 6 8 10 A) geometric, r = 1 2 B) geometric, r = 2 D) neither 1 2 29) C) arithmetic, d =