Activity: Counting Theory (Rule of Sum and Rule of Product) Alyssa is trying to decide what to wear. She has shirts in the following colors: red, purple, and blue, and she has pants in the following colors: black and white. How many different outfits can Alyssa choose from (assuming she selects one shirt and one pair of pants)?

Q: Find L" 55+1

A: As per as our guideline i am supposed to answer only one question from these two question please…

Q: |8 -5 1| 5. If 5 16 1 = 2, then what is value of x 1l 3 а. 6 b. 5 c. 8 d. 4

A: using the concept of determinant.

Q: Solve the equation for positive integer n: ()-() (4,

A: Given that:n9=n4n!9!(n-9)!=n!4!(n-4)!9!(n-9)!=4!(n-4)!

Q: O y = |x| 5- 4 1 O y = 3- 2 O y = V¤ а. -5 -4 -3 -2 - 4 5 O y = a? -2 O y = x³ -3 -4 O y = x -5+ 1 2…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: 7. Let ƒ(x) = 4x − 3, g(x) = x² + 4, h(x) = x + 5. Evaluate the following.

A: Given f(x) = 4x - 3 g( x ) = x2 + 4 h( x ) = x + 5

Q: 4.) 40- (8 x 9) 3+ 10

A: Given expression: 40-8×9÷3+10

Q: あ。(12イ45 bt-ef e

A: 2x+53ax-53

Q: (2+Si)• (2 + 7i)

A: Rational Numbers: All the numbers which can be written in the form of pq. Here, p and q are integers…

Q: 3. 4. 7 X 6√2 X X 24

A: 3. We have given diagram of a square Using pythagoras theorem  (Hypotenuse)^2=(Perpendicular)^2 +…

Q: Consider the following equation f (x,y) = x²y. Find the derivative of f in the direction of (1, 2)…

A:

Q: 5 2. 14x dx

A:

Q: 12

A:

Q: 7. dz | zV 36z2 - 25

A:

Q: 1 Select one: а. x - 1 1 1 In 2 x2 b. 1 2 In C. 4 In X 2 x2 d. In X 2 + C 2 x2

A:

Q: 3. Find the LCM of 15a b5 and 40a 64. O 120a 65 O 120a*65 O 120a b O 120a 64

A:

Q: 2 |12-x²+ x) dz. -3

A: Given: ∫-32(2-x2+x)dx

Q: XP If x=Y Vi-y!.find d

A: x =y1-y2 dy/dx = ? now derivate with x dx/dx = (dy/dx)1-y2 - (2y2/21-y2)(dy/dx) 1 = (dy/dx)(1-y2 -…

Q: f z dz z+1 Ans. 1 - Int

A:

Q: 25 25y" + 20y + 4y = 0

A: we have to solve the given differential equation.

Q: Evaluate [4/5+91 +12(5+91)' dt .

A: Given,        ∫45+9t+125+9t7dt

Q: - |xVx +1 dx

A:

Q: Enter the value of L- 1.27].

A: Floor value of x  is given as the greatest integer that is less than or equal to x

Q: 7 (x+1)2 dx а. 11 x 2

A: Use the substitution method, to simplify the integral ∫x+172x112dx.…

Q: 97 45. -x³dx +

A:

Q: A laboratory blood test is 95 % effective in detecting a certain disease when it is actually…

A: Bayes' Theorem: Let A1, A2, ... , An be n mutually exclusive and exhaustive events with P(Ai) > 0…

Q: 8 n (-2) n 3231 7zZ

A:

Q: 24 %24 3. ぶ3 3.

A:

Q: 214 500 %3D

A: The obtain the value of 214500, divide the number 214 by the number 500. That is, here the dividend…

Q: Consider the following. y 10r (4, 9) 8 (0,7)

A: (a). Obtain the least squares equation: Given data represents the graph for the dependent variable…

Q: 1 Evaluate dz . +=11.0 (z – 9.0) (2 + 144)?

A:

Q: bim nto

A: when we get 0/0 form, libnitz rule is used.

Q: -4 (70 -1 1 7

A: Given,          70-1-417

Q: 千 How muchr is Bc ? A to

A: The Pythagoras theorem is very significant in geometry. IT is related to a  right angle triangle. By…

Q: 2 x -dx 6. Jo 1-x

A:

Q: graph of f(x) is shown below. Find the graph of f'(x). HI -6-5-4-3-2- 5 -2 I N I T m A 10 16 1 Im 14…

A: Given query is to find the graph of derivative.

Q: 1. (-√6 + i√2)*

A: To simplify: -6+i24=-6+i222=(-6)2-262i+(i2)22=6-23(2)2i+2i22=6-43i-22=(4-43i)2