Sequences, Angles, and Probability Concepts

The video tutorial covers homework questions 27 to 32, focusing on slope ratios in triangles, arithmetic and geometric sequences, probability in shape selection and music playlists, and angle calculations in triangles. Each section provides detailed explanations and encourages students to think critically about the problems presented.

What is the slope ratio for a triangle with a 35-degree angle if the opposite side is 7 and the adjacent side is 10?

• 7/10

• 10/7

• 2/1

• 1/2

If a triangle has a 55-degree angle, what would the slope ratio be if the opposite side is 10 and the adjacent side is 7?

• 2/1

• 1/2

• 10/7

• 7/10

Why can both Ben and Carla be correct about the slope ratio?

• Because the triangle is isosceles

• Because the ratio depends on the angle used

• Because both ratios are equal

• Because the triangle is equilateral

Delilah claims the slope angle must be more than 45 degrees if the slope ratio is greater than one. Do you agree?

• No, because slope angles are always less than 45 degrees

• No, because a slope ratio greater than one indicates an angle less than 45 degrees

• Yes, because all slope angles are greater than 45 degrees

• Yes, because a slope ratio greater than one indicates an angle greater than 45 degrees

Isaiah disagrees with Lyra's slope ratio calculation of 2.675 for a 19-degree angle. Who is correct?

• Both are incorrect

• Neither, because the angle is irrelevant

• Lyra, because the ratio is correct

• Isaiah, because the ratio should be less than one for a 19-degree angle

What must be true about X if the angle is 76 degrees and the ratio 9/X is greater than one?

• X must be greater than 9

• X must equal 9

• X must be less than 9

• X must be greater than 45

What type of sequence is it if each term is obtained by adding 3 to the previous term?

• Arithmetic

• Neither

• Both

• Geometric

If a sequence starts at 1 and each term is multiplied by 2, what type of sequence is it?

• Both

• Arithmetic

• Geometric

• Neither

What is the common difference in an arithmetic sequence where the first term is 1 and the second term is 4?

• 1

• 2

• 3

• 4

In a sequence where each term is obtained by adding 7, what is the equation for the nth term if the first term is 5?

• T(n) = 7n + 5

• T(n) = 7n - 2

• T(n) = 7n + 2

• T(n) = 7n - 5