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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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![### Directions: Find each angle and arc measures.
**Problem 1.**
- **Figure Description:** A circle with chord WX and chord ZY intersecting at point V inside the circle. The angle WVZ is given as 62°.
- **Question:** \( m\angle WXY = \_\_\_\_\_\_ \)
**Problem 2.**
- **Figure Description:** A circle with points D, G, F, and E on the circumference. Arc DEF is highlighted, and angle DEG is given as 113°.
- **Question:** \( mDG\!F = \_\_\_\_\_\_ \)
**Problem 3.**
- **Figure Description:** A circle with chord PQ intersecting chord QR at point P inside the circle. Angle PQR is required to be measured, and arc QR is labeled with measure S.
- **Question:** \( m\angle PQR = \_\_\_\_\_\_ \)
**Problem 4.**
- **Figure Description:** A circle with points A, B, C, and D on the circumference. Arc AC is labeled and needs to be measured. Angle AB is given as 47°.
- **Question:** \( mBC = \_\_\_\_\_\_ \)
**Problem 5.**
- **Figure Description:** A circle with points J, K, L, and M on the circumference. Chord JK and segment ML intersect at point N within the circle. Angle KNM is given as 53° and angle JML (exterior) is labeled as 65°.
- **Question:** \( m\angle JKL = \_\_\_\_\_\_ \)
**Problem 6.**
- **Figure Description:** A circle with labeled points R, S, T, U. Arcs between these points are labeled with measures. Arcs RS equals 64°, ST equals 75°, and TU equals 139°.
- **Questions:**
- \( m\angle RST = \_\_\_\_\_\_ \)
- \( m\angle RUT = \_\_\_\_\_\_ \)
### Detailed Explanation of Diagrams:
**1.**
- Figure shows intersecting chords which creates vertical angles. The angle given is outside the area, which is 62°.
**2.**
- The major arc DEF is clear with 113° represented as the measurement of angle DEG.
**3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F200b2461-3314-4728-9c25-6d3af737e402%2F0cdae505-1cdd-47de-985d-0341efdb5460%2Fqud3sgk_processed.png&w=3840&q=75)
Transcribed Image Text:### Directions: Find each angle and arc measures.
**Problem 1.**
- **Figure Description:** A circle with chord WX and chord ZY intersecting at point V inside the circle. The angle WVZ is given as 62°.
- **Question:** \( m\angle WXY = \_\_\_\_\_\_ \)
**Problem 2.**
- **Figure Description:** A circle with points D, G, F, and E on the circumference. Arc DEF is highlighted, and angle DEG is given as 113°.
- **Question:** \( mDG\!F = \_\_\_\_\_\_ \)
**Problem 3.**
- **Figure Description:** A circle with chord PQ intersecting chord QR at point P inside the circle. Angle PQR is required to be measured, and arc QR is labeled with measure S.
- **Question:** \( m\angle PQR = \_\_\_\_\_\_ \)
**Problem 4.**
- **Figure Description:** A circle with points A, B, C, and D on the circumference. Arc AC is labeled and needs to be measured. Angle AB is given as 47°.
- **Question:** \( mBC = \_\_\_\_\_\_ \)
**Problem 5.**
- **Figure Description:** A circle with points J, K, L, and M on the circumference. Chord JK and segment ML intersect at point N within the circle. Angle KNM is given as 53° and angle JML (exterior) is labeled as 65°.
- **Question:** \( m\angle JKL = \_\_\_\_\_\_ \)
**Problem 6.**
- **Figure Description:** A circle with labeled points R, S, T, U. Arcs between these points are labeled with measures. Arcs RS equals 64°, ST equals 75°, and TU equals 139°.
- **Questions:**
- \( m\angle RST = \_\_\_\_\_\_ \)
- \( m\angle RUT = \_\_\_\_\_\_ \)
### Detailed Explanation of Diagrams:
**1.**
- Figure shows intersecting chords which creates vertical angles. The angle given is outside the area, which is 62°.
**2.**
- The major arc DEF is clear with 113° represented as the measurement of angle DEG.
**3
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