## SAT - Math

LEAP Administrator
3 months ago
**Math** |
**Probability**

### Results on the Bar Exam of Law School Graduates The table above summarizes the results of 200 (more)

Passed Bar Exam | Did not pass bar exa | |

Took review course |
18 | 82 |

Did not take review course |
7 | 93 |

Results on the Bar Exam of Law School Graduates. The table above summarizes the results of 200 law school graduates who took the bar exam. If one of the surveyed graduates who passed the bar exam is chosen at random for an interview, what is the probability that the person chosen did not take the review course?

x= total Law School Graduates- Did not pass bar exam- who took review course who passed the bar exam. x= 200-175-18 x=7

LEAP Administrator
3 months ago
**Math** |
**Quadratic Equations**

### In the equation above a b and c are constants If the equations is true for all values of x what is the value of b (more)

2x(3x 5) 3(3x 5) = ax^{2} bx c

In the equation above, a, b, and c are constants. If the equations is true for all values of x, what is the value of b?

2x(3x + 5) + 3(3x + 5) = ax^{2} + bx + c

expanding LHS

6x^{2} + 10x + 9x + 15 = ax^{2} + bx + c

6x^{2} + 19x + 15 = ax^{2} + bx + c

comparing coeficients

b = 19

LEAP Administrator
3 months ago
**Math** |
**Probability**

### The data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. (more)

The data in the table above were produced by a sleep researcher studying the number of dreams people recall when asked to record their dreams for one week. Group X consisted of 100 people who observed early bedtimes, and Group Y consisted of 100 people who observed later bedtimes. if a person is chosen at random from those who recalled at least 1 dream, what is the probability that the person belonged to Group Y?

Event X: A person chosen randomly recalls dream at least once

Event Y: Probability that the person belonged to Group Y

P(Y) = 100/200 = 1/2

P(X) = 1 - (15+21) / 200 = 1- 36/200 = 1-9/50 = 41/50

P(X|Y) = (11 + 68) / 100 = 79/100

P(

LEAP Administrator
3 months ago
**Math** |
**Time and Work**

### Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour (more)

Wyatt can husk at least 12 dozen ears of corn per hour and at most 18 dozen ears of corn per hour. Based on this information, what is a possible amount of time, in hours, that it could take Wyatt to husk 72 dozen ears of corn?

Minimum time taken for 72 dozen ears of corn

time taken for 12 dozen ears of corn = 1 hour

time taken for 1 dozen ears of corn = 1/12 hours

time taken for 72 dozen ears of corn = 1/12 * 72 = 6 hours

Maximum time taken for 72 dozen ears of corn

time taken for 18 dozen ears of corn = 1 hour

time taken for 1 dozen ears of corn = 1/18

time taken for 72 dozen ears of corn = 1/18 * 72 = 4 hours

thus

time taken will be between 4 and 6 hours

LEAP Administrator
3 months ago
**Math** |
**Geometry**

### A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. (more)

A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. The lengths represented by AB, EB, BD and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and the angle AEB and the angle CBD have the same measure. What is the value of x?

∠ABE = ∠CBD (Vertically Opposity angles)

∠BEA = ∠BDC (Given)

thus triangle ABE ~ triangle CBD

thus

BE/BD = AE/CD

1400/700 = x / 800

x = 1600 ft.