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The first term in a geometric sequence is 64, and the common ratio is 1/4. For what value of n is
\[t_n = \frac{1}{4}\]
Answer: A geometric series is represented as
\[t_1, t_1r, t_1r^2, t_1r^3, ......, t_1r^{n1} = t_n\]
\[\frac{1}{4} = 64(\frac{1}{4})^{n1}\]
\[4^{n2} = 4^3\]
n = 5
Final Answer: n = 5
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Find the relationships between words in the following questions. Select the choice that best completes the meaning of the sentence. 1. Scissors is to cut as pencil is to (A) snip. (B) write. (C) raze. (D) turn. (E) read. 2. Pasta is to sauce as (A) noodle is to dough. (B) tomato is to vine. (C) napkin is to plate. (D) toast is to jam. (E) cheese is to milk. 3. Bread is to crust as orange is to (A) butter. (B) pudding. (C) rind. (D) tree. (E) lemon. 4. Team is to captain as
(A) sport is to player. (B) paper is to reporter. (C) republic is to president. (D) game is to opponent. (E) navy is to ensign.
On the SAT, you may be asked to solve a system of inequalities. For example, you may be asked to solve for x that satisfy both inequalities.
Solve for x in the following inequalities:
\[ 7x \ge 21 \]
\[ 2x \lt 10 \]
Chameleon Tail: The tail of the West African chameleon is coiled up in a shape similar to that of a nautilus shell. 1. What is this type of curve called? In the figure below, AC is perpendicular to BD and angle ABC and angle EFG are right angles. 2. What is BP called with respect to triangle ABC? 3. Between which two segments is BP the geometric mean? 4. Which segment is the projection of EF on the hypotenuse of triangle EFG? 5. Between which two segments is EF the geometric mean? Answers:
1. Spiral. 2. The altitude to the hypotenuse. 3. AP and PC. 3. EP. 4. EP and EG. The polygons below were created by a mathematician Waclaw Sierpinski. These are also known as fractal polygons.
1. Voracious most nearly means ...
A) Hungry B) Loud C) Foolish D) Vast 2. Malignant most nearly means ... A) Possessive B) Deadly C) Positive D) Parallel 3. Liberate most nearly means ... A) Weigh B) Think C) Free D) Listen Domain and range are often confused by students. Let's start with the basic definitions (always a good thing to do).
The domain is the set of all first elements of ordered pairs (xcoordinates). The range is the set of all second elements of ordered pairs (ycoordinates). Let's take a simple example. What is the domain and range for points {(2,5), (4,8), (2,1), (3,5)}? Well, the set of x coordinates is {2,4,2,3} and the set of y coordinates is {5,8,1,5}. So the domain of these ordered pairs is {2,4,2,3} and the range is {5,8,1,5}. What about the domain of range of y = x^2 + 2? 1. Which word does not belong with the others?
A. bicycle B. minivan C. automobile D. motorcycle 2. Which word does not belong with the others? A. glum B. pleasant C. kindly D. amiable 3. Which word does not belong with the others? A. poodle B. greyhound C. working dog D. collie There are 42 integers in a group. If there are 5 times as many odd integers as there are even integers, how many numbers are even integers?
If 3x  y = 12, what is the value of
A trundle wheel can be used to measure distance along the ground. The distance traveled in one revolution of the wheel is equal to the circumference of the wheel. Given that the circumference of a trundle wheel is 3 feet, find
a) its diameter to the nearest 0.1 inch. b) the distance that the wheel travels in making five revolutions. The relationship between speed, mass, weight, and friction was studied using a toy car that carried additional masses. The car was placed on a 1m inclined plane and released. The time it took to go down the incline and the time it took to go one meter beyond the incline were recorded. Experiment 1: Additional masses were added to the car as it was released down the incline plane. The car has a mass of 50 g. The plane was angled at a 25 degree angle.
Experiment 2: The incline of the plane was changed to determine its effect on the time it took the car to travel down the plane. There were no additional masses placed on the car.
How is the design of Experiment 1 different from that of Experiment 2?
A. Experiment 2 varied the mass on the car while Experiment 1 varied the angle of the plane. B. Experiment 1 varied the mass on the car while Experiment 2 varied the angle of the plane. C. Experiment 1 and Experiment 2 tested the same variable in different ways. D. Experiment 1 and Experiment 2 have no differences. A square and a rectangle have the same perimeter. The square has a length and width of 4 and the rectangle has a length of 5. What is the area of the rectangle?
A. 3 B. 6 C. 15 D. 30 Upper Level ISEE: A fair sixsided die is rolled twice. What is the probability that the first roll produces a 2 and the second roll does NOT produce a 4?
(A) 1/36 (B) 1/18 (C) 5/36 (D) 1/6 (E) 1/3
If x is the average, the arithmetic mean, of m and 9, y is the average of 2m and 15, and z is the average of 3m and 18, what is the average of x, y and z in terms of m?
The pupil of the eye controls the amount of light entering the eye. The widest that it gets, in dim light, is about 8mm in diameter. In very bright light, it gets as narrow as 2mm. What is the approximate area of the pupil when its diameter is:

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