AuthorWrite something about yourself. No need to be fancy, just an overview. Archives
January 2018
Categories
All

Back to Blog
The volume of a 3 dimensional solid is the amount of space it occupies. â€‹
Since the end (base) of a cylinder is a circle, the area of that circle is given by the formula:
\[area = Ï€ r^2\]
The volume of a cylinder is found my multiplying the area of one end of the cylinder by its height. So the formula of the volume of a cylinder is:
\[volume = Ï€ r^2 h\]
where:
Ï€ is Pi, approximately 3.142 r is the radius of the circular end of the cylinder h height of the cylinder
Our problem involves calculating the volume of Amazon Echo. The height of the Echo is 235mm while the diameter of the base is 84 mm or 8.4cm . Let's first find the area of the base.
The area of the base of Amazon Echo is:
\[area = Ï€ r^2\]
\[= 3.142 x 8.4^2\]
= 221.56 cm^2
To calculate the volume, we multiply the area with the height of the Echo, which is 235mm or 23.5cm
So, volume of Alexa Echo = 221.56 * 23.5 = 5,206.6224 cm^3
0 Comments
read more
Back to Blog
N.B: SAT Subject Test Math Level 2 Question
Question
What is the sum of the roots of the equation?
\[(x  \sqrt{2})(x^2  \sqrt{3x} + \pi) = 0\]
(A) 0.315
(B) 0.318 (C) 1.414 (D) 3.15 (E) 4.56
Back to Blog
Question:If there are known to be 4 broken transistors in a box of 12, and 3 transistors are drawn at random, what is the probability that none of the 3 is broken?
(A) 0.250 (B) 0.255 (C) 0.375 (D) 0.556 (E) 0.750
Back to Blog
N.B. This is for SAT Subject Test Math Level 2 Problem:What is the sum of the infinite geometric series:
6 + 4 + 8/3 + 16/9 + ... ? (A) 18 (B) 36 (C) 45 (D) 60 (E) There is no sum.
Back to Blog
ProblemIn April of 2004, d dogs and c cats lived in an animal shelter. If 4 cats arrived at the shelter in May of 2004 and the ratio of dogs to cats remained unchanged, in terms of c and d, how many dogs arrived at the shelter in May of 2004?
(A) 4 (B) 4d/c (C) d/c (D) d^2  4d (E) (2cd + 4d)/c
Back to Blog
In the complex plane, the horizontal axis is called the real axis and the vertical axis is called the imaginary axis. The complex number a + bi graphed in the complex plane is comparable to the point (a, b) graphed in the standard (x, y) coordinate plane. The modulus of the complex number a + bi is given by:
\[\sqrt{a^2 + b^2}\]
Question:
Which of the complex numbers z1, z2, z3, z4 and z5 below has the greatest modulus?
Back to Blog
Question:Consider the functions f(x) = sqrt(x) and g(x) = 7x + b. In the standard (x,y) coordinate plane, y = f(g(x)) passes through (4,6). What is the value of b?
A. 8 B. 8 C. 25 D. 26 E. 4  7. sqrt(6)
Back to Blog
Question:
N.B: This question is for SAT Subject Test Math Level 2
\[if \ log_a 5 = x \ and \ log_a 7 = y, \ then \ log_a \sqrt{1.4} = \]
(A) (xy)/2
(B) x/2  y (C) (x + y)/2 (D) (y  x)/2 (E) y/(2x)
Back to Blog
Two whole numbers have a greatest common factor of 8 and a least common multiple of 48. Which of the following pairs of whole numbers will satisfy the given conditions?
F. 4 and 9 G. 5 and 10 H. 10 and 16 J. 14 and 20 K. 16 and 24
Back to Blog
ProblemA total of f men went on a fishing trip. Each of the r boats that were used to carry the fishermen could accommodate a maximum number of m passengers. If one boat had 5 open spots and the remaining boats were filled to capacity, which of the following expresses the relationship among f , r, and m?
F. rm+5=f G. rm−5=f H. r+m+5=f J. rf = m + 5 K. rf = m − 5
Back to Blog
ProblemSamantha is making gluten free brownies for the family picnic. If the recipe calls for 2 ½ cups of cocoa to serve 4 people, how many cups will he need if there will be 60 people at the picnic?
N.B: Recipe is on the next page.
Back to Blog
Problem:
An interior designer is creating a custom coffee table for a client. The top of the table is a glass triangle that needs to balance on a single support. If the coordinates of the vertices of the triangle are at (3, 6), (5, 2), and (7, 10), at what point should the support be placed?
Back to Blog
A proportion is a set of 2 fractions that equal each other. This article focuses on how to use proportions to solve cooking problems, especially when the numbers are not friendly. But first, let's start with an easy problem.
Let's say you are cooking rice to serve exactly 3 people. The recipe calls for 2 cups of water and 1 cup of dry rice. However, you found out that there are 12 guests coming. How would the recipe change? If you’ve ever made rice, you know that this ratio — 1 part dry rice and 2 parts water — is important. Mess it up, and your rice will become soggy or something else. Because you are quadrupling your guest list (3 people * 4 = 12 people), you must quadruple your recipe. Cook 8 cups of water and 4 cups of dry rice. This demonstrates how you can use ration to solve proportion problems in real life. What happens when the numbers are not so friendly? Let's say you are throwing a party for 25 people. How much water do you need?
Back to Blog
The following problem appeared on the SAT.
A cubic box with edge of length x inches is tied with a string 106 inches long. The string crosses itself at right angles on the top and bottom of the box. If the bow required 10 inches of string, what is the maximum number of inches x could be? 1. Write an equation based on this information. 2. Solve the equation for x.
Back to Blog
Are we born with the ability to tell which things are close and which are far away? Or, do we learn it? Two psychologists at Cornell University, Eleanor Gibson and Richard Walk, did an interesting experiment to answer this question.
The kitten in the photograph above is sitting on a strip in the middle of a sheet of glass. Behind the kitten is a floor directly underneath the glass; in front of it is another floor several feet below the glass. Even when the kitten is just old enough to move about, it is afraid to move off the "cliff" to the "deep" side. Chicks and baby goats just 1 day old and human infants just old enough to crawl behave exactly the same way. What explains this phenomenon? Surprisingly, it all about inequalities!
Back to Blog
Randall is scheduling his classes for next term. He has a choice of 3 different science classes, 4 different math classes, and 5 different humanities classes. How many different class schedules can Randall create if he must take 1 science class, 1 math class, and 1 humanities class?
F. 14 G. 23 H. 30 J. 45 K. 60
Back to Blog
The figure above appeared in a problem on an SAT exam. All of the triangles are congruent, the area of the shaded region is 84, and the area of square ABCD is 100.
1. What is the area of one of the triangles? 2. What is the total area of the entire figure?
Back to Blog
QuestionA prime number is a whole number greater than 1, whose only two whole number factors are 1 and itself. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
What’s the big deal about prime numbers? Encryption. Large prime numbers are used for encryption. RSA encryption is based on prime numbers — two prime numbers multiplied together. The original two prime numbers are known as your ‘private key’. When you multiply them together, the product (a number that’s only divisible by one, itself and those two prime numbers) is called the ‘public key’. Question: One prime number divided by another prime number is always A) a fraction between 0 and 1 B) an integer C) a positive noninteger D) a prime number
Back to Blog
QuestionCarter was on a diet. When he weighed himself as the start of his diet, he weighed 220 pounds. At the end of 6 months, Carter weighed 180 pounds. What fraction of his original weight did he lose?
(A) 1/8 (B) 4/13 (C) 3/16 (D) 2/11
Back to Blog
Question
What is the solution set for the above equation?
A) {5} B) {20} C) {−5, 20} D) {5, 20}
Back to Blog
Question
\[ (x^2 + bx  2)(x + 3) = x^3 + 6x^2 + 7x 6 \]
In the equation above, b is a constant. If the equation is true for all values of x, what is the value of b?
A) 2 B) 3 C) 7 D) 9
Back to Blog
QuestionMaizah bought a pair of pants and a briefcase at a department store. The sum of the prices before sales tax was $130.00. There was no sales tax on the pants and a 9% sales tax on the briefcase. The total Maizah paid, including the sales tax, was $136.75. What was the price, in dollars, of the pants?
Back to Blog
QuestionA department store marks up its clothing 80% over cost. If it sells blue jeans for $14, how much did the store pay for them?
(A) $7.78 (B) $17.50 (C) $11.20 (D) $1.12
Back to Blog
QuestionThe ratio of teachers to students in a certain school is 1:14. If there are fourteen teachers in the school, how many students are there?
(A) 14 (B) 196 (C) 206 (D) 176
Back to Blog
Question2y + 6x = 3
y + 3x = 2 How many solutions (x, y) are there to the system of equations above? A) Zero B) One C) Two D) More than two 