### The missing number in the series 9, ? , 6561, 43046721 is: 81, 25, 62, 31, 18.

This problem aims to familiarize us with missing numbers in different sets of series. The concept required to solve the given problem is basic calculus involving sequences and series. Sequence and series are the basic topics of arithmetic’s. We define a sequence as an enumerated group of numbers or elements in which recurrences of any […]

### List five integers that are congruent to 4 modulo 12.

The aim of this question is to introduce the concept of congruency of an integer with another integer under some modulo. Whenever we divide one integer over another, we have two results, namely a quotient and a remainder. The quotient is the part of the result that defines the perfect division while the existence of […]

### Find the least integer n such that f(x) is O(x^n) for each of these functions.

$f(x)=2x^{2}+x^{3}log x$ $f(x)=3x^{5}+(log x)^{4}$ $f(x)=dfrac{x^{4}+x^{2}+1}{x^{4}+1}$ The article aims to find the value of the n for each function given to satisfy the O(x^n) notation. Big-O notation represents the maximum operating time of the algorithm. Therefore, it provides the worst possible algorithm. In computer science, big O notation is used to classify algorithms according to how their working time or […]

### Write an algebraic expression for: 6 more than a number c.

This problem aims to find an algebraic expression for a given verbal expression, using the knowledge of simple mathematics and some commonly known algebraic and arithmetic techniques. This kind of problem requires the understanding of the keywords that are used in mathematics as a way to express algebraic terminology. Similarly, some problems are so […]

### What does a 2:1 ratio mean?

This article aims to find the ratio between two numbers. The article uses the simple concept of ratio. In mathematics, a ratio shows how many times one number contains another. For example, if there are eight pears and six lemons in a bowl of fruit, then ratio of pears to lemons is eight to six (i.e. $8:6$, which corresponds to a ratio […]

### Prove or disprove that the product of two irrational numbers is irrational.

The aim of this question is to understand deductive logic and the concept of irrational and rational numbers. A number (N) is said to be rational if it can be written in the form of a fraction such that the numerator and denominator both belong to a set of integers. Also it’s a necessary condition […]

### Given the proportion a/b = 8/15, what “ratio” completes the equivalent proportion a/8.

This problem aims to familiarize us with fractions and their ratio and proportion. Basically, this problem is related to fundamental calculus. Ratio and Proportion are described mainly founded on fractions. When a fraction is expressed in the form of a:b, it is called a ratio, whereas a proportion declares that two ratios are equivalent. Here, […]

### The next number in the series 38, 36, 30, 28, 22 is ?

This question aims to find the next number in the series of the given numbers. Number series is a sequential arrangement of numbers following a certain defined pattern.   Different types of number series The most common pattern in the number series are the following:   Series consisting of perfect squares A series based on perfect squares is mostly based on perfect […]

### Use a direct proof to show that the product of two odd numbers is odd.

This article aims to prove that product of two odd numbers is an odd number. This article uses the concept of odd numbers. Odd numbers are any number that cannot be divided by two. In other words, numbers of the form $2 k + 1$, where $k$ is an integer, are called odd numbers. It should […]

### How do I interpret this equation 5+1×10=? Is the answer 15 or 60?

This question aims to interpret the equation as having two operations: product and sum. What do we do first when we have a math problem involving more than one operation—such as addition and subtraction or subtraction and multiplication? What do we do for the expression 10 – 5 X 2 = ? Do we subtract first (10 – 5 = 5) and then multiply (5 X […]

### Perform the indicated operation and simplify the result. Leave your answer in factored form.

$[dfrac {4x-8}{-3x}] .[dfrac {12}{12-6x}]$ This question aims to simplify a fraction in its simplest form. A rational expression is reduced to the lowest terms if the numerator and denominator have no common factors. Steps to simplify the fraction: Step 1: Factor the numerator and denominator. Step 2: List restricted values. Step 3: Cancel the common […]

### How many bit strings of length seven either begin with two 0s or end with three 1s?

The purpose of this question is to find the number of bit-strings of length $7$ beginning with two $0$s and ending with three $1$s. The sequence of binary digits is usually called a bit-string. The number of bits signifies the value length in the sequence. A bit-string having no length is regarded as a null […]

### What does a 1:1 ratio mean?

In this question, we have to find what it means by $1$ ratio $1$, also written as $1:1$. The basic concept behind this questionnaire is the knowledge and definition of ratios in mathematics. Expert Answer Generically, a ratio is the comparison of two quantities that have the same unit and can be expressed […]

### Prove or disprove that if a and b are rational numbers, then a^b is also rational.

The article aims to prove or disprove that if two numbers a and b are rational, then a^b is also rational. Rational numbers can be expressed as fractions, positive, negative, and zero. It can be written as p/q, where q is not equal to zero. The word rational comes from the word ratio, a comparison of two or more numbers […]

### Assume that a procedure yields a binomial distribution.

With n=6 trials and a probability of success of p=0.5 . Use a binomial probability table to find the probability that the number of successes x is exactly 3. The target of this question is to find the probability using a binomial distribution table. With the given number of trials and probability of success, the […]