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2 years ago

Show all four symbols of multiplication using the variables a/b

Mathematics

1 answer:

OlgaM077 [116]2 years ago

5 0

Answer:

Multiplication Symbols:

1. Times ×

2. Dot ⋅

3. Parentheses ()

4. Variables next to each other ab

Step-by-step explanation:

The symbols can be used like this...

Times: a × b = c

Dot: a ⋅ b = c

Parentheses: (a)(b) = c

Variables next to each other: ab = c

You might be interested in

Which expressions are polynomials?

igor_vitrenko [27]

Option A: z + 1

Option B: 6 + w

Option D: $2 x^{4}-y$

Solution:

Let us first define the polynomial.

A polynomial can have constants, variables, exponents and fractional coefficients.

A polynomial cannot have negative exponents, fractional exponents and never divided by a variable.

To find which expressions are polynomial:

Option A: z + 1

By the definition, z + 1 is a polynomial.

It is polynomial.

Option B: 6 + w

By the definition, 6 + w is a polynomial.

It is polynomial.

Option C: $y^{2}-\sqrt[3]{y}+4$

$y^{2}-\sqrt[3]{y}+4=y^{2}-{y}^{1/3}+4$

Here, y have fractional exponent.

So, it is not a polynomial.

Option D: $2 x^{4}-y$

By the definition, $2 x^{4}-y$ is a polynomial.

It is polynomial.

Hence z + 1, 6 +w and $2 x^{4}-y$ are polynomials.

6 0

3 years ago

The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are indepen

vfiekz [6]

Answer:

a) 0.2581

b) 0.4148

c) 17

Step-by-step explanation:

For each call, there are only two possible outcomes. Either they are answered in less than 30 seconds. Or they are not. The probabilities for each call are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem we have that:

$p = 0.75$

a. If you call 12 times, what is the probability that exactly 9 of your calls are answered within 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X = 9)$ when $n = 12$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 9) = C_{12,9}.(0.75)^{9}.(0.25)^{3} = 0.2581$

b. If you call 20 times, what is the probability that at least 16 calls are answered in less than 30 seconds? Round your answer to four decimal places (e.g. 98.7654).

This is $P(X \geq 16)$ when $n = 20$