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3 years ago

What is the next term of the following sequence? 20, 10, 5, 21/2, ...

Mathematics

1 answer:

ycow [4]3 years ago

6 0

Answer:

1 $\frac{1}{4}$

Step-by-step explanation:

Note there is a common ratio between consecutive terms, that is

10 ÷ 20 = 5 ÷ 10 = 2 $\frac{1}{2}$ ÷ 5 = $\frac{1}{2}$

Thus to obtain the next term in the sequence multiply the previous term by $\frac{1}{2}$

2 $\frac{1}{2}$ × $\frac{1}{2}$ = 1 $\frac{1}{4}$

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Which statement is true about the polynomial

pantera1 [17]

Question:

Which statement is true about the polynomial

–3x4y3 + 8xy5 – 3 + 18x3y4 – 3xy5 after it has been fully simplified?

It has 3 terms and a degree of 5.

It has 3 terms and a degree of 7.

It has 4 terms and a degree of 5.

It has 4 terms and a degree of 7.

Answer:

Option D: It has 4 terms and a degree of 7.

Explanation:

The given polynomial is $3x^4y^3+8xy^5-3+18x^3y^4-3xy^5$

We need to simplify the polynomial to determine the number of terms and the degree of the polynomial.

Hence, the simplified polynomial is given by

$3 x^{4} y^{3}+5x y^{5}-3+18 x^{3} y^{4}$

Term of a polynomial:

The term of a polynomial consists of a number multiplied by a variable or it may be a constant.

Thus, the simplified polynomial has 4 terms.

Degree of a polynomial:

The degree of a polynomial is the sum of exponents of the variables in a term.

Thus, the simplified polynomial has a degree of 7.

Hence, the polynomial has 4 terms and a degree of 7.

Therefore, Option D is the correct answer.

4 0

3 years ago

The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, So

pshichka [43]

Answer:

There is a 32.22% probability that at least 3 flights arrive late.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it arrives on time, or it arrives late. This means that we can solve this problem using binomial probability concepts.

Binomial probability distribution

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

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

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

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

And $\pi$ is the probability of X happening.

In this problem, we have that:

There are 10 flights, so $n = 10$ .

A success in this case is a flight being late. 80% of its flights arriving on time, so 100%-80% = 20% arrive late. This means that $\pi = 0.2$ .

(a) Find the probability that at least 3 flights arrive late.

Either less than 3 flights arrive late, or at least 3 arrive late. The sum of these probabilities is decimal 1. This means that:

$P(X < 3) + P(X \geq 3) = 1$

$P(X \geq 3) = 1 - P(X < 3)$

In which

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)$

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

$P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074$

$P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684$

$P(X = 2) = C_{10,2}.(0.2)^{2}.(0.8)^{8} = 0.3020$

$P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.1074 + 0.2684 + 0.3020 = 0.6778$

Finally

$P(X \geq 3) = 1 - P(X < 3) = 1 - 0.6778 = 0.3222$

There is a 32.22% probability that at least 3 flights arrive late.

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3 years ago

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Xelga [282]

Step-by-step explanation:

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variable

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operations

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3 years ago

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The wheel in the adjacent figure has a radius of 61 feet. The clearance between the wheel and the ground is 11 feet. The rectang

Zanzabum

61 divide by 11 times 3

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3 years ago

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IgorLugansk [536]

Answer:

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