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3 years ago

(3a+2.5b)^2=9a^2+6.25b^2+* Please help before Thursday

Mathematics

1 answer:

Anon25 [30]3 years ago

5 0

Step-by-step explanation:

We have (x + y)² = (x + y)(x + y) = x² + 2xy + y².

Let x be 3a and y be 2.5b.

Therefore (3a + 2.5b)²

= (3a)² + 2(3a)(2.5b) + (2.5b)²

= 9a² + 15ab + 6.25b².

Hence the '*' sign should be replaced with 15ab.

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Answer:

1) 0.3

2) 12

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3b) 4/5

Step-by-step explanation:

1) There are;

12 white balls, 6 green balls and 2 red balls.

Total number of balls = 12 + 6 + 2 = 20

Probability of selecting a green ball at random = 6/20 = 3/10 = 0.3

2) we are told that number of marbles is 28 marbles.

Now, theoretical probability of drawing a blue marble = 3/7

This fraction is; number of favorable outcomes/number of possible outcomes.

Thus;

Number of blue marbles = 3/7 × 28 = 12 blue marbles

3a) theoretical probability is what we expect to happen.

There are 5 numbers less than 6 in the table.

Thus;

Theoretical probability of getting a number less than 6 in the next throw = 5/6

3b) Experimental probability is what actually happens.

Number of times a number less than 6 appears = 6 + 4 + 7 + 11 + 12 = 40 times

There was a total of 50 trials. Thus;

Experimental probability of getting a number less than 6 in the next throw = 40/50 = 4/5

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Which graph represents the sequence: 1/2, 1, 2, 4, 8...?

Aleonysh [2.5K]

The graph represents the sequence is Option D.

<h3>Further explanation </h3>

A function defined in the set of natural numbers is called a sequence.

Allow $\boxed{a_n \ as \ n^{th} \ term}$ , or general term.

In a sequence, n should always represent a natural number, i.e.,

n > 0, n = 1, 2, 3, ...,

but the value of $\boxed{a_n}$ may be any real number depending on the formula for the general term of the sequence.

A sequence is considered geometric if the ratio between each consecutive term is common.

In our problem, the sequence is $\boxed{ \ \frac{1}{2}, 1, 2, 4, 8, ... \ }$

The ratio of each term $\boxed{a_{n+1}}$ to the previous term $\boxed{a_n}$ is equal 2, so we can formalize the sequence as

$\boxed{\frac{a_{n+1}}{a_n} =2}.$

The consecutive terms of the sequence have a common ratio r = 2, so this sequence is geometric.

The general term of a geometric sequence $\boxed{a_n}$ with common ratio r is $\boxed{\boxed{ \ a_n = a_1 \cdot r^{n-1} \ }}.$

Presently we go back to the question. The graph shows the horizontal axis as n and the vertical axis is the general term $\boxed{a_n}$ . The relationship between n, the terms, and the coordinates as written below:

$\boxed{n = 1 \rightarrow the \ 1st \ term \ a_1 = \frac{1}{2} \rightarrow \bigg( 1, \frac{1}{2} \bigg)}$

$\boxed{n = 2 \rightarrow the \ 2nd \ term \ a_2 = 1 \rightarrow (2, 1)}$

$\boxed{n = 3 \rightarrow the \ 3rd \ term \ a_3 = 2 \rightarrow (3, 2)}$

$\boxed{n = 4 \rightarrow the \ 4th \ term \ a_4 = 4 \rightarrow (4, 4)}$

$\boxed{n = 5 \rightarrow the \ 5th \ term \ a_5 = 8 \rightarrow (5, 8)}$

Therefore, the graph representing the sequence is Option D.

The general term of a geometric sequence is exponential.
From the common ratio (r > 1) and graph, the type is an increasing sequence.

<h3>Learn more </h3>

Combining two functions to create a geometric sequence brainly.com/question/1695742
A word problem about arithmetic and geometric sequences brainly.com/question/3395975
Drawing graph of the geometric sequence brainly.com/question/3166290

Keywords: which, the graph, geometric sequences, common ratio, general term formula, natural numbers, The consecutive terms, arithmetic

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