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4 years ago

Please answer this correctly

Mathematics

2 answers:

Margaret [11]4 years ago

8 0

Answer:

$22.1

Step-by-step explanation:

To solve this, you must multiply the amount of the items by its cost.

This is the amount of yams in decimal form: $4\frac{1}{2}$ = 4.5

This is the amount of carrots in decimal form: $4\frac{3}{10}$ = 4.3

4.5 * 3 = 13.5

4.3 * 2 = 8.6

Now we add them together to get the total cost.

13.5 + 8.6 = 22.1

Len [333]4 years ago

8 0

Answer:

$22.10

Step-by-step explanation:

This is simple multiplication.

1. It may help you to simplify the pound values. 4 and 1/2 is really 4.5, and 4 and 3/10 is really 4.3

2. We know what the cost is per pound, and we know how many pounds we have. We simply multiply.

4.5 pounds of yams * $3 per pound = 13.5

4.3 pounds of carrots * $2 per pound = 4.3*2 = 8.6

3. Add the values

13.5+8.6 = 22.1 = $22.10

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3 years ago

The first, third and thirteenth terms of an arithmetic sequence are the first 3 terms of a geometric sequence. If the first term

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Answer:

The first three terms of the geometry sequence would be $1$ , $5$ , and $25$ .

The sum of the first seven terms of the geometric sequence would be $127$ .

Step-by-step explanation:

Let $d$ denote the common difference of the arithmetic sequence.

Let $a_1$ denote the first term of the arithmetic sequence. The expression for the $n$ th term of this sequence (where $n\!$ is a positive whole number) would be $(a_1 + (n - 1)\, d)$ .

The question states that the first term of this arithmetic sequence is $a_1 = 1$ . Hence:

The third term of this arithmetic sequence would be $a_1 + (3 - 1)\, d = 1 + 2\, d$ .
The thirteenth term of would be $a_1 + (13 - 1)\, d = 1 + 12\, d$ .

The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let $r$ denote the ratio of the geometric sequence in this question.

Ratio between the second term and the first term of the geometric sequence:

$\displaystyle r = \frac{1 + 2\, d}{1} = 1 + 2\, d$ .

Ratio between the third term and the second term of the geometric sequence:

$\displaystyle r = \frac{1 + 12\, d}{1 + 2\, d}$ .

Both $(1 + 2\, d)$ and $\left(\displaystyle \frac{1 + 12\, d}{1 + 2\, d}\right)$ are expressions for $r$ , the common ratio of this geometric sequence. Hence, equate these two expressions and solve for $d$ , the common difference of this arithmetic sequence.

$\displaystyle 1 + 2\, d = \frac{1 + 12\, d}{1 + 2\, d}$ .

$(1 + 2\, d)^{2} = 1 + 12\, d$ .

$d = 2$ .

Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be $1$ , $(1 + (3 - 1) \times 2) = 5$ , and $(1 + (13 - 1) \times 2) = 25$ , respectively.

These three terms ( $1$ , $5$ , and $25$ , respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be $r = 25 /5 = 5$ .

Let $a_1$ and $r$ denote the first term and the common ratio of a geometric sequence. The sum of the first $n$ terms would be:

$\displaystyle \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}$ .

For the geometric sequence in this question, $a_1 = 1$ and $r = 25 / 5 = 5$ .

Hence, the sum of the first $n = 7$ terms of this geometric sequence would be:

$\begin{aligned} & \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}\\ &= \frac{1 \times \left(1 - 2^{7}\right)}{1 - 2} \\ &= \frac{(1 - 128)}{(-1)} = 127 \end{aligned}$ .

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3 years ago

In the school library, 28% of the books are non-fiction. If there are 1.224 fiction books in

denis-greek [22]

Answer:

1700 books

Step-by-step explanation:

We are given;

% of non-fiction books in the library as 28%
Number of fiction books in the library as 1,224 books

We are required to determine the total number of books.

First we determine the percentage of non-fiction books

We need to know that;

% of fiction books + % of non-fiction books = 100%

Therefore;

% of non-fiction books = 100 % - 28 %

= 72%

Second we determine the total number of books

We know that;

Total number of books = 100%

But;

72% = 1,224 books

Therefore;

Total number of books = (1,224 × 100%) ÷ 72%

= 1700 books

Hence, the library has a total number of 1700 books

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3 years ago