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3 years ago

Rhada has a 6-pound bag of day . Her craft project requires 6 ounces of clay for each batch of 3 ornaments,

Mathematics

1 answer:

kirill [66]3 years ago

3 0

Answer:

Rhada can make 48 ornaments if she uses all of the clay.

Step-by-step explanation:

The complete question is:

Rhada has a 6-pound bag of day . Her craft project requires 6 ounces of clay for each batch of 3 ornaments. If she uses all of the clay, how many ornaments can Rhada make?

Solution:

The amount of clay Rhada has, <em>X</em> = 6-pound.

Convert the weight of clay bag into ounces as follows:

1 pound = 16 ounces

6 pound = 16 × 6

= 96 ounces.

So, Rhada has 96 ounces of clay.

It is provided that her craft project requires 6 ounces of clay for each batch of ornaments.

Compute the number of batches that can be made by 96 ounces of clay as follows:

Number of batches = Total weight of clay ÷ Amount required for each batch

$=\frac{96}{6}\\=16$

Thus, Rhada can make 16 batches of ornaments.

Now, it is also provided that each batch has 3 ornaments.

Compute the number of ornaments in 16 batches as follows:

Number of ornaments = Number of batches × No. of ornament in 1 batch

$=16\times 3\\=48$

Thus, Rhada can make 48 ornaments if she uses all of the clay.

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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