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3 years ago

12

A forest covers 66,000 acres. A survey finds that 0.2% of the forest is old-growth trees. How many acres of old-growth trees are

there?

1 answer:

marshall27 [118]3 years ago

6 0

Answer:

132

Step-by-step explanation:

easy 66,000 * .002

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

Salsk061 [2.6K]

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:

<h3>1.</h3>

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 $r = 25 /5 = 5$ .

<h3>2.</h3>

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:

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

7 0

3 years ago

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean o

prohojiy [21]

Answer:

The percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds is 66.87%

Step-by-step explanation:

For a normal random variable with mean Mu = 3.2 and standard deviation sd = 0.8 there is a distribution of the sample mean (MX) for samples of size 4, given by:

Z = (MX - Mu) / sqrt (sd ^ 2 / n) = (MX - 3.2) / sqrt (0.64 / 4) = (MX - 3.2) / 0.4

For a sample mean of 3.0, Z = (3 - 3.2) / 0.4 = -0.5

For a sample mean of 3.0, Z = (4 - 3.2) / 0.4 = 2.0

P (3.2 <MX <4) = P (-0.5 < Z <2.0) = 0.6687.

The percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds is 66.87%

6 0

3 years ago

Kate bought $23.40 worth of two types of bird seed. Thistle bird seed sells for $1.60 per pound and wild bird seed sells for $0.

earnstyle [38]

Answer:

Ax+By=C and 7.5 lb of Thistle

Step-by-step explanation:

6 0

3 years ago

in the past month,karen rented 7 7 videos games and 6 d v d . the rental price for each video game was $ 2

Savatey [412]

232.4 hope tthis helps

3 0

3 years ago

Your friend tells you that if you let her keep 2020 of your Pokemon cards for three months, she will give you 22 cards extra whe

Dmitrij [34]

Answer: 40 %

Step-by-step explanation:

Let the amount of one card = x

Hence, the value of 20 cards ( Principal amount ) = 20x

And, the value of 22 cards ( Total amount after 3 month ) = 22x

⇒ Total interest in 3 month = 22x - 20x =2x

Let the annual interest rate = r %

$\frac{20x\times r\times 3/12}{100}=2 x$ ( By the formula of simple interest rate )

$\implies \frac{10\times r\times 1/4}{100}=1$

$\implies \frac{10r}{400}=1$

$\implies 10r=400$

$\implies r=40\%$

Hence, the annual rate of interest = 40%

8 0

3 years ago