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2 years ago

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The temperature in degrees Celsius can be expressed by the function C(f)=59(f−32) where f is the temperature in degrees Fahrenhe

it. Find the temperature in degrees Celsius (to the nearest degree) if it is 39 °f.

1 answer:

Vlad [161]2 years ago

6 0

C(f) = 5/9(f - 32).....f = 39

C(39) = 5/9(39 - 32)
C(39) = 5/9(7)
C(39) = 35/9
C(39) = 3 8/9......rounds to 4

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Scientists were studying a rare species of parrot. They went to a forest in the year

Brrunno [24]

Answer:

$P(t) = 608(1.5)^{t}$

Step-by-step explanation:

The number of parrots in t years after 2010 can be modeled by the following function:

$P(t) = P(0)(1+r)^{t}$

In which P(0) is the number of parrots in 2010 and r is the growth rate, as a decimal.

608 parrots in the forest in 2010.

This means that $P(0) = 608$

Then

$P(t) = 608(1+r)^{t}$

When the scientists went back 5 years later, they found 4617 parrots.

This means that $P(5) = 4617$

We use this to find 1 + r. So

$P(t) = 608(1+r)^{t}$

$4617 = 608(1+r)^{5}$

$(1+r)^{5} = \frac{4617}{608}$

$1 + r = \sqrt[5]{\frac{4617}{608}}$

$1 + r = 1.5$

So

$P(t) = 608(1.5)^{t}$

8 0

3 years ago

Determine formula of the nth term 2, 6, 12 20 30,42

nalin [4]

Check the forward differences of the sequence.

If $\{a_n\} = \{2,6,12,20,30,42,\ldots\}$ , then let $\{b_n\}$ be the sequence of first-order differences of $\{a_n\}$ . That is, for n ≥ 1,

$b_n = a_{n+1} - a_n$

so that $\{b_n\} = \{4, 6, 8, 10, 12, \ldots\}$ .

Let $\{c_n\}$ be the sequence of differences of $\{b_n\}$ ,

$c_n = b_{n+1} - b_n$

and we see that this is a constant sequence, $\{c_n\} = \{2, 2, 2, 2, \ldots\}$ . In other words, $\{b_n\}$ is an arithmetic sequence with common difference between terms of 2. That is,

$2 = b_{n+1} - b_n \implies b_{n+1} = b_n + 2$

and we can solve for $b_n$ in terms of $b_1=4$ :

$b_{n+1} = b_n + 2$

$b_{n+1} = (b_{n-1}+2) + 2 = b_{n-1} + 2\times2$

$b_{n+1} = (b_{n-2}+2) + 2\times2 = b_{n-2} + 3\times2$

and so on down to

$b_{n+1} = b_1 + 2n \implies b_{n+1} = 2n + 4 \implies b_n = 2(n-1)+4 = 2(n + 1)$

We solve for $a_n$ in the same way.

$2(n+1) = a_{n+1} - a_n \implies a_{n+1} = a_n + 2(n + 1)$

Then

$a_{n+1} = (a_{n-1} + 2n) + 2(n+1) \\ ~~~~~~~= a_{n-1} + 2 ((n+1) + n)$

$a_{n+1} = (a_{n-2} + 2(n-1)) + 2((n+1)+n) \\ ~~~~~~~ = a_{n-2} + 2 ((n+1) + n + (n-1))$

$a_{n+1} = (a_{n-3} + 2(n-2)) + 2((n+1)+n+(n-1)) \\ ~~~~~~~= a_{n-3} + 2 ((n+1) + n + (n-1) + (n-2))$

and so on down to

$a_{n+1} = a_1 + 2 \displaystyle \sum_{k=2}^{n+1} k = 2 + 2 \times \frac{n(n+3)}2$

$\implies a_{n+1} = n^2 + 3n + 2 \implies \boxed{a_n = n^2 + n}$

6 0

2 years ago

What times 5 equals 75

saveliy_v [14]

15 the answer is 15 because 15 x 5 = 75

5 0

2 years ago

Read 2 more answers

There are 2820 cars in Farmington. The ratio of medium size cars to compacts is 7 to 5 and the ratio of compacts to full-size ca

oee [108]

Answer:

Number of full size cars = 900

Step-by-step explanation:

The ratio of medium size cars to compacts is 7 to 5 and the ratio of compacts to full-size cars is 8 to 9. Since compact cars are there in both ratios , we need to make the number in the ratio for compact cars to be the same.

$\frac{medium}{compact} = \frac{7}{5}$

Multiply by 8 on numerator and denominator

$\frac{medium}{compact} = \frac{56}{40}$

$\frac{compact}{full size} = \frac{8}{9}$

Multiply numerator and denominator by 5.

$\frac{compact}{full size} = \frac{40}{45}$

Ratio of medium, compact and full size are in ratio 56,40,45.

Total number of cars =2820.

(56 + 40 + 45)x = 2820

x = $\frac{2820}{141}$

x = 20

Number of full size cars = $20\times 45$ =900

3 0

3 years ago

A line segment is defined by which of the following statements?

kaheart [24]

The only given option that correctly defines a line segment is;

<u><em>Option C; All points between and including two given points.</em></u>

In geometry in mathematics, a line segment is defined as a part of a line that is bounded by two distinct end points.

Now, let us look at the options;

Option A; This is not correct because a line segment must have 2 distinct endpoints

Option B; This is not correct because a line segment is a part of a line and not a set of points.

Option C; This is correct because it tallies with our definition of line segment.

Option D; This is not correct because a line segment does not extend infinitely.

Read more at; brainly.com/question/18089782

7 0

2 years ago