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Nostrana [21]
3 years ago
8

Given h(x) = 2x – 3, find h(5)

Mathematics
1 answer:
kobusy [5.1K]3 years ago
3 0

Answer:

h(5) = 7

Step-by-step explanation:

Step 1: Define

h(x) = 2x - 3

h(5) is x = 5

Step 2: Substitute and Evaluate

h(5) = 2(5) - 3

h(5) = 10 - 3

h(5) = 7

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3. A rare species of aquatic insect was discovered in the Amazon rainforest. To protect the species, environmentalists declared
navik [9.2K]

The number of months until the insect population reaches 40 thousand is 14.29 months and the limiting factor on the insect population as time progresses is 250 thousands.

Given that population P(t) (in thousands) of insects in t months after being transplanted is P(t)=(50(1+0.05t))/(2+0.01t).

(a) Firstly, we will find the number of months until the insect population reaches 40 thousand by equating the given population expression with 40, we get

P(t)=40

(50(1+0.05t))/(2+0.01t)=40

Cross multiply both sides, we get

50(1+0.05t)=40(2+0.01t)

Apply the distributive property a(b+c)=ab+ac, we get

50+2.5t=80+0.4t

Subtract 0.4t and 50 from both sides, we get

50+2.5t-0.4t-50=80+0.4t-0.4t-50

2.1t=30

Divide both sides with 2.1, we get

t=14.29 months

(b) Now, we will find the limiting factor on the insect population as time progresses by taking limit on both sides with t→∞, we get

\begin{aligned}\lim_{t \rightarrow \infty}P(t)&=\lim_{t \rightarrow \infty}\frac{50(1+0.05t)}{2+0.01t}\\ &=\lim_{t \rightarrow \infty}\frac{50(\frac{1}{t}+0.05)}{\frac{2}{t}+0.01}\\ &=50\times \frac{0.05}{0.01}\\ &=250\end

(c) Further, we will sketch the graph of the function using the window 0≤t≤700 and 0≤p(t)≤700 as shown in the figure.

Hence, when the population P(t) (in thousands) of insects in t months after being transplanted by P(t)=(50(1+0.05t))/(2+0.01t) then the number of months until the insect population reaches 40 thousand 14.29 months and the limiting factor on the insect population is 250 thousand and the graph is shown in the figure.

Learn more about limiting factor from here brainly.com/question/18415071.

#SPJ1

8 0
2 years ago
Finding percents<br> 6% of 300
adell [148]
6% means 6/100 or 0.06

"of" means "times"

0.06 x 300 = 18
7 0
3 years ago
Read 2 more answers
If you work 8 hours every two days, how many hours will he work in 7 days
zubka84 [21]

Answer:

28 hours for 7 days

Step-by-step explanation:

8/2 =

4

4 hours for 1 day

1 x 7 =

7

7 x 4

28

28 for 7 days

6 0
2 years ago
Read 2 more answers
what is an equationof the line that passes through the points (0,-7) and (-8,3) put your answer in fully reduced form pleaseee h
Lelu [443]

Answer:

y = -5/4x - 7

Step-by-step explanation:

First, find the slope:

3 - -7 / -8 - 0 = -5/4

Put it in point slope form:

y + 7 = -5/4(x-0)

y + 7 = -5/4x

y = -5/4x - 7

5 0
3 years ago
A sports marketing company interviewed 250 Supersport United fans and has found that the average fan spends R101 on non-ticket p
antiseptic1488 [7]

The 90% confidence interval is between R96.94 and R105.06

The confidence (C) = 90% = 0.9, Mean (μ) = 101, standard deviation (σ) = 39, sample size (n) = 250

α = 1 - C = 1 - 0.9 = 0.1

α/2 = 0.1 / 2 = 0.05

The z score of α/2 corresponds with the z score of 0.45 (0.5 - 0.05) which is equal to 1.645

The margin of error (E) is given by:

E=Z_\frac{\alpha }{2} *\frac{\sigma}{\sqrt{n} } \\\\E=1.645 *\frac{39}{\sqrt{250} } =4.06

The confidence interval = μ ± E = 101 ± 4.06 = (96.94, 105.06)

Therefore the 90% confidence interval is between R96.94 and R105.06

Find out more at: brainly.com/question/18914334

8 0
3 years ago
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