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3 years ago

The number of subscribers y to a newspaper after t years is shown by the equation below.

Mathematics

2 answers:

LiRa [457]3 years ago

7 0

Answer: It decreased by 5% every year.

Explanation:-

The number of subscribers y to a newspaper after t years is shown by the equation $y=75(0.95)^t$ , where 75 is the initial number of subscribers to a newspaper and t is the time period is years.

The above equation can be rewrite as

$75(1-0.05)^t$ which is equivalent to the exponential decay function with rate r=0.05=5%

⇒ The number of subscribers to a newspaper decreased by 5% every year.

⇒ Fourth option is correct.

cupoosta [38]3 years ago

6 0

Answer:

Option 4 - It decreased by 5% every year.

Step-by-step explanation:

Given : The number of subscribers y to a newspaper after t years is shown by the equation $y = 75(0.95)^t$

To find : Which conclusion is correct about the number of subscribers to the newspaper?

Solution :

Equation - $y = 75(0.95)^t$

where y is the subscribers to a newspaper and t is the time in years.

Comparing the given equation with the exponential equation

75 is the initial number of subscribers to a newspaper and t is the time period is years.

And their is an exponential decay function with rate r=0.05=5% (1-0.95=0.05)

This all imply that :

The number of subscribers to a newspaper decreased by 5% every year.

Therefore, Option 4 is correct.

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The probability that a single radar station will detect an enemy plane is 0.65.

taurus [48]

Answer:

a) We need 4 stations to be 98% certain that an enemy plane flying over will be detected by at least one station.

b) If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.

Step-by-step explanation:

For each station, there are two two possible outcomes. Either they detected the enemy plane, or they do not. This means that we can solve this problem using concepts of the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

In this problem, we have that:

The probability that a single radar station will detect an enemy plane is 0.65. This means that $n = 0.65$ .

(a) How many such stations are required to be 98% certain that an enemy plane flying over will be detected by at least one station?

This is the value of n for which $P(X = 0) \leq 0.02$ .

n = 1.

$P(X = 0) = C_{1,0}.(0.65)^{0}.(0.35)^{1} = 0.35$

n = 2

$P(X = 0) = C_{2,0}.(0.65)^{0}.(0.35)^{2} = 0.1225$

n = 3

$P(X = 0) = C_{3,0}.(0.65)^{0}.(0.35)^{3} = 0.0429$

n = 4

$P(X = 0) = C_{4,0}.(0.65)^{0}.(0.35)^{4} = 0.015$

We need 4 stations to be 98% certain that an enemy plane flying over will be detected by at least one station.

(b) If seven stations are in use, what is the expected number of stations that will detect an enemy plane?

The expected number of sucesses of a binomial variable is given by:

$E(x) = np$

So when $n = 7$

$E(x) = 7*(0.65) = 4.55$

If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.

6 0

3 years ago

*please help*

Furkat [3]

So I'm going to make student tickets be s, and non-students n. So the equation would be s+2n=450. Hope this helped. :3

5 0

4 years ago

The carnival committee has purchased 985 small prizes. The prizes are to be divided equally among the 29 game booths

Vladimir [108]

Answer:

1 The first digit of the quotient is 3

2. 34 prizes per booth

3. 19 prizes left over

Step-by-step explanation:

We need to divide 985 by 29

29 goes into 98 3 times

29*3 = 87 with 13 left over

135 divided by 29

29*4 =116 135-116 =19

985÷29 = 34 with 19 left over

7 0

3 years ago

An animal shelter has 4/5 of its crates filled with animals. 1/2 of the filled crates are holding cats. What fraction of the tot

matrenka [14]

It should be 2/5 because half of the 4/5 is cats

5 0

4 years ago

Read 2 more answers

a man invested one third of his money at 5%, half of his money st 5.5%. if his total annual investment income was 735,how much h

stepan [7]

Remark
Let the amount invest = x

(1/3 x) * 5/100 + (1/2 x) * 5.5/100 = 735 Multiply numerators and denominators together on each side of the plus sign.

5x/300 + 5.5x / 200 = 735

Multiply both sides of the equation by 600 to get rid of the denominators.
(5x/300)*600 + (5.5x/200)*600 = 735 * 600
(5x * 2) + 5.5x * 3 = 441000
10x + 16.5x = 441000 Combine the like terms on the left.
26.5 * x = 441000 Divide by 26.5 on both sides.
x = 441000/26.5
x = 16641.51 = invested amount <<<<< answer

Check
1/3 * 5/100 * 16641.51 = 277.36
1/2 * 5.5/100*16641.51 = 457.63
The total = 735 which is what it should be.

4 0

3 years ago