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2 years ago

A population of 175 snails is increasing at an annual rate of 12%. what will the population

1 answer:

3 0

$\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &175\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ t=years\dotfill &10\\ \end{cases} \\\\\\ A=175(1 + 0.12)^{10}\implies A=175(1.12)^{10}\implies A\approx 543.52$

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Mike and Ike are twins. Mike’s age is one more than twice a certain number. Ike’s age is 10 less than triple that same number. F

Misha Larkins [42]

Mike age is 3 less then twice the age of his brother nuke.
M = Mike's age now
N = Nuke's age now
M = 2N - 3

Ten years ago, four times nuke's age was one more mike's age.
M-10 = Mike's age 10 years ago
N-10 = Muke's age 10 years ago
4(N - 10) = 1 + M -10

what are their present ages

find M and N

substitute M = 2N - 3 into 4(N - 10) = 1 + M -10:

4(N - 10) = 1 + [2N - 3] - 10
4N - 40 = 2N - 12
2N = 28
N = 14

M = 2(14) - 3 = 28 - 3 = 25

Mike is 25 and Nuke is 14.

check:
4(14 - 10) = 4(4) = 16 = 26 -10 = 1 + 25 - 10

4 0

3 years ago

The riding stables just received an unexpected rush of registrations for the next horse show, and quickly needs to create some a

liraira [26]

Answer:

Maximum added area will be 60,000 ft²

Each paddock measure 200 ft by 150 ft, and the paddocks share a 200-ft long side.

Step-by-step explanation:

Consider the provided information.

There is sufficient funding to rent 1200 feet of temporary chain-link fencing.

The plan is to form two paddocks with one shared fence running down the middle.

The total length of fencing is 1200 feet that is same as the total perimeter including that shared line down the middle.

Therefore, the perimeter is

$P = 1200 = 2L + 3w$

Solve for L

$1200-3w = 2L$

$L=600-\frac{3w}{2}$

As we know the area of rectangle is A=L×W

Substitute the value of L in above formula.

$A=(600-\frac{3w}{2})\times w\\A=600w-\frac{3w^2}{2}$

$A=-\frac{3w^2}{2}+600w$

The above equation makes a downward parabola.

In order to find the maximum, find the vertex of parabola as shown:

$W=\frac{-b}{2a}=\frac{600}{2\times\frac{3}{2}}=200$

Hence, the width should be 200 ft in order to get maximum area,

Therefore, the length will be:

$1200 = 2L + 3(200)$

$L=300$

Now substitute the value of L and W in area formula.

A=300×200=60,000

Hence, maximum added area will be 60,000 ft²

Hence, the length should be 300 ft, and each paddock should then be 150 feet long.

Each paddock measure 200 ft by 150 ft, and the paddocks share a 200-ft long side.

5 0

4 years ago

You are given the information that P(A) = 0.30 and P(B) = 0.40.

Ad libitum [116K]

Answer:

1.B. No. You need to know the value of P(A and B). 2.C. Yes P(A and B) =0, so P(A or B) = P(A) + P(B).

Step-by-step explanation:

We can solve this question considering the following:

For two mutually exclusive events:

$\\ A_{1}\;and\;A_{2}$

$\\ P(A_{1} or A_{2}) = P(A_{1}) + P(A_{2})$ (1)

An extension of the former expression is:

$\\ P(A_{1} or A_{2}) = P(A_{1}) + P(A_{2}) - P(A_{1} and A_{2})$ (2)

In mutually exclusive events, P(A and B) = 0, that is, the events are independent one of the other, and we know the probability that both events happen at the same time is zero (P(A and B) = 0). There are some other cases in which if event A happens, event B too, so they are not mutually exclusive because P(A and B) is some number different from zero. Notice the difference between OR and AND. The latter implies that both events happen at the same time.

In other words, notice that the formula (2) provides an extension of formula (1) for those events that are not mutually exclusive, that is, there are some cases in which the events share the same probabilities in a way that these probabilities must be subtracted from the total, so those probabilities in common do not "inflate" the actual probability.

For instance, imagine a person going to a gas station and ask for checking both a tire and lube oil of his/her car. The probability for checking a tire is P(A)=0.16, for checking lube oil is P(B)=0.30, and for both P(A and B) = 0.07.

The number 0.07 represents the probability that both events occur at the same time, so the probability that this person ask for checking a tire or the lube oil of his/her car is:

P(A or B) = 0.16 + 0.30 - 0.07 = 0.39.

That is why we cannot simply add some given probabilities without acknowledging if the events are or not mutually exclusive, whereas we can certainly add the probabilities in question when we know that both probabilities are mutually exclusive since P(A and B) = 0.

In conclusion, knowing the events are mutually exclusive does provide extra information and we can proceed to simply add the probabilities of either event; thus, the answers are those in which we need to previously know the value of P(A and B).

7 0

3 years ago

When an exponent is a negative number, we can think of it as taking the...?

STALIN [3.7K]

Answer:

We can think of it as the zeros after the decimal point.

Step-by-step explanation:

Negative exponents always move the number to the right putting the decimal in front of it.

5 0

4 years ago

From experience, an airline knows that only 80% of the passengers booked for a certain flight actually show up. If 9 passengers

Olenka [21]

Answer: 0.74

Step-by-step explanation:

Given : The probability that the passengers booked for a certain flight actually show up : p=0.80

The number of passengers are randomly selected : n= 9

Binomial probability formula to find the probability of getting success in x trial :-

$P(x)=^nC_xp^x(1-p)^{n-x}$

Then , the probability that more than 6 of them show up will be :-

$P(x>6)=P(7)+P(8)+P(9)\\\\=^9C_7(0.8)^7(0.2)^{2}+^9C_8(0.8)^8(0.2)^{1}+^9C_9(0.8)^9(0.2)^{0}\\\\=\dfrac{9!}{7!(9-7)!}(0.8)^7(0.2)^{2}+(9)(0.8)^8(0.2)+(1)(0.8)^9\approx0.3020+0.3020+0.1342=0.7382\approx0.74$

Hence, the probability that more than 6 of them show up = 0.74

7 0

3 years ago