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Answer:

[tex]\frac{dP}{dt} \ =\ \frac{1}{5}P[/tex]

Step-by-step explanation:

Given

Variation: Directly Proportional

Insects = 10 million when Rate = 2 million

i.e. [tex]P = 10\ million[/tex] when [tex]\frac{dP}{dt} = 2\ million[/tex]

Required

Determine the differential equation for the scenario

The variation can be represented as:

[tex]\frac{dP}{dt} \ \alpha\ P[/tex]

Which means that the rate at which the insects increase with time is directly proportional to the number of insects

Convert to equation

[tex]\frac{dP}{dt} \ =\ k * P[/tex]

[tex]\frac{dP}{dt} \ =\ kP[/tex]

Substitute values for [tex]\frac{dP}{dt}[/tex] and P

[tex]2\ million = k * 10\ million[/tex]

Make k the subject

[tex]k = \frac{2\ million}{10\ million}[/tex]

[tex]k = \frac{2}{10}[/tex]

[tex]k = \frac{1}{5}[/tex]

Substitute [tex]\frac{1}{5}[/tex] for k in [tex]\frac{dP}{dt} \ =\ k * P[/tex]

[tex]\frac{dP}{dt} \ =\ \frac{1}{5}* P[/tex]

[tex]\frac{dP}{dt} \ =\ \frac{1}{5}P[/tex]

Answer:

Trigonometry can be used to measure the height of a building or mountains: if you know the distance from where you observe the building and the angle of elevation you can easily find the height of the building.

Answer:

y=-4x+15

Step-by-step explanation:

Answer:

68m squared or the first option

Step-by-step explanation:

Answer:

X=2

Step-by-step explanation:

9x+8(-4x+7)=10

9x+(-32x)+56=10

-23x=10-56

-23x=-46

X=-46/-23

so X=2

Answer:

x = -5

Step-by-step explanation:

3x + 1 = 2x - 4

x + 1 = -4

x = -5

The x-coordinate in the solution of the system is -5.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Given the equations y = 3x + 1

y = 2x - 4

comparing both equations for equal values of y,

3x + 1 = 2x - 4

3x  - 2x = -4 - 1

x = -5

substitute value of x in equation,

and y = 3x + 1

y = 3(-5) + 1

y = -14

Hence the value of x is -5.

Learn more about linear equations;

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Answer:

Step-by-step explanation:

Here the answer

Answer:

Angle X i belive is a right angle

Answer: 170 degree difference

Answer:

The difference between two numbers canbbe obtained substracting.

The diffence between 130 °F and -40 °F would be the same as substracting both numebrs (we should put an absolute value as the difference is positive).

130 - (-40) = 130 + 40 = 170 ° F

So the difference is of 179 °F

Answer:

B

Step-by-step explanation:

Because

Answer:

a) [tex]n = 20[/tex] and [tex]p = 0.25[/tex]

b) The mean number of correct guesses in 20 cards for subjects who are just guessing is 5.

c) 0.2023 = 20.23% probability of exactly 5 correct guesses in 20 cards if a subject is just guessing

Step-by-step explanation:

Binomial probability distribution

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

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

A. The count of correct guesses in 20 cards has a binomial distribution. What are n and p?

20 cards mean that [tex]n = 20[/tex]

A subject who is just guessing has a one in four chance of guessing correctly on each card, which means that [tex]p = \frac{1}{4} = 0.25[/tex]

B. What is the mean number of correct guesses in 20 cards for subjects who are just guessing?

Expected value, so

[tex]E(X) = np = 20*0.25 = 5[/tex]

The mean number of correct guesses in 20 cards for subjects who are just guessing is 5.

C. What is the probability of exactly 5 correct guesses in 20 cards if a subject is just guessing?

This is P(X = 5). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 5) = C_{20,5}.(0.25)^{5}.(0.75)^{15} = 0.2023[/tex]

0.2023 = 20.23% probability of exactly 5 correct guesses in 20 cards if a subject is just guessing

Answer:

They multiplied by 100

Step-by-step explanation:

1 x 1.5 = 1.5

10 x 1.5 = 15

100 x 1.5 = 150

Answer:

the temperature dropped 5 degrees in four hours

Step-by-step explanation:

Answer:

It should be 530 inches, so 44 feet.

Step-by-step explanation:

I am not 100% but I did 13.25 times 40.

Answer:

$93.

Step-by-step explanation:

Given that David went out for a dinner that cost $ 75, the price at which a sales tax of 4% was applied, and left a 20% tip on $ 75, to determine the total cost of his meal the following calculation must be performed:

75 + (75 x 0.2) + (75 x 0.04) = X

75 + 15 + 3 = X

93 = X

Therefore, the total cost he payed for his meal was $ 93.

Answer:

ok

Step-by-step explanation:

ok

Answer:

10

Step-by-step explanation:

Let N represent the set of 5 hearts cards that are not flushes

From the image attached below; there are thirteen (13) denominations on deck

i.e.  (A,K,Q,J,10,9,8,7,6,5,4,3,2) in the deck

Let us take an integral look at the set of cards that contains consecutive dominations in hearts. Relating them from the lowest denomination to the highest denomination. Also, for hand to be in a straight all cards, they must be in consecutive order.

So, starting from the lowest straight A-2-3-4-5 to the highest straight, we would have a royal flush 10, J, Q, K, A

∴

[tex]N = \left \{ {{(A,2,3,4,5,),(2,3,4,5,6),(3,4,5,6,7),(4,5,6,7,8)(5,6,7,8,9)} \atop {(6,7,8,9,10),(7,8,9,10,J),(8,9,10,J,K),(9,10,J,K,L),(10,J,Q,K,A)}} \right. \}[/tex]

Hence, the total no of outcome for N = 10

Answer:

5/8 +8/15m+ 14t

Step-by-step explanation:

Combine your like terms, and you will get this.

Answer:

Diagram 2, 12 foul balls

Step-by-step explanation:

12/3=4

12-4=8

Answer:

y=2, x=3

Step-by-step explanation:

We can see that because triangle EHF has all 3 of the angles the same, EFH is an equilateral triangle and all of the sides are the same. So, we now know that y+2=4. if we simplify that, we find that y=2. Now, because the angles FHG and angle FGH are the same, triangle FHG is an isosceles triangle, and y+2=x+1. we now know that y+2=4, so x+1=4. simplify and x=3

Answer:

24

Step-by-step explanation:

that is what   thinkof ur answer

Answer:

Height=61 feet

Step-by-step explanation:

Height=sin 55 degrees x 75

Height=0.8192 x 75

Height=61.43

Answer:

27 minutes

Step-by-step explanation:

33% of 24.5 is 8.1 ounces

.3 oz / 1 min = 8.1 oz / 'x' min

cross-multiply:

.3x = 8.1

x = 8.1 / .3

x = 27

Answer:

algebraic terms = 4- -4 = 8

Step-by-step explanation:

-4 is our lowest value as 5 is not equal or counted

4 is our highest value and is counted.

Answer:

-48.015

Step-by-step explanation

Answer:W=5x15

HTH

Step-by-step explanation:

Answer:

One book would cost $13.

Step-by-step explanation:

To solve this all you have to do is divide 65 by 5. Since 65 divided by 5 is 13, 13 is your answer. So one book would cost $13.

I hope this helps you.

Answer:

5351.2

Step-by-step explanation:

596 times 9 = 5364

64 divided by 5 = 12.8

5364 minus 12.8 = 5351.2