Frank grows evergreen trees. He grew 535 trees for
the holiday season. In November he sold 215 trees
and in December he sold 275.
a. Write an expression. Then solve.
b. Frank replanted the left over trees with the
addition of 650 more trees. How many trees will
he have for next season?

Using separation of variables, it is found that the solution to the initial value problem is of y(x) = x² + 2.

In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.

In this problem, the differential equation is given by:

[tex]\frac{dy}{dx} = 2x[/tex]

Then, applying separation of variables:

[tex]dy = 2x dx[/tex]

[tex]\int dy = \int 2x dx[/tex]

[tex]y = x^2 + K[/tex]

Since y(0) = 2, we have that the constant of integration is K = 2, and the solution is:

y(x) = x² + 2.

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The differential equation is y(x) = x² + 2.

Differential Equations In Mathematics, a differential equation is an equation that contains one or more functions with their derivatives.

The given equation is;

[tex]\rm \dfrac{dy}{dx}=2x[/tex]

Applying the variable separation method;

[tex]\rm \dfrac{dy}{dx}=2x\\\\\int\limits \, dy=\int\limits\, 2x. dx\\\\y = 2 \times \dfrac{x^{1+1}}{1+1} +c\\\\y = 2 \times \dfrac{x^{2}}{2} +c\\\\y = x^2+c[/tex]

The value of c when y( 0 ) = 2 is c =2.

Hence, the required differential equation is y(x) = x² + 2.

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The geometric sequence can be represented explicitly or as recursions

The explicit formula of the geometric sequence is b(n) = 2 * 3^(n-1)

The sequence is given as:

2, 6, 18, 54, ....

Start by calculating the common ratio (r)

r = b2/b1

This gives

r = 6/2

Evaluate the quotient

r = 3

A geometric sequence is represented as:

b(n) = b1 * r^(n-1)

This gives

b(n) = 2 * 3^(n-1)

Hence, the explicit formula of the geometric sequence is b(n) = 2 * 3^(n-1)

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Answer:

-2 to the third power is -8

-2 to the second power is -4

Step-by-step explanation:

-2 to the 3 power = -2× -2×-2

-2 to the second power is -2×-2

Answer: y = 32/7

Step-by-step explanation:

Solve the first equation for x by subtracting the 2y from the left side and getting: x = 1 - 2y.

Plug this in to the second equation: 2(1 - 2y) - 3y = -30 → 2 - 4y - 3y = -30 →

-7y = -32 → y = 32/7. Hope this helps!

Answer:

-5

Step-by-step explanation:

-5 is less than -4, and -4 is greater than -5.

Negative numbers become smaller to the left on the number scale.

There are infinite possible answers to this. :)

Answer:

-5

Step-by-step explanation:

-5 is less than -4 and -4 is bigger than -5

If [tex]P(x) = x^2-4x+4[/tex]  and x =2

   --> [tex]P(2) = 2^2-4(2)+4=4-8+4=0[/tex]

Hope that helps!

Answer:

N = 9

Step-by-step explanation:

N^2 = 81

NxN = 81

N = 9 because 81/9 = 9 and if you don't trust me use a calculator

Answer:

15:11 ,where 15 = 435

So, 11 = 435×11//15 = 29×11 = 319

Hence, No. of girls = 319

Answer:

319 girls

Step-by-step explanation:

Given

Solving

Answer:

I think it's the fourth one.

The length of the colony is the product of 5. 3 × 10^3 and the length of the bacteria

The total length of the colony is 143.1 mm

The given parameters are:

Bacteria = 2.7 × 10^–2 mm.

Colony = 5. 3 × 10^3 of the bacteria

So, the length (L) of the colony is:

[tex]L = 5.3 * 10^3 * 2.7 * 10^{-2[/tex]

Rewrite as:

[tex]L = 5.3 * 2.7* 10^3 * 10^{-2[/tex]

Evaluate the products

[tex]L = 14.31* 10[/tex]

Evaluate the product

[tex]L = 143.1[/tex]

Hence, the total length of the colony is 143.1 mm

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Answer:

rational

Step-by-step explanation:

Hope this helps!

If not I am sorry

let's keep in mind that that same/same = 1 always, so then we can say

[tex]\cfrac{spaghetti}{spaghetti}~~ = ~~\cfrac{hippopotamus}{hippopotamus}~~ = ~~\cfrac{meatballs}{meatballs}~~ = ~~\cfrac{dog}{dog}~~ = ~~\cfrac{0.\overline{55}}{0.\overline{55}}~~ = ~~\textit{\huge 1}[/tex]

well, "1" is a whole number

"1" is also an integer oddly enough

"1" can be written as a ration like 1/1, so is also rational.

Answer:

side length = 4

Step-by-step explanation:

Let x = the side length

Area is x•x, which is x^2.

Perimeter is x+x+x+x, which is 4x.

x^2 = 4x

x^2 - 4x = 0

Factor.

x(x-4) = 0

x = 0 or x = 4

Discard 0 as an answer as it is not useful.

x = 4.

Area = 4^2 = 16

Perimeter = 4(4)= 16

The side length is 4.

Option c is the best option that can be recommended since it has the least total cost for a year.

An upfront cost is an initial sum of money owed in a purchase or business venture.

Option a:

Monthly cost = $618

Up-front cost = $24000

Total cost for a year= 618*12+24000 = $31416

Option b:

Monthly cost = $950

Up-front cost = $1900

Total cost for a year= 950*12+1900= $13300

Option c:

Monthly cost = $600

Up-front cost = $1200

Total cost for a year= 600*12+1200= $8400

Therefore, option c is the best option that can be recommended since it has the least total cost for a year.

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Answer:

1st question is A and C only, 2nd question is A only

Step-by-step explanation:

Got it right on edge. Have a great day :)

The sound will travel fastest at an elevation of 500m,

Elevation      Temperature

500m              11.8°C (MAXIMUM)

1000m               8.5°C

1500m               5.3°C

2000m               2.0°C

Molecules at higher temperatures have more energy and they can vibrate faster and allow sound waves to travel more quickly because the more is the medium, the more quickly sound waves propagate.

So, when the temperature is maximum i.e. 11.8°C, the sound will travel fastest. The elevation corresponding to 11.8°C is 500m.

So, Sound will travel fastest at 500m elevation.

Therefore, At an elevation of 500m, the sound will travel fastest.

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Answer:

500 meters

Step-by-step explanation:

Answer:

b no. is the correct answer

Answer:

A. Line
<------------->

B. Angle
⦟

C. Line Segment
.___________.

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

[tex]6x^2+8x[/tex]

Step-by-step explanation:

Hey there!

In order to find the answer to this question, what you need to do is first find the area of the whole grey box as a whole (including the white box to)

The dimensions for this is 3x+2 and 4x

Now we know that to find area, we need to multiply length by height

So (3x+2)(4x) is what we have to solve to get the area

Now we simplify:

1. Distribute

2. [tex]12x^2+8x[/tex]

So now we know that the total area is [tex]12x^2+8x[/tex]

Now what we do is take out the area of the white box from the area of the grey box

Lets find the area of the white box:

l=3x   (l - length)

h=2x (h - height)

[tex]3x*2x=6x^2[/tex]

Now we have the area of both shapes

Since we have all the information we need to find the final answer, the following steps below will be using the information we found to find the final answer:

In order to find the final answer which is the area of the shaded region, we take out the area of the white region from the total area of the grey region (including the white region)

So now we can formulate this new equation:

[tex]12x^2+8x-6x^2= ta[/tex]

(ta= total area)

Now we simplify:

[tex]6x^2+8x\\[/tex] is going to be our final answer

So our final answer is [tex]6x^2+8x[/tex]

Answer:

11

Step-by-step explanation:

the area of a triangle is bc/2

b = 8.8

c = ?

area = 48.4

48.4 = 8.8c/2

96.8 = 8.8c

c = 11

Please mark as brainliest!

11

Step-by-step explanation:

[tex] \frac{1}{2} \times 8.8 \times c = 48.4[/tex][tex] \frac{8.8 \times c}{2} = 48.4 \\ 8.8 \times c = 48.4 \times 2 \\ 8.8 \times c = 96.8 \\ c = \frac{96.8}{88} \\ c = 11[/tex]mark me brainiest please

Using the Poisson distribution, it is found that the probabilities are given by:

a) 0.1009 = 10.09%.

b) 0.8262 = 82.62%.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

Item a:

The mean is of 7 customers for 60 minutes, hence, for 90 minutes = 1.5 x 60 minutes, the mean is given by:

[tex]\mu = 1.5 \times 7 = 10.5[/tex]

The probability of exactly 8 customers is of P(X = 8), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 8) = \frac{e^{-10.5}10.5^{8}}{(8)!} = 0.1009[/tex]

Item b:

Probability of at least one patient in 15 minutes, hence:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

For 15 minutes, the mean is given by:

[tex]\mu = 0.25 \times 7 = 1.75[/tex]

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 8) = \frac{e^{-1.75}1.75^{0}}{(0)!} = 0.1738[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1738 = 0.8262[/tex]

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Answer:

17

Step-by-step explanation:

replace x with 5

3*5+2

next you use pemdas

you multiply before you add

3*5=15

15+2=17

Answer:

-(12+a)(a+2)

Step-by-step explanation:

this is to ez

The expression as a product is (a+12)(-a-2)

An expression in math is a statement having minimum of two numbers, or variables, or both and an operator connecting them.

Given that, is an expression, 25-(a+7)², we need to write it in product form, 25-(a+7)²

= 25 - (a²+49+14a)

= 25-a²-49-14a

= -a²-14a-24

Factorizing,

= -a²-12a-2a-24

= -a(a+12)-2(a+12)

= (a+12)(-a-2)

Hence, the expression as a product is (a+12)(-a-2)

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The relationship between e, f and g is an illustration of ratio

The ratio e : g is 2 : 7

The given parameters are:

e : f = 3 : 7

f : g = 2 : 3

Multiply e : f by 2.

So, we have:

e : f = 6 : 14

Multiply f : g by 7.

So, we have:

f : g = 14 : 21

Merge both ratios

e : f : f : g = 6 : 14 : 14 : 21

Remove repetition

e : f : g = 6 : 14 : 21

Remove f

e : g = 6 : 21

Divide by 3

e : g = 2 : 7

Hence, the ratio e : g is 2 : 7

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Answer:

2

Step-by-step explanation:

Basically you plug in -6 where all the x's are.

(-6)² + 7(-6) + 8, Multiply -6 * -6 (AKA (-6)²)

36 + 7(-6) + 8, Multiply 7 by -6

36 - 42 + 8, Add 36 + 8

44 - 42, Subtract

2

Answer:

They have more resources and yeah they just do

Step-by-step explanation:

I have no clue why im just guessing

Answer:

12000

Step-by-step explanation:

Using this information, you can make a ratio: 12.2/50 = x/48744

By simplifying this ratio you get that 50x = 594676. Dividing both sides by 50 you get about 11900, which you can round up to 12000

Answer:

11,894 women

Step-by-step explanation:

ratio of women to employees = 12.2 : 50

Let x = number of women employees to 48744 employees

12.2 : 50 = x : 48744

⇒ 12.2 / 50 = x / 48744

⇒ 0.244 = x / 48744

⇒ x = 0.244 · 48744

⇒ x = 11893.536

⇒ x = 11894 (nearest whole number)

Therefore, there are approximately 11,894 women in a company with a total of 48,744 employees

Answer:

Price/Cost

Step-by-step explanation:

They may reduce the cost due to the lack of people buying that product, or vice versa.

Using proportions, it is found that the birth rate fell to 13.5 births for every 1000 people.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

In this problem, for 306,370,370 people, there were 4,136,000 births. How many births were there for 1,000 people? The rule of three is given by:

306,370,370 people - 4,136,000 births

1,000 people - x births

Applying cross multiplication:

306370370x = 1000 x 4136000

x = 1000 x 4136000/306370370

x = 13.5

The birth rate fell to 13.5 births for every 1000 people.

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Answer:

As Per Given Information

we have been asked to determine the consine ratio of ∠K .

[tex] \bf \: cos \: k = \cfrac{Base}{Hypotenuse} [/tex]

with respect to ∠K .

substitute the given value & let's solve it for k .

[tex] \longrightarrow\sf \: cos \: k \: = \cfrac{30}{50} \\ \\ \\ \longrightarrow\sf \: cos \: k \: = \cfrac{ 3\cancel0}{5 \cancel0} \\ \\ \\ \longrightarrow\sf \: cos \: k \: = \cfrac{3}{5} [/tex]

Therefore,

Your answer is (c) 3/5

Answer:

8 1/2

Step-by-step explanation:

14 inch - 5 1/2 inches = 8 1/2 inches

Aba's dog grew 8 1/2 inches.

Answer:

8.5 Inches, 2.78 pounds approximately

Step-by-step explanation:

14- n = 5.5. In this case you will have to subtract 5.5 from 14. 14 - 5.5 = 8.5. You get 2.5 pounds because, 1.10 x 2 = 2.20. 2.75 - 2.20= .55. $1.10 is 70 cents. 55/70 = 11/14= is around .78. 2+.78 = 2.78