What are the restrictions on the domain for the following rational expression?

The correct answer is A.

500 is the size of the population at the moment of maximum growth.

Given data:

To find the size of the population at the moment when the population is growing most rapidly, we need to determine the maximum value of the derivative dP/dt.

Given the logistic differential equation [tex]\frac{dP}{dt} = (\frac{1}{10})P - (\frac{1}{5000})P^2[/tex], find the derivative by taking the derivative of each term separately:

[tex]\frac{dP}{dt} = (\frac{1}{10})P - (\frac{1}{5000})P^2[/tex]

To find the critical points where the derivative is zero or undefined, set dP/dt equal to zero:

[tex](\frac{1}{10})P - (\frac{1}{5000})P^2=0[/tex]

Simplifying:

[tex](\frac{1}{10})P= (\frac{1}{5000})P^2[/tex]

[tex]10P^2=5000P[/tex]

Dividing both sides by P and rearranging:

[tex]10P(P-500)=0[/tex]

This equation has two solutions: P = 0 and P = 500.

To determine which solution corresponds to the moment when the population is growing most rapidly, examine the second derivative. Taking the second derivative of the logistic differential equation, we have:

[tex]\frac{d^2P}{dt^2} = \frac{1}{10} - \frac{2}{5000}P[/tex]

Evaluating the second derivative at P = 0 and P = 500, we get:

[tex]\frac{d^2P}{dt^2}_{P=0} = \frac{1}{10} - \frac{2}{5000}(0)[/tex]

[tex]\frac{d^2P}{dt^2}_{P=0}= \frac{1}{10} > 0[/tex]

[tex]\frac{d^2P}{dt^2}_{P=500} = \frac{1}{10} - \frac{2}{5000}(500)[/tex]

[tex]\frac{d^2P}{dt^2}_{P=0}= -\frac{1}{10} < 0[/tex]

Since the second derivative is positive at P = 0 and negative at P = 500, the moment when the population is growing most rapidly occurs at P = 500.

Hence, the size of the population at the moment when the population is growing most rapidly is 500.

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Answer:

Hypotenuse = 7.3 cm

Step-by-step explanation:

We can find the hypotenuse using the Pythagorean Theorem, which is:

[tex]a^2+b^2=c^2[/tex], where a and b are the legs of the right triangle and c is the hypotenuse.

By plugging in 2 and 7 for a and b, we have:

[tex]2^2+7^2=c^2\\4+49=c^2\\53=c^2\\7.2801=7.3=c[/tex]

Answer:

8.8 minutes

Step-by-step explanation:

first we figure out how many liters are being lost

57 - 35 = 22

then divide that by 2.5

22 / 2.5 = 8.8

8.8 minutes

Yosef's average weekly fuel cost is $24.35.

Yosef drove 11,190 miles last year.  His truck's fuel efficiency averages 19 mpg, and the average cost of gas last year was $2.15 per gallon.

Yosef average weekly fuel cost can be computed as follows:

Yosef used 11190 / 19 = 588.95 gallons to drive 11190 miles.

Therefore, the average cost of gas last year was 2.15 dollars per gallon.

Therefore, Yosef's average weekly fuel cost would be as follows:

Yosef's average weekly fuel cost = 2.15 x 588.95 ÷ 52 = $1266.23684211 ÷ 52

Yosef's average weekly fuel cost = 24.350708502

Yosef's average weekly fuel cost = $24.35

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Answer:

The 3rd statement is a lie and other two are truth.

Step-by-step explanation:

when two same numbers with power are divided their respective powers are subtracted.

1.

[tex] {b}^{a } \div {b}^{c} = {b}^{a - c} [/tex]

Using this formula for

[tex] {b}^{9} \div {b}^{y} = {b}^{4} [/tex]

[tex] {b}^{9 - 5} = {b}^{4} [/tex]

Here RHS =LHS

so the equation is true

2.

[tex] {b}^{z} \div {b}^{x} = {b}^{5} [/tex]

[tex] {b}^{7 - 2} = {b}^{2} [/tex]

Here RHS=LHS,

so the equation is true

[tex] {b}^{8} \div {b}^{x} = {b}^{8} [/tex]

[tex] {b}^{8 - 2} = {b}^{8}[/tex]

Here RHS is not equal to LHS

so the equation is false

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The expression that is an equivalent expression of 12x+10+4y is D 2(6x + 5 + 2y).

In Mathematics, expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

In this case, the expression that is an equivalent expression of 12x+10+4y is 2(6x + 5 + 2y). The correct option is D.

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Which expression is an equivalent expression of 12x + 10 + 4y?

A.) 2(6x + 2y + 6)

B.) 3(4x + y + 10)

C.) 2(6x + 4y + 8)

D.) 2(6x + 5 + 2y)

Answer: 33%

Step-by-step explanation: a third of the items in the bag are pretzels.

Answer:

answer :J LOOK THE DIAGRAM CAREFULLY AND UNDERSTAND

Answer:

A <c - <b = 10

Step-by-step explanation:

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=2\\ k=3 \end{cases}\implies y=a(x-2)^2 +3\hspace{5em}\textit{we also know that} \begin{cases} x=0\\ y=2 \end{cases} \\\\\\ 2=a(0-2)^2 + 3\implies -1=a(-2)^2\implies -1=4a\implies \cfrac{-1}{4}=a \\\\\\ ~\hfill {\Large \begin{array}{llll} y=-\cfrac{1}{4}(x-2)^2 + 3 \end{array}} ~\hfill[/tex]

The answers to all the parts are given below.

We have a function h = -16t² + 1800, that gives the height of the person at time [t] seconds.

[A] -

For [x] = 1000ft, we can write -

1000 = -16t² + 1800

16t² = 800

t² = (800/16)

t² = 50

t = 7.07 seconds

[B] -

For [x] = 950ft, we can write -

950 = -16t² + 1800

16t² = 850

t² = 53.125

t² = √(53.125)

t = 7.29 seconds

[C] -

The domain of the function will be -

0 ≤ x ≤ 10

[D] -

The range of the function will be -

0 ≤ h ≤ 1800

Therefore, the answers to all the parts are given above.

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Answer:

Step-by-step explanation:

17/5

Answer:

2 and 2/5

Step-by-step explanation:

28 mph is  the average speed of the bus in mph.

What is speed?

The speed of a change in an object's location in any direction. The distance traveled relative to the time it took to travel that distance is how fast something is moving.

                                 Meters per second (m/s), kilometers per hour (km/h), and miles per hour (mph) are the most popular speed units (mph). The distance an object covers in a given amount of time is its speed. Speed = distance x time is the speed formula. The meter per second, also known as the m/s or ms-1, is the SI unit of velocity.

time = (1+ 1/2)hr = 3/2 hr = 1.5 hr

distance = 42 miles

average speed = total distance/total time

42/1.5 = 28 mph

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Answer:

a=10

m=28

Step-by-step explanation:

2/3= 0.666666666666666

a/15=??????

try all numbers divided by 15 untill you found 0.666666666666666 which is =10/15

4/7=0.571428571428571

44/m=???????

do the same as the first one

it will be 44/28=0.571428571428571

y = -1.893x + 31.901

Detailed explanation:

We are given the following values in a table:

x  y

2  30

5  19

7  20

12  9

16  2

It is now abundantly evident from the set of values that when x increases, the y-value decreases, indicating a negative connection.

Therefore, the line of best fit will have a negative slope.

Consequently, a scatter plot is used to display the data values.

As can be seen, the line of best fit equation

y = -1.893x + 31.901T

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Answer:

256 feet.

Step-by-step explanation:

The equation for the surface area of a rectangular prism is lw x lh x hw. That means it would be 12x4, 12x5, and 4x5. In total that is 256.

A) The probability that the tyre wears out before 60000 miles is 0.4221

B) The probability that the tyre lasts more than 83000 miles is 0.49534

The distance the tyres can run until wear-out is a normally distributed, the formula for normal distribution is expressed as

z = (x - u)/s

Where

x = the distance the tyres can run until wear-out

u = mean distance

s = standard deviation

From the information given,

u = 70000 miles

s = 7000 miles

A) We want to find the Probability that the tyre wears out before 60000 miles. It is expressed as

P(x lesser than 60000)

For x = 60000,

z = (60000 - 70000)/7000 = - 1.42

Looking at the normal distribution table, the corresponding z score is 0.4221

B)We want to find the probability that the tyre lasts more than 83000 miles. It is expressed as

P(x greater than 83000) = 1 - P(x lesser than or equal to 83000)

For x = 83000,

z = (83000 - 70000)/5000 = 2.6

Looking at the normal distribution table, the corresponding z score is 0.49534

P(x greater than 83000)

= 1 - 0.49534  = 0.50466

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Answer:

7330.36

Step-by-step explanation:

A = P (1+i)^n

n  = 4×5 = 20

i = 0.03075

12.3% / 4 = 3.075  × 1/100

= 0.03075

A = 4000 ( 1+ 0.03075 ) ^20

= 7330.36

1. G is incompressible- True

2. F is irrotational- True

3. G is irrotational- False

4. F is incompressible- False

Divergence and Curl In Mathematics, divergence is a differential operator, which is applied to the 3D vector-valued function. Similarly, the curl is a vector operator which defines the infinitesimal circulation of a vector field in the 3D Euclidean space .

So if we calculate for F:

F has a divergence potentially

divF = df/dx + dg/fy + dh/dz

But curl(F )= 0(all cross derivatives df/dy df/dz, dg/dx etc = 0)

For G

G has zero divergence.

divG = df/dx + dg/fy + dh/dz = 0 + 0 + 0 = 0

But it may have a curl.

curl(G) = df/dy may be non-zero

df/dz, dg/dx etc may all be non-zero

Now, we also know that if the divergence is zero, the vector field is incompressible and if the curl is zero, the vector field is irrotational, that is,  

div = 0 = incompressible and

curl = 0= irrotational  

Thus,

1. G is incompressible- True

2. F is irrotational- True

3. G is irrotational- False

4. F is incompressible- False

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The given lines L1 ⇒ x = 5-12t, y = 3+9t, z = 1-3t and L2 ⇒ x = 3+8s, y = -6s, z = 7+2s  are parallel lines .

In the question ,

it is given that ,

the two lines are :

L1 ⇒ x = 5-12t, y = 3+9t, z = 1-3t

L2 ⇒ x = 3+8s, y = -6s, z = 7+2s

If the lines are intersecting then :

5 - 12t = 3 + 8s

8s + 12t = 2

4s + 6t = 1 ;   .....equation(1)

and 3 + 9t = -6s

3t + 2s + 1 = 0

multiplying both sides by 2 ,

we get ,

6t + 4s + 2 = 0  ....equation(2)

Solving equation(1) and equation(2) , we get

3 ≠ 0 .

So , the lines are not intersecting .

For lines to be parallel , the cross product of their directions must be 0 .

So , [tex]\left|\begin{array}{ccc}i&j&k\\-12&9&-3\\8&-6&2\end{array}\right|[/tex]

On simplifying further ,

we get ,

⇒ 0i - 0j + 0k

= 0

So , the cross product is 0 ,  lines will be parallel .

Therefore , the lines L1 and L2 are parallel .

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The number of cups she can make is 2 cups

From the question, we have the following parameters that can be used in our computation:

Cups of sugar needed = 1/4

Cups of sugar available  = 1/2

Assume there exist a proportional relationship between the cups

The number of cups she needs can be calculated using the following equation

number of cups = (1/2)/(1/4)

Evaluate the quotient

number of cups = 2

Hence, the cups is 2 cups

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(p-124) / 9 min many liters of water are in the tank after 109 seconds.

for 4 min =  65 + (6.5x4) = 91 lit

for  109 sec = 65 + (9x 109/60) = 81.35 lit

for m min = 65 + (9m) lit

how long time

for 151 lit = (151 - 124)/9 = 3 min

for 191.5 lit = (191.5-124) /9 = 67.5/9 = 7.5 min means 7 min 30 sec

for 270.25 lit = (270.25 - 124)/9 = 146.25/9 = 16.25 means 16 min 15 sec

for p lit = (p-124) / 9 min

What is liters ?

The water must be measured and expressed in the same unit for all of the containers. The litre is the name of that common unit for measuring liquid. Liquids are measured in litres, millilitres, centilitres, kiloliters, etc., including water, milk, gasoline, and oil.

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Answer:

- 7 < x < 6

Step-by-step explanation:

- 8 < x - 1 < 5 ( add 1 to each interval )

- 7 < x < 6

Answer:

y = x - 2

Step-by-step explanation:

Since m = 0, what we have so far is y=x+b

We have a point, which is (3,1)

Substitute the x and y with the x and y values in the coordinate point to solve for b (y-intercept).

1=3+b

1-3=3+b-3                  undo the 3 by subtracting

-2 = b

y = x + -2                   simplify

y = x - 2

Answer: (x-5)²=8

Step-by-step explanation:

x²-10x+17=0

x²-2(x)(5)+5²-5²+17=0

(x²-2(x)(5)+5²)-25+17=0

(x-5)²-8=0

(x-5)²-8+8=0+8

(x-5)²=8

Answer:

(x - 5)² = 8

--------------------------

Given

Expression  x² - 10x +17.

Convert this to vertex form by completing the square.

Recall identity (a ± b)² = a² ± 2ab + b² and apply as given below:

x² - 10x + 17  =

x² - 2*5*x + 5² - 5² + 17  =

(x - 5)² - 25 + 17 = (x - 5)² - 8

(x - 5)² = 8

The given statement can be written in terms of inequality as b + 10.7 ≤ 3.2. The correct option is (d).

Linear inequality refers to the relation between a linear algebraic expression to some known value that contains inequality sign.

Unlike a linear equation it can have a range of values inside an interval.

The given statement can be written in terms of inequality as follows,

The statement is, "the sum of a number and 10.7 is at most −3.2".

Suppose the number be b.

The following expression can be written,

b + 10.7 ≤ 3.2

Hence, the required inequality expression for the given problem is b + 10.7 ≤ 3.2.

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Answer:

X=1 Y=0

Step-by-step explanation:

Multiply the second equation (-2x + 8y = -2) by 2 in order to get -4x+16y=-4.
Using this equation, you can eliminate the x

4x - 8y = -4
-4x+16y=-4.
=
8y=0
y = 0

Now, knowing that y=0, plug y into the second equation:

-2x+8(0)=-2
simplify
-2x=-2
lastly, divide both sides by -2
x=1

The no. of cars that must drive by until a white one drives by is 40.

In an experiment with two possible outcomes, the likelihood of exactly x successes on n repeated trials is known as the binomial probability (commonly called a binomial experiment). The binomial probability is

[tex]^nC_xp^Xq^{n-x}[/tex].

We know the expected value of a binomial distribution E(x) = np.

Given, Suppose that 40% of the cars in a certain town are white.

Therefore 50% of cars in the town are not which.

Let, The no. of cards in the town be 'n'.

So, p = 40/n and q = 60/n

Therefore from the formula E(x) = np we get,

E(x) = n×40/n

E(x) = 40.

So, The expected value of X is 40.

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Answer: We expect 2.5 cars to

The expected value of X is 2.5.

Step-by-step explanation:

In this case, it is a geometric distribution because we do not have a fixed number of trials.

We use the formula of a geometric distribution to find the mean (the expected value) such that mu_x = 1/p.

In this case:

mu_x=1/0.4 = 2.5

In this case, we do not round up or down even if we cannot have half a car because we want the expected value (mean).

Answer:

i think the answer will be 6%

Answer:

below

Step-by-step explanation:

46 / 780  * 100% = 5.9 %

The equation for the line of best fit from the given data, will be y = 2.12 x + 4.42.

The line of best fit would be the line that has an equal number of points above it, as the number of points beneath it.

Going by this definition, two points that would be on the line are (6, 17) and ( 7, 19 ).

The slope of this line would be:

= ( Y2 - Y1 ) / ( X 2 - X1)

= ( 19 - 17 ) / (7 - 6 )

= 2.12

The y intercept would be:

y = mx + c

19 = 2.12 (7 ) + c

c = 4.42

The equation of the  line of best fit is then :
y = 2.12 x + 4.42

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