A square has a area of 63 square inches. What is the length of a side of the square, in inches?

The hourly growth rate parameter for the bacterial population is approximately 0.0415, indicating an exponential growth model.

In a continuous exponential growth model, the population size can be represented by the equation P(t) = P0 * e^(rt), where P(t) is the population size at time t, P0 is the initial population size, e is the base of the natural logarithm, and r is the growth rate parameter. We can use this equation to solve for the growth rate parameter.

Given that the initial population size (P0) is 3000 bacteria and the population size after 6 hours (P(6)) is 3622 bacteria, we can plug these values into the equation:

3622 = 3000 * e^(6r)

Dividing both sides of the equation by 3000, we get:

1.2073 = e^(6r)

Taking the natural logarithm of both sides, we have:

ln(1.2073) = 6r

Solving for r, we divide both sides by 6:

r = ln(1.2073) / 6 ≈ 0.0415

Therefore, the hourly growth rate parameter for the bacterial population is approximately 0.0415.

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For the Random variables, X and Y where both are nonnegative for all points in a sample space S. The expected value of Z ( random variable) is, E(Z) = E(X) + E(Y).

We have X and Y are random variables and that X and Y are non-negative for all points in a sample space S. Let us consider X be another random variable defined as Z(s) = max( X(s), Y(s))

for all elements s belongs to S. We have to show that E( Z) = E(X) + E(Y)

Now, for simple way of representation let

Max ( X(s),Y(s)) = Max(X,Y)

We know that Max(X,Y) = [(X+Y) + |X-Y|]

So, Z = Max(X,Y) = [(X+Y) + |X-Y|]

Taking expectations E(Z) = E(Max(X,Y)

= E{[(X+Y) + |X-Y|]}

\(E(Z)= \frac{1}{2} [E(X+Y) + E|X-Y|] = [E(X) + E(Y) + E|X-Y|] \\ \) (Since E(X + Y) = E(X)+ E(Y))

\(E(Z) = \frac{1}{2}[E(X)+ E(Y) + E|X| + E|-Y|]\\ \)

\(= \frac{1}{2} [E(X) + E(Y) + E(X) + E(Y)]\) (Since X and Y are non negative so E|X| = E(X) and E(-Y)=E(Y) )

=> E(Z) = E(X)+ E(Y)

Hence, required results occurred.

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Answer:

Here, Hope it helps its only the answer

Answer:

(4x-9)²

Step-by-step explanation:

If you want to simplify 16x² - 72x + 81, you can use a cool trick called the square of a binomial rule. This rule says that if you have something like (a + b)², you can expand it as a² + 2ab + b². So, how do we apply this rule to our problem? Well, first we need to find a and b that make our expression look like (a + b)². We can do this by noticing that 16x² is the same as (4x)² and 81 is the same as 9². Then we can check that the middle term is -2 times the product of 4x and 9, which is -72x. So we can write our expression as (4x - 9)². That's it! We have simplified our expression using the square of a binomial rule.

Answer: $650 + $450 divide it and then subtract it then it should be the answer X

Step-by-step explanation: answer

Answer:

$18 for each carpet.

Step-by-step explanation:

This is how I did it.

Money Spent                              288

Amount of Carpets                     16

288/16 = 18

$18 per carpet.

Step-by-step explanation:

5940 = 2×2×3×3×3×5×11

HOPE IT HELPS YA

Answer:

5940= 2 x 2 x 3 x 3 x 3 x 5 x  11

Step-by-step explanation:

It will take 7.76 years (rounded off to two decimal places) for $5600 to earn $3552.50 at an annual interest rate of 7.25%.

To calculate the time taken by $5600 to earn $3552.50 at an annual interest rate of 7.25%, the first step is to identify the appropriate formula to use.

The formula used in this case is Time = (Interest / Principal) / Rate. Using this formula, we can now calculate the time taken for the investment to earn $3552.50

From the question above, Principal = $5600, Interest = $3552.50, and Rate = 7.25%

Convert the percentage rate to decimal by dividing by 100:

7.25% / 100 = 0.0725 Time = (Interest / Principal) / Rate Time = ($3552.50 / $5600) / 0.0725 Time = 0.5625 / 0.0725 Time = 7.7586 (rounded off to four decimal places)

Therefore, it will take 7.76 years (rounded off to two decimal places) for $5600 to earn $3552.50 at an annual interest rate of 7.25%.

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Step-by-step explanation:

\( \frac{ {4}^{7} }{ {4}^{6} } \)

= 4

.......

Answer:

f(-3) = 6

Step-by-step explanation:

\(f(-3)=\frac{2}{3} (-3)+8=\frac{2(-3)}{3} +8=-\frac{6}{3}+8= -2+8=6\)

Hope this helps.

Answer:

f(x) = 6

Step-by-step explanation:

f(-3) means replace the x in f(x) with a -3, and replace every x in the equation with -3.

f(-3) = (2/3)x + 8

      = (2/3) (-3) + 8

      = (2 X -3)/3 + 8

      = -6/3   + 8

      = - 2 + 8

      = 6

The correct answer is d) p = 20 and q = 18. For these values of p and q

\(x^{36} + px^q + 100\) is a perfect square for all integer values of x

To explain why p = 20 and q = 18 are the correct values, let's analyze the expression \(x^{36} + px^q + 100\). For this expression to be a perfect square for all integer values of x, it must be in the form (ax^18 + b)^2, where a and b are integers.

Expanding (ax^18 + b)^2 gives us \(ax^{36} + 2abx^{18} + b^2\). Comparing this with the given expression \(x^{36} + px^q + 100\), we can deduce the following:

1. The constant term in both expressions must be the same, which gives us b^2 = 100. The only possible integer value for b is 10, as it is the only square root of 100.

2. The coefficient of x^36 in both expressions must also be the same, which gives us a^2 = 1. The only possible integer value for a is 1.

3. The coefficient of x^18 in the expanded form is 2ab, which should be equal to px^q in the given expression. Therefore, we have 2ab = px^q. Since a = 1, this simplifies to 2b = px^q.

We know that b = 10, so we can substitute it into the equation: 2 * 10 = px^q. Simplifying further, we get 20 = px^q.

Now, we need to find a value for p and q that satisfies the equation for all integer values of x. If we set q = 18, then x^q = x^18, and the equation becomes 20 = px^18. This is satisfied for any value of x.

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Answer:

2. When substituting x=2 and y=1 into the equation, you get a true statement.

Hope this helps you.

Answer:

B 17,500

Step-by-step explanation:

I Know this answer because i pay attention to the work

rate 5 stars

Answer: decay

Step-by-step explanation: decay is when the input is less than 1 and greater than 0. 0.75 falls in between these numbers

the tell-tale factor is the value inside the parenthesis, if that's less than 1 is Decay, if more than 1 is Growth

\(\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &2.5\\ r=rate\to \text{\LARGE 28\%}\to \frac{28}{100}\dotfill &0.28\\ t=\textit{elapsed time}\dotfill &x\\ \end{cases} \\\\\\ A=2.5(1 - 0.28)^{x} \implies A = 2.5(0.72)^x\hspace{5em}y= 2.5(0.72)^x\)

Answer:

the answer is 29 degrees F  i am a you tuber please subscribe to nikolys on you tube

Step-by-step explanation:

Answer:

It's the fourth answer, D.

A. The total mass is 40π.

B. The moment about the x-axis is 1024/5.

C. The moment about the y-axis is also 1024/5.

D. The center of mass is located at (8/5, 8/5).

E. The moment of inertia about the origin is 1024/3.

A. The total mass can be found by integrating the density function over the region:

m = ∬D p(x,y) dA

= ∫0^2π ∫0^4 5(r^2)(r dr dθ)

= 40π

Therefore, the total mass is 40π.

B. The moment about the x-axis can be found by integrating the product of the density function and the square of the distance to the x-axis over the region:

Mx = ∬D y p(x,y) dA

= ∫0^2π ∫0^4 5(r^2)(r sinθ)(r dr dθ)

= 1024/5

Therefore, the moment about the x-axis is 1024/5.

C. The moment about the y-axis can be found by integrating the product of the density function and the square of the distance to the y-axis over the region:

My = ∬D x p(x,y) dA

= ∫0^2π ∫0^4 5(r^2)(r cosθ)(r dr dθ)

= 1024/5

Therefore, the moment about the y-axis is 1024/5.

D. The center of mass can be found using the formulas:

xbar = My / m

ybar = Mx / m

Plugging in the values we found in parts B and C, we get:

xbar = (1024/5) / (40π) = 8/5

ybar = (1024/5) / (40π) = 8/5

Therefore, the center of mass is at the point (8/5, 8/5).

E. The moment of inertia about the origin can be found by integrating the product of the density function and the square of the distance to the origin over the region:

I = ∬D (x^2 + y^2) p(x,y) dA

= ∫0^2π ∫0^4 5(r^2)((r^2 sin^2θ) + (r^2 cos^2θ))(r dr dθ)

= 1024/3

Therefore, the moment of inertia about the origin is 1024/3.

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Answer:

A swimming pool charges an entrance fee of $2 per person plus $0.25 for each 10 minutes they spend in the pool.  How much did it cost for Katy to swim for 90 minutes?

let y = total cost

let x = number of 10 minute periods spent in pool

⇒ y = 0.25x + 2

If Katy spent 90 minutes in the pool, x = 9:

⇒ y = 0.25 x 9 + 2 = 4.25

So it cost Katy $4.25 to swim for 90 minutes.

the slopes would look like this

Answer:    1/4

Answer:

Step-by-step explanation:

Here is the complete question: Find the rate of change for the situation:

A chef cooks 9 lbs of chicken for 36 people and 17 lbs of chicken for 68 people.

Given: 1st situation, A chef cook 9 lbs chicken for 36 people.

          2nd situation, chef cook 17 lbs chicken for 68 people.

∴ 1st situation, weight of chicken per person=  

 Weight of chicken per person=  

2nd situation, weight of chicken per person=  

Weight of chicken per person=  

In both the situation chef cook same amount of chicken per person, which is  

∴ Rate of change is

Step-by-step explanation:

There are several important information's already given in the question. Based on those information's the answer can be easily deduced.

In the first case,

The amount of chicken the chef cooks for 36 people = 9 pounds

Then

The amount of chicken the chef cooks for 1 person = 9/36

                                                                                 = 1/4 pounds

Now let us take the second case

The amount of chicken the chef cooks for 68 people = 17 pounds

Then

The amount of chicken the chef cooks for 1 person = 17/68

                                                                                 = 1/4 pounds

From the above deductions, it can be concluded that the correct option among all the options given in the question is the third option or option "B".

Answer: Ham and soft

Ham and milk shake

Hot dog and soft

Hot dog and milk shake

Chicken and soft

Chicken and milkshake

Total number of possiblities 3 × 2 = 6 or listed above

Step-by-step explanation:

Given point and line are Po(-4, 5, -1) and x = -4 - t, y = 5 + 3t, z = -5t, -[infinity]o respectively. To find the equation for the plane through Po(-4,5,-1) perpendicular to the line, we will use the following steps  First, we will calculate the direction vector for the given line.

We know that the direction ratios of the line are (-1, 3, -5)Therefore, the direction vector of the line is given as V1 = (-1, 3, -5) We know that the given plane is perpendicular to the given line and passes through the given point, therefore the normal vector of the plane is equal to the direction vector of the given line.Let the normal vector of the plane be V2 = (a, b, c) = V1 = (-1, 3, -5) Therefore, a = -1, b = 3, and c = -5.

Now, we will use the equation of the plane in the normal form that is (a, b, c) . (x - x1, y - y1, z - z1) = 0Here, (x1, y1, z1) = (-4, 5, -1)Therefore, the equation of the plane is (-1, 3, -5) . (x + 4, y - 5, z + 1) = 0 Simplifying the above equation, we get the following equation:: The equation of the plane through Po(-4,5,-1) perpendicular to the given line is x + 3y - 5z + 32 = 0.:Given point and line are Po(-4, 5, -1) and x = -4 - t, y = 5 + 3t, z = -5t, -[infinity]o respectively. To find the equation for the plane through Po(-4,5,-1) perpendicular to the line, we will use the following steps.Step 1: First, we will calculate the direction vector for the given line.

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Answer:

0.25

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

To solve this expression, we need to remember that division should be done before multiplication or addition/subtraction.

So we first simplify the expression by dividing 1/2 by 6:

1/2 ÷ 6 = 1/2 × 1/6

Next, we multiply the two fractions by multiplying their numerators and denominators:

1/2 × 1/6 = (1 × 1)/(2 × 6) = 1/12

Therefore, the value of the expression 1/2 ÷ 6 is equal to 1/12.

By increasing their recycling by 500 pounds per month, the school conserves 4,800 gallons of water in a year.

Determine the ratio of water conserved per pound of paper recycled:

8 gallons of water are saved for every 10 pounds of paper recycled.

Calculate the water saved for each pound of paper:

8 gallons/10 pounds = 0.8 gallons/pound.

Find the increase in paper recycled per month:

500 pounds/month.

Calculate the water saved per month:

\(500 $ pounds/month \times  0.8 $ gallons/pound = 400 $ gallons/month.\)

Calculate the water saved in a year:

\(400 $ gallons/month \times  12 months = 4,800 $ gallons/year.\)

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Answer:

The correct range is thus;

(-6,-12,-9)

Step-by-step explanation:

Here, we want to get the range given the domain

we simply make a substitution of the domain in the equation so as to get the range

So let us substitute the value of the domain one after the other

f(3) is 3-9 = -6

f(-3) = -3-9 = -12

f(0) = 0-9 = -9

C. True, because to use the Law of Sines, at least two sides must be known.

The Law of Sines is a trigonometric rule that relates the sides and angles of any triangle. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle.

To use the Law of Sines, at least two sides and the angle opposite one of them (or two angles and one side) must be known.

Therefore, the statement "The Law of Sines can be used to solve triangles where three sides are known" is false, as it is not necessary to use the Law of Sines to solve a triangle where all three sides are known.

In summary, the correct answer is C. True, because to use the Law of Sines, at least two sides must be known.

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Answer:

first get their difference and then get positions of the difference and get the factors and then you will get the nth term