To the nearest ten thousand , the population of Vermont was estimated to be about 620,000 in 2008. What might have been the exact population of Vermont in 2008?

To get a mixture that is 70% antifreeze, you would need 600 gallons of 80% antifreeze solution mixed with 100 gallons of 10% antifreeze solution.

To solve this problem, we will use the six step method. Let's assign variables to our unknown quantities:

Now we can set up the equation using the information given:

Simplifying the equation:

Therefore, you would need 600 gallons of the 80% antifreeze solution to mix with 100 gallons of the 10% antifreeze solution to get a mixture that is 70% antifreeze.

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Rounding the coefficients to four decimal places:

[tex]\[ n(t) = 50000 \times \left(1 - e^{-20.2020t + 0.0101}\right) \][/tex]

The logistic equation governing the number of people exposed to the advertisement in the community is given by:

[tex]\[ \frac{{dn}}{{dt}} = kn \left(1 - \frac{n}{M}\right) \][/tex]

Where:

n(t)  is the number of people exposed to the advertisement at time t

k  is the growth rate constant

M  is the limiting number of people who will see the advertisement

Given:

[tex]\( n(0) = 500 \)[/tex]

[tex]\( n(1) = 1000 \)[/tex]

[tex]\( M = 50000 \)[/tex]

We first need to find the growth rate constant \( k \):

[tex]\[ 1000 = 500 \times \left(1 - \frac{500}{50000}\right) \times k \][/tex]

[tex]\[ 1000 = 500 \times \left(1 - \frac{1}{100}\right) \times k \][/tex]

[tex]\[ 1000 = 500 \times \frac{99}{100} \times k \][/tex]

[tex]\[ k = \frac{1000 \times 100}{500 \times 99} \][/tex]

[tex]\[ k = \frac{2000}{99} \][/tex]

Now, we integrate to find [tex]\( n(t) \)[/tex]:

[tex]\[ \int \frac{{dn}}{{n(1 - \frac{n}{50000})}} = \int \frac{{2000}}{{99}} dt \][/tex]

[tex]\[ -\ln|1 - \frac{n}{50000}| = \frac{{2000}}{{99}}t + C \][/tex]

Using the initial condition [tex]\( n(0) = 500 \)[/tex], we find[tex]\( C \)[/tex]:

[tex]\[ -\ln|1 - \frac{500}{50000}| = 0 + C \][/tex]

[tex]\[ -\ln\left(\frac{99}{100}\right) = C \][/tex]

So, the equation becomes:

[tex]\[ -\ln|1 - \frac{n}{50000}| = \frac{{2000}}{{99}}t - \ln\left(\frac{99}{100}\right) \][/tex]

Solving for n(t) :

[tex]\[ |1 - \frac{n}{50000}| = e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]

[tex]\[ 1 - \frac{n}{50000} = e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]

[tex]\[ \frac{n}{50000} = 1 - e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)} \][/tex]

[tex]\[ n(t) = 50000 \times \left(1 - e^{-\frac{{2000}}{{99}}t + \ln\left(\frac{99}{100}\right)}\right) \][/tex]

This is the solution for [tex]\( n(t) \)[/tex]. Now, rounding the coefficients to four decimal places:

[tex]\[ n(t) = 50000 \times \left(1 - e^{-20.2020t + 0.0101}\right) \][/tex]

The answer to  [tex]72 - (-58) - 62[/tex] is 68.

Understanding Double Negatives: When we subtract a negative number, it is equivalent to adding that number. Therefore, [tex]-(-58)[/tex] becomes [tex]+58[/tex].

So, the expression can be rewritten as:

[tex]72 + 58 - 62[/tex]

Performing the Addition: Now we add [tex]72[/tex] and [tex]58[/tex]:  

[tex]72 + 58 = 130[/tex]

Performing the Final Subtraction: Next, we subtract [tex]62[/tex] from [tex]130[/tex]:  

[tex]130 - 62 = 68[/tex]

Therefore, the final answer is [tex]68[/tex].

The expression 4 × 24 in distributive form will be 4 × ( 20 + 4 ) and the value of 96.

An expression 4x24 is given.

We have to write it using distributive property.

What is the distributive property of multiplication ?

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.

As per the question ;

Expression is 4x24.

Let's rewrite it in form of distributive property ;

4 × 24

= 4 × ( 20 + 4 )

So ,

It is now in form A ( B + C ) , where ; A = 4 , B = 20 and C = 4

⇒ 4 × ( 20 + 4 )

= 80 + 16

= 96

Thus , the expression 4 × 24 in distributive form will be 4 × ( 20 + 4 ) and the value of 96.

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Segments and lines can be named using the letters that represent the points on them, such as AB or line AB.

In geometry, segments and lines are fundamental elements. A line is an infinite set of points extending in opposite directions, while a segment is a finite portion of a line with two distinct endpoints. These concepts are essential for understanding geometric shapes, angles, and spatial relationships in mathematics.

In mathematics, the name of a segment and the name of a line can be written differently by using the letters that represent the points on the segment or the line. For example, a segment between points A and B can be written as AB, while a line passing through points A and B can be written as line AB or simply AB. It is important to note that in both cases, the order of the points does not matter, as AB is the same as BA.

c=PI*d

divide both sides by PI to get d by itself

d = c/PI

It would cost $2338.75 to build a deck that is 22 feet by 18.5 feet at a rate of $5.75 per square foot.

To calculate the cost of building a deck, we need to find the total area of the deck and then multiply it by the cost per square foot.

The area of a rectangle (deck) is given by the formula:

Area = length * width

Given that the deck has a length of 22 feet and a width of 18.5 feet, we can calculate the total area:

Area = 22 feet * 18.5 feet

Area = 407 square feet

Now, to find the total cost of building the deck, we multiply the area by the cost per square foot:

Total cost = Area * Cost per square foot

Total cost = 407 square feet * $5.75/square foot

Total cost = $2338.75

So, it would cost $2338.75 to build a deck that is 22 feet by 18.5 feet at a rate of $5.75 per square foot.

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Answer:

A)up

Step-by-step explanation:

Given : f(x)=log x +3

            g(x)= log x

To Find :

The graph of f(x) = log x + 3 is the graph of  g(x) = log x translated 3 units

a)up

b)down

c)left

d) right

Solution:

Rule: f(x)→f(x)+b

So, the graph f(x) is translated up by b units

So, on comparing given f(x) with rule , we can say that the graph g(x) is translated up by 3 units

Thus option A is correct.

Hence The graph of f(x) = log x + 3 is the graph of  g(x) = log x translated 3 units up

Answer:

the answer is 6.

Step-by-step explanation:

on edge i got my question wrong and the answer was 6 <33.

To find (g-f)(3), evaluate g(3) and f(3), then subtract f(3) from g(3).

To find (g-f)(3), we need to subtract the function f(x) from g(x) and then evaluate the result at x = 3. Let's first simplify the expressions for f(x) and g(x):

f(x) = 4 - x^2

g(x) = 6x

Now substitute these into (g-f)(3) and simplify:

(g-f)(3) = g(3) - f(3)

= 6(3) - (4 - 3^2)

= 18 - (4 - 9)

= 18 - (-5)

= 23

Therefore, (g-f)(3) is equivalent to 23.

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since they are both negative numbers just subtract 7 from 54

54-7 = 47

The Greates Common Factor (GCF) is:   2

Equation for the length L of the rope as a function of the distance x from P to the ground is,

⇒ L = √((x-2)²+50²)

Since L is to the second pole, not x, we can't simply say that;

⇒ x² + y²= L² using the Pythagorean Theorem.

Since, due to that we simply increase the original height by 2, decreasing x by 2.

We can, however, say that ;

⇒ (x-2)² + y² = L²

Plugging 50 as y in, we get ;

⇒ (x-2)² + 50² = L².

Square rooting both sides, we get;

⇒ L = √((x-2)²+50²)

Thus, Equation for the length L of the rope as a function of the distance x from P to the ground is,

⇒ L = √((x-2)²+50²)

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An equation is formed of two equal expressions. The value of y for the given equation is (1.5x - 6)/3.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

1.5x - 3y = 6

Subtract 1.5x from both the sides of the equation,

1.5x - 3y - 1.5x = 6 - 1.5x

-3y = 6 - 1.5x

Divide both the sides of the equation by -3,

-3y/(-3) = (6 - 1.5x)/(-3)

y = (1.5x - 6)/3

Hence, the value of y for the given equation is (1.5x - 6)/3.

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