i really need help algebra​

t is the number of years since the initial count of 5,400 birds is \(N(t) = 5,400 * e^{(-0.03*t)}\)

A function is a rule that assigns to each input value, or argument, a unique output value. The input values are typically drawn from a set called the domain of the function, while the output values are typically drawn from a set called the range of the function.

Functions are often represented using algebraic expressions, such as.

by the question.

Let's call the initial number of birds "N" and the percentage decrease per year "r". The formula for exponential decay is:

\(N(t) = N₀ * e^{(-r*t2)}\)

where:

N(t) is the number of birds at time t.

N₀ is the initial number of birds.

e is the mathematical constant e (approximately 2.71828)

r is the annual decay rate (as a decimal)

t is the time elapsed (in years)

In this case, N₀ = 5,400 and r = 0.03 (since the birds are decreasing by 3% per year).

So, the exponential function that models this situation is:

\(N(t) = 5,400 * e^{(-0.03*t)}\)

\(N(t) = 5,400 * e^{(-0.03*t)}\)

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Answer:

416.7pounds

Step-by-step explanation:

Given parameters:

         Weight of the small box  = 125pounds

Unknown:

Weight of the larger box = ?

Solution:

The large box weighs \(3\frac{1}{3}\) times as the small box:

               So;

                =   125pounds x \(\frac{10}{3}\)

                = 416.7pounds

The two surfaces intersect orthogonally at the point (2, 1, -1).

The equation of the tangent line to the curve e^(xy) = e^2 at the point (2, 1) is x - 2y = 0.

The surfaces are given by:

Surface 1: z = 7x² - 12x - 5y²

Surface 2: xyz² = 2

We need to find the gradients of these surfaces:

Surface 1:

∇(z) = (∂z/∂x, ∂z/∂y, ∂z/∂z)

= (14x - 12, -10y, 1)

Surface 2:

∇(xyz²) = (∂(xyz²)/∂x, ∂(xyz²)/∂y, ∂(xyz²)/∂z)

= (yz^2, xz^2, 2xyz)

Now, let's evaluate the gradients at the point (2, 1, -1):

Gradient of Surface 1 at (2, 1, -1) = (14(2) - 12, -10(1), 1) = (16, -10, 1)

Gradient of Surface 2 at (2, 1, -1) = (1(-1)^2, 2(-1)^2, 2(2)(1)) = (1, 2, 4)

To check if the gradients are orthogonal, we can calculate their dot product:

(16, -10, 1) · (1, 2, 4) = 16(1) + (-10)(2) + (1)(4) = 16 - 20 + 4 = 0

Since the dot product is 0, the gradients are orthogonal. Therefore, the two surfaces intersect orthogonally at the point (2, 1, -1).

Let's define the function \(f(x, y) = e^{xy} - e^2.\)

First, we need to calculate the partial derivatives of f(x, y) with respect to x and y:

\(\frac{\partial f}{\partial x}=\:ye^{xy}\)

\(\frac{\partial f}{\partial y}=\:xe^{xy}\)

Next, we evaluate these partial derivatives at the given point (2, 1):

∂f/∂x at (2, 1) = e²

∂f/∂y at (2, 1) =2e²

Using the partial derivatives, we can determine the slope of the tangent line at (2, 1).

Slope of the tangent line = ∂f/∂x / ∂f/∂y

= 1/2

Now, we have the slope of the tangent line, and we know that it passes through the point (2, 1).

We can use the point-slope form of a line to find the equation of the tangent line:

y - y₁ = m(x - x₁), where (x₁, y₁) is the point and m is the slope.

Plugging in the values (x₁, y₁) = (2, 1) and m = 1/2:

y - 1 = (1/2)(x - 2)

Simplifying the equation:

2y - 2 = x - 2

Rearranging the terms:

x - 2y = 0

Therefore, the equation of the tangent line to the curve e^(xy) = e^2 at the point (2, 1) is x - 2y = 0.

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Show that the surfaces z=7x^2 −12x−5y^2 and xyz^2 =2 intersect orthogonally at the point (2,1,−1). Find the equation of the tangent line to the curve e^{xy} =e^2 at the point (2,1).

Answer:

Step-by-step explanation:

a^2+b^2=c^2

c^2-b^2=a^2

2^2-1^2=c^2

c^2=3

c=\(\sqrt{3}\)

espero que esto te ayude, pero no se si esta correcto lo siento

The addition equation to represent Jackson's net change in money is x + (-y) = 4.63

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Jackson receives 4.63 as his change at the grocery store. He places it into a charity donation jar at the register.

WE need to Write an addition equation to represent Jackson's net change in money.

Given that :

The change received = 4.63

The Net change in money :

Let initial amount before purchase is represented by  x

The Cost of item purchased = y (negative as it is incurred)

The Net change in money:

Initial amount + cost of item purchased = change received

x + (-y) = 4.63

Therefore, an addition equation to represent Jackson's net change in money is x + (-y) = 4.63

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Answer:

2.6 kilometers

Step-by-step explanation:

To find the circumference of a circle, we can use the formula:

Circumference = π * diameter

Given that the diameter of the volcanic crater is 840 meters, we can substitute this value into the formula:

Circumference = π * 840

Using the approximate value of π as 3.14159, we can calculate the circumference:

Circumference = 3.14159 * 840

Circumference ≈ 2643.1796 meters

To convert the circumference to kilometers, we divide the value by 1000:

Circumference in kilometers = 2643.1796 / 1000

Circumference ≈ 2.6432 kilometers

Therefore, the circumference of the rim of the volcanic crater is approximately 2.6 kilometers (rounded to 1 decimal place).

central angle measure

The probability density function (pdf) of the largest of the five waiting times is given by: f(x) = 4/10^5 * x^4, where x is a real number between 0 and 10. The expected value of the largest of the five waiting times is 8.33 minutes.

The pdf of the largest of the five waiting times can be found by considering the order statistics of the waiting times. The order statistics are the values of the waiting times sorted from smallest to largest.

In this case, the order statistics are X1, X2, X3, X4, and X5. The largest of the five waiting times is X5.

The pdf of X5 can be found by considering the cumulative distribution function (cdf) of X5. The cdf of X5 is given by: F(x) = (x/10)^5

where x is a real number between 0 and 10. The pdf of X5 can be found by differentiating the cdf of X5. This gives: f(x) = 4/10^5 * x^4

The expected value of X5 can be found by integrating the pdf of X5 from 0 to 10. This gives: E[X5] = ∫_0^10 4/10^5 * x^4 dx = 8.33

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Answer:

y=-x-1

Step-by-step explanation:

Answer:

y = - x - 1

Step-by-step explanation:

move x over and it becomes negative

When the strength is 256 pascals, the logarithmic function g(x) would yield x = 8, indicating that there are 8 woven strands in the rope.

To convert the exponential function f(x) = 2^x to a logarithmic function when the strength is 256 pascals, we can use the logarithmic property that relates exponential and logarithmic functions.

The exponential function f(x) = 2^x can be expressed as a logarithmic function using the logarithm base 2. Let's denote the logarithmic function as g(x).

If we rewrite the exponential function as a logarithmic equation, it would look like this:

2^x = y   becomes   x = log2(y)

In this case, we want to find the value of x (the number of woven strands) when the strength (y) is 256 pascals. So, the equation becomes:

x = log2(256)

Using the logarithmic property, we can rewrite log2(256) as:

x = log2(2^8)

Since 256 is equal to 2 raised to the power of 8 (2^8), we can simplify the equation as:

x = 8

Therefore, when the strength is 256 pascals, the logarithmic function g(x) would yield x = 8, indicating that there are 8 woven strands in the rope.

In summary, Wendy can convert the exponential function f(x) = 2^x to a logarithmic function by using the logarithm base 2. When the strength is 256 pascals, the logarithmic function g(x) would give x = 8, representing the number of woven strands in the rope.

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The value of the additional data point is 36

To find the value of the additional data point, we can use the concept of the sample mean.

Given the data set: 23, 28, 20, 33, 42, 12, 19, 50, 36, 25, 19.

The sample mean of this data set is 26.5.

To find the value of the additional data point, we can use the formula for the sample mean:

(sample mean) = (sum of all data points) / (number of data points)

In this case, we have 11 data points in the original data set. Let's denote the value of the additional data point as x.

Therefore, we can set up the equation:

26.5 = (23 + 28 + 20 + 33 + 42 + 12 + 19 + 50 + 36 + 25 + 19 + x) / 12

Multiplying both sides of the equation by 12 to eliminate the fraction, we have:

318 = 282 + x

Subtracting 282 from both sides of the equation, we find:

x = 318 - 282

x = 36

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.

Answer:

2 over 3

Step-by-step explanation:

Answer:

The answer is D (The last one)

Answer:

(d). c = 0.25d + 60

Step-by-step explanation:

$60.00 is a constant

$0.25 per Mb is a coefficient

(d). c = 0.25d + 60

The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. If dN/dt > 0, then N increases.

The statement "As long as N is significantly less than K, logistic growth is indistinguishable from exponential" is false. Logistic growth takes into account the carrying capacity of the environment, represented by K, which limits the growth of a population as it approaches this limit. In contrast, exponential growth assumes an unlimited supply of resources and no constraints on population growth. Therefore, as N approaches K, logistic growth begins to level off, while exponential growth continues to increase indefinitely.
If dN/dt > 0, then N increases. This means that the population size is growing at a positive rate. If dN/dt is equal to zero, then N remains stable, indicating that the population size is not changing. Finally, if dN/dt is negative, then N decreases, indicating that the population size is shrinking. Therefore, the correct answer to this question is "increases."

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Answer:

$1053

Step-by-step explanation:

If we have that £1 = $1.62, then we can multiply both sides by 650 in order to get £650 on the left side of the equality. We must multiply the right side also by 650, and so we get £650=$1.62 * 650.

To do this multiplication, we can break 1.62 down  simply into $1.00 +$0.6+$0.02

650*$1.00=$650, 650*$0.6=650*6/10=65*6=$390, and 650*$0.02=650*2/100=6.5*2=$13.

When we add these three products together, we get $650+$390+$13=$1053. And so, £650=$1053

The probability that at least one of the pets selected is a puppy is approximately 0.7887 or 78.87%.

To calculate the probability that at least one of the pets is a puppy, we can find the probability of the complement event (none of the pets being a puppy) and subtract it from 1.

The total number of pets in the store is 6 puppies + 9 kittens + 4 lizards + 5 snakes = 24.

The probability of selecting a pet that is not a puppy on the first selection is (24 - 6) / 24 = 18 / 24 = 3 / 4.

Similarly, on the second selection, the probability of selecting a pet that is not a puppy is (24 - 6 - 1) / (24 - 1) = 17 / 23.

For the third selection, it is (24 - 6 - 1 - 1) / (24 - 1 - 1) = 16 / 22.

For the fourth selection, it is (24 - 6 - 1 - 1 - 1) / (24 - 1 - 1 - 1) = 15 / 21.

For the fifth selection, it is (24 - 6 - 1 - 1 - 1 - 1) / (24 - 1 - 1 - 1 - 1) = 14 / 20 = 7 / 10.

To find the probability that none of the pets is a puppy, we multiply the probabilities of not selecting a puppy on each selection:

(3/4) * (17/23) * (16/22) * (15/21) * (7/10) = 20460 / 96840 = 0.2113 (approximately).

Finally, to find the probability that at least one of the pets is a puppy, we subtract the probability of the complement event from 1:

1 - 0.2113 = 0.7887 (approximately).

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The only cardinal number whose letters are in alphabetical order in English is "forty". This word meets the criteria because its letters appear in alphabetical order: "f", "o", "r", "t", "y".
To find the cardinal number with letters in alphabetical order, we need to examine each number individually. Starting from zero, we can see that "zero" does not have letters in alphabetical order. Similarly, "one" and "two" do not meet the criteria. The word "three" has letters in alphabetical order, but it is not a cardinal number. Continuing our search, we find that "forty" is the first and only cardinal number where the letters are arranged in alphabetical order.
In English, the only cardinal number whose letters are in alphabetical order is "forty".

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Answer:

-8

Step-by-step explanation:

m∠3 + m∠5 = 180 (interior angles are supplementary)

-4x + 5 + (-13x + 39) = 180

-4x + 5 -13x +39 = 180

-17x = 180 - 5 - 39

-17x = 136

x = 136/(-17) = -8

Marcy has 6 quarters and 1 penny.

Let's solve this problem step by step. Let's assume Marcy has x quarters and y pennies.

According to the problem, Marcy has a total of 7 coins. So we can write the equation:x + y = 7 (Equation 1)

Now, we know that the total value of her quarters and pennies is $1.51.

The value of each quarter is $0.25, and the value of each penny is $0.01. We can write the second equation as:

0.25x + 0.01y = 1.51 (Equation 2)

To solve this system of equations, we can multiply Equation 1 by 0.01 to eliminate the decimals:

0.01x + 0.01y = 0.07 (Equation 3)

Now we can subtract Equation 3 from Equation 2 to eliminate the variable y:

0.25x + 0.01y - (0.01x + 0.01y) = 1.51 - 0.07

0.24x = 1.44

x = 1.44 / 0.24

x = 6

Substituting the value of x into Equation 1:

6 + y = 7

y = 7 - 6

y = 1

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Answer:

It would be the second option...

Hope this helps:)

The point prevalence of brilliance at the end of Week 1 is 0.08 or 8%.

The point prevalence of brilliance at the end of Week 2 is 0.17 or 17%.

The point prevalence of brilliance at the end of Week 3 is 0.33 or 33%.

Using person-weeks as denominator, the incidence of brilliance over the course of the 10-week course is 0.017 or 1.7%

In epidemiology context, brilliance can be calculated through calculating point prevalence, cumulative incidence, and incidence rate. The provided data table can be used to determine the point prevalence, incidence, and incidence rate of brilliance among PHE 450 students. So, the calculations of point prevalence, cumulative incidence, and incidence rate based on the provided data are as follows:

The point prevalence of brilliance at the end of Week 1 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #8 was the only existing case of brilliance at the beginning of Week 1, so the point prevalence of brilliance at the end of Week 1 is; Point prevalence = 1 ÷ 12 = 0.08 or 8%.

The point prevalence of brilliance at the end of Week 2 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #3 and Student #8 were existing cases of brilliance at the beginning of Week 2, so the point prevalence of brilliance at the end of Week 2 is; Point prevalence = 2 ÷ 12 = 0.17 or 17%.

The point prevalence of brilliance at the end of Week 3 can be calculated by the following formula; Point prevalence = Total number of existing cases at a given time ÷ Total population at that time

Student #3, #4, #6, and #8 were existing cases of brilliance at the beginning of Week 3, so the point prevalence of brilliance at the end of Week 3 is; Point prevalence = 4 ÷ 12 = 0.33 or 33%.

The incidence of brilliance can be calculated by the following formula; Incidence = Total number of new cases ÷ Total person-weeks of observation

Student #5 and Student #7 developed brilliance during the 10-week course, so the incidence of brilliance over the course of the 10-week course is; Incidence = 2 ÷ 120 = 0.017 or 1.7%.

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Answer: 3t + 5 = 32 and 3t+ 2 = 20

Step-by-step explanation:

We know that someone eats 3 meals per day.

Then if we define the variable t, as the number of days passed since we started counting, we can write the total number of meals eaten as:

M(t) = 3*t

With that in mind, we only can have multiples of 3 (and the coefficient must be 3)

Then the options that remain are:

1) 3*t + 5 = 32

2) 4 - 3*t = 6

3) 3*t + 2 = 20.

Now, let's go to our linear equation:

M(t) = 3*t

As t can only take whole numbers, we can see that M(t) can only be a multiple of 3.

Then we must have:

3*t = multiple of 3.

So let's see our options:

1) 3*t + 5 = 32

3*t = 32 - 5 = 27

27 is a multiple of 3, such that 3*9 = 27, this means that in 9 days, this person would eat 27 meals, then this equation can represent our situation.

2) 4 - 3*t = 6

 3*t = 4 - 6 = -2

3*t = -2

-2 is not a multiple of 3 and is a negative number, so this does not make any sense with our initial situation.

3) 3*t + 2 = 20

3*t = 20 - 2 = 18

3*t = 18

18 is a multiple of 3, such that 3*6 = 18

This says that in 6 days, this person would eat 18 meals, then this equation can represent the situation of this problem.

Answer:

3t + 5 = 32

and

3t+ 2 = 20

Answer:

1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

ANSWER

12

EXPLANATION

Based on the given conditions, formulate: 3 \div \dfrac{1}{4}

Divide a fraction by multiplying its reciprocal:3 \times 4

Calculate the product or quotient:12

get the result:12

Answer: 12

Based on the given conditions, formulate: 3 divided by 1

                                                                                            _

                                                                                            4

Divide a fraction by multiplying its reciprocal: 3 x 4

Calculate the product or quotient: 12

get the result: 12

Answer: 12

The arc length parametrization of the curve\(r(t) = 7e^t cos(t)i + 7e^t sin(t)j\), 0 ≤ t ≤ φ/2, with the same orientation and a reference point at t = 0, is given by s(t) = ∫[0,t] √(r'(u)·r'(u)) du, where r'(t) is the derivative of r(t) with respect to t.

To find the arc length parametrization, we need to calculate the integral of the magnitude of the derivative of r(t). Let's start by finding the derivative of r(t):

r'(t) =\((7e^t cos(t) - 7e^t sin(t))i + (7e^t sin(t) + 7e^t cos(t))j\)

|r'(t)| = \(\sqrt{((7e^t cos(t) - 7e^t sin(t))^2 + (7e^t sin(t) + 7e^t cos(t))^2)}\)

       = \(7e^t\)\(\sqrt{(cos^2(t) + sin^2(t))}\)

       = \(7e^t\)

Now, we integrate |r'(t)| from 0 to t to obtain the arc length parametrization:

s(t) =\(\int\limits^t_0 {} 7e^{u} \, du\)

     =\(7(e^t - e^0)\)

    = \(7(e^t - 1)\)

Therefore, the arc length parametrization of the curve\(r(t) = 7e^t cos(t)i + 7e^t sin(t)j\), 0 ≤ t ≤ φ/2, with the same orientation and a reference point at t = 0, is given by \(s(t) = 7(e^t - 1)\).

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The appropriate value for M1 in the linking constraint for product A is $17.

In the given scenario, the decision variable Yi is defined as 1 if the amount of product i produced (Xi) is greater than 0, and 0 if Xi equals 0. This implies that Yi represents whether or not product i is produced. In this case, we are dealing with product A.

The linking constraint is used to ensure that if product A is produced (Yi = 1), then the amount produced (Xi) must be greater than 0. This can be expressed as Xi ≥ Yi * M1, where M1 is a sufficiently large value that ensures the constraint holds.

Since the profit per unit of A is $17, setting M1 equal to this value guarantees that if Yi is 1 (product A is produced), then Xi must be greater than 0 (at least one unit of A is produced). This ensures that the linking constraint is satisfied and reflects the condition that the company can sell all the units it produces.

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Answer:

The statement that best represents step 5 of Jeremy's proof is;

Explanation:

Given the statement 2 and 4 in the attached proof;

2.

Reason: definition of congruency.

4.

Reason: Transitive property of equality.

substituting statement 2 into statement 4, we will replace angle S with angle P and angle T with angle Q.

So, we will have;

5.

Reason: substitution property.

Therefore, the statement that best represents step 5 of Jeremy's proof is;