what is a doubling time? suppose a population has a doubling time of 15 years.by what factor will it grow in 15years?

Answer:

C. y=-4x^2

Step-by-step explanation:

To eliminate a and b the parabola is a negative and neither one of those are negative. When the parabola is facing down its a negative.

To eliminate D the parabola is going down on the y-axis so it cant be d.

Which leaves us with C.

So the answer is indeed C.

Answer: $212.52

Step-by-step explanation:

first we have to find the right equation for the problem. a "pen" is an enclosure for animals that is fenced in, meaning we have to find how much fencing we need.

the question gives us two values, 8 meters wide and 13 meters long. we can infer that this "pen" is in the shape of a rectangle meaning two sides will be 8 meters wide and the two others sides are 13 meters long.

this means we will be finding the perimeter of the pen, which is all the sides of a shape added together. for a rectangle the perimeter you use (lenght+width) *2.

when we add the given values we have (8+13)*2 → 21*2 → 42. we need 42 meters of fencing to complete the "pen."

since each meter of fencing is worth $5.06, we multiply the amount of fencing me need by the cost. 5.06*42= 212.52.

this means the farmer will need to spend $212.52 in order to make his goat pen with a perimeter of 42 meters.

B. A greater percentage of second-lunch students (39%) eat outside.

From the table above, the percentage second-lunch students who eat outside is calculated as follows:

%= number of students who eat outside/total number of students who have second lunch × 100/1

%=18/46 x 100/1

%=39.1%

Percent is usually used to describe data in percentage form. This mathematical science is often used when calculating population percentages, discounts, interest rates, and so on. Percent is a number that represents part or all of the value or goods by forming a ratio of one hundred. Percent has an infinitely high value, while its lowest value is 0 percent. The amount of the percentage is denoted by "%".

This number was born in ancient Rome to be precise from the collection of auction taxes by using a fraction of 1/100 of the auction value or called centesima rerum venalium. the percent symbol has changed several times. Originally the Latin word percento was used. However, in the next generation, the word percento was changed to two symbols, namely the word per which changed to "/" and cento which changed to "00". Until finally the symbol "%" was known.

The simple formula for calculating percent is: Percentage (%) = (Total parts)/(Total amount) X 100%. The general percentage formula for calculating the percentage of a number that is considered as part of the whole is written in percent or 100%.

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The probability that a student chosen randomly from the class is a male who does not have an A is given as follows:

p = 13/29.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

Out of a total of 3 + 5 + 8 + 13 = 29 students, 13 are males that do not have an A, hence the probability is given as follows:

p = 13/29.

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Spherical coordinates are a system of coordinates that describe points in three-dimensional space using a distance from the origin, an angle of inclination from the positive z-axis, and an angle of rotation around the z-axis.

To calculate the triple integral of f(x, y, z)=x2 y2 over the region rho≤2 using spherical coordinates, we first need to express the function in terms of the spherical coordinates.

We know that in spherical coordinates,

x = ρ sin(φ) cos(θ)
y = ρ sin(φ) sin(θ)
z = ρ cos(φ)

where ρ is the radial distance, θ is the azimuthal angle, and φ is the polar angle.

So, f(x, y, z) = x2 y2 can be expressed as

f(ρ, φ, θ) = (ρ sin(φ) cos(θ))2 (ρ sin(φ) sin(θ))2

= ρ4 sin2(φ) cos2(θ) sin2(φ) sin2(θ)

= ρ4 sin4(φ) cos2(θ)

Now, we can set up the triple integral using spherical coordinates.

∫∫∫ f(ρ, φ, θ) ρ2 sin(φ) dρ dφ dθ

= ∫0^2π ∫0^π/2 ∫0^2 f(ρ, φ, θ) ρ2 sin(φ) dρ dφ dθ

= ∫0^2π ∫0^π/2 ∫0^2 ρ4 sin4(φ) cos2(θ) ρ2 sin(φ) dρ dφ dθ

= ∫0^2π ∫0^π/2 ∫0^2 ρ6 sin5(φ) cos2(θ) dρ dφ dθ

= ∫0^2π ∫0^π/2 [ρ7/7 sin5(φ) cos2(θ)]0^2 dφ dθ

= ∫0^2π ∫0^π/2 32/7 sin5(φ) cos2(θ) dφ dθ

= 32/7 ∫0^2π cos2(θ) dθ ∫0^π/2 sin5(φ) dφ

= 32/7 [π sin6(π/2)/6]

= 32π/21

Therefore, the triple integral of f(x, y, z) = x2 y2 over the region rho≤2 using spherical coordinates is 32π/21.

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Answer:

y = -2/3x + 300

Step-by-step explanation:

Since the line is linear, we can find the equation of the line in y=mx+b form.

First, you have to find the slope using the slope formula.  Pick two points from the graph and plug it into the equation.  It doesn't matter which ones; you will get the right answer regardless.  I picked the points (0, 300) and (450, 0).

\(m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\\m=\frac{300 -0 }{0 -450 }\\m=\frac{300}{-450} \\m=-\frac{2}{3}\)

You now have slope (m).  You have to find the y-intercept (b) next.  The y-intercept is the point where the line crosses the y-axis.  For this graph, the line crosses the y-axis at (0, 300), making the y-intercept 300.

Since you have m and b, you can plug the values into y=mx+b.

y = mx + b

y = -2/3x + 300

Answer:

For one toy car = 5

for step by step explanation

For six toy car = 30

then

for one toy car = 30 ÷ 6 = 5

To find the price of one chocolate divide the total number of cost with how many chocolates and u get the answer 5 dollars

After solving the given  logarithmic expression we get

1. \(log_5 k + log_5 2 = log_5 (k\times2)\)

2. \(2 log_5 k = log_5 k^2\)

3. \(log_5 k - log_5 7 = log_5 (k/7)\)

4. \(log_3 k/log_3 5 = log_5 k/log_5 3\)

5. \(log_5 k + log_25 k = log_5 k^3\)

6.  \(log_3 k^2\)/\(log_3\) 25 = \(2 log_3 (k/5)\)

The power to which a number must be increased in order to obtain another number is known as a logarithm.

Following are the Four Basic Properties of Logs by using which we can solve the given expressions.

\(log_b(xy) = log_bx + log_by\\log_b(x/y) = log_bx - log_by\\log_b(xn) = n log_bx\\log_bx = log_ax / log_ab\)

Using logarithmic properties, we can rewrite each expression as follows:

1. \(log_5 k + log_5 2 = log_5 (k\times2)\)

2. \(2 log_5 k = log_5 k^2\)

3. \(log_5 k - log_5 7 = log_5 (k/7)\)

4. \(log_3 k/log_3 5 = log_5 k/log_5 3\)

5. \(log_5 k + log_25 k = log_5 k + 2 log_5 k\)

\(log_5 k + log_25 k = 3 log_5 k\)
\(log_5 k + log_25 k = log_5 k^3\)

6.  \(log_3 k^2\)/\(log_3\) 25 = \(2 log_3 k - 2 log_3 5\)

 \(log_3 k^2\)/\(log_3\) 25 = \(2 log_3 (k/5)\)

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Question

For each expression, give an equivalent expression that is of the form \(log_5(*)\), where * is an expression with numbers and possibly the variable k.

1. \(log_5\) k + \(log_5\) 2 =          2. 2 \(log_5\) k =

3. \(log_5\) k - \(log_5\) 7 =          4. \(log_3\)k / \(log_3\) 5 =

5. \(log_5\) k + \(log_{25}\) k =       6. \(log_3 k^2\)/\(log_3\) 25 =

Answer: x= √5, x = -√5

Step-by-step explanation:

To simplify x^2 = 5, square root both sides to get:

√(x^2) = √5

Then, to simplify √(x^2), you can cross out the √ and the exponent, and add a +-, as the square root of x^2 is |x|, or +-x.

You then get x = √5, and -x = √5, and for the -x = √5, multiply both sides by -1 to get x = -√5.

Answer: 261/10

Step-by-step explanation:

Answer:

125

Step-by-step explanation:

28% is male, which means that 100 - 28 = 72.

This means that 72% are women which is 90

90/72 = 1.25/1

1.25 is 1% of the whole attandees.

1.25 x 100 = 125

Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

Answer: -13

Explanation: First, convert the -12 1/4 into a mixed number. It should become -1/2 + (-49/4) - 1/4. Now, you can add the numbers to give you -13.

we get that the expected value is

The area of the window is 305.12 square inches.

given that

jaylon created this stained glass window the upper two coners are quater ciecleseach with a radius of 4 inches.

The window's area is equal to the sum of the areas of a rectangle, two quarter circles, and the smaller square between the two upper corners.

The quantity of space occupied by a flat surface with a specific shape is referred to as the area.

now, find the area of rectangle

A = length x breadth

A = 12 x (26-4)

A = 12 x 22

A = 264 square inches

find the area of the two quarter circle

\( A= 2( \frac{1}{4} (3.14) \times {4}^{2} ) \\ A = 25.12 {in}^{2} \)

Find the area of the smaller square between the two upper corners

A = (12-8) (4)

A = 4 x 4

A = 16 sq.in

now, find the total area

A = 264 + 25.12 + 16

A = 305.12 square inches

Hence, the area of the window is 305.12 square inches.

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The determinant of the transpose of A is equal to the determinant of A. And since the transpose of a skew-symmetric matrix is its negative, this implies that the determinant of A should also be equal to its negation. The only possible value that satisfies this condition is zero. Therefore, det(A) = 0 when "n" is an odd number.

We can use the property of skew-symmetric matrices, which states that the determinant of a skew-symmetric matrix of odd order is always 0. This means that for the given matrix A, which is skew-symmetric and of order n, where n is odd, det(A) = 0. In order to prove this property, we can use the fact that the determinant of a matrix is equal to the product of its eigenvalues. Since A is skew-symmetric, all its eigenvalues are imaginary and come in pairs of the form λ and -λ. Since n is odd, there is at least one eigenvalue that is equal to 0, and therefore det(A) = 0. The answer to problem 4 is that the determinant of the skew-symmetric n x n matrix A, where n is an odd number, is equal to 0.

When dealing with a skew-symmetric matrix "A" of odd order "n" (n x n matrix), the determinant of A is always zero.
In a skew-symmetric matrix, the elements below the main diagonal are the negation of the elements above the main diagonal, and the elements on the main diagonal are zero. Mathematically, this can be represented as A(i,j) = -A(j,i) for all i and j.  Since "n" is an odd number, multiplying an odd number of negative pairs will result in a negative value for the determinant.

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The distance that a person with a height of 6 feet can see is given as follows:

10.5 feet.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

d = 1.75h.

For the person with a height of 6 feet, the distance is obtained replacing the lone instance of h by 6, hence:

d = 1.75 x 6

d = 10.5 feet.

The problem asks for the distance that a person with a height of 6 feet can see.

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Answer:

x³+8 = x³+2³ = (x+2)(x²-2x+4)

a³+125 = a³+5³ = (a+5)(a-5a+25)

27a³+125b³

= (3a)³+(5b)³

= (3a+5b)(9a²-15ab+25b²)

Answer: -28

Step-by-step explanation:

\(|J|=(5)(-2)-(6)(3)=-10-18=-28\)

(i) To find the solution for yt in the given equation yt = yt−1 + εt + 0.3εt−1, we can rewrite it as yt - yt−1 = εt + 0.3εt−1. By applying the lag operator L, we have (1 - L)yt = εt + 0.3εt−1.

Solving for yt, we get yt = (1/L)(εt + 0.3εt−1). The solution for yt involves lag operators and depends on the values of εt and εt−1.  (ii) For the equation yt = 1.2yt−1 + εt, to find the s-step-ahead forecast Et[yt+s], we can recursively substitute the lagged values. Starting with yt = 1.2yt−1 + εt, we have yt+1 = 1.2(1.2yt−1 + εt) + εt+1, yt+2 = 1.2(1.2(1.2yt−1 + εt) + εt+1) + εt+2, and so on. The s-step-ahead forecast Et[yt+s] can be obtained by taking the expectation of yt+s conditional on the available information at time t.

To make this model stationary, we need to ensure that the coefficient on yt−1, which is 1.2 in this case, is less than 1 in absolute value. If it is greater than 1, the process will be explosive and not stationary. To achieve stationarity, we can either decrease the value of 1.2 or introduce appropriate differencing operators.

(iii) For the equation yt = yt−1 + t + εt, finding the solution for yt and the s-step-ahead forecast Et[yt+s] involves incorporating the time trend t. By recursively substituting the lagged values, we have yt = yt−1 + t + εt, yt+1 = yt + t + εt+1, yt+2 = yt+1 + t + εt+2, and so on. The s-step-ahead forecast Et[yt+s] can be obtained by taking the expectation of yt+s conditional on the available information at time t.

To make this model stationary, we need to remove the time trend component. We can achieve this by differencing the series. Taking first differences of yt, we obtain Δyt = yt - yt-1 = t + εt. The differenced series Δyt eliminates the time trend, making the model stationary. We can then apply forecasting techniques to predict Et[Δyt+s], which would correspond to the s-step-ahead forecast Et[yt+s] for the original series yt.

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Answer:

B: y= -2/7 x - 1/5

Step-by-step explanation:

Slope-Intercept Form equation: y=mx+b

m = slope

b = y-intercept

y = mx + b

y = -2/7 x + (-1/5)

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called the dummy variable.

We know that,

A dummy variable is a binary variable that takes a value of 0 or 1.

In regression analysis, a dummy variable is one that takes only the value 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome.

The number of dummy variables we must create is equal to k - 1, where k is the number of different values that the categorical variable can take on.

It is an artificial variable created to represent an attribute with two or more distinct categories/levels.

These are being used in order to sort out data into mutually exclusive groups.

It is used typically in time series analysis, response modelling, bio-medical studies, economic forecasting and credit scoring.

Therefore, a variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called the dummy variable.

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Answer:

The function is:

\(f(t) = -16t^2 + 50t + 3\)

Step-by-step explanation:

Given

\(height = 3ft\)

\(velocity = 50ft/s\)

\(acceleration = -16ft/s^2\)

Required

The function

Let t represents time;

So, we have:

\(f(t) = acceleration * t^2 + velocity * t + height\)

So, we have:

\(f(t) = -16* t^2 + 50* t + 3\)

\(f(t) = -16t^2 + 50t + 3\)

Answer:

b on edge

Step-by-step explanation:

Answer:

(- 1, - 8 )

Step-by-step explanation:

Under a counterclockwise rotation about the origin of 180°

a point (x, y ) → (- x, - y ) , thus

(1, 8 ) → (- 1, - 8 )

The number of  blueberry muffins she is left with is 9.

The quantitative relation between two amounts, showing the number of times one value contains or is contained within the other.

Given that, Sarah baked blueberry and chocolate muffins in the ratio of 5:2. she gave 6 blueberry muffins to her brother, and now the ratio of blueberry to chocolate muffins has changed to 3:2.

Let the number of muffins before be 5x and after be 3x, then

5x-6 = 3x

2x = 6

x = 3

Therefore, the number of muffins after = 3*3 = 9

Hence, The number of  blueberry muffins she is left with is 9.

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Answer:

They're all false??? Do them on a calculator!

Step-by-step explanation:

x - 8 > -3

x > -3 + 8 (add 8 to both sides)

x > 5

Hence 3.{x|x€R,x>5} is correct.

Answer:

P = 5/12

Step-by-step explanation:

The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function \(y(t)=e^t\)  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

\(y_1(t) = e^t\)

Given differential equations are,

y''-y = 0

 So that,  

\(y' (t) = e^t, y'' (t) = e^t\)

Substitute values in the given differential equation.

\(e^t -e^t=0\)

Therefore, the function \(y(t)=e^t\)  is the solution of the given differential equation.

Another function;

\(y(t)=cosht\)  

So that,  

\(y"(t)=sinht\\\\y"(t)=cosht\)

Hence, function y(t)=cosht is solution of given differential equation.

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The relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”.

Now, According to the question:

What is inequality?

A statement involving the symbols '>', '<', ' ≥', '≤' is called an inequality. For example 5 > 3, x ≤ 4, x + y ≥ 9.

(i) Inequalities which do not involve variables are called numerical inequalities. For example 3 < 8, 5 ≥ 2.

We use the equal sign "=" to say that two things are the same. However, sometimes we just want to show that something is bigger or smaller than something else. Or maybe we just want to say that two things are not equal. These cases are called inequalities.

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