Can you simply these fractions?

The Malthusian law for population growth states that the rate of population growth is proportional to the current population size.

Mathematically, we can express this as:

dP/dt = rP

where P is the population size, t is time, and r is the growth rate.

Assuming a constant growth rate, we can integrate this equation to get:

ln(P) = rt + C

where C is an integration constant. We can solve for C using the initial population estimate:

ln(1200) = r(1980) + C

C = ln(1200) - r(1980)

Substituting the values of C and P from the second estimate (P=7500 in 2008), we get:

ln(7500) = r(2008) + ln(1200) - r(1980)

Solving for r, we get:

r = [ln(7500) - ln(1200)] / (2008 - 1980) = 0.0496

Using this value of r, we can predict the alligator population in 2020, which is 12 years after the second estimate (2008). We have:

ln(P) = rt + ln(7500)

ln(P) = 0.0496(12) + ln(7500) = 9.058

P = e^9.058 = 8656

Therefore, the estimated alligator population in the region in the year 2020 is 8656.

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To find the common ratio and the first four terms of the geometric sequence {(9^n+2)/(3)}, let's first rewrite the given expression to make it easier to understand i.e. Term a_n = (9^n+2)/3

Now, let's find the first four terms:
a_1 = (9^(1)+2)/3 = (9+2)/3 = 11/3
a_2 = (9^(2)+2)/3 = (81+2)/3 = 83/3
a_3 = (9^(3)+2)/3 = (729+2)/3 = 731/3
a_4 = (9^(4)+2)/3 = (6561+2)/3 = 6563/3

The first four terms are:
a_1 = 11/3
a_2 = 83/3
a_3 = 731/3
a_4 = 6563/3

To find the common ratio, divide the second term by the first term (or any consecutive terms):
Common ratio = a_2 / a_1 = (83/3) / (11/3) = 83/11 = 3

So, the common ratio is indeed 3, and the first four terms are 11/3, 83/3, 731/3, and 6563/3.

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The required rate of return (or minimum acceptable rate of return) is 20 percent. If the net cash flows are $15,000 per year for ten years, the total cash flow is $150,000. The project's cost is $47,500. We can now apply the net present value formula to determine whether or not the project is feasible.

Net Present Value (NPV) = Cash flow / (1 + r)^n - Cost Where, r is the discount rate, n is the number of years, and Cost is the initial outlay.

Net Present Value = 150000 / (1 + 0.20)^10 - 47500

Net Present Value = $67,482.22

Since the NPV is positive, the project is feasible. When calculating net present value, it's important to remember that a positive NPV implies that the project is expected to generate a return that exceeds the cost of capital, whereas a negative NPV indicates that the project is expected to generate a return that is less than the cost of capital, and as a result, it should be avoided.

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Answer:

2 nonreal solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the nature of the roots are determined by the discriminant

b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational solutions

• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

5x² - 2x + 6 = 0 ← in standard form

with a = 5 , b = - 2 , c = 6

b² - 4ac

= (- 2)² - (4 × 5 × 6)

= 4 - 120

= - 116

since b² - 4ac < 0

then there are 2 nonreal solutions to the equation

Answer:

when f(x)=y=-3 then x =0

Step-by-step explanation:

\(x = 0\)

Answer:

Answer. 48

maybe I am not sure

Step-by-step explanation:

first I multiplied 7 X 6

next I got answer 42, by multiplying

then I added 6 to the answer and

FINALLY THE ANSWER IS 48

but I am not sure

Answer:

x = -1

Step-by-step explanation:

7x+6 = -1

7x = - 7

x = -1

The solution to the equations are given below.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

1. System A          System B

−12x+9y=7           −12x+9y=7

9x−12y=6             −9x+5y=9

Solving system A

x= -46/21 and y= -15/7

and, solving system B

x= -46/21 and y= -15/7

We can say that

Yes, they have the same solution because the second equation in system B is obtained by multiplying the second equation in system A by 1/3 and adding to the first equation in system A.

2. -7 should be multiply the second equation by so that the sum of the x-coefficients is zero.

3. x−y=3

2x−3y=−1

Solving the above equation gives

x= 10 and y= 7.

The equation yields the same solution as above is

2x−2y=6

2x−3y=−1

4. Equation A: 5x+9y=12

Equation B: 4x−3y=8

Now, solving both equations we can proceed as Multiply equation B by 3 and add the result to equation A.

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Answer:

To determine which system of equations would have the same solution, we evaluate each system of equations.

System 1 4x − 5y = 2, 3x − y = 8

x = 38/11

y = 26/11

System 2 4x − 5y = 2, 3x − 2y = 1

x = 1/7

y = -2/7

System 3 4x − 5y = 2, 3x − 8y = 4

x = -4/17

y = -10/17

System 4 4x − 5y = 2, 10x − 9y = 4

x = 1/7

y = -2/7

Therefore, the correct answer is option 3. System 2 and system 4 are equal, because the second equation in system 4 is obtained by adding the first equation in system 2 to two times the second equation in system 2.

    4x− 5y = 2 2( 3x − 2y = 1)

-----------------------    10x - 9y = 4

Step-by-step explanation:

Give me a brainilest please...

Answer:

109 is 63% of 173.02(Rough estimate)

Step-by-step explanation:

X = Y/P%

X = 109/63% or 109/0.63

X = 173.02

Hope this helps!

Answer:

109 is 63% of 173.02

Step-by-step explanation:

Formula = Number x 100/Percent = 109 x 100/63 = 173.02

Answer:

sometimes used to distinguish between the measure of the angle

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

12^2+5^2=x^2

144+25=x^2

169=x^2

Take the square root of 169 and get 13

A good scale to use for the x axis in this is 10 units represent 2 hours

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

The chart

First, it should be noted that the Age data will be plotted on the y-axis

So, the bar chart or graphical representation will have an horizontal alignment

Next, we have

Hours data

Here, we have

Time = 9 to 18 hours

From the above, a good scale to use for the x axis in this is 10 units represent 2 hours

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Answer:

C

Step-by-step explanation:

You need to multiply the variable by how much each ride costs.

Answer:

1/3=2/6

Step-by-step explanation:

1*2=2

3*2=6

Answer: 1/3=2/6

Step-by-step explanation: the numerator (1) in the first fraction is half it is in the second (2). This means the denominator in the first question (unknown) will be half the second (6). Half of (6) is (3). Your answer is 3.

Answer:

it's True

Step-by-step explanation:

it's true

it's just true ik it I got it right

Answer:

First i do not know sorry please help me

Step-by-step explanation:

Answer:

second to last first, and then the third second and first and then last There u go :^

Step-by-step explanation:

The discrete random variables from the given options are: 1, 2, 4, and 5.

The number of CDs that a college student owns: This is a discrete random variable because the number of CDs can only be a whole number. You cannot have a fractional or continuous value for the number of CDs.

The number of dogs you own: This is a discrete random variable because you can only own a whole number of dogs. You cannot own a fractional or continuous number of dogs.

Number of 6s you get when you throw 5 number cubes: This is a discrete random variable because the number of 6s can only be a whole number from 0 to 5. You cannot have a fractional or continuous value for the number of 6s obtained.

The number of dog sleds that a competitor uses in an annual sled dog race: This is a discrete random variable because the number of dog sleds can only be a whole number. You cannot have a fractional or continuous value for the number of dog sleds used.

On the other hand, the following option is not a discrete random variable:

The amount of gas in your car: This is a continuous random variable because the amount of gas can be any non-negative real number. It can have fractional or continuous values, such as 10.5 liters or 20.25 gallons. Option 1,2,3,4 and 5

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Total price paid by Michael for the basket of mangoes is $4.48.

For the calculation of total price, price of sales tax will be added with selling price. Forming the equation -

Total price = 4 + 12%×4

Calculating the percentage of sales tax on Right Hand Side of the equation

Total price = 4 + 12×4/100

Solving the percentage part on Right Hand Side of the equation

Total price = 4 + 0.48

Performing addition on Right Hand Side of the equation

Total price = $4.48

Hence, Michael has to pay $4.48 after addition of sales tax for the basket of mangoes.

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Learn more

Answer:

f = 1.2

Step-by-step explanation:

locate x = - 6 on the x- axis, then go vertically up to meet the graph at (- 6, 1.2)

Then when x = - 6, f is 1.2

The graph that is indicative of the equation y = (x - 5)(x - 5) is hereby attached accordingly. When simplified, the function becomes y = (x-5)².

The domain of the above function is - ∞ < x < ∞;

The range is f(x) ≥  0

The vertex is given as Minimum (5,0)/.

The alternative form of y = (x - 5)(x - 5) is given as:

-x^2 + 10 x + Y - 25 = 0

-25 + 10 x - x^2 + Y = 0

Y = x^2 - 10 x + 25

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The number in the exponential scientific form is A = 5.729 x 10⁸

Given data ,

Let the number be represented as A

Now , the value of A is

A = 572,900,000

On simplifying , we get

From the laws of exponents , we get

The exponential form of a number is a way of representing a number using exponents, where the base is typically a number greater than 1

So , the value of A is

When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

A = 5.729 x 10⁸

Hence , the scientific form is A = 5.729 x 10⁸

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This result indicates that the side length of the white square is 0. The area of one of the white squares can be determined by subtracting the area of the green border from the total area of each face of the cube.

The total area of each face of the cube is given by the formula: side length * side length.

Given that the edge of the cube is 10 feet, the total area of each face is:

Area of each face = 10 feet * 10 feet = 100 square feet

Now, let's consider the green border. Since each face has a white square centered on it, the dimensions of the white square will be smaller than the face itself.

Let's assume the side length of the white square is "x" feet. This means that the side length of the green border is (10 - x) / 2 feet on each side.

The area of the green border on each face is then:

Area of green border = (10 - x) / 2 * (10 - x) / 2 = (10 - x)^2 / 4 square feet

To find the area of the white square, we subtract the area of the green border from the total area of each face:

Area of white square = Area of each face - Area of green border

= 100 square feet - (10 - x)^2 / 4 square feet

Given that Marla has enough green paint to cover 300 square feet, we can set up the equation:

Area of white square * 6 (number of faces) = 300 square feet

(100 - (10 - x)^2 / 4) * 6 = 300

Now we can solve for x:

100 - (10 - x)^2 / 4 = 50

100 - (10 - x)^2 = 200

(10 - x)^2 = 100

Taking the square root of both sides:

10 - x = 10

x = 0

This result indicates that the side length of the white square is 0, which doesn't make sense in this context. It seems there might be an error or inconsistency in the given information or calculations.

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Step-by-step explanation:

\( \frac{ log_{5}(25) + log_{5}(125) - log_{5}(625)}{ log_{5}(100) } \)

\( \frac{ log_{5}( \frac{25 \times 125}{625} ) }{ log_{5}(25 \times 4) } \)

\( \frac{ log_{5}(5) }{ log_{5}(25) + log_{5}(4) } \)

\( \frac{1}{2 + 2 log_{5}(2) } \)

\(0.3495 = 0.35\)

Answer:

121.5

Step-by-step explanation:

6 x 4.5 x 9 = rectangular prism the divide by 2 to get triangular prism

Step-by-step explanation:

2x-2<8

2x<8+2

2x<10

x>10/2

x>5

26a)729

b)2,457.6

c)3,500

d)8,100

e) 89,600

Step-by-step explanation:

just multiply first and divide with upper number to the lower

Answer: 1/6

Step-by-step explanation:

Answer:

What steps are used to solve this equation?

6f = 48

Complete each statement.

First,

✔ divide by 6

on both sides of the equation.

Next, simplify the equation to determine that the solution of the equation is

✔ f = 8

.

Check the solution by substituting

✔ 8

for f and simplifying.

Step-by-step explanation:

The solution of the given equation would be 8.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between.

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

We are given the equation as;

6f = 48

We have to Complete each statement.

First, divide by 6 into both sides of the equation.

f = 48/6

Next, simplify the equation to determine that the solution of the equation is

f = 8

Check the solution by substituting for f and simplifying.

6  x8 = 48

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In the given question, the following information is given

Sandra music player randomly selects music from her playlist. Sandra’s playlist contains:

traditional country songs = 3

traditional rock songs = 6

hip-hop rap songs = 4

contemporary country songs' = 5

Latin rap song = 1

traditional pop songs = 3

Total sample space = 3 + 1+ 5 + 4+ 6+3 = 22 songs

We need to find the probability, that her music player will play a rap song = \(\frac{Number of sample sample space for rap song}{Total space} \\\)

= \(\frac{4 + 1}{22}\) = \(\frac{5}{22}\)

P (traditional), that is, the probability that the player will randomly select traditional music of any kind = \(\frac{Number od sample space for traditional song}{total sample space}\)

= \(\frac{3 + 6+3}{22}\)

= \(\frac{12}{22}\) = \(\frac{6}{11}\)

P (traditional pop) = \(\frac{sample space for pop songs}{total sample space}\)

= \(\frac{3}{22}\)

P  (country), the probability that the next song is country music = \(\frac{Sample space fpr country music}{total sample space}\)

= \(\frac{8}{22}\)

= \(\frac{4}{11}\)

P (not country), the probability that the next song is NOT country music.=

1 - \(\frac{4}{11}\)

= \(\frac{11 -4}{11}\)

= \(\frac{7}{11}\)

Hence, this is the final answer.

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Based on the conversion done, the figure gotten is larger. Therefore, Carson cannot mail the package

From the information given, the package is 87 cm long.

Also, the shipping company only mails packages that are up to 35 in. long. Then, we convert inches to cm. This will be:

= 35 × 2.54 = 88.9 cm.

Therefore, he can't mail the package.

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