The number of people in a town of 10,000 who have heard a rumor started by a small group of 10,000 people is given by the following function: N(t)= 10000/5 + 1245e^-0.97(t)
Part I: On Day #0 (t = 0), how many people knew the rumor?

Maricopa Success invested $18,000 in CDs, $32,000 in bonds, and $24,000 in stocks.

What is investment?

Property acquired or invested in to build wealth and save hard-earned income or appreciation is called investment.

Let's start by assigning variables to represent the amounts invested in each type of account:

Let x be the amount invested in CDs.

Let y be the amount invested in bonds.

Let z be the amount invested in stocks.

From the problem statement, we know that:

Here total invested amount is $95,000,

So, we have

[tex]x + y + z = 95,000.[/tex]

The amount invested in bonds is $35,000 more than the amount invested in CDs,

So we have

[tex]y = x + 35,000.[/tex]

The annual income from the investments is $6,845, which we can express as:

0.0475x + 0.042y + 0.112z = 6,845........ (1)

Now we can use the system of equations formed by the three equations above to solve for x, y, and z. First, we can substitute [tex]y = x + 35,000.[/tex] into the equation [tex]x + y + z = 95,000[/tex] to get,

[tex]x + (x + 35,000) + z = 95,000[/tex]

Simplifying this equation, we get:

2x + z = 60,000........ (2)

Next, we can substitute y = x + 35,000 and simplify the equation (1) using equation (2) to get:

[tex]0.0475x + 0.042(x + 35,000) + 0.112z = 6,845[/tex]

Simplifying and rearranging this equation, we get:

0.0895x + 0.112z = 8,545 ..........(3)

Let's use substitution by solving equation (2) for z and substituting into equation (3):

Now, z = 60,000 - 2x

So, 0.0895x + 0.112(60,000 - 2x) = 8,545

Simplifying and solving for x, we get:

x = 18,000

Substituting this value of x into equation (2) to solve for z, we get:

2(18,000) + z = 60,000

z = 24,000

Finally, we can use equation (1) to solve for y:

[tex]0.0475(18,000) + 0.042(y) + 0.112(24,000) = 6,845[/tex]

Simplifying and solving for y, we get:

y = 32,000

Therefore, Maricopa Success invested $18,000 in CDs, $32,000 in bonds, and $24,000 in stocks.

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Answer:

10x^2 - 4x - 32

Step-by-step explanation:

(2x - 4)(5x + 8)

10x^2 + 16x - 20x - 32

10x^2 - 4x - 32

Both the domain and range of the transformed function are the same as those of the parent function.

What are Range and Domain?

The collection of all potential output values that a function can generate given its domain is known as its range.

The set of all potential input values for which a function is specified is referred to as its domain.

The function that results from translating the left 5 units and reflecting the function f(x) = |x| across the y-axis is g(x) = |-x + 5|.

Since any real number's absolute value is always non-negative, the original function's domain is all real numbers, or f(x) = |x|.

A function's domain remains unaffected when it is reflected across the y-axis. Since all real numbers fall within the domain of the modified function g(x) = |-x + 5|, this is also true.

Since each real number's absolute value is always non-negative, the original function's range is also all non-negative real numbers, f(x) = |x|.

A function's sign is reversed when it is reflected across the y-axis. Since all non-negative real numbers fall within this range, the transformed function g(x) = |-x + 5| also has this range as well

So, the correct statement about the domain and range of each function is: Both the domain and range of the transformed function are the same as those of the parent function.

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The scale of the drawing is 1 cm = 4.5 m. This means that each centimeter in the drawing represents 4.5 meters in the actual field. The length of the field in the drawing is 7.2 cm, so the actual length of the field is 7.2 cm × 4.5 m/cm = 32.4 m. The width of the field in the drawing is 3 cm, so the actual width of the field is 3 cm × 4.5 m/cm = 13.5 m. The area of a rectangle is found by multiplying its length by its width, so the area of the actual field is 32.4 m × 13.5 m = 437.4 m²

Note :- I'm sorry to bother you but can you please mark me BRAINLEIST if this ans is helpfull

Answer: It is not possible for the length of the third side of a triangle to be an integer when the lengths of the other two sides are not integer.

Step-by-step explanation:

When the other two sides of a triangle are 5.3 and 0.4 in length, the third side cannot possibly have an integer length. This is so because any two sides of a triangle must have lengths that are greater than the length of the third side. In this instance, 5.3 + 0.4 = 5.7, which still falls short of any integer number for the third side's length.

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Answer: 5

Step-by-step explanation:

5.3+0.4=5.7

5.3-0.4=4.9

4.9<x<5.7

The only possible integer between these two numbers is 5, so the correct answer is 5.

Answer:

Step-by-step explanation:

(0,0)

i hope this helps

Answer: C. 3/(t-1)

Step-by-step explanation:

Answer:

[tex] \dfrac{3}{t - 1} [/tex]

Step-by-step explanation:

[tex] \dfrac{t^2 - 2t - 3}{t^2 - 1} \cdot \dfrac{3t - 3}{t^2 - 4t + 3} = [/tex]

Start by factoring every numerator and denominator.

[tex] = \dfrac{(t - 3)(t + 1)}{(t + 1)(t - 1)} \cdot \dfrac{3(t - 1)}{(t - 3)(t - 1)} [/tex]

Every factor that exists in both a numerator and denominator can be eliminated.

[tex] = \dfrac{1}{t - 1} \cdot \dfrac{3}{1} [/tex]

Multiply numerators together. Multiply denominators together.

[tex] = \dfrac{3}{t - 1} [/tex]

In summary |-13.5 - (-4 1/5)| × 1.4 + (-2)²2 is equal to 17 3/5.

How to solve?

|-13.5 - (-4 1/5)| = |-13.5 + 4 1/5| [Subtracting a negative is equivalent to adding a positive]

= |-9 4/5|

= 9 4/5

Now, we can substitute the values and simplify the expression:

|-13.5 - (-4 1/5)| × 1.4 + (-2)²2

= 9 4/5 × 1.4 + (-2)²2

= 13 3/5 + 4

= 17 3/5

Therefore, |-13.5 - (-4 1/5)| × 1.4 + (-2)²2 is equal to 17 3/5.

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides, a left-hand side (LHS) and a right-hand side (RHS), connected by an equal sign (=).

For example, the equation 3x + 5 = 14 is an equation that shows that the expression 3x + 5 is equal to the expression 14. This equation can be solved for x to find the value of x that makes the equation true.

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Answer:

9207 divided by 4 = 2301 with a remainder of 3

Step-by-step explanation:

  (check the attached document)

The values of Sin A, Cos B and Tan A are: 41.8, 2.8 and 6.9 respectively

The ratios of the sides of a right triangle are called trigonometric ratios.", if in trigonometry the ratios of the sides of a triangle are called 'trigonometric ratios' then what if the triangle is not a right triangleA =

In triangle 1

SinA = Opposite/Hypothenuse

Son A = 6/9

Sin A = 0.6669

A = Sin ⁻¹0.6667

A = 41.8⁰

For triangle 2

Cos B = Adjacent /Hypothenuse

Cos 45 = x/4

AB = 4*0.7071

AB = 2.8

For triangle 3

Tan a = Opp/Adjacent

Tan60 = AB/4

AB = 4*Tan60

AB = 4* 1.7321

AB = 6.9

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Tyler invested $5800 in the first account and $3900 in the second account.

Simple interest is interest that is calculated solely on a loan's or investment's principal amount, without taking into account any interest that has accrued over time. For instance, regardless of how long you keep the money in the account, if you deposit $1,000 in a savings account that offers 5% simple interest annually, you will make $50 in interest each year. Contrarily, compound interest accounts for both the original principal and the interest that has accrued over time. This means that interest is calculated on the new, higher balance after the interest collected during each period is applied to the principal amount.

Let us suppose the amount invested in first account = x.

The amount in second account = y.

Thus, according to the statements we have:

x + y = 9700 (total amount invested is $9700)

0.10x + 0.09y = 931

Now from the first equation we can write:

y = 9700 - x

Substituting the value of y we have:

0.10x + 0.09(9700 - x) = 931

0.10x + 873 - 0.09x = 931

0.01x = 58

x = 5800

Now, substituting the value of x we have:

y = 9700 - 5800

y = 3900

Hence, Tyler invested $5800 in the first account and $3900 in the second account.

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Answer:

B.

Step-by-step explanation:

Since the line is from the top left to bottom right it's negative but if it was the opposite it would be positive.

Answer:

A = 15.87 m²

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

here b = 6.9 and h = 4.6 , then

A = [tex]\frac{1}{2}[/tex] × 6.9 × 4.6 = 3.45 × 4.6 = 15.87 m²

Answer:

C. 9 times larger

Explanation:

where, r = radius of a cylinder and h = height of the cylinder. This means that the volume of a cylinder will be 9 times larger if the radius is multiplied by 3.

The volume of the display case is 60 + 120 = 180. The correct answer is B. 36.

Volume is a measure of the three-dimensional space something occupies or contains. It is often expressed as a calculation of length x width x height. It can also refer to the amount of something, such as the volume of a liquid, or the amount of space a container holds. Volume is an important concept in mathematics, science, engineering, and many other fields. It is used to measure the size of a solid, liquid, or gas, and to quantify the amount of material in an object or a space.

The volume of a rectangular prism is determined by multiplying its length, width, and height. The volume of a display case made of one rectangular prism stacked on top of a second rectangular prism is equal to the sum of the volumes of each rectangular prism.

The volume of the first rectangular prism is 3 x 4 x 5 = 60.
The volume of the second rectangular prism is 4 x 5 x 6 = 120.

Therefore, the volume of the display case is 60 + 120 = 180. The correct answer is B. 36.

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The selection method that assures a fair chance of being selected to go first between Carla and Hattie is A) Flip a fair coin. If it lands on heads, Carla will go first. If it lands on tails, Hattie will go first.

A fair chance is based on an equal probability of being selected.

A fair coin of head and tail offers a fair chance to two contenders on who should play the game first.

In this situation, since Carla gets the heads, he has 50% chance of being selected to go first.

Equally, Hattie has a 50% chance to go first getting the tails.

Thus, the correct selection method is Option A.

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Answer:

The completed statements are:

The y-intercept represents the base price of $200.

The slope represents a cost of 30 cents per mile traveled.

According to the equation given, someone who traveled 2000 miles from NYC would pay $800 for their airfare. (y = 200 + 0.30x, where x is the distance traveled in miles)

According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1,000 miles. (500 = 200 + 0.30x, solving for x gives x = 1,000)

If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y = 50 + 0.30x. (The slope remains the same, while the y-intercept changes to 50.)

Note that the statement "According to the equation given, someone who traveled 2000 miles from NYC would pay $2500 for their airfare" is incorrect. The correct calculation using the given equation y = 200 + 0.30x is:

y = 200 + 0.30(2000) = 800

Therefore, someone who traveled 2000 miles from NYC would pay $800 for their airfare.

1.The set of all mathematical concepts .

2.The set of possible weather conditions in which an area can experience.

3.The set of countries that make up the North American continent.

Sets, in mathematics , are a coordinated assortment of articles and can be addressed in set-manufacturer structure or list structure. Curly braces are typically used to represent sets.

1- Mathematics:

The collection of all mathematical concepts and guiding principles pertaining to the investigation of quantity, structure, space, and change. Math, algebra, geometry, trigonometry, calculus, probability, and statistics are all included in this.

2- Rain, Snow, Sunny:

The arrangement of conceivable weather patterns where a region can insight. This includes rain, which is the term used to describe the liquid water droplets that fall from clouds; snow, which refers to ice crystals falling from clouds; and sunny, a weather condition characterized by abundant sunlight and clear skies.

3- Canada, Mexico, United States:

The group of nations that make up the continent of North America. Canada, which is in the north of the continent, is included in this. Mexico, which is in the continent's southernmost region; and the United States of America, which is in the middle of the continent. The numerous cultures, histories, and geographies of these nations define them.

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Answer:

OD:24

Step-by-step explanation:

3*3”2 = 27

-(4+3) = -7

8divided by 2= 4

27 + 4 -7=24

Answer: p=[tex]\frac{4m}{3}[/tex]  last one

Step-by-step explanation:

Varies directly means y=kx

here p=km

m= 1 1/2 =3/2

p=2

plug to solve for k

2=k(3/2)

k=4/3

plug back in p=4m/3

Answer:

Step-by-step explanation:

D

1. Depreciation expense = $7,400 per year

2. Incremental net operating income = $10,000 per year

3. The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.

4. The simple rate of return on the new bottling machine is 13.5%.

Investment refers to the act of allocating money or resources to acquire an asset or property, with the expectation of generating income, profit, or appreciation in value over time. It involves forgoing the use of funds in the present, in order to potentially receive a greater benefit in the future.

Annual Depreciation Expense:

The new bottling machine would have a useful life of 10 years, and no salvage value. Therefore, the annual depreciation expense associated with the new bottling machine is:

Depreciation expense = (Cost of the machine - Salvage value) / Useful life

Depreciation expense = ($74,000 - $0) / 10 = $7,400 per year

Annual Incremental Net Operating Income:

To calculate the annual incremental net operating income provided by the new bottling machine, we need to compare the annual operating costs of the old machine and the new machine.

Annual operating cost of the old machine = $19,000

Annual operating cost of the new machine = $9,000

Incremental net operating income = Annual operating cost of the old machine - Annual operating cost of the new machine

Incremental net operating income = $19,000 - $9,000 = $10,000 per year

Initial Investment:

The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.

Simple Rate of Return:

The simple rate of return is the ratio of the annual incremental net operating income to the initial investment. We have already calculated the annual incremental net operating income in step 2, and the initial investment in step 3.

Simple rate of return = Annual incremental net operating income / Initial investment

Simple rate of return = $10,000 / $74,000 = 0.1351 or 13.5% (rounded to one decimal place)

Therefore, the simple rate of return on the new bottling machine is 13.5%.

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1. Depreciation expense = $7,400 per year

2. Incremental net operating income = $10,000 per year

3. The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.

4. The simple rate of return on the new bottling machine is 13.5%.

What is investment?

Investment refers to the act of allocating money or resources to acquire an asset or property, with the expectation of generating income, profit, or appreciation in value over time. It involves forgoing the use of funds in the present, in order to potentially receive a greater benefit in the future.

Annual Depreciation Expense:

The new bottling machine would have a useful life of 10 years, and no salvage value. Therefore, the annual depreciation expense associated with the new bottling machine is:

Depreciation expense = (Cost of the machine - Salvage value) / Useful life

Depreciation expense = ($74,000 - $0) / 10 = $7,400 per year

Annual Incremental Net Operating Income:

To calculate the annual incremental net operating income provided by the new bottling machine, we need to compare the annual operating costs of the old machine and the new machine.

Annual operating cost of the old machine = $19,000

Annual operating cost of the new machine = $9,000

Incremental net operating income = Annual operating cost of the old machine - Annual operating cost of the new machine

Incremental net operating income = $19,000 - $9,000 = $10,000 per year

Initial Investment:

The initial investment associated with this project is the cost of the new bottling machine, which is $74,000.

Simple Rate of Return:

The simple rate of return is the ratio of the annual incremental net operating income to the initial investment. We have already calculated the annual incremental net operating income in step 2, and the initial investment in step 3.

Simple rate of return = Annual incremental net operating income / Initial investment

Simple rate of return = $10,000 / $74,000 = 0.1351 or 13.5% (rounded to one decimal place)

Therefore, the simple rate of return on the new bottling machine is 13.5%.

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The evaluations of the given expressions are:

(a) ln e⁻³ = -3

(b) e^(ln 5) = 5

(c) e^(ln √3) = √3

(d) ln (1 / e⁵) = -5

From the question, we are to evaluate the given expressions.

The given expressions contain natural logarithm and exponential functions.

The natural logarithm is the inverse of the exponential function.

Thus,

ln eˣ = x

Likewise

e^(ln x) = x

Applying these rules to the given expressions, we get

(a) ln e⁻³ = -3

(b) e^(ln 5) = 5

(c) e^(ln √3) = √3

(d) ln (1 / e⁵)

This can be written as

ln (e⁻⁵) = -5

Thus,

ln (1 / e⁵) = -5

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Answer:

the abswer is D

Step-by-step explanation:

[f○g](x)=(9x+12)/9+8/3=x+8/3

[g○f](x)=9(x/9 + 4/3)+12=x+24

so for the same x they are not inverses

Answer:28 or 29 can't tell if the x is supposed to be on the 28 or 29

Step-by-step explanation:

The perimeter of the rectangle created by the given points (-4, 4), (3, 4), (-4, -3), and (3, -3) is 28 units. The length of each side is calculated, and the sum of all four sides gives the perimeter. Option D.

To find the perimeter of the rectangle created by the given points, we need to calculate the sum of the lengths of all four sides.

Let's calculate the length of each side:

Side 1: The distance between (-4, 4) and (3, 4) along the x-axis is 3 - (-4) = 7 units.

Side 2: The distance between (-4, 4) and (-4, -3) along the y-axis is 4 - (-3) = 7 units.

Side 3: The distance between (-4, -3) and (3, -3) along the x-axis is 3 - (-4) = 7 units.

Side 4: The distance between (3, -3) and (3, 4) along the y-axis is 4 - (-3) = 7 units.

Now, let's sum up the lengths of all four sides:

Perimeter = Side 1 + Side 2 + Side 3 + Side 4

Perimeter = 7 + 7 + 7 + 7

Perimeter = 28 units

Therefore, the perimeter of the rectangle created by the given points is 28 units. Option D is correct.

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The percentage of the sample selected at random that would be expected to be afflicted by stress would also be = 80%

The percentage of a data set is when part of the data is represented per 100 with a symbol of %.

It was stated in the question that 80% of Americans report being afflicted by stress.

Therefore when a sample is randomly selected from an American population, the percentage that is expected to be afflicted by stress should also be 80%.

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