The function f (x) = 125,000 (1.028)x models the change in population of Pool City, where x represents the number of years since 2010. Which statement is NOT true?

A.) The domain of the function includes all real values of x .

B.) The point (1, 128500) represents the population of Pool City in 2011.

C.) The population of Pool City in 2010 is 125,000.

D.) The function has an asymptote at y = 125,000 .

Answer:

22 feet

Step-by-step explanation:

As the given measurements are not all in the same units, convert all measurements to inches using the conversion 1 ft = 12 inches:

Therefore:

Draw a diagram using the given information (see attachment).

From the diagram, we can see that the flagpole and the person are parallel.  Therefore, the two triangles are similar.

In similar triangles, corresponding sides are always in the same ratio.

Therefore, set up a ratio of height to shadow length and solve for h:

[tex]\implies \sf Flagpole\;height:Flagpole:shadow=Person\;height:Person\;shadow[/tex]

[tex]\implies \sf h:168=66:42[/tex]

[tex]\implies \sf \dfrac{h}{168}=\dfrac{66}{42}[/tex]

[tex]\implies \sf h=\dfrac{66}{42} \cdot 168[/tex]

[tex]\implies \sf h=\dfrac{11088}{42}[/tex]

[tex]\implies \sf h=264\;inches[/tex]

Convert the height into feet by dividing by 12:

[tex]\implies \sf h=\dfrac{264}{12}=22\;feet[/tex]

Therefore, the height of the flagpole is 22 feet.

The reflection of point (-6, -5) across the x-axis will give (-6, 5)

A reflection point occurs when a figure is constructed around a single point, known as the point of reflection or center of the figure.

Given is a point (-6, -5), we need to find the coordinates of the point when it is reflected across the x-axis,

The rule for a reflection across the x-axis -:

The rule for reflecting over the x-axis is to negate the value of the y-coordinate of each point, but leave the x-value the same.

i.e, (x, y) → (x, -y)

Therefore,

(-6, -5) → (-6, 5)

Hence, the reflection of point (-6, -5) across the x-axis will give (-6, 5)

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The question is incomplete, the question is solved for:

Reflect point (-6, -5) across x-axis

Someone who is not a stakeholder in this business does not have any interest or concern in Biketown's decision to purchase a new automated machine.

In this scenario, stakeholders for Biketown's decision to purchase are Customers who appreciate the workmanship of Biketown's bicycles, Employees who are involved in the assembly process, Shareholders who have invested in the company, Suppliers who provide materials or components for the bicycles.

Local community members who may be impacted by the company's operations or decisions. An individual who has no knowledge of or interaction with Biketown or the bicycle industry, and therefore has no stake in the decision.

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An equation of a line that has a slope of -5/7 and passes through the point (-35, 10) is y = -5x/7 - 15.

In Mathematics, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁)

Where:

At data point (-35, 10), a linear equation in standard form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 10 = -5/7(x - (-35))

y - 10 = -5/7(x + 35)

y - 10 = -5x/7 - 25

y = -5x/7 - 15

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Answer:

Step-by-step explanation:

The international company has 21,800 employees in one country, which represents 32.2% of the company's total employees. We can use this information to find the total number of employees by solving for the missing value.

Let's call the total number of employees in the company "X".

If the 21,800 employees in one country represent 32.2% of the total employees, we can write an equation to represent this relationship:

0.322 * X = 21,800

Next, we'll isolate X by dividing both sides of the equation by 0.322:

X = 21,800 / 0.322

Using a calculator, we can find that:

X = 68,062.5

Rounding to the nearest whole number, the company has 68,063 employees in total.

So, that's how you can use a percentage to find the total number of employees in the company. By knowing the number of employees in one country and the percentage that this represents of the total, we can find the total number of employees in the company.

Desert 2 will be 4,000,000 square miles and Desert 1 will be 12,000,000 square miles.

The area of a shape simply means the total space that is taken by the shape. It simply expresses the extent of the region on a particular plane as well as a curved surface.

Desert 1 = 3x

Desert 2 = x.

Total area = 16,000,000

x + 3x = 16000000

4x = 16,000,000

Divide

x = 16000000 / 4

x = 40000000

Desert 2 = 4,000,000 square miles

Desert 1 = 12,000,000 square miles.

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The correct answer would be an option (C) y = 5x - 1 is not an exponential function.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

As per option (A), we have

y = 5ˣ

This is an exponential function.

As per option (B), we have

y = 5ˣ - 1

This is an exponential function.

As per option (C), we have

y = 5x - 1

This is not an exponential function because it is a linear function.

As per option (D), we have

D. y = 3.5ˣ

This is an exponential function.

Thus, the correct answer would be an option (C) y = 5x - 1

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The complete question would be as:

Which of the following is not an exponential function?

A. y = 5ˣ

B. y = 5ˣ - 1

C. y = 5x - 1

D. y = 3.5ˣ

Joan completed the race 1.66 standard deviations faster than the typical female of her age group. The standard deviation will be denoted by the symbol “” and the women's average finish time by the symbol “”. Then, Joan's remaining time was plus 1.66.

The proportion of women who finished the race sooner than Joan. In this case, it is possible to apply the normal distribution.

The percentage of values to the left of z = 1.66 can then be calculated or found using a standard normal distribution table. The number of women who finished the race ahead of Joan is represented by the percentage in the table below.

According to a normal distribution table or calculator, there are approximately 0.9525 numbers to the left of the value z = 1.66.

Therefore, This means that out of the 410 female runners in Joan's age group, about 0.9525 × 410 = 391.23 of them beat her. The final count is 391 women, rounded to the next whole number.

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The equation of line is y = ( -1/2 )x + 7/2 , where the slope is m = -1/2

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -1 , 4 )

Let the second point be Q ( -5 , 6 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 6 - 4 ) / ( -5 - ( - 1 ) )

Slope m = 2 / ( -5 + 1 )

Slope m = -2/4 = -1/2

Now , the equation of line is y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 4 = ( -1/2 ) ( x + 1 )

On simplifying the equation , we get

y - 4 = ( -1/2 )x - 1/2

Adding 4 on both sides of the equation , we get

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

Hence , the equation of line is y = ( -1/2 )x + 7/2

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Answer:

$175,000

Step-by-step explanation:

We can use a system of inequalities to solve this problem

Let X be the sales of jewelry in $

Option A

Base salary = $17,000
Commission: 8% of sales

Commission at 8% =8% x $X = 8/100 x $X = $0.08X

Total remuneration = 17,000 + 0.08X

Option B

Base salary = $24,000

Sales = X$

Commission = 4% of $X = 4/100 x $X = $0.04X

Total remuneration = 24,000 +  0.04X

For Option A to be a better deal(higher income)
Total remuneration on Option A > Total remuneration on Option B

17,000 + 0.08X  ≥ 24,000 +  0.04X

(we are using ≥ symbol though the question does state larger income, later on it states at least how many $ worth of sales)

Subtract 0.04X from both sides:
17,000 + 0.08X - 0.04X >=   24,000 +  0.04X -0.04X

17,000 + 0.04X >= 24,000

Subtract  17,000 both sides:
17,000  - 17,000 + 0.04X ≥ 24,000 - 17,000

0.04X ≥ 7,000

X ≥7000/0.04

X ≥ $175,000

So under Option A, you would need to sell at least $175,000 worth of jewelry to make a larger income.

Actually at $175,000 the income from both options are equal

Actual distance from Spokane to Missoula = 100 miles

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Given,

On map one inch represents 20 miles

Distance between Spokane to Missoula on map = 5 inches

Actual distance = 5 × 20 = 100 miles

Hence, 100 miles is the actual distance from Spokane to Missoula.

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Answer: w=9cm l=21cm

Step-by-step explanation

l=3w-6

l+l+w+w=60

3w-6+3w-6+w+w=60

8w-12=60

8w=60+12=72

w=72/8

w=9

l=3w-6

l=27-6

l=21

Answer:

6.28375

Step-by-step explanation:

times the radius will fit = x

8 * x = 50.27

x= 50.27÷8

x=6.28375

If AD = 12 and BD = 36 in the right triangle ABC with altitude BD was drawn to hypotenuse AC, then the length of AC is 12√82.

What is the similarity law for triangles?

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the complementary angles are congruent.

We can use the property of similar triangles to find the length of AC.

Since BD is an altitude of triangle ABC, we can write:

(AD)(DC) = (BD)²

Substituting the given values, we get:

12(DC) = 36²

Solving for DC, we get:

DC = (36)²/12 = 3 x 36 = 108

Now, using the Pythagorean theorem, we can write:

(AC)² = (AD)² + (DC)²

Substituting the given values, we get:

(AC)² = 12² + 108²

Simplifying and solving for AC, we get:

AC = √(12² + 108²) = √(12² x (1 + 9²)) = 12 x √(1 + 9²) = 12 x √(82)

Therefore,  If AD = 12 and BD = 36 in right triangle ABC with altitude

BD was drawn to hypotenuse AC, then the length of AC is 12√82.

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Answer

D. 4.2794....

Step-by-step explanation:

A, B, and C all have repeating decimal numbers, meaning they are rational. D's decimals are not repeating but infinite, meaning it is an irrational number.

The amount of money that is invested in the first and second accounts will be 40,000 and 60,000, respectively.

The possible value of the variables that satisfy the equation which is known as the solution of the equation.

The interest is given as,

I = PRT / 100

Let 'x' be the amount invested in the first bank. Then the amount of investment in the second bank is (100,000 - x). Then the equation is given as,

x · 0.06 · 1 + (100,000 - x) · 0.08 · 1 = 7,200

0.06x + 8,000 - 0.08x = 7,200

-0.02x = -800

x = 40,000

The amount in the second bank is given as,

⇒ 100,000 - 40,000

⇒ 60,000

The amount of money that is invested in the first and second accounts will be 40,000 and 60,000, respectively.

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The probability that the average length of a random sample of 40 fish is less than 10 inches is 0.8869 or 88.69%.

What is probability ?

Probability is a metric used to determine how likely an event or result is to occur. It is a number between 0 and 1, where 0 denotes an improbable event and 1 denotes a certain event.

A group of potential possibilities is referred to as an event in probability theory. By dividing the number of positive possibilities by the total number of possible outcomes, the probability of an event happening is determined.

The fish in the hatchery tank are distributed in length according to a normal distribution, with a mean length of 9.7 inches and a standard deviation of 1.2 inches.

With a mean that is equal to the population mean and a standard deviation that is equal to the population standard deviation divided by the square root of the sample size, the distribution of the sample means will also follow a normal distribution.

The formula to calculate the z-score for the sample mean is:

z = (x - μ) / (σ /[tex]\sqrt{n}[/tex] )

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, we want to find the probability that the sample mean is less than 10 inches. So we need to calculate the z-score for a sample mean of 10 inches:

z = (10 - 9.7) / (1.2 /[tex]\sqrt{40}[/tex]) = 1.21

Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 1.21 is approximately 0.8869. This means that there is an 88.69% chance of getting a sample mean less than 10 inches.

Therefore, the probability that the average length of a random sample of 40 fish is less than 10 inches is 0.8869 or 88.69%.

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The graph of the quadratic equation y = -x² - 1 is on the image at the end.

Here we want to graph the quadratic function:

y = -x² - 1

To do so, we need to find some points on the quadratic equation's graph, we can evaluate the equation in sokme values of x to get that.

if x = 0

y = -0² - 1 = -1

if x = 1

y = -1² - 1 = -2

if x = -1

y = -(-1)² - 1 = -2

And so on.

Above we can see that we have the points (0, -1), (1, -2), and (-1,-2) (you could try to find more points, so the graph will be more exact).

Now just graph all the points that you have and connect them with a parabola. The graph can be seen on the image at the end.

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The number of gallons of paint that the painter should buy is; 4 gallons

The parameters given are;

Side length of cube = 20 ft

Area that a gallon of paint can cover = 400 square feet

Since the room is shaped like a cube, then it will have 4 equal wall areas.

Area of one wall = 20 * 20 = 400 square feet

Area of 4 walls = 4 * 400 = 1600 square feet

Since 400 sq.ft  is covered by 1 gallon, then;

1600 sq.ft = (1600 * 1)/400

= 4 gallons

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Answer:

I don't know

Step-by-step explanation:

The required scale factor for the first rectangle is 5.

What is a scale factor?

In mathematics, a scale factor is a numerical factor that describes the relationship between two similar shapes. It is the ratio of the length of a side or the measure of any other corresponding linear dimension of one shape to the length or corresponding dimension of another similar shape.

Given that,

A rectangle with a short side of 2.5,

And an arrow points to a smaller rectangle with a short side of 0.5

We have to find,

The scale factor was applied to the first rectangle.

According to the question,

The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the other figure.

Then,

Scale factor = Dimensions of the short side ÷ Dimensions of the small rectangle with the same side.

Scale factor = 2.5/0.5

Scale factor = 5

Hence, The required scale factor for the first rectangle is 5.

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The required cost of the dinner not including sales tax was $34.28.

A sales tax is a fee that is paid to the government when specified goods and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing authority.

To find out how much the dinner cost before sales tax, we need to subtract the sales tax amount from the total cost.

We know that the sales tax rate is 8%. To find the sales tax amount, we can multiply the total cost by 8% (or 0.08):

Sales tax = 0.08 * $37.26 = $2.98

To find the cost of the dinner before sales tax, we can subtract the sales tax amount from the total cost:

Cost before sales tax = $37.26 - $2.98 = $34.28

Therefore, the cost of the dinner not including sales tax was $34.28.

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a. The vertex form of its equation is,  y = a(x-1)² + 16

b. The value of x is, 7

c. The equation of the axis of symmetry is,  x = 1

d. The domain and range are respectively, all real values of x and y ≤ 16

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

a. The vertex form of a quadratic equation is given by y = a(x-h)²+ k, where (h, k) is the vertex of the parabola.

From the given information, we know that the vertex is at (1, 16), so the equation in vertex form is y = a(x-1)² + 16.

b. We are given that the parabola has one root at (-5, 0) and another root at (x, 0). Since the parabola is symmetric about the axis of symmetry, the x-coordinate of the vertex must be the midpoint of -5 and x. Using the midpoint formula, we get:

(-5 + x)/2 = 1

Solving for x, we get x = 7.

c. The axis of symmetry of a parabola is the vertical line that passes through the vertex. In this case, the vertex is at (1, 16), so the equation of the axis of symmetry is x = 1.

d. The domain of a quadratic function is all real numbers, since the function is defined for all values of x. The range of this function is y ≤ 16, since the vertex is at (1, 16) and the parabola opens downward.

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Answer:

The expansion of (3x² - k/x)^9 can be found using the binomial theorem. The binomial theorem states that for any real numbers a and b and any positive integer n, the expansion of (a + b)^n is given by:

(a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^(n-1)b^1 + C(n, 2)a^(n-2)b^2 + ... + C(n, n-1)a^1b^(n-1) + C(n, n)a^0b^n

where C(n, k) = n! / (k! (n-k)!).

Using this formula, we can find the coefficient of the term in x^6 in the expansion of (3x² - k/x)^9. The term in x^6 will be of the form C(9, 3) (3x²)^3 (-k/x)^6. We can find the value of C(9, 3) as follows:

C(9, 3) = 9! / (3! (9 - 3)!) = 84.

So, the coefficient of the term in x^6 is 84 * (3^3) * (-k/x)^6 = 84 * 27 * (-k)^6.

Since we are told that this coefficient is 6048, we can set these two expressions equal to each other:

6048 = 84 * 27 * (-k)^6

Dividing both sides by 84 * 27, we get:

k^6 = -6048 / (84 * 27) = -1.

Taking the sixth root of both sides, we find:

k = -1^(1/6).

So the value of k is approximately -1.122462048309372981433.

The correct solution to the problem is m = 92 and the error made was subtracting 7 from both sides of the equation instead of dividing both sides by 7

Incorrect Work/Solution:

m = the number of messages Nigel sent

644 = 7m

subtract 7 from both sides

644 - 7= 7m - 7

637 = m

Nigel sent an average of 637 messages

each day last week.

Correct solution:

644 = 7m

divide both sides by 7

m = 644/7

m = 92

Therefore, Nigel sent an average of 92 messages

each day last week.

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Answer:

96

Step-by-step explanation:

z-scores are defined as: [tex]z=\frac{x-\mu }{\sigma}[/tex], and this may look a bit confusing at first but by looking at the numerator and then denominator we can get a more understandable definition.

The numerator is first finding the difference between the statistic and the mean. It then divides by the standard deviation, so essentially it's telling us  how far the statistic is from the mean in terms of standard deviation.

We can actually rewrite the equation to express this:

[tex]z=\frac{x-\mu }{\sigma}\\\\z\sigma = x-\mu\\\mu + z\sigma=x[/tex]

So in essence, how many standard deviations the statistic is away from the mean.

Now this may seem very off topic compared to what the problem is asking, but we want to convert the top 5% to a z-score. Now let's first convert this top 5% to a percentile. To be in the top 5% you just need to be in the 95th percentile and using technology we can convert this into a z-score which is approximately 1.645.

So this means the 95th percentile is 1.645 standard deviations away and in this case above (since it's positive) from the mean.

The good thing is we know the standard deviation and mean, now let's just apply it: [tex]76+1.645(12)=95.74[/tex]. We now want to round this to the nearest integer of 96, and now we have our answer!

On solving the provided question we can say that the quadratic equation is  3x²+15x+9=0

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

the quadratic equation is 3x²+15x+9=0

by Shridhara Charya formula method, we have

x=−0.697224

x=−4.30278

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Reciprocal of 0.0002 is:

Reciprocal of c/d:

Reciprocal of 1 2/3 is:

Use identity x² - y² = (x - y)(x + y) to solve the following questions.

Evaluate  173² - 127²:

Evaluate (8.70)²- (8.60)²:

Evaluate 1003²- 9​:

Using the fact that the figures are similar, we will find that MN = 12.4

We know that both figures are similar, then there is a scale factor that relates them.

We know the length of two correspondent sides, these are:

HI and LM

HI = 3

LM = 18.6

if k is the scale factor, then we can wite:

3*k = 18.6

k = 18.6/3 = 6.2

Now the length of MN will be 6.2 times the length of the correspondent side on the smaller figure:

MN = 6.2*2 = 12.4

That is the lenght.

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