A quantity with an initial value of 3600 decays continuously at a rate of 80% per year.
What is the value of the quantity after 0.2 decades, to the nearest hundredth?

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.

Learn more about quadratic equations at:

https://brainly.com/question/1214333

#SPJ1

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.

To know more about Tax in sale visit:

brainly.com/question/29115944

#SPJ1

Amelia and Lucas' son's weight is 17.41 kilograms.

It is the conversion of one unit to another unit with its standard conversion.

Example:

1 hour = 60 minutes

1 km = 1000 m

We have,

Amelia and Lucas' son's Weight = 38.3 pounds.

1 kilogram = 2.2 pounds

Multiply 38.3/2.2 on both sides.

17.41 kilograms = 38.3 pounds

Thus,

Amelia and Lucas' son's weight is 17.41 kilograms.

Learn more about unit conversion here:

https://brainly.com/question/13899873

#SPJ9

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

Learn more about exponential function here:

brainly.com/question/11487261

#SPJ9

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

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

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ9

There are a total of 13 different ornaments to choose from, with 3 types of ornaments.

Total number is a term used to describe the sum of all the values or items within a set. It is usually used to calculate an aggregate or grand total, such as the sum of all the numbers in a list or the total number of people in a population. Total number can also be used to describe the absolute value or quantity of something, such as the total number of days in a year.

When Cherry chooses at least 1 of each type, she will have to select a total of 5 ornaments. This means that Cherry can make a total of 13C5 (13 choose 5) different selections. This is equal to 715 different selections.

This can also be calculated by first selecting 1 ornament from each of the 3 types, which gives 3 different selections. Then, for the 2 remaining ornaments, Cherry can select any of the 13 ornaments, giving a total of 3 x 13 = 39 different selections. In total, this gives 3 + 39 = 42 different selections.

To conclude, Cherry can make a total of 715 different selections when she chooses at least 1 of each type of ornament.

To know more about total number click-
https://brainly.com/question/23286885
#SPJ1

Answer:

A = 0.50x+20

B= 0.75x+22

4 games

$19

Step-by-step explanation:

For abbey, the 20 dollars she starts with is the initial value. the 50 cents per game would be the constant rate of change/slope. So, the equation(y=mx+b) would be A = 0.50x + 20. For Bianca, the 22 dollars she starts with is her initial value. the 75 centers per game would be the constant rate of change/slope. So, the equation(y=mx+b) would be B = 0.75x + 22.

We can find out when they will have the same amount of money left by making two small tables -> one for abbey and one for Bianca.

Abbey: (the number is the number of games and the corresponding value next to it is the amount of money left ---- its kind of hard to make a table on BRAINLY)

Bianca: (the number is the number of games and the corresponding value next to it is the amount of money left ---- its kind of hard to make a table on BRAINLY)

For both girls after four games, they have the same amount of money- $19.

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.

Read more on algebra:

https://brainly.com/question/4344214

#SPJ1

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.

To know more about Stake holders:

https://brainly.com/question/28404310

#SPJ4

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​:

Answer:10 1/2

Step-by-step explanation:

Jasper is approximately 18.67 years old as per the given ratio.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given, the ratio of your age and the age of Jasper is 3:4.

Let's use this ratio to find out how old Jasper is if you are 14.

First, we can set up a proportion:

3/4 = 14/x

where x is Jasper's age.

To solve for x, we can cross-multiply:

3x = 4 * 14

3x = 56

x = 56/3

x ≈ 18.67

So if you are 14 and the ratio of your age to Jasper's age is 3:4, then Jasper is approximately 18.67 years old.

Learn more about ratios here:

https://brainly.com/question/13419413

#SPJ2

Answer:The first question requires the calculation of the 6.5% of $400, which is equal to $26.

The second question requires the calculation of 12.5% of $100, which is equal to $12.50.

For the third question, 130 is 20% of 650.

For the fourth question, $5.40 is 120% of $4.50.

For the fifth question, $8.40 is 30% of $28.

For the sixth question, 56% of 39 is $21.84

For the seventh question, $495 is 55% of $900.

For the last question, 144 is 60% of 240.

Step-by-step explanation:

Answer:

Step-by-step explanation:

26

12.5

20%

120%

30%

12.23

900

60%

Answer:

I don't know

Step-by-step explanation:

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.

To learn more about the similarity of triangles visit,

brainly.com/question/8045819

#SPJ1

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%.

Learn more about probability click here:

https://brainly.com/question/25839839

#SPJ1

Organizar la riqueza a través de la pro- ducción de bienes y servicios es una característica de la empresa que se relaciona con su A) fin lucrativo.

Las empresas tienen como objetivo principal la maximización de sus ganancias y el crecimiento económico a través de la producción y venta de bienes y servicios. La obtención de ganancias es el fin lucrativo de la empresa y es a través de él que se organiza la riqueza generada por la empresa.

Sin embargo, las empresas también tienen una serie de responsabilidades sociales y éticas, por lo que pueden combinar su fin lucrativo con una cierta responsabilidad social o económica.

Learn more about profit from

https://brainly.com/question/1078746

#SPJ1

The number of bags of sand that has to be used would be 92

diameter = 30 yards

width of path = 5 yards

diameter with path

30 + 2 * 5

= 40 Yd

area of path = area of garden with path - ara of garden

= 3.14 * 40² / 4 - 3.14 * 30² / 4

= 1256 - 706.5

= 549.5

area covered by bag = 549.5 / 6

= 91.58

= 92 bags

Read more on area here:https://brainly.com/question/25292087

#SPJ1

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

To know more about quadratic equation visit:

brainly.com/question/30098550

#SPJ1

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.

To know more about Equation check:

https://brainly.com/question/1529522

#SPJ1

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

Answer:

The complement of a set A, denoted A', is the set of all elements that are not in A. The complement of B, denoted B', is the set of all elements that are not in B.

Step-by-step explanation:

(a) A' = {b, d}

(b) B' = {a, c, d}

(c) A' U B = {a, b, c, d, e} (the union of A' and B contains all elements in both sets)

(d) A U B' = {a, b, c, e} (the union of A and B' contains all elements in both sets)

(e) A' n B = {} (the intersection of A' and B is an empty set)

(f) A n B' = {c} (the intersection of A and B' contains all elements that are in A but not in B)

(g) A' U A = {a, b, c, d, e} (the union of A' and A is the universal set, containing all elements)

(h) B' n B = {} (the intersection of B' and B is an empty set)

(i) A U B = {a, b, c, e} (the union of A and B contains all elements in both sets)

(j) A' U B' = {a, b, c, d, e} (the union of A' and B' is the universal set, containing all elements)

(k) [A n B]' = {b, d} (the complement of the intersection of A and B is the union of the complements of A and B)

(l) A' n B' = {} (the intersection of A' and B' is an empty set).

Aɳʂɯҽɾҽԃ Ⴆყ ɠσԃKEY ꦿ

Answer:

6.28375

Step-by-step explanation:

times the radius will fit = x

8 * x = 50.27

x= 50.27÷8

x=6.28375

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.

For more information about Scale factor, visit:

https://brainly.com/question/30215119

#SPJ1

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

Read more about Algebra Word Problems at; https://brainly.com/question/21405634

#SPJ1

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)

Learn more about reflection of point, click;

https://brainly.com/question/29726971

#SPJ9

The question is incomplete, the question is solved for:

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

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.

Learn more about multiplication here:

https://brainly.com/question/24327271

#SPJ9

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.

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.

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!