Choose the best answer to the following question. Explain your reasoning with one or more complete sentences.
Which of the following is an example of exponential​ decay?

A. The population of a rural community decreasing by 100 people per year is an example of exponential decay because population growth and decay are represented​ exponentially, and in this case it is decreasing.
B. Government support for education decreasing by​ 1% per year is an example of exponential decay because the support decreases by the same percentage each year.
C. The price of gasoline decreasing by​ $0.02 per week is an example of exponential decay because the price decreases very slowly at first.
D. The price of gasoline decreasing by​ $0.02 per week is an example of exponential decay because the amount at which the price is decreasing increases by​ $0.02 each week.
E. The population of a rural community decreasing by 100 people per year is an example of exponential decay because the population decreases at a steady rate.
F. Government support for education decreasing by​ 1% per year is an example of exponential decay because the amount of support is decreasing over time.

* The probability that Ahmad has to stop at both P and Q is: 7/40

* The probability that Ahmad has to stop at least once is: 27/50

* The probability that Ahmad would have stopped at P if he stops at Q is 7/13.

What is probability ?

The study of randomness or experiments falls within the canopy of the mathematical discipline of probability. When represented as a number between 0 and 1, where 0 denotes an impossibility and 1 denotes a certain event, it is the gauge of the probability or chance that an event will occur. When making predictions based on a statistical study of the data at hand, probability is employed to characterise uncertain events. To aid in decision-making and risk assessment, it is utilised in a variety of disciplines, including science, architecture, finance, finance, and social sciences. Concepts like likelihood function, random variables, and anticipated values are all part of the study of probability.

given

We multiply the chances of stopping at P and Q assuming that he has already stopped at P to determine the likelihood that he must stop at both locations:

Stop at P Equals P(Stop at P and Q) P(Stop at Q | Stop at P)=7/20*7/10

= 49/200

P(Stop at least once) = 1 - P(Not stop at P) * P(Not stop at Q | Not stop at P) = 1 - (13/20) * P(Not stop at Q | Not stop at P) (2/5)\s= 37/50

The chance that he likewise stopped at P must be determined if he had stopped at Q.

Stopping at P and Q equals P(Stop at P and Q) / P(Stop at Q) = (7/20 * 7/10) / (7/20) = 7/10.

Hence, the likelihood that he would have stopped at P is 7/10 if he must stop at Q.

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Answer:

D

Step-by-step explanation:

The parabola of m(x) is thinner than the parabola of f(x) since 4 times 2 squared is 16 while 2 squared is 4

Answer:

w = 6 ft.; l = 9 ft.

Step-by-step explanation:

We know that the formula for area of a rectangle is A = lw, where l is the length and w is the width.

Because we're told that the length of the flower bed is 3 ft less than twice its width, we have l = 2w - 3

To find the length and width, can plug in 54 into the equation and substitute our formula for length into the equation.

This gives us 54 = (2w - 3)*w

If we rewrite the equation, we'll see that its quadratic:

[tex]54=(2w-3)w\\54=2w^2-3w\\0=2w^2-3w-54[/tex]

Now, we can first solve for width using the quadratic formula, which yields a positive and negative solution.

(For the sake of the quadratic equation, 0= ax^2 + bx + c is the standard form of quadratic equation and in our equation 2 is a, -3 is b, and -54 is c)

Positive:

[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a} \\\\w=\frac{-(-3)+\sqrt{(-3)^2-4(2)(-54)} )}{2(2)}\\ \\w=\frac{3+\sqrt{441} }{4}\\ \\w=\frac{3+21}{4}\\ \\w=\frac{24}{4}\\\\w=6[/tex]

Negative:

[tex]x=\frac{-b-\sqrt{b^2-4ac} }{2a} \\\\w=\frac{-(-3)-\sqrt{(-3)^2-4(2)(-54)} )}{2(2)}\\ \\w=\frac{3-\sqrt{441} }{4}\\ \\w=\frac{3-21}{4}\\ \\w=\frac{-18}{4}\\\\w=-4.5[/tex]

We know that we can't have a negative measure, so the width is 6 ft.

Twice the width is 12 (6 * 2) and 3 less than this is 9 (12 - 3), so the length is 9 ft.

Answer:

The term that completes the sentence is "variance".

Step-by-step explanation:

In statistics, variance is a measure of how spread out a set of numerical data is. It is calculated by finding the average of the sum of the squared differences of each element in the set from the mean of the set. The formula for variance is:

Variance = (Σ(x - μ)²) / n

where Σ is the sum, x is each element in the set, μ is the mean of the set, and n is the number of elements in the set.

Answer:

27 18*3=2*r18/2*3=r9*3=rr=27

Step-by-step explanation:

Answer:

I think the answer is B?

Step-by-step explanation:

An equation for a circle with centre (-15, 3√7) and an area of 2π in standard form is (x + 15)² + (y - 3√7)² = 2.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

For the radius, we have:

Area of a circle = πr²

2π = πr²

r = √2

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - (-15))² + (y - 3√7)² = (√2)²

(x + 15)² + (y - 3√7)² = 2.

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The machine's second-year depreciation is $6,660 and the year-end book value under the straight-line method is $65,280.

The cost of a tangible asset is spread out throughout the course of depreciation. It symbolises the asset's value dropping over time as a result of damage, obsolescence, or other circumstances. Depreciation is crucial because it enables firms to account for an asset's cost over the course of its useful life rather than just in the year it was purchased.

Depreciation can be calculated using a number of different approaches, such as the straight-line method, the decreasing balance method, and the sum-of-years' digits method.

The annual depreciation expense is:

Annual Depreciation Expense = (Cost of Asset - Salvage Value) / Useful Life in Units

Annual Depreciation Expense = ($84,600 - $6,000) / 393,000

Annual Depreciation Expense = $0.20 per unit

For second year we have:

Second-Year Depreciation = Annual Depreciation Expense x Units Produced in Second Year

Second-Year Depreciation = $0.20 x 33,300

Second-Year Depreciation = $6,660

Now, the year-end book value is:

Accumulated Depreciation = Annual Depreciation Expense x Number of Years

Accumulated Depreciation = $0.20 x 2

Accumulated Depreciation = $0.40 per unit

For:

Accumulated Depreciation = $0.40 x 33,300

Accumulated Depreciation = $13,320

Also,

Book Value = Cost of Asset - Accumulated Depreciation - Salvage Value

Book Value = $84,600 - $13,320 - $6,000

Book Value = $65,280

Hence, the machine's second-year depreciation is $6,660 and the year-end book value under the straight-line method is $65,280.

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Answer:

awnser is 288 seriously  15 x 12 = 180

and 9 x12 =108 add together is 288

According to the table, the complete sentence would be: 96 students chose art as their favorite subject.

To complete the sentences correctly we must read the information and analyze the table. Once we have done these procedures we can establish how many students chose each of the subjects as their favorite. According to the above, the sentence would be as follows:

96 students chose art as their favorite subject.

According to Riley's survey, 12 out of 53 students chose art as their favorite. We then divide the total number of students (424) by the sample size (53) and multiply the number of students who chose art in the sample by the result of the division.

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Answer:

a. A linear equation would best represent the total cost a shopper will pay for an order.

b. y = .7x + 5 would model this situation.

Answer:

Step-by-step explanation:

just guess if not use the internet

No mayfly in the group can live for a full day (24 hours), as the maximum life span is 6 hours.

We can start by calculating the lower and upper limits of the range of possible values for the life spans of the mayflies.

The lower limit can be found by subtracting the MAD from the mean, and the upper limit can be found by adding the MAD to the mean:

Lower limit = mean - MAD = 4 - 2 = 2 Upper limit = mean + MAD = 4 + 2 = 6

Since we know there are 10 mayflies in the group, we can fill in the table below with values between 2 and 6 (inclusive) that add up to 40 (the total number of hours for all 10 mayflies combined):

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Answer:

the answer is b

Step-by-step explanation:

every 1 unit of 4 inches, there are 27 units of 3 yards. It's important to note that ratios represent a proportional relationship between two quantities and do not necessarily represent the actual values themselves.

How to solve ratio?

To find the ratio of 4 inches to 3 yards, we need to convert both measurements to a common unit of measurement.

Firstly, let's convert the 3 yards to inches, since inches are already given. There are 36 inches in a yard (3 feet in a yard, and 12 inches in a foot), so:

3 yards = 3 x 36 inches = 108 inches

Now we can compare the two measurements:

Ratio of 4 inches to 108 inches = 4/108

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 4 in this case:

4/108 = 1/27

So, the ratio of 4 inches to 3 yards is 1:27.

This means that for every 1 unit of 4 inches, there are 27 units of 3 yards. It's important to note that ratios represent a proportional relationship between two quantities and do not necessarily represent the actual values themselves.

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This is a binomial distribution problem with the following parameters:

We want to find the probability that at least 20 characters are numbers. We can use the complement rule and find the probability that fewer than 20 characters are numbers, and subtract that from 1:

P(at least 20 numbers) = 1 - P(fewer than 20 numbers)

Using the binomial probability formula, we have:

P(fewer than 20 numbers) = Σ[k=0 to 19] C(n,k) * p^k * q^(n-k)

where C(n,k) is the binomial coefficient "n choose k". This can be calculated using a calculator or software that has a binomial probability function. For example, in Python, we can use the scipy.stats.binom.cdf() function:

from scipy.stats import binom

n = 32

p = 5/8

q = 3/8

prob_fewer_than_20 = binom.cdf(19, n, p)

This gives prob_fewer_than_20 = 0.04903110366420758.

Therefore,

P(at least 20 numbers) = 1 - 0.04903110366420758 = 0.9509688963357924

Rounding to three decimal places, the answer is 0.951.

The number of bald eagles in the state during the winter of 1999 would be 34.

The equation is 84= h₀ -16t² and

Solving the equation we get the time taken by the object will be √6 seconds.

What is equation?

An equation is a mathematical statement which is built by two expressions connected by an equal sign ('='). There must be  at least one unknown variable which is to be determined. For example, 3x – 8 = 16 is an equation. Solving this equation, we get  x = 8.

When an object is dropped vertically from a platform, its height after

seconds can be estimated with the formula shown.

ℎ=ℎ₀−16t²

where ℎ is the height of the object in feet.

and ℎ₀ is the initial height of the object in feet.

t is the time in seconds after the drop.

If the object reach the height 84 feet then the equation will be,

                     84= h₀ -16t²

If the initial height is 180 feet then the equation will be

                        84 = 180- 16t²

Solving the equation we get,

                       ⇒ 16t² = 180- 84

                        ⇒ 16t² = 96

                       ⇒ t² = 6

                      ⇒ t= ±√6

As time can't be negative so t= √6

Hence solving the equation we get the time taken by the object will be √6 seconds.

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The common ratio is the factor by which each term is multiplied to get the next term, which in this case is 4.

To find the common ratio of a geometric sequence, you can divide any term in the sequence by the previous term.

Looking at the sequence: 1, 1, 1, 2, 8, 32, 128, ...

To get from the 1st term to the 2nd term, we multiply by 1.

To get from the 2nd term to the 3rd term, we multiply by 1.

To get from the 3rd term to the 4th term, we multiply by 2.

To get from the 4th term to the 5th term, we multiply by 4.

To get from the 5th term to the 6th term, we multiply by 4.

The constant ratio between succeeding words is known as the common ratio in a geometric progression (GP). Any phrase in the progression must be divided by the term before it in order to compute it.

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ln[(5x)² × (2x)⁻³ × (8x)⁷] . The logarithm expression is written in the form of ln(x) which is logarithm to the base e. The expression contains log2(x) which is logarithm to the base 2.

The base number is the number that is raised to a certain power, the exponent is the power that the base number is raised to, and the logarithmic function is the equation which is used to calculate the result of the base number and the exponent.

The given expression can be written as a logarithm as follows:

ln[(5x)² × (2x)⁻³ × (8x)⁷]

This can be simplified to

2ln(5x) - 3ln(2x) + 7log2(8x)

The logarithm expression is written in the form of ln(x) which is logarithm to the base e. The expression contains log2(x) which is logarithm to the base 2.

The logarithm expression can be used to simplify complex equations and calculations, and it can also be used to solve for a particular variable.

This expression can be used to solve for x if the other values are known. The value of x can be calculated by taking the antilogarithm of each term and then solving the equation.

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Answer: w = -13

Step-by-step explanation:

    To solve, we will isolate the variable with inverse operations.

Given:

   4 + w = -9

Subtract 4 from both sides of the equation:

   w = -13

Therefore, the equation of the circle that passes through the point (2, -5) and has its center at (4,0) is.[tex](x - 4)^2 + y^2= 29[/tex].

A circle is a closed, two-dimensional geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of all points in a plane that are at a given distance (called the radius) from the center point. The circumference of a circle is the distance around its outer boundary, and the diameter is the distance across the center of the circle. Circles have several important properties and are used extensively in mathematics, science, and engineering.

To find the equation of a circle, we need to know the coordinates of its center and its radius. We are given the center of the circle, which is (4,0). To find the radius, we can use the distance formula between the center and the point on the circle (2, -5):

[tex]radius = \sqrt{[(4 - 2)^2 + (0 - (-5))^2]}[/tex]

[tex]= \sqrt{[2^2 + 5^2]}[/tex]

[tex]= \sqrt{29}[/tex]

So the equation of the circle can be written in the standard form as:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where (h, k) is the center of the circle and r is its radius.

Substituting the values we found, we get:

[tex](x - 4)^2 + (y - 0)^2 = (\sqrt{29})^2[/tex]

Simplifying, we get:

[tex](x - 4)^2 + y^2 = 29[/tex]

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Therefore, the correct option is B. ∠EGF with the angle measure of 138°.

A quadrilateral is a four-sided polygon with four vertices and four angles. It is a closed figure with four straight sides that do not intersect. Examples of quadrilaterals include squares, rectangles, parallelograms, trapezoids, and rhombuses. The sum of the interior angles of a quadrilateral is always 360 degrees.

Here,

In an inscribed quadrilateral, opposite angles are supplementary. That is, the sum of the measures of any two opposite angles is 180 degrees. Therefore, to find the angle that has the same measure as ∠EDF, we need to look for the angle that is also opposite ∠EDF in the inscribed quadrilateral.

In the inscribed quadrilateral with points D, E, F, and G, we know that ∠EDF has a measure of 42 degrees. We also know that the opposite angle to ∠EDF is ∠EGF, because they share side EF.

Since opposite angles in an inscribed quadrilateral are supplementary, we can find the measure of ∠EGF by subtracting 42 degrees from 180 degrees:

∠EGF = 180° - ∠EDF

= 180° - 42°

= 138°

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Gretchen's final score, out of 10, is 8.35 based on weighted averages of scores in four categories.

To calculate Gretchen's final score, we need to calculate the weighted average of her scores in each category.

The weight of each category is given, so we can calculate the weighted score for each category by multiplying the weight by the score.

For Taste, the weighted score is 0.30 * 8.6 = 2.58

For Presentation, the weighted score is 0.35 * 9.8 = 3.43

For Use of Ingredients, the weighted score is 0.25 * 7.7 = 1.93

For Practicality, the weighted score is 0.10 * 4.1 = 0.41

To find the final score, we add up the weighted scores for all categories:

2.58 + 3.43 + 1.93 + 0.41 = 8.35

Therefore, Gretchen's final score is 8.35 out of 10.

The question is incomplete, below is the complete question given -

Gretchen is a celebrity chef competing in a celebrity cooking competition. Contestants receive ratings ranging from 1 to 10, with 10 being the highest. There are four categories, each with its own weighting. The judges' scores were added together, and the results are presented in the table below. What is Gretchen's final score, out of 10? Do not round.

Table -
Category                   Weight      Score

Taste                             30%          8.6

Presentation                 35%          9.8

Use of Ingredients       25%           7.7

Practicality                    10%            4.1

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If cοs θ equals negative 5 square rοοt 29 οver 29 and θ is in quadrant 2  sin(θ) = οppοsite/hypοtenuse = 2√21/29.

The links between triangles' sides and angles are studied in the mathematic discipline knοwn as trigοnοmetry.

We knοw that cοsine is negative in quadrant 2, sο we can draw a triangle in quadrant 2 where the adjacent side is negative and the hypοtenuse is pοsitive. Let's call the οppοsite side οf the triangle "a", the adjacent side "b", and the hypοtenuse "c".

Using the Pythagοrean theοrem, we can find the length οf the third side οf the triangle:

c² = a² + b²

29² = a² + (-5√29)²

29² = a² + 725

a² = 29² - 725

a² = 84

a = √84 = 2√21

Nοw that we knοw the lengths οf the οppοsite and adjacent sides οf the triangle, we can use the definitiοn οf sine:

sin(θ) = οppοsite/hypοtenuse = 2√21/29

Therefοre,  sin(θ) equals 2√21/29.

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Complete Question:

Given that cos(θ)=−5√29/29, and θ is in Quadrant II, what is sin(θ)? Give your answer as an exact fraction with a radical, if necessary.

The answer is (B) 125 1/3×, which is equivalent to (3/125) times approximately 18.048.

Equivalent fractions are fractions that have the same value but are written in different forms. They represent the same portion of a whole or a set, but their numerators and denominators may have different values.To find equivalent fractions, you can multiply or divide both the numerator and denominator of a fraction by the same number. This does not change the value of the fraction, but it changes its form.

The expression is (3/125) times something, but the value of that something is missing.

To solve the problem, we can simplify the expression (3/125) as a fraction in its lowest terms:

(3/125) = (3/5³)

Now, let's look at each of the answer choices:

125

If we multiply (3/5³) by 125, we get:

(3/5^3) * 125 = 3/5

Therefore, 125 is not equivalent to (3/125) times something.

1/3 × 125

If we multiply (3/5³) by (1/3 × 125), we get:

(3/5^3) * (1/3 × 125) = 1/5

Therefore, 1/3 × 125 is not equivalent to (3/125) times something.

125 1/3 ×

If we interpret "125 1/3 ×" as 125 and one-third multiplied by something, then we can write it as a mixed number fraction:

125 1/3 = 376/3

If we multiply (3/5³) by 376/3, we get:

(3/5³) ×(376/3) = 2256/125 = 18.048

Therefore, 125 1/3 × is equivalent to (3/125) times approximately 18.048.

125× 3x

If we interpret "125 3x" as 125 multiplied by 3 times something, then we can write it as:

125 ×3x = 375x

Therefore, 125 3x is not equivalent to (3/125) times something.

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The population of Medina, Ohio will be approximately 34,052.89 people in 7.3 years.

A number can be expressed as a fraction of 100 using a percentage. It is represented by the number %.

A decimal or fraction can be multiplied by 100 to become a percentage. For instance, multiplying 0.75 (a decimal) by 100 yields 75% when converted to a percentage. The same can be done to convert 3/4 (a fraction) to a percentage by dividing 3 by 4 to get 0.75, then multiplying that number by 100 to get 75%.

To calculate the population of Medina, Ohio in 7.3 years, we can use the formula:

Population after n years = Population before ×(1 + r/100)²

where r is the annual growth rate and n is the number of years.

Substituting the given values, we get:

Population after 7.3 years = 26,190 × (1 + 3.7/100)^7.3

Population after 7.3 years = 26,190 * 1.037^7.3

Population after 7.3 years = 26,190 * 1.301

Population after 7.3 years = 34,052.9

Rounding to the nearest hundredth, we get:

Population after 7.3 years = 34,052.90 ≈ 34,052.89

Therefore, the population of Medina, Ohio will be approximately 34,052.89 people in 7.3 years.

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The surface area of the square pyramid is 89.4 ft² as the lateral area is  80.4 ft².

The surface area of a square pyramid is calculated by the formula

SA = B + 4ℓ, where B is the area of the base and ℓ is the lateral area.

In this case, the base area is 9 square feet (3 ft x 3 ft). The lateral area is 4ℓ, which is calculated by multiplying the slant height by the perimeter of the base.

The slant height of a square pyramid is calculated by the formula

s = √(h² + (a/2)²), where h is the height of the pyramid and a is the length of one side of the base.

In this case, the height is 3 ft and the length of one side of the base is 3 ft. Therefore, the slant height is

s = √(3² + (3/2)²)

= √(9 + 2.25)

= √11.25

= 3.35 ft.

The perimeter of the base is 6 ft (3 ft x 2). Therefore, the lateral area is

4ℓ = 4 x 3.35 ft x 6 ft

= 80.4 ft².

The surface area of the square pyramid is then

SA = B + 4ℓ

= 9 ft² + 80.4 ft²

= 89.4 ft².

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