Which of the contexts below represents exponential growth?
A town's population grows at a rate of 9.2% every year.
A radioactive compound decays at a rate of 25% per hour.
A town's population shrinks at a rate of 3.5% every year.
A music service has a fixed monthly cost and charges $0.25 for each downloaded
song.
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The rate at which the height of the water is increasing when water is being pumped in at a rate of 2/3 m/s and the water is 9m deep is 0.667 m/s.

We can start by using the formula for the volume of a square pyramid to find the volume of water in the tank. Let V be the volume of water in the tank and h be the height of the water.

V = (s² [h])/3

We know that the base of the pyramid is 3m by 3m, so s = 3. Also, the height of the pyramid is 16m, so we have:

V = (3² [h])/3

V = 3h

Now, we can find the rate of change of the volume with respect to time:

dV/dt = 3 [dh/dt]

We know that water is being pumped in at a rate of 2/3 m/s, so dh/dt = 2/3. We want to find how fast the height increases when the water is 9m deep, so h = 9. Substituting these values, we get:

dV/dt = 3 [dh/dt]

dV/dt = 3 [2/3]

dV/dt = 2

Therefore, the rate at which the volume of water is increasing is 2 cubic meters per second. To find the rate at which the height of the water is increasing, we need to solve for dh/dt:

dV/dt = 3 [dh/dt]

2 = 3 * dh/dt

dh/dt = 2/3

So the height of the water is increasing at a rate of 2/3 m/s when the water is 9m deep. Rounded to 3 decimal places, the answer is 0.667 m/s.

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Answer: 53

Step-by-step explanation:

90- 37 = 53

Two angles are Complementary when they add up to 90 degrees (a Right Angle)  

1. Let us suppose the amount saved = s. 2. The inequality is 62 + s ≥ 100. 3. The value of s is: s ≥ 38. 4. Vin can save at least $38 from now until the end of the month to meet his goal of saving at least $100.

A mathematical statement illustrating the relationship between two amounts or expressions that are not always equal is known as an inequality. To represent the connection between the two values, an inequality may employ a number of symbols, including (less than), > (greater than), (less than or equal to), or (greater than or equal to). In algebra and other branches of mathematics, inequalities are frequently used to indicate restrictions, such as limitations on a variable, and to address issues with variables or unknown numbers. An inequality's solution, which may be a range of values rather than a single value, is the collection of all values that meet the inequality.

1. Let us suppose the amount saved = s.

2. The inequality is 62 + s ≥ 100

3. Solving for s we have:

62 + s ≥ 100

s ≥ 100 - 62

s ≥ 38

On the number line, all values greater than or equal to 38 would satisfy this inequality.

4. Vin can save at least $38 from now until the end of the month to meet his goal of saving at least $100.

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Answer: 1 1/24

Step-by-step explanation:

2/3 - 3/8 = 25/24. Reduce it and you get 1 1/24

Answer:

We cannot determine the exact number of votes for Tim or Selena without additional information. However, we can determine the fraction of the whole class that voted for each candidate based on the given information.

If only one third of the students cast votes, that means that two thirds did not vote. Therefore, the fraction of the whole class that voted for Tim and Selena is each equal to one third of the total number of students.

To calculate these fractions, we can use the following formula:

Fraction of class = Number of students who voted / Total number of students

Let's assume that there are N students in the class. Then, the number of students who voted for Tim is (1/3)N, and the number of students who voted for Selena is also (1/3)N.

So, the fraction of the whole class that voted for Tim is:

(1/3)N / N = 1/3

Similarly, the fraction of the whole class that voted for Selena is also 1/3.

Since we don't know the exact number of votes for each candidate, we cannot determine who received more votes.

To the total of 99 cookies, there are 27 cookies in middle pile.

Let's call the number of cookies in the first pile "x". Then, the number of cookies in the second pile is 1/2 of x, or (1/2)x, and the number of cookies in the third pile is 1/3 of x, or (1/3)x.

We know that the total number of cookies is 99, so we can write an equation:

x + (1/2)x + (1/3)x = 99

To solve for x, we can first find a common denominator:

(6/6)x + (3/6)x + (2/6)x = 99

(11/6)x = 99

x = (6/11) * 99

x = 54

So, there are 54 cookies in the first pile, (1/2)x = (1/2)*54 = 27 cookies in the second pile, and (1/3)x = (1/3)*54 = 18 cookies in the third pile. In the middle pile there are 27 cookies.

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Therefore, the area of the shaded region is 72 square meters.

A triangle is a three-sided polygon that is formed by connecting three straight lines or line segments. It is a basic geometric shape that is commonly studied in mathematics, geometry, and trigonometry. Triangles have a wide range of properties and characteristics that are important in various fields of study, including their angles, sides, and area. Triangles can be classified based on their angles (as acute, right, or obtuse triangles) or based on their sides (as equilateral, isosceles, or scalene triangles). The study of triangles is fundamental in many areas of mathematics and physics and is also important in practical applications such as engineering, architecture, and surveying.

by the question.

To find the area of the shaded region, we first need to find the area of the entire rectangle. The area of a rectangle is given by the formula: length x width.

The length of the rectangle is 12 meters, and the width is 8 meters, so the area of the entire rectangle is:

12m x 8m = 96 square meters

Next, we need to find the area of the triangle that is not shaded. The base of the triangle is 6 meters, and the height is 8 meters. The area of a triangle is given by the formula: 1/2 x base x height.

1/2 x 6m x 8m = 24 square meters

Finally, we can find the area of the shaded region by subtracting the area of the triangle from the area of the entire rectangle:

96 square meters - 24 square meters = 72 square meters

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The value of T(v), express v as linear combination in the basis B and the matrix representation of T obtain is T(v) = [4, -4].

To find T(v), we need to express v as a linear combination of the basis vectors of R^3 with respect to B:

v = (-1)[0] + (-1)[0] + (1)[1]

This means that the coordinate vector of v with respect to B is [-1, -1, 1].

To find the matrix representation of T with respect to the standard bases of R^3 and R^2, we can apply T to each of the basis vectors:

T([1, 0, 0]) = [1, 3]

T([0, 1, 0]) = [-1, 1]

T([0, 0, 1]) = [2, -2]

We can arrange the results in a matrix:

[1 -1 2]

[3 1 -2]

The matrix [1 -1 2; 3 1 -2] represents T with respect to the standard bases of R^3 and R^2.

To find T(v), we can multiply the matrix representation of T with the coordinate vector of v with respect to B:

T(v) = [1 -1 2; 3 1 -2] * [-1; -1; 1] = [4; -4]

Therefore, T(v) = [4, -4].

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The equation that represents the given equation model is: 4.99p + 3.79c = 35

The most common form of representing a linear equation model is:

y = mx + b

where:

m is slope

b is y-intercept

Let the number of pounds of Pecans she can buy be p

Let the number of pounds of cashews she can buy be c

We are told that:

Cost of pecans = $4.99 per pound

Cost of Cashews = $3.79 per pound

Thus, for $35 to spend we have the equation as:

4.99p + 3.79c = 35

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It's important to note that ordering more than 15 slices would exceed your budget of $48, while ordering fewer slices would allow you to save money for other expenses.

To determine how many pizza slices you can order with $48, we divide the total amount of money by the cost of each slice of pizza, which is $3.20. This gives us:

48 ÷ 3.20 = 15

So you can order up to 15 slices of pizza with $48. However, since you cannot order a fraction of a slice, the actual number of slices must be a whole number. Therefore, the possible numbers of pizza slices you can order are:

0 slices

1 slice

2 slices

3 slices

4 slices

5 slices

6 slices

7 slices

8 slices

9 slices

10 slices

11 slices

12 slices

13 slices

14 slices

15 slices

So, any of the above numbers represents the amount of pizza slices you can order for you and your friends. It's important to note that ordering more than 15 slices would exceed your budget of $48, while ordering fewer slices would allow you to save money for other expenses.

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Para resolver este problema, primero tenemos que multiplicar las fracciones:

3/5 x 4/7 = 12/35

Luego, encontramos cuántas docenas son 12/35 de 420 docenas:

(12/35) x 420 = 144

Así que 3/5 de 4/7 de 420 docenas (que es equivalente a 12/35 de 420 docenas) representa 144 docenas de huevos.

Para encontrar el número total de huevos, multiplicamos 144 docenas por 12 huevos por docena:

144 x 12 = 1,728

Por lo tanto, 3/5 de 4/7 de 420 docenas representa 1,728 huevos.

Answer:

Ratios are fractions, right? Set the two fractions equal to each other and then cross-multiply them. If each side of the equation is equal, then the ratios are equal; if not, then the ratios are not equivalent.

Ex. 1

Comparing ratios 4:2 and 2:1

[tex]\frac{4}{2} = \frac{2}{1}[/tex]

Cross-multiplying, we get 4 = 4, but we can also simplify each side of the equation to get 2 = 2.

Ex. 2

Comparing ratios 3:5 and 6:7

[tex]\frac{3}{5} =? \frac{6}{7}[/tex]

Cross-multiply, we get 21 = 30, so the ratios are not equal. This is an example of a case where you can't simplify the ratios.

Ex. 3

Comparing rations 5:12 and 10:24

[tex]\frac{5}{12} = \frac{10}{24}[/tex]

Cross-multiply, 120 = 120 so the ratios are equal.

Hope this helps!

so (0,-3) and  (2,0) is a solution.   (2,2) and (-3,0) is not a solution. as  the equation of the line passing through the points (0,-3) and (2,0) is y = (3/2)x - 3 we need to substitute points to check valid or not

what is equation ?

An equation is a mathematical statement that asserts that two expressions are equal. In other words, an equation says that one expression on the left side of the equals sign is the same as the expression on the right side of the equals sign. An equation typically includes variables

In the given question,

To determine the equation of the line passing through the points (0,-3) and (2,0), we can use the slope-intercept form of a linear equation:

y = mx + b

where m is the slope and b is the y-intercept.

The slope of the line can be found using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) = (0,-3) and (x₂, y₂) = (2,0)

m = (0 - (-3)) / (2 - 0) = 3/2

So the equation of the line is:

y = (3/2)x - 3

Now we can check which ordered pair is a solution to this equation by plugging in the x and y values into the equation and seeing if it holds true.

A. (0,-3)

y = (3/2)x - 3

-3 = (3/2)(0) - 3

-3 = -3

This is true, so (0,-3) is a solution.

B. (2,0)

y = (3/2)x - 3

0 = (3/2)(2) - 3

0 = 0

This is true, so (2,0) is a solution.

C. (2,2)

y = (3/2)x - 3

2 = (3/2)(2) - 3

2 = 0

This is false, so (2,2) is not a solution.

D. (-3,0)

y = (3/2)x - 3

0 = (3/2)(-3) - 3

0 = -9/2

This is false, so (-3,0) is not a solution.

Therefore, the solutions to the equation represented by the graph are A. (0,-3) and B. (2,0).

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Answer:

  5.7y^2 +2y +2

Step-by-step explanation:

You want to simplify the expression 4.7y^2+5.3+4y-3.3-2y+y^2.

Identify like terms and combine their coefficients:

  4.7y^2+5.3+4y-3.3-2y+y^2

  = (4.7 +1)y^2 +(4 -2)y +(5.3 -3.3)

  = 5.7y^2 +2y +2

The probability of the first three cards being 3 aces and the last one being a king is 1/66,300.

The probability of drawing an ace from a deck of 52 cards is 4/52 (since there are 4 aces in the deck), and the probability of drawing a king is 4/52 as well.

Since the cards are dealt with no replacement, the probability of drawing three aces in a row is

(4/52) × (3/51) × (2/50) = 1/5525

This is because after each card is drawn, there is one less ace in the deck, and one less card overall.

Now, we need to multiply this probability by the probability of drawing a king as the fourth card. Since there are only 48 cards left in the deck at this point (since three cards have already been drawn), the probability of drawing a king is

4/48 = 1/12

Therefore, the probability of drawing 3 aces and 1 king in a row is

(1/5525) × (1/12) = 1/66300

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Answer:

56.54 inches

Step-by-step explanation:

If the radius is 3 inches, to find the area of the circle your equation would be A = (pi) x r^2

Your equation would look like this:

A = (pi) x 3^2

A = 28.27

Now to get the volume of the pie, you would multiply 28.27 x 2 which gives you an answer of 56.54 inches.

Answer:

A semicircle has an angle measure of pi radians. Therefore, the fraction of a semicircle that an angle of 29pi/18 radians represents is:

(29pi/18) / pi = 29/18

So the fraction of a semicircle that an angle of 29pi/18 radians represents is 29/18.

Step-by-step explanation:

The total amount of water supplied per hour inside a circle of radius 14 is approximately79.90 ft^3 per hour, and the total amount of water that goes through the sprinkler per hour is approximately  2π ft^3 per hour. As R approaches infinity, the total amount of water supplied per hour approaches  2 ft^3 per hour.

To find the total amount of water supplied per hour inside of a circle of radius 14, we need to integrate the function e^(-r) over the region of the circle total amount of water = ∫∫ e^(-r) dA

where the integration is over the circular region of radius 14, and dA is the differential area element.

Using polar coordinates, we can write dA = r dr dθ, and the limits of integration are 0 ≤ r ≤ 14 and 0 ≤ θ ≤ 2π. Substituting these values, we get:

total amount of water = ∫(0 to 2π) ∫(0 to 14) e^(-r) r dr dθ

Integrating with respect to r first, we get:

total amount of water = ∫(0 to 2π) [-e^(-r)](0 to 14) dθ

total amount of water = ∫(0 to 2π) (1 - e^(-14)) dθ

total amount of water = (1 - e^(-14)) ∫(0 to 2π) dθ

total amount of water = 2π(1 - e^(-14))

Thus, the total amount of water supplied per hour inside of a circle of radius 14 is approximately 79.90 ft^3 per hour.

To find the total amount of water that goes through the sprinkler per hour, we need to integrate the function e^(-r) over the entire plane:

total amount of water = ∫∫ e^(-r) dA

where the integration is over the entire plane, and dA is the differential area element.

Using polar coordinates, we can write dA = r dr dθ, and the limits of integration are 0 ≤ r ≤ ∞ and 0 ≤ θ ≤ 2π. Substituting these values, we get:

total amount of water = ∫(0 to 2π) ∫(0 to ∞) e^(-r) r dr dθ

Integrating with respect to r first, we get:

total amount of water = ∫(0 to 2π) [-e^(-r)](0 to ∞) dθ

total amount of water = ∫(0 to 2π) (1) dθ

total amount of water = 2π

Thus, the total amount of water that goes through the sprinkler per hour is exactly 2π ft^3 per hour.

To calculate the total amount of water supplied per hour inside a circle of radius R, then let R → ∞, we can use the result from part B and multiply it by the ratio of the areas of the two circles:

total amount of water = (total amount of water inside circle of radius R) × (area of circle of radius R)/(area of entire plane)

total amount of water = (2πR^2(1-e^(-R))) / (πR^2)

total amount of water = 2(1-e^(-R))

Now we can let R → ∞:

total amount of water = 2

Thus, the total amount of water supplied per hour inside a circle of infinite radius is exactly 2 ft^3 per hour.

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

"A sprinkler distributes water in a circular pattern, supplying water to a depth of e^-r feet per hour at a distance of r feet from the sprinkler. A. What is the total amount of water supplied per hour inside of a circle of radius 14? ft^3 per hour B. What is the total amount of water that goes through the sprinkler per hour? ft^3 per hour Calculate the total amount of water supplied per hour inside a circle of radius R, then let R rightarrow infinity."--

The cost of 4 kilograms is $13 if the unit rate is $3.25kg.

What is the unit rat?

The unit rate is a rate in which the second term in the ratio is 1. For example, if you have a rate of 60 miles per hour, the unit rate would be 60 miles per 1 hour, or simply 60 miles per hour. Another example is if you have a unit price of $2.50 per pound of apples, the unit rate would be $2.50 per 1 pound, or simply $2.50 per pound.

If the unit rate is $3.25/kg, then the cost of 1 kg is $3.25. To find the cost of 4 kg, we can multiply the cost of 1 kg by 4:

4 kg x $3.25/kg = $13

Therefore, the cost of 4 kilograms is $13 if the unit rate is $3.25kg.

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Answer:

Step-by-step explanation:

(i-j)×(j-k)×(k-i)

{(i×j)-(i×k)-(j×j)+(j×k)}×(k-i)

(k+j-i)×(k-i)

( j+i+k-j)

(i+k)

Step-by-step explanation:

1st method:-

Using congurency:-

In ∆AOC AND ∆COD

1) CO= CO {common side}

2) <OAC = <ODC { inscribed angel on same base CO}

3)OD = OC {radius}

4)∆AOC ≅ ∆COD {SAS fact}

5)∆AOC = ∆ COD {area of congurent traingle is equal}



2nd method:-

Using property of traingles:-

Construction:- Join DA and CB

<ACB = 90° { angle substended by diameter}

CO⊥AB

Now we know that,

Area of traingle = 1/2 B*H

CO is height { of both traingle's}

AO is base {of both traingle's}

Now, ∆AOC= 1/2*CO*AO--1

and, ∆ COD = 1/2 *CO*AO--2

∆AOC= ∆COD {from above 1 and 2}

the reference points for the transformation given by g(x) = 2*f(x) + 2 are (0, 4) and (1, 6).

The given function f has reference points (0, 1) and (1, 2). To find the reference points for the transformation given by g(x) = 2*f(x) + 2, we need to apply the transformation to each of the original reference points.

For the first reference point (0, 1), we have:

g(0) = 2f(0) + 2 = 21 + 2 = 4

So the transformed point is (0, 4).

For the second reference point (1, 2), we have:

g(1) = 2f(1) + 2 = 22 + 2 = 6

So the transformed point is (1, 6).

Therefore, the reference points for the transformation given by g(x) = 2*f(x) + 2 are (0, 4) and (1, 6).

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Based on my knowledge, I would expect a negative correlation between the amount of gas in a car's gas tank and the total distance the car has traveled since last being filled with gas.

As the car travels, the amount of gas in the tank decreases. Thus, if the car has traveled a long distance since being filled up, it is likely that there is less gas in the tank. Therefore, there should be a negative correlation between the amount of gas in the tank and the distance traveled, meaning that as the distance traveled increases, the amount of gas in the tank decreases.

A scatter plot of these two variables should show a downward-sloping trend, indicating the negative correlation.

Therefore the correct answer is negative correlation.

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Step-by-step explanation:

There are (9+8+7)  = 24 parts  that add up to 144

each part is then 144/24 = 6

then each side is    9 parts =  9*6 = 54

                8 parts = 8 * 6 = 48

       7 parts    7 * 6 = 42

Answer:

  $12

Step-by-step explanation:

You want to know the amount that has a tax of $0.72 when the tax rate is 6%.

The tax is computed by multiplying the price by the tax rate.

  tax = price × (tax rate)

  $0.72 = price × 0.06

  price = $0.72/0.06 = $(72/6) = $12

The original price of the bracelet is $12.

If Allie spins the spinner 2 times. the probability that Allie spins A on the first spin and & on the second spin is: B. 1/16.

Based on the information provided, the spinner has four possible outcomes: K, S, A, and %, each with equal probability of 1/4.

To find the probability that Allie spins A on the first spin and & on the second spin, we need to multiply the probability of spinning A on the first spin (1/4) by the probability of spinning & on the second spin (1/4), because the two events are independent.

Therefore, the probability is:

P(A on first spin and & on second spin) = P(A) × P(&) = (1/4) × (1/4) = 1/16

So the probability that Allie spins A on the first spin and & on the second spin is 1/16.

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The average rate of change from year 1 to year 10 is: (150 - 69)/9 = 9 based on the given function.

The amount of maize the farmer's land is yielding in pounds per acre over x years is represented by the function f(x)=[tex]-x^2+20x+50[/tex].

We must compute the change in f(x) for the range [1,10] and divide by the interval's length to determine the average rate of change from year 1 to year 10.

f(1) = [tex]-(1)^2[/tex] + 20(1) + 50 = 69

f(10) = [tex]-(10)^2[/tex] + 20(10) + 50 = 150

Hence, the change in f(x) throughout the range [1,10] is as follows:

f(10) - f(1) = 150 - 69 = 81

And the interval [1,10] has the following length:

10 - 1 = 9

Thus, from year one to year ten, the average rate of change is:

(150 - 69)/9 = 9

By interpreting the average rate of change, we can conclude that from year 1 to year 10, the farmer's land's yield of maize per acre is growing at a pace of 9 pounds each year. This indicates that, on average, throughout the course of these ten years, the farmer can anticipate harvesting 9 extra pounds of maize per acre.

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Answer:

g(4)=-2 and g(-4)=1

Step-by-step explanation:

The expression 61+x when x = 18 evaluates to 79.

Expression is a combination of numbers, symbols and operators that represent a mathematical quantity or operation.

To find the value of the expression, we must first substitute 18 in for x.  To evaluate this expression, we must add 61 and 18. 61+18 = 79. Therefore, the expression 61+x when x = 18 evaluates to 79.

To verify the answer, we can use the distributive property of multiplication to expand the expression. 61+x is equivalent to 61+18, which can be written as

61+18 = 61+1*18.

We can now distribute the 1 to the 18,

so 61+1*18 = 61+18 = 79.

Therefore, the expression 61+x when x = 18 evaluates to 79.

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Question: Evaluate-61+x

Enter your answer in the box.

Find the value of equation, when x = 18.