What is the growth factor?
Hint: the "growth factor" is the number that each term is multiplied by, to get the next term.
​With exponential decay, the "growth factor" will be a fraction.
Growth Factor:

300m of the fruit farm land will produce 300 kilograms of oranges. Given that 1 acre of land produces 2 tons of oranges, we can calculate the equivalent amount of oranges produced on 300m of land.

We know that 1 acre of land produces 2 tons of oranges. To find the equivalent amount of oranges produced on 300m of land, we need to convert the units of measurement.

First, we convert 1 acre to square meters. 1 acre is equal to 4046.86 square meters.

Next, we need to determine the proportion of land used. We have 300m of land, which is equivalent to 300 square meters.

Now we can calculate the amount of oranges produced on 300m of land. Since 1 acre produces 2 tons of oranges, we can set up a proportion:

1 acre / 2 tons = 300 square meters / x kilograms

Cross-multiplying the proportion, we get:

1 acre * x kilograms = 2 tons * 300 square meters

Simplifying the equation, we find:

x = (2 tons * 300 square meters) / 1 acre

x = (2 * 300) kilograms

x = 600 kilograms

Therefore, 300m of the fruit farm land will produce 600 kilograms of oranges.

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Answer:

$ 528000

Step-by-step explanation:

buying price = $ 600000

100% = 600000

loss = 12%

selling price = 88%

= 88% × 600000

= $ 528000

in a triangle, the sum of the angles is always 180 degrees. so, if we have one angle of 65 degrees and another angle of (10x + 3) degrees, the third angle must be:

180 - 65 - (10x + 3) = 112 - 10x

since the sum of the angles in a triangle is always 180 degrees, we can set up an equation:

65 + (10x + 3) + (112 - 10x) = 180

simplifying the equation:

180 - 3 = 65 + 112 - 10x + 10x

177 = 177

the equation is true for all values of x. this means that x could be any value and the triangle would still be valid.

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U.S. dollars can be purchased for one Canadian dollar is 0.63 U.S. dollar.

One U.S. dollar buys 1.59 Canadian dollar

1 U.S. dollar = 1.59 CAD dollar

By using the unitary method to calculating the value of 1 Canadian dollar.

The unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit .

Value of one Canadian dollar

1/1.59 U.S. dollar = 1 CAD dollar

1 CAD dollar = 0.63 U.S. dollar

1 CAD dollar can buy 0.63 U.S. dollar.

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Step-by-step explanation:

Let x be the number of days the skier goes to the mountain.

The total cost for using a season pass is:

Cost_season_pass = 450 (initial cost) + 10x (daily fee)

The total cost for using one day tickets is:

Cost_one_day_tickets = 100x (daily cost)

In order to justify buying a season pass, the total cost of the season pass must be less than the total cost of using one day tickets:

450 + 10x < 100x

Subtract 10x from both sides:

450 < 90x

Now, divide both sides by 90:

x > 5

So the skier must go to the mountain for more than 5 days to justify buying a season pass. The minimum number of days to justify the pass would be 6 days.

After 30 minutes, there will be 100 pounds of salt in the tank.

Initially, the tank contains 40 pounds of salt.

For every minute, the amount of salt being added is 2 pounds/gallon * 3 gallons/minute = 6 pounds/minute.

The amount of salt being drained off is 2 pounds/gallon * 2 gallons/minute = 4 pounds/minute.

After 30 minutes, the total amount of salt added is 6 pounds/minute * 30 minutes = 180 pounds.

The total amount of salt drained off is 4 pounds/minute * 30 minutes = 120 pounds.

Therefore, the net increase in the amount of salt in the tank is 180 pounds - 120 pounds = 60 pounds.

The final amount of salt in the tank after 30 minutes is 40 pounds (initial amount) + 60 pounds (net increase) = 100 pounds.

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The required equation is y = 1/3 x.

Given that the slope of the line is 1/3 and y - intercept is 0.

To find the equation of the line by using slope (m) and y-intercept (c) is given by

y = mx + c.

That implies, the equation of the line is y = 1/3x + 0= 1/3 x.

Therefore, the equation of line y = 1/3 x and graph is given below,

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To be continuous at x=0, you need three things:

1. f(0) must be defined

2. limit as x –> 0 must exist

3. f(0) = limit as x –> 0

f(0) in this case is the following:

    [tex]f(0) = k + 2 \ln(0+e^{0+1}) = k + 2 \ln(e) = k + 2[/tex]

We have to pause on this, since this by itself cannot give us the value of k.

For the limit, you need to make sure the limit from the left matches the limit from the right.

    [tex]\lim\limits_{x\to 0^+} k+2\ln(x+e^{x+1}) = k+2[/tex]

    [tex]\lim\limits_{x\to 0^-} \frac{\sin(7x)}{2x} =\frac{7}{2}[/tex]

The only way this limit can exist is if [tex]k+2 = \dfrac{7}{2}[/tex], which means [tex]k = \dfrac{3}{2}[/tex].

Using that k-value also allows f(0) = 7/2, which makes your function continuous.  

If you need to know how to make that second limit work out to 7/2, there are two steps to take.  

The first is to bring the 1/2 out front, since it's a constant factor inside the limit.

    [tex]\lim\limits_{x\to 0^-} \frac{\sin(7x)}{2x} =\frac{1}{2}\cdot\lim\limits_{x\to 0^-} \frac{\sin(7x)}{x}[/tex]

The second is to manipulate the what you're taking the limit of to turn it into a "sin(u)/u" situation.  To do this, we'll multiply by 7/7 inside the limit:

    [tex]\frac{1}{2}\cdot\lim\limits_{x\to 0^-} \frac{\sin(7x)}{x}=\frac{1}{2}\cdot\lim\limits_{x\to 0^-} \frac{{\boldsymbol7\cdot{}}\sin(7x)}{{\boldsymbol7\cdot{}}x}[/tex]

We'll then factor out the 7 in the numerator like we did with the 1/2:

    [tex]=\frac{7}{2}\cdot\lim\limits_{x\to 0^-} \frac{\sin(7x)}{7x}[/tex]

And now with a quick u-substitution, we'll let u = 7x and x->0 is the same as u->0, we have

    [tex]=\frac{7}{2}\cdot\lim\limits_{u\to 0^-} \frac{\sin(u)}{u}[/tex]

This is useful because a good limit to know in calculus is that [tex]\lim\limits_{u\to 0} \frac{\sin(u)}{u}=1[/tex].

The y-value of the y-intercept of the line is approximately 5.819. The correct answer is (D).

The equation of a regression line is y = mx + b, where m is the slope and b is the y-intercept. We are given that the slope is 1.885, so we have:

y = 1.885x + b

To find the y-intercept, we need to substitute the mean x and y values into this equation and solve for b. We have:

12.318 = 1.885(3.448) + b

Simplifying this equation gives:

12.318 = 6.50668 + b

Subtracting 6.50668 from both sides gives:

5.81132 = b

Rounding this value to three decimal places gives:

b ≈ 5.819

Therefore, the y-value of the y-intercept of the line is approximately 5.819.

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Answer:

48%

Step-by-step explanation:

 25 is 100% of 25

      so

25----------------100%

12------------------ X

   Cross multiplication

 25X = 12x100

25X = 1200

  X = 48

    I makes sense since half (50%) of 25 is 12.5   So 12 is a little less than half

Answer:

48

Step-by-step explanation:

to solve this you would use the [tex]\frac{part}{whole}[/tex] = [tex]\frac{percent}{100}[/tex] equation.

the whole would be 25 as that is what you are taking the percent out of.

the part would be 12, as that is what the percent of the whole equals.

plug those in:

[tex]\frac{12}{25} = \frac{percent}{100}[/tex]

change the percent to an x, as that is what we're solving for

[tex]\frac{12}{25} = \frac{x}{100}[/tex]

cross multiply to get

[tex]25x=1200[/tex]

isolate the variable by dividing by 25 on both sides

[tex]\frac{25x}{25} = \frac{1200}{25}[/tex]

you should get[tex]x=48[/tex]

48 is your answer

Answer:

1/3

Step-by-step explanation:

X is exactly halfway between 1/6 and 1/2, ie it is the average of those values.

average of 1/6 and 1/2 = (1/6 + 1/2) /2

= (1/6 + 3/6) /2

= (4/6) /2

= (2/3) /2

= 1/3

The area of a square is given by the formula A = s^2, where s is the length of a side of the square.

Here, the length of a side of the square is given as 25 32 by 24 m. This means that the side length is somewhere between 25 and 26 meters, since 32 by 24 is a fraction between 1 and 2.

To find the exact side length, we can convert the mixed number 25 32 by 24 to an improper fraction:

25 32 by 24 = (25 x 32 + 24) / 32 = 824 / 32

Simplifying this fraction by dividing both the numerator and denominator by 8 gives:

824 / 32 = 103 / 4

Therefore, the side length of the square is 103/4 meters.

Now we can find the area of the square:

A = (103/4)^2

 = 10609/16

 = 663.06 square meters (rounded to two decimal places)

Therefore, the area of the square is approximately 663.06 square meters.

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a. f(x) = 37(1.04)^x

i. The initial value (IV) is 37, which represents the starting point or value of the function when x=0.

ii. The percent increase or decrease can be found by comparing the function value at x=1 to the initial value.

When x=1, f(1) = 37(1.04)^1 = 38.48

The percent increase is [(38.48 - 37)/37] x 100% ≈ 4.05%

Therefore, the initial value is 37 and the percent increase is approximately 4.05%.

b. f(x) = (-0.7) (0.6)^x

i. The initial value (IV) is -0.7, which represents the starting point or value of the function when x=0.

ii. The percent increase or decrease can be found by comparing the function value at x=1 to the initial value.

When x=1, f(1) = (-0.7)(0.6)^1 = -0.42

The percent decrease is [(−0.42 - (−0.7))/−0.7] x 100% ≈ 40%

Therefore, the initial value is -0.7 and the percent decrease is approximately 40%.

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Answer:

To find the perimeter (or arc length) of an ellipse, you'll need to use an elliptic integral

The perimeter is a distance around the outlines or edge of any shape. A practical example of measuring the perimeter of an ellipse would be the distance you cover when you walk along the edges of an elliptical-shaped field. Or the length of fence you need to surround it

a. The mean of the ages is 6.8 years.

b. Without doing any calculations, we know that the mean age after 10 years will be larger.

c. The mean after 10 years will be 16.8 years.

The mean of the 5 rivers is 2203 miles. Thus, the correct answer is option D. The mean length of the major rivers in North America is 2203 miles.

a. The mean of the ages is (2+7+8+10)/4

= 6.75 ~ 6.8 years.

b. Without doing any calculations, we know that the mean age after 10 years will be larger. This is beacuse each of the the ages will be greater by 10.

Thus, the correct answer is option a.

The mean after 10 years will be (12+17+18+20)/4

= 16.75 ~ 16.8 years.

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The base of the rhombus would be = 10.2m.

To calculate the base of the given Rhombus, the the formula for the area of the Rhombus should be used. That is;

Area of Rhombus = b²/2

But area = 52cm²

That is:

52 = b²/2

make ab the subject of formula;

b² = 52×2 = 104

b =√104

= 10.2m

Therefore the base of the Rhombus whose area is given should be = 10.2m.

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The normal approximation can be used in a two-sample test of proportions when the sample sizes are sufficiently large.

The rule of thumb is that each sample should have at least 10 successes and 10 failures. When these conditions are met, the sampling distribution of the difference in sample proportions can be approximated by a normal distribution with a mean equal to the difference in population proportions and a standard deviation calculated from the sample proportions. This approximation allows us to calculate probabilities and make inferences using the standard normal distribution. It is important to note that this approximation may not be accurate for small sample sizes, in which case exact methods such as the Fisher's exact test should be used instead. In summary, the normal approximation can be used in a two-sample test of proportions when the sample sizes are large enough and the conditions are met.

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The volume of the triangular prism is 18.9 yd³.

The volume of a triangular prism is given by the formula:

V = (1/2) x base x height x length

where base is the area of the triangular base, height is the height of the triangular base, and length is the height of the prism.

In this case, the base area is:

= (1/2) x 9yd x 2.1

= 9.45 yd²

So the volume of the prism is:

V = (1/2) x 9.45 x  4

= 18.9 yd³

Therefore, the volume of the triangular prism is 18.9 yd³.

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No, it is not possible to draw more than one triangle with side lengths of 5 inches and 7 inches and an included angle with a measure of 50 degrees.

In a triangle, the measure of an included angle between two sides determines the length of the third side. In this case, we have fixed side lengths of 5 inches and 7 inches, and an included angle of 50 degrees.

According to the Law of Sines, the ratio of the length of a side to the sine of its opposite angle is constant in a triangle. Using this law, we can calculate the length of the third side.

Let's denote the unknown side length as "x". Using the Law of Sines:

sin(50°) / 5 = sin(opposite angle) / x

We can solve this equation to find the value of x. However, it's important to note that there will be only one solution for x. This means that there is only one possible triangle that can be formed with the given side lengths and included angle measure.

No,it is not possible to draw more than one triangle with the given specifications.

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Answer:

If we are using the Triangle Inequality Theorem the answer would be:

Step-by-step explanation:

1: Yes

2: Yes

3: Yes

4: No

5: Yes

6: No

7: No

I hope this helps! :)

Step-by-step explanation:

Due to the triangle side length rule :

  any two sides summed must be greater than the remaining side

yes

yes

yes

no    3+4 is not greater than the remaining side 8

yes

no     8+3  not greater than 15

no    4 + 8 not greater than 15

The given exponential function will grow with,

⇒ 7.1%

We have to given that;

The exponential function is,

⇒ y = 25 (1.071)ˣ

Since, We know that;

A relation in between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Now, For identify the change represents growth or decay, and determine the percentage rate of increase or decrease as,

Since, We have,

⇒ y = 25 (1.071)ˣ

Clearly, The equation is shows exponential growth because the growth factor is 1.071 which is greater than 1.

And, The general form equation is:

y(x) = a(1 + r)ˣ

Where, r is the growth percent.

Hence,

⇒ 1 + r = 1.071

⇒ r = 0.071 = 7.1%

Therefore, We get;

Rate = 7.1%

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By use the similar slope triangles, the slope of segment AD, segment DF, and the line of m are all equal.

In Mathematics and Geometry, two (2) triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

Additionally, the lengths of corresponding sides or corresponding side lengths are proportional to the lengths of corresponding altitudes when two (2) triangles are similar and the slopes of side JL and side MP are equal;

Slope of segment AD = AB/BD

Slope of segment DF = DE/EF

Slope of line m = DE/EF = AB/BD

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Answer: The diameter is is 9, the circumference is 199 inches

Step-by-step explanation:

hope that helps! For the last one, substitute with the formula of a circle. It will make sense.

The graph shows that Addison drives away from home, reaches a maximum distance of 20 blocks away from home, and then drives back home, arriving at the same distance of 0 blocks away from home.

A graph of Addison's distance from her home over time, we can plot time on the x-axis and distance on the y-axis.

Here's a step-by-step process to create the graph:

Start by drawing the x-axis and labeling it "Time (minutes)".

Mark the minimum value as 0 and the maximum value as 24 (7 + 5 + 6 + 7 + 7 = 32 minutes total, but we only need to plot until Addison gets home).

Draw the y-axis and label it "Distance from Home (blocks)".

Mark the minimum value as 0 and the maximum value as 13 (7 blocks to the store + 6 blocks to the bank).

Plot Addison's starting point, which is at (0,0).

Addison drives to the store at a speed of 2 blocks per minute, so after 7 minutes she is 14 blocks away from home (7 minutes × 2 blocks/minute = 14 blocks). Plot a point at (7, 14).

Addison stops at the store for 5 minutes, so her distance from home doesn't change during that time.

Draw a horizontal line from the point at (7,14) to (12,14).

Addison drives from the store to the bank at a speed of 3 blocks per minute, so it takes her 2 minutes to travel 6 blocks (6 blocks / 3 blocks/minute = 2 minutes).

After 12 minutes total (7 minutes to the store + 5 minutes at the store), she is 20 blocks away from home (14 blocks + 6 blocks). Plot a point at (12, 20).

Addison stops at the bank for 7 minutes, so her distance from home doesn't change during that time.

Draw a horizontal line from the point at (12,20) to (19,20).

Drives from the bank to home at a speed of 5 blocks per minute, so it takes her 2.6 minutes to travel 13 blocks (13 blocks / 5 blocks/minute = 2.6 minutes).

After 19 minutes total (7 minutes to the store + 5 minutes at the store + 6 minutes to the bank + 1 minute waiting at the bank), she is 13 blocks away from home (20 blocks - 13 blocks). Plot a point at (19,13).

Addison arrives home after 24 minutes (7 minutes to the store + 5 minutes at the store + 6 minutes to the bank + 7 minutes at the bank + 2.6 minutes driving home).

Draw a point at (24,0) to represent her arrival home.

Connect the points with a line to complete the graph:

Distance from Home

    ^

13 _|                •

   |                    |‾‾‾•‾‾‾‾‾‾

12 _|                |     /

   |                    |    /

11 _|                 |   /

   |                    |  /

10 _|                | /

   |                    |/

 9 _|_ ___ _ _|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

    0               7 12         19                   24    → Time

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Akbar paid Rs 864.50 for the watch after applying the 5% discount.

Akbar bought a watch that was originally priced at Rs 910, but he was able to purchase it at a 5% discount. To calculate how much he paid for the watch, we need to first find out how much the discount was.

To do this, we can use the formula:
Discount = Original price x Discount rate

In this case, the original price of the watch is Rs 910 and the discount rate is 5%, which we can express as a decimal by dividing by 100:

Discount = Rs 910 x 0.05
Discount = Rs 45.50

So the discount Akbar received on the watch was Rs 45.50.

To find out how much he actually paid for the watch, we can subtract the discount from the original price:

Price paid = Original price - Discount
Price paid = Rs 910 - Rs 45.50
Price paid = Rs 864.50

Therefore, Akbar paid Rs 864.50 for the watch after applying the 5% discount.

In summary, Akbar bought a watch at a 5% discount, which amounted to Rs 45.50. He paid Rs 864.50 for the watch after the discount was applied, even though the original price of the watch was Rs 910.

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Heuristics refers to rules of thumb that simplify the decision-making process. Heuristics are mental shortcuts that help individuals make decisions quickly, often relying on previous experience or intuition rather than a more systematic approach.

While heuristics can be useful, they can also lead to biases and errors in judgment if they are applied too broadly or without careful consideration. It is important to be aware of these heuristics and how they can affect decision-making processes, especially in complex or high-stakes situations where careful consideration is necessary.

The answer is C.

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Answer:

$ 14.50

Step-by-step explanation:

So 2/3 is $7, right?

If we multiply to find how much it would be to get to one pound, you would find that 1.5 would get you to that number.

So, that means two 2/3, and a half, meaning:

7+7+0.5=14.5

Leading to your answer: $ 14.50

Hope this helps :)

Answer:

10x - 8 = y

Step-by-step explanation:

This question was hard to read so i used the variables! I hope you do good! :)

Answer:

x=4

Step-by-step explanation:

LM=JK

3x+1=13

3x=12

x=4