The number of fish in a lake is growing exponentially. The table shows the values, in thousands, after different numbers of years since the population was first measured.



years population


0 10


1


2 40


3


4


5


6


By what factor does the population grow every two years? Use this information to fill out the table for 4 years and 6 years.


By what factor does the population grow every year? Explain how you know, and use this information to complete the table

The area of the circle whose diameter is 14 is approximately 153.94 square units or 49π square units..

The area of a circle is given by the formula A = πr², where r is the radius of the circle. Since the diameter of the circle is given as d = 14, we know that the radius is half of the diameter, which is r = d/2 = 7.

Substituting the value of the radius in the formula, we get:

A = πr² = π(7)² = π(49) ≈ 153.94 (rounded to two decimal places using 3.14 for π)

Therefore, the area of the circle is approximately 153.94 square units. Alternatively, the exact answer can be left in terms of π, which would be A = 49π square units.

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Answer:

252 mi

Step-by-step explanation:

volume= L x W x H

9x 7 x 4 = 252 mi

Answer:

5,005

Step-by-step explanation:

This is a combination problem. The formula for combination is:

nCr = n! / (r!(n-r)!)

Where n is the total number of items, and r is the number of items to be selected.

Using this formula, we can calculate the number of ways to choose 9 varieties from 15:

15C9 = 15! / (9!(15-9)!) = 5005

Therefore, there are 5,005 ways to choose 9 varieties from 15 varieties of pansies.

Approximately 37.71 lbs of butter would be used to make 132 cookies.

we can use a proportion:

[tex]2 lbs of butter / 7 dozen cookies = x lbs of butter / 132 cookies\\[/tex]

To find x, we can cross-multiply and solve for x:

[tex]2 lbs of butter * 132 cookies = 7 dozen cookies * x lbs of butter264 lbs of cookies = 7xx = 264 / 7x = 37.71[/tex]

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The mistake, Aleks made, while measuring the angle is, he measure the angle from the wrong side of the line.

Angle is a dimensionless vector quantity, that is, it is very important, to take care of the directions, while measuring the angle.

That is, to measure the angle, say ∠ABC, the 0°(reference) line of the protractor, must be on one either AB or BC, to measure the angle rightly.

And since the angles between two lines are supplementary in nature, that is, the two angles will add up to make 180°, that is why, the angle measure by Alek and Melanie, add up to make 180°.

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Answer:

Hello! I'd be happy to help you with your math question. Based on the information you've provided, the aircraft flying in a north easterly direction turned through one whole number 2 over 3 right angle to the right of its path. To determine its new course, we need to know the original course of the aircraft. Do you happen to have that information? Once we have that, we can use some trigonometry to calculate the new course. Let me know and I'll be happy to guide you through the process.

Answer:

hope it helps________________

Step-by-step explanation:

Answer:

To find the face value (p) of the note, we need to use the formula for simple interest:

I = P * r * t

where:

I = interest

P = principal or face value

r = interest rate per year

t = time in years

Since the note has a 6% interest rate and a 150-day term, we need to convert the time to years:

t = 150 / 365

t = 0.41096 years

Now we can solve for the face value:

I = P * r * t

2550 = P * 0.06 * 0.41096

2550 = 0.0246576P

P = 2550 / 0.0246576

P = 103364.99

So the face value (p) of the note is $103,364.99.

To find the interest (i), we can subtract the face value from the balloon payment:

i = 2550 - 103364.99

i = -100814.99

The negative interest result may seem strange, but it's because the balloon payment was higher than the face value of the note. In other words, Averi paid more than the note was worth in order to fully pay off the principal and interest.

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Answer:

w ≈ 68,3

Step-by-step explanation:

Use trigonometry:

[tex] \sin(42) = \frac{w}{102} [/tex]

Cross-multiply to find w:

[tex]w = 102 \times \sin(42°) ≈68.3[/tex]

The transformations performed on f(x) to create g(x) is a reflection over the y-axis and a translation 4 units up.

An equation for g(x) in terms of f(x) is g(x) = f(-x) + 4.

In Mathematics and Geometry, a reflection over or across the y-axis or line x = 0 is represented and modeled by this transformation rule (x, y) → (-x, y).

By applying a reflection over the y-axis to coordinate A of the image ABCD, we have the following:

(x, y)                               →              (-x, y)

Coordinate = (-1, 1/10)   →  Coordinate A' = (-(-1), 1/10) = (1, 1/10).

Furthermore, the transformation rule for the translation of a point by k units up is given by;

(x, y + k)         →  (x', y')

(1, 1/10 + k)       →  E(1, 4 1/10)

1/10 + k = 4 1/10

k = 4 1/10 - 1/10

k = 4.

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If lakeside is 7 miles due north of the airport, and Seaside is 5 miles due east of the airport, the distance between Lakeside and Seaside is approximately 8.6 miles.

To find the distance between Lakeside and Seaside, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the distance between Lakeside and Seaside is the hypotenuse of a right triangle with legs of 5 miles and 7 miles.

To apply the Pythagorean theorem, we can square the lengths of the legs and then take the square root of their sum:

distance = √(5² + 7²)

distance = √(25 + 49)

distance = √74

distance ≈ 8.6 miles (rounded to the nearest tenth)

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The mean is 35 minutes and the median is 34 minutes.

let's first calculate the mean, median, and mode for Sarah's exercise times: 34, 30, 45, 30, 40, 38, and 28 minutes.

Step 1: Calculate the mean
Add up all the values and divide by the total number of values:
(34 + 30 + 45 + 30 + 40 + 38 + 28) / 7 = 245 / 7 = 35 minutes (rounded)

Step 2: Calculate the median
Arrange the values in ascending order: 28, 30, 30, 34, 38, 40, 45
There are 7 values, so the median is the middle value: 34 minutes

Step 3: Calculate the mode
Determine the value(s) that occur most often: 30 minutes (occurs twice)

Now, should Sarah use the mean or the median to show she exercises for large amounts of time each day? The mean is 35 minutes and the median is 34 minutes. Both values are close and represent the central tendency of the data. However, since the mean is slightly higher than the median, Sarah should use the mean (35 minutes) to show she exercises for a larger amount of time each day.

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a) equation will be 0.5x + 3 = 18.50

b)  equation will be (0.75x - 0.10x) + 3 = 21.00

a) Sydney made $18.50 selling lemonade.

she sold each cup for $0.50 and received a $3 tip from a neighbor.

let x be the cost of cup she sold.

equation will be 0.5x + 3 = 18.50

b) Daria made a profit of $21.00 selling lemonade

she sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbor.

equation will be (0.75x - 0.10x) + 3 = 21.00

c) Sydney don't have to pay for the cups used while Daria paid.

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A. An equation to represent the situation in part A is 18.50 = (0.50) x + 3.

B. An equation to represent the situation in part B is 21.00 = (0.75) y - (0.10) y + 3.

C. The equations differ in the fact that one accounts for the cost per cup while the other does not.

In general, the profit is defined as the amount gained by selling a product, which should be more than the cost price of the product.

Part A: Let x be the number of cups of lemonade sold.

Then, the total amount of money Sydney made is given by:

Total money = (selling price per cup) × (number of cups sold) + tip

Substituting the given values, we get:

18.50 = (0.50) x + 3

Part B: Let y be the number of cups of lemonade sold.

Then, the total profit made by Daria is given by:

Total profit = (selling price per cup) × (number of cups sold) + tip - (cost per cup) × (number of cups sold)

Substituting the given values, we get:

21.00 = (0.75) y - (0.10) y + 3

Part C: The equation for Sydney's lemonade stand only takes into account the total amount of money she made, which includes the selling price per cup and a fixed tip.

On the other hand, the equation for Daria's lemonade stand takes into account both the total profit made (which includes the selling price per cup and a fixed tip) and the cost per cup of lemonade sold. So, the equations differ in the fact that one accounts for the cost per cup while the other does not.

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Complete question is

Part A : Sydney made $18.50 selling lemonade, by the cup, at her yard sale. She sold each cup for $0.50 and received a $3 tip from a neighbour. Write an equation to represent this situation.

Part B : Daria made a profit of $21.00 selling lemonade. She sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbour, but also had to buy each plastic cup she used for $0.10 per cup. Write an equation to represent this situation.

Part C: Explain how the equation from part A and part B differ.

The surface area of the first triangular prism is 174.58 square feet and second triangular prism is 1721.6 square feet.

To calculate the surface area of a triangular prism, we need the measurements of the base and the height of the triangular bases, as well as the length of the prism.

For the first triangular prism with measurements:

Base: 5 ft

Height: 8 ft

Length: 6 ft

To calculate the surface area, we need to find the areas of the two triangular bases and the three rectangular faces. The formula for the surface area of a triangular prism is:

Surface Area = 2 * (Area of triangular base) + (Perimeter of triangular base * Length)

The area of a triangle can be calculated using the formula: Area = 1/2 * Base * Height.

Area of triangular base = 1/2 * 5 ft * 8 ft = 20 ft²

The perimeter of a triangle is the sum of its three sides.

Perimeter of triangular base = 5 ft + 8 ft + √(5 ft² + 8 ft²) = 5 ft + 8 ft + √89 ft ≈ 5 ft + 8 ft + 9.43 ft ≈ 22.43 ft

Surface Area = 2 * 20 ft² + (22.43 ft * 6 ft) = 40 ft² + 134.58 ft² = 174.58 ft²

Therefore, the surface area of the first triangular prism is approximately 174.58 square feet.

For the second triangular prism with measurements:

Base: 6 ft

Height: 2.5 ft

Length: 115 ft

Area of triangular base = 1/2 * 6 ft * 2.5 ft = 7.5 ft²

Perimeter of triangular base = 6 ft + 2.5 ft + √(6 ft² + 2.5 ft²) = 6 ft + 2.5 ft + √40.25 ft ≈ 8.5 ft + 6.34 ft ≈ 14.84 ft

Surface Area = 2 * 7.5 ft² + (14.84 ft * 115 ft) = 15 ft² + 1706.6 ft² = 1721.6 ft²

Therefore, the surface area of the second triangular prism is approximately 1721.6 square feet.

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The surface area of the triangular prism is x - 0 = -3

If the solution to an absolute value equation is x = -3, then we know that the distance between x and 0 is 3 units. Since the absolute value of a number is the distance between the number and 0 on the number line, we can write the absolute value equation that corresponds to x = -3 as:

| x - 0 | = 3

To write this equation in the form x - b = c, we can simplify the absolute value expression by removing the absolute value bars. This gives us two possible equations:

x - 0 = 3 or x - 0 = -3

Simplifying further, we get:

x = 3 or x = -3

Therefore, the absolute value equation in the form x - b = c that has the solution set {x = -3} is:x - 0 = -3

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Answer:

make me brainalist

Step-by-step explanation:

34.16

[tex] \frac{3416}{100} [/tex]

The square root of the sample size (n=37), which is approximately 0.820 seconds:

X ~ N(8, 5/√37)

The sample distribution of the mean, denoted as X, is the distribution of all possible sample means of a certain sample size taken from a population. In this case, we have a population of couples in conflict, and we have a sample size of 37. The mean length of time couples in conflict listen to each other is known to be 8 seconds with a standard deviation of 5 seconds.

Since we have a large enough sample size (n=37), we can assume that the sample mean follows a normal distribution according to the Central Limit Theorem. The Central Limit Theorem states that the sample means from a large enough sample size will be approximately normally distributed regardless of the population distribution, given that the samples are independent and randomly selected.

Thus, the sample distribution of X can be represented by a normal distribution with a mean of 8 seconds (same as the population mean) and a standard deviation of 5 seconds divided by the square root of the sample size (n=37), which is approximately 0.820 seconds:

X ~ N(8, 5/√37)

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Answer:

Step-by-step explanation:

(2-5)3=-9. (-9)5 =-45

The solution for the given linear expression is 11.25 (45/4).

A linear expression can be represented by a line. The standard form for this equation is: y=mx+b , for example, y=11x+9. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=11 and b=9.

The question gives the expression:7z+9z+7-7 =180. Then, you should find the variable z.

7z+9z+7-7 =180

16z+0=180

16z=180

z=180/16=90/8=45/4=11.25

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The mean of a single roll is given as μ = 3.5, and the variance is given as [tex]σ^2[/tex] = 2.92.

The sample size for the first five rolls is n1 = 5, and the sample size for the remaining ten rolls is n2 = 10.

The mean of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:

μ(x¯1−x¯2) = μ(x¯1) - μ(x¯2) = μ - μ = 0

The variance of the sampling distribution of the difference in sample means x¯1−x¯2 is given as:

σ^2(x¯1−x¯2) = (σ^2(x¯1)/n1) + (σ^2(x¯2)/n2)

where σ^2(x¯1) is the variance of the sample mean for the first five rolls and σ^2(x¯2) is the variance of the sample mean for the remaining ten rolls.

Since each roll of the die is independent, the variance of the sample mean for each sample is given as:

σ^2(x¯1) = σ^2/ n1 = 2.92/5 = 0.584

σ^2(x¯2) = σ^2/ n2 = 2.92/10 = 0.292

Substituting these values in the above equation, we get:

σ^2(x¯1−x¯2) = (0.584/5) + (0.292/10) = 0.1468

Therefore, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is:

σ(x¯1−x¯2) = sqrt(σ^2(x¯1−x¯2)) = sqrt(0.1468) = 0.3835 (rounded to four decimal places)

Hence, the standard deviation of the sampling distribution of the difference in sample means x¯1−x¯2 is 0.3835.

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Answer:

Step-by-step explanation:

Rounded percent of change = 500.0% Therefore, the percent of change is an increase of 500.0%.

I think sorry if I’m wrong

Hi there! Your question involves Ms. Castellano filling containers with strawberries, weighing them, and then sorting them by weight. To better assist you, I would need more information such as the line plot or the specific question you have about this process. Please provide the necessary details so I can help you with your question.

Based on the information you provided, it seems that Ms. Castellano is filling small containers with strawberries from a large basket. After filling each container, she weighs it and records its weight in pounds. She then sorts the containers by weight.

The line plot shows the number of containers at each weight, which can be helpful for analyzing the data. It sounds like Ms. Castellano is doing a careful job of tracking the weight of each container, which will likely help her make informed decisions about the strawberries she's working with.

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The radius of circle A is 4.

From the given information, we can draw a right triangle ABC where BC is the tangent to circle A at point C, AB is the hypotenuse, and AC is the radius of the circle. By the Pythagorean theorem, we have:

AC² + BC² = AB²

Substituting the given values, we get:

AC² + 3² = 5²

AC² = 25 - 9

AC² = 16

Taking the square root of both sides, we get:

AC = 4

Therefore, the length of the radius of circle A is 4.

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The resultant component of the vector addition is (-9, 0).

The resultant component of the vector is calculated as follows;

a = (-9, 6)

b = (3, 1)

The result of 1/3a = ¹/₃ (-9), ¹/₃(6) = (-3, 2)

The result of 2b = 2(3, 1) = (6, 2)

The result of the vector addition is calculated as follows;

1/3a - 2b

= (-3, 2) - (6, 2)

= (-3 -6, 2 -2)

= (-9, 0)

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Answer:

push-up = 1 second

sit-up = 3 seconds

Step-by-step explanation:

let p represent the # of push-ups

let s represent the # of sit-ups

System of equations:

19p+8s=43

12p+12s=48

i'll eliminate s by multiplying the top equation by 3 and the bottom equation by -2

57p+24s=129

-24p-24s=-96

33p=33

p=1 second

now solve for s (i'll plug p into the 2nd equation)

12(1) + 12s=48

12s=36

s=3 seconds

The area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2 is 96π/5 square units.

To find the area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2, we can use the formula for surface area of revolution:
A = 2π ∫_a^b f(x) √(1+(f'(x))^2) dx
In this case, we need to first find the function y = f(x) that represents the curve. Using the given parametric equations, we can eliminate θ to get:
x = 6 cos^3 θ
x = 6 (1-sin^2 θ) cos^2 θ
y = 6 sin^3 θ
y = 6 (1-x/6)^(3/2)

So the function that represents the curve is y = 6 (1-x/6)^(3/2). Now we can use the formula for surface area of revolution:
A = 2π ∫_0^6 (6 (1-x/6)^(3/2)) √(1+(-3/4 (1-x/6)^(-1/2))^2) dx
A = 2π ∫_0^6 (6 (1-x/6)^(3/2)) √(1+9/16 (1-x/6)^(-1)) dx
A = 2π ∫_0^6 (6 (1-x/6)^(3/2)) √((25-9x)/(16(1-x/6))) dx
This integral can be evaluated using substitution and partial fractions. The final answer is:
A = 96π/5

Therefore, the area of the surface obtained by rotating the curve of parametric equations x = 6 cos^3 θ, y = 6sin^3 θ, 0 ≤ θ ≤ π/2 is 96π/5 square units.

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It would take approximately 7.62 years to reach $8000 if $5400 is invested in an account that pays 7% compounded continuously.

The formula for calculating the future value (FV) of an investment that is continuously compounded is FV = Pe^(rt), where P is the principal amount, r is the annual interest rate, and t is the time in years. In this case, P = $5400, r = 7% = 0.07, and FV = $8000. Substituting these values into the formula, we get:

$8000 = $5400e^(0.07t)

Dividing both sides by $5400 and taking the natural logarithm of both sides, we get:

ln(8000/5400) = 0.07t

Simplifying the left side of the equation, we get:

ln(4/3) = 0.07t

Solving for t, we get:

t = ln(4/3)/0.07 ≈ 7.62 years

Therefore, it would take approximately 7.62 years to reach $8000 if $5400 is invested in an account that pays 7% compounded continuously.

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The area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi is 0.

To find the area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi, we can use the following steps:

1. Determine the function: In this case, the function is y=sin(x).

2. Identify the interval: The interval is from x=0 to x=4pi.

3. Integrate the function over the given interval: We'll integrate y=sin(x) with respect to x from 0 to 4pi.

∫(sin(x) dx) from 0 to 4pi.

4. Find the antiderivative: The antiderivative of sin(x) is -cos(x).

-∫(cos(x) dx) from 0 to 4pi.

5. Apply the fundamental theorem of calculus: We'll evaluate the antiderivative at the upper limit (4pi) and subtract the antiderivative evaluated at the lower limit (0).

[-cos(4pi)] - [-cos(0)]

6. Calculate the values: cos(4pi) = 1 and cos(0) = 1.

[-1] - [-1]

7. Determine the area: The area is the difference between the values calculated in step 6.

[-1 - (-1)] = 0

The area of the region bounded by the curve y=sin(x) and the x-axis between x=0 and x=4pi is 0.

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The possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.

(a) Let A be the area of the square tile. The differential of A with respect to the side length x is dA/dx = 2x.

dA ≈ (dA/dx)dx

At the lower end of the possible range for x, we have:

x = 9 31/32 inches

dx = 1/32 inch

dA = (2x)(dx) = (2(9 31/32))(1/32) = 19/32 square inches

At the upper end of the possible range for x, we have:

x = 10 1/32 inches

dx = 1/32 inch

dA = (2x)(dx) = (2(10 1/32))(1/32) = 21/32 square inches

Therefore, the possible propagated error in computing the area of the square is between 19/32 and 21/32 square inches.

(b) The percent error in computing the area of the square is given by:

(percent error) = (error / actual value) x 100

(percent error) = [(21/32 - 100) / 100] x 100% = -79/1600 x 100% ≈ -4.94%.

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If sales increase by 66,000, income will increase by 220,000.00

Net operating income 37,200.00

The margin of safety is 14.01%

Statement showing Computations  

particulars Amount Per unit

Sales 628,000.00 40.00

Variable Expenses 439,600.00 28.00

Contribution Margin 188,400.00 $ 12.00

Fixed Expenses 151,200.00

Net operating income 37,200.00

'

1)  BEP in unit sales = 151,200/12 12,600.00

.BEP in sales $ = 12,600 * 40 504,000.00

2)  Total Contribution margin at BEP = Fixed costs 151,200.00

3)a Target Profit $ 64,800.00

Fixed Expenses 151,200.00

Desired Contribution 216,000.00

3b. No of units to be sold = 216,000/12 18,000.00

Sales 720,000.00

Variable Expenses 504,000.00

Contribution Margin 216,000.00

Fixed Expenses 151,200.00

Net operating income 64,800.00

4)  Margin of safety = 628,000.00-540,000.00 88,000.00

MOS in % = 88,000/6280001 14.01%

5)CM Ratio = 188,400/628,000 0.3

If sales increase by 66,000, income will increase by 220,000.00

66,000/0.3

=220,000.

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Option C is correct i.e. A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.

Given integers are m, n, p and q

And q ≠ 0 and p ≠ 0

A = m / p

B = n/ q

Adding A and B

A + B = m / p + n / q

A + B = (mq + np) / pq

as p ≠ 0 and q ≠ 0 so, pq ≠ 0

So, A + B = (mq + np) / pq is a rational number

Therefore, option C is correct i.e. A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.

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Given question is incomplete, the complete question is below:

Keisha's teacher gives her the following information:

• m, n, p, and q are all integers, and p≠ 0 and q≠0

•A= m/q and B= n/p

What conclusion can Keisha make?

A: A +B = (mp + nq)/pq, so the sum of a rational number and an irrational number is an irrational number.

B: A•B= (mp + nq)/pq, so the product of two irrational numbers is an irrational number.

C: A+B= (mp + nq)/pq, so the sum of two rational numbers is a rational number.

D: A•B= (mp + nq)/pq, so the product of two rational numbers is a rational number.​