What is the approximate carrying capacity of the
population?

In which year, did the population reach the carrying capacity?

About how many years did it stay at carrying capacity?

The probability that the sample mean will be between 8 and 14 is approximately 0.785 or 78.5%. The 15th percentile of the population is 2.57.

To find the probability that the sample mean will be between 8 and 14, we need to calculate the standard error of the mean (SEM) first. The SEM is the standard deviation of the sampling distribution of the mean, and it is given by the formula SEM = σ/√n, where σ is the population standard deviation and n is the sample size.

In this case, σ = 12 and n = 75, so SEM = 12/√75 ≈ 1.386.

Next, we need to standardize the sample mean using the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We do this by calculating the z-score for each endpoint of the interval:

z1 = (8 - 10) / 1.386 ≈ -1.441

z2 = (14 - 10) / 1.386 ≈ 2.882

We then use a standard normal distribution table or calculator to find the area under the curve between these two z-scores. Alternatively, we can use the formula for the cumulative distribution function (CDF) of the standard normal distribution:

P(-1.441 < Z < 2.882) ≈ Φ(2.882) - Φ(-1.441) ≈ 0.985 - 0.204 ≈ 0.785

So, the probability that the sample mean will be between 8 and 14 is approximately 0.785 or 78.5%.

To find the 15th percentile of the population, we use the inverse of the CDF of the standard normal distribution. That is, we find the z-score that corresponds to a cumulative probability of 0.15:

Φ(z) = 0.15

z ≈ -1.036

Finally, we use the formula for the sample mean in terms of the standard normal distribution to find the corresponding value in the original units:

X = μ + z(σ/√n)

X = 10 + (-1.036)(12/√75)

X ≈ 2.57

Therefore, the 15th percentile of the population is 2.57

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The surface area of the cuboid is 3.286 cm²

A cuboid is a solid shape or a three-dimensional shape.

Surface area is the amount of space covering the outside of a three-dimensional shape.

The surface area of a cuboid is expressed as;

SA = 2( lb + lh + bh)

length = 1 2/5 = 7/5

breadth = 5/8

height = 3/8

lb = 7/5 × 5/8 = 7/8

bh = 5/8 × 3/8 = 15/64

lh = 7/5 × 3/8 = 21/40

surface area =2( 7/8 + 15/64+21/40)

= 2( 0.875 + 0.234 + 0.525)

= 2( 1.634)

= 3.268 cm²

The surface area of the cuboid is 3.268 cm²

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The solution to the linear system is unique solution which is  x₁ = 1/6, x₂ = 3/2, and x₃ = 17/6.

The correct answer is option  A.

To solve the given system of linear equations using elementary row operations and back substitution, let's start by representing the augmented coefficient matrix:

[1  -4  5  |  23]

[2   1   1  |  10]

[-3  2  -3 |  -23]

We'll apply row operations to transform this matrix into echelon form:

1. Multiply Row 2 by -2 and add it to Row 1:

[1  -4   5   |  23]

[0   9   -9  |  -6]

[-3  2  -3  |  -23]

2. Multiply Row 3 by 3 and add it to Row 1:

[1  -4  5   |  23]

[0   9  -9  |  -6]

[0   -10 6  |  -68]

3. Multiply Row 2 by 10/9:

[1  -4  5    |  23]

[0   1   -1   |  -2/3]

[0   -10 6  |  -68]

4. Multiply Row 2 by 4 and add it to Row 1:

[1  0   1   |  5/3]

[0  1   -1  |  -2/3]

[0  -10 6  |  -68]

5. Multiply Row 2 by 10 and add it to Row 3:

[1  0   1   |  5/3]

[0  1   -1  |  -2/3]

[0  0   -4  |  -34/3]

Now, we have the augmented coefficient matrix in echelon form. Let's solve the system using back substitution:

From Row 3, we can deduce that -4x₃ = -34/3, which simplifies to x₃ = 34/12 = 17/6.

From Row 2, we can substitute the value of x₃ and find that x₂ - x₃ = -2/3, which becomes x₂ - (17/6) = -2/3. Simplifying, we get x₂ = 17/6 - 2/3 = 9/6 = 3/2.

From Row 1, we can substitute the values of x₂ and x₃ and find that x₁ + x₂ = 5/3, which becomes x₁ + 3/2 = 5/3. Simplifying, we get x₁ = 5/3 - 3/2 = 10/6 - 9/6 = 1/6.

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Answer:

A. 38, 49, 60

Step-by-step explanation:

1. Find the difference between each number in the sequence

To go from -6 to 5, you add 11

To go from 5 to 16, you add 11

To go from 16 to 27, you add 11.

Therefore, the difference in all of the numbers is 11, so the pattern should continue and you should add 11 to the last number (27) making the next numbers 38, 49, 60

Answer:

so simplified it would be = (90-54w)

Step-by-step explanation:

Answer:

SP = (100-d%)/100 × MP

ans.12.36

Answer:

So, after 6 months, they both have the same number of coins.  

Step-by-step explanation:

Jack has 56 coins

Jill has 80 coins

Jack collect 12 coins per month

Jill collect 8 coins per month

Let after m months, they both have the same coin.

56 + 12 m = 80 + 8 m

12 m - 8 m = 80  - 56

4 m = 24

m = 6

So, after 6 months, they both have the same number of coins.  

Answer:

18 sides

Step-by-step explanation:

I'm not sure what the question is, but this is what I think the question is.

"An interior angle of a regular polygon measures 160 degrees. How many sides does the polygon have?"

The sum of the measures of the interior angles of a polygon of n sides is

(n - 2)180

If the polygon is a regular polygon, then the measure of each interior angle is

(n - 2)180/n

Here, we are told an interior angle measures 160 deg.

(n - 2)180/n = 160

(n - 2)180 = 160n

(n - 2)18 = 16n

(n - 2)9 = 8n

9n - 18 = 8n

n = 18

Answer: 18 sides

Answer:

2/65

Step-by-step explanation:

trust me

The probability that Sam picks two blue pens is,

⇒ 5 / 26

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

A box has 26 pens —6 red, 8 green, 5 blue, and 7 black.

Here, Sam picks two pens at a time without replacement.

Hence, We get;

The probability that Sam picks two blue pens is,

⇒ P =  5 / 26

Thus, The probability that Sam picks two blue pens is,

⇒ 5 / 26

\

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The variance of a sample is 4,096. And for interquartile, the difference between the largest and smallest values. The correct answer is option D

To calculate the variance we have a small formula:

v=s^2-----(1)

v=variance

s=Standard deviation

so, given that s=64

substitute in equation(1)

v=64*64

v=4096.

variance: The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean.

Variance is denoted by a symbol: σ2.

Interquartile range (IQR) is a measure of statistical dispersion, which is used to spread the data. The IQR is also called midspread.

To calculate the IQR, the data set is divided into quartiles. These quartiles are denoted by Q1 (another name is the lower quartile), Q2 (the median), and Q3 (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = Q3 −  Q1

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The possible amount of time for which they could rent the meeting room is 1, 2, and 3 hours.

In the question,

It is given that,

Reservation fee is $49.

Additional fee is $5.80 per hour.

The math club can spend maximum of $72.20.

The inequality will be:

49 + 5.8*t < 72.20

5.8*t < 23.2

t < 4

Hence, the possible amount of time for which they could rent the meeting room is 1, 2, and 3 hrs.

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The present value (P) that needs to be invested to achieve a future value (A) of $5000.00 at a simple interest rate (R) of 14.0% after a time period (T) of 13 weeks is approximately $1773.05 (rounded to the nearest cent).

To calculate the present value, we use the formula P = A / (1 + R * T), where A is the future value, R is the interest rate, and T is the time period. Plugging in the given values, we get P = 5000 / (1 + 0.14 * 13). After evaluating this expression, the result is approximately $1773.05.

Therefore, in order to have a future value of $5000.00 with a simple interest rate of 14.0% after 13 weeks, one would need to invest approximately $1773.05.

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Answer:are you fr bro??

1.true

2.true

3.true

4.true

5.true

6.true

7.true

8.true

9.y=2

10.true

11.true

12.y=1

Step-by-step explanation:

1. 5x+12=5x+12

2.7x+12=7x+12

3.5x=5x

4.12y=12y

5.6y+12=6y+12

6.7x+6=7x+6

7.7y+10=7y+10

8.7x+4=7x+4

9.3+3y=13+y

2y=10

y=2

10.14y+13=14y+13

11.5x+1=5x+1

12.12y=12

y=1

Answer:y=10

Step-by-step explanation:u see the right side numbers increase by 7

Answer:

Step-by-step explanation:

According to quadratic formula:

y = - b  ±  √ b²- 4ac / 2a

y = - (-5) ± √ -5²- 4(2x-12) / 2(2)

y = 5 ± √ 25 - 4(-24) / 4

y = 5 ± √ 25 - (-96) / 4

y = 5 ± √ 121 / 4

y = 5 ± √ (11)² / 4

y = 5 ± 11 / 4

Now either,

y = 5 + 11 / 4

y = 4

Or,

y = 5 - 11 / 4

y = -3/2 = -1.5

The number in the exponential scientific form is A = 5.729 x 10⁸

Given data ,

Let the number be represented as A

Now , the value of A is

A = 572,900,000

On simplifying , we get

From the laws of exponents , we get

The exponential form of a number is a way of representing a number using exponents, where the base is typically a number greater than 1

So , the value of A is

When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

A = 5.729 x 10⁸

Hence , the scientific form is A = 5.729 x 10⁸

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The area of the circle is 12.56 square units whose radius is 2 meter.

The formula to find the area of a circle is A = πr²

where A represents the area of circle

r is the radius of the circle.

The radius is given as 2 meters.

Plug in the value of radius r in the area formula

A = π(2)²

We know that 2 square is 4

A = π(4)

A = 4π

We know that the value of π is 3.14

Plug in the π value

A=4×3.14

A=12.56 square units

Therefore, the area of the circle is 12.56 square units

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The set of side lengths that would form a triangle is Option C: 1.14 in, 1.41 in, and 2.55 in.

In order for a set of side lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Let's analyze each option:

Option A: 1.12 in, 1.25 in, 2.55 in 1.12 + 1.25 = 2.37, which is less than 2.55. Therefore, this set of side lengths does not form a triangle. Option B: 1.13 in, 1.40 in, 2.55 in 1.13 + 1.40 = 2.53, which is less than 2.55. Therefore, this set of side lengths does not form a triangle. Option C: 1.14 in, 1.41 in, 2.55 in 1.14 + 1.41 = 2.55, which is equal to 2.55. Therefore, this set of side lengths does form a triangle. Option D: 1.15 in, 1.45 in, 2.55 in 1.15 + 1.45 = 2.60, which is greater than 2.55. Therefore, this set of side lengths does form a triangle.

Based on the analysis, only Option C, with side lengths of 1.14 in, 1.41 in, and 2.55 in, would form a triangle.

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The graph of the system of equations:

Is the one in the bottom right.

Here we want to see which graph represents the system of equations:

So we have a linear equation that crosses the y-axis at y = 1, and a parabola that crosses the y-axis also at y = 1 (you can verify that by evaluating both equations in x = 0).

Only with that, we can conclude that the correct graph for the system of equations is the last one (bottom right graph)

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Answer:

x,y=(4, 15)

Step-by-step explanation:

We need to substitute the value of y=4x-1 and plug it into the equation 2x+y=23.

By this we get:

2x+4x-1=23

6x-1=23

6x=24

x=4

We can now solve for y using the given value of x.

2x+y=23

2×4+y=23

8+y=23

y=23-8

y=15

Hope this helps!

Answer:

x,y=(4, 15)

Step-by-step explanation:

We need to substitute the value of y=4x-1 and plug it into the equation 2x+y=23.

By this we get:

2x+4x-1=23

6x-1=23

6x=24

x=4

We can now solve for y using the given value of x.

2x+y=23

2×4+y=23

8+y=23

y=23-8

y=15

Step-by-step explanation:

The scale factor of your design is 1 / 6.

A scale factor is defined as the ratio between the scale of a given original object and a new object.

In other words, scale factor is the ratio between corresponding measurements of an object and a representation of that object.

Hence, you are in charge of creating a billboard advertisement that is 16 feet long and 8 feet tall. You make a scale drawing that is 32 inches wide and 16 inches high.

The scale factor of the design can be calculated as follows:

1 feet = 12 inches

8 feet  = 96 inches

96 inches  = 16 inches

1 inch = ?

cross multiply

scale factor = 16 / 96

scale factor =  2 / 12 = 1 / 6

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Answer:

B. 3^(-5) and D. 2^5 × 6^(-5)

Step-by-step explanation:

Recall that \(\displaystyle\\x^{-n}=\frac{1}{x^n}\)

Manipulating, we get:

\(\displaystyle \\\frac{2^5}{6^5}=\left(\frac{2}{6}\right)^5=\left(\frac{1}{3}\right)^5=\boxed{\text{B. }3^{-5}}=2^5\cdot \frac{1}{6^5}=\boxed{\text{D. }2^5\cdot 6^{-5}}\)

⇒Answer choices B and D

Answer:

(B) 3^-5 and (D) 2^5 . 6^-5

Step-by-step explanation:

Answer : a ) Variance = (21 - 6.5)^2/12 = 13.7708, b) 1, 21 <= x, c) Probability = 0.5862, D) Probability = 0.8552

The uniform distribution on the interval (6.5, 21) can be represented as U(6.5, 21).
(a) The mean and variance of a uniform distribution can be calculated using the following formulas:
Mean = (a + b)/2
Variance = (b - a)^2/12
where a and b are the lower and upper bounds of the distribution, respectively.
For the given distribution, a = 6.5 and b = 21.
Therefore, the mean and variance of depth are:
Mean = (6.5 + 21)/2 = 13.75
Variance = (21 - 6.5)^2/12 = 13.7708

(b) The cdf of a uniform distribution can be calculated using the following formula:
F(x) = (x - a)/(b - a)
For the given distribution, F(x) = (x - 6.5)/(21 - 6.5) for 6.5 <= x < 21.
Therefore, the cdf of depth is:
F(x) = {
0, x < 6.5
(x - 6.5)/14.5, 6.5 <= x < 21
1, 21 <= x

(c) The probability that observed depth is at most 10 can be calculated using the cdf:
P(X <= 10) = F(10) = (10 - 6.5)/14.5 = 0.2414
The probability that observed depth is between 10 and 15 can be calculated using the cdf:
P(10 <= X <= 15) = F(15) - F(10) = (15 - 6.5)/14.5 - (10 - 6.5)/14.5 = 0.5862

(d) The standard deviation of a uniform distribution can be calculated using the following formula:
Standard deviation = sqrt(Variance)

For the given distribution, the standard deviation is:
Standard deviation = sqrt(13.7708) = 3.7118
The probability that the observed depth is within 1 standard deviation of the mean value can be calculated using the cdf:
P(13.75 - 3.7118 <= X <= 13.75 + 3.7118) = F(13.75 + 3.7118) - F(13.75 - 3.7118) = (13.75 + 3.7118 - 6.5)/14.5 - (13.75 - 3.7118 - 6.5)/14.5 = 0.5118
The probability that the observed depth is within 2 standard deviations of the mean value can be calculated using the cdf:
P(13.75 - 2*3.7118 <= X <= 13.75 + 2*3.7118) = F(13.75 + 2*3.7118) - F(13.75 - 2*3.7118) = (13.75 + 2*3.7118 - 6.5)/14.5 - (13.75 - 2*3.7118 - 6.5)/14.5 = 0.8552

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Answer:

The answer is -11(3x-1)

Step-by-step explanation:

Thats what the calculator said

Hope this helps!!!

The value of x in the equation given as x - 2(x - 6) = -x + 12 is 0

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the equation is given as

x - 2(x - 6) = -x + 12

Open the bracket

So, we have

x - 2x + 12 = -x + 12

Evaluate the like terms

So, we have

x - 2x = -x

This gives

x = 0

Hence, the solution of x in the equation is 0

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Answer:

\(h^-^1(x)=0.5x+1.5\)

Step-by-step explanation:

Finding the inverse of a function is similar to solving for the complete opposite of a function. An easy trick to do so is the think of the resulting value (h(x)) as another variable. Solve the equation for (x) in terms of (h(x)). Finally, switch the variable and evalutator so that one has the funciton in inverse function notation.

\(h(x) = 2x - \frac{4}{3}\)

Inverse operations,

\(h(x)=2x-\frac{4}{3}\\\\h(x)+\frac{4}{3}=2x\\\\\frac{h(x)+\frac{3}{4}}{2}=x\)

Simplify,

\(0.5(h(x))+1.5=x\)

Write in inverse function notation,

\(h^-^1(x)=0.5x+1.5\)

Answer:

Im not entirely sure but I think its C. 7 to 9

Answer:

8 and -10

Step-by-step explanation:

B. x = 8 and x = -10

To find the area of the surface z = 5 + 5x + 3y^2 above the triangle with vertices (0, 0), (0, 1), and (2, 1), we need to use the surface integral formula.

First, calculate the partial derivatives with respect to x and y:
∂z/∂x = 5
∂z/∂y = 6y

Now, compute the magnitudes of the cross product of the gradient vectors:
|∂z/∂x × ∂z/∂y| = √((5^2) + (6y)^2) = √(25 + 36y^2)

The area of the surface can be found using the double integral of the magnitudes over the triangle:
Area = ∬(√(25 + 36y^2)) dA

We'll use the triangle's vertices to set the integration limits for x and y:
x: 0 to 2 - y
y: 0 to 1

Area = ∫(y=0 to 1) ∫(x=0 to 2-y) (√(25 + 36y^2)) dx dy

Evaluating this integral will provide the area of the surface above the given triangle.

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