A population of sea turtles is growing at a rate of 3% on North Carolina's coast due to great protection
programs on the beaches. If there are currently 3,000 sea turtles, how many years will it take for the
population to double?

Answer:

length x width = area

14 x 11 = 154

154 / 22 = 7 fertilizer needed

Hope this helps

Step-by-step explanation:

Answer:

Step-by-step explanation:

x = -35,814 ft ⋅ (1 sec)/(-4 ft) = 8,953.5 sec

The required model suggests that it would take approximately 8957.5 seconds for DeepSea Challenger to reach the bottom.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

To find the time it takes for the DeepSea Challenger to reach the bottom, we need to find the value of x when y = -35,814 ft.

We can substitute the desired depth into the equation y = -4x:

-35,814 = -4x

35,814 = 4x

x = 35,814 / 4

x = 8953.5 seconds

So, the model suggests that it would take approximately 8957.5 seconds for DeepSea Challenger to reach the bottom.

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With Alpha set to .05, increasing the sample size would not directly reduce the probability of a Type I error. The probability of a Type I error is determined by the significance level (Alpha) and remains constant regardless of the sample size.

However, increasing the sample size can indirectly affect the probability of a Type I error by increasing the statistical power of the test. With a larger sample size, it becomes easier to detect a statistically significant difference between groups, reducing the likelihood of falsely rejecting the null hypothesis (Type I error).

Increasing the sample size generally decreases the probability of a Type II error, which is failing to reject a false null hypothesis. With a larger sample size, the test becomes more sensitive and has a higher likelihood of detecting a true effect if one exists, reducing the likelihood of a Type II error. However, it's important to note that other factors such as the effect size, variability, and statistical power also play a role in determining the probability of a Type II error.

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The ending balance is $1032.5.

What is simple interest?

Simple interest is an interest rate that is solely calculated on the principal amount or the portion of the principal that is still owed. It does not take compounding into account. Simple interest may be used on a schedule other than annually, such as every month, week, or even every day.

Here, we have

Given: P = $2,500, r = 5.9%, t = 7 years

Convert 5.9% to a decimal

5.9% = 5.9 ÷ 100

 = 0.059

Substitute the values into the simple interest formula,

I = Prt   and we get

I = Prt

= 2500 × 0.059 × 7

= $1032.5

Hence, the ending balance is $1032.5.

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Answer:

hey, i think it's the first alternative

Step-by-step explanation:

1.The decimal number 124 is equivalent to the binary number 1111100. 2.The binary number 01110111 is equivalent to the decimal number 119. 3.The binary calculation of 10111 + 11001 + 01110 equals 111010.

1.To convert the decimal number 124 into binary, we divide the number by 2 repeatedly until the quotient becomes 0. The remainders obtained from each division form the binary digits, with the last remainder being the least significant digit. Therefore, 124 in binary is 1111100.

2.To convert the binary number 01110111 into decimal, we multiply each digit by the corresponding power of 2 and sum the results. The leftmost digit has a power of 2 equal to the number of digits minus 1. Thus, 0 x 2^7 + 1 x 2^6 + 1 x 2^5 + 1 x 2^4 + 0 x 2^3 + 1 x 2^2 + 1 x 2^1 + 1 x 2^0 equals 119 in decimal.

3.To perform the binary calculation 10111 + 11001 + 01110, we add each corresponding bit from right to left, carrying over any excess from the previous addition. The result is 111010, which is the binary representation of the sum of the three numbers.

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To factor out the greatest common factor of the expression 9-12x+6y, we need to identify the greatest common factor of all three terms. The numbers 9, 12, and 6 have a common factor of 3, and the variables x and y have no common factors. Therefore, we can factor out 3 from each term using the distributive property.

9-12x+6y = 3(3-4x+2y)

This is the fully factored form of the expression, and we can see that the greatest common factor of all three terms is 3. By factoring out the greatest common factor, we simplify the expression and make it easier to work with.
To apply the distributive property and factor out the greatest common factor (GCF) of the terms in the expression 9 - 12x + 6y, follow these steps:

1. Identify the GCF of the coefficients (9, -12, and 6). The GCF is 3.
2. Factor out the GCF from each term: 3(3 - 4x + 2y).
3. The factored expression is now 3(3 - 4x + 2y).

By applying the distributive property and factoring out the GCF, we simplified the expression to its factored form, making it easier to work with in further calculations.

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The percent of those interviewed said they like orange juice for breakfast is 58%.

A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred. The term % refers to one hundred percent.

The percent of those interviewed said they like orange juice for breakfast will be:

= Orange juice taker /  Total respondent

= 29/50

= 0.58

= 58%

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Answer:

y-1=\(\frac{5}{6}\)(x+8)

Step-by-step explanation:

1. y-y1=m(x-x1) (point slope form)

2. y1 is the y of your given point and x1 is the x of your given point

3. m is the slope

The sampling distribution of the sample mean will be approximately normal due to the central limit theorem, even if the population is symmetric but not perfectly normal.

If the population is symmetric but not perfectly normal, the sampling distribution of the sample mean will still be approximately normal due to the central limit theorem. The central limit theorem states that regardless of the shape of the population distribution, as long as the sample size is sufficiently large (typically n > 30), the distribution of the sample mean will tend to be approximately normal.

This is because the sample mean is an average of individual observations, and the averaging process tends to smooth out any deviations from normality in the population. Therefore, even if the population is not perfectly normal, the sampling distribution of the sample mean will approach a normal distribution as the sample size increases.

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Answer:

Therefore, the length of the ladder is 13 feet.

Step-by-step explanation:

This is a classic example of a right triangle problem in geometry. The ladder serves as the hypotenuse of the triangle, while the distance from the building to the ladder and the height of the window serve as the other two sides. Using the Pythagorean theorem, we can solve for the length of the ladder:

ladder^2 = distance^2 + height^2 ladder^2 = 5^2 + 12^2 ladder^2 = 169 ladder = √169 ladder = 13

Therefore, the length of the ladder is 13 feet.

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The given system of differential equations is:

y1' = y1 + 3y2

y2' = 3y1 + y2

We need to verify that the functions:

y1(t) = c1e^(ut) + c2e^(-2t)

y2(t) = c1ue^(ut) - c2e^(-2t)

satisfy the system. In part (a), we find the value of each term in the equation y1' = y1 + 3y2 in terms of the variable f. In part (b), we find the value of each term in the equation y2' = 3y1 + y2 in terms of the variable f.

(a) To find the value of each term in y1' = y1 + 3y2, we differentiate y1(t) with respect to t. The derivative of c1e^(ut) is c1ue^(ut), and the derivative of c2e^(-2t) is -2c2e^(-2t). Thus, we have:

y1' = c1ue^(ut) - 2c2e^(-2t) + 3(c1ue^(ut) - c2e^(-2t))

Combining like terms, we get:

y1' = (2c1u + 3c1u)e^(ut) + (-2c2 - 3c2)e^(-2t)

(b) Similarly, we differentiate y2(t) with respect to t. The derivative of c1ue^(ut) is c1u^2e^(ut), and the derivative of c2e^(-2t) is -2c2e^(-2t). Thus, we have:

y2' = c1u^2e^(ut) - 2c2e^(-2t) + 3(c1e^(ut) + c2e^(-2t))

Combining like terms, we get:

y2' = (c1u^2 + 3c1)e^(ut) + (-2c2 + 3c2)e^(-2t)

Therefore, the value of each term in y1' = y1 + 3y2 is given by:

Term 1: (2c1u + 3c1)e^(ut)

Term 2: (-2c2 - 3c2)e^(-2t)

And the value of each term in y2' = 3y1 + y2 is given by:

Term 1: (c1u^2 + 3c1)e^(ut)

Term 2: (-2c2 + 3c2)e^(-2t)

These results verify that the functions y1(t) and y2(t) satisfy the given system of differential equations.

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hope you find this helpful. :D

Answer:

below

Step-by-step explanation:

-2(2x+6)=-3x

1. distribute

-4x-12=-3x

2. add 3x to both sides

-x-12=0

3. add 12 to both sides

-x = 12

4. divide both sides by -x or -1

-x/-1 = 12/-1

ANSWER : x = -12

Answer:

remainder = 2

Step-by-step explanation:

A polynomial f(x) is divided by (x - a) then the remainder is f(a)

Here f(x) = 4x³ - 5x² + 2x - 14 is divided by (x - 2) then remainder is f(2)

f(2) = 4(2)³ - 5(2)² + 2(2) - 14

      = 4(8) - 5(4) + 4 - 14

      = 32 - 20 - 10

      =  12 - 10

      = 2

The value of c that makes the given function a probability density function is 3/2.

A probability density function is a function that describes the likelihood of a random variable taking on a specific value within a given range.

In order for a function to be a probability density function, it must satisfy certain conditions, such as being non-negative and integrating to 1 over its domain.

In this problem, we are given a function:

c(5x - 4 - x²)if 1 ≤ x ≤ 4, and 0 otherwise.

We need to find the value of c that will make this function a probability density function. That means we need to check whether the function is non-negative and integrates to 1 over the interval [1, 4].

First, let's check whether the function is non-negative. Since c is a constant, we just need to look at the expression inside the parentheses.

For this expression to be non-negative, we need to find its roots:5x - 4 - x² = 0⇒ x² - 5x + 4 = 0⇒ (x - 1)(x - 4) = 0The roots are x = 1 and x = 4.

We can see that the expression inside the parentheses is negative between these two roots, and positive outside this interval.

Therefore, the function is only non-negative for values of x between 1 and 4.Next, let's check whether the function integrates to 1 over the interval [1, 4].

We can do this by evaluating the integral:

integral(1, 4, c(5x - 4 - x²)) = 1

We can simplify this expression by pulling the constant c outside the integral and then integrating the expression inside the parentheses:

integral(1, 4, 5x - 4 - x²) = 1

Using the power rule of integration, we get:

[(5/2)x² - 4x - (1/3)x³]1⁴ = 1

Simplifying this expression, we get:

(5/2)(4²) - 4(4) - (1/3)(4³) - (5/2)(1²) + 4(1) + (1/3)(1³) = 1

Solving for c, we get:

c = 3/2

So the value of c that makes the given function a probability density function is 3/2.

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Answer:

B

Step-by-step explanation:

The two lines will never intersect regardless of the distance they go

Answer:

B. AD parallel CB

Step-by-step explanation:

If angles F D C = G C H, that makes them corresponding angles.

The transversal being EH, so AD must be parallel to BC, or

alternatively, AD parallel CB.

Answer:

26

Step-by-step explanation:

Let jaya's age be a, so consecutive EVEN #s can be written as

a, a+2, a+4

sum = 84 = 3a +6

so 3a = 78

a=26

Answer:

A is -4, 6

Y is 4, 5

B is 7, -1

D is -8, -1

Answer:

D

B

Step-by-step explanation:

1. x² - 5x = 14

x² -5x -14 = 0

x² +2x -7x -14 = 0

x(x + 2) -7(x + 2) = 0

x - 7 or x + 2 = 0

x = 7 or x = -2

2. y² + 6y + 9 = 49

y² + 6y +9 -49 = 0

y² +6y -40 = 0

y² +10y -4y -40 = 0

y(y + 10) -4(y + 10) = 0

y -4 or y + 10 = 0

y = 4 or y = -10

Answer:

Step-by-step explanation:

5x^5 - 2x - 4x^4 - 3x^2

5x^5 - 4x^4 - 3x^2 - 2x

The pieces of cloth are beyond the standard at 0.05 level of significance.

We can use a one-sample t-test to determine if the mean length of the 35 pieces of cloth is significantly different from the standard length of 3.25 meters.

The null hypothesis is that the mean length of the cloth pieces is equal to the standard length:

H0: μ = 3.25

The alternative hypothesis is that the mean length of the cloth pieces is greater than the standard length:

Ha: μ > 3.25

We can calculate the test statistic as:

t = (x - μ) / (s / √n)

where x is the sample mean length, μ is the population mean length (3.25 meters), s is the sample standard deviation (0.52 meters), and n is the sample size (35).

Plugging in the values, we get:

t = (3.52 - 3.25) / (0.52 / √35) = 3.81

Using a t-table with 34 degrees of freedom (n-1), and a significance level of 0.05 (one-tailed test), the critical t-value is 1.690.

Since our calculated t-value (3.81) is greater than the critical t-value (1.690), we reject the null hypothesis and conclude that the mean length of the 35 pieces of cloth is significantly greater than the standard length at the 0.05 level of significance.

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Answer:

Nature : The phenomena of the physical world collectively, including plants, animals, the landscape, and other features and products of the earth, as opposed to humans or human creations. (according to Oxford Dictionary)

Answer:

MYSTREET AND MY INNER DEMONS YES

Step-by-step explanation:

watch them

Answer:

  j = -1

Step-by-step explanation:

Eliminate parentheses:

  -24 -3j = -16 +5j

Add 3j+16

  -8 = 8j

Divide by the coefficient of j.

  -1 = j

\(\rm⇢ \: \: - 3(8 + j) = - 16 + 5j\)

\(\rm⇢ \: \: - 24 - 3j = - 16 + 5j\)

\(\rm⇢ \: \: 5j + 3j = - 24 + 16\)

\(\rm⇢ \: \: 8j = - 8\)

\(\rm⇢ \: \: j = - 1\)

The absolute minimum amount of gold produced during the California gold rush was at t = 40 years (1888), with a production of G(40) ≈ 0.195 troy ounces.

A function's varied rate of change with respect to an independent variable is referred to as a derivative. When there is a variable quantity and the rate of change is irregular, the derivative is most frequently utilised.

To find the absolute maximum and minimum values of G(t) on the closed interval [0, 40], we need to first find the critical points and endpoints of G(t) on this interval.

Taking the derivative of G(t), we have:

G'(t) = (25(t² + 16) - 25t(2t))/ (t² + 16)²

     = 25(16 - t²) / (t² + 16)²

Setting G'(t) equal to zero, we get:

25(16 - t²) / (t² + 16)² = 0

Simplifying this expression, we have:

16 - t² = 0

This gives us t = ±4.

However, we need to check whether these critical points are actually maximum or minimum points, or neither.

We can do this by using the first derivative test, which involves checking the sign of G'(t) on either side of the critical points.

For t < -4, G'(t) < 0, indicating that G(t) is decreasing.

For -4 < t < 4, G'(t) > 0, indicating that G(t) is increasing.

For t > 4, G'(t) < 0, indicating that G(t) is decreasing.

Therefore, we can conclude that t = -4 is a local maximum point, and t = 4 is a local minimum point.

Next, we need to check the endpoints of the interval [0, 40].

At t = 0, G(0) = 0.

At t = 40, G(40) = 25(40) / (40² + 16) ≈ 0.195 troy ounces.

Comparing all of these values, we can see that the absolute maximum amount of gold produced during the California gold rush was at t = 4 years (1852), with a production of G(4) ≈ 1.562 troy ounces.

The absolute minimum amount of gold produced during the California gold rush was at t = 40 years (1888), with a production of G(40) ≈ 0.195 troy ounces.

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Answer:

-12

Step-by-step explanation:

Ok so I'm guessing that's a -4 but if its not, please correct me.

y= -5 is going to be plugged into 2y+2-4

This means that 2(-5)+2-4=?

2(-5) is the equivalent to 2 times -5, which is -10 (you solve multiplication first because order of operations)

Now, 2-4=-2

So using this, let's combine both equations!

-10+-2=?

?=-12

It's a lot of steps but they get easier the more you do them <3

Answer:

Buy 8 pack with £2.04 and buy 1 pack with £0.52 will be more value

Step-by-step explanation:

To calculate 1 roll:

2.04/4= £0.51

4.68/9= £0.52

(0.51+0.52)/2= £0.515 = £0.52 per roll

which pack is better value:

2.04 (4 pack) x2= £4.08 for 8 pack

4.08+0.52= £4.6 for 9 pack

£4.6<£4.68

Therefore, buy 8 pack with £2.04 and buy 1 pack with £0.52 will be more value.

Answer:

The answer is 90.

Thank you

Answer:

89.6

Step-by-step explanation:

The formula to convert Celsius to Fahrenheit is given by °F = °C × (9/5) + 32

F = [ C × (9/5) + 32 ]

Given that, C = 32

F = 32 × (9/5) + 32

F = 32 [ 1 + (9/5) ]

F = 32 [ 1 + 1.8 ]

F = 32 × 2.8

F = 89.6

Answer:

0,1,2,3 is the domain

-2,1,2,4 is the range

Answer: dy/dx|(x,y)=(18,19)

= -0.0275

The given equation is:

0.1x³ + 7xy + 7.7y³

= 55791.5

To find: Find dy/dx if

x = 18 and

y = 19.

Solution:Given, the equation: 0.1x³ + 7xy + 7.7y³

= 55791.5

We have to find the value of dy/dx when x = 18 and

y = 19.

Therefore, differentiating both sides with respect to x and using the Chain Rule, we get:

0.3x² + 7y dx/dx + 7x dy/dx + 23.1y² dy/dx

= 0

Now, we have to find the value of dy/dx when x = 18 and

y = 19.

At (18, 19), we get: 0.3(18)² + 7(19) (1) + 7(18) dy/dx + 23.1(19)² dy/dx

= 0⇒ 97.2 + 133 + 126 dy/dx + 8231.1 dy/dx

= 0⇒ 8359.1 dy/dx

= −230.2⇒ dy/dx

= −230.2 / 8359.1≈ −0.0275

Therefore, the value of dy/dx when x = 18 and y = 19 is approximately -0.0275.

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