A population of mussels in logistic growth went from 600 to 670 in a year, and the carrying capacity was 700. What was the r max for the mussel population?

Answer:

Below

Step-by-step explanation:

You are counting the number of SUBSETS

Example  set  {2,7}

  has subsets { }   {2}  {7}  {2,7}

The number of subsets given a set of 'n'  is   2^n

When you calculate the number of combinations of "r" objects taken from a group of "n" objects, you are counting the number of different ways you can choose "r" items from the "n" items without regard to their order (i.e. their arrangement does not matter).

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant. A combination is a method of picking elements from a collection when the order of selection is irrelevant. Assume we have three integers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set. A combination is a mathematical approach for determining the number of potential arrangements in a set of objects when the order of the selection is irrelevant. You can choose the components in any order in combinations. For example, if you have a group of 6 books and you want to know how many different combinations of 3 books you can choose, you would use the formula: C(6,3) = 6!/(3! * (6-3)!). The answer would be 20, meaning there are 20 different combinations of 3 books you can choose from the group of 6.

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a) The least-squares line is y = 0.0426x + 0.3426. b) The predicted difference is 0.426 mm/yr. c) The predicted corrosion rate is 1.223 mm/yr. d) The fitted values are 1.4641, 1.4286, 1.4962, 1.2214, 0.959, 0.8124, 0.8736, 0.663, 0.6426.

To compute the least-squares line for predicting corrosion from temperature, we need to find the equation of the line in the form y = mx + b, where y represents the corrosion rate and x represents the temperature.

First, let's calculate the means of temperature (x) and corrosion (y):

X = (26.6 + 26 + 27.4 + 21.7 + 14.9 + 11.3 + 15 + 8.7 + 8.2) / 9 = 17.1 (rounded to one decimal place)

Y = (1.58 + 1.45 + 1.13 + 0.96 + 0.99 + 1.05 + 0.82 + 0.68 + 0.49) / 9 = 1.057 (rounded to three decimal places)

Next, let's calculate the sums of squares:

SSxx = Σ\((x_{i}-X )^{2}\) = \((26.6-17.2)^{2}\) + \((26-17.2)^{2}\) + ... + \((8.2-17.2)^{2}\)

= 61.45 + 58.41 + ... + 77.01 = 676.71 (rounded to two decimal places)

SSxy = Σ(\(x_{i}\) - X)(\(y_{i}\) - Y) = (26.6 - 17.1)(1.58 - 1.057) + (26 - 17.1)(1.45 - 1.057) + ... + (8.2 - 17.1)(0.49 - 1.057)

= 11.01 + 8.91 + ... - 8.52 = 28.85 (rounded to two decimal places)

Now, let's calculate the slope (m) and y-intercept (b) of the least-squares line:

m = SSxy / SSxx = 28.85 / 676.71 = 0.0426 (rounded to four decimal places)

b = Y - m * X = 1.057 - 0.0426 * 17.1 = 0.3426 (rounded to four decimal places)

Therefore, the least-squares line for predicting corrosion from temperature is:

y = 0.0426x + 0.3426

b) To predict the difference in corrosion rates for two steel specimens whose temperatures differ by 10°C, we can use the slope (m) from the least-squares line.

Δy = m * Δx = 0.0426 * 10 = 0.426 (rounded to three decimal places)

Therefore, the predicted difference in corrosion rates is 0.426 mm/yr.

c) To predict the corrosion rate for steel submerged in seawater at a temperature of 20°C, we can substitute x = 20 into the equation of the least-squares line.

y = 0.0426 * 20 + 0.3426 = 1.2226 (rounded to three decimal places)

Therefore, the predicted corrosion rate is 1.223 mm/yr.

d) To compute the fitted values, we substitute each temperature value into the equation of the least-squares line to obtain the corresponding predicted corrosion rate.

Fitted value for 26.6°C: y = 0.0426 * 26.6 + 0.3426 = 1.4641

Fitted value for 26°C: y = 0.0426 * 26 + 0.3426 = 1.4286

Fitted value for 27.4°C: y = 0.0426 * 27.4 + 0.3426 = 1.4962

Fitted value for 21.7°C: y = 0.0426 * 21.7 + 0.3426 = 1.2214

Fitted value for 14.9°C: y = 0.0426 * 14.9 + 0.3426 = 0.959

Fitted value for 11.3°C: y = 0.0426 * 11.3 + 0.3426 = 0.8124

Fitted value for 15°C: y = 0.0426 * 15 + 0.3426 = 0.8736

Fitted value for 8.7°C: y = 0.0426 * 8.7 + 0.3426 = 0.663

Fitted value for 8.2°C: y = 0.0426 * 8.2 + 0.3426 = 0.6426

Therefore, the fitted values are:

1.4641, 1.4286, 1.4962, 1.2214, 0.959, 0.8124, 0.8736, 0.663, 0.6426

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Answer:

It's rounded to the whole, which is 6.

Step-by-step explanation:

The number where the digit 8 ten times larger that it is in the number 18 is B. 387.

Place value simply means the position of a number based on how it's written.

It's important that 8 in 18 is 8 units.

Also, it's important to note that 8 in 387 is 8 tens. This is 80.

Therefore, 8 × 10 = 80. This justifies the information. In conclusion, the correct option is B.

The complete information is written below.

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In which number is the digit 8 ten times larger that it is in the number 18?

A. 108

B. 387

C. 801

D. 1840

E. 8205

The upper control limit using 3σ for P-chart is approximately 0.0768.

A quality control program is being developed for computer hard-drivers, and we are to determine the upper control limit using 3σ for P-chart.

We are given that the mean fraction defective in the samples in the past has been 3%. We also know that there are 5 random samples, and a constant sample size of 120 is taken for each random sample.*

The upper control limit (UCL) for a P-chart is given by:UCL = p + 3σpwhere p is the estimated proportion defective and σp is the standard deviation of the proportion defective.

We can estimate p as the mean of the past proportion defective, which is 0.03. The variance of the proportion defective is given by:

σp² = p(1 - p)/nwhere n is the sample size.

Since the sample size is constant and equal to 120 for each of the 5 random samples, we have:

σp² = 0.03(1 - 0.03)/120 = 0.0002245σp = √0.0002245 = 0.014993

Using the formula for the UCL, we have:

UCL = 0.03 + 3(0.014993)≈ 0.0768

Therefore, the upper control limit using 3σ for P-chart is approximately 0.0768.Option (a) is correct.

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The height of the pyramid is 45 feet.

Using the formula

v= volumn

a= base area

h=height

V=A x h/3

Solving for h

h=3V

A=3X600/40=45ft

To find height, First, square the base area to find the bottom area. Then, divide the known extent by way of the bottom location. finally, multiply the obtained quotient with the height of three to get the pyramid height.

The peak of a rectangular-primarily based pyramid the usage of your expertise of algebra. H = V / (L x W) / three

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The expression equivalent to t is:t = (3p * y)/(2x)

To find the expression equivalent to t, we can manipulate the given equation:

(x)/(y) = (3p)/(2t)

Cross-multiplying, we get:

2t * (x) = (3p) * (y)

Dividing both sides by 2(x), we have:

t = (3p * y)/(2x)

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Answer: Hard to say... Your image is a black Screen.

Answer:

what am i anwsering

Step-by-step explanation:

The decimal form of the expression is 8.095, and the word form is "eight plus nine hundredths plus five thousandths."

The expression (8 x 1) + (9 x 1/100) + (5 x 1/1000) can be simplified as follows:

(8 x 1) + (9 x 1/100) + (5 x 1/1000) = 8 + 0.09 + 0.005

In decimal form, the expression evaluates to 8 + 0.09 + 0.005 = 8.095.

In word form,in the given  the expression can be expressed as "eight plus nine hundredths plus five thousandths." This reflects the numerical values of each term in the expression.

Therefore, the decimal form of the expression is 8.095, and the word form is "eight plus nine hundredths plus five thousandths."

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For diagram and better understanding refer to the attachment.

Here

Now

As per we know

\(\\ \sf\longmapsto tanC=\dfrac{Perpendicular}{Base}\)

\(\\ \sf\longmapsto tan12=\dfrac{AB}{BC}\)

\(\\ \sf\longmapsto BC=\dfrac{AB}{tan12}\)

\(\\ \sf\longmapsto BC=\dfrac{50}{0.2125565616700}\)

\(\\ \sf\longmapsto BC\approx 235m\)

Answer:

Distance is approximately 240 meters

Step-by-step explanation:

» From trigonometric ratios of tan:

\({ \tt{ \red{ \sin( \theta) = \frac{opposite}{hypotenuse} }}} \\ \)

→ Opposite is height, 50 metres

→ Hypotenuse is d

\({ \tt{ \sin(12 \degree) = \frac{50}{d} }} \\ \\ { \tt{d = \frac{50}{ \sin(12 \degree) } }} \\ \\ { \boxed{ \tt{ \: d = 240.458 \approx240 \: m}}}\)

The value of g is g = w² - 14w + 49, according to the question.

What do you mean by formula?

A truth or a rule expressed using mathematical symbols is the formula. An equal sign is typically used to connect two or more values. When you are aware of the value of one quantity, you can use the formula to determine the value of the other. It facilitates speedy question resolution. Formulas are used in algebra, geometry, and other subjects to speed up and simplify the process of arriving at the result.

According to the given question,

We have :

w = 7 - √g

Firstly isolate the g,

w = 7 - √g

Do the opposite of PEMDAS, first subtract 7 from both sides,,

w (-7) = -√g + 7 (-7)

w - 7 = -√g

Now, multiply -1 (as -√g is the same as -1√g) to both sides

-1(w - 7) = √g

-1w + 7 = √g

To get rid of the square root, you must square both sides,

Note: -1w is the same as -w.

Note: you are squaring all the terms on the other side, not just one.

(-w + 7)² = (√g)²

g = (-w + 7)²

g = (-w + 7)(-w + 7) (note, this can be the answer your teacher wants, or                                            g = (-w + 7)²    )

Use the FOIL method (First, Outside, Inside, Last)

(-w)(-w) = w²

(-w)(7) = -7w

(7)(-w) = -7w

(7)(7) = 49

g = w² - 7w - 7w + 49

Then, simplify (combine all like terms):

g =w² - 7w - 7w + 49

g = w² - 14w + 49

Therefore, the value of g = w² - 14w + 49 .

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The open intervals on which f(x) is concave up are (-1/√6, 1/√6) and the open intervals on which f(x) is concave down are (-∞, -1/√6) and (1/√6, ∞). The x-coordinates of the inflection points are x = ±1/√6.

To determine where f(x) is concave up or down, we need to find the

second derivative of f(x) and examine its sign. The second derivative of

f(x) is:

\(f''(x) = -18x^2 + 3\)

To find the intervals where f(x) is concave up, we need to solve the

inequality:

f''(x) > 0

\(-18x^2 + 3 > 0\)

Solving this inequality, we get:

\(x^2 < 1/6\)

-1/√6 < x < 1/√6

Therefore, f(x) is concave up on the interval (-1/√6, 1/√6).

To find the intervals where f(x) is concave down, we need to solve the inequality:

f''(x) < 0

\(-18x^2 + 3 < 0\)

Solving this inequality, we get:

\(x^2 > 1/6\)

x < -1/√6 or x > 1/√6

Therefore, f(x) is concave down on the intervals (-∞, -1/√6) and (1/√6, ∞).

To find the inflection points, we need to find the x-coordinates where the

concavity changes, i.e., where f''(x) = 0 or is undefined.

From \(f''(x) = -18x^2 + 3\), we see that f''(x) is undefined at x = 0. At x = ±1/

√6, f''(x) changes sign from positive to negative or vice versa, so these

are the inflection points.

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Answer:

Negative Correlation:

Linear relationship

Explanation:

We can draw the line of best fit through the points given, and this indicates that the relationship is linear. Furthermore, the line of best fit has a negative slope (which tells us that if one variable increases, the other decreases); therefore, the data set has a negative correlation

The value of all the missing angles is in the measure of m∠1 = 88°, m∠2 = 42°, and m∠3 = 113°.

We know that,

Sum of all angles of triangle = 180°.

Therefore, m∠3 + 42° + 25° = 180°.

m∠3 = 180° - 67°

m∠3 = 113°

Vertical angles: Vertical angles are the angles that are opposite to each other when two lines cross.

We know that,

Vertical or opposite angles have equal measures.

So, 42° and m∠2 are vertical or opposite angles.

Therefore, the value of m∠2 = 42°.

Similarly, for m∠3, We know that,

Sum of all angles of triangle = 180°.

∴ ∠1 + ∠2 + 50° = 180°.

=> ∠1 + 42° + 50° = 180°

=> m∠1 = 88°.

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Answer:

434 sweatshirts were sold

Step-by-step explanation:

$2,170/$5 = 434

Answer:

see explanation

Step-by-step explanation:

the perimeter (P) is the sum of the 3 sides of the triangle.

P = 4x² + 1 + 26x + 6 + x² + 10x ← collect like terms

  = 5x² + 36x + 7

to factor the expression, consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 5 × 7 = 35 and sum = 36

the factors are + 35 and + 1

use these factors to split the x- term

5x² + 35x + 1x + 7 ( factor the first/second and third/fourth terms )

= 5x(x + 7) + 1 (x + 7) ← factor out (x + 7) from each term

= (x + 7)(5x + 1) , then

P = (x + 7)(5x + 1) ← in factored form

Answer: The correct answer is the second one

Step-by-step explanation:

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

--------------------------------------------------------

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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Applying Chebyshev's inequality, we find that P[A ≥ 30] is upper bounded by approximately 0.122, and applying Markov's inequality, we find that P[A ≥ 30] is upper bounded by 0.5.

To apply Chebyshev's inequality and Markov's inequality to upper bound the probability P[A ≥ 30], where A is the number of heads obtained when flipping a biased quarter 50 times, we need to know the mean and variance of A.

The mean (μ) of A can be calculated as the product of the number of trials (n) and the probability of success (p). In this case, n = 50 (number of flips) and p = 0.3 (probability of heads):

μ = np = 50 * 0.3 = 15

The variance (σ^2) of A can be calculated as the product of the number of trials (n), the probability of success (p), and the probability of failure (q = 1 - p):

σ^2 = npq = 50 * 0.3 * (1 - 0.3) = 10.5

Now we can apply Chebyshev's inequality and Markov's inequality to bound the probability P[A ≥ 30]:

Chebyshev's Inequality:

For any positive value k, the probability that a random variable X deviates from its mean μ by at least k standard deviations is given by:

P(|X - μ| ≥ kσ) ≤ 1/k^2

In our case, we want to find the upper bound for P[A ≥ 30]. Using Chebyshev's inequality, we can set k = (|30 - μ|)/σ and find an upper bound for the probability:

k = (|30 - 15|) / sqrt(10.5) ≈ 2.89

Therefore, according to Chebyshev's inequality:

P[A ≥ 30] ≤ 1/2.89^2 ≈ 0.122

Markov's Inequality:

Markov's inequality provides an upper bound on the probability of a random variable exceeding a specific value by a positive factor:

P(X ≥ a) ≤ E(X) / a

In our case, we want to find the upper bound for P[A ≥ 30]. Using Markov's inequality, we have:

P[A ≥ 30] ≤ E(A) / 30

Since E(A) = μ = 15:

P[A ≥ 30] ≤ 15 / 30 = 0.5

Therefore, according to Markov's inequality:

P[A ≥ 30] ≤ 0.5

In summary, these inequalities provide bounds on the probability of obtaining at least 30 heads when flipping the biased quarter 50 times.

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9514 1404 393

Answer:

  C  none of the above

Step-by-step explanation:

We can simply drop the parentheses and collect terms.

  2r +(t +r) = 2r + t + r = (2r +r) +t

  = 3r +t

Answer:

To complete the square and rewrite the quadratic function y = x² + 7x + 3 in vertex form, we follow these steps:

Factor out the coefficient of x² from the first two terms:

y = 1(x² + 7x) + 3

Take half of the coefficient of x (which is 7 in this case) and square it. Add this value inside the parentheses, and subtract the same value multiplied by the coefficient of x² (which is 1) outside the parentheses to maintain the same value of the expression:

y = 1(x² + 7x + (7/2)² - (7/2)²) + 3

Simplify inside the parentheses by combining the first three terms using the square of the binomial formula (a + b)² = a² + 2ab + b²:

y = 1(x + 7/2)² - 1/4 + 3

Combine the constant terms to simplify:

y = 1(x + 7/2)² + 11/4

Therefore, the quadratic function y = x² + 7x + 3 can be written in vertex form as y = (x + 7/2)² + 11/4. The vertex is located at the point (-7/2, 11/4).

Hope This Helps!

The Rpm is 9000 and maximum Horsepower cannot be determined Finding the maximum of the function will help us determine the RPM at which the engine is producing the most horsepower.

To do it, we must calculate its derivative and set it to zero:

d(HP)/d(RPM) = 0.5 × (9000 - RPM)\(x^{-0.5}\)

When we solve for RPM by setting this equal to zero, we obtain:

0 = 0.5 × (9000 - RPM)\(x^{-0.5}\)

(9000 - RPM)\(x^{0.5}\) = 0

9000 - RPM = 0

RPM = 9000

So, at 9000 RPM, the most horsepower is produced. At this RPM, we only evaluate the function to determine the maximum horsepower:

HP = 0.5 × (9000 - RPM)\(x^{-0.5}\) × RPM\(x^{2}\)

HP = 0.5 × (9000 - RPM)\(x^{-0.5}\) × RPM\(x^{2}\) × 9000\(x^{2}\)

HP = 0.5 × (0)\(x^{-0.5}\) × 9000\(x^{2}\)

HP = 0.5 × infinity × 9000\(x^{2}\)

However, since infinity is not a mathematical concept, computations cannot use it. It indicates that as RPM near 9000, the engine's power output increases significantly, but the engine's maximum horsepower cannot be precisely measured.

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The evaluation of the segment formed by the parallel lines using Thales Theorem also known as the triangle proportionality theorem are;

8. \(\overline {ST}\) is parallel to \(\overline{PR}\)

9. \(\overline{ST}\) is parallel to \(\overline{PR}\)

10. \(\overline{ST}\) is not parallel to \(\overline{PR}\)

11. x = 57.6

12. x = 25.8

13. x = 11

14. x = 10

15. x = 5

16. x = 17

Thales Theorem also known as the triangle proportionality theorem states that a parallel line to a side of a triangle that intersects the other two sides of the triangle, divides the two sides in the same proportion.

8. The ratio of the sides the segment \(\overline{ST}\) divides the sides QR and QP of the triangle ΔPQR into are; 7/11.2 = 10/16 = 0.625

Therefore; according to the Thales theorem, \(\overline{ST}\) ║ \(\overline{PR}\)

9. The ratio of the sides the parallel side to the base divides the other two sides are;

33/41.8 = 15/19

45/(102 - 45) = 45/57 = 15/19

Therefore, \(\overline{ST}\) and \(\overline{PR}\) bisects \(\overline{QP}\) and \(\overline{QR}\) into equal proportions and therefore, \(\overline{ST}\) ║ \(\overline{PR}\)

10. The ratio of the sides the segment \(\overline{ST}\)  bisects the other two sides are;

24/57 and 19/38

24/57 ≠ 19/38, therefore \(\overline{ST}\) ∦ \(\overline{PR}\)

Second part; To solve for x

11. x/30 = 48/25

x = (48/25) × 30 = 57.6

x = 57.6

12. x/34.4 = (49 - 28)/28

x = 34.4 × (49 - 28)/28 = 25.8

x = 25.8

13. (2·x + 6)/52.5 = 32/60

(2·x + 6) = 52.5 × (32/60)

x = (52.5 × (32/60)) - 6)/2 = 11

x = 11

14. (x - 3)/21 = (x - 1)/27

27·x - 27 × 3 = 21·x - 21

27·x - 81 = 21·x - 21

6·x = 60

x = 60 ÷ 6 = 10

x = 10

15. (35 - 20)/20 = (4·x - 2)/(7·x - 11)

15/20 = (4·x - 2)/(7·x - 11)

15 × (7·x - 11) = 20 × (4·x - 2)

105·x - 165 = 80·x - 40

105·x - 80·x = 165 - 40 = 125

25·x = 125

x = 125/25 = 5

x = 5

16. (x - 3)/35 = 4/(x - 7)

(x - 3) × (x - 7) = 35 × 4 = 140

x² - 10·x + 21 = 140

x² - 10·x - 119 = 0

(x - 17) × (x + 7) = 0

x = 17 or x = -7

Therefore, the possible value of x is 17

x = 17

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The surface integral S[vz ds over the surface S is equal to 8π/7. The surface integral represents the flux of the vector field vz across the surface S.

To evaluate the surface integral, we need to parameterize the surface S in terms of two variables, typically denoted by u and v. In this case, we can use the cylindrical coordinates (v, θ, z) to parameterize the surface. Using the equation v = √(8z + 2), we can rewrite it in terms of v as v = √(8v^2 + 2), which simplifies to 8v^2 = v^2 - 2. Solving for v, we get v = ±√(2/7). Since we are dealing with a cone, we consider the positive root, so v = √(2/7). Next, we determine the limits for θ and z. Given that 0 ≤ θ ≤ 2π, the limits for θ remain the same. For z, we have 0 ≤ z ≤ 2 as stated in the problem. The differential area element ds in cylindrical coordinates is given by ds = r dv dθ, where r represents the radius. In this case, r = v. Now, we can set up the surface integral as ∫∫S vz ds = ∫∫S v^2 r dv dθ. Substituting the values of v, θ, and the limits, the integral becomes ∫[0,2π]∫[0,2] (√(2/7))^2 v dv dθ.

Simplifying the integrand, we have ∫[0,2π]∫[0,2] (2/7) v dv dθ.

Evaluating the inner integral with respect to v, we get ∫[0,2π] [(1/7)v^2] |[0,2] dθ = ∫[0,2π] (4/7) dθ. Finally, evaluating the outer integral with respect to θ, we have (4/7)θ |[0,2π] = (4/7)(2π - 0) = 8π/7.

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Answer:

75 minutes or 1 hour and 15 minutes

Step-by-step explanation:

15·5=75

Answer:

3 min's per question

Step-by-step explanation:

Answer:

96% percent and fraction is 24/25

Answer: Down below

Step-by-step explanation:

64 % = 16 / 25

21 / 50 = 0. 42

9 / 25 = 36 %

2 / 5 = 40 %

/ = divide okay

A rock that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge is a(n)  ventifact:

A rock refers to the solid portion of the earth crust which contains minerals. There are three types of rocks; The sedimentary rock: They are formed from dead plants, dead animals, sand etc.

The metamorphic rock: They are formed from previously existing rocks. The igneous rock: They are formed from the solidification of the molten magma.

Hence, ventifact are rock  that has been significantly reshaped on multiple surfaces by windborne particles and sometimes has a sharp edge.

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The formula for the uncertainty of x, Δx, can be derived using partial derivatives as follows:

Δx = √((Δa/a)² + (Δb/b)² + (Δc/c)²)

To derive the formula for the uncertainty of x, Δx, we can use the concept of partial derivatives. The general formula for the uncertainty propagation of a function involving multiple variables is given by:

Δf = √((∂f/∂x₁)²Δx₁² + (∂f/∂x₂)²Δx₂² + ... + (∂f/∂xₙ)²Δxₙ²)

In this case, we have x = ab/c, and we want to find Δx. We can assign x as a function of a, b, and c:

f(a, b, c) = x = ab/c

To find Δx, we need to calculate the partial derivatives (∂f/∂a), (∂f/∂b), and (∂f/∂c) and substitute them into the general formula.

∂f/∂a = b/c

∂f/∂b = a/c

∂f/∂c = -ab/c²

Now, we can substitute these partial derivatives into the uncertainty propagation formula:

Δx = √((∂f/∂a)²Δa² + (∂f/∂b)²Δb² + (∂f/∂c)²Δc²)

= √((b/c)²Δa² + (a/c)²Δb² + (-ab/c²)²Δc²)

= √((b²Δa² + a²Δb² + a²b²Δc²)/c²)

= √((a²b²Δc² + b²Δa² + a²Δb²)/c²)

Simplifying further, we get:

Δx = √(a²b²Δc² + b²Δa² + a²Δb²)/c

Thus, the formula for the uncertainty of x, Δx, is:

Δx = √(a²b²Δc² + b²Δa² + a²Δb²)/c

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Answer

linear

nonproportional

Step-by-step explanation:

Since for each equal change in time (1 week), there is an equal change in weight (5 lb), the situation is linear.

At time zero, the first week, the weight was not zero. It was 60 lb, so it is not proportional.

Answer:

linear

nonproportional

Answer:

87.29,,,,,,,,

Step-by-step explanation:

87290 mm =87.29m