Differentiate implicitly to find dy/dx. Then find the slope of the curve at the given point.

x2y - 2x2 - 8 = 0 : (2, 4)

if x =7 then plug in 7 for x

4(7) - 2((7)+a) = 8

28 - 14 -2a = 8

14 - 2a = 8

-2a = -6

a = 3

Answer:

Step-by-step explanation:

Darwin's geometric ratio of increase pertains specifically to the growth rate of populations in biological organisms. According to Darwin's theory of evolution, populations have the potential to increase exponentially over time if certain conditions are met. The geometric ratio of increase, often denoted as "r" or the intrinsic rate of natural increase, represents the factor by which a population multiplies during each reproductive cycle or generation.

In the context of natural selection, individuals with higher reproductive rates (higher r-values) have a greater chance of passing on their genetic traits to the next generation. Over time, this can lead to significant population growth and evolutionary changes within a species. However, the geometric ratio of increase is limited by various factors, such as availability of resources, competition, predation, and environmental constraints, which can result in a balance between population growth and environmental carrying capacity.

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The rewritten expression in the form of xⁿ is \(x^{\frac{-3}{16}}\)

Expression:

In math, the expression refers the combination of variables, constants and exponents.

Given,

Here we have the expression \(\sqrt{x^{^{\scriptsize\dfrac34}}x^{-1}}\)

Now, we have to rewrite this expression into the form of xⁿ.

As per the law of exponents, we have rewrite the given expression as,

=> \((x^{^{\scriptsize\dfrac34}}x^{-1})^{\frac{1}{2})\)

Now, as per the law of exponent of multiplication, we can write it as,

=> \(x^{\frac{3}{8}}x^{\frac{-1}{2}}\)

Now, it can be further simplified as,

=> \(x^{\frac{-3}{16}}\)

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If Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove faster because the speed of the Mr. Giordano greater than Mr. Baras

Total distance traveled by the Mr. Giordano = 4.5 miles

The time taken = 5 minutes

Speed = Distance / Time

Speed = 4.5/5

= 0.9 miles per minutes

Total distance traveled by the Mr. Baras = 6.3 miles

The time taken = 8 minutes

Speed = Distance / Time

Speed = 6.3/8

= 0.78 miles per minutes

Hence, if Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove faster because the speed of the Mr. Giordano greater than Mr. Baras

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Answer:

20

Step-by-step explanation:

Triangle inequality says that the third side can only be 18-3...15, that is bigger than 15.

And 18+3... 21, that is smaller than 21.

If the third side is 21, the 18 and the 3 will just lay right on top of the 21 and not make a triangle. So it has to be 20 in order to be a whole number.

Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

9514 1404 393

Answer:

  x = 5, x = 11

Step-by-step explanation:

Set f(x) = 0 and solve for x.

  0 = (x -8)² -9

  9 = (x -8)² . . . . . add 9

  ±√9 = x -8 . . . . . take the square root

  ±3 +8 = x . . . . . . . add 8

That is, ...

  x = 8 -3 = 5 . . . . lesser x

  x = 8 +3 = 11 . . . greater x

Answer:

Candy canes are a classic Christmas treat, traditionally white with red stripes and flavored with peppermint. They have been popular since the 1600s and are thought to have originated in Germany. Today, 90 percent of all candy canes are sold between Thanksgiving and Christmas.

In a bag of Christmas treats, there are 3 red candy canes for every 5 gingerbread men. If there total is 40 treats, then the number of candy canes will be 24. This can be calculated by taking 40 divided by 8 (5+3) which equals 5, and then multiplying this by 3 which equals 15. Therefore, 24 candy canes are included in the bag of 40 Christmas treats.

Step-by-step explanation:

The correct answer is B. For a 95% confidence level, the z* value should be calculated using qnorm(0.975).

The proposed solution to construct a 95% confidence interval for the population proportion has several errors. Let's review each of them in detail:

A. phat was already provided, so dividing that value by the sample size is incorrect:

This is incorrect because phat represents the sample proportion, which is the point estimate of the population proportion. The sample proportion alone is not enough to estimate the variability of the sample proportion, which is required to construct a confidence interval. Therefore, we need to divide phat by the sample size to obtain the standard error of the sample proportion.

B. For a 95% confidence level, the z* is calculated by qnorm(0.95):

This is incorrect because a 95% confidence level corresponds to a 1.96 standard error for a two-tailed test, not a 1.645 standard error. Therefore, we need to use qnorm(0.975) or qnorm(1 - 0.025) to find the z* value.

C. You cannot use "phat" in an R Studio command. The decimal must be written:

This is incorrect because "phat" is a valid R Studio command that represents the sample proportion. However, it is important to define this variable beforehand to avoid any errors.

D. You cannot have negative values as one of the limits on your interval. This should be made positive:

This is correct. A confidence interval cannot have negative values as limits since proportions must be between 0 and 1. Therefore, we need to take the absolute value of the lower limit.

E. The proposed solution is correct:

This is incorrect, as discussed above. The correct solution should use the formula:

phat +/- z* * sqrt(phat*(1-phat)/n)

where phat = 0.43, n = 200, and z* is the critical value of the standard normal distribution corresponding to a 95% confidence level, which is approximately 1.96. Therefore, the correct 95% confidence interval is:

0.43 +/- 1.96 * sqrt(0.43*(1-0.43)/200) = (0.369, 0.491).

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Answer:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the initial balance

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

We know that P = $3500, A = $4390.40, r = unknown, n = 1 (compounded annually), and t = 2. Plugging in these values and solving for r:

$4390.40 = $3500(1 + r/1)^(1*2)

$4390.40/$3500 = (1 + r)^2

1.2544 = (1 + r)^2

√1.2544 = 1 + r

1.12 = 1 + r

r = 0.12 or 12%

Therefore, the annual interest rate is 12%.

The length of the uncut shelf is not long enough.

Given a wooden shelf 4½ feet long.

The length of two small shelves is  1¼ and 2⅜ feet long respectively.

To find an uncut shelf long enough or not subtract shelf's piece length from the total length of the wooden shelf length.

The length of an uncut shelf can be calculated as:

⇒1¼ + 2⅜+x= 4½

⇒5/4 + 19/8 + x = 9/2

To solve this equation make variable and constant different sides.

⇒x= 9/2-5/2-19/8

⇒x=2-19/8

⇒x=-3/8

The length of the uncut shelf is -3/8 feet, which is not valid (∵ Length cannot be negative).

∴ The length of the shelf is not long enough.

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The formula of the sequence based on geometric progression is  2(3/8)ⁿ⁻¹

The term geometric progression is defined as let a, r are real numbers and an infinite sequence of the form{arⁿ⁻¹} is said to be a geometric sequence this one is refers n'th term of the sequence.

Here we have know that the sequence is written as,

=> {2/1, 3/4, 4/9, 5/16, 6/25, 7/36, 8/49, 9/64..}

Here the value of r is calculated as,

=> (3/4) / (2/1) = 3/4 x 1/2 = 3/8

Then the general formula by using the geometric progression is written as,

=> 2 x (3/8)ⁿ⁻¹

Complete Question:

Find the formula for the general term a subscript n of the sequence {2/1, 3/4, 4/9, 5/16, 6/25, 7/36, 8/49, 9/64..}

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Answer:

$1.58

Step-by-step explanation:

To figure out this answer we must use division, units, and ratios to calculate. We know that 3 cartons is equivalent $4.67. So to calculate the price of one carton we have to divide by 3.

\(4.76/3=1.58\)

Answer:

i think its b

Step-by-step explanation:

Using the inscribed angle theorem, the value of x in the circle shown is calculated as: m<x = 36°.

According to the inscribed angle theorem an inscribed angle has an angle measure that is always half of the measure of the arc it intercepts.

Measure of arc EFG = 2(25 + 47) [inscribed angle theorem]

Measure of arc EFG = 144°

Measure of angle EHG = 1/2(m(EFG)) [inscribed angle theorem]

Substitute:

Measure of angle EHG = 1/2(144) = 72°

m<EHG = m<EGH = 72° [this is because triangle EHG is an isosceles triangle since sides EG = EH].

Therefore, we have:

m<x = 180 - 2(72)

m<x = 36°

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The pseudo-inverse of A is:

A+ =

⎡ cosφ/σ1 -sinφ/σ2 ⎤

⎢ sinφ/σ1 cosφ/σ2 ⎥

⎣ 0 0 ⎦

The pseudo-inverse of a 2x3 matrix A, we first need to compute the singular value decomposition (SVD) of A.

The SVD of A can be written as A = \(U\Sigma V^T\), where U and V are orthogonal matrices and Σ is a diagonal matrix with non-negative diagonal elements in decreasing order.

Since A is a 2x3 matrix, we can assume that the rank of A is either 2 or 1. If the rank of A is 2, then Σ will have two non-zero diagonal elements, and we can compute the pseudo-inverse as A+ = \(V\Sigma ^{-1}U^T\).

If the rank of A is 1, then Σ will have only one non-zero diagonal element, and we can compute the pseudo-inverse as A+ = \(V\Sigma^{-1}U^T\), where \(\Sigma^{-1\) has the reciprocal of the non-zero diagonal element.

Let's assume that the rank of A is 2, so we need to compute the SVD of A.

Since A is a 2x3 matrix, we can use the formula for SVD to write:

A = \(U\Sigma V^T\) =

⎡ cosθ sinθ ⎤

⎣-sinθ cosθ ⎦

⎡ σ1 0 0 ⎤

⎢ 0 σ2 0 ⎥

⎣ 0 0 0 ⎦

⎡ cosφ sinφ 0 ⎤

⎢-sinφ cosφ 0 ⎥

⎣ 0 0 1 ⎦

where θ and φ are angles that satisfy 0 ≤ θ, φ ≤ π, and σ1 and σ2 are the singular values of A.

The diagonal matrix Σ contains the singular values σ1 and σ2 in decreasing order, with σ1 ≥ σ2.

The pseudo-inverse of A, we first compute the inverse of Σ.

Since Σ is a diagonal matrix, its inverse is easy to compute:

\(\Sigma^{-1\)=

⎡ 1/σ1 0 0 ⎤

⎢ 0 1/σ2 0 ⎥

⎣ 0 0 0 ⎦

Next, we compute \(V\Sigma^{-1}U^T\):

A+ = VΣ^-1U^T =

⎡ cosφ -sinφ ⎤

⎣ sinφ cosφ ⎦

⎡ 1/σ1 0 ⎤

⎢ 0 1/σ2 ⎥

⎡ cosθ -sinθ ⎤

⎣ sinθ cosθ ⎦

The pseudo-inverse is not unique, and there may be different ways to compute it depending on the choice of angles θ and φ.

Any valid choice of angles will yield the same result for the pseudo-inverse.

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The pseudo-inverse A+ of a 2x3 matrix A does not exist.

The pseudo-inverse of a matrix is a generalization of the matrix inverse for non-square matrices. However, not all matrices have a pseudo-inverse.

In this case, we have a 2x3 matrix A, which means it has more columns than rows. For a matrix to have a pseudo-inverse, it needs to have full column rank, meaning the columns are linearly independent. If a matrix does not have full column rank, its pseudo-inverse does not exist.

Since the given matrix A has more columns than rows (2 < 3), it is not possible for A to have full column rank, and thus, its pseudo-inverse does not exist.

Therefore, the pseudo-inverse A+ of the 2x3 matrix A is undefined.

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To determine if a matrix is a linear combination of other matrices, we need to check if it can be written as a weighted sum of those matrices where the weights are scalar values (numbers).

If a matrix can be expressed in this way, it is said to be a linear combination of the other matrices.

For example if we have matrices: A, B & C and we can write matrix D as follows:

Then D is a linear combination of matrices A, B and C. This concept is important in linear algebra as it allows us to express one matrix in terms of others. Making it easier to manipulate & analyze the matrices. A matrix is a linear combination of other matrices if it can be expressed as a weighted sum of those matrices where the weights are scalar values.

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Queremos resolver un problema sobre porcentajes, donde conociendo el porcentaje que un dado número representa, queremos encontrar el número equivalente al 100%.

Veremos que el número total de arboles es 250.

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

Sabemos que el 18% de los arboles son almendros y el resto son naranjos, es decir, el porcentaje de naranjos es 100% - 18% = 82%

Y sabemos que hay 45 almendros.

Entonces el 18% del número total de arboles es 45.

Es decir, si hay N arboles en total, el 18% de N es igual a 45, esto se puede escribir como:

(18%/100%)*N = 45

0.18*N = 45

N = 45/0.18 = 250

Así podemos concluir que hay un total de 250 arboles en la plaza.

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The correct answer would be an option (D) Associative Property of Addition.

The associative property of addition is a rule which states that when adding three or more numbers, we can arrange them in any configuration, and the resultant sum is unaffected by how they are arranged.

(a + b) + c = a + (b + c)

Given Line 1 and Line 2 are shown below.

Line 1 as :

⇒ (3 + 9) + 5

Line 2 as :

⇒ 3 + (9 + 5)

According to Associative Property of Addition,

Line 1 as :

(3 + 9) +5 equals 12 + 5 which equals 17

Line 2 as :

3 + (9 + 5) equals 3 + 14 which equals 17

The correct answer would be an option (D) Associative Property of Addition.

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Answer:

c; y = 2x

Step-by-step explanation:

if it was without the coupon the fee would be the $2 per mile (2x) with the $35 which would be

y = 2x + 35

but with the coupon the $35 reservation is removed so only 2x is left

y = 2x

An equivalent fraction to -(7/8) can be obtained by multiplying both the numerator and denominator by the same non-zero integer. Since we want the fraction to be negative, we can multiply by -1/-1, which is equivalent to multiplying by 1.

(-1/-1) * (7/8) = -(7/8)

Therefore, an equivalent fraction to -(7/8) is:

(1/1) * (7/8) = -7/8

So, the fraction that is equivalent to -(7/8) is -7/8.

The definition of a regression equation is an equation used to assess whether a relationship exists between two sets of data.

What is the regression equation?

In statistics, a regression equation is used to determine whether or not there is a link between two sets of data. For instance, you might discover that a child grows roughly 3 inches a year if you measure their height each year. A regression equation can be used to model the three-inch growth tendency. In reality, most aspects of the real world—from gas prices to hurricanes—can be described using an equation of some form, which enables us to foretell the future.

The "best fit" line for your data is a regression line. In essence, you design a line that most accurately depicts the data points. It resembles the average of the points' locations. The regression line in a linear regression is a completely straight line:

An equation is used to express the regression line. The formula in this instance is 2.2923x + 4624. The line would be a rough approximation of your data if you plotted the equation -2.2923x + 4624.4.

It is unusual for all of the data points to actually lie on the regression line. The dots in the image above are a little dispersed around the line. The dots in the following picture are on the line. Polynomial regression, which fits the points to a polynomial equation, produced the curved curvature of this line.

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Answer:

The third one. A group of tissues joined together to perform a specific function.

Answer:

C) A group of tissues joined together to perform a specific function

Step-by-step explanation:

Each organ in your body has a job, each organ is designed to do one special thing to keep your body working and in shape, as the heart is an organ that is meant to pump blood into our bodies, and every organ has tissue, as the brain tissue helps keep it intact.

Hope this helps!

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Answer:

choice c has a value of .9, so c

Step-by-step explanation:

i hope this helps

Let the cost of a dozen apples be x and the cost of a loaf of bread be y.As per the given information, a dozen apples and 2 loaves of bread cost $5.76.Thus we can write the first equation as:

12x+2y = 5.76 .....(1)  Half a dozen apples and 3 loaves of bread cost $7.68.Thus we can write the second equation as:6x+3y = 7.68 .....(2)Now, let's solve for the value of y, which is the cost of a loaf of bread, using the above two equations.

In order to do so, we'll first eliminate x. For that, we'll multiply equation (1) by 3 and equation (2) by -2 and then add the two equations. This is given by:36x + 6y = 17.28 .....(3)-12x - 6y = -15.36 .....(4)Adding equations (3) and (4), we get:

24x = 1.92Thus,x = 1.92/24 = 0.08 Substituting the value of x in equation (1), we get:12(0.08) + 2y = 5.76 => 0.96 + 2y = 5.76 => 2y = 5.76 - 0.96 = 4.8Therefore,y = 4.8/2 = $2.40Hence, the cost of a loaf of bread is $2.40.

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The solutions to the equation 5x³=405x are x=0, x=9, x=-9.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign = The word equation and its cognates in other languages may have subtly different meanings; for example, in French, an equation is defined as containing one or more variables, whereas in English, an equation is any well-formed formula consisting of two expressions related with an equals sign.

An equation is similar to a scale into which weights are placed. When equal weights of material  are placed in the two pans, the scale is balanced and the weights are said to be equal.

Solving an equation with variables entails determining which variables values make the equality true.

Given, 5x³=405x

5x³-405x=0

5x(x²-81)=0

5x=0 and x²-81=0

If 5x=0 then,

x=0

If x²-81=0

x²=81

x=±9

Therefore, x=0, x=±9

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Answer:

Area = 16sq inches

Perimeter =  16 inches

Step-by-step explanation:

The shape of body is a square:

 Area = S²

 Perimeter = 4S

S is the side length

So;

      S  = 4inches

Therefore;

       Area = S²   = 4²   = 16sq inches

       Perimeter  = 4S  = 4(4)  = 16inches

Answer:

1.8

Step-by-step explanation:

just divide 60 and 32