calculate the sum of the series [infinity] an n = 1 whose partial sums are given. sn = 4 − 3(0.7)n

The coordinates of point P are (-3, -1).

The coordinates of point P that divides the line segment AB in the ratio 1:4 is calculated as follows;

let the ratio = a : b = 1:4

P = ( (bx₂ + ax₁)/(b + a), (by₂ +  ay₁)/( b + a) )

Where;

The coordinate of point P is calculated as follows;

P = ( (4(-2) + 1 (-7))/(4 + 1),  (4(0) + 1(-5) )/(4 + 1))

P = (-8 - 7)/(5), (0 - 5)/(5)

P = (-15/5), (-5/5)

P = (-3, - 1)

Thus, the coordinate of point P is determined by applying  ratio formula on a line segment.

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Answer:

a

Step-by-step explanation:

every second it goes down my 10

The point of inflection is at x = 8.19

To discuss the extrema of the function[tex]C(x) = 0.0049x^3 -0.1206x^2 + 0.839x + 48.72[/tex],

we will take the first and second derivatives with respect to x:

[tex]C'(x) = 0.0147x^2 - 0.2412x + 0.839[/tex]

[tex]C''(x) = 0.0294x – 0.2412[/tex]

Setting C'(x) = 0 to find critical points:

[tex]0.0147x^2 - 0.2412x + 0.839 = 0[/tex]

Using the quadratic formula, we can solve for x:

[tex]x=\frac{ [0.2412 ± \sqrt{(0.2412)^{2}-4(0.0147)(0.839) }] }{2(0.147)}[/tex]

x ≈ 4.27, 11.50

We also note that C''(x) > 0 for all x, which means that the function is concave up everywhere.

Therefore, we have two critical points: x = 4.27 and x = 11.50. To determine whether these are maxima or minima, we can use the second derivative test.

C''(4.27) ≈ 0.356 > 0, so x = 4.27 is a relative minimum.

C''(11.50) ≈ 0.323 > 0, so x = 11.50 is a relative minimum.

Since the function is concave up everywhere, these relative minima are also absolute minima.

To find the point of inflection, we set C''(x) = 0:

0.0294x – 0.2412 = 0

x ≈ 8.19

The point of inflection is at x = 8.19, and its meaning in the context of this problem is that it represents the day when the rate of change of the stock price changes from decreasing to increasing. Before the point of inflection, the rate of decrease of the stock price is slowing down, while after the point of inflection, the rate of increase of the stock price is accelerating

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The length of the base is 5 feet

A quadratic equation is a second-degree polynomial equation that can be written in the form "ax² + bx + c = 0", where "x" is the variable, and "a", "b", and "c" are constants. The coefficient "a" cannot be zero, as this would result in a linear equation.

The area of a triangle is gotten from;

A = 1/2bh

2A = bh

A = 35 square feet

70= b (2b +4)

70 = 2b^2 + 4b

2b^2 + 4b - 70 = 0

b = 5 or -7

Since length can not be negative;

b = 5 feet

length = 2(5) + 4 = 14 feet

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Cos L as a fraction in simplest terms is equal to √803 / 121

The mathematical subject of trigonometry is the study of the connections between the angles and sides of triangles.

It entails investigating trigonometric functions like sine, cosine, and tangent, which relate a triangle's angles to its sides' lengths.

To find cos L, we need to use the ratio of the adjacent side to the hypotenuse in the right triangle LMN.

cos L = LM / LN

We know that LM = √73 and LN is the hypotenuse of the triangle, which can be found using the Pythagorean theorem:

LN = √(LM² + MN²)

= √(73 + 48)

= √121

= 11

Therefore, cos L = LM / LN = √73 / 11.

To simplify this fraction, we can rationalize the denominator by multiplying the numerator and denominator by 11:

cos L = √73 / 11 × 11 / 11

= √(73 × 11) / 121

= √803 / 121

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Okay, let's solve this step-by-step:

* The box is shaped like a rectangular prism

* It has dimensions:

** 18.5 inches long

** 32 inches wide

** 12.2 inches deep

To find the volume of a rectangular prism, we use the formula:

Volume = Length x Width x Depth

So in this case:

Volume = 18.5 inches x 32 inches x 12.2 inches

= 18.5 * 32 * 12.2

= 5796 cubic inches

Therefore, the volume of the box is 5796 cubic inches.

Let me know if you need more details!

The electric field strength decreases as the distance from the plane increases.

The electric field strength near an infinite plane of charge is given by:

E = σ/2ε0

where E is the electric field strength, σ is the surface charge density of the plane, and ε0 is the electric constant.

The electric field strength at a point near the plane depends on the distance from the plane and the orientation of the point relative to the plane.

Assuming that the surface charge density is constant, we can rank the electric field strength from largest to smallest based on the distance from the plane:

Point closest to the plane

Point at a distance of 2 times the distance from point 1

Point at a distance of 3 times the distance from point 1

Point at a distance of 4 times the distance from point 1

Point at a distance of 5 times the distance from point 1

This is because the electric field strength decreases as the distance from the plane increases.

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The probability that the proportion of sampled teenagers who own a smartphone is between 0.45 and 0.55 is:

0.9564 - 0.2296 ≈ 0.7268

What is Probability ?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents impossibility (an event that can never occur) and 1

Part 1: The mean is calculated as:

mean = gp = 0.48

Part 2: The standard deviation is calculated as:

σ = √[(gp * (1 - gp))÷n]

where n is the sample size.

σ = √[(0.48 * 0.52)÷150]

σ ≈ 0.0408

Part 3: To find the probability that more than 50% of the sampled teenagers own a smartphone, we need to calculate the z-score and use a standard normal distribution table. The z-score is calculated as:

z = (x - gp)÷σ

where x is the proportion of teenagers owning smartphones. We want to find the probability that x is greater than 0.50. So,

z = (0.50 - 0.48)÷0.0408 ≈ 0.49

Using a standard normal distribution table, the probability corresponding to a z-score of 0.49 is approximately 0.3120.

Part 4: To find the probability that the proportion of sampled teenagers who own a smartphone is between 0.45 and 0.55, we need to standardize the range of values using the z-score formula:

z1 = (0.45 - 0.48)÷0.0408 ≈ -0.74

z2 = (0.55 - 0.48)÷0.0408 ≈ 1.71

Using a standard normal distribution table, the probability corresponding to a z-score of -0.74 is approximately 0.2296, and the probability corresponding to a z-score of 1.71 is approximately 0.9564.

Therefore, the probability that the proportion of sampled teenagers who own a smartphone is between 0.45 and 0.55 is:

0.9564 - 0.2296 ≈ 0.7268

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The solution to the differential equation is: [tex]y(x) = c1 (x-9)^4 + c2 (x-9)[/tex]where c1 and c2 are constants of integration.

To solve this differential equation using the method of "reducing to a polynomial equation", we can make the substitution:

x - 9 = t,

so that x = t + 9 and y(x) = y(t+9).

We can then rewrite the differential equation in terms of t as follows:

[tex][(t+9)^2] y'' - 9(t+9) y' + 16y = 0[/tex]

We can now make the substitution [tex]y = (t+9)^m[/tex], where m is some constant to be determined.

Taking the first and second derivatives of y with respect to t, we get:

[tex]y'=m(t+9)^{(m-1)}[/tex]

[tex]y'' = m(m-1) (t+9)^{(m-2)}[/tex]

Substituting these expressions into the differential equation, we get:

[tex][(t+9)^2] m(m-1)(t+9)^{m-2} - 9(t+9) m(t+9)^{m-1} + 16(t+9)^m = 0[/tex]

Simplifying, we get:

m(m-1) - 9m + 16 = 0

Solving this quadratic equation for m, we get:

m = 4 or m = 1

Therefore, the general solution to the differential equation is given by:

[tex]y(t) = c1 (t+9)^4 + c2 (t+9)[/tex]

where c1 and c2 are constants of integration.

Substituting back to x, we have:

[tex]y(x) = c1 (x-9)^4 + c2 (x-9)[/tex]

where c1 and c2 are constants of integration.

Therefore, the solution to the differential equation is:

[tex]y(x) = c1 (x-9)^4 + c2 (x-9)[/tex]

where c1 and c2 are constants of integration.

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The recursion, and subsequent terms are defined in terms of previous terms in the sequence

A) The recursive definition for the sequence An is:

An = (4n-2)An-1 + 4Ao, with A1 = 4Ao.

B) The recursive definition for the sequence An is:

An = n(n+1)An-1 + Ao, with A1 = Ao.

C) The recursive definition for the sequence An is:

An = 1 + (-1)nAn-2tAo, with A1 = Ao and A2 = 1 - Ao.

D) The recursive definition for the sequence An is:

An = n^2An-1 + Ao, with A1 = Ao.

These recursive definitions define each term of the sequence An as a function of one or more previous terms in the sequence, starting with a basis case. The basis case provides the starting point for the recursion, and subsequent terms are defined in terms of previous terms in the sequence.

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The alternating series error bound is (C) 1/26.7!, since 26.7! is the smallest factorial greater than [tex]120*M_5.[/tex]

The alternating series error bound for an alternating series of the form [tex]\sum (-1)^n b_n[/tex]is given by [tex]|R_n| < = b_{(n+1)}[/tex], where [tex]R_n[/tex] is the remainder term and [tex]b_n[/tex] is the absolute value of the (n+1)th term in the series.

In this case, the fourth degree Taylor polynomial for f about x = 0 is given by:

[tex]P_4(x) = f(0) + f'(0)x + (f''(0)/2)x^2 + (f'''(0)/6)x^3 + (f''''(0)/24)x^4[/tex]

The alternating series error bound for the approximation of f(x) by [tex]P_4(x)[/tex]is therefore:

[tex]|R_4(x)| < = |f(x) - P_4(x)| < = (M/5!) |x - 0|^5,[/tex]

where M is an upper bound for [tex]|f^{(5)}(c)[/tex]| on the interval [0,x] for some c between 0 and x.

Since the Taylor series for f about x=0 converges to f for all real x, we know that M is finite. Therefore, we can find an upper bound for [tex]|f^{(5)}(c)|[/tex]on [0,-1] using the Mean Value Theorem.

Let g(x) = f''''(x). Then, by the Mean Value Theorem, there exists some c between 0 and -1 such that:

g(c) = (g(0) - g(-1))/(-1 - 0) = g(0) - g(-1)

Since the fourth derivative of f is continuous, g is continuous on the interval [0,-1]. Therefore, by the Extreme Value Theorem, g attains its maximum and minimum values on [0,-1].

Let[tex]M_5 = max{|g(x)| : x in [0,-1]}[/tex]. Then we have:

[tex]|R_4(x)| < = M_5/5! |x|^5 = M_5/120[/tex]

Therefore, the alternating series error bound is (C) 1/26.7!, since 26.7! is the smallest factorial greater than [tex]120*M_5.[/tex]

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Okay, here are the steps to solve this problem:

1) Since ACDE is isosceles with base EC, the angles at the base (mECD and mCEA) are equal. Let's call this common angle measure θ.

2) We know: mZD = (2x + 42)°

So, (2x + 42) + θ = 180° (angles sum to 180° in a triangle)

2x + 42 + θ = 180

=> 2x = 138

=> x = 69

3) Substitute x = 69 into mZE = (4x + 14)°

=> mZE = (4(69) + 14) = 278°

4) Now we have all 3 angles:

mECD = mCEA = θ (these are equal, common base angle)

mZD = (2)(69) + 42 = 174°

mZE = 278°

5) As a check:

174 + 278 + θ = 180

θ = 128

So the degree measures of the angles are:

mECD = mCEA = 128° (common base angle)

mZD = 174°

mZE = 278°

Let me know if you have any other questions! I'm happy to explain further.

The given sequence [tex]a_{n}[/tex]  does not converge, but instead diverges to infinity.

In mathematics and analysis, the terms "convergence" and "divergence" are used to describe the behavior of a sequence, which is an ordered list of numbers that are generated according to a certain pattern.

[tex]\begin{}|a_n| &= \left| \frac{(-1)^{n+1} \cdot n}{n \cdot \sqrt{n}} \right| \\&= \frac{n}{\sqrt{n}} \\\lim_{{n \to \infty}} |a_n| &= \lim_{{n \to \infty}} \frac{n}{\sqrt{n}} \\&= \lim_{{n \to \infty}} \frac{\sqrt{n} \cdot \sqrt{n}}{\sqrt{n}} \\&= \lim_{{n \to \infty}} \sqrt{n}\end{align*}[/tex]

As n approaches infinity, √n also approaches infinity. Therefore, the limit of ∣[tex]a_{n}[/tex]| as n approaches infinity is also infinity.

Since, the absolute value of the sequence |[tex]a_{n}[/tex]| approaches infinity as

n approaches infinity, the sequence [tex]a_{n}[/tex] does not converge, but instead diverges to infinity.

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Correct Question:find whether the sequence converges or diverges [tex]\begin{}|a_n| &= \left| \frac{(-1)^{n+1} \cdot n}{n \cdot \sqrt{n}} \right| \\&[/tex] ?

The given sequence [tex]a_{n}[/tex]  does not converge, but instead diverges to infinity.

In mathematics and analysis, the terms "convergence" and "divergence" are used to describe the behavior of a sequence, which is an ordered list of numbers that are generated according to a certain pattern.

[tex]\begin{}|a_n| &= \left| \frac{(-1)^{n+1} \cdot n}{n \cdot \sqrt{n}} \right| \\&= \frac{n}{\sqrt{n}} \\\lim_{{n \to \infty}} |a_n| &= \lim_{{n \to \infty}} \frac{n}{\sqrt{n}} \\&= \lim_{{n \to \infty}} \frac{\sqrt{n} \cdot \sqrt{n}}{\sqrt{n}} \\&= \lim_{{n \to \infty}} \sqrt{n}\end{align*}[/tex]

As n approaches infinity, √n also approaches infinity. Therefore, the limit of ∣[tex]a_{n}[/tex]| as n approaches infinity is also infinity.

Since, the absolute value of the sequence |[tex]a_{n}[/tex]| approaches infinity as

n approaches infinity, the sequence [tex]a_{n}[/tex] does not converge, but instead diverges to infinity.

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Correct Question:find whether the sequence converges or diverges [tex]\begin{}|a_n| &= \left| \frac{(-1)^{n+1} \cdot n}{n \cdot \sqrt{n}} \right| \\&[/tex] ?

The area of the segment is 1.68 squared.

The area of the shaded segment is the subtraction of the area of the triangle from the area of the sector OMN.

Therefore,

area of the segment  = ∅ / 360 πr² - 1 / 2r²sin(∅)

area of the segment  = 30 / 360 π(12)² - 1 / 2 (12)² sin 30°

area of the segment  = 1 / 12 π(144) - 1 / 2(144)0.5

area of the segment  = 12π  - 36

area of the segment  = 12(3.14) - 36

area of the segment  = 37.68 - 36

area of the segment  = 1.68 inches squared.

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Working together, Evan and Ellie can do the garden chores in 6 hours. it takes Evan twice as long as Ellie to do the work alone. Thus it takes Evan 18 hours to do the work alone.

Let x be the number of hours Ellie takes to do the garden chores alone. Then, Evan takes 2x hours to do the same work alone.

We can express their work rates as follows:
- Ellie's work rate: 1/x (jobs per hour)
- Evan's work rate: 1/(2x) (jobs per hour)

Now, we know that if they work together, they can do the garden chores in 6 hours. This means that their combined work rate is 1/6 of the job per hour.

When they work together, their work rates add up:
1/x + 1/(2x) = 1/6 (since they complete the work together in 6 hours)

Now, let's solve for x:
1/x + 1/(2x) = 1/6
To clear the fractions, multiply both sides by 6x:
We can solve for "x", which is Ellie's time to do the work alone:
1/6 = 3/2x
2x = 18
x = 9

So, Ellie takes 9 hours to complete the garden chores alone. Since Evan takes twice as long as Ellie, he takes 2 * 9 = 18 hours to complete the garden chores alone.

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The answer to the given statement is as follows:

It is inappropriate to apply the Empirical Rule to a population that is right-skewed

b. False.

The given statement is false because the rule of thumb, also known as the 68-95-99.7 rule, is a statistical rule that applies to the normal distribution. This rule was lost in our sample, with about 68% of the data falling within one standard deviation of the mean for a normal distribution, and about 95% of the data falling within two standard deviations from the mean, and about 99.7% of the data being lost in our sample. The deviation from the mean is the difference between the mean of the standard deviation.

Although the rule of thumb is most true for symmetric normal distributions, it can also be used for distributions, including right-skewed distributions.

However, as the distribution becomes more skewed, the rule of thumb may not be correct. In a right-skewed distribution, the mean is greater than the median and the tails of the distribution are to the right. In such a distribution, a rule of thumb might estimate the proportion of data that is one or two standard deviations from the mean.

Despite this limitation, the rule of thumb can be a useful tool for understanding the spread of data in right-skewed distributions. However, it is important to know that this law can predict the percentage of data in a given situation.

In such cases, other methods such as quartiles or percentages are more effective for analyzing the distribution of the data.

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We can successfully multiplied n by 35 using only five multiplications by 2, two additions, and intermediate storage of results.

We can use the following sequence of operations:

Multiply n by 4 using two multiplications by 2.

Multiply n by 8 using three multiplications by 2.

Add the result of step 1 to the result of step 2 using one addition.

Multiply n by 2 using one multiplication by 2.

Add the result of step 3 to the result of step 4 using one addition.

Multiply the result of step 5 by 4 using two multiplications by 2.

Add the result of step 5 to the result of step 6 using one addition.

The final result is n × 35.

Here's how it works:

Step 1: 4n

Step 2: 8n

Step 3: 4n + 8n = 12n

Step 4: 24n

Step 5: 12n + 24n = 36n

Step 6: 144n

Step 7: 36n + 144n = 180n

So, we have successfully multiplied n by 35 using only five multiplications by 2, two additions, and intermediate storage of results.

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The ratios that are equivalent to the ratios in the table are 1:3 and 10:30. (optio a or d).

The given table shows two columns, A and B, with four entries each. Each entry in column A is paired with a corresponding entry in column B. To determine which ratios in the form A:B are equivalent to the ratios in the table, we need to find the common factor between each pair of entries.

Similarly, for the second row with A=3 and B=9, we can simplify the ratio to 1:3 by dividing both A and B by their greatest common factor, which is 3.

For the third row with A=4 and B=12, we can simplify the ratio to 1:3 by dividing both A and B by their greatest common factor, which is 4/2=2.

For the fourth row with A=5 and B=15, we can simplify the ratio to 1:3 by dividing both A and B by their greatest common factor, which is 5/5=1.

Therefore, the ratios in the form A:B that are equivalent to the ratios in the table are 1:3 for all four rows.

The ratio 10:30 can be simplified by dividing both terms by their greatest common factor of 10, which gives 1:3. This ratio is equivalent to the ratios in the table.

Hence the correct option is (a) or (d).

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Answer: x * y = 2x + 5y. Formula used: x * y = 2x + 5y. Calculation: When x = 3, and y = 5. ⇒ 2x + 5y = (2 × 3) + (5 × 5) = 6 + 25 = 31

Step-by-step explanation:

When a regression model is created to fit a sample set of data, its prediction ability is reduced overfitting. Thus, option C is correct.

Overfitting is a phenomenon in machine learning where a regression model is trained too well on the sample data.

to the point where it starts to memorize the data instead of learning the underlying patterns or trends. As a result, the overfitted model may not generalize well to unseen data and may exhibit poor predictive power when used for making predictions on new data.

The term "compromising predictive power" in the question suggests that the model is not able to accurately predict outcomes on new, unseen data due to overfitting.

Essentially, the model becomes too specialized to the sample data it was trained on and loses its ability to generalize to new data points.

Flooding is not a term related to machine learning or regression modeling. Binary choice refers to a decision between two options and is not related to overfitting.

Therefore, When a regression model is created to fit a sample set of data, its prediction ability is reduced overfitting

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The velocity and position of a body moving through a resisting medium with resistance proportional to its velocity are given by v(t) = v₀e^(-kt) and x(t) = x₀ + (v₀/k)(1-e^(-kt)), respectively.

We are given that the resistance of the medium is proportional to the velocity of the body, so we can write

F = -kv

where F is the force acting on the body, k is the proportionality constant, and v is the velocity of the body. Since F = ma (Newton's second law), we have

ma = -kv

Dividing both sides by m and rearranging, we get

dv/dt = -k/m × v

We can now solve this differential equation by separation of variables

dv/v = -k/m × dt

Integrating both sides, we obtain

ln|v| = -k/m × t + C

where C is the constant of integration. Exponentiating both sides, we get

|v| = e^(-k/m × t + C) = e^C × e^(-k/m × t)

Note that since v is always positive (it's the speed of the body), we can drop the absolute value signs. Also, since e^C is just a constant, we can write

v = v₀ × e^(-k/m × t)

where v₀ = e^C is the velocity of the body at time t=0.

Next, we can find the position of the body by integrating the velocity

dx/dt = v

Integrating both sides, we obtain

x(t) = x₀ + ∫ v(t) dt

where x₀ is the position of the body at time t=0. Substituting v(t) = v₀ × e^(-k/m × t), we get:

x(t) = x₀ + ∫ v₀ × e^(-k/m × t) dt

Integrating, we obtain:

x(t) = x₀ - (m/k) × v₀ × e^(-k/m × t) + A

where A is the constant of integration. We can determine A by using the initial condition x(0) = x₀, which gives

x(0) = x₀ - (m/k) × v₀ × e^(0) + A

A = x₀ + (m/k) × v₀

Substituting this into the equation for x(t), we finally get

x(t) = x₀ + (v₀/k) × (1 - e^(-k/m × t))

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The given question is incomplete, the complete question is:

Suppose that a body moves through a resisting medium withresistance proportional to its velocity v , so that dv/dt =-kv. Show that its velocity and position at time t are given by v(t)= v₀e^(-kt) and x(t) = x₀ +(v₀ / k)(1-e^(-kt)).

The amount of money we can make is $0.05.

We have,

P= $710

R= 5.1%

T= 12 year

Compounded Continuously:

A = P[tex]e^{rt[/tex]

A = 710.00(2.71828[tex])^{(0.051)(12)[/tex]

A = $1,309.32

Compounded Daily:

A = P(1 + r/n[tex])^{nt[/tex]

A = 710.00(1 + 0.051/365[tex])^{(365)(12)[/tex]

A = 710.00(1 + 0.00013972602739726[tex])^{(4380)[/tex]

A = $1,309.27

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The general solution is: y(x) = c1e^x + c2e^-x + c3cos x + c4sin x.

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When x = -3 and dx = -0.4, dy = -0.3386. This means that when x decreases by 0.4, y decreases by approximately 0.3386 units.

To find dy, we need to take the derivative of the function y=6cos(x) with respect to x. The derivative of cos(x) is -sin(x), so the derivative of 6cos(x) is -6sin(x). Therefore, dy/dx = -6sin(x).

Now, we can evaluate dy when x = -3 and dx = -0.4. Plugging in x = -3 into the derivative we just found, we get dy/dx = -6sin(-3). Using the unit circle, we know that sin(-3) is approximately equal to -0.1411. Therefore, dy/dx = -6(-0.1411) = 0.8466.

To find dy, we can use the formula dy = dy/dx * dx. Plugging in the values we have, we get dy = 0.8466 * (-0.4) = -0.3386.

Therefore, when x = -3 and dx = -0.4, dy = -0.3386. This means that when x decreases by 0.4, y decreases by approximately 0.3386 units. This information can be useful in understanding the behavior of the function y=6cos(x) in the neighborhood of x = -3.

Overall, finding the derivative of a function allows us to understand how the function changes as its input (in this case, x) changes. By evaluating the derivative at a specific point, we can find the rate of change (dy/dx) and use it to find the change in output (dy) for a given change in input (dx).

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Answer: D

Explanation: Since 21 out of 24 bean seeds sprouted in the first class, the probability of a bean seed sprouting is 21/24, or 0.875. This information does not provide any information about the seeds in the other five classes, other than that they were all planted using the same method. Therefore, we cannot make a definitive statement about how many seeds will or will not sprout in the other classes. Option A is supported by the given information, since 87.5% of the seeds in the first class sprouted. Option B is not necessarily supported by the given information, as it depends on how many seeds were used in total. Option C is not directly supported by the given information, but is a possible conclusion based on the probability of a seed sprouting. Option D is contradicted by the given information, since at most 3 out of 24 seeds did not sprout in the first class.

The width and height of the rectangle is w = 23 cm and h = 18 cm

Given data ,

Let the prism be represented by the figure A

Now , the width of the prism = 23 cm

The height of the prism = 12 cm

Now , the width of the rectangle = width of prism

So , w = 23 cm

And , the height of the rectangle is = breadth of the prism = 18 cm

So , h = 18 cm

Hence , the rectangle is solved

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