A box is 3 feet long, 18 inches wide and 7 inches tall. How much would it cost to cover the box in material if the material costs 2 cents per square inch? Explain how you found your cost.

The simplified expression is: x(x - 6) + y(y + 14) - 40

The given expression is:

x² - 6x - 40 + 14y + y²

This is a quadratic expression in terms of x and y. To factorize it, group the terms that involve x together and the terms that involve y together:

(x² - 6x) + (y² + 14y) - 40

Now, factorize the terms involving x and y:

x(x - 6) + y(y + 14) - 40

So, the simplified expression is:

x(x - 6) + y(y + 14) - 40

Note that this expression cannot be simplified any further.

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The complete question goes thus:

Factorize: x ^ 2 - 6x - 40 + 14y + y ^ 2

The probability of observing the sequence r, b, b, r, r in the given scenario is 1/120.

To find the probability of observing the sequence r, b, b, r, r in the given scenario, we can break it down step by step:

Probability of drawing the first ball as red (r):

Since the urn initially contains one red and one black ball, the probability of drawing a red ball is 1/2.

Probability of drawing the second ball as black (b) after the first ball was red:

After drawing the first red ball, it is returned to the urn along with another red ball, so the urn now contains two red balls and one black ball.

The probability of drawing a black ball is 1/3.

Probability of drawing the third ball as black (b) after the previous sequence was r, b:

After drawing the second black ball, it is returned to the urn along with another black ball, so the urn now contains two red balls and two black balls.

The probability of drawing a black ball is now 2/4 = 1/2.

Probability of drawing the fourth ball as red (r) after the previous sequence was r, b, b:

After drawing the third black ball, it is returned to the urn along with another black ball, so the urn still contains two red balls and two black balls.

The probability of drawing a red ball is 2/4 = 1/2.

Probability of drawing the fifth ball as red (r) after the previous sequence was r, b, b, r:

After drawing the fourth red ball, it is returned to the urn along with another red ball, so the urn now contains three red balls and two black balls.

The probability of drawing a red ball is 3/5.

To find the overall probability of observing the sequence r, b, b, r, r, we multiply the probabilities of each individual step:

[tex]P(r, b, b, r, r) = (1/2) \times (1/3) \times (1/2) \times (1/2) \times (3/5)[/tex]

= 1/120.

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The concept of marginal thinking suggests that you should only consider the marginal benefit and marginal cost of accepting the piece of chocolate.

Marginal benefit refers to the additional pleasure or satisfaction that you will receive from consuming the chocolate, while marginal cost refers to any negative consequences, such as calories or sugar intake, or potential discomfort if you have an allergy. It's important to consider the trade-off between these two factors and decide whether the marginal benefit outweighs the marginal cost. If it does, then accepting the piece of chocolate may be a good decision. However, if the marginal cost is too high, then it may be better to decline the offer and seek alternative sources of pleasure or satisfaction. In this way, the concept of marginal thinking helps you make rational and informed decisions that optimize your well-being and resources.

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There is a 5% chance that we have wrongly rejected the null hypothesis and that the new ingredient does not actually reduce the drying time.

Hypothesis testing is a statistical method used to determine whether an assumption about a population parameter is supported by the sample data. In this case, the product developer is interested in determining whether the new ingredient in the primer paint reduces the drying time.

The null hypothesis assumes that there is no difference between the population means of drying time for the two formulations, while the alternative hypothesis assumes that the new ingredient reduces the drying time.

To determine the effectiveness of the new ingredient, the product developer can perform a hypothesis test.

Let's assume that the null hypothesis (H₀) is that the new ingredient does not reduce the drying time, and the alternative hypothesis (Hₐ) is that the new ingredient reduces the drying time.

H₀: μ₁ - μ₂ = 0

Hₐ: μ₁ - μ₂ > 0

Where μ₁ and μ₂ are the population means of drying time for formulation 1 and formulation 2, respectively.

Since the population standard deviation (σ) is known and the sample size is large enough (n = 10), we can use a two-sample z-test.

The test statistic can be calculated as:

z = (x₁ - x₂) / [σ × √(1/n₁ + 1/n₂)]

Where x₁ and x₂ are the sample means of drying time for formulation 1 and formulation 2, respectively.

Plugging in the given values, we get:

z = (121 - 112) / [8 × √(1/10 + 1/10)] = 4.14

Using a one-tailed test and a significance level of α = 0.05, the critical z-value is 1.645.

Since the calculated z-value (4.14) is greater than the critical z-value (1.645), we can reject the null hypothesis and conclude that there is evidence that the new ingredient reduces the drying time.

However, it's important to note that this conclusion is subject to a type I error, which is the probability of rejecting the null hypothesis when it is actually true. The probability of type I error is equal to the significance level (α), which in this case is 0.05.

Therefore,

There is a 5% chance that we have wrongly rejected the null hypothesis and that the new ingredient does not actually reduce the drying time.

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The radius of convergence of the series is 1/8.

The radius of convergence, r, of the given series can be found using the ratio test.

Taking the limit of the ratio of the (n+1)th and nth term as n approaches infinity gives:

lim |(8(n+1) -1)/(n+1)| / |8n-1)/n| = lim |(8n +7)/(n+1)| = 8

Since the limit is finite and less than 1, the series converges absolutely.

Therefore, the radius of convergence, r, is given by the formula r = 1/lim sup(|an|^1/n) where an is the nth term of the series.

Substituting the given values and simplifying, we get r = 1/8.

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The probability of exactly 1 seed not growing is 31.36%. we can use the binomial probability formula, which is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k). P(X=k) is the probability of getting k successes in n trials n is the number of trials

k is the number of successes p is the probability of success in each trial.

To calculate the probability of exactly 1 failure, we can use the binomial probability formula, which is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

P(X=k) is the probability of getting k successes in n trials

n is the number of trials

k is the number of successes

p is the probability of success in each trial

(n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items

In this case, n=6, k=1, p=0.65, and (n choose k) = 6. Plugging these values into the formula, we get:

P(X=1) = (6 choose 1) * 0.65^1 * (1-0.65)^(6-1) = 6 * 0.65 * 0.35^5 = 0.3136

Therefore, the probability of exactly 1 seed not growing is 31.36%.

In this case, the probability of getting exactly 1 failure in 6 trials, where the probability of success is 0.65. We use the binomial coefficient to count the number of ways to choose 1 item (the failure) from a set of 6 items (the seeds). We then multiply this by the probability of getting 1 failure and 5 successes, which is given by the formula p^k * (1-p)^(n-k), where p is the probability of success and k and n-k represent the number of successes and failures, respectively. Finally, we calculate the probability of exactly 1 failure by multiplying the binomial coefficient and the probability of getting 1 failure and 5 successes.

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For values of y near 0, the functions can be ordered in increasing order as follows: 1 - cos(y) < ln(1 + y^2) < 1/(1 - y^2) - 1.

To determine the increasing order of the functions for values of y near 0 using their Taylor expansions, let's calculate the Taylor series expansions for each function and compare them.

(a) 1 - cos(y):

The Taylor series expansion for 1 - cos(y) centered at y = 0 is:

1 - cos(y) = 0 + (1/2!)y^2 + (0) + ...

The second-order term is positive, and all higher-order terms are non-negative. Therefore, for values of y near 0, the function 1 - cos(y) is increasing.

(b) ln(1 + y^2):

The Taylor series expansion for ln(1 + y^2) centered at y = 0 is:

ln(1 + y^2) = (0) + (1/1)(y - 0) + (0) + ...

The first-order term is positive, and all higher-order terms are non-negative. Therefore, for values of y near 0, the function ln(1 + y^2) is increasing.

(c) 1/(1 - y^2) - 1:

The Taylor series expansion for 1/(1 - y^2) - 1 centered at y = 0 is:

1/(1 - y^2) - 1 = 1/(1 - 0^2) - 1 + (0) + ...

The constant term is positive, and all higher-order terms are non-negative. Therefore, for values of y near 0, the function 1/(1 - y^2) - 1 is increasing.

Therefore, in increasing order for values of y near 0, we have:

1 - cos(y) < ln(1 + y^2) < 1/(1 - y^2)

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Answer:

pick the first one

Step-by-step explanation:

The following characteristics are true of the graph of all proportional relationships. The graph is linear. The line of the graph passes through the origin. The slope of the line is the constant of proportionality.

the only graph that goes through the origin (0,0) is the first one. it doesn't have an intercept.

so pick y=(2/3)x

Answer:

First choice:  y = 2/3x

Step-by-step explanation:

A linear equation is proportional if it is straight AND passes through the origin (0,0).  The only equation that meets this definition is the first one,

y = 2/3x

Calculated t-test statistic (-2.21) is less than the critical value (-1.711), we reject the null hypothesis

The critical value for this hypothesis test can be found using a t-distribution with degrees of freedom (df) equal to the sample size minus one (df = 25-1 = 24) and a significance level of 5%.

Using a t-distribution table or calculator, the critical value for a one-tailed test (since we are testing if the mean is less than 1,150 hours) with 24 degrees of freedom and a 5% significance level is approximately -1.711. Therefore, the answer is B) -1.711.

To conduct the hypothesis test, we would calculate the t-test statistic using the formula:

[tex]t = (sample mean - hypothesized population mean) / (sample standard deviation / \sqrt{sample size})[/tex]
In this case, the sample mean is 1,097 hours, the hypothesized population mean is 1,150 hours, the sample standard deviation is 133 hours, and the sample size is 25. Plugging these values into the formula, we get:

[tex]t = (1,097 - 1,150) / (133 / \sqrt{25} )[/tex]= -2.21

Since the calculated t-test statistic (-2.21) is less than the critical value (-1.711), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the mean life of light bulbs produced by this company is less than 1,150 hours.

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All of the criteria's are fulfilled the survey is valid.

We have the information from the question:

The proportion of college football players who have had at least one concussion is estimated to be 34% in the united states.

Then, 34% = 0.34

The sample size of the data is = 100

p: the ‘proportion’ of ‘college’

The required conditions for testing the hypothesis of population proportion are,

(i) The population is larger than the sample

(ii) np > 10

=> 100 × 0.34

      =34

(iii) n(1-p) > 10

100 × (1 - 0.34)

=> 100 × 0.66

      =66

iv)The ‘sample’ is drawn randomly from the population.

Since all of the above criteria's are fulfilled the survey is valid.

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[tex]x + x^3[/tex] is the simplified expression of [tex]x/4x + x^2[/tex]

To simplify , we will find common denominator. A common denominator means the number which can be divided by all the denominators in a group of fractions.

The denominator of first fraction is 4x, so we will rewrite the expression as:

From [tex]x/4x + x^2[/tex]

To: [tex](x/4x) + (x^2(4x)/4x).[/tex]

Simplifying second fraction gives us:

(4x^3)/4x.

We will cancel out common factor of 4x, so, we are left with [tex]x + x^3[/tex]as the simplified expression.

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The set of parametric equations for the line y = 3x - 2, with t = 0 at the point (2,4), is x = t + 2, y = 3t + 4.

We can use the point-slope form of a line to find the parametric equations:

y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope of the line.

The slope of the line y = 3x - 2 is 3, so we have:

y - 4 = 3(x - 2)

Simplifying, we get:

y = 3x - 2

We can rewrite this as a set of parametric equations:

x = t + 2

y = 3t + 4

So the set of parametric equations for the line y = 3x - 2, with t = 0 at the point (2,4), is:

x = t + 2, y = 3t + 4.

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If the rate of interest is the same in both years, the rate of interest is 12%.

The man took a loan of Rs.10,000 at simple interest. He paid Rs. 5,000 at the end of first year in which interest is also included and Rs. 6,944 at the end of the second year and clears the debt.

Here is the solution:

Interest paid in the first year = Rs. (10,000 - 5,000) = Rs. 5,000

Interest paid in the second year = Rs. (6,944 - 10,000) = Rs. -3,056

Total interest paid = Rs. (5,000 + (-3,056)) = Rs. 1,944

Principal amount = Rs. 10,000

Rate of interest = (100 * 1,944) / (10,000 * 2) = 12%

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The equations for each object's velocity, in meters/second, in terms of its mass in kilograms are:

[tex]V_A=\sqrt{\frac{200}{m} }\\\\V_B=\sqrt{\frac{50}{m} }[/tex]

A graph of the two functions is shown below.

In Mathematics, the kinetic energy of an object can be calculated by using the following equation (formula):

K.E = 1/2 × mv²

Where:

By making velocity (v) the subject of formula, we have:

[tex]V= \sqrt{\frac{2K.E}{m} }[/tex]

In this context, the equations for each object's velocity, in terms of its mass can be written as follows;

Velocity of object A = [tex]V_A= \sqrt{\frac{2(100)}{m} }[/tex]

Velocity of object A = [tex]V_A= \sqrt{\frac{200}{m} }[/tex]

Velocity of object B = [tex]V_B= \sqrt{\frac{2(25)}{m} }[/tex]

Velocity of object B = [tex]V_B= \sqrt{\frac{50}{m} }[/tex]

When mass (m) = 2 kg, the velocity of object A can be calculated as follows;

[tex]V_A=\sqrt{\frac{200}{m} } \\\\V_A=\sqrt{\frac{200}{2} }\\\\V_A=10 \;m/s[/tex]

When mass (m) = 2 kg, the velocity of object B can be calculated as follows;

[tex]V_B=\sqrt{\frac{50}{m} } \\\\V_B=\sqrt{\frac{50}{2} }\\\\V_B=5 \;m/s[/tex]

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Complete Question:

The kinetic energy, E₁, in kilograms meters squared per second squared (kg.m²/sec) of an object can be modeled with the equation E, = 1/2mv².

where m is the object's mass in kilograms and v is the object's velocity in meters per second.

A physics student is investigating 2 moving objects:

Object A's kinetic energy is 100 kg m²/sec².

Object B's kinetic energy is 25 kg m²/sec²

Write equations for each object's velocity, in meters/second, in terms of its mass in kilograms. Then graph the two functions on the same coordinate grid. Provide evidence to support your answer.

The probability of selecting a sample with a mean of 1450 or less, given a known population mean of 1500 and a known standard error of the mean of 42.50, is approximately 11.90%.

Probability plays a significant role in statistics and helps us understand the likelihood of an event occurring. In this case, we will discuss the probability of selecting a sample with a mean of 1450 or less, given a known population mean of 1500 and a known standard error of the mean of 42.50.

To calculate the probability of selecting a sample with a mean of 1450 or less, we will use the concept of the standard normal distribution. The standard normal distribution is a probability distribution that has a mean of 0 and a standard deviation of 1.

We can convert any normal distribution to a standard normal distribution by using the formula z = (x - μ) / σ, where z is the standard score, x is the raw score, μ is the population mean, and σ is the standard deviation.

In this case, we know the population mean is 1500, and the standard error of the mean is 42.50. The standard error of the mean is the standard deviation of the sample means, and we can calculate it using the formula σ/√n, where σ is the population standard deviation and n is the sample size. However, in this case, we already know the standard error of the mean.

Using the formula z = (x - μ) / σ, we can find the z-score for a sample mean of 1450:

z = (1450 - 1500) / 42.50

z = -1.18

We can then use a standard normal distribution table to find the probability of a z-score of -1.18 or less.

The probability of a z-score of -1.18 or less is 0.1190, or approximately 11.90%.

Therefore, the probability of selecting a sample with a mean of 1450 or less, given a known population mean of 1500 and a known standard error of the mean of 42.50, is approximately 11.90%.

This means that if we were to randomly select samples from the population, about 11.90% of them would have a mean of 1450 or less.

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The smallest integer k that satisfies the given condition is k = 1. In Big O notation, this can be expressed as √n = O([tex]n^1[/tex]) or simply √n = O(n).

The smallest integer k such that √n = O([tex]n^k[/tex]) can be determined by comparing the growth rates of the functions. In this case, we want to find the value of k that makes the function √n grow at most as fast as n^k.
The square root function, √n, is less complex than any positive integer power of n. In other words, as n becomes large, any positive integer power of n will grow faster than the square root of n. To satisfy the condition √n = O([tex]n^k[/tex]), we need to find the smallest integer value of k such that[tex]n^k[/tex] grows faster than √n.
Since k must be an integer, the smallest possible value is k = 1. This means we are comparing the growth rates of √n and n^1 (which is simply n). As n becomes large, n will indeed grow faster than √n.

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[tex]f(4c+1)=9(4c+1)+5=36c+9+5=36c+14[/tex]

you can choose to add the common factor which is 2(18c+7)

Answer:

[tex]\frac{3}{26}[/tex] of pulling a queen or a black 3.

Step-by-step explanation:

Since there's 52 cards in an average deck and there's 4 queens, divide 52 with 4 and you'll get 13, so that means it's a [tex]\frac{1}{13}[/tex] chance of getting a queen.

Also because there's 4 "3"s and 50% of those cards are black (clubs and spades), divide 52 with 2 and you'll get a [tex]\frac{1}{26}[/tex] chance of getting a black 3.

Add both quotients to a common denominator of 52 and you will end up with 6/52. Then simplify the sum.

You should end up with [tex]\frac{3}{26}[/tex].

The statement that is true when calculating a 95% confidence interval for the difference between two means is that when the confidence interval ranges from a negative value to a positive value.

When calculating a 95% confidence interval for the difference between two means, the confidence interval represents a range of values that is likely to contain the true difference between the two population means. A confidence interval that ranges from a negative value to a positive value indicates that there is a range of possible differences between the two population means, including the possibility of no difference (i.e., the difference is zero).

However, since the confidence interval does not include zero, we can conclude (at 95% confidence) that there is a statistically significant difference between the two population means. On the other hand, if the confidence interval ranges from a negative value to a negative value or from a positive value to a positive value, we can conclude (at 95% confidence) that both population means are either negative or positive, respectively. Finally, if the confidence interval includes zero, we cannot conclude that there is a significant difference between the two population means.

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Answer:

y < 106

Step-by-step explanation:

In this equation, we simply add 21 to both sides, so we get y < 106.

Answer:A

Step-by-step explanation:

using the raiload racks

The particular solution is y = (-9/8) * (9x + 81) e^(-x/9) + 85.125.

To solve this differential equation, we can use separation of variables.

dy/dx = -9x/8 e^(-x/9)

dy = (-9/8)x e^(-x/9) dx

Integrating both sides, we get:

y = (-9/8) * (9x + 81) e^(-x/9) + C

where C is the constant of integration.

To find the particular solution, we need to use the initial condition. Let's say that y(0) = 4.

Then, when x = 0, we have:

4 = (-9/8) * (0 + 81) e^(0) + C

C = 4 + (9/8) * 81

C = 85.125

Therefore, the particular solution is:

y = (-9/8) * (9x + 81) e^(-x/9) + 85.125

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Therefore, the approximate value of the solution at t = 0.2 using the improved Euler's method with h = 0.1 is y ≈ 0.6994.

To approximate the solution of the differential equation y' = 1 - 2t^3y, with the initial condition y(0) = 0.5, at t = 0.2 using the improved Euler's method with h = 0.1, we can follow these steps:

Step 1: Initialize the values

Let t0 = 0 and y0 = 0.5 be the initial values.

Let h = 0.1 be the step size.

Let N = (t - t0) / h = (0.2 - 0) / 0.1 = 2 be the number of iterations.

Step 2: Iterate using the improved Euler's method

For i = 1 to N:

Calculate the slope at the current point using the equation:

k1 = 1 - 2t^3y

Calculate the value of y at the midpoint using the equation:

ymid = y0 + h * k1

Calculate the slope at the midpoint using the equation:

k2 = 1 - 2(t + h/2)^3 * ymid

Update the value of y using the equation:

y1 = y0 + h * k2

Update the value of t:

t = t0 + i * h

Update the value of y0 for the next iteration:

y0 = y1

Step 3: Calculate the approximate value of y at t = 0.2

After N iterations, the value of y at t = 0.2 will be y1.

Let's calculate the values using the above steps:

Iteration 1:

t = 0

y0 = 0.5

k1 = 1 - 2(0)^3 * 0.5 = 1

ymid = 0.5 + 0.1 * 1 = 0.6

k2 = 1 - 2(0.05)^3 * 0.6 = 0.99999375

y1 = 0.5 + 0.1 * 0.99999375 = 0.599999375

Iteration 2:

t = 0.1

y0 = 0.599999375

k1 = 1 - 2(0.1)^3 * 0.599999375 = 0.99800000624

ymid = 0.599999375 + 0.1 * 0.99800000624 = 0.6997994375

k2 = 1 - 2(0.15)^3 * 0.6997994375 = 0.99437500348

y1 = 0.599999375 + 0.1 * 0.99437500348 = 0.699437537823

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Answer:

68 boys

Step-by-step explanation:

8 girls + 17 boys = 25 students.

boys make up 17/25.

17 out of 25 = (17 X 100) / 25 = 68 (%)

so, out of 100 students, there will be 68 boys

(1) False. A p-value of 4 indicates that there is a high probability of obtaining the observed results by chance alone.
(2) False. The p-value is the probability of obtaining the observed results or more extreme results if the null hypothesis is true.

False. A p-value of .4 means we should not necessarily accept that the null hypothesis is true. The p-value represents the probability of obtaining a result as extreme or more extreme than the one observed, assuming the null hypothesis is true. A common threshold to reject the null hypothesis is a p-value less than 0.05. Since 0.4 is greater than 0.05, we do not have enough evidence to reject the null hypothesis, but it does not mean we should accept it as true.

False. The p-value is not the probability that the null hypothesis is true. It is the probability of observing the given results (or more extreme results) assuming the null hypothesis is true.

In the strep test scenario, the first test made a Type II error. This occurs when the test fails to reject a false null hypothesis, meaning the test showed a negative result (no strep) when the student actually had strep.

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To find the area of the surface, we will use the formula. Therefore, the area of the surface is $\frac{4\pi}{3}(b^2-a^2)$.

$A=\iint\limits_{S},dS$

where $S$ is the surface of the sphere inside the cylinder.

Since the surface of the sphere and the cylinder are both symmetric about the $z$-axis, we can use cylindrical coordinates.

$x=r\cos\theta, y=r\sin\theta, z=z$

The sphere has the equation $x^2+y^2+z^2=b^2$, so substituting the cylindrical coordinates we get:

$r^2+z^2=b^2$

The cylinder has the equation $x^2+y^2=a^2$, so substituting the cylindrical coordinates we get:

$r^2=a^2$

The limits of integration for $r$ are from $0$ to $a$, and for $\theta$ are from $0$ to $2\pi$. The limits of integration for $z$ are from $-\sqrt{b^2-r^2}$ to $\sqrt{b^2-r^2}$.

$A=\int\limits_{0}^{2\pi}\int\limits_{0}^{a}\sqrt{1+(\frac{\partial z}{\partial r})^2+(\frac{\partial z}{\partial\theta})^2},r,dr,d\theta$

$\frac{\partial z}{\partial r}=\frac{-r}{\sqrt{b^2-r^2}}$, and $\frac{\partial z}{\partial\theta}=0$.

$A=\int\limits_{0}^{2\pi}\int\limits_{0}^{a}\sqrt{1+\frac{r^2}{b^2-r^2}},r,dr,d\theta$

Letting $u=\frac{r^2}{b^2-r^2}$, we have $\frac{du}{dr}=\frac{2b^2}{(b^2-r^2)^2}$, and so $du=\frac{2b^2}{(b^2-r^2)^2},r,dr$. Substituting $u$ and $du$ we get:

$A=\int\limits_{0}^{2\pi}\int\limits_{0}^{\frac{a^2}{b^2-a^2}}\sqrt{1+u},du,d\theta$

Using the substitution $v=1+u$, we get $dv=du$, and so:

$A=\int\limits_{0}^{2\pi}\int\limits_{1}^{1+\frac{a^2}{b^2-a^2}}\sqrt{v},dv,d\theta$

$A=\int\limits_{0}^{2\pi}\frac{2}{3}(1+\frac{a^2}{b^2-a^2})^{\frac{3}{2}},d\theta$

$A=\frac{4\pi}{3}(b^2-a^2)$

Therefore, the area of the surface is $\frac{4\pi}{3}(b^2-a^2)$.

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To find the margin of error, we need to first determine the formula for it. The margin of error (ME) is calculated by multiplying the critical value of the confidence level (in this case 90%) with the standard error (SE) of the sample mean.

The critical value for a 90% confidence interval can be found using a t-distribution table with n-1 degrees of freedom (where n is the sample size). For a sample size of 30, the degrees of freedom would be 29. Using the table, the critical value for a 90% confidence interval is approximately 1.697.

Next, we need to calculate the standard error. The formula for the standard error of the sample mean is the standard deviation of the population divided by the square root of the sample size. However, we don't know the standard deviation of the population, so we will use the sample standard deviation as an estimate.

Assuming that the sample is representative of the population, we can assume that the sample standard deviation is an unbiased estimate of the population standard deviation. Therefore, we can use the formula:

SE = s / sqrt(n)

where s is the sample standard deviation and n is the sample size.

Since we are not given the sample standard deviation, we cannot calculate the standard error. However, we can use the range of the confidence interval to estimate it. The range of the confidence interval is equal to the margin of error multiplied by 2. Therefore:

ME = (51.3 - 48.7) / 2 = 1.3

Using the formula for the margin of error, we can solve for the standard error:

ME = t*SE

1.3 = 1.697*SE

SE = 0.767

Therefore, the margin of error is approximately 1.3 inches.

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the instantaneous velocity function of the object moving along the line described by y=f(x)=6x^2-5x at time x (in seconds) is v = f'(x) = 12x - 5 feet per second.

the instantaneous velocity of an object is the rate of change of its position at a particular moment in time. In other words, it is the slope of the tangent line to the position function at that specific point.

To find the instantaneous velocity function, we take the derivative of the position function with respect to time. In this case, the derivative of f(x) is f'(x) = 12x - 5.

To find the velocity at times x = 1, 3, and 5 seconds, we simply plug in those values for x into the instantaneous velocity function. Therefore, the velocity at x = 1 second is v(1) = f'(1) = 12(1) - 5 = 7 feet per second. The velocity at x = 3 seconds is v(3) = f'(3) = 12(3) - 5 = 31 feet per second. Finally, the velocity at x = 5 seconds is v(5) = f'(5) = 12(5) - 5 = 55 feet per second.

the instantaneous velocity function of the object is v = f'(x) = 12x - 5 feet per second, and the velocity at times x = 1, 3, and 5 seconds is 7 feet per second, 31 feet per second, and 55 feet per second, respectively.

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Let's denote the cost of making one vegetable sandwich as x. Then we know that the cost of a vegetable burger is x + 12. The cost of a vegetable burger is 14.75 rupee

From the problem statement, we know that the cost of making one sandwich is 2.75 rupees, so we can set up the equation:

x = 2.75

Then the cost of a vegetable burger is:

x + 12 = 2.75 + 12 = 14.75

In summary, the cost of a vegetable burger from the school canteen is 14.75 rupees. We can find this by adding the cost of making one sandwich (2.75 rupees) to the extra cost of 12 rupees for the burger.

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Let's denote the cost of making one vegetable sandwich as x. Then we know that the cost of a vegetable burger is x + 12. The cost of a vegetable burger is 14.75 rupee

From the problem statement, we know that the cost of making one sandwich is 2.75 rupees, so we can set up the equation:

x = 2.75

Then the cost of a vegetable burger is:

x + 12 = 2.75 + 12 = 14.75

In summary, the cost of a vegetable burger from the school canteen is 14.75 rupees. We can find this by adding the cost of making one sandwich (2.75 rupees) to the extra cost of 12 rupees for the burger.

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Answer:

To begin, we set each component to zero:

x + 3 = 0 x^2 - 4 = 0

When we solve for x in the first equation, we get:

x = -3

We may factor the second equation further using the difference of squares formula which is:

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

Then, in each factor, we solve for x:

x + 2 = 0 or x - 2 = 0

x = -2 or x = 2

As a result, the function's zeroes are x = -3, x = -2, and x = 2.

Answer:

-3, -2, and 2.

Step-by-step explanation:

Solving for x in the first equation gives:

x+3 = 0

x = -3

Solving for x in the second equation gives:

x^2-4 = 0

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

x+2 = 0 or x-2 = 0

x = -2 or x = 2

Therefore, the zeroes of the function F(x) are -3, -2, and 2.