how do you choose the coefficient with the greatest value

After cross multiplying and simplifying the given equation 5/17 = x/10, the value if the missing variable x is equal to 50/17 or 5.88.

To solve the equation 5/17 = x/10 for x, we can use cross-multiplication. This means we can multiply both sides of the equation by 10 to isolate x on one side:

5/17 = x/10

10 * 5/17 = x

Simplifying the left-hand side of the equation:

50/17 = x

So x is equal to 50/17. This is the solution to the equation, and it represents the value of x that would make the equation true. When 5 is 17% of 10, the missing variable x is 5.88.

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Answer:

Step-by-step explanation:

The answer is choice B.

No matter what the equation for each angle,

they still add to 180°.  All interior angles of a triangle

add to 180°.

the final simplified form of the expression is cot X + cot y + cot Y + tan y, which verifies the given identity.

Starting with the given expression: tan x + cot y tan y + cot X tan x cot y tan X + cot Y tan x cot y cot tan Itan y cot X tan y cot x tan y (cot x_ cot X tany tan y cot X cot X cot X tan y + cot X tan Y tan y

Rearranging the terms and grouping like terms: tan x + cot x cot X + cot y (tan y + cot y) + cot X (tan x + cot X) + cot Y (tan x + cot Y) + tan y

Simplifying cot x cot X + cot y (tan y + cot y) + cot X (tan x + cot X) + cot Y (tan x + cot Y):

cot x cot X can be simplified to 1 using the identity cot x cot X = 1.

tan y + cot y can be simplified to cot y using the identity tan y + cot y = cot y.

tan x + cot X can be left as it is.

cot Y (tan x + cot Y) can be simplified to cot Y using the identity cot Y (tan x + cot Y) = cot Y.

The remaining term tan y stays as it is.

Combining the simplified terms: cot X + cot y + cot Y + tan y.

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The Evaluated integral is - (cos(x)^3/3) + C

To evaluate the given integral ∫[sec(x) cos(x)^2cos(x)]dx, we can use the u-substitution method. Let's make the substitution:

u = cos(x)

Taking the derivative of u with respect to x gives:

du/dx = -sin(x)

Rearranging the equation, we have:

dx = -du/sin(x)

Substituting u = cos(x) and dx = -du/sin(x) into the integral, we get:

∫[sec(x) cos(x)^2cos(x)]dx = ∫sec(x) u^2

The sin(x) term in the denominator cancels out with sec(x) in the numerator, giving:

∫u^2

Integrating, we get:

∫[u^2] du = - (u^3/3) + C

Now, substitute back u = cos(x) to obtain the final result:

(cos(x)^3/3) + C

To check our answer, we can differentiate the obtained result:

d/dx [- (cos(x)^3/3)] = sin(x)(cos(x)^2)

Which is the same as the integrand in the original integral, confirming the correctness of our answer.

Therefore, the evaluated integral is - (cos(x)^3/3) + C

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Substituting back u = sin(x), we get: (1/2) sin^(-1)(sin(x)) + C = (1/2) x + C

We can start by applying the substitution u = sin(x) and du = cos(x) dx, which transforms the integral into:

∫[sec(x) cos(x)2cos(x)]dx = ∫[1/cos(x) cos(x)2cos(x)]dx = ∫[cos(x)]dx

Then, using u = sin(x), we have:

∫[cos(x)]dx = ∫[√(1-u^2)]du = (1/2) sin^(-1)(u) + C

To check our answer, we can differentiate (1/2) x + C and see if we get the integrand:

d/dx[(1/2) x + C] = 1/2 cos(x)

Now, using the identity sec^2(x) = 1 + tan^2(x), we can also rewrite the integrand as:

cos(x)2cos(x)/sec(x) = 2cos^2(x)/[1 + tan^2(x)] = 2(1/cos^2(x))/[1 + tan^2(x)] = 2/cos^2(x)

Using this alternate form of the integrand, we can also evaluate the integral by using the substitution u = tan(x), which leads to:

∫[2/cos^2(x)]dx = ∫[2(1 + u^2)]du = 2u + (2/3)u^3 + C = 2tan(x) + (2/3)tan^3(x) + C

Again, we can check our answer by differentiating:

d/dx[2tan(x) + (2/3)tan^3(x) + C] = 2sec^2(x) + 2tan^2(x) sec^2(x) = 2cos^2(x)/cos^4(x) = 2/cos^2(x)

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the p-series with p = 4 is:  1/1 + 1/16 + 1/81 + ...

This series converges to a specific value, which is approximately 1.082323.

The p-series is defined as the sum of the reciprocals of the powers of positive integers raised to a certain exponent p. In this case, Euler calculated the sum of the p-series with p = 4, which can be expressed as 1 + 1/16 + 1/81 + ...

Euler utilized his mathematical skills and knowledge to manipulate the series and find a closed-form solution. The process likely involved applying various techniques such as algebraic manipulation, mathematical identities, and possibly calculus or infinite series summation methods.

The result obtained by Euler, 490, signifies that the infinite series converges to a finite value. It demonstrates the concept of convergence, where even though there are an infinite number of terms, the sum can be determined and yields a finite result.

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Answer:

There is a 35/138 chance that the first is a woman and the second is a man.

Step-by-step explanation:

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The probability distribution for X is:

X P(X)

0 1/9

1 1/2

2 1/9

Since there are 5 men and 5 women in the group, the total number of ways to select 2 people is 10C2 = 45.

Let X be the number of men selected. We can calculate the probability of each possible value of X using combinations.

P(X=0) = 5C2 / 10C2 = 1/9

P(X=1) = (5C1 x 5C1) / 10C2 = 1/2

P(X=2) = 5C2 / 10C2 = 1/9

Note that the sum of probabilities for all possible values of X is equal to 1, as it should be for a probability distribution.

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No, this situation cannot be accurately modeled without knowing the specific values of Kara's allowance.

The given situation of Kara spending half of her allowance on Saturday and one-third of what she had left on Sunday cannot be accurately modeled without knowing the specific values of Kara's allowance.

The information provided lacks the necessary numerical values to perform calculations and determine the exact amounts Kara spent on each day. Without knowing the precise amount of her allowance, it is impossible to calculate the exact proportions and evaluate the situation.

To accurately model this situation, it would be necessary to know the actual numerical value of Kara's allowance.

With that information, we could calculate half of her allowance for Saturday and then one-third of what she had left for Sunday, allowing us to determine the specific amounts spent on each day. Without these values, any modeling or further analysis would be purely speculative.

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The upper and lower bounds on the moduli of the zeros of the given polynomial, we construct the companion matrix using its coefficients. The eigenvalues of this matrix provide the zeros.

To begin, we construct the companion matrix associated with the given polynomial, which is a square matrix formed by coefficients. In this case, the companion matrix is:

C = [[0, 0, 0, 0, 0, 0, 0, 20i24], [1, 0, 0, 0, 0, 0, 0, -i], [0, 1, 0, 0, 0, 0, 0, 2i], [0, 0, 1, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0, 2], [0, 0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 0, 1, 0]].

The eigenvalues of this matrix are precisely the zeros of the polynomial. By applying Gershgorin's theorem, we can establish upper and lower bounds on the moduli of these eigenvalues. Gershgorin's theorem states that each eigenvalue lies within at least one Gershgorin disc, which is a circular region centered at each diagonal entry of the matrix with a radius equal to the sum of the absolute values of the off-diagonal entries in the corresponding row.

By examining the Gershgorin discs for the companion matrix C, we can determine upper and lower bounds for the moduli of the eigenvalues (zeros of the polynomial). These bounds provide valuable information about the possible locations and values of the zeros. By calculating the radius of each disc and considering the diagonal entries, we can estimate the upper and lower limits for the moduli of the zeros.

In conclusion, by utilizing companion matrices and applying Gershgorin's theorem, we can establish upper and lower bounds on the moduli of the zeros of the given polynomial. These bounds offer insights into the possible values and locations of the zeros, aiding in the understanding of the polynomial's behaviour and properties.

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Based on the provided evidence, the analysis suggests that "b" is more likely than 20% to be the correct choice

To evaluate whether "b" is more likely than 20% to be the correct choice, we can conduct a hypothesis test. The null hypothesis (H0) assumes that the probability of "b" being the correct choice is 20% (or 0.2), while the alternative hypothesis (Ha) assumes that the probability is greater than 20%.

Using the binomial distribution, we can calculate the expected number of questions with "b" as the correct choice if the probability is 20%. In this case, the expected number would be 0.2 multiplied by the total number of questions (400), resulting in 80 questions.

Next, we can perform a one-sample proportion test to determine if the observed proportion of 90/400 (0.225) significantly deviates from the expected proportion of 0.2. By comparing the observed proportion to the expected proportion using appropriate statistical tests (such as a z-test or chi-square test), we can assess if the difference is statistically significant.

If the p-value associated with the test is less than the chosen significance level (commonly 0.05), we can reject the null hypothesis and conclude that "b" is more likely than 20% to be the correct choice.

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A symbol that could be written in both circles in order to represent this system algebraically include the following: C. <.

In Mathematics, there are several rules that are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a graph and these include the following:

In this context, we can logically deduce that the most appropriate inequality symbol to represent the solution to the system of inequalities is the less than (<) because the dashed boundary lines are shaded below.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

1. The two shapes that make the figure are Rectangular prism and Trapezoidal prism

2. The volume of shape 1 is 200 cubic centimeters

3. The volume of shape 2 is 360 cubic centimeters

4. The total volume of the shape is 560 cubic centimeters

From the question, we have the following parameters that can be used in our computation:

The figure

The two shapes that make the figure are

This is calculated as

Volume = Length * Width * Height

So, we have

Volume = 5 * 5 * 8

Volume = 200

This is calculated as

Volume = 1/2 * (Sum of parallel sides) * Height * Length

So, we have

Volume = 1/2 * (5 + 10) * 6 * 8

Volume = 360

This is calculated as

Volume = Sum of the volumes of both shapes

So, we have

Volume = 200 + 360

Evaluate

Volume = 560

Hence, the total volume of the shape is 560 cubic centimeter

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The probability that there will be fewer than 20 no-shows among 150 advanced reservations, using the normal approximation with continuity correction, is approximately 0.116.

To determine this probability, we can use the normal distribution as an approximation to the binomial distribution with the given parameters. The continuity correction is applied to account for the fact that the binomial distribution is discrete while the normal distribution is continuous.

Given that the rate of no-shows is 15% and there are 150 advanced reservations, we can calculate the mean (μ) and standard deviation (σ) of the binomial distribution using the formula: μ = np and σ = sqrt(np(1-p)), where p is the probability of a no-show.

In this case, p = 0.15, so μ = [tex]150 * 0.15[/tex] = 22.5 and σ = sqrt([tex]150 * 0.15 * 0.85[/tex]) ≈ 3.35.

To find the probability of fewer than 20 no-shows, we can use the normal distribution with a continuity correction. We calculate the z-score for 20 as (20 - μ + 0.5) / σ and then use a standard normal distribution table or calculator to find the corresponding cumulative probability.

Using the z-score, we find z ≈ (20 - 22.5 + 0.5) / 3.35 ≈ -0.746. Looking up this z-score in a standard normal distribution table or calculator, we find a cumulative probability of approximately 0.229.

Since we want the probability of fewer than 20 no-shows, we subtract this probability from 0.5 (to account for the area in the right tail of the distribution) and multiply by 2 to include the left tail as well: P(Z < -0.746) ≈ [tex]2 * (0.5 - 0.229)[/tex] ≈ 0.542.

Therefore, the probability that there will be fewer than 20 no-shows among 150 advanced reservations is approximately 0.116 (rounded to three decimal places).

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The values of the function f(x,y) at the specified points are:
f(-2,4) = 14
f(5,5) = 130
f(-4,5) = 76

To evaluate the function f(x,y)=x+yx^2 at the specified points (?2,4), (5,5), and (?4,5), we simply substitute the given values of x and y into the function. For the point (?2,4), we have:
f(-2,4) = -2 + 4(-2)^2 = -2 + 16 = 14
For the point (5,5), we have:
f(5,5) = 5 + 5(5)^2 = 5 + 125 = 130
For the point (?4,5), we have:
f(-4,5) = -4 + 5(-4)^2 = -4 + 80 = 76

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The hydroxide ion concentration in the solution is 10.0 M.

The hydroxide ion concentration ([OH-]) in the solution, the reaction between [tex]KOH[/tex] and [tex]NH_3[/tex]

The balanced chemical equation for the reaction is:

[tex]KOH[/tex] + [tex]NH_3[/tex] -> [tex]K[/tex]+ [tex]NH_4OH[/tex]

From the equation, that 1 mole of [tex]KOH[/tex] reacts with 1 mole of [tex]NH_3[/tex] to form 1 mole of [tex]NH_4OH[/tex].

First, the number of moles of [tex]NH_3[/tex] in the solution:

Moles of [tex]NH_3[/tex] = Concentration of [tex]NH_3[/tex] × Volume of Solution

= 10.0 mol/L × 1.00 L

= 10.0 mol

Since 1 mole of [tex]KOH[/tex] reacts with 1 mole of [tex]NH_3[/tex], the number of moles of [tex]KOH[/tex] is also 10.0 mol.

calculate the number of moles of [tex]OH[/tex]- ions produced from [tex]KOH[/tex]:

Moles of [tex]OH[/tex]- = Moles of [tex]KOH[/tex] = 10.0 mol

The concentration of [tex]OH[/tex]- ions ([[tex]OH[/tex]-]) in the solution:

Volume of Solution = 1.00 L

[[tex]OH[/tex]-] = Moles of [tex]OH[/tex]- / Volume of Solution

= 10.0 mol / 1.00 L

= 10.0 M.

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The part of the figure of a circle labeled as angle APB is

The part of the circle marked by a question marked as angle APB is solved using the relationship below

given angle formed by the tangents = major arc ACB - 180 degrees

information given in the problem includes

given angle formed by the tangents = angle APB

major arc ACB = 266

substituting in these values results to

given angle formed by the tangents = 266 degrees - 180 degrees

given angle formed by the tangents = 86 degrees

hence the required side, which is angle APB is 86 degrees

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The t-distribution table to find the critical value for a two-tailed test at the 0.05 significance level.

To test whether a change in price will have any impact on sales, one could conduct a hypothesis test using the t-distribution with a significance level of 0.05.

The critical values for this test depend on the degrees of freedom, which are determined by the sample size and the number of parameters being estimated.
If we are comparing two means (i.e. before and after prices), then the degrees of freedom would be the total sample size minus two.

For example, if we have a sample size of 30, then the degrees of freedom would be 28.
Using a t-table or a calculator, we can find the critical values for the t-distribution with 28 degrees of freedom and a significance level of 0.05.

The critical values would be ±2.048.
If the calculated t-value falls within the critical region (i.e. outside of the range of -2.048 to 2.048), then we can reject the null hypothesis and conclude that there is a significant difference in sales before and after the price change.

If the calculated t-value falls within the non-critical region (i.e. within the range of -2.048 to 2.048), then we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference in sales.
Therefore, based on the given options, the critical value would be d. 2.5706 for a t-distribution with 28 degrees of freedom and a significance level of 0.05.

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(a) This is a valid probability function because the probabilities assigned to each outcome (four games, five games, six games, seven games) are non-negative (greater than or equal to zero) and the sum of all probabilities is equal to 1 (0.1919 + 0.2121 + 0.2222 + 0.3737 = 1).

The given probabilities satisfy the fundamental properties of a valid probability function. Each probability value is non-negative, indicating that they are within the valid range of probabilities. Additionally, when we sum up all the probabilities, the total equals 1, which is the requirement for a probability distribution. Therefore, this set of probabilities forms a valid probability function.

(b) To find the mean and standard deviation for the number of games in World Series contests, we need to calculate the expected value and variance based on the given probabilities. The mean, also known as the expected value, is calculated by multiplying each outcome by its respective probability and summing up the results. The variance is computed by subtracting the square of the mean from the expected value of the square of each outcome, weighted by their probabilities. Finally, the standard deviation is the square root of the variance.

(c) Whether it is unusual for a team to "sweep" by winning in four games can be determined by examining the z-score associated with the probability of winning in four games. The z-score measures the number of standard deviations an observation is from the mean. If the z-score falls within a certain range, it is considered usual or unusual based on a predetermined threshold.

To determine if winning in four games is unusual, we would need to calculate the z-score for the probability of winning in four games using the mean and standard deviation derived in part (b). If the z-score is beyond a certain threshold, typically set at ±2 standard deviations, then winning in four games would be considered unusual.

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We see that the absolute minimum value of the function occurs at x = 2, where f(2) = 4. Therefore, the answer is b. 2.

The absolute minimum value of f(x) = x3-3x2 + 12 on the closed interval [-2,4] can be found by evaluating the function at the critical points and endpoints of the interval.

To do this, we first take the derivative of the function:
f'(x) = 3x2 - 6x

Then we set f'(x) = 0 and solve for x:
3x2 - 6x = 0
3x(x - 2) = 0
x = 0 or x = 2

Next, we evaluate the function at the critical points and endpoints:
f(-2) = -4
f(0) = 12
f(2) = 4
f(4) = 28

We see that the absolute minimum value of the function occurs at x = 2, where f(2) = 4. Therefore, the answer is b. 2.

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The value of x from a random sample of size 9 is approximately 7.345 years.

To find the value of x to the right of which 15% of the means computed from a random sample of size 9 would fall, we need to consider the sampling distribution of the sample means.

For a normal distribution, the sampling distribution of the sample means will also follow a normal distribution.

The mean of the sampling distribution will be the same as the population mean, which is 7 years in this case.

The standard deviation of the sampling distribution, also known as the standard error, can be calculated by dividing the population standard deviation by the square root of the sample size.

Standard error = σ / [tex]\sqrt(n)[/tex]

Given that the population standard deviation is 1 year and the sample size is 9, we can calculate the standard error:

Standard error = 1 / [tex]\sqrt(9)[/tex] = 1/3

Since the distribution is symmetric, we can find the value of x to the right of which 15% of the means fall by finding the z-score corresponding to the 85th percentile (100% - 15% = 85%).

Using a standard normal distribution table or statistical software, we can find that the z-score corresponding to the 85th percentile is approximately 1.036.

Now, we can calculate the value of x:

x = μ + z * SE

where μ is the population mean (7 years), z is the z-score (1.036), and SE is the standard error (1/3).

x = 7 + 1.036 * (1/3) = 7 + 0.345 = 7.345

Therefore, the value of x to the right of which 15% of the means computed from a random sample of size 9 would fall is approximately 7.345 years.

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The total cost to produce 6 items whose marginal cost function of a product, in dollars per unit, is c′(q)=2q²−q+ 100 and if the fixed costs are $1000 is $1726.

The marginal cost function of a product

c′(q)=2q²−q+ 100

To find the cost-taking integration on both side

[tex]\int\limits{c'} \, dq = \int\limits {2q^{2} - q + 100 } \, dx[/tex]

c = [tex]\frac{2q^{2} }{3} -\frac{q^{2} }{2} + 100q[/tex]

Cost to produced = 6 items , fixed cost of the product = 1000

Total cost = 1000 + [tex]\frac{2q^{2} }{3} -\frac{q^{2} }{2} + 100q[/tex]

q = 6

Total cost = 1000 +[tex]\frac{2(6)^{2} }{3} -\frac{6^{2} }{2} + 100(6)[/tex]

Total cost  = 1000 + 144 - 18 + 600

Total cost = 1726

The total cost to produce 6 items is 1726 .

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The value of the integral

∫ d t ( 1 − 3 t ) 5 = (-1/243)(1-3t)⁶/6 + (5/81)(1-3t)⁵/15 - (10/36)(1-3t)⁴/36 + (10/81)(1-3t)³/81 - (5/324)(1-3t)²/243 + c

To evaluate this integral using the given substitution, we need to first find an expression for dt in terms of du. To do this, we can differentiate the substitution equation u = 1 - 3t with respect to t, giving:

du/dt = -3

Solving for dt, we get:

dt = -du/3

Now we can substitute for dt and for 1-3t in the integral, giving:

∫ d t ( 1 − 3 t ) 5 = ∫ (1-u/3)⁵ (-du/3)

Expanding the binomial and factoring out the constant -1/243, we get:

∫ (u⁵ - 5u⁴/3 + 10u³/9 - 10u²/27 + 5u/81 - 1/243) du

Integrating each term separately, we get:

(u⁶/6 - 5u⁵/15 + 10u⁴/36 - 10u³/81 + 5u²/324 - u/243) + c

Substituting back for u, we get the final answer:

∫ d t ( 1 − 3 t ) 5 = (-1/243)(1-3t)⁶/6 + (5/81)(1-3t)⁵/15 - (10/36)(1-3t)⁴/36 + (10/81)(1-3t)³/81 - (5/324)(1-3t)²/243 + c

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Jane's rate is 30 miles per hour

Let's assume Jane's rate is x miles per hour.

Since Peter drives 15 mph faster than Jane, his rate would be x + 15 miles per hour.  

To find the total distance traveled by both Jane and Peter after 3 hours, we can use the formula:

distance = rate × time.

Jane's distance after 3 hours is:

Jane's distance = x miles per hour × 3 hours = 3x miles

Peter's distance after 3 hours is:

Peter's distance = (x + 15) miles per hour × 3 hours = 3(x + 15) miles

The total distance traveled by both Jane and Peter is given as 225 miles.

Therefore, we can set up the following equation:

3x + 3(x + 15) = 225

Simplifying the equation:

3x + 3x + 45 = 225

6x + 45 = 225

6x = 225 - 45

6x = 180

x = 180 / 6

x = 30.

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The frequency table for the given data is                                                                      

                        Girls    Boys

Drama                5         8

Adventure         14        15.

Given that, each of forty two students was asked "Do you perfer drama books or adventure books.

Here are the results

8 boys and 5 girls chose drama.

15 boys and 14 girls chose adventure.

                        Girls    Boys

Drama                5         8

Adventure         14        15

Therefore, the frequency table for the given data is                                                                      

                        Girls    Boys

Drama                5         8

Adventure         14        15.

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The value of the range of function y = sin x is,

⇒ Range = -1 ≤ y ≤ 1

Since, A relation between sets of inputs which having exactly one output each is called a function.

And, an expression, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Here, The function is,

y = sin x

Now, We know that;

The range of y = sin x is,

⇒ Range = -1 ≤ x ≤ 1

Hence, Option A is true.

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true - searching for a value in a binary search tree takes O(log n) time.

a binary search tree is a data structure where each node has at most two children, and the left child is always smaller than the parent while the right child is always larger. This structure allows for efficient searching, as we can compare the value we are searching for with the value of the current node and traverse either the left or right subtree accordingly. By doing so, we can eliminate half of the remaining nodes with each comparison, leading to a time complexity of O(log n).

searching for a value in a binary search tree takes O(log n) time, which is a relatively efficient algorithmic complexity. However, it's important to note that this assumes the tree is balanced and does not take into account worst-case scenarios where the tree may be heavily skewed.

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Over the time interval [2,5], the object traveled a distance of 450 meters.

To find the distance traveled over the time interval [0,2], we can use the formula for distance traveled, which is given by:

distance = velocity x time

Since the velocity is given by v(t) = 18t m/s, we can substitute t = 2 seconds to find the velocity at time t=2:
v(2) = 18(2) = 36 m/s

Now we can use this velocity and the time interval [0,2] to find the distance traveled:
distance = velocity x time
distance = 18t x t = 18t²

For t = 2 seconds, the distance traveled is:
distance = 18(2)² = 72 meters

Therefore, over the time interval [0,2], the object traveled a distance of 72 meters.

To find the distance traveled over the time interval [2,5], we can use the same formula, but this time we need to find the velocity at t=5 seconds:
v(5) = 18(5) = 90 m/s

Now we can use this velocity and the time interval [2,5] to find the distance traveled:
distance = velocity x time
distance = 18t x t = 18t²

For t = 5 seconds, the distance traveled is:
distance = 18(5)² = 450 meters

Therefore, over the time interval [2,5], the object traveled a distance of 450 meters.

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The integration  ∫20x⋅f′(x)ⅆx is 1. The answer is (A) 1.

We can use integration by parts to solve this problem. Let u = x and v = f(x), then we have:

∫2^0 x f'(x) dx = [x f(x)]2^0 - ∫2^0 f(x) dx

Using the given values of f(0) and f(2), we get:

∫2^0 x f'(x) dx = -2f(0) + 2f(2) - ∫2^0 f(x) dx

Now, we need to find the value of ∫2^0 f(x) dx. We are given that ∫2^0 f(x) dx = 7, so substituting this value in the above equation, we get:

∫2^0 x f'(x) dx = -2 + 2f(2) - 7 = -9 + 2f(2)

We are also given that f(2) = 5, so substituting this value, we get:

∫2^0 x f'(x) dx = -9 + 2(5) = 1

Therefore, the answer is (A) 1.

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We can solve this problem using integration by parts. Let's let u = x and dv = f'(x)dx, which means that du = dx and v = ∫f'(x)dx = f(x). Using the integration by parts formula, we get:

∫2 0 x*f'(x)dx = [x*f(x)]2 0 - ∫2 0 f(x)dx

We know that f(0) = 1 and f(2) = 5, so:

[x*f(x)]2 0 = 2*5 - 0*1 = 10

Now we need to evaluate ∫2 0 f(x)dx. We know that ∫2 0 f(x)dx = 7, so:

∫2 0 x*f'(x)dx = 10 - 7 = 3

Therefore, the answer is (B) 3.
To find the value of the integral ∫2₀xf′(x)dx, we can use integration by parts. Let u = x and dv = f′(x)dx. Then, du = dx and v = ∫f′(x)dx = f(x).

Now apply the integration by parts formula: ∫udv = uv - ∫vdu. So, ∫2₀xf′(x)dx = xf(x)│₂₀ - ∫2₀f(x)dx.

Evaluate the terms: (2f(2) - 0f(0)) - ∫2₀f(x)dx = (2 * 5) - (0 * 1) - 7 = 10 - 7 = 3.

Therefore, the value of the integral ∫2₀xf′(x)dx is 3, which corresponds to option (B).

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Student get wrong, because there is no any inequality is given in equation of line.

We have to given that,

A student's analysis of this graph:

Slope: 3/2

y-intercept: -1

line: solid

shade: above the line

Now, We know that;

Equation of line is,

⇒ y - y₁ = m (x - x₁)

Where, m is slope and (x₁, y₁) is a point on line.

Here, m = 3/2

And, y - intercept = (0, - 1)

Hence, Equation of line is,

⇒ y - (- 1) = 3/2 (x - 0)

⇒ y + 1 = 3/2x

⇒ y = 3/2x - 1

Since, There is no any inequality is given in equation of line.

Hence, Student get wrong.

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The system of inequalities that represent the constraint on the number of pots that can be included in one shipment are;

2 ≤ x + y ≤ 8

15·x + 7.5·y ≤ 79 lbs.

The system of inequalities can be obtained from the given information on the allowable weights and number of pots.

Methods used to find the system of inequalities

The inequality that represents the number total number of clay, T, in each shipment is 2 ≤ T ≤ 8

The inequality that represents weight of each shipment is w < 100 lbs

The weight of each shipment container = 20 lbs

The weight of the packing material = 1 lb

Therefore;

The maximum weight of the flower pots = 100 lbs - 21 lbs = 79 lbs

The weight of each clay flower pot = 15 lbs

The weight of each plastic flower pot = 7.5 lbs

Let "x" represent the number of clay flower pot included in one shipment

and let "y" represent the number of plastic flower pot included in one

shipment, we have;

The system of inequalities that represent the constraint on the number of pots that can be included in one shipment are as follows;

2 ≤ x + y ≤ 8

15·x + 7.5·y ≤ 79 lbs.

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A gardening company sells clay flower pots and plastic flower pots. There must be at least 2 pots in each shipment, but there cannot be more than 8 in a shipment. Additionally, the shipment must weigh less than 100 lbs. Each shipment container weighs 20 lbs., and there is 1 lb. of packing material. A clay flower pot weighs 15 lbs., whereas a plastic flower pot weighs 7.5 lbs.

(A) Write a system of inequalities that represent the constraints on the number of pots that can be included in one shipment.

Answer:

Step-by-step explanation:

The standard equation for a parabola is [tex]y=x^2[/tex]

The given equation is: y = 2(x+2)(x-2)

The given equation is factored out. Since it is factored, we can set each x expression to zero, to solve for the x intercepts.

x+2 = 0

-2      -2

x = -2

x-2 = 0

+2     +2

x = 2

We can therefore graph, (-2, 0) and (2, 0), because we know that it is the x intercepts of the given quadratic function.

to find the vertex, you will take both x intercepts, divide them by two, and that will get you the x cooridnate. Following that you can plug in that value as x into the equation solve for the y coordinate.

[tex]\frac{(-2 + 2)}{2} = 0\\\\x=0\\y = 2(x+2)(x-2)\\\\y = 2(0+2)(0-2)\\y=-8\\\\vertex = (0, -8)[/tex]

finally graph that point and create the parabola shape. If you'd like to make your parabola more accurate, you can always make a t chart of x and y values. and plug in x values into the equation to find the other y values.

I've attached a graph of the given parabola.