The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.

A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.

Which drive-thru typically has more wait time, and why?

Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean

Answer:

The answer to your problem is, A. 4(2a • 5) = (4 • 2a) • 5

Step-by-step explanation:

The APM ( Association Property of Multipaction ) states that multiplication of group of numbers in any combination of any type of number.

Like: a × ( b×c ) = ( a × b ) × c

Option A. Has that;

4(2a • 5) = (4 • 2a) • 5

Thus the answer to your problem is, A. 4(2a • 5) = (4 • 2a) • 5

The answer of the given question based on the statistics is , Part A X= 370 , S= 36 , n= 50 . Part B =  5 . Part C = 9.8 . Part D=  360 and 380.   Part E: the reason is explained below.

The mean is measure of central tendency that represents average value of set of numbers. It is calculated by adding up all the numbers in the set and then dividing the sum by the total number of values. The mean is a useful statistic for describing the typical or average value of a data set, and is often used in data analysis and statistical inference.

Part A:

X= 370 (sample mean)

S= 36 (sample standard deviation)

n= 50 (sample size)

Part B:

s/n = 36/√50 = 5 (rounded to the nearest whole number)

Part C:

The margin of error for a 95% confidence level can be found using the formula: margin of error = z*(standard error), where z is the z-score associated with a 95% confidence level. z-score can found using  standard normal distribution table or calculator. For a 95% confidence level, the z-score is approximately 1.96. Therefore, the margin of error is:

margin of error = 1.96*5 = 9.8 (rounded to one decimal place)

Part D:

The 95% confidence interval can be found by adding and subtracting the margin of error from the sample mean:

95% confidence interval = X ± margin of error = 370 ± 9.8 = (360, 380)

The confidence interval means that we can be 95% confident that the true population mean number of recharges for IQ laptop batteries from Elusive Electronics falls between 360 and 380.

Part E:

Since the 95% confidence interval does not include the claimed average of 400 recharges, we cannot accept the claim that each IQ laptop battery will last for an average of 400 recharges. It is possible that the true population mean is close to 400 recharges, but based on the sample data, we cannot make that conclusion with 95% confidence.

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[tex]\textit{lateral area of a cone}\\\\ LA=\pi r\sqrt{r^2+h^2}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=4\\ r=3 \end{cases}\implies LA=\pi (3)\sqrt{3^2 + 4^2} \\\\\\ LA=3\pi\sqrt{9+16}\implies LA=3\pi \sqrt{25}\implies LA=3\pi (5)\implies LA=15\pi~cm^2[/tex]

The empirical probability of getting exactly 3 heads in 6 coin flips is 20/64 = 0.3125 or 31.25% and the theoretical probability of getting exactly 3 heads in 6 coin flips is also 0.3125 or 31.25%.

What is probability?

Probability is the measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event will not occur and 1 indicating that the event is certain to occur.

Empirical Probability:

If you flip a coin 6 times and record the outcomes, there are a total of [tex]2^6 = 64[/tex] possible outcomes, where each flip can result in either heads or tails.

To calculate the empirical probability of getting exactly 3 heads, you would need to count the number of outcomes in which exactly 3 of the 6 flips result in heads.

For example, one possible outcome is HTHTHH, which has exactly 3 heads.

By enumerating all possible outcomes, we can count that there are 20 outcomes with exactly 3 heads.

Therefore, the empirical probability of getting exactly 3 heads in 6 coin flips is 20/64 = 0.3125 or 31.25%.

Theoretical Probability:

The theoretical probability of getting exactly 3 heads in 6 coin flips can be calculated using the binomial distribution formula, which is:

[tex]P(X=k) = (n\ choose\ k) * p^k * (1-p)^{(n-k)[/tex]

where P(X=k) is the probability of getting exactly k successes, n is the number of trials, p is the probability of success in a single trial, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n.

In this case, we have n=6 trials, k=3 successes, and p=0.5 (assuming a fair coin).

Plugging in these values, we get:

[tex]P(X=3) = (6\ choose\ 3) * 0.5^3 * (1-0.5)^{(6-3)} = 20 * 0.125 * 0.125 = 0.3125 or 31.25%[/tex]

Therefore, the theoretical probability of getting exactly 3 heads in 6 coin flips is also 0.3125 or 31.25%.

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[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-2)}) \implies y -1 = \cfrac{1}{3} ( x +2) \\\\\\ y-1=\cfrac{1}{3}x+\cfrac{2}{3}\implies y=\cfrac{1}{3}x+\cfrac{2}{3}+1\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x+\cfrac{5}{3} \end{array}}[/tex]

The cost is $8712 when the two companies charge the same for 12 tons of sugar.

What is equality?

Equality is a concept in mathematics that refers to the idea that two values, expressions, or equations are equal to each other. In an equality, the values on either side of an equals sign have the same numerical or algebraic value.

Let x be the amount of sugar in tons. The total cost for the first company is given by:

C1 = 7500 + 100.50x

The total cost for the second company is given by:

C2 = 6597 + 175.75x

We want to find the amount of sugar x for which the two companies charge the same, so we can set the two expressions equal to each other and solve for x:

7500 + 100.50x = 6597 + 175.75x

Subtracting 6597 from both sides gives:

903 = 75.25x

Dividing both sides by 75.25 gives:

x ≈ 12

So the two companies charge the same for 12 tons of sugar. To find the cost, we can plug x = 12 into either expression:

C1 = 7500 + 100.50(12) = 8712

C2 = 6597 + 175.75(12) = 8712

So the cost is $8712 when the two companies charge the same for 12 tons of sugar.

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Answer:

  (A)  x² +8

Step-by-step explanation:

You want to select the quadratic binomial from the given list.

The term "quadratic" is used interchangeably with "degree 2" when referring to a polynomial's degree.

A "binomial" is a 2-term polynomial. The prefixes mono-, bi-, tri- are used with -nomial to describe the number of terms as being 1, 2, or 3, respectively.

The quadratic binomial in the list is ...

  x² +8

__

Additional comment

This is a vocabulary question. You are expected to be familiar with the meaning of these descriptive terms. The others on the list are ...

Troy needs a score of 80.28 or higher to be in the top 10% of his class. Since he scored 83, he did perform in the top 10% of his class on this exam.

Percentage is a way of expressing a fraction or a proportion as a portion of 100.

To convert Troy's score to a z-score, we use the formula:

z = (X - M) / SD

where X is Troy's score, M is the class average, and SD is the standard deviation. Plugging in the values we have:

z = (83 - 76.80) / 3.10 = 2.00

To plot this on a distribution, we look up the corresponding area in the z-table. A z-score of 2.00 corresponds to an area of 0.9772.

To convert Troy's score to a percentile rank, we use the formula:

Percentile rank = (number of scoreS below X / total number of scores) x 100%

His percentile rank is approximately:

Percentile rank = (0.9772) x 100% = 97.72%

We can do this by subtracting the area to the left of Troy's z-score from the area to the left of the class average's z-score:

Area  = 0.9772 - 0.5000 = 0.4772

This means that about 47.72% of the scores are between Troy's score and the class average.

Using the formula for z-scores, we can solve for X:

X = (z)(SD) + M = (1.28)(3.10) + 76.80 = 80.28

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For a large sample size (greater than 30), distribution is normal.

An insurance company claims that in the population of homeowners, the mean loss and standard deviation from fire is

μ = $250

o = $5000

The distribution of loss is strongly right skewed.

a). Since for a simple random sample of size n= 15 drawn from  the population of homeowners.

Since the given sample size is small. Therefore for small sample size less the 30 the distribution of

follow t- distribution.

Since t distribution has more variance than normal distribution.

Also t- distribution is symmetric as normal distribution at t=0.

For small sample size sampling distribution is t -distribution.

b). Now if the simple random sample of size n = 10000 drawn from the population of homeowners.

Thus for the large sample size and given mean and standard deviation sampling distribution of x follow normal distribution. Also we know that normal distribution have a bell-shaped curve which is symmetric to z=0.

For a large sample size (greater than 30), distribution is normal.

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In order to fulfill the requirements, we need to draw exactly 5 quadrilaterals with appropriate markings on the grid. Here's an example design:

. . . . . 1 . . . .

. . . . / \ . . .

. . . ./. \.\ . .

. . . / . . \ \ .

. . ./. 5 . \.\ .

. . / . . . . \ \ .

. ./. . 4 . . \.\ .

. 2-----------3 .

. .\ . . . . . /. .

. . \ . . . ./. .

. . .\.\ . / /. .

. . . \.\./ / . .

. . . . \  / . .

. . . . .\/. . .

A parallelogram has two pairs of parallel sides.

A rectangle is a type of parallelogram where all angles are right angles.

A rhombus is a type of parallelogram where all sides are equal in length.

A square is a type of rectangle where all sides are equal in length.

A trapezoid has one pair of parallel sides.

A quadrilateral with no other classification is any quadrilateral that does not fit into the above categories

In this design, we have:

Parallelogram 1, marked with arrows to indicate its parallel sides.

Rectangle 2, marked with right-angle symbols to indicate its right angles.

Rhombus 3, marked with tick marks to indicate its equal sides.

Square 4, marked with tick marks and a right-angle symbol to indicate its equal sides and right angles.

Trapezoid 5, marked with a line and arrows to indicate its parallel sides and non-parallel sides.

All of the shapes in this design are quadrilaterals, and we have exactly 3 parallelograms, 2 rectangles, 1 rhombus, 1 square, 1 trapezoid, and 1 quadrilateral with no other classification.

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The surface area of a cell phone screen is 117 cm².

What is unit conversion?

Unit conversion is the process of converting a quantity expressed in one unit of measurement to an equivalent quantity expressed in another unit of measurement.

We can convert mm² to cm² by dividing the area in mm² by the square of the conversion factor, which is (10 mm / 1 cm) = 100 mm² / cm². Therefore, we have:

11700 mm² / (100 mm² / cm²) = 117 cm²

Rounding to the nearest whole number, we get 117 cm².

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The point (4, 4) is a solution to the equation 2y + x = 12 because it is on the graph of that equation. However, the point (4, 4) is not on the graph of the equation y = x – 2. Therefore, (4, 4) cannot be a solution to the system of equations.

Answer:

3657

Step-by-step explanation:

I multiplied the number of people by how much the tickets cost (23x159) which got me 3657

The reasonable prediction through which a green or black marble will be drawn is 35 times.

What about prediction?

In mathematics, prediction refers to the process of using existing data or patterns to make an educated guess about a future event or outcome. It is the process of estimating an unknown value or quantity based on a set of known data or observations.

Prediction is often used in statistics, where data analysis techniques are used to identify patterns and trends in data. Once these patterns are identified, they can be used to make predictions about future events or outcomes. For example, in finance, prediction models are often used to forecast stock prices or market trends.

The accuracy of predictions in mathematics can be improved by using more data, improving the quality of the data, or refining the models and algorithms used to make the predictions. However, even with the best models and data, there is always some degree of uncertainty or error associated with predictions, and this should be taken into account when using predictions to make decisions.

According to the given information:

Given, there are  5 red marbles, 6 blue marbles, 3 green marbles

4 black marbles, 2 yellow marbles .

Here, it is given that marble will be drawn and replace 100 times.

To find reasonable prediction for no of times green or black marble will be drawn

⇒ Total no of times = 100 times

⇒ [tex]\frac{4}{20}[/tex] x 100 +   [tex]\frac{3}{20}[/tex]  x 100

⇒ [tex]\frac{7}{20}[/tex]  x 100

⇒ 35 times

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Answer: The answer is B

Step-by-step explanation:

Answer:

[tex]\dfrac{1}{4}(y - 2)[/tex]

Step-by-step explanation:

To take out (1/4) as a common term, multiply the denominator and the numerator of the second term by 2.

    [tex]\dfrac{1}{4}y- \dfrac{1}{2}=\dfrac{1}{4}y - \dfrac{1*2}{2*2}\\[/tex]

                [tex]= \dfrac{1}{4}y-\dfrac{1}{4}*2\\\\=\dfrac{1}{4}(y-2)[/tex]

To find out how many pounds of cheese there are, you can divide the total cost by the cost per pound:

$58.88 ÷ $3.68/lb ≈ 16 lbs

So there are approximately 16 pounds of cheese.

Answer:

Step-by-step explanation:

f(x) = x^5 -2x^2 + 2

f(1)=1-2+2

f(1)=1

The volume of the right rectangular prism is 1/18 cubic feet.

What is a rectangular prism?

A rectangular prism is a three-dimensional shape with six rectangular faces. It is also known as a rectangular parallelepiped or a rectangular cuboid.

The volume of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height of the prism, respectively.

In this case, the length l is 2/3 ft, the width b is 1/3 ft, and the height h is 1/4 ft. Therefore, the volume of the prism is:

V = lbh = (2/3 ft)(1/3 ft)(1/4 ft) = 1/18 cubic feet

So the volume of the right rectangular prism is 1/18 cubic feet.

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The statement "X⁻¹ = X" means that for each element X in the set or group, its inverse is itself.

An even number is any integer ( whole number) that is divisible by 2, i.e., it leaves no remainder when divided by 2. In other words, an even number is a multiple of 2.

For example, 2, 4, 6, 8, 10, and so on are even numbers, while 1, 3, 5, 7, 9, and so on are odd numbers. Zero (0) is also considered an even number because it is divisible by 2.

The statement "an even number of elements X such that X⁻¹ = X" means that there are a certain number of elements (which is even) in a set or group, and for each element X in that set or group, its inverse is also equal to X.

In mathematics, the inverse of an element X in a group is an element Y such that their product XY (or YX) equals the identity element of the group. The identity element is the element in the group that, when combined with any other element, produces that element unchanged. For example, the identity element of the group of real numbers under addition is 0, because 0 + a = a + 0 = a for any real number a.

So, the statement  X⁻¹ = X" means that for each element X in the set or group, its inverse is itself. This is only possible if the set or group has elements that are their own inverses. In other words, each element is equal to its negative (or additive inverse) or its reciprocal (or multiplicative inverse).

The requirement that there must be an even number of such elements in the set or group means that if we count the number of elements that satisfy this condition, the count must be an even number.

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Answer:

0,95

Step-by-step explanation:

[tex] \frac{19}{20} [/tex]

Multiply the fraction by 5, so that the denominator would be equal to 100:

[tex] \frac{19 \times 5}{20 \times 5} = \frac{95}{100} = 0.95[/tex]

The average rate of change for this function for the interval from x=2 to x=4 is B. 27.5.

The average rate at which one quantity changes in relation to another's change is referred to as the average rate of change function.

A method that determines the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.

For this special case from the info in the table, we have:

a = 2, f(2) = 9

b = 4, f(4) = 64

And replacing the data into the average rate formula we got:

m = 64-9/4-2 = 27.5

Thus, the correct option is B. 27.5.

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The first monthly payment is for interest in dollars for the mortgage loan of $750,000 at an interest rate of 7% is equal to $437,475.00 with first principal payment is $612.75.

Amount balance of mortgage loan = $750,000

Interest rate = 7%

To calculate first monthly payment is for interest

= calculate the portion of the payment that goes towards interest and the portion that goes towards the principal.

First, find the monthly interest rate by dividing the annual interest rate by 12.

Monthly interest rate

= 7% / 12

= 0.5833%

Next, calculate the interest portion of the first payment by multiplying the loan balance by the monthly interest rate,

Interest portion of first payment

= Loan balance x Monthly interest rate

= $750,000 x 0.5833%

= $437,475.00 /100

= $4374.75

Principal portion of first payment

= Total payment - Interest portion

=$4,987.50 - $4374.75

= $612.75

Therefore, $437,475.00 of the first monthly payment of $4,987.50 is for interest.

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angle ACD=20°

Therefore option A is correct

ABCD is a cyclic quadrilateral..

so angle b+ angle D = 180°

angle d = 180°-110°

angle d=70°

AB is the diameter

so angle ACB is 90°

angle CAB+ Angle ABC+ Angle BCA =180° ( corrresponding to angle sum property)

=70°+90°+BAC=180°

angle BAC=20°

We have seen that angle BAC= angle ACD (interior alternate) (because in trapezium it's parallel)

Therefore angle ACD=20°

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After 29 years of compounded interest at a rate of 5% quarterly, the retirement account would be worth approximately $455527.25.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.

We can use the formula for compound interest to find the future value of the retirement account:

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

where FV is the future value, P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years.

In this case, P = $100509, r = 0.05 (5% expressed as a decimal), n = 4 (since interest is compounded quarterly), and t = 29. Plugging these values into the formula, we get:

[tex]FV = $100509(1 + 0.05/4)^{(4*29)[/tex]

FV ≈ $455527.25

Therefore, after 29 years of compounded interest at a rate of 5% quarterly, the retirement account would be worth approximately $455527.25.

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Answer: Approximately 21.093 grams of silicon-32 will be present after 200 years.

Step-by-step explanation: The formula for the amount of substance remaining after a certain amount of time can be given by:

A = A0 (1/2)^(t/T)

where:

A0 = initial amount of substance

A = amount of substance remaining after time t

T = half-life

Plugging in the given values:

A0 = 30 grams

t = 200 years

T = 710 years

A = 30 * (1/2)^(200/710)

A ≈ 21.093 grams

Therefore, approximately 21.093 grams of silicon-32 will be present after 200 years.

47) Given the above f(30) = 4(30) - 3 = 117.

48) The differences between the areas are 5 and 16, respectively, which are not the same.
49) The range of an arithmetic sequence is also discrete, since the terms of the sequence are usually integers.
50) the range of an arithmetic sequence can contain both positive and negative numbers.

47- We can see that the areas of the figures form an arithmetic sequence. The common difference is 4, since each subsequent figure has 4 more square inches than the previous one. The first term is 1, so the function that represents this arithmetic sequence is f(n) = 4n - 3, where n is the number of the figure.

Thus, f(30) = 4(30) - 3 = 117.

48- We can see that the areas of the figures do not form an arithmetic sequence. The differences between the areas are 5 and 16, respectively, which are not the same.

49- The domain of an arithmetic sequence is discrete, since it consists of a set of integers. The range of an arithmetic sequence is also discrete, since the terms of the sequence are usually integers.

50- Your friend is not entirely correct. While it is true that the domain of an arithmetic sequence is a set of positive integers and the output values either constantly increase or constantly decrease, this does not necessarily mean that the range contains only positive or negative numbers.

For example, consider the arithmetic sequence with first term 0 and common difference 1/2: 0, 1/2, 1, 3/2, 2, ... The range of this sequence includes both positive and negative numbers. Therefore, the range of an arithmetic sequence can contain both positive and negative numbers.

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The main difference between a pyramid and a prism is their base shape and the number of faces, edges, and vertices they possess.

A pyramid is a 3D shape that has a base in the form of a polygon, with triangular faces that meet at a single point known as the apex. The shape of the base can vary, with some common ones being triangles, squares, and pentagons. Pyramids have a total of five faces, including the base. The number of edges and vertices depends on the number of sides of the polygonal base. Pyramids are commonly found in ancient architecture, such as the Egyptian pyramids, and are often used to represent power and strength.

A prism, on the other hand, is a three-dimensional shape that has two identical polygonal bases that are connected by rectangular faces. The shape of the bases can vary, with some common ones being triangles, rectangles, and hexagons. Prisms have a total of six faces, including the two identical polygonal bases. The number of edges and vertices of a prism depends on the shape and number of sides of its bases. Prisms are often found in modern architecture, such as in the design of buildings and bridges.

Pyramids and prisms are two distinct three-dimensional geometric shapes that differ primarily in their base shape. A pyramid's base is a polygon, whereas a prism has two parallel polygonal bases connected by rectangular faces. Pyramids have a total of five faces, including the base, while prisms have six faces, with two identical polygonal bases. The number of edges and vertices of both shapes is determined by the shape and number of sides of their respective bases.

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The complete question is: "The difference between a pyramid and a prism."

After answering the presented questiοn, we can cοnclude that equatiοn Therefοre, there are 144 wοrds οn the vοcabulary list.

A mathematical equatiοn is a fοrmula that cοnnects twο statements and denοtes equivalence with the equals symbοl (=). An equatiοn is a mathematical statement that shοws the equality οf twο mathematical expressiοns in algebra. In the equatiοn 3x + 5 = 14, fοr example, the equal sign separates the variables 3x + 5 and 14.

A mathematical fοrmula describes the cοnnectiοn between the twο sentences that οccur οn οppοsite sides οf a letter. The symbοl and the single variable are frequently the same. As in 2x - 4 Equals 2, fοr instance.

1/4 x = tοtal number οf wοrds Miguel has nοt memοrized

1/4 x = x - 36

x/4 = 36

x = 144

Therefοre, there are 144 wοrds οn the vοcabulary list.

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a. Robert's cumulative GPA can be calculated by adding the grade point values for each of his classes and dividing by the number of classes he has taken:  GPA = 2.67

what is  cumulative GPA  ?

Cumulative GPA (Grade Point Average) is a measure of a student's overall academic performance, which takes into account the grade points earned in all of the courses taken by the student.

In the given question,

a. Robert's cumulative GPA can be calculated by adding the grade point values for each of his classes and dividing by the number of classes he has taken:

GPA = (2(3.0) + 1(2.0)) / 3 = 2.67

Therefore, Robert's cumulative GPA is 2.67.

b. Robert should be worried about meeting SAP (Satisfactory Academic Progress) if there is a minimum GPA requirement for him to remain in good standing at his school.

c. The reason why Robert should be worried is that his cumulative GPA of 2.67 may not meet the minimum GPA requirement set by his school. If he does not meet this requirement, he may be placed on academic probation or face other consequences, such as being ineligible for financial aid or scholarships.

d. The SAP criterion that relates to this scenario is the cumulative GPA requirement. Many schools have a minimum GPA requirement that students must meet to remain in good standing and to be eligible for financial aid and other benefits. In this scenario, Robert's cumulative GPA will be compared to the minimum GPA requirement set by his school to determine if he is meeting SAP.

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a) The average rate of change from x= π/3 to x= 2π/3 is -6√3 + 2π/3. b) The instantaneous rate of change at x= π/2 is -5√3/2, or approximately -4.3.

A formula for calculating the derivative of a composite function is the chain rule. When two or more functions are combined, the output of one function becomes the input of the following function, creating a composite function. According to the chain rule, the derivative of a composite function can be calculated by multiplying the inner function's derivative by the outer function's derivative with regard to the inner function.

a) The average rate of change is given by:

average rate of change = (f(2π/3) - f(π/3)) / (2π/3 - π/3)

The value of f(2π/3) and f(π/3) is:

f(2π/3) = 5 cos(2π/3 - π/6) - 1

= 5 cos(π/2) - 1

= 0

And,

f(π/3) = 5 cos(π/3 - π/6) - 1

= 5 cos(π/6) - 1

= 5(√3/2) - 1

= (5√3 - 2) / 2

Substituting the values we have:

average rate of change = ((0) - ((5√3 - 2) / 2)) / (2π/3 - π/3)

= (-5√3 + 2) / (π/3)

= -6√3 + 2π/3

Hence, the average rate of change from x= π/3 to x= 2π/3 is -6√3 + 2π/3.

b) The instantaneous rate of change at x= π/2 is given by the derivative thus,

y = 5 cos (x- π/6) - 1

Taking the derivative we have:

y' = -5 sin (x- π/6)

For  x= π/2 into y':

y'(π/2) = -5 sin(π/2 - π/6)

= -5 sin(π/3)

= -5(√3/2)

= -5√3/2

Hence, the instantaneous rate of change at x= π/2 is -5√3/2, or approximately -4.3.

Learn more about chain rule here:

https://brainly.com/question/28972262

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