Find the derivative of sin(4x) at x = pi / 6 (a) -2v3 (b) – 2 (c) v3/ 2 (d) 4V3 (e) None of the above

Seraphina's speed has increased by a factor of around 23% compared to the first hour.

What Is a Change in Percentage?

The ratio of the difference in the amount to its starting value multiplied by 100 is known as the percentage change. When a number's final value is determined by increasing or decreasing a percentage of its starting value, the percentage change of that quantity will always change.

How can you determine the percentage to the closest tenth?

Rounding to the closest tenth entails adding one integer after the decimal point. The number in the thousandths place, or the second number from the right of the decimal, must be considered while rounding. If the amount is five or more, we add one percent to the number in the tenth position.

Percent Change Formula = \(\frac{ (Final value -Initial value)}{ (Initial value)}\)× 100

Percent Change               = \(\frac{(74-60)}{60}\)× 100

…                                     = \(\frac{14}{60}\) × 100

...                                     ≈ 0.23333 × 100

Percent Change             ≈ 23.33%

The pace of Seraphina increased by around 23% in the second hour compared to the first.

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Answer: Look below =3

The greatest common factor of numerator and denominator is (x-4).

Step-by-step explanation:

I hope this answer is helpful ):

Answer:

A is 1

B is 5

Step-by-step explanation:

0 times 2 is 0 plus 1 is 1 that gives the answer to A

2 times 2 is 4 plus 1 is 5 which gives you B

Answer:

The answer to the mean of those numbers is 90.26.

Step-by-step explanation:

90.26

The property of real numbers that was illustrated in the above example is known as the: D. inverse property.

The inverse property of real numbers states that if you add the opposite of a number together with that number, the result would be zero.

For example, if "a" represents a number, the opposite of the number "a" is -a.

Applying the inverse property of real numbers, it states that: a + (-a) = a - a = 0. Both numbers will cancel each other to give zero.

In the same vein, as shown in the image given above:

6 is a number

The opposite of 6 is -6.

Applying the inverse property of real numbers, we have:

6 + (-6) = 0.

In conclusion, we can state that given the expression, 6 + (-6) = 0, the property of real numbers that was illustrated in the above example is known as the: D. inverse property.

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Answer:

B

This is a 30-60-90 Triangle which means that the long side is twice the short side and the hypotenuse is Square Root 3 times bigger

Component 3 must be started on day 197 to meet the delivery date of day 200.

To illustrate the backward schedule, we need to start from the delivery date (day 200) and work our way backward, taking into account the lead times and dependencies of each operation.

(a) Backward schedule:

Operation    |  Work Center  |  Time (hours)  |  Start Day

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

Final Assembly |   Work Center 1  |        1       |     200

Sub-assembly 1 |   Work Center 2  |        2       |     199

Component 4     |   Work Center 3  |        3       |     197

Component 2     |   Work Center 4  |        4       |     196

Component 3     |   Work Center 5  |        3       |     ????

(b) To identify when component 3 must be started to meet the delivery date, we need to consider its dependencies and lead times.

From the backward schedule, we see that component 3 is required for sub-assembly 1, which is scheduled to start on day 199. The time required for sub-assembly 1 is 2 hours, which means it should be completed by the end of day 199.

Since component 3 is needed for sub-assembly 1, we can conclude that component 3 must be started at least 2 hours before the start of sub-assembly 1. Therefore, component 3 should be started on day 199 - 2 = 197 to ensure it is completed and ready for sub-assembly 1.

Hence, component 3 must be started on day 197 to meet the delivery date of day 200.

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The maximum error in volume of ball is ± 235.619 cm³

The margin of error, also known as the maximum error of estimation, is equal to one-half the breadth of a confidence interval and serves as a measure of how accurate an estimate is.

The formula for the confidence limits on can be written as follows: where is half of the confidence interval's breadth.

Volume of ball is given by:

V =  (4/3)πr³

Change in volume (ΔV) = (4/3)π × 3r² (Δr)

= 4π × 3r² (Δr)

= 4π × 3* 25² (±0.01)

= ± 235.619 cm³

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Answer:

Many errors were shown in the text

Step-by-step explanation:

How to explain the word problem It should be noted that to determine if Jenna's score of 80 on the retake is an improvement, we need to compare it to the average improvement of the class. From the information given, we know that the class average improved by 10 points, from 50 to 60. Jenna's original score was 65, which was 15 points above the original class average of 50. If Jenna's score had improved by the same amount as the class average, her retake score would be 75 (65 + 10). However, Jenna's actual retake score was 80, which is 5 points higher than what she would have scored if she had improved by the same amount as the rest of the class. Therefore, even though Jenna's score increased from 65 to 80, it is not as much of an improvement as the average improvement of the class. To show the same improvement as her classmates, Jenna would need to score 75 on the retake. Learn more about word problem on; brainly.com/question/21405634 #SPJ1 A class average increased by 10 points. If Jenna scored a 65 on the original test and 80 on the retake, would you consider this an improvement when looking at the class data? If not, what score would she need to show the same improvement as her classmates? Explain.

The proportion of students who scored higher than Willa is 0.7389. Hence, Option B is correct.

The given information is:

Mean (μ) = 78, Standard deviation (σ) = 5, and Willa scores = 74.8

The formula for the Z-score is:

Z = (x-μ) / σ

Where, x is the value, μ is the mean and σ is the standard deviation.

Substitute the values in the above formula, we get:

Z = (74.8 - 78) / 5

= -0.64

The negative sign indicates that Willa's score is less than the mean score.

Now, find the proportion of students who scored higher than Willa.

It can be done in two steps as shown below:

Step 1: Find the area under the standard normal distribution curve corresponding to the calculated Z-score.

The Z-table gives the area to the left of Z = -0.64.

The area to the right of Z is 1 - area to the left of Z.= 1 - 0.2611

= 0.7389

Therefore, the proportion of students who scored higher than Willa is 0.7389.

Hence, Option B is correct.

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The possible algebraic equations, obtained based on the algebraic expressions in the question are;

1. \(\frac{x}{8} = y\)

2. 15 - n = m

3. 25 + x = y

An algebraic expression is a collection of numbers and variables that are combined together, but without indicating the value indicated by the collection.

What is an algebraic equation?

An algebraic equation is a mathematical statement that expresses the equivalence of two expressions.

The algebraic expressions can be presented as follows;

1. Some number divided by 8

Let x represent the number divided by 8, and let y represent the result when x is divided by 8. The variables x and y can be defined based on the details in the question

The equation with x as the number and y as the result can be presented as follows;

2. n less than 15

The expression n less than 15 is; 15 - n

Let m represent the value of the expression; 15 - n, an algebraic equation based on the details is therefore;

3. 25 more than a number

Let x represent the number, we get

25 more than a number = 25 + x

The y represent the result or value of the expression 25 + x, we get the following algebraic equation;

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Answer:

(x + 1)(x - 1)(x² + 9)

Step-by-step explanation:

Factorise the following:

\( \longrightarrow \) x⁴ + 8x² - 9

\( \sf x^4 = {(x^2)}^{2}: \)

\( \longrightarrow \) \( \sf {(x^2)}^{2} + 8x^2 - 9\)

The factors of -9 that sum to 8 are 9 and -1.

So,

\( \longrightarrow \) \( \sf {(x^2)}^{2} + (9 - 1)x^2 - 9\)

\( \longrightarrow \) \( \sf {(x^2)}^{2} + 9x^2 - x^2 - 9\)

\( \longrightarrow \) x²(x² + 9) - 1(x² + 9)

\( \longrightarrow \) (x² - 1)(x² + 9)

x² - 1 = x² - 1²:

(x² - 1²)(x² + 9)

Factor the difference of two squares.

x² - 1² = (x + 1)(x - 1):

\( \longrightarrow \) (x + 1)(x - 1)(x² + 9)

To make everything easier, it's best to turn the mixed numbers into improper fractions.

24 * 8 = 192 + 3/8 = 195/8

4 * 8 = 32 + 7/8 = 39/8

The question asks how many 39/8-inch long pieces the worker cut from a 195/8-inch long board, meaning we have to divide.

195 / 39 = 5

The worker cut the board into 5 pieces.

Answer:

\( \hookrightarrow \: { \rm{density = \frac{mass}{volume} }} \\ \)

\({ \rm{density = \frac{10}{1} }} \\ \\ { \boxed{ \rm{density = 10 \: g {cm}^{ - 3} }}}\)

Answer:

indirect measurement

Answer:

b.d-6 that's the correct answer

Answer:

it is a

Step-by-step explanation:

The solutions to the equation, 2x²-1=5x are approximately x ≈2.68 and x ≈ -0.18

The given quadratic equation is,

2x²- 1 =  5x

To solve this equation bring all the terms to one side, so we get:

2x² - 5x - 1 = 0

Now we can use the quadratic formula to find the solutions for x:

x = (-b ± √(b² - 4ac)) / 2a

In this case, a = 2, b = -5, and c = -1, so we get:

x = (-(-5) ± √((-5)² - 4(2)(-1))) / 2(2)

x = (5 ± √(33)) / 4

x = (5 ± 5.74) / 4

Rounding to the nearest hundredth, we get:

x ≈2.68 and x ≈ -0.18

Hence,

The solutions to the equation are approximately x ≈2.68 and x ≈ -0.18

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Points are said to be collinear if they are on the same line. The possible lengths of CD are 31.6cm and 12.6cm

Given that:

\(CE=22.1cm\)

\(DE = 9.5cm\)

If E is between C and D, then:

\(CD =CE + DE\)

So, we have:

\(CD =22.1cm + 9.5cm\)

\(CD =31.6cm\)

Another possible scenario is:

If D is between C and E, then:

\(CE = CD + DE\)

Make CD the subject

\(CD = CE - DE\)

So, we have:

\(CD = 22.1cm -9.5cm\)

\(CD = 12.6cm\)

Hence, the possible values of CD are 31.6cm and 12.6cm

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The results for each case of congruence are listed below:

9) Congruent

10) No congruent

11) No congruent

12) Congruent

13) Congruent

14) No congruent

There are several ways to determine if two line segments are congruent to each other. One form consists in finding the vector associated with each line segment and the length is found by the Pythagorean theorem:

Now we proceed to show how to apply the vector criterion:  

9) AB = (- 4, 8) - (- 4, 5) = (0, 3), CD = (2, 0) - (2, - 3) = (0, 3).

AB = 3, CD = 3. Congruent

10) AB = (1, - 1) - (6, - 1) = (- 5, 0), CD = (4, - 3) - (2, - 3) = (2, 0).

AB = 5, CD = 2. No congruent

11) AB = (- 1, 3) - (8, 3) = (- 9, 0), CD = (5, 3) - (5, 10) = (0, - 7).

AB = 9, CD = 7. No congruent

12) AB = (6, 1) - (6, - 8) = (0, 9), CD = (- 2, - 2) - (7, - 2) = (- 9, 0).

AB = 9, CD = 9. Congruent

13) AB = (- 5, - 1) - (- 5, 6) = (0, - 7), CD = (3, 3) - (- 4, 3) = (7, 0).

AB = 7, CD = 7. Congruent

14) AB = (3, - 4) - (10, - 4) = (- 7, 0), CD = (- 1, 5) - (- 1, 2) = (0, 3).

AB = 7, CD = 3. No congruent

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The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.

the expression for the area of the new playground is A2 = x² + 30x - 1000.

the area of the new playground is always greater than the area of the old playground for any valid side length.the areas of the new playground for the given side lengths of the original playground are 5000 ft², 11000 ft², and 19500 ft², respectively.

The subpart of the question are solved as following :-

A) Let the original playground be a square with side length x, then the area of the original playground is A1 = x². After the change, the new playground is a rectangle with length x + 50 and width x - 20, so the area of the new playground is:

A2 = (x + 50)(x - 20) = x² + 30x - 1000

Thus, the expression for the area of the new playground is A2 = x² + 30x - 1000.

B) To evaluate the expression for the given side lengths of the original playground (50 ft, 100 ft, and 150 ft), we substitute each value in turn for x in the expression A2 = x² + 30x - 1000:

When x = 50 ft: A2 = (50 ft)² + 30(50 ft) - 1000 = 5000 ft²

When x = 100 ft: A2 = (100 ft)²+ 30(100 ft) - 1000 = 11000 ft²

When x = 150 ft: A2 = (150 ft)²+ 30(150 ft) - 1000 = 19500 ft²

Therefore, the areas of the new playground for the given side lengths of the original playground are 5000 ft², 11000 ft², and 19500 ft², respectively.

C) No, there will never be a time when the new playground does not have a larger area than the old playground. This is because the expression for the area of the new playground, A2 = x² + 30x - 1000, is a quadratic function with a positive leading coefficient, which means it opens upwards and has a minimum value. The minimum value occurs at x = -15, which is not a valid value for the side length of a playground. Therefore, the area of the new playground is always greater than the area of the old playground for any valid side length.

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scalene triangle

hope it helps...

Answer:

down below - hope this helped :)

Step-by-step explanation:

you can make a scalene traingle with these mesurements

since none of the sides are equal :)

Answer:

Explanation: Let's make the number = n. Cube the number (power of 3) = n3. Add five to the cube of a number = n3 + 5.

Step-by-step explanation:

BRAINLIEST ME PLEASE

To look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

For a regular polygon with n sides, the sum of its interior angles is given by ((n - 2) × 180) degrees. In the case of a round table seating 6 people, the table can be considered as a hexagon, which has 6 sides. Using the formula, we can calculate the sum of the interior angles:

((6 - 2) × 180) / 6 = (4 × 180) / 6 = 720 / 6 = 120 degrees

Since the table forms a complete circle, the sum of the interior angles is divided equally among the guests. Therefore, each guest sits at an angle of 120 degrees. To look from the guest to their left to the guest to their right, you need to rotate by the angle between adjacent guests, which is half of the angle they sit at:

120 / 2 = 60 degrees

Thus, to look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

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After 8 seconds the ball height was 42 units.

It is given that on a game show, contestants shoot a foam ball toward a target. The table includes points along one path the ball can take to hit the target where x is the time that has passed since the ball was launched and y is the height at this time.

It is required to find how high was the ball after 8 seconds.

It is defined as the graph of a quadratic function that has something bowl-shaped.

The orbit of the ball will be a parabola.

We know the standard form of a quadratic function:

\(\rm y=ax^2+bx+c\)      where \(\rm \\a\neq 0\)

At x = 0 and y = 10, we get:

\(\rm 10 =a(0)^2+b(0)+c\\\rm 10= c\\\rm c=10\)

At x = 2 and y=24, we get:

\(\rm 24= a(2)^2+b(2)+c\\\rm 24=4a+2b+10\\\rm 4a+2b=14\)....(1)

At x = 16 and y = 10, we get:

\(\rm 10= a(16)^2+b(16)+c\\\rm 10=256a+16b+10\\\rm 256a+16b=0 \\\)....(2)

By solving equations (1) and (2), we get;

a = - 1/2, b = 8 and c = 10

Putting these values in the standard form of a quadratic function, we get:

\(\rm y = - \frac{1}{2} x^2+8x+10\\\)

Now, after 8 seconds means when x = 8, we get:

\(\rm y=-\frac{1}{2}\times 8^2 +8\times8+10\\\rm y = -32+64+10\\\rm y= 42\)

Thus, after 8 seconds the ball height was 42 units.

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Answer:

b

Step-by-step explanation:

All of the following statements are true:

a. Effective listening is vital to success in selling.

b. visual aids play a part in the listening process.

c. people can talk approximately twice as fast as they can listen.

d. you should listen closely to everything you hear.

e. listening refers to the process of trying to detect sounds.

Listening is the act of paying attention to sounds that are happening around you. It involves both hearing the sounds and interpreting what they mean. Good listening skills are important for many reasons, including being able to communicate effectively with others and understand instructions. To listen effectively, you need to be able to focus on the speaker and try to understand their perspective, rather than just waiting for your turn to talk.

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Answer:

No solutions

Step-by-step explanation:

Hello!

First, isolate the absolute value bracket.

Now think. Absolute value changes all values inside into their positive form. So the output should be a positive value. Here it is given as a negative value, so there are no solutions.

Answer: No solution

Ok done. Thank to me :333

The domain of the function is a semicircle with a radius of 5 and centered at the origin, where y is non-negative.

The domain of a function is the set of all possible input values for which the function is defined. In this case, the function is defined as:

\(f(x,y) = \sqrt{y} + \sqrt{[25 - x^2 - y^2} ]\)

To find the domain of this function, we need to determine the values of x and y that would result in the function producing a real-valued output.

For the square root of y to be real, y must be non-negative. That is, y ≥ 0.

For the square root of [\(25 - x^2 - y^2\)] to be real, we must have:

\(25 - x^2 - y^2 \geq 0\\x^2 + y^2 \leq 25\)

This is the equation of a circle with radius 5 centered at the origin. Therefore, the domain of the function is the set of all points (x, y) that lie inside or on this circle and have y ≥ 0.

In interval notation, we can write:

Domain: {(x, y) |\(x^2 + y^2 \leq 25, y \geq 0\)}

To sketch the domain, we can plot the circle with radius 5 centered at the origin and shade the region above the x-axis. This represents all the valid input values for the function. The boundary of the domain is the circle, and the domain includes all points inside the circle and on the circle itself, but not outside the circle.

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