Determine the error term for the formula (5) 1 2h 2-2. Use the above formula to approximate f'(1.8) with f(x) = In using h=0.1, 0.01 and 0.001. Display your results in a table and then show that the order of accuracy obtained from your results is in agreement with the theory in question 2-1. [10] ${(z) *27448(a+h) – 3f (a) – f(a +26)

The difference between the predicted value and actual value is known as residual, which is 10.577.

We have,

Achievement test score = 61

Final Calculus Grade = 86

The residual interpretation is as follows:

The regression equation is obtained as follows:-

Final calculus grade = 37.908 + 0.615 (Achievement test score)

Final calculus grade = 37.908 + 0.615 (61)

Final calculus grade = 37.908 + 37.515

Final calculus grade = 75.423

The actual final calculus grade of the student is 86. Therefore, the difference between the predicted value and the actual value is known as the residual. It is calculated as follows:

Residual = actual value - predicted value

Residual = 86 - 75.423

Residual = 10.577

So, the residual interpretation is that the predicted value of the final calculus grade was 75.423 while the actual final calculus grade was 86.

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The relationships between the numerator and denominator coefficients of a circuit and the values of resistance (R), inductance (L), and capacitance (C) depend on the specific circuit configuration and the transfer function associated with it.

In general, the numerator coefficients of the transfer function represent the output variables of the circuit, while the denominator coefficients represent the input variables. The coefficients are determined by the circuit elements (R, L, C) and their interconnections.

For example, in a simple RC circuit (resistor and capacitor), the transfer function can be written as a ratio of polynomials in the Laplace domain. The denominator coefficients correspond to the characteristic equation of the circuit and involve the resistance and capacitance values. The numerator coefficients may be related to the initial conditions or external inputs.

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Answer: 360

Step-by-step explanation:

done

The percentage by which the price of the car went up from the original price is 60% (third option)

The first step is to determine the price of the car after the percentage increase. Percentage is the fraction of a number as a value out of 100. The sign that is used to represent percentage is %.

Price of the car after the percentage increase = (1 + percent increase/100) x original cost of the car

Price of the car after the percentage increase = (1 + 20/100) x 20,000

Price of the car after the percentage increase = (1 + 0.2) x 20,000

Price of the car after the percentage increase = 1.2 x 20,000 = $24,000

Price after the $8,000 increase = $24,000 + 8,000 = $32,000

Percentage of the original price = (32,000 / 20,000) - 1 = 0.60 = 60%

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The proportion of Gala apples weighing less than 162 grams is approximately 0.0628 or 6.28% (rounded to four decimal places).

To solve this problem, we need to use the standard normal distribution formula and z-score. The z-score is a measure of how many standard deviations a value is away from the mean. In this case, we want to find the z-score for a Gala apple weighing 162 grams:

z = (162 - 208) / 30 = -1.5333

We can look up the probability of a z-score being less than -1.5333 in a standard normal distribution table, which gives us a value of 0.0628.

In other words, if we were to randomly select a large number of Gala apples from the population with the given mean and standard deviation, we would expect about 6.28% of them to weigh less than 162 grams.

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Complete question is:

The weights of Gala apples are normally distributed with a mean of 208 grams and a standard deviation of 30 grams. Determine the proportion of Gala apples weighing less than 162 grams. Round your answer to 4 decimal places.

The true statements are f(-5) = -40,  f(0) = 3 and  f(3) = 0

Given the function;

f(a) = 3a – a2

For f(-5), we substitute the value of a as -5, we have

f(-5) = 3(-5) - (-5)²

f(-5) = -15 - 25

f(-5) = -40

For f(4), we have

f(4) = 3(4) = 3(16)

f(4) = 12 - 48

f(4) = -36

For f(-1), we have

f(-1) = 3(-1) - (-1)²

f(-1) = -3 - 1

f(-1) = -4

For f(0), we have

f(0) = 3(0) -(0)

f(0) = 0

For f(3), we have

f(3) = 3(3) - 3²

f(3) = 0

Thus, the true statements are f(-5) = -40,  f(0) = 3 and  f(3) = 0

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Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

Question: Express the following as a linear combination of u =(3, 1,6), v = (1.-1.4) and w=(8,3,8). (14, 9, 14) = ____ u- _____ v+ _____

Current Progress: To express the given vector as a linear combination of u, v, and w, we need to find scalars a, b, and c such that (14, 9, 14) = a*u + b*v + c*w.

Step 1: Write the equation in component form:
(14, 9, 14) = (3a + b + 8c, a - b + 3c, 6a + 4b + 8c)

Step 2: Equate the corresponding components and solve for a, b, and c:
3a + b + 8c = 14
a - b + 3c = 9
6a + 4b + 8c = 14

Step 3: Solve the system of equations using any method (substitution, elimination, etc.). One possible solution is a = 1, b = -1, and c = 3.

Step 4: Plug the values of a, b, and c back into the linear combination equation:
(14, 9, 14) = 1*u + (-1)*v + 3*w

Step 5: Simplify the equation:
(14, 9, 14) = u - v + 3w

Answer: The given vector can be expressed as a linear combination of u, v, and w as (14, 9, 14) = u - v + 3w.

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Answer:

12.5%

Step-by-step explanation:

So, Mika did do the division right. So we can get that out of the way. In order to convert to a percent, you just simply move the decimal point over two times. In this case, we have 0.125. We move it over twice to get 12.5. Now, we just plop the percentage next to it to get: 12.5%.

May I have Brainliest please? I am so close to getting my next ranking! I just need 2 more for it! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

Answer:

12.5%

(can also be written as:)12\(\frac{1}{2}\)%

Step-by-step explanation:

She should bring the decimal point over two places to the right.

To convert decimals to percents ALWAYS bring the decimal point two places to the right and and a percentage sign.

The number of failures of a testing instrument due to contamination particles on a product follows a Poisson distribution with an average rate of 0.02 failures per hour.

In a Poisson distribution, the probability of an event occurring a certain number of times within a given interval is determined by the average rate of occurrence. In this case, the average rate is 0.02 failures per hour.

(a) To find the probability that the instrument does not fail in an 8-hour shift, we can use the Poisson probability formula. The parameter λ (lambda) represents the average rate, which is equal to 0.02 failures per hour multiplied by 8 hours. The probability of no failures is calculated by plugging λ and the number of events (0) into the formula. The result gives the probability that the instrument does not fail in an 8-hour shift.

(b) To calculate the probability of at least one failure in a 24-hour day, we can use the complement rule. The complement of "at least one failure" is "no failures." We can calculate the probability of no failures using the same approach as in part (a). Then, subtracting this probability from 1 gives us the probability of at least one failure.

By applying the appropriate formulas and rounding the results to four decimal places, we can determine the probabilities requested in the problem.

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The diameter of the igloo's circular floor is 4 meters. It represents the longest distance across the circular floor, passing through the center.

The diameter of a circle is a measurement that extends from one side of the circle to the opposite side, passing through the center. It is equal to twice the length of the radius. In this case, the radius of the igloo's circular floor is given as 2 meters. To find the diameter, we multiply the radius by 2.

By substituting the given value into the formula, we get:

Diameter = 2 * 2 meters

Diameter = 4 meters

Therefore, the diameter of the igloo's circular floor is 4 meters. It represents the longest distance across the circular floor, passing through the center. Understanding the relationship between the radius and diameter helps in various calculations and geometric analyses involving circles.

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Answer:

Anthony worked to earn $25.00. Joyce worked for $8.00 per hour. If Anthony earns $5.00 per hour, how many hours did he work?

for 5 hours they work

One month is approximately equal to 4.3 weeks

The average length of a month in days is 30.44 (365.24 divided by 12 months), and there are 7 days in a week.

Therefore, for the conversion of months to days dividing the average number of days in a month by the number of days in a week gives us:

30.44 days/month ÷ 7 days/week ≈ 4.3 weeks/month

It's important to note that the number of weeks in a month can vary slightly depending on the actual number of days in the month.

For example, a month with 28 days has exactly 4 weeks, while a month with 31 days has slightly more than 4 weeks (4.43 weeks, to be more precise). However, using the average of 4.3 weeks per month is a good approximation for most purposes.

Therefore, one month is 4.3 weeks

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We have to find the amount of money raised by all three schools.

The first school: EON, raised $286.00

The second school: Hackett raised $192.84

The third school: Myers raised $113.25 more than Hackett

To calculate the amount that the third school raised, we add $113.25 to the amount that the second school raised $192.84:

Myers raised $306.09

Finally, we add the money that the three schools raised to find the total:

The total amount of money raised was $784.93

Answer:

$784.93

Answer:    15/10

Step-by-step explanation:

Answer:

15 cookies and 10 brownies

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

9+2=11

a) The 95% confidence interval for the probability (p) that a randomly selected component lasts more than 350 hours is estimated to be between 0.4947 and 0.8753. b) The 95% confidence interval for the probability (p) that a system consisting of two components connected in series lasts more than 350 hours is estimated to be between p² and 2p - p²

a) To calculate the confidence interval, we can use the formula for the confidence interval of a proportion. The point estimate for p is the proportion of components in the sample that lasted longer than 350 hours, which is 24/37 = 0.6486. We can calculate the standard error (SE) using the formula:

SE = \(\sqrt{\frac{p\times(1-p)}{n}\)

where p is the point estimate and n is the sample size. Plugging in the values, we get:

SE = sqrt[(0.6486*(1-0.6486))/37] ≈ 0.0841

Next, we can use the standard normal distribution (Z-distribution) for a 95% confidence interval, which corresponds to a Z-score of 1.96 (for a two-tailed test). We can then multiply the SE by the Z-score to get the margin of error (ME):

ME = Z * SE = 1.96 * 0.0841 ≈ 0.1648

Finally, we can construct the confidence interval by adding and subtracting the margin of error from the point estimate:

95% Confidence Interval = p ± ME = 0.6486 \(\pm\) 0.1648

So the confidence interval for p is approximately (0.4947, 0.8753), which means we are 95% confident that the true probability of a component lasting more than 350 hours is between 0.4947 and 0.8753.

b) Since the two components in the system are connected in series, the system will operate only if both components operate properly. Therefore, the probability that the system lasts more than 350 hours is the probability that both components operate properly, which is the product of their individual probabilities. Let p1 and p2 be the probabilities of the first and second components lasting more than 350 hours, respectively.

Based on the assumption that the life times of the two components are independent, the probability that both components operate properly is given by p1 * p2. Since p1 and p2 are assumed to be equal to p (the probability of a single component lasting more than 350 hours), we can write the probability of the system lasting more than 350 hours as p * p = p².

To calculate the lower bound of the confidence interval, we can simply square the lower bound of the confidence interval for p (i.e., p²). To calculate the upper bound of the confidence interval, we can subtract the lower bound of the confidence interval for p from 2p (i.e., 2p - p²).

So the 95% confidence interval for the probability that the system lasts more than 350 hours is estimated to be between p² and 2p - p², where p is the probability of a single component lasting more than 350 hours.

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Answer:

reduce 3/6 to lowest terms which would be, 1/2 because 3 goes into 3 once and 3 goes into 6 twice.  

Making your equation simplified to

1/2 + 1/2

which is equal to 1

1/2 + 1/2 = 1

Step-by-step explanation:

Hope this helps! Have a fantastic day and please mark brainliest

Answer:

3/6+1/2

find the lcm of 6&2 = 6

3+3/6= 6/6 = 1

The sum of the geometric sequence is 6 + 6² + 6³ + ... + 6ⁿ can be written as \(\frac{6^n^+^1-6}{5}\)  in closed forms.

The sum of n terms of G.P. is given by:

\(\frac{a(r^n-1)}{r-1}\)

Here, a, r are the first term and the common ratio respectively.

To write the sum of the geometric sequence 6 + 6² + 6³ + ... + 6ⁿ in closed form, we can use the formula for the sum of a geometric sequence:

=> \(\frac{a(r^n-1)}{r-1}\)

In our sequence, a = 6, r = 6, and n is any integer with n ≥ 1.

Now, We have substitute the values in above formula:

=> \(\frac{6.6^n-6}{6-1}\)

Now you have the closed form for the sum of the geometric sequence:

=> \(\frac{6^n^+^1-6}{5}\)

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The critical numbers of g(θ) on the interval 0 ≤ θ < 2π are:  θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.

To find the critical numbers of g(θ) = 4θ - tan(θ) on the interval 0 ≤ θ < 2π, we need to find the values of θ where the derivative of g(θ) is equal to 0 or undefined.

First, we find the derivative of g(θ) using the chain rule and quotient rule:

g'(θ) = 4 - sec²(θ)

To find where g'(θ) is equal to 0, we set the derivative equal to 0 and solve for θ:

4 - sec²(θ) = 0

sec²(θ) = 4

Taking the square root of both sides, we get:

sec(θ) = ±2

Since sec(θ) = 1/cos(θ), we can rewrite this as:

cos(θ) = ±1/2

We know that on the interval 0 ≤ θ < 2π, the cosine function is positive in the first and fourth quadrants and negative in the second and third quadrants.

Therefore, we need to find the values of θ in the first and fourth quadrants where cos(θ) = 1/2, and the values of θ in the second and third quadrants where cos(θ) = -1/2.

For cos(θ) = 1/2, we have:

θ = π/3 or 5π/3 in the first quadrant
θ = 7π/3 or 11π/3 in the fourth quadrant

For cos(θ) = -1/2, we have:

θ = 2π/3 or 4π/3 in the second quadrant
θ = 8π/3 or 10π/3 in the third quadrant

Therefore, the critical numbers of g(θ) on the interval 0 ≤ θ < 2π are:

θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.

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The equation that represents the sentence "28 is the quotient of a number and 4" is 28 = n/4.

In the given sentence, "28 is the quotient of a number and 4," we can break down the sentence into mathematical terms. The term "quotient" refers to the result of division, and "a number" can be represented by the variable "n." The divisor is 4.

1) Define the variable.

Let's assign the variable "n" to represent "a number."

2) Write the equation.

Since the sentence states that "28 is the quotient of a number and 4," we can write this as an equation: 28 = n/4.

The equation 28 = n/4 represents the fact that the number 28 is the result of dividing "a number" (n) by 4. The left side of the equation represents 28, and the right side represents "a number" divided by 4.

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The radius of the smaller windmill with a circumference of about 376 feet is D. 60 feet.

The radius of a circle represents the distance from the center of the circle to any point on its circumference.

The radius can be determined by dividing the circumference by 2π.

r = C/2π

r = radius

C = circumference

π = pi (22/7 or 3.143)

The circumference of the large windmill = 660 feet

The diameter = 210 feet

The circumference of the small windmill = 376

The radius of the circumference = 376 ÷ 2(22/7)

= 60 feet

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When our goal is to establish an assertion, the negation of the assertion is False.

The negation of an assertion is the statement that asserts the opposite or denies the original assertion. In logic and reasoning, negation is an important concept that allows us to explore the validity and truth of statements. If we have an assertion that we want to prove or establish as true, its negation would be false.

For example, let's say we have the assertion:

"The sky is blue." The negation of this assertion would be: "The sky is not blue." By negating the original assertion, we are asserting that the sky is not of the stated color, which in this case, would imply that the sky is not blue.

Negation plays a crucial role in logic, reasoning, and proof techniques. It allows us to examine both sides of an argument or claim and assess their validity. By considering the negation of an assertion, we can evaluate its truth value and ultimately determine the strength and validity of the original assertion.

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Answer:

B.) 12

Step-by-step explanation:

2+1/4 is the fraction and all values less than two are on the line.

1 brown circle represents 1 feather

there are 7 dots for 2+1/4

4 dots for 2

1 dot for 3/4

Hope that helps :)

Answer:

answer is B. Aka 12

Step-by-step explanation:

thanks mark brainliest…:) please.

Answer:

Step-by-step explanation:

To find Length or Breadth when Area of a Rectangle is given

When we need to find length of a rectangle we need to divide area by breadth.

Length of a rectangle = Area ÷ breadth.

ℓ = A ÷ b.

Similarly, when we need to find breadth of a rectangle we need to divide area by length.

Breadth of a rectangle = Area ÷ length.

Answer:

The width of the rectangle is x + 3.

Step-by-step explanation:

Area of the rectangle = 4x² + 12x

Length of the rectangle = 4x

Width of the rectangle = ?

So,

↬ Area = Length × Width

Now,

4x² + 12x = 4x × Width

4x² + 12x ÷ 4x = Width

x + 3 = Width

Width = x + 3

Thus, The width of the rectangle is x + 3.

-TheUnknownScientist 72

Answer:

Facility with the arithmetic of fractions, decimals and percentages. ... we all need to be competent in our understanding of commercial or consumer arithmetic.

Step-by-step explanation:

Facility with the arithmetic of fractions, decimals and percentages. ... we all need to be competent in our understanding of commercial or consumer arithmetic.

In a right - angled triangle, the square of the hypotenuse of a triangle is equal to the sum of the square of the other two sides.

Step 1: Make a right - angled triangle with base, perpendicular and hypotenuse has length of their side a, b, c respectively.

Step 2: Make squares on the base, perpendicular and hypotenuse with side length a, b and c respectively.

Step 3: Now measure the area of square with side b and a, which are on perpendicular and base of a triangle respectively.

Step 4: Measure the area of the with side c, which is on the hypotenuse of a triangle, area is: \(c^{2}\).

Step 5: Add the area of squares with sides a and b, sum of their area is: \(a^{2} + b^{2}\).

Observation and Result:

We will notice that the area of square with side a and b is equal to the area of square with side c.

⇒ \(a^{2} + b^{2} = c^{2}\)

∴ The square of the hypotenuse in a right-angled triangle is equal to the sum of the square of the other two sides.

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In a right  triangle, the square of the hypotenuse of the triangle is equal to the sum of the squares of the other two sides.

Note that the area of ​​the square with sides a and b is equal to the area of ​​the square with side c.  

a² + b² = c²

Therefore, the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

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Answer:

Angle ADB = 80 degrees

Step-by-step explanation:

This is a parallelogram so:

AD || BC

AB || DC

Using the Alternate Interior Angles Postulate, you can find that:

Angle BDC = Angle DBA

So because Angle BDC is 28 degrees, we know that Angle DBA is also 28 degrees.

Now, we can figure out what angle ADB is using the property of triangles that all the angles of add up to 180:

Angle ADB + 72 + 28 = 180

Angle ADB + 100 = 180

Angle ADB = 80

So, Angle ADB is 80 degrees.

Step-by-step explanation:

15 x 3 = 45

13 x 3 = 39

So

45 ÷ 3 = 15

39 ÷ 3 = 13

36 ÷ 3 = 12

X=12

The correct option is cone and plane. A conic section is the intersection of a plane and a cone. The best definition of a conic section is "cone and plane".

The definition of conic section is a conic section is a shape that is formed when a right circular cone intersects a plane. Depending on the angle of the plane concerning the center line of the cone, the conic sections are classified into four types. They are a circle, parabola, ellipse, and hyperbola. Each type of conic section has a unique shape and properties.

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