1. Mrs. Sanders farm is 413 acres. She divided the farm into 52 equal parts. How many acres are in each part? 2. Which of the following numbers are prime? a) 53 b) 12 c) 18 d) 28​

Answer:

9 1-inch squares will cover the bigger square. Its area is the same as the amount of squares needed, 9 inches.

the larger Area will be 9 square inch.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

To cover a 3 inch square with 1 inch squares, we can arrange the 1 inch squares in a 3 by 3 grid.

So, we need 9 of the 1 inch squares to cover the 3 inch square.

The area of the larger square can be found by squaring the length of one of its sides.

Since the side length of the 3 inch square is 3 inches, the area of the larger square is:

Area = (side length)² = 3² = 9 square inches

Therefore, the larger Area will be 9 square inch.

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Answer:

A)  \(\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx\)

General Formulas and Concepts:

Calculus

Discontinuities

Integration

Step-by-step explanation:

Let's define our answer choices:

A)  \(\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx\)

B)  \(\displaystyle \int\limits^3_1 {\frac{x + 1}{3x - 2}} \, dx\)

C)  \(\displaystyle \int\limits^0_{-1} {\frac{x + 1}{3x - 2}} \, dx\)

D) None of these

We can see that we would have a infinite discontinuity if x = 2/3, as it would make the denominator 0 and we cannot divide by 0. Therefore, any interval that includes the value 2/3 would have to be rewritten and evaluated as an improper integral.

Of all the answer choices, we can see that A's bounds of integration (interval) includes x = 2/3.

∴ our answer is A.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit:  Integration

Book: College Calculus 10e

Answer:

B. y = -6x+7

Step-by-step explanation:

change in x is positive 6 change in y is negative 1

6/-1 is the slope

-6 is the slope

The answer doesn't exist for lim x → 0 tan−1(ln(x)).

To find the limit of the function as x approaches 0, lim(x→0) arctan(ln(x)), we need to analyze the behavior of the function near x = 0.

1. Consider the domain of the function. The natural logarithm ln(x) is only defined for x > 0, so we cannot evaluate the function at x = 0. However, we can still analyze the limit as x approaches 0 from the right.

2. As x approaches 0 from the right (x → 0+), the natural logarithm ln(x) approaches negative infinity (ln(x) → -∞).

3. The arctan function is continuous and has horizontal asymptotes at y = -π/2 and y = π/2. When its argument approaches negative infinity (ln(x) → -∞), the arctan function approaches its horizontal asymptote at y = -π/2.

Therefore, the limit of the function as x approaches 0 from the right is -π/2: lim(x→0+) arctan(ln(x)) = -π/2.

Since the function is not defined for x ≤ 0, the limit as x approaches 0 does not exist. Your answer is DNE (does not exist).

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The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Step-by-step explanation:

Pythagoras formula for the relation of the side lengths in a right-angled triangle :

c² = a² + b²

c is the Hypotenuse, the side opposite of the 90 degree angle.

a and b are the "legs".

3.

c² = 10² + 21² = 100 + 441 = 541

c = sqrt(541) = 23.2594066...in

so, none of the provided answers. are you sure you put the right numbers ? maybe the second leg is sqrt(21) instead of 21 ? because then it would be

c² = 10² + sqrt(21)² = 100 + 21 = 121

c = 11in

4.

10² = a² + 6²

100 = a² + 36

64 = a²

a = 8 m

5.

again, there must be something wrong. the height of the triangle cannot be longer than the legs of the triangle.

given the answer options of 5 - 9 cm it cannot be 32cm. maybe you mean 3.2 cm ?

also interesting that it says "attitudes" - plural. what do you mean by that ?

because there is something else missing. like how long are the segments of the Hypotenuse where the height (or altitude) is touching the Hypotenuse ?

with just the Hypotenuse length and the height length we cannot calculate the other parts of the triangle, because we can move the height freely along the Hypotenuse and draw fitting right-angled triangles on that "skeleton".

6.

similar triangles. that means the lengths of corresponding lines (like sides or heights) are all in relation with the same scaling factor.

so, the small triangle has its "height" side of 1 ft, and multiplying with the scaling factor would then give us the height of the flag pole.

what is the scaling factor ? we get that from the pair of corresponding sides we already know : the shadows.

going from the small to the large triangle we have to transform 4ft into 60ft.

what do I have to multiply 4 with to get 60 ?

4 × x = 60

x = 60/4 = 15

so, the flag pole is

15×1 = 15ft tall.

1)The time complexity of the Eratosthenes' Sieve algorithm in unary notation is O(n) + O(n) + O(n) + O(1) = O(n). 2)when implemented on a Turing machine with unary notation input, the Eratosthenes' Sieve algorithm runs in O(n) time complexity, not O(n^2)

In unary notation, a positive integer n is represented by a string of n ones, denoted as '1n'. For example, 5 is represented as '11111' and 10 is represented as '1111111111'.

Eratosthenes' Sieve is an algorithm used to determine whether a given number n is prime by checking its divisibility with integers up to √n. To analyze the time complexity of the Sieve when implemented on a Turing machine with unary notation input, we need to understand the steps involved in the algorithm.

1. Input: The input to the Sieve is the number n represented in unary notation, '1n'.

2. Initialization: Initialize a boolean array of size n, initially assuming all numbers as prime.

3. Sieve: For each number from 2 to √n, check if it is marked as prime. If it is prime, mark all its multiples as non-prime in the boolean array.

4. Primality Check: Finally, check if the number n is marked as prime in the boolean array. If it is, then n is prime; otherwise, it is not prime.

Let's analyze the time complexity of each step:

1. Input: Representing the number n in unary notation takes O(n) time.

2. Initialization: Initializing the boolean array of size n takes O(n) time.

3. Sieve: In unary notation, the value of n is represented by a string of n ones. So, iterating from 2 to √n would require iterating from '11' to '1√n'. Since we are considering unary notation, the number of iterations required will be proportional to n itself. Therefore, this step takes O(n) time.

4. Primality Check: Checking whether n is marked as prime in the boolean array takes constant time, i.e., O(1).

Overall, the time complexity of the Eratosthenes' Sieve algorithm in unary notation is O(n) + O(n) + O(n) + O(1) = O(n).

Therefore, when implemented on a Turing machine with unary notation input, the Eratosthenes' Sieve algorithm runs in O(n) time complexity, not O(n^2) as mentioned in the problem statement.

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The partial fraction decomposition of the function "(x - 20)/(x² + x - 20)" is A/(x + 5) + B/(x - 4) .

The function of which we have to find the partial fraction decomposition is (x - 20)/(x² + x - 20) ;

In order to find the partial fraction decomposition of the function (x - 20)/(x² + x - 20),

We factor the denominator into linear factors ;

We get ;

⇒ x² + x - 20 = (x + 5)(x - 4)

Now, we use the partial fraction decomposition method , to write

⇒ (x - 20)/(x² + x - 20) = (x - 20)/(x + 5)(x - 4)

⇒ (x - 20)/(x² + x - 20) = A/(x + 5) + B/(x - 4)

Therefore , the partial fraction decomposition form is A/(x + 5) + B/(x - 4) .

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The given question is incomplete , the complete question is

Write out the form of the partial fraction decomposition of the function . Do not determine the numerical values of the coefficients. (x - 20)/(x² + x - 20) .

The given function is f(x) = (x+3)^4 * (x-4)^3 * (x-6)^6. The interval on which f(x) is increasing is (4, ∞).

To determine the intervals on which f(x) is increasing or decreasing, we need to analyze the sign of f'(x), the first derivative of f(x). In this case, f'(x) can be calculated using the product and chain rules of differentiation:

f'(x) = 4(x+3)^3 * (x-4)^3 * (x-6)^6 + 3(x+3)^4 * (x-4)^2 * (x-6)^6 + 6(x+3)^4 * (x-4)^3 * (x-6)^5

Simplifying f'(x) and factoring out common terms, we get:

f'(x) = (x+3)^3 * (x-4)^2 * (x-6)^5 * [4(x-6) + 3(x+3)(x-4) + 6(x-4)]

We can now analyze the sign of f'(x) for different values of x:

Thus, the interval on which f(x) is increasing is (4, ∞).

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The given function is f(x) = (x+3)^4 * (x-4)^3 * (x-6)^6. The interval on which f(x) is increasing is (4, ∞).

To determine the intervals on which f(x) is increasing or decreasing, we need to analyze the sign of f'(x), the first derivative of f(x). In this case, f'(x) can be calculated using the product and chain rules of differentiation:

f'(x) = 4(x+3)^3 * (x-4)^3 * (x-6)^6 + 3(x+3)^4 * (x-4)^2 * (x-6)^6 + 6(x+3)^4 * (x-4)^3 * (x-6)^5

Simplifying f'(x) and factoring out common terms, we get:

f'(x) = (x+3)^3 * (x-4)^2 * (x-6)^5 * [4(x-6) + 3(x+3)(x-4) + 6(x-4)]

We can now analyze the sign of f'(x) for different values of x:

Thus, the interval on which f(x) is increasing is (4, ∞).

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Multiply 360 by 3/4

360 x 3/4 = (360 x3)/4 = 1080/4 = 270

Answer : 270 degrees

The concepts of right and wrong encompass both the basic value concepts and the evaluation of morality in actions, as well as the evaluation of persons, things, experiences, and states of affairs. Therefore, the correct option is (e) "a and c."

The concepts of right and wrong are fundamental to ethics and moral reasoning. They serve as foundational value concepts, guiding individuals in distinguishing between what is considered morally good (right) and morally bad (wrong).

These concepts are not limited to evaluating the morality of actions alone (option b), but they also extend to evaluating the moral character of individuals and the ethical aspects of various entities, such as things, experiences, and states of affairs (option c). The moral evaluation of persons encompasses judgments about their intentions, virtues, and overall ethical conduct.

Hence, both options a and c accurately capture the comprehensive nature of the concepts of right and wrong.

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Personal experience generates firsthand knowledge that is derived from an individual's direct involvement or observation of a particular event, situation, or phenomenon. This type of sample is unique to each person and provides a subjective understanding of the subject matter.

Personal experience is an essential source of learning and understanding as it allows individuals to gain insight, develop skills, and form opinions based on their own encounters. It can provide a deep understanding of emotions, perspectives, and nuances that cannot be fully grasped through secondhand information. Personal experiences are often considered valuable as they offer authenticity and a sense of relatability, enabling individuals to connect with others on a personal level. Additionally, personal experiences can serve as a foundation for personal growth and development, shaping one's beliefs, values, and decision-making processes.

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Answer:

the 13th term, if you plug in 13 for n and solve you would get 20 :)

Answer:

13th term

Step-by-step explanation:

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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Answer:

29 minutes

Step-by-step explanation:

Let

x = number of minutes

y = the height of the airplane above sea level in feet

y = 32,000 - 1000x

y = 3,000

Therefore,

y = 32,000 - 1000x

3,000 = 32,000 - 1000x

3,000 - 32,000 = -1000x

-29,000 = -1,000x

x = -29,000 / -1,000

x = 29 minutes

it will take 29 minutes for the airplane to land at an airport 3000 feet above sea level

Answer:

14+14 + 4pi= 28 + 4pi

\(\pi\)

No, it does not follow that y is an interval or a ray in x. A convex subset of an ordered set is a set that contains all the points between any two points in the set.

This means that a convex subset of an ordered set could be a collection of points, it could be an interval, or it could be a ray. A proper subset of an ordered set is any subset except the entire set, so a proper subset of an ordered set could be any of these possibilities.

Therefore, while a proper subset of an ordered set that is convex in that set must be a collection of points, an interval, or a ray, it does not necessarily have to be one of those three options.

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Answer:

x=42

Step-by-step explanation:

so they u the exterior angle is 132

line makes 180 degree

180-132 =48

now they tell u a right angle

that is 90

triangles interior angles add up to 180

180-90-48=

42

\(x + 90 = 132\)

(exterior angle property)

\(x = 132 - 90\)

\(x = 42\)

Answer: y=4x+9

Slope = 4

Step-by-step explanation:

y2-y1/x2-x1

Given 3,21 and 4,25

25-21/4-3 = 4/1 = 4

Slope = 4

You can use the point-slope formula to get the following equation in slope-intercept formula.

y-y1 = m(x-x1)

(4,25)

->

y-25=4(x-4)

Distribute

y-25=4x-16

Cancel 25

y=4x+9

Answer:

\(y^{-5}\)

Step-by-step explanation:

The Exponent Quotient Rule states that if two terms of the same base are being divided by each other, then the simplified expression is the base to the first power subtracted by the second power. As an algebraic equation, that would be \(\frac{x^{a} }{x^{b} } =x^{a-b\), where \(x\) is the common base and \(a\) and \(b\) are the exponents.

In this case, \(x=y\), \(a=2\), and \(b=7\), so we know that \(\frac{y^{2} }{y^{7} } =y^{2-7}=y^{-5}\). Hope this helps!

Since the terms oscillate but do not approach one single value, the sequence appears to diverge

To find the first n terms of the sequence with the given terms a1 = 1, a2 = 2, and the rule for n ≥ 2, \(an = 1/2((an-1)(an-2))\), let's use n = 30.

1. Start with the given terms: a1 = 1 and a2 = 2.
2. Use the formula to find the next terms, up to n = 30.

It's important to calculate some of the terms in the sequence to determine if it converges or diverges. However, due to the character limit, I can't list all 30 terms here. Nevertheless, let's calculate the first few terms:

⇒ \(a_{3}= \frac{1}{2} ((a_{3})(a_{3})\)

= \(= \frac{1}{2} ((2)(1))\)

= 1
⇒\(= a_{4}= \frac{1}{2} ((a_{3})(a_{2}))\)

= \(\frac{1}{2} ((1)(2))\)

= 1
⇒\(a_{5}= \frac{1}{2} ((a_{4}) (a_{3}))\)

\(=\frac{1}{2} ((1)(1))\)

= 0.5

By examining the terms of the sequence, we can see that they oscillate but do not approach one single value. Therefore, the sequence appears to diverge.

Since the terms oscillate but do not approach one single value, the sequence appears to diverge.

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the area of the triangle is 7.5

Answer:

-3 ≤ 3x ≤ 6

To solve for "x", we can divide each part of the inequality by 3:

-1 ≤ x ≤ 2

Therefore, the number "x" must lie between -1 and 2 in order to satisfy the condition in the sentence.

Step-by-step explanation:

Answer:

124

Step-by-step explanation:

Answer: x = 5

Step-by-step explanation:

The area of a rectangle is the length times the width. Since the dimensions are given as functions of x, youre going to have to use FOIL to combine them, then set that answer equal to the given value of 72.

l*w = (x+3)*(x+4) = x^2 + 7x +12 = 72

Subtract 72 on both sides. There is a reason why we'll do this instead of subtracting 12. The quadratic formula will help us to solve for x.

x^2 + 7x - 60 = 0

Apply the quadratic formula

\(\frac{-7 (+/-)\sqrt{7^2-(4)*(1)*(-60} }{2*1} =\frac{-7(+/-)17}{2}\)

We cant have a negative x value because that would result in negative dimensions and a negative area, which is impossible in this context. So you want to add the 17 instead of subtracting it.

x = 5 and x = -12

An alternate way is just factoring the trinomial to:

(x+12)(x-5) = 0