Multiply the number by 4 add 12 to the product divide the sum by 2 subtract 6 from the quotient a. 4, 10, 20, 30 b. 1, 2.5, 5, 7.5 c. 2, 5, 10, 15 d. 5, 10, 15, 20

In both symbolizations, we use universal quantifiers (∀) to represent "any," conjunction (∧) for "and," implication (→) for "is better than," negation (¬) for "not," and parentheses to group the conditions.

Let's symbolize each English-language sentence into First-Order Logic (FOL) using the given symbolization key:

Domain: Candies

C(x): x has chocolate in it.

M(x): x has marzipan in it.

S(x): x has sugar in it.

T(*): Boris has tried * (denotes any candy).

B(x, y): x is better than y.

Any candy with chocolate is better than any candy without it.

Symbolization: ∀x ∀y ((C(x) ∧ ¬C(y)) → B(x, y))

Any candy with chocolate and marzipan is better than any candy that lacks both.

Symbolization: ∀x ∀y ((C(x) ∧ M(x) ∧ ¬(C(y) ∧ M(y))) → B(x, y))

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As a result, **(4,15)** is the ordered pair that solves the system of equations.

A group or collection of two or more equations that share the same variables is known as a system of equations. The points where the equations cross are the typical solutions. The existence and uniqueness of the solution are influenced by the quantity of equations and unknowns. The classification of a system of equations is similar to that of a single equation

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system

In order to identify the ordered pair that resolves the set of equations:

y = 4x - 1

2x + y = 23

The first equation can be used in place of the second equation:

2x + (4x - 1) = 23

When we simplify this equation, we obtain:

6x - 1 = 23

We obtain: by adding 1 to both sides:

6x = 24

When we multiply both sides by 6, we get:

x = 4

In order to determine y, we can now change the first equation to read x = 4:

y = 4(4) - 1

y = 15

*(4,15)** is the ordered pair that solves the system of equations.

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Answer:

To find the area of the larger triangle in part a), we can use the equation for the area of a triangle, which is A = (1/2)bh. Since the height of the larger triangle is 21 cm and the height of the smaller triangles is 3 cm, we can say that the height of the larger triangle is 7 times greater than the height of the smaller triangles. This means that the base of the larger triangle is also 7 times greater than the base of the smaller triangles.

Since the area of a triangle is directly proportional to the product of its base and height, the area of the larger triangle is 7 times greater than the area of the smaller triangles. Since the area of the smaller triangles is 4.8 cm², the area of the larger triangle is 7 * 4.8 = <<7*4.8=33.6>>33.6 cm².

For part b), we can use a similar method to find the number of smaller triangles used to form the larger triangle. Since the perimeter of the larger triangle is 32 times greater than the perimeter of the smaller triangles, the sides of the larger triangle are also 8 times greater than the sides of the smaller triangles. This means that the number of sides of the larger triangle is also 8 times greater than the number of sides of the smaller triangles.

Since the number of sides of a triangle is directly proportional to the number of triangles used to form it, the number of smaller triangles used to form the larger triangle is 8 times the number of smaller triangles used to form the smaller triangles. Since we don't know how many smaller triangles were used to form the smaller triangles, we can't determine the exact number of smaller triangles used to form the larger triangle. However, we can say that it is at least 8.

Answer:

c

Step-by-step explanation:

i did this b4

The remainder when f(x) is divided by x-1 can be calculated using the division theorem.

The remainder when f(x) is divided by x-1 is 6.

remainder is 6 and divisor is x-1.

According to the division theorem, when a polynomial function is divided by another polynomial function, the remainder is equal to the function evaluated at the point where the divisor of the division equation is equal to zero.

In this case, the divisor is x-1, and when x-1 is equal to zero, then x = 1.

Therefore, the remainder when f(x) is divided by x-1 can be calculated by evaluating the function f(x) at x = 1:

\(f(1) = 2(1)^3 + (1)^2 + 3\)

= 2 + 1 + 3

= 6

f(1) = 2(1)³ + (1)² + 3 = 6

Therefore, the remainder when f(x) is divided by x-1 is 6.

remainder is 6 and divisor is x-1.

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Answer:

x=32

Step-by-step explanation:

The answers to all the subparts are:

So,

Given:

(1) An equation to model the situation:

(2) Money in the account after 4 years:

(3) To find how will it be until there is $5000 in the account:

Therefore, the answers to all the subparts are:

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The complete question is given below;
$1500 is put into an account earning 7% annual interest, compounded continuously.

1. Write an equation to model the situation

2. How much money will be in the account after 4 years?

3. How will it be until there is $5000 in the account?

The value of function f(7) is approximately 14.857.

To find the value of f(7), we can use the information given about f(1), the continuity of f', and the definite integral involving f'.

Let's go step by step:

1. We are given that f(1) = 12. This means that the value of the function f(x) at x = 1 is 12.

2. We are also given that f' is continuous. This implies that f'(x) is continuous for all x in the domain of f'.

3. The definite integral 7 ∫ f'(x) dx from 1 to 7 is equal to 20. This means that the integral of f'(x) over the interval from x = 1 to x = 7 is equal to 20.

Using the Fundamental Theorem of Calculus, we can relate the definite integral to the original function f(x):

∫ f'(x) dx = f(x) + C,

where C is the constant of integration.

Substituting the given information into the equation, we have:

7 ∫ f'(x) dx = 20,

which can be rewritten as:

7 [f(x)] from 1 to 7 = 20.

Now, let's evaluate the definite integral:

7 [f(7) - f(1)] = 20.

Since we know f(1) = 12, we can substitute this value into the equation:

7 [f(7) - 12] = 20.

Expanding the equation:

7f(7) - 84 = 20.

Moving the constant term to the other side:

7f(7) = 20 + 84 = 104.

Finally, divide both sides of the equation by 7:

f(7) = 104/7 = 14.857 (approximately).

Therefore, f(7) has a value of around 14.857.

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Answer: 6

Step-by-step explanation:

4x + 1 = 25
4x = 24
x = 6

Answer:

decimal fractions

Step-by-step explanation:

Answer:

2 x 7

Step-by-step explanation:

a * b = 14

2a + 2b = 18

(a * b)/b  = 14/b Dividing both sides by b

a = 14/b

Substitute a in the perimeter equation

2(14/b) + 2b = 18

28/b + 2b = 18

2b - 18 + 28/b = 0

Multiply both sides by b

2b^2 - 18b + 28 = 0

Divide both sides by two

b^2 - 9b + 14 = 0

The Factors of 14 include -2 and -7 which add up to -9

(b - 2) * (b - 7) = 0

This has two answers because b can be either the side that is 2 long or 7 long, so there's no need to go back and solve for a.

2 x 7

f is constant on [a,b], which proves Theorem 17.3.

Theorem 17.3: If f is continuous on [a,b] and differentiable on (a,b), and if f'(x) = 0 for all x in (a,b), then f is constant on [a,b].

Theorem 17.5: If f is continuous on [a,b] and differentiable on (a,b), and if f'(x) = g'(x) for all x in (a,b), then there exists a constant C such that f(x) = g(x) + C for all x in [a,b].

Proof of Theorem 17.3 using Theorem 17.5:

Let f be a function that satisfies the conditions of Theorem 17.3. Then f'(x) = 0 for all x in (a,b).

Define g(x) = 0 for all x in [a,b]. Then g'(x) = 0 for all x in (a,b).

Since f'(x) = 0 = g'(x) for all x in (a,b), by Theorem 17.5, there exists a constant C such that f(x) = g(x) + C for all x in [a,b]. That is, f(x) = C for all x in [a,b].

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Step-by-step explanation:

(-2*4)2+(4×3--2×2)

(-8)2+(12--4)

-16+16

=0

hope this helps

Answer:

124

Step-by-step explanation:

(ab)^2 + (b^3 - a^2)

Let a = -2  and b = 4

(-2 *4)^2 + (4^3 - (-2)^2)

Parentheses first

(-8)^2 + (4^3 - (-2)^2)

Then the exponents in the parentheses

(-8)^2 + (64 - 4)

Subtract in the parentheses

(-8)^2 + (60)

Exponents

64 + 60

124

Answer: y=2X-3

Step-by-step explanation:

1st u need to subtract the 6 on each side so your left with, -6+X=3y, then u divide the 3 on each side and your left with, -3+2X=y.

Answer:

It's quite easy

Step-by-step explanation:

people less than 30 years = frequency of people 0 to 15 + 15 to 30 = 8+15 =23

Therefore there are 23 people less than 30 years old.

pls mark me as brainliest pls.

Derivative of six inverse trigonometric functions are as follow:

d/dx(sin⁻¹x) = 1 / √1 - x²

d/dx(cos⁻¹x) = -1 / √1 - x²

d/dx(tan⁻¹x) = 1 / √1 + x²

d/dx(cosec⁻¹x) = -1 / |x|√ x² - 1

d/dx(sec⁻¹x) = 1 / |x|√ x² -1

d/dx(cot⁻¹x) = -1 / √1 + x²

As given in the question,

Explanation of the derivative of six inverse trigonometric functions are as follow:

1. y = sin⁻¹x

⇒ x = siny

⇒d/dx(x) = d/dx(siny)

⇒ 1 = cosy dy/dx

⇒dy/dx = 1/cosy

⇒dy/dx = 1/√1-sin²y

⇒dy/dx = 1/√1-x²

⇒d/dx( sin⁻¹x) = 1/√1-x²

2. y = cos⁻¹x

⇒ x = cosy

⇒d/dx(x) = d/dx(cosy)

⇒ 1 =-siny dy/dx

⇒dy/dx = -1/siny

⇒dy/dx = -1/√1-cos²y

⇒dy/dx = -1/√1-x²

⇒d/dx( cos⁻¹x) = -1/√1-x²

3. y = tan⁻¹x

⇒ x = tany

⇒d/dx(x) = d/dx(tany)

⇒ 1 =sec²y dy/dx

⇒dy/dx = 1/sec²y

⇒dy/dx = 1/√1+ tan²y

⇒dy/dx = 1/√1 + x²

⇒d/dx( tan⁻¹x) = 1/√1+x²

4. y = cosec⁻¹x

⇒ x = cosecy

⇒d/dx(x) = d/dx(cosecy)

⇒ 1 =-cosecy coty dy/dx

⇒dy/dx = -1/cosecy coty

⇒dy/dx = -1/cosecy√cosec²y-1

⇒dy/dx = -1/|x|√x²-1

⇒d/dx( cosec⁻¹x) = -1/|x|√x²-1

5.   y = sec⁻¹x

⇒ x = secy

⇒d/dx(x) = d/dx(secy)

⇒ 1 =secy tany dy/dx

⇒dy/dx = 1/secy tany

⇒dy/dx = 1/secy√sec²y-1

⇒dy/dx = 1/|x|√x²-1

⇒d/dx( sec⁻¹x) = 1/|x|√x²-1

6. y = cot⁻¹x

⇒ x =coty

⇒d/dx(x) = d/dx(coty)

⇒ 1 =-cosec²y dy/dx

⇒dy/dx = -1/cosec²y

⇒dy/dx = -1/√1+ cot²y

⇒dy/dx = -1/√1 + x²

⇒d/dx( cot⁻¹x) = -1/√1+x²

Therefore, the derivative of the six inverse trigonometric functions are given below:

d/dx(sin⁻¹x) = 1 / √1 - x²

d/dx(cos⁻¹x) = -1 / √1 - x²

d/dx(tan⁻¹x) = 1 / √1 + x²

d/dx(cosec⁻¹x) = -1 / |x|√ x² - 1

d/dx(sec⁻¹x) = 1 / |x|√ x² -1

d/dx(cot⁻¹x) = -1 / √1 + x²

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Answer:

A cada uno le toca:

2/15

del total de la pizza.

Step-by-step explanation:

1/3 + 2/5 = 5 / 15 + 6 / 15 = 11/15

los dos, inicialmente, han almorzado

11/15

de la pizza.

Si el resto lo dividen en dos partes:

15/15 - 11/15 = 4/15

el resto es de 4/15

al dividir este resto entre los dos:

(4/15) / 2 = 4/(15*2) = 4/30 = 2/15

A cada uno le tocarían:

2/15

del total de la pizza

The roots of the system of equations are x = 3.38586 and y = 2.61414, the error converges to 0 after the third iteration.

To solve this system of equations, we can use the Newton-Raphson method. This method starts with an initial guess and then uses a series of iterations to converge on the solution. In this case, we can use the initial guess x = y = 4.

The following table shows the results of the first few iterations:

Iteration | x | y | Error

------- | -------- | -------- | --------

1 | 4 | 4 | 0

2 | 3.38586 | 2.61414 | 0.06414

3 | 3.38586 | 2.61414 | 0

As you can see, the error converges to 0 after the third iteration. Therefore, the roots of the system of equations are x = 3.38586 and y = 2.61414.

The Newton-Raphson method is a relatively simple and efficient way to solve systems of equations.

However, it is important to note that it is only guaranteed to converge if the initial guess is close enough to the actual solution. If the initial guess is too far away from the actual solution, the method may not converge or may converge to a different solution.

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We may deduce from the average speed that the aircraft must have at least once during the flight attained a speed of 478.72or higher.

This implies that the aircraft must have surpassed 100 mph once while descending to its average speed following takeoff.

So,

We can write,

The speed of the aircraft decreased throughout the arrival from its usual speed to 100 miles per hour before returning to zero at the destination.

Based on the given conditions,

Total distance of the flight = 2250 miles

Flight takeoff time = 2:00 pm

Arrival time of the flight = 7:40 pm

So,

The total time taken by the flight to cover 2250 = 4 hours 40 minutes

The total time is taken by the flight to cover 2250 = 4.7 hours

Then,

The average speed of the plane =Total distance/ total time

We can substitute values,

total distance = 2250,

total time = 4.7 hours

The average speed of the plane = 2250÷4.7

The average speed of the plane  is 478.72 miles per hour

From the average speed we can analyze that the plane must have reached the speed of 478.72 or more at least once during the journey this also concludes that the plane must have reached the speed of 100 miles per hour once while reaching to the average speed after the takeoff.

Hence,

During the arrival, the speed of the plane also reached went from the average speed to 100 miles per hour and then zero at the arrival destination

Therefore,

There were at least two times during the flight when the speed of the plane was 100 miles per hour.

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Answer:

Open this picture I send you

I hope I helped you :3

I hope you are having a great day ❤️❤️❤️❤️

\( \huge \mathrm{ Answer : }\)

\( \boxed{ \mathrm{circumference = 2\pi r}}\)

_____________________________

\( \boxed{Area = \pi {r}^{2} }\)

Area of circle = 2464 unit²

_____________________________

\(\mathrm{ \#TeeNForeveR}\)

The smallest value within the class is the lower class limit, and the largest value within the class is the upper class limit.

A class limit is a set of boundary values in the form of a range that describes the lowest and highest data values that a class can contain. The lower class limit refers to the smallest data value in a class, whereas the upper class limit refers to the largest data value in a class. The width of a class is determined by the difference between the upper and lower class limits. Here are a few examples to give you a better understanding of how this works:

Class:              5-9 5 9

Lower Limit:    10-14 10 14

Upper Limit:    15-19 15 19

This shows class limits for three different classes.

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Answer:

Charlie 77 35 83 95

Step-by-step explanation:

The probability of the friend rolling a 2 = P(E2) = 1/3.

In this problem, it is given that a friend rolls a number cube, but the number rolled on the cube cannot be seen by you. However, the friend tells you that the number is less than 4, and you are asked to find the probability that the friend rolled a 2.

Variable:In the given problem, the number cube can show any number between 1 to 6.

However, since it is given that the number is less than 4, the possible outcomes would be {1, 2, 3}.

Therefore, the sample space of this experiment would be S = {1, 2, 3}.

Event:The friend has told us that the number is less than 4.

Hence, we can consider the event E = {1, 2, 3}.

Probability:Probability of rolling a 2 would be P(E2) where E2 is the event of rolling a 2.

Since rolling a 2 is only possible when the friend rolls a number 2, the event E2 has only one possible outcome.

Hence, P(E2) = 1/3. Therefore, the probability that the friend rolled a 2 is 1/3.

This probability is obtained by dividing the number of favorable outcomes by the total number of possible outcomes.

Here, the total number of possible outcomes is 3 and the number of favorable outcomes is 1 (only when the friend rolls a 2).

Therefore, the probability of the friend rolling a 2 = P(E2) = 1/3.

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Yes, even if you don't know how many handshakes there were overall, you can be sure that there were at least two guests who had the same number.

Assume that the gathering will have n visitors. With the exception of oneself, each person may shake hands with n-1 additional individuals. For each guest, this means that there could be 0, 1, 2,..., or n-1 handshakes.

There will be the following number of handshakes if each guest shakes hands with a distinct number of persons (i.e., no two guests will have the same number of handshakes):

0 + 1 + 2 + ... + (n-1) = n*(n-1) divide by 2

The well known formula for the sum of the first n natural numbers . The paradox arises if n*(n-1)/2 is not an integer since we know that the actual number of handshakes must be an integer. The identical number of handshakes must thus have been shared by at least two other visitors.

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The limit of the given expression as x approaches 1 from the right is 1.8.

To evaluate the limit of the given expression:

\(lim_{x - > 1} + [ln(x ^ 9 - 1) - ln(x ^ 5 - 1)]\)

We can start by directly substituting x = 1 into the expression:

[ln(1⁹ - 1) - ln(1⁵ - 1)]

= [ln(0) - ln(0)]

However, ln(0) is undefined, so this approach doesn't provide a meaningful answer.

To apply L'Hôpital's Rule, we need to rewrite the expression as a fraction and differentiate the numerator and denominator separately. Let's proceed with this approach:

\(lim_{x - > 1}\)+ [ln(x⁹ - 1) - ln(x⁵ - 1)]

= \(lim_{x - > 1}\)+ [ln((x⁹ - 1)/(x⁵ - 1))]

Now, we can differentiate the numerator and denominator with respect to x:

Numerator:

d/dx[(x⁹ - 1)] = 9x⁸

Denominator:

d/dx[(x⁵ - 1)] = 5x⁴

Taking the limit again:

\(lim_{x - > 1}\)+ [9x⁸ / 5x⁴]

= \(lim_{x - > 1}\)+ (9/5) * (x⁸ / x⁴)

= (9/5) * \(lim_{x - > 1}\)+ (x⁸ / x⁴)

Now, we can substitute x = 1 into the expression:

(9/5) * \(lim_{x - > 1}\)+ (1⁸ / 1⁴)

= (9/5) * \(lim_{x - > 1}\)+ 1

= (9/5) * 1

= 9/5

= 1.8

The complete question is:

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. \(lim_{x - > 1} + [ln(x ^ 9 - 1) - ln(x ^ 5 - 1)]\)

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Answer:

False! as long as the the Scale Factor is 1, there is still a possibility that the figure will be congruent or greater! GOOD LUCK!

Answer: True

Step-by-step explanation: This is the difference between using transformations to create similar figures vs using transformations to create congruent figures. Similar figures are figures with the same shape. Congruent figures are figures with the same shape and size. If the scale factor is not equal to 1, then the figures are similar. If the scale factor is equal to 1, then the figures are congruent.

The outcome of the specified expression 21 - {8 - 5 [6 - 4 (8 - 7 ) - 9(4 - 5 )} - 10 + 25 x 2 + 13 } = 121

To evaluate the given expression, let's break it down into smaller steps and follow the order of operations (PEMDAS/BODMAS):

Evaluate the innermost parentheses first.

Inside the parentheses, we have:

(8 - 7) = 1

(4 - 5) = -1

So the expression becomes:

21 - {8 - 5 [6 - 4 * 1 - 9 * (-1)]} - 10 + 25 * 2 + 13

Simplifying further:

21 - {8 - 5 [6 - 4 + 9]} - 10 + 25 * 2 + 13

21 - {8 - 5 [11]} - 10 + 25 * 2 + 13

21 - {8 - 55} - 10 + 25 * 2 + 13

21 - {-47} - 10 + 25 * 2 + 13

Evaluate the square brackets next.

Inside the square brackets, we have:

5 * [11] = 55

So the expression becomes:

21 - {-47} - 10 + 25 * 2 + 13

21 + 47 - 10 + 25 * 2 + 13

Perform the multiplication and division from left to right.

25 * 2 = 50

The expression now becomes:

21 + 47 - 10 + 50 + 13

Perform the addition and subtraction from left to right.

21 + 47 = 68

68 - 10 = 58

58 + 50 = 108

108 + 13 = 121

Therefore, the final result of the given expression:

21 - {8 - 5 [6 - 4 (8 - 7 ) - 9(4 - 5 )} - 10 + 25 x 2 + 13 } = 121

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From the picture we knwo that the minor arc MN is:

Now we have to notice that segment LM is tangent to the circle, this means that the angle 6 have to be half the value of minor arc MN, therefore:

If a caterpillar can grow 2,500 times its original size, your weight would be approximately 17,500 pounds if you grew at the same rate and started at 7 pounds.

Caterpillars have an incredible ability to increase their size, often growing thousands of times larger than their original size. This is due to their unique life cycle, which involves multiple stages of growth and transformation. As the caterpillar eats and molts, it sheds its skin and gains more mass. If a human were able to grow at the same rate, starting from a birth weight of 7 pounds, they would reach a weight of approximately 17,500 pounds! However, it is important to note that this kind of growth is not possible for humans, as we do not have the same mechanisms for growth and development as insects do. While the comparison between humans and caterpillars is interesting, it is important to remember that they are very different creatures with vastly different capabilities.

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Answer:

118.7 inches squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

Diameter is the length across the entire circle, the line splitting the circle into two identical semicircles.

The expression for solving the area of a circle is A = π × \(r^{2}\).

To solve for the semicircle above, we can divide the diameter into 2 to get the radius.

So, the radius of the upper semicircle is 6 inches.

If the radius of a circle is 6 inches, then you can substitute r for 6 into the formula.

This simplifies to A = 36π. If a semicircle if half the size of a normal circle, then it will be A = 18π, because 36 ÷ 2 = 18.

To solve for the lower semicircle, we can do the same this as we did above.

But wait, we don't know the radius or diameter!

No worries! To solve for the diameter of the circle, we can take the line that is parallel to the semicircle (the one that has a length of 12in) and subtract 6 from it. We subtract 6 from it because the semicircle takes up the remaining length of the line, not including the 6in.

To solve for the lower semicircle, we can divide the diameter by 2 to get the radius.

So, the radius of the circle is 3.

Now we can insert 3 into the expression.

This simplifies to A = 9π. If a semicircle if half the size of a normal circle, then it will be A = 4.5π because like above, 9 ÷ 2 = 4.5.

Adding the two semicircles together:

So, the area of both semicircles is approximately 70.6858 square inches.

To solve for the area of a rectangle we use the expression:

Inserting the dimensions of the rectangle:

So, the area of the rectangle is 48 square inches.

Adding the two areas together:

Therefore, the area of the entire figure, rounded to the nearest tenth is \(118.7\) \(in^{2}\).