Find the sum of 6 and 18.
12
× (6 +18) = X
?

Statements a, c, d, e, and f are true, while statements b and g are false.

a) True. The derivative of a sinusoidal function is another sinusoidal function. This can be observed from the derivative formulas of trigonometric functions.

b) False. A sinusoidal function can be differentiated regardless of the unit of measurement of the independent variable. The derivative of a sinusoidal function is not dependent on the unit of measurement.

c) True. A sinusoidal curve has an infinite number of tangents with a given non-zero slope. This is because the slope of a sinusoidal function changes continuously as the function oscillates.

d) True. The rate of change of a sinusoidal function is periodic in nature. This is because the derivative of a sinusoidal function is also a sinusoidal function with the same frequency.

e) True. Another way of expressing ln x is logex. Both notations represent the natural logarithm of x with base e.

f) True. If y = e^x, then its nth derivative will always be e^x. The exponential function e^x and its derivatives have the same value.

g) False. If y = e^f(x), then y' is not necessarily equal to e^f'(x). The derivative of e^f(x) involves the chain rule, so the derivative of y with respect to x depends on both f(x) and f'(x).

In summary, statements a, c, d, e, and f are true, while statements b and g are false.

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The fractional equivalent of the repeating decimal 0.2 is 2/9

From the question, we have the following parameters that can be used in our computation:

Repeating decimal = 0.2

Represent properly

So, we have

Repeating decimal = 0.2222

Express as fraction

So, we have

Fraction = 2/(10 - n)

In this case

n = 1

So, we have

Fraction = 2/(10 - 1)

Evaluate

Fraction = 2/9

Hence, the fractional equivalent is 2/9

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Using graph, the value of g(x) = 8 and the y- intercept at the point (0,-1).

A graph is a "mathematical representation of a network and it describes relationship between lines and points".

According to the question,

f(x) = \(10^x\)

g(x) = -4f(x) +12

g(x) = -4 (10ˣ) +12

The graph intersect at y-axis then x-coordinate should be zero.

Let take any two points on y-axis (0, 1) and substitute g(0) = -4 (10⁰) + 12

= 8

Hence, the value of g(x) = 8 and the y- intercept at the point (0,-1).

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If cosA = 24/25 tanB = 4/3 and angles A and B are in Quadrant I. The value of tan(A-B) is -23/33.

We can start by using the identity: tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

From the given information, we have:

cos A = 24/25, which means sin A = sqrt(1 - cos^2 A) = 7/25 (since A is in Quadrant I)

tan B = 4/3, which means sin B = 4/sqrt(4^2 + 3^2) = 4/5 and cos B = 3/sqrt(4^2 + 3^2) = 3/5

Now, we can use the definitions of sine and cosine to find tan A:

tan A = sin A / cos A = (7/25)/(24/25) = 7/24

Substituting the values we have found into the formula for tan(A - B), we get:

tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

= [(7/24) - (4/3)]/[1 + (7/24)(4/3)]

= (-13/72)/(25/72)

= -13/25

Therefore, tan(A - B) = -13/25.

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In a set S whic is said to be infinite if there is a one-to-one correspondence between S and a proper subset of S, then
the set of integers is infinite, the set of real numbers is infinite and if a set S has a subset A which is infinite, then S must be infinite.

Given that a set S is said to be infinite if there is a one-to-one correspondence between S and a proper subset of S, we want to prove the following statements:

(a) The set of integers is infinite.

(b) The set of real numbers is infinite.

(c) If a set S has a subset A which is infinite, then S must be infinite.

(a) Let A be the set of positive integers, i.e., A = {1, 2, 3, 4, 5, ...}. We define a function f: A → Z (the set of integers) by f(n) = n - 1. It can be shown that f is both one-to-one and onto. This means that there is a one-to-one correspondence between A and Z. By repeating the same argument, we can also prove that there is a one-to-one correspondence between the negative integers and A. Hence, Z is infinite.

(b) Suppose, for contradiction, that the set of real numbers, R, is finite. Then there would be a one-to-one correspondence between R and some finite set F. Without loss of generality, let F = {a_1, a_2, ..., a_n} where a_1 < a_2 < ... < a_n. Let ε > 0 be such that ε < min{|a_1|, |a_2| - |a_1|, ..., |a_n| - |a_(n-1)|, |a_n|}. For any x ∈ R, we consider different cases:

- If x < 0, then x < -ε < a_1.

- If 0 ≤ x < a_1, then 0 ≤ x + ε < a_1.

- If a_i < x < a_(i+1) where 1 ≤ i ≤ n - 1, then a_i + ε < x + ε < a_(i+1) - ε < a_(i+1).

- If x > a_n, then x - ε > a_n.

We define a function g: R → F by:

- g(x) = a_1 + ε if x < 0,

- g(x) = x + ε if 0 ≤ x < a_n,

- g(x) = a_(i+1) - ε if a_i < x < a_(i+1) where 1 ≤ i ≤ n - 1,

- g(x) = a_n - ε if x > a_n.

It can be shown that g is both one-to-one and onto. This contradicts the assumption that R is finite. Therefore, R must be infinite.

(c) Let S be a set such that A is a subset of S, and A is infinite. Suppose, for contradiction, that S is finite. Then, there would be a one-to-one correspondence between S and some finite set F. Let F = {a_1, a_2, ..., a_n}. There are finitely many elements in S that are not in A, denoted as {b_1, b_2, ..., b_m}. We choose ε > 0 such that ε < min{|a_1 - b_1|, |a_2 - b_2|, ..., |a_m - b_m|}. We define a function f: A → S as follows: f(a_i) = a_i for 1 ≤ i ≤ n, and f(a_i) = b_i + ε for 1 ≤ i ≤ m. It can be shown that f is both one-to-one and onto. This contradicts the assumption that S is finite. Therefore, S must be infinite.

Hence, we have proved the statements:(a) The set of integers is infinite, (b) The set of real numbers is infinite and (c) If a set S has a subset A which is infinite, then S must be infinite.

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Answer:

The value of x is 54 degrees.

Explanation:

The two angles are in a right triangle.

The angles in a right triangle add up to 90. So:

Next, solve for x.

The value of x is 54 degrees.

Answer:

\(2*x+1+\frac{2*x-5}{x^2+x+1}\)

Step-by-step explanation:

Where, the quotient is 2·x + 1, and the reminder is 2·x - 5

Hence, the above is correct is as follows:

The given dividend is 2·x³ + 3·x² + 5·x - 4

The divisor is x² + x + 1

By long division of a polynomial we have;

2·x + 1 [Quotient]

(2·x³ + 3·x² + 5·x - 4) ÷ (x² + x + 1 )

2·x³ + 2·x² + 2·x

0    +   x²  + 3·x - 4

          x² + x    + 1

          0  + 2·x - 5

Thurs, we have:

\(\frac{(2*x^3 + 3*x^2 + 5*x - 4)}{x^2+x+1} =2*x+1+\frac{2*x-5}{x^2+x+1}\)

Hence, the correct answer is \(2*x+1+\frac{2*x-5}{x^2+x+1}\)  

[RevyBreeze]

9514 1404 393

Answer:

  3.  rhombus

Step-by-step explanation:

If the diagonals are perpendicular, adjacent sides are congruent. If adjacent sides of a parallelogram are congruent, it is a rhombus.

__

Diagonals are congruent in a rectangle or square, so those choices don't apply. In a general parallelogram, the diagonals may not be perpendicular.

each cookie is like $2

Step-by-step explanation:

24 divided by 12 equals 2

Answer:

5x+7

Step-by-step explanation:

every time it goes up by 5 so if that's the case if you 12 and subtract 5 then that's your constant cause that is where it started.

I hope this is good enough:

Answer:

Step-by-step explanation:

The number of pennies they lose altogether is 288 pennies.

How to find the number of pennies they lost together?

Together, Katya and Mimi have 480 pennies in their piggy banks.

Therefore, there total amount of pennies is 480.

After Katya loses 1/2 of her pennies and Mimi loses 2/3 of her pennies, they have an equal number of pennies left.

Therefore,

let

x = number of pennies Katya have

y = number of pennies Mimi have

Hence,

x + y = 480

x = 480

Katya pennies left = x - 1 / 2x = 1 / 2x

Mimi pennies left = y - 2 / 3 y = 1 / 3 y

1 / 2 x  = 1 / 3 y

2y = 3x

y = 3  / 2 x

Substitute the value in equation(i)

x + 3 / 2 x  = 480

2.5x = 480

x = 480 / 2.5

x = 192

Therefore,

192 + y = 480

y = 480 - 192

y = 288

The number of pennies they lose can be calculated as follows;

Katya losses = 1 / 2 × 192 = 96

Mimi losses = 2 / 3 × 288  = 192

Therefore, they lost 96 + 192 = 288 pennies altogether.

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The dot product of two vectors u and v can be represented using index notation as u_i v_i.

A mathematical language called index notation is used to describe the components of a vector or tensor. It consists of an element's position in the vector or tensor and a symbol, typically a Latin or Greek letter.

A mathematical language called index notation is used to describe the components of a vector or tensor. The element's position in the vector or tensor is indicated by a symbol (often a Latin or Greek letter) with an integer subscript. How to utilise index notation is as follows:

Vectors can be represented by a single letter with a subscript, such as v i, where I stands for the element's position in the vector.

Tensors are multidimensional arrays that can be described using an index notation for each element. For instance, T i,j can be used to represent the element in a matrix's ith row and jth column.

Executing operations: Index notation can be used to express operations like matrix multiplication and the vector dot product. For instance, u_i v_i can be used to denote the dot product of the two vectors u and v.

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Answer:

\(\frac{-x^{2}+5x-1}{2x^{2} -x-1}\)

Step-by-step explanation:

Step-by-step explanation:

To find the mean, you add all the numbers and divide by how many there are.

In this case, you add -54,-32,-70,-25,-65, and -42. Then you divide by 6 because there are 6 numbers.

When you add them all, you get -288.

Now divide.

-288/6=-48

Hope it helps!

Answer:

-48

so you add all the numbers together, which will give you -288

there are 6 terms, so you divide -288 by 6

gives you your answer of -48

Answer: The dimensions are 7cm and 3cm.

Step-by-step explanation:

The following equation can be deduced from the question

L × W = 21 ....... i

2L + 2W = 20 .......... ii

Divide equation ii through by 2

(2L + 2W = 20) / 2

L + W = 10 ....... iii

From equation iii

L = 10 - W ......... iv

Put equation iv into I

L × W = 21

(10 - W) × W = 21

10W - W² = 21

W² - 10W + 21 = 0

W² - 7W - 3W + 21 = 0

W(W - 7) - 3(W - 7) = 0

W - 3 = 0

W = 0+3

W = 3 centimeter

Since,

Length × Width = 21

Length = 21/3

Length = 7 centimeters

The dimensions are 7cm and 3cm.

Answer:11

Step-by-step explanation:

Answer:

57% of students

Step-by-step explanation:

14 + 29 = 43%

100% - 43% = 57%

Answer:

(0, 4)

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

According to the graph, the line passes the y-axis at y = 4. Therefore, our y-intercept is (0, 4).

Answer:

678.987Answer:

Step-by-step explanation:

The probability of a penny falling out is 0.3 or 30%.

The study of probability is a branch of mathematics that focuses on calculating the possibility or chance that an event will occur. It is expressed as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty, and numbers in between denoting likelihood.

The number of favourable outcomes for an event A divided by the total number of possible outcomes is the definition of P(A), which stands for probability. The classical definition of probability is this.

From the given table we see that, the total coins in the cup are:

3+5+2+1=11.

Now, for the number of penny are: 3

Thus,

P(penny falls out) = 3/10 = 0.3

Hence, the probability of a penny falling out is 0.3 or 30%.

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The conditions for a sampling distribution of a sample mean, when you know the true involve random sampling, independence, and a large enough sample size.

The conditions for a sampling distribution of a sample mean, when you know the true mean, are as follows:

1. Random Sampling:

The samples should be selected randomly from the population to ensure that they are representative of the entire population.

2. Independence:

Each sample should be independent of the others.

This means that the outcome of one sample should not influence the outcome of another sample.

3. Sample Size:

The sample size should be large enough to ensure that the sampling distribution approximates a normal distribution.

In general, a sample size greater than 30 is considered sufficient.

Random sampling is important because it helps to minimize bias and ensure that the sample is representative of the population.

Independence is necessary to avoid any potential confounding factors that may influence the results.

Lastly, a sufficiently large sample size is needed to satisfy the central limit theorem, which states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution.

These conditions are important to ensure the validity and reliability of the statistical analysis.

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Line perpendicular to a given line is = 1/m

To find m, use m =y2-y1/x2-x1 formula

m = (8-(-3))/(-7-4)

m = 11/-11,

m = -1

Use y= mx+c to find equation of line

Plug in a pair of values,

-3= -1(4)+ c

c= 1

Thus, equation is:

y = -x+1

Equation of line perpendicular to this line is:

y= x+1

Hope it helps :)

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Sample variance and sample standard deviationThe sample variance of the group is given by the sample standard deviation of the group$n$ - the number of observations in the sample group$\overline{x}$ - the mean value of the sample$x_i$ - each observation of the sampleNow we can get started with the solution to the problem.

Given the data set of scores, we can find the sample variance of the group using the following steps: Step 1: Compute the mean value of the sample Find the squared difference between each value and the mean value

$(x_i - \overline{x})^2$20 - 19.3 = 0.72(0.72)^2 = 0.519619 - 19.3 = -0.319(-0.319)^2 = 0.10176122 - 19.3 = 2.7(2.7)^2 = 7.290420 - 19.3 = 0.7(0.7)^2 = 0.34315 - 19.3 = -4.3(-4.3)^2 = 18.4918 - 19.3 = -1.3(-1.3)^2 = 1.690419 - 19.3 = 1.7(1.7)^2 = 4.91321 - 19.3 = 1.7(1.7)^2 = 4.91320 - 19.3 = 0.7(0.7)^2 = 0.343

Step 3: Add the squared differences to obtain the numerator of the sample variance equation$\sum_{i=1}^{n}(x_i - \overline{x})^2$= 0.5196 + 0.1018 + 7.2904 + 0.3431 + 18.4918 + 1.6904 + 4.9132 + 4.9132 + 0.343=

Calculate the sample variance

$(n - 1)s^2 = \sum_{i=1}^{n}(x_i - \overline{x})^2$$9s^2 = 38.1073$$s^2 = \frac{38.1073}{9}$$s^2 = 4.234144$

Thus, the sample variance of the given data set is 4.234144. We can now move on to finding the sample standard deviation.The sample standard deviation of the group is given by:

$s = \sqrt{\frac{\sum_{i=1}^{n}(x_i - \overline{x})^2}{n - 1}}$

Using the value of the sample variance obtained above, we can easily find the sample standard deviation using the formula above.

$s = \sqrt{\frac{38.1073}{9 - 1}}$$s = \sqrt{\frac{38.1073}{8}}$$s = \sqrt{4.76341}$$s = 2.18$

Thus, the sample standard deviation of the given data set is 2.18. Therefore, the correct option is a. 2.21.

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To know if the classmate’s family is actually wealthy, one will need to know their assets and their debt.

In financial accounting, an asset means a resource that is owned or controlled by a business or an economic entity. An asset is anything that can be used to produce positive economic value.

Assets represent the value of ownership that can be converted into cash and the examples of personal financial assets include cash and bank accounts, real estate, personal property like furniture and vehicles, and investments such as stocks, mutual funds, and retirement plans.

In this case, through the assets, one will be able to know that they're wealthy. The debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. This is the money that they owe.

The asset should more than the debt.

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Answer:

120

Step-by-step explanation:

This is the desired 4x4 matrix that produces the translation by the vector (4,-6,-3) using homogeneous coordinates.

To find the 4x4 matrix that produces a translation by the vector (4,-6,-3) using homogeneous coordinates, we start with the identity matrix:

[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]

We then replace the last column with the translation vector in homogeneous coordinates, which is [4, -6, -3, 1]:

[1 0 0 4]
[0 1 0 -6]
[0 0 1 -3]
[0 0 0 1]

This is the desired 4x4 matrix that produces the translation by the vector (4,-6,-3) using homogeneous coordinates.

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The total cost  of he meat with tax and tip is $ 22.42

To calculate the total cost with tax and tip, we need to follow these steps:

multiply the meal cost by the tip rate. when  the tip rate is 18%, we have:

Tip amount = $19.00 * 0.18 = $3.42

Add the meal cost, sales tax, and tip amount to get the total cost:

Total cost = Meal cost + Sales tax + Tip amount

= $19.00 + $3.42

= $ 22.42

Therefore, the total cost with tax and tip is $22.42

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