The nth term of a sequence is 2n2 − 1 The nth term of a different sequence is 40 − n2 Show that there is only one number that is in both of these sequences.

The argument is valid based on the truth table. Whenever p implies (p and q) is true, p is also true. No counterexample can be found to invalidate the argument.

In order to test the validity of the argument, we can construct a truth table to evaluate the relationship between the premises and the conclusion. The argument states that if p implies (p and q), then p is true.

Using a truth table, we can assign the values of true (T) or false (F) to the variables p and q and determine the resulting truth value of the expression. The truth table for the argument would look as follows:

p q p implies (p and q)

T T T

T F T

F T F

F F T

From the truth table, we can observe that whenever p implies (p and q) is true, p is also true. Therefore, the argument is valid.

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The decision between the two cities involves tradeoffs: the first city offers a wide range of class sizes but a smaller sample, while the second city has a larger sample but a narrower class size range.

The decision of which city to choose for the study involves tradeoffs. The first city allows for a wide range of class sizes, providing a comprehensive analysis of the relationship between class size and academic performance. However, the smaller sample size limits generalizability.



The second city offers a larger sample size, increasing generalizability, but with a narrower range of class sizes. Researchers should consider their specific research objectives, available resources, and constraints. If the goal is to assess the impact of extreme variations in class size, the first city is suitable. If obtaining highly generalizable results is paramount, the second city, despite the narrower range, should be chosen.



Therefore, The decision between the two cities involves tradeoffs: the first city offers a wide range of class sizes but a smaller sample, while the second city has a larger sample but a narrower class size range.

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Answer:

9(2x-1)

Step-by-step explanation:

common factor of both 9 and 18 is 9

thus, you can take a 9 out

9(2x-1)

(to check if it is correct, you can expand it, and if it is the same as original then it is correct )

Answer:

9 (2x-1)

Step-by-step explanation:

Grouping

1. Common factor:

18x-9

Solution:

9 (2x-1)

The answers, rounded to the appropriate number of significant figures, are as follows:

(a) 1.088 ×\(10^2\)

(b) 2.132

(c) 1.3331 ×\(10^1\) and

(d) 1.05.

Let's calculate the answers to the given operations using the appropriate number of significant figures.

(a) 8.370×1.3×10

To perform this multiplication, we multiply the decimal numbers and add the exponents of 10:

8.370 × 1.3 × 10 = 10.881 × 10 = 1.0881 × \(10^2\)

Since the original numbers have four significant figures, we round the final answer to four significant figures:

1.088 × \(10^2\)

(b) 4.265/2.0

For division, we divide the decimal numbers:

4.265 ÷ 2.0 = 2.1325

Since both numbers have four significant figures, the answer should be rounded to four significant figures:

2.132

(c) (1.2588×\(10^3\))×(1.06×\(10^-^2\))

To multiply these numbers, we multiply the decimal numbers and add the exponents:

(1.2588 × \(10^3\)) × (1.06 × \(10^-^2\)) = 1.333128 × \(10^1\)

Since the original numbers have five significant figures, we round the final answer to five significant figures:

1.3331 × \(10^1\)

(d) \((1.11)^(^1^/^2^)\)

To calculate the square root, we raise the number to the power of 1/2:

\((1.11)^(^1^/^2^)\)= 1.0524

Since the original number has three significant figures, the answer should be rounded to three significant figures:

1.05

It's important to note that the significant figures in a result are determined by the original data and the operations performed. The final answers provided above reflect the appropriate number of significant figures based on the given information and the rules for significant figures.

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Answer:

360

Step-by-step explanation:

120 = 1/3 x

120 x 3 = x

360 = x

The function that gives the amount of money in dollars, j(n), in Jamie’s account n years after the initial deposit is J(n) = P(1 + (r/3)/100)³ⁿ.

Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.

We know the formula for compound interest is,

A = P(1 + r/100)ⁿ.

Where, A = amount, P = principle, r = rate, and n = time in years.

Given, Jamie deposits $627 into a savings account and the account has an interest rate of 3.5%, compounded quarterly.

P = $627, r =  3.5%.

We know the formula for compound interest compounded quarterly is

A = P(1 + (r/3)/100)³ⁿ.

Or

J(n) = P(1 + (r/3)/100)³ⁿ. (here t is replaced by n).

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Step-by-step explanation:

119°+29°+n°=180°. (Sum of all the angles of triangle)

So,

158°+n= 180°

n= 180°-158°

n= 22°

Answer:

n = 22°

Step-by-step explanation:

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The correct statements are:

1). Comparatively to traditional variable sampling, monetary unit sampling typically chooses lesser dollar transactions or components from an account for analysis.

3). The central limit theorem and the principles of probability are used in traditional variable sampling.

A sample technique called the monetary unit is used in accounting and auditing to check the quality and completeness of financial information.

Each dollar in a population or account balance has an equal chance of being chosen for testing in monetary unit sampling. This implies that larger transactions or components are more likely than smaller ones to be chosen for investigation.

The first and third sentences are true, respectively:

Comparatively to the traditional variables sample, monetary unit sampling tends to examine the smaller dollar transactions or components within the account.

The central limit theorem and the principles of probability are used in traditional variable sampling.

The second assertion is both somewhat true and false:

The monetary unit or the traditional variables sampling are used for variable sampling.

This claim that variables can be sampled using traditional variables sampling is true. However, it is false to claim that variables sampling may be accomplished by monetary unit sample because this kind of non-statistical sampling excludes variables sampling from its scope.

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Answer:

5. b

6. d

7. b

8. d

If three balls are picked at random from the box, the chance of obtaining two white balls and one black ball is 1/28.

The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the probability formula. The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

a box contains 7 white balls and 8 black balls. if 3 balls are drawn from the box at random,

=2/7*1/8

=1/28

The probability of drawing 2 white balls and 1 black ball is 1/28 if 3 balls are drawn from the box at random.

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Answer:

726 minutes

Step-by-step explanation:

Answer:

its 726

Step-by-step explanation:

Answer:

f(4)=7

Step-by-step explanation:

f(x)=3x-5

f(4)=3(4)-5

f(4)=12-5

f(4)=7

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Answer:

50°

Step-by-step explanation:

We are to find m ∠2

And lines A and B are parallel

m ∠2 and 50° are Vertical angles. This means m ∠2 is the same as 50°

Hence,

m ∠2 = 50°

Therefore, m ∠2 = 50°

Answer:

8 sundaes

4:32

.......

.......

...

Step-by-step explanation:

To make 1 sundae, the total number of spoons use of sprinkles=4. Let the number of sundaes made in 32 spoonfuls of sprinkles be x. Also the number of sprinkles and the number of sundaes are directly proportional. Therefore, Hence, if 32 spoonfuls of sprinkles is used, then the ice-cream shop can make 8 sundaes.

There is no horizontal asymptote because the function does not approach a specific y-value as x approaches infinity. The intercept occurs when the function equals zero, resulting in the point (-2, 2) on the x-axis.

I selected functions f(x) = -√(9-x) + 1 and h(x) = 1/(x+2) + 2. For f(x), the graph is a downward-sloping curve with a vertical asymptote at x = 9 and a horizontal asymptote at y = 1. The intercepts are (9, 0) and (0, 1). For h(x), the graph is a hyperbola that approaches the vertical asymptote at x = -2. There is no horizontal asymptote, and the intercept is (-2, 2).

The function f(x) = -√(9-x) + 1 represents a square root function that has been transformed. The square root function is shifted horizontally 9 units to the right due to the term inside the radical. The graph has a vertical asymptote at x = 9 because the expression inside the square root becomes zero at that point. There is also a horizontal asymptote at y = 1 because as x approaches infinity or negative infinity, the radical term becomes negligible, and the function approaches 1.

The intercepts occur when the function equals zero, resulting in the points (9, 0) and (0, 1) on the x and y axes, respectively. The function h(x) = 1/(x+2) + 2 represents a rational function, specifically a hyperbola. The function has been transformed by shifting it horizontally 2 units to the left due to the term inside the parentheses. The graph approaches a vertical asymptote at x = -2 because the denominator becomes zero at that point.

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The value of "k" for which the determinant of the given matrix is zero is 2.5

The given problem asks to find the values of "k" for which the determinant of the given matrix is zero.

The given matrix can be represented as:

| 6 0 0 |
| 7 2 0 |
| 0 2 k+7 |

The determinant of the matrix is calculated as:

6 * (2(k+7)) - 0 - 0 - 7 * (2) * 0 + 0 - 0 = 12k - 30

To find the values of "k" for which the determinant is zero, we need to solve the equation:

12k - 30 = 0

Simplifying the equation, we get:

k = 2.5

Therefore, the value of "k" for which the determinant is zero is 2.5.

In general, the determinant of a matrix is a scalar value that represents some important properties of the matrix, such as invertibility and eigenvalues. If the determinant of a matrix is zero, it means that the matrix is singular and does not have an inverse. In the given problem, we have calculated the determinant of the matrix and found the values of "k" for which the determinant is zero. This helps us understand the properties of the matrix and the possible solutions to any equations involving the matrix.

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Answer:

The polynomial x3 + 8 is equal to (x + 2)(x2 - 2x + 4).

Answer: The vertex of the function h(x)=-16(x-1)²+23 is (1, 23).

This means that the ball reaches its maximum height of 23 feet after 1 second, and then starts to fall back down. The vertex also represents the highest point of the ball's trajectory, also known as the maximum value of the function.

Step-by-step explanation: The given function h(x) represents the height of a ball in feet after x seconds, and it is given by:

h(x) = -16(x - 1)² + 23

This is a quadratic function in standard form, where the coefficient of x^2 is negative, which means that the graph of the function is a downward-facing parabola. The vertex of this parabola is given by the formula:

Vertex = (-b/2a, f(-b/2a))

where a = -16, b = 0, and c = 23 are the coefficients of the quadratic function. Substituting these values into the formula, we get:

Vertex = (-b/2a, f(-b/2a))

= (-0/2(-16), f(0/2(-16)))

= (0, 23)

Therefore, the vertex of the parabolic function h(x) is (0, 23), which indicates that the ball reaches its maximum height of 23 feet after 1 second, and then starts to fall back to the ground.

y = 2q'( p1p2p3...pn/q)Let x = p1p2p3...pn/q and k = q'/2. Then y = 2kx, where x is odd and k is nonnegative.

The Fundamental Theorem of Arithmetic, also known as the Unique Factorization Theorem, states that every positive integer greater than 1 can be uniquely expressed as a product of prime numbers, up to the order of the factors.

Let y N. Use the Fundamental Theorem of Arithmetic to prove that there exists an odd natural number x and a nonnegative integer k such that y = 2kx.

In order to show that y = 2kx, where x is an odd natural number and k is a nonnegative integer, we will use the Fundamental Theorem of Arithmetic.

The theorem states that every positive integer greater than 1 can be written as a unique product of prime numbers.

For y > 1, we can write: y = p₁p₂p₃...pn

where p₁, p₂, ..., pn are prime numbers (not necessarily distinct).If all the pi are odd, then we can take x = 1 and k = y/2. Since y is odd, y/2 is an integer, and we have:

y = p₁p₂p₃...pn = 2( p₁p₂p₃...pn/2) = 2kx(where k = p₁p₂p₃...pn/2 is a nonnegative integer)

If some pi are even, let q be the smallest even prime number that divides y.

Then we can write: y = q( p₁p₂p₃...pn/q)

Since q is even, we can write q = 2q', where q' is an odd natural number.

Then we have: y = 2q'( p₁p₂p₃...pn/q)

Let x = p₁p₂p₃...pn/q and k = q'/2.

Then y = 2kx, where x is odd and k is nonnegative.

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The given expression 5y² + 12y - 32 can be factorized as (5y + 16) (y - 2).

The given expression is 5y² + 12y - 32.

To factorize the given expression, we need to follow the below steps.

Step 1: Multiply the coefficient of the first term with the constant term.

(5 × -32 = -160)

Step 2: Find the two factors of -160 whose sum is equal to the coefficient of the middle term, i.e., 12. (-10) and (16)

Step 3: Rewrite the given expression by breaking the middle term into the above two terms.

5y² - 10y + 16y - 32

Step 4: Now, take the common factors from the first two terms and the last two terms.

5y(y - 2) + 16(y - 2)

Step 5: Take the common factor (y - 2) out from the expression,

5y(y - 2) + 16(y - 2) = (5y + 16) (y - 2)

Thus, the given expression 5y² + 12y - 32 can be factorized as (5y + 16) (y - 2).

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The equation y = -x² + 9 accurately represents the path of the ball as it moves back and forth between you and your friend, with the ball's height at each horizontal position governed by the parabolic trajectory of the equation.

The equation that models the path of the ball in standard form is y = -x² + 9. This equation represents a downward-opening parabola that accurately represents the trajectory of the ball as it moves back and forth between you and your friend at a height of 3 feet.

The reasoning behind this equation is as follows:

Since the ball is being tossed back and forth at waist level, the height of the ball can be represented by the y-coordinate. The x-coordinate represents the horizontal distance from the person throwing the ball. We can assume that the ball is initially thrown from a position of x = 0.

To model the trajectory, we consider that the ball starts at a height of 3 feet and then follows a parabolic path. The negative coefficient in front of the x² term indicates that the parabola opens downward.

The constant term, 9, represents the maximum height of the ball. Since the ball is being tossed at waist level (3 feet), the maximum height reached by the ball is 3 + 6 = 9 feet. The additional 6 feet accounts for the vertical displacement of the ball from its starting height of 3 feet.

Therefore, the equation y = -x² + 9 accurately represents the path of the ball as it moves back and forth between you and your friend, with the ball's height at each horizontal position governed by the parabolic trajectory of the equation.

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The total number of hours Eric worked is 7 3/4 hours.

What is addition in mathematics?

Addition is one of the four basic arithmetic operations in mathematics, along with subtraction, multiplication, and division. Addition is the process of combining two or more quantities or numbers to find their sum, or total. The symbol used to represent addition is the plus sign (+).

For example, if we want to find the sum of 3 and 4, we would write:

3 + 4 = 7

The number 3 and the number 4 are called addends, and the result of the addition operation is called the sum. Addition can involve whole numbers, fractions, decimals, and even negative numbers.

Addition has many applications in mathematics, science, and everyday life. It is used to calculate simple arithmetic problems, such as adding up the cost of items in a shopping cart, as well as more complex calculations, such as adding up the values in a data set or solving equations in algebra.

To find the total number of hours Eric worked in the neighborhood garden, we need to add the number of hours he worked on Monday and Wednesday.

Eric worked 3 1/2 hours on Monday, which can also be written as 7/2 hours.

Eric worked 4 1/4 hours on Wednesday, which can also be written as 17/4 hours.

To add these two amounts, we need to find a common denominator. The smallest number that both 2 and 4 divide into is 4. So we can convert 7/2 to 14/4 by multiplying the numerator and denominator by 2:

7/2 = 14/4

Now we can add the two fractions:

14/4 + 17/4 = 31/4

This is the total number of hours Eric worked in the neighborhood garden, in fraction form. To write it as a mixed number, we can divide the numerator by the denominator:

31 ÷ 4 = 7 with a remainder of 3

So the total number of hours Eric worked is 7 3/4 hours.

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Answer:

  Exponential

Step-by-step explanation:

If the depreciation is 6% of the current value each year, the function is exponential. (We believe this is the intent of the problem statement.)

__

If the depreciation is 6% of the original value each year, the function is linear.

_____

Comment on percent

Whenever you're working with percentages, you need to be clear about what it is a percentage of.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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The value of x that makes 25x^2 + 70x + c a perfect square trinomial is c = 1225.

To make the quadratic expression 25x^2 + 70x + c a perfect square trinomial, we need to determine the value of c.

A perfect square trinomial can be written in the form (ax + b)^2, where a is the coefficient of the x^2 term and b is half the coefficient of the x term.

In this case, a = 25, so b = (1/2)(70) = 35.

Expanding (ax + b)^2, we have:

(25x + 35)^2 = 25x^2 + 2(25)(35)x + 35^2

= 25x^2 + 70x + 1225.

Comparing this with the given quadratic expression 25x^2 + 70x + c, we can see that c = 1225.

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The probability of drawing an ace and a queen from a pack of cards without replacement is 1/78. This can be explained as follows:

In a standard pack of 52 cards, there are 4 aces and 4 queens. When two cards are drawn without replacement, the probability of drawing an ace and then a queen is 4/52 x 3/51 = 12/2652. This can be simplified to 1/78.

Without replacement means that the card that is drawn is not replaced in the deck before the next card is drawn. In this case, when the first card is an ace, there are only 3 queens left in the deck so the probability of the second card being a queen is 3/51.

To put it another way, the chances of drawing an ace and a queen when the cards are drawn without replacement can be thought of as a ratio of the favorable outcomes to the total number of possible outcomes. There is only one favorable outcome (ace-queen) out of a total of 78 possible outcomes (4 aces and 4 queens combined with the remaining 44 cards). Thus, the probability of drawing an ace and a queen is 1/78.

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Answer:

The answer is actually b and c

Step-by-step explanation:

Answer:

Last option

Step-by-step explanation:

Step 1: Write out equation

x² + 8x - 10 = 0

Step 2: Add 10 to both sides

x² + 8x = 10

Step 3: Complete the Square

x² + 8x + 16 = 10 + 16

(x + 4)² = 26

Step 4: Square root both sides

x + 4 = ±√26

Step 5: Subtract 4 on both sides

x = -4 ± √26