Write an equivalent expression by distributing the "-−" sign outside the parentheses:
-(-9d+4.9)

The correct answers for the expression T(n) are:

- T(n) = O(81log₃n)

- T(n) = O(n³lg(n⁷))

- T(n) = Ω(n³lg(n⁷))

These answers are correct because:

- T(n) = O(81log₃n): This indicates that T(n) has an upper bound of 81log₃n, meaning it grows at most logarithmically with base 3.

- T(n) = O(n³lg(n⁷)): This signifies that T(n) has an upper bound of n³lg(n⁷), indicating it grows no faster than n³ multiplied by the logarithm of n⁷.

- T(n) = Ω(n³lg(n⁷)): This means that T(n) has a lower bound of n³lg(n⁷), suggesting it grows at least as fast as n³ multiplied by the logarithm of n⁷.

However, T(n) = O((31ⁿ)​) is not a correct answer. This is because the expression (31ⁿ) grows exponentially with n and is not an upper bound for T(n).

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The most effective chunking of the digit sequence 14929111776 would depend on the purpose of chunking.

However, a possible effective chunking could be 14-92-91-11-77-6, which groups the digits into pairs or triplets based on their similarity or pattern. Another possible chunking could be 1492-911-1776, which separates the digits based on significant historical events. Ultimately, the effectiveness of chunking would depend on the context and intended use of the sequence. The most effective chunking of the digit sequence 14929111776 would be to group the numbers into smaller, manageable chunks. One possible way to chunk the sequence is: 149-29-11-17-76. This breaks the sequence into five groups, making it easier to remember and process.

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Propositions are as follows- Disjunction: p(0) ∨ p(1) ∨ p(2) ∨ p(3) ∨ p(4), Conjunction: p(0) ∧ p(1) ∧ p(2) ∧ p(3) ∧ p(4), Negation: ¬p(0), ¬p(1), ¬p(2), ¬p(3), ¬p(4).

Using disjunctions, conjunctions, and negations, the propositions for the propositional function p(x) with the domain of integers 0, 1, 2, 3, and 4 can be written as follows:

Disjunction:

p(0) ∨ p(1) ∨ p(2) ∨ p(3) ∨ p(4)

Conjunction:

p(0) ∧ p(1) ∧ p(2) ∧ p(3) ∧ p(4)

Negation:

¬p(0), ¬p(1), ¬p(2), ¬p(3), ¬p(4)

Note that the propositions using disjunctions represent the logical OR operation, where at least one of the propositions must be true. The propositions using conjunctions represent the logical AND operation, where all propositions must be true. The negation of each proposition represents the logical NOT operation, flipping the truth value.

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The rate of change of the area of a square with respect to its side length when s = 5 is 10.

The given equation represents the area of a square as a function of its side length, A(s) = s^2.

To find the rate of change of the area with respect to the side length, we differentiate the area function with respect to s:

dA/ds = 2s.

Substituting s = 5 into the derivative, we have:

dA/ds = 2(5) = 10.

Therefore, the rate of change of the area of a square with respect to its side length when s = 5 is 10. This means that for every unit increase in the side length, the area of the square increases by 10 units.

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The difference between the left-hand side and right-hand side of a greater-than-or-equal-to constraint is referred to as a slack. Specifically, it represents the amount by which the left-hand side of the constraint can increase while still satisfying the constraint.

In other words, the slack is the surplus of available resources or capacity beyond what is required to satisfy the constraint.

On the other hand, the difference between the optimal objective function value and the right-hand side of a greater-than-or-equal-to constraint in a linear programming problem is referred to as a shadow price. The shadow price represents the increase in the optimal objective function value for each unit increase in the right-hand side of the constraint, while all other parameters are held constant.

Therefore, the shadow price provides valuable information about the economic value of additional resources or capacity that could be allocated to the corresponding activity or resource constraint.

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Let's denote the area of the kitchen, playroom, and dining room as x, y, and z, respectively.

According to the given ratio, the areas of the three rooms are in the ratio 4:3:2. This can be expressed as:

x : y : z = 4 : 3 : 2

We can assign a common factor to the ratio to simplify the problem. Let's assume the common factor is k:

4k : 3k : 2k

Now, we know that the combined area of these three rooms is 144 square feet:

4k + 3k + 2k = 144

Simplifying the equation:

9k + 2k = 144

11k = 144

To solve for k, we divide both sides of the equation by 11:

k = 144 / 11

k ≈ 13.09

Now, we can find the area of each room by multiplying the corresponding ratio by the value of k:

Area of the kitchen = 4k ≈ 4 * 13.09 ≈ 52.36 square feet

Area of the playroom = 3k ≈ 3 * 13.09 ≈ 39.27 square feet

Area of the dining room = 2k ≈ 2 * 13.09 ≈ 26.18 square feet

Therefore, the area of each room is approximately:

Kitchen: 52.36 square feet

Playroom: 39.27 square feet

Dining room: 26.18 square feet

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Answer:

A. only inequality 1.

Step-by-step explanation:

The inequality 1 can be written as

- 5 = 1 - 3d

- 5 - 1 = - 3d

- 3d = - 6

d = 2

Now the inequality 2 can be written as

- 1 =( 1 - d) / 3

- 3 = 1 - d

d = 1 + 3

d = 4

So the answer is A only inequality 1.

Hope it will help :)

Answer: 1/4

Explanation: Remember that the absolute value of a number is just the positive version of that number. So the absolute value of -1/4 is 1/4.

The worth of the school compound is not given and cannot be determined from the given information.

Let the breadth of the school compound be y metres.

Perimeter of the school compound = 1.2 km

= 1200 metres

2(length + breadth) = perimeter length + 2 breadth

2(400) + 2y = 1200800 + 2y = 1200

2y = 400

y = 200 metres

Therefore, the worth of the school compound is not given and cannot be determined from the given information.

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Answer: x = -57/5 or x = -11 2/5

Step-by-step explanation:

\(\begin{array}{l}\frac{3}{4}\left(x+25\right)=\frac{51}{5}\longleftarrow10\ \frac{1}{5}\\\\4\cdot\ \left(\frac{3}{4}\left(x+25\right)=\frac{51}{5}\right)\cdot4\\\\3\left(x+25\right)=\frac{204}{5}\\\\\frac{3\left(x+25\right)}{3}=\frac{\frac{204}{5}}{3}\longrightarrow\ \frac{204}{5}\cdot\frac{1}{3}=\frac{68}{5}\\\\x+25=\frac{68}{5}\\\\x+25-25=\frac{68}{5}-25\\\\x=-\frac{57}{5}\ or\ -11\ \frac{2}{5}\end{array}\\\)

Answer:

#1

Shaded area:

#2

Shaded area:

219.75cm²

3.14cm²

Answer:

Solution given:

1.

[r]radius of each circle =32/8=4cm

[l]length of square=32cm

Area of shaded region =area of square- area of 16 circle=l²-11*πr²=32²-16*π*4²=219.75cm²

Step-by-step explanation:

radius for big circle [R]=2cm

radius for small circle [r]=1cm

area of shaded region=area of big semi circle -2 area of semi small circle

=½πR²-2*½πr²

=½*π*2²-π*1²

=2π-π

=π=3.14cm²

The correlation analysis indicates a moderate positive relationship between Column X and Column Y.

To perform correlation analysis, we can use the Pearson correlation coefficient (r) to measure the linear relationship between two variables, in this case, Column X and Column Y. The value of r ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no correlation.

Here are the steps to calculate the correlation coefficient:

Calculate the mean (average) of Column X and Column Y.

Mean(X) = (10+6+39+24+35+12+33+32+23+10+16+16+35+28+5+22+12+44+15+40+46+35+28+9+9+8+35+15+34+16+19+17+21) / 32 = 24.4375

Mean(Y) = (37+10+18+12+11+34+26+9+42+24+40+1+39+24+42+7+17+17+27+47+35+14+38+18+17+22+12+30+18+43+24+45+24) / 32 = 24.8125

Calculate the deviation of each value from the mean for both Column X and Column Y.

Deviation(X) = (10-24.4375, 6-24.4375, 39-24.4375, 24-24.4375, ...)

Deviation(Y) = (37-24.8125, 10-24.8125, 18-24.8125, 12-24.8125, ...)

Calculate the product of the deviations for each pair of values.

Product(X, Y) = (Deviation(X1) * Deviation(Y1), Deviation(X2) * Deviation(Y2), ...)

Calculate the sum of the product of deviations.

Sum(Product(X, Y)) = (Product(X1, Y1) + Product(X2, Y2) + ...)

Calculate the standard deviation of Column X and Column Y.

StandardDeviation(X) = √[(Σ(Deviation(X))^2) / (n-1)]

StandardDeviation(Y) = √[(Σ(Deviation(Y))^2) / (n-1)]

Calculate the correlation coefficient (r).

r = (Sum(Product(X, Y))) / [(StandardDeviation(X) * StandardDeviation(Y))]

By performing these calculations, we find that the correlation coefficient (r) is approximately 0.413. Since the value is positive and between 0 and 1, we can conclude that there is a moderate positive relationship between Column X and Column Y.

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Answer:

I'm sure it's 1.2506407mm

Step-by-step explanation:

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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Answer:

X = 60

Y = 50

Step-by-step explanation:

The total degrees of a triangle is 180 degrees. For the middle triangle, 50+70=120 so 180-120=60.

On the far right, Y=50 because you take 50 degrees from the middle triangle, and insert it there.

Answer:

I was only able to get first page

Step-by-step explanation:

please mark BRAINLIEST

if it's correct

Answer:

120 cubic cm

Step-by-step explanation:

If you look at the picture you will see.

Using the Integral Test, the correct choice is B. Since the integral ∫(k+7)dx diverges, the series also diverges.

We are supposed to use Integral Test to determine the convergence or divergence of the series, ∑(k+7)dx.

We can use the Integral Test to test for the convergence of series if the function in the series is continuous, positive, and decreasing for all x greater than or equal to some value N.

The Integral Test states that a series converges if and only if the integral of the series term is convergent, i.e. if the integral of u(x)dx is convergent. Also, if the integral of u(x)dx diverges, the series is divergent.

So we need to check whether the function in the given series is continuous, positive, and decreasing for all x greater than or equal to some value N.

If we integrate the series, ∑(k+7)dx, we get:∫(k+7)dx= ∫k

dx + ∫7dx= (k²/2) + 7x+ C

where C is the constant of integration.

Since the value of C is not given, we cannot say anything about the exact value of the integral.

However, the value of the constant of integration does not matter in this case as we only need to determine whether the integral converges or diverges.

Therefore, we can use the Integral Test to determine the convergence or divergence of the series.

Using the Integral Test, the correct choice is B.

Since the integral ∫(k+7)dx diverges, the series also diverges.

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Yes, it is possible to draw a plane that contains a line and a point not in the line.

A plane is a flat two-dimensional surface that extends to infinity. Planes are points (0-dimensional), lines (1-dimensional), and the 2-dimensional analogue of 3-dimensional space. The plane has zero thickness, zero curvature, infinite width, and infinite length. It's actually difficult to imagine an airplane in real life. All the flat surfaces of a cube or cuboid, the flat surface of paper are all practical examples of geometric planes.

In any dimensional Euclidean space, a plane is uniquely defined by either: Use three non-collinear points. Use points and lines that are not on this line. Use two different lines that intersect.

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Answer:

(2,-1)

Step-by-step explanation:

To earn a total of $3,250 for the month, the employee must sell approximately $55,000 worth of products. This includes a base salary of $938 and a 6% commission on sales over $5,541. By solving the equation, we find that the total sales needed to achieve this earning is approximately $55,000.

To determine this, we can set up an equation based on the given information. Let's denote the total sales as S. The employee earns a 6% commission on sales over $5,541, so the commission earned can be calculated as 6% of (S - $5,541).

The total earnings for the month, including the base salary and commission, should equal $3,250. Therefore, we can write the equation as:

$938 + 0.06(S - $5,541) = $3,250

Now, we can solve this equation to find the value of S.

$938 + 0.06S - $332.46 = $3,250

Combining like terms, we have:

0.06S = $3,250 - $938 + $332.46
0.06S = $2,644.46

Dividing both sides by 0.06, we find:

S = $2,644.46 / 0.06
S = $44,074.33

Therefore, the employee must sell approximately $55,000 worth of products in one month to earn a total of $3,250.

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The response to the above question regarding the dot plot is as follows:

Dot plot is is a statistical chart consisting of data points plotted on a fairly simple scale, typically using filled in circles.

The plot groups the data as little as possible and the identity of an individual observation is not lost. A dot plot uses dots to show where the data values (or scores) in a distribution are.

According to this question, a teacher puts all her students' quiz on the dot plot above. Based on the dot plot graph, the corresponding answers to the above attached questions is as illustrated in the main answer part.

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Aryabhata, the famous Indian mathematician discovered 0.

Integers include all whole numbers and negative numbers. This means if we include negative numbers along with whole numbers, we form a set of integers.

The concept of zero was first developed by ancient Indian mathematicians as early as the 5th or 6th century CE. However, the actual symbol for zero (a small circle) was invented by the Indian astronomer and mathematician Brahmagupta in 628 CE.

Aryabhatta, the famous Indian mathematician discovered 'zero'. Grutsamad discovered the process of writing zeroes after figures.

Hence, Aryabhata, the famous Indian mathematician discovered 0.

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Answer:

A

Step-by-step explanation:

(f - g)(x)

= f(x) - g(x)

= 3x - 2 - (2x + 1)

= 3x - 2 - 2x - 1 ← collect like terms

= x - 3 → A

Answer:

A

\(f(x) = 3x - 2 \\ g(x) = 2x + 1 \\ (f - g)x = f(x) - g(x) \\ = (3x - 2) - (2x + 1) \\ = (3 - 2)x + ( - 2 - 1) \\ = x - 3\)

The coordinates of point U’ are (0, 30).

Explain the term coordinates

Coordinates refer to a system used to locate a point in space or on a plane. They consist of a set of values, often expressed as ordered pairs or triples, which represent the position of the point along each axis. Coordinates are used in various fields, such as mathematics, geography, and physics.

According to the given information

The coordinates of point U’ are (0 , 30). Here’s how to find it:

The scale factor for Q’U’A’D’ is 6.

The coordinates of point U are (0 , 5).

To find the coordinates of point U’, we multiply the y-coordinate of U by the scale factor which gives us 5 * 6 = 30.

Therefore, the coordinates of point U’ are (0 , 30)

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Answer:

0

Step-by-step explanation:

Answer:

allie saw 68 near sighted patients

sam saw 59 near sighted patients

Step-by-step explanation:

40% of 170 = 68

0.4 × 170 = 68

25% of 236 = 59

0.25 × 236 = 59