Expand and simplify the expression 4x² + 4x + 2(x² - 3) + x².​

Answer:

20

Step-by-step explanation:

Answer:

Step-by-step explanation:

It's a both times

If speed is important and the array is large, the a. Binary search algorithm should be used. This algorithm is designed to efficiently search through sorted arrays by repeatedly dividing the search interval in half.

It has a time complexity of O(log n), which means that as the size of the array increases, the time it takes to search for an item will not increase at the same rate.
On the other hand, ascending bubble sort and other sorting algorithms such as selection sort and insertion sort have a time complexity of O(n^2), which means that as the size of the array increases, the time it takes to sort the array will increase exponentially. Therefore, these algorithms are not efficient for large arrays and should not be used if speed is important.
In summary, when dealing with large arrays and speed is important, binary search is the best algorithm to use for searching, while ascending bubble sort and other sorting algorithms with a time complexity of O(n^2) should be avoided.

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Answer: N=6

Step-by-step explanation:

Add 34 degrees with the 90 degree angle and you get 124

Then add 124 to your other equation (9n +2)

Make that equation equal to your straight angle 180 and solve.

9n + 126 = 180

9n = 54

n= 6

I recommend hiring "Pane "less Window Cleaners since it's less expensive compared to Sunshine Express Window Cleaners.

I recommend hiring "Pane "less Window Cleaners". This is because for a fixed number of windows, "Pane "less Window Cleaners" is less expensive compared to Sunshine Express Window Cleaners. The difference in cost can be calculated by subtracting the cost of "Pane "less Window Cleaners" from that of Sunshine Express Window Cleaners.

For example, for 10 windows, the cost of Sunshine Express Window Cleaners is $50 + 10 * $10 = $150, whereas the cost of "Pane "less Window Cleaners" is $25 + 10 * $15 = $175.

Therefore, the difference in cost is $175 - $150 = -$25, meaning that "Pane "less Window Cleaners" is cheaper. This recommendation is reasonable because it provides the best value for their money.

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Answer:

75 shots and 15.1%

Step-by-step explanation:

The general solution of the second-order linear homogeneous differential equation y'' - 6y' + 5y = 0 using the Power Series Method is y = c₁e^x + c₂e^(5x).

To solve the given differential equation using the Power Series Method, we assume a power series solution of the form y = ∑ₙ=0∞ aₙxⁿ, where a₀ and a₁ are given coefficients, and we need to determine the values of a₂, a₃, and a₄ in terms of a₀ and a₁.

1) Differentiating y, we obtain y' = ∑ₙ=1∞ (aₙn)xⁿ⁻¹.

Then, differentiating y' again, we have y'' = ∑ₙ=2∞ (aₙn(n-1))xⁿ⁻².

2) Substituting y, y', and y'' into the original differential equation, we get ∑ₙ=2∞ (aₙn(n-1))xⁿ⁻² - 6∑ₙ=1∞ (aₙn)xⁿ⁻¹ + 5∑ₙ=0∞ aₙxⁿ = 0.

3) Grouping terms according to their powers of x, we obtain the following equation:

∑ₙ=0∞ [(aₙ(n+2)(n+1) - 6aₙ₋₁n + 5aₙ₋₂)xⁿ] + [2a₂ - 6a₁ + 5a₀] = 0.

Since the terms with the same power of x must sum to zero, we set each coefficient equal to zero:

aₙ(n+2)(n+1) - 6aₙ₋₁n + 5aₙ₋₂ = 0 for n ≥ 2,

and solve for a₂, a₃, and a₄ in terms of a₀ and a₁.

4) Solving the equations, we find:

a₂ = (6a₁ - 5a₀) / 2,

a₃ = (20a₀ - 12a₁) / 6,

a₄ = (42a₁ - 30a₀) / 24.

5) Finally, we can write the solution y(x) up to x³ terms by substituting the values of a₀, a₁, a₂, a₃, and a₄ into the power series representation of y:

y(x) = a₀ + a₁x + (6a₁ - 5a₀)x²/2 + (20a₀ - 12a₁)x³/6 + ...

This is the solution to the given second-order linear homogeneous differential equation using the Power Series Method.

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The ratio for sin A, written as a fraction in simplest form, is 3 / (2√3).

The sine function is a mathematical function that takes an angle as its input and returns the ratio of the length of the side opposite to the angle to the length of the hypotenuse in a right triangle

In a right triangle, the sine of an angle A is defined as the ratio of the length of the side opposite to angle A to the length of the hypotenuse. Therefore, we have:

sin A = Opposite / Hypotenuse

Substituting the given values, we get

sin A = CB / AB = 8√3 / 16 = √3 / 2

To simplify this fraction further, we can multiply both the numerator and denominator by √3:

sin A = (√3 / 2) × (√3 / √3) = 3 / (2√3)

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The given question is incomplete, the complete question is:
Which is the ratio for sin A, written as a fraction in simplest form?

The research reveals that emotional people tend to be more satisfied with their jobs, committed to their employer, and produce more work than conscientious individuals is False.

Emotional intellect is the capacity to recognize and regulate a person's emotions and comprehend the emotions the others. A high EQ helps you to build connections, lower team stress, defuse battles and improve job fulfillment.

It can help a graduate evolve the best at what they do, be the best coworker possible, and achieve professional victory. Communication, partnership, and relationship-building skills are enhanced by higher levels of emotional intelligence. It also enables best focus on the work.

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The complete question is-

research reveals that emotional people tend to be more satisfied with their jobs, committed to their employer, and produce more work than conscientious individuals.

a. True

b. False

When analyzing a consumer's utility function: preferences, marginal utility, optimal consumption, and substitution and income effects.

From a consumer's utility function alone, you may determine the following:

1. Preferences: A consumer's utility function represents their preferences for different goods and services. By analyzing the function, you can determine which items the consumer prefers and how much they value them.

2. Marginal utility: The marginal utility is the additional satisfaction a consumer receives from consuming one more unit of a good or service. It can be derived from the utility function by taking its first derivative with respect to the quantity of the good or service.

3. Optimal consumption: By analyzing a consumer's utility function and taking into account their budget constraint, you can determine the optimal consumption bundle that maximizes their utility.

4. Substitution and income effects: The utility function can also help you analyze how changes in prices or income will affect a consumer's consumption choices, through the substitution and income effects.

Remember to keep these terms in mind when analyzing a consumer's utility function: preferences, marginal utility, optimal consumption, and substitution and income effects.

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The value of a new car worth $45,000 is depreciating by $5,000 per year. It will take 7 years for the car's value to reach $10,000.

To determine the number of years it will take for the car's value to reach $10,000, we need to calculate the depreciation per year. Given that the car's value is decreasing by $5,000 per year, we can set up an equation:

$45,000 - ($5,000 * n) = $10,000

Here, 'n' represents the number of years. To solve for 'n', we can rearrange the equation:

$45,000 - $10,000 = $5,000 * n

$35,000 = $5,000 * n

Dividing both sides of the equation by $5,000, we find:

7 = n

Therefore, it will take 7 years for the car's value to reach $10,000.

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Answer:

Step-by-step explanation:

The experimental probability of the cube landing on three is 1/10.

Answer:

First, let's explain the transformations in a general way:

Vertical shift.

If we have a function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

This will move the graph of f(x) up or down a distance of N units.

if N is positive, then the shift is upwards

if N is negative, then the shift is downwards.

Horizontal shift.

If we have a function f(x), a horizontal shift of N units is written as:

g(x) = f(x + N)

This will move the graph of f(x) to the right or left a distance of N units.

if N is positive, then the shift is to the left

if N is negative, then the shift is to the right.

Horizontal dilation/contraction.

For a function f(x), an horizontal contraction dilation is written as:

g(x) = f(k*x)

where:

k is called the "scale factor"

If k < 1, then the graph "dilates" horizontally.

if k > 1, then the graph "contracts" horizontally.

Now, in this problem we have:

f(x) = log(x)

And the transformed function is:

g(x) = f(0.25*(x - 5)) + 3

Then, the transformations that take place here are, in order:

Vertical shift of 3 units up:

g(x) = f(x) + 3.

Horizontal shift of 5 units to the right:

g(x) = f(x - 5) + 3

Horizontal dilation of scale factor 0.25

g(x) = f( 0.25*(x - 5)) + 3

replacing f(x) by log(x) we have

g(x) = log(0.25*(x - 5)) + 3.

Answer:

18.65%

Step-by-step explanation:

We know

The regular price of each song is $0.89

0.89 x 15 = $13.35

Using a special discount, you download 15 songs for $10.86

What is the percentage of the discount​?

We Take

13.35 - 10.86 = $2.49

Then we take

2.49 divided by 13.35, time 100 = 18.65%

So, the percent of the discount is 18.65%

The experimental probability that the next time Audra rolls the number cube, she will roll a 2 is 3/22.

Experimental probability is the ratio of the number of times an event occurs to the total number of trials conducted. In this case, we want to find the experimental probability of rolling a 2.

Looking at the data provided, we can see that Audra rolled a 2 three times out of the total 22 rolls. So, the experimental probability of rolling a 2 can be calculated as:

Experimental probability = number of times the event occurred / total number of trials

Experimental probability of rolling a 2 = 3 / 22

Therefore, the correct option is (B) 3/22. This means that based on Audra's experiment, the probability of rolling a 2 is approximately 0.136 or 13.6%. It is important to note that this is the experimental probability based on a small sample size, and the actual probability of rolling a 2 in a large number of rolls may differ.

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Answer:

the area of a circle is equal to pi r square that is 3.14×3×3 = 28.26.

Answer:

Step-by-step explanation:

Given values:

Put the values in ascending order:

There are even values, the middle numbers are:

Median is the average of the middle two numbers:

The storm rainfall flux is 0.00127 m2/hr, 1.27 kg liquid water/m2hr, 2.8 lb liquid water/m2hr, 1.27 liters liquid water/m2hr, and 0.335 gallons liquid water/m2hr. The amount of liquid water fell on the garden is 80.6 L, 21.3 gallons.

Dimensions of outdoor vegetable garden = 2 m × 2 m

Storm rainfall = 0.8 inches of rain

Time of storm = 1 hr(

a) The rainfall flux is the amount of rainfall per unit area and unit time. It is given as:

Rainfall flux = (Amount of rainfall) / (Area × Time)

Given the area of the garden is 2 m × 2 m, and the time is 1 hr, the rainfall flux is:

Rainfall flux = (0.8 inches of rain) / (2 m × 2 m × 1 hr)

Converting inches to meters, we get:

1 inch = 0.0254 m

Therefore,

Rainfall flux = (0.8 × 0.0254 m) / (2 m × 2 m × 1 hr) = 0.00127 m/hr

Converting the rainfall flux to other units:

In kg/hr:

1 kg of water = 1000 g of water

Density of water = 1000 kg/m3

So, 1 m3 of water = 1000 kg of water

So, 1 m2 of water of depth 1 m = 1000 kg of water

Therefore, 1 m2 of water of depth 1 mm = 1 kg of water

Therefore, the rainfall flux in kg/hr = (0.00127 m/hr) × (1000 kg/m3) = 1.27 kg/m2hr

In lbs/hr:

1 lb of water = 453.592 g of water

So, the rainfall flux in lbs/hr = (0.00127 m/hr) × (1000 kg/m3) × (2.20462 lb/kg) = 2.8 lbs/m2hr

In liters/hr:

1 m3 of water = 1000 L of water

So, 1 m2 of water of depth 1 mm = 1 L of water

Therefore, the rainfall flux in L/hr = (0.00127 m/hr) × (1000 L/m3) = 1.27 L/m2hr

In gallons/hr:

1 gallon = 3.78541 L

So, the rainfall flux in gallons/hr = (0.00127 m/hr) × (1000 L/m3) × (1 gallon/3.78541 L) = 0.335 gallons/m2hr

(b) To calculate the amount of water that fell on the garden, we need to calculate the volume of water.

Volume = Area × Depth.

The area of the garden is 2 m × 2 m.

We need to convert the rainfall amount to meters.

1 inch = 0.0254 m

Therefore, 0.8 inches of rain = 0.8 × 0.0254 m = 0.02032 m

Volume of water = Area × Depth = (2 m × 2 m) × 0.02032 m = 0.0806 m3

Converting the volume to other units:

In liters:

1 m3 of water = 1000 L of water

Therefore, the volume of water in liters = 0.0806 m3 × 1000 L/m3 = 80.6 L

In gallons:

1 gallon = 3.78541 L

Therefore, the volume of water in gallons = 80.6 L / 3.78541 L/gallon = 21.3 gallons.

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Answer:

Step-by-step explanation:

99

Answer:

A and E

Step-by-step explanation:

This is an example of the distributive property.

28n-25 is the base

E shows 7(4n-5)

7*4=28=28n

7*5=35

7(4n-5)=28n-35

Answer:

each steak burger costs $6.50

each order of fries costs $2.25

Answer: C and E

Step-by-step explanation: P would equal 13. For A, 25 more than 38 would equal 63 so that would be incorrect. For B it says 25 times as p (13) would equal 38. That is incorrect. And for D, for Rachel to jog 38 more times as Will, who jogged 25 blocks, wouldn't make sense for the equation. C and E makes the most sense.

Answer:

uihuii

Step-by-step explanation:

The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°

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

The transversal lines and the other lines

So, we have

∠1 = 180 - 53

Evaluate

∠1 = 127°

Also, we have

∠5 = 53°

By vertical angles, we have

∠2 = 53°

∠3 = 127°

Next, we have

∠4 = 127 - 90°

∠4 = 37°

Solving further, we have

∠6 = 90°

By corresponding angles, we have

∠7 = 37°

∠9 = 180 - 90 - 53°

∠9 = 37°

∠10 = 90 + 53°

∠10 = 143°

∠8 = 143°

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a. The equation in standard form is x + y = 2.

b. The x-intercept is (3/2, 0), the y-intercept is (0, -3), and another point can be (2, -1).

c.  In point-slope form, it can be written as y - 4 = -3(x - 9).

a. To find the equation of the line passing through (-2, 4) and (1, 3), we can use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is one of the given points and m is the slope of the line.

Slope (m) = (change in y) / (change in x) = (3 - 4) / (1 - (-2)) = -1 / 3

Using the first point (-2, 4):

y - 4 = (-1/3)(x - (-2))

y - 4 = (-1/3)(x + 2)

y - 4 = (-1/3)x - 2/3

y = (-1/3)x + 2/3 + 4

y = (-1/3)x + 2/3 + 12/3

y = (-1/3)x + 14/3

The equation in slope-intercept form is y = -x + 14/3.

To write the equation in standard form, we can multiply through by 3 to eliminate fractions:

3y = -3x + 14

3x + 3y = 14

b. To graph the equation 8x - 4y = 12, we can find the x and y intercepts and plot one additional point.

For x-intercept, set y = 0:

8x - 4(0) = 12

8x = 12

x = 12/8

x = 3/2

So the x-intercept is (3/2, 0).

For y-intercept, set x = 0:

8(0) - 4y = 12

-4y = 12

y = -12/4

y = -3

So the y-intercept is (0, -3).

Another point can be found by choosing a value for x and solving for y. Let's choose x = 2:

8(2) - 4y = 12

16 - 4y = 12

-4y = 12 - 16

-4y = -4

y = -4/-4

y = 1

So another point is (2, 1).

Plotting these points and connecting them will give us the graph of the equation.

c. To find the equation of the line perpendicular to -3x + y = 2 and passing through the point (9, 4), we need to determine the slope of the perpendicular line. The slope of the given line is 3 (since the coefficient of x is -3).

The slope of the perpendicular line will be the negative reciprocal of 3, which is -1/3.

Using the point-slope form y - y1 = m(x - x1), we have:

y - 4 = (-1/3)(x - 9)

y - 4 = (-1/3)x + 3

y = (-1/3)x + 3 + 4

y = (-1/3)x + 7

Rewriting in standard form:

3y = -x + 21

x + 3y = 21

Therefore, the equation of the line perpendicular to -3x + y = 2 and passing through the point (9, 4) is 3x + y = 31 in standard form. In point-slope form, it can be written as y - 4 = -3(x - 9).

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Answer:

ab, ac, bc

Step-by-step explanation:

a=30, b=60, c=180-(30+60) = 180-90=90

Based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.

How closely a value relates to the mean of a set of values is expressed by a Z-score.

The Z-score is created using standard deviations from the mean.

A data point's total value is equal to the mean value when the Z-score of the data point is equal to 0.

So, in order to determine how far the raw score deviates from the mean, the Z score is used.

The following steps are used to determine the Z score:

z = (x - μ)/σ

We know that:  x > 550 and μ = 500, σ = 40

z = 550 - 500 / 40

z = 1.25

The graph of the normal distribution indicates:

P(z > 1.25) = 1 - P(z < 1.25)

P(z > 1.25) = 1 - 0.8944

P(z > 1.25) = 0.1056

Therefore, based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.

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