um i am very confused about how do u multiple decimals like this question 6000 x 0.15 here how do i get the answer 900.

Answer:

147

Step-by-step explanation:

10% of $210.00 is $21.00

21X3 = 63

210.00 - 63.00 = $147.00

The most suitable data type for storing annual employee salaries ranging from $25,000 to $700,000 would be option (c) decimal(10,4).

Next, we can consider float and double data types, which can store decimal values with a higher range and precision than integers. However, they can be imprecise and cause rounding errors when used to store currency values, which can be a significant issue in financial calculations.

The most appropriate data type for storing currency values is the decimal data type, which is designed to handle decimal values with high precision and accuracy. The decimal data type can store exact numeric values up to 38 digits, with a user-defined scale (the number of digits to the right of the decimal point).

Therefore, option (c) decimal(10,4) would be the best data type for storing annual employee salaries ranging from $25,000 to $700,000.

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Complete Question:

Annual salary of each employee has to be stored in dollars and cents. The salaries vary from minimum of $25,000 to maximum of $700,000. Which of the following would be the most suitable data type?

a) decimal(8.2)

b) decimal

c) decimal(10.4)

d) Small money

e) money

Answer:

r² = (9 - 4)² + (6 - 4)² = 5² + 2² = 25 + 4 = 29

So the equation of this circle is

(x - 4)² + (y - 4)² = 29

Answer: 30

Step-by-step explanation:

It to be 30 but this look hard so I’m not sure

Answer:

672 quarts in 48 hours

Step-by-step explanation:

240q : 10h

first, find the unit rate

240q : 10h

/10       /10

24q : h

now multiply by 48 to find the number of quarts made in 48 hours

24q : h

*48    *48

672 q : 48h

Answer:

240 in 10 hours

simply means 1152 in 48 hours as the no. of quarts Is directly varies with the amount of time they invest.

Step-by-step explanation:

240=10

?=48

simply cross multiply it and solve

240*48/10

=1152 ans.

hope it works

Answer:

5.628547 x 10 to the 6th power

The given points, only the point (4, -9, -8) lies on line 1.

To determine whether certain points lie on the line 1, which is perpendicular to the plane x - 2y - 4z = 5 and contains the point (2, -5, 0), we can check if the coordinates of those points satisfy the equation of the line.

The direction vector of the line 1 is perpendicular to the plane and can be determined from the coefficients of x, y, and z in the plane equation. In this case, the direction vector of the line is (1, -2, -4).

Now, we can write the parametric equation of the line l as:

x = 2 + t * 1

y = -5 + t * (-2)

z = 0 + t * (-4)

To check if a point (x₀, y₀, z₀) lies on the line 1, we need to find a value of t that satisfies the parametric equations.

Let's consider the following points and determine if they lie on line 1:

Point (3, -6, -4)

To check if this point lies on line 1, we substitute the coordinates (x₀, y₀, z₀) = (3, -6, -4) into the parametric equations:

x₀ = 2 + t * 1 --> 3 = 2 + t --> t = 1

y₀ = -5 + t * (-2) --> -6 = -5 - 2 --> t = -1

z₀ = 0 + t * (-4) --> -4 = 0 - 4t --> t = 1

The value of t is not consistent across all equations, so the point (3, -6, -4) does not lie on line 1.

Point (2, -5, 0)

This point is given as the point that line 1 contains. Therefore, it lies on line 1.

Point (4, -9, -8)

To check if this point lies on line 1, we substitute the coordinates (x₀, y₀, z₀) = (4, -9, -8) into the parametric equations:

x₀ = 2 + t * 1 --> 4 = 2 + t --> t = 2

y₀ = -5 + t * (-2) --> -9 = -5 - 2t --> t = 2

z₀ = 0 + t * (-4) --> -8 = 0 - 8t --> t = 1

The value of t is consistent across all equations, so the point (4, -9, -8) lies on line 1.

Therefore, among the given points, only the point (4, -9, -8) lies on line 1.

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The complete question is:

Let l be the line perpendicular to the plane x - 2y - 4z = 5 and containing the point (2, -5, 0). determine whether the following points lie on line l.

Answer:

\(\frac{29}{50}\)

Step-by-step explanation:

We have two fractions and are being asked to add them both.

5/10 and 8/100 don't have the fractions, but 5/10 can be simplified to 1/2, meaning that to make the same denominator, we have to find the half of 100, which would be 50. Now turn the fraction into 50/100.

50/100 + 8/100

58/100

This can be simplifed :

\(\frac{58/2}{100/2}\)

\(\frac{29}{50}\)

Answer:

300 million

Step-by-step explanation:

Answer:

5,000 people = 1520000%

Step-by-step explanation:

Two sides of triangle are equal triangle ABC acute scalene triangle. Option B right choice.

The type of triangle ABC can use the Pythagorean to check if it is a right triangle and the distance formula to check if it is an isosceles or scalene triangle.

Using the distance formula can find the lengths of the three sides of triangle ABC:

AB = √((6-0)² + (0-0)²) = 6

BC = √((3-6)² + (7-0)²) = √(58)

AC = √((3-0)² + (7-0)²) = √(58)

BC=AC ≠AB , and the triangle is a acute scalene triangle.

The triangle is a right triangle can use the Pythagorean:

If the triangle is a right triangle, then one of the sides must be the hypotenuse and the other two sides must be the legs.

Let's assume that AC is the hypotenuse and AB and BC are the legs. Then, we have:

(AC)² = (AB)² + (BC)²

Substituting the values we found earlier, we have:

(√58)² = 6² + (BC)²

58 = 36 + (BC)²

(BC)² = 22

22 is not a perfect square so (BC)² cannot be equal to the difference between two perfect squares.

Triangle ABC is not a right triangle.

Option B right choice.

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The slope of a line perpendicular to the line that has equation is 5x - 2y = -10 is -2/5.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line. Slope of parallel lines are same. Slopes of perpendicular lines are negative reciprocal of each other.

Given that

5x - 2y = -10

This equation to be in slope-intercept form: y = mx + b.

Now Start by adding 2y to both sides of the equation;

5x = -10 + 2y

Then add 10 to both sides of the equation.

5x + 10 = 2y

Now Divide both sides of the equation by 2;

(5x + 10)/2 = y

(5/2)x + 5 = y

The slope of this line is  5/2.

The slope of the line perpendicular to this line, we take the opposite reciprocal.

The slope 5/2 becomes -2/5.

Hence, the slope of a line perpendicular to the line that has equation is 5x - 2y = -10 is -2/5.

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Answer:

No, because the radicands are not the same

Step-by-step explanation:

A threat to internal validity occurs only if a potential design confound varies systematically with the independent variable.

In experimental research, an independent variable is a variable that the researcher manipulates or systematically varies in order to study its effect on the dependent variable. It is called "independent" because it is not influenced by any other variables in the experiment, and its effects on the dependent variable can be observed and measured independently of any other factors.

Only when a possible design confound fluctuates systematically with the independent variable does internal validity come under threat. In other words, it might be challenging to distinguish between the effects seen on the dependent variable and the independent variable if there is a component that fluctuates consistently or predictably with changes in the independent variable. Internal validity is less likely to be threatened by random or unplanned variation.

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A threat to internal validity occurs only if a potential design confound varies systematically with the independent variable. This means that if the confound varies randomly or haphazardly, it is less likely to affect the results of the study.

This means that the confound is consistently related to the independent variable, making it difficult to determine if the observed effects are due to the independent variable or the confound. If the confound varies spontaneously or haphazardly, it is less likely to pose a threat to internal validity, as it would not be consistently associated with the independent variable.

However, if the confound is related to the independent variable in a consistent and predictable way, it can introduce bias and undermine the internal validity of the study. It is important for researchers to carefully control for potential confounds and ensure that any observed effects are truly due to the independent variable and not some other factor.

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Answer:

Therefore, the book value of the equipment at the end of year four (including year four) is $2,880.

Step-by-step explanation:

To calculate the book value of the equipment at the end of year four using the MACRS method with GDS recovery period of five years, we can use the following steps in Excel:

1. Open a new Excel spreadsheet and create the following headers in row 1: Year, Cost, Depreciation Rate, Annual Depreciation, Cumulative Depreciation, and Book Value.

2. Fill in the Year column with the years 1 through 6 (since the truck has a life of six years).

3. Enter the cost of the truck, $12,000, in cell B2.

4. Use the following formula in cell C2 to calculate the depreciation rate for each year:

=MACRS.VDB(B2, 5, 5, 1, C1)

This formula uses the MACRS.VDB function to calculate the depreciation rate for each year based on the cost of the truck (B2), the GDS recovery period of five years, the useful life of six years, the salvage value of $2,000, and the year (C1).

5. Copy the formula in cell C2 and paste it into cells C3 through C7 to calculate the depreciation rate for each year.

6. Use the following formula in cell D2 to calculate the annual depreciation for each year:

=B2*C2

This formula multiplies the cost of the truck (B2) by the depreciation rate for each year (C2) to get the annual depreciation.

7. Copy the formula in cell D2 and paste it into cells D3 through D7 to calculate the annual depreciation for each year.

8. Use the following formula in cell E2 to calculate the cumulative depreciation for each year:

=SUM(D$2:D2)

This formula adds up the annual depreciation for each year from D2 to the current row to get the cumulative depreciation.

9. Copy the formula in cell E2 and paste it into cells E3 through E7 to calculate the cumulative depreciation for each year.

10. Use the following formula in cell F2 to calculate the book value of the equipment for each year:

=B2-E2

This formula subtracts the cumulative depreciation for each year (E2) from the cost of the truck (B2) to get the book value.

11. Copy the formula in cell F2 and paste it into cells F3 through F7 to calculate the book value for each year.

12. The book value of the equipment at the end of year four (including year four) is the value in cell F5, which should be $2,880.

Step-by-step explanation:

\( \bf \underline{Given \:Question} \\ \)

Evaluate the following

\(\displaystyle\int_{2}^{4}\rm \frac{ \sqrt{ln(9 - x)} }{ \sqrt{ln(9 - x)} + \sqrt{ln(x + 3)} } \: dx\)

\( \red{\large\underline{\sf{Solution-}}}\)

Given integral is

\(\rm :\longmapsto\:\displaystyle\int_{2}^{4}\rm \frac{ \sqrt{ln(9 - x)} }{ \sqrt{ln(9 - x)} + \sqrt{ln(x + 3)} } \: dx\)

Let assume that

\(\rm :\longmapsto\:I = \displaystyle\int_{2}^{4}\rm \frac{ \sqrt{ln(9 - x)} }{ \sqrt{ln(9 - x)} + \sqrt{ln(x + 3)} } \: dx - - - (1)\)

We know that

\(\rm :\longmapsto\:\boxed{\tt{ \displaystyle\int_{a}^{b}\rm f(x) \: dx \: = \: \displaystyle\int_{a}^{b}\rm f(a + b - x) \: dx \: }}\)

So, using this property, we get

Change

\( \red{\rm :\longmapsto\:x \to \: 2 + 4 - x = 6 - x}\)

\(\rm :\longmapsto\:I = \displaystyle\int_{2}^{4}\rm \frac{ \sqrt{ln(9 - (6 - x))} }{ \sqrt{ln(9 -(6 - x))} + \sqrt{ln(6 - x + 3)} } \: dx\)

\(\rm :\longmapsto\:I = \displaystyle\int_{2}^{4}\rm \frac{ \sqrt{ln(3 + x)} }{ \sqrt{ln(3 + x)} + \sqrt{ln(9 - x)} } \: dx - - - (2)\)

On adding equation (1) and (2), we get

\(\rm :\longmapsto\:2I = \displaystyle\int_{2}^{4}\rm \frac{ \sqrt{ln(9 - x)} }{ \sqrt{ln(9 - x)} + \sqrt{ln(x + 3)}}dx + \displaystyle\int_{2}^{4}\rm \frac{ \sqrt{ln(x + 3)} }{ \sqrt{ln(9 - x)} + \sqrt{ln(x + 3)}}dx\)

\(\rm :\longmapsto\:2I = \displaystyle\int_{2}^{4}\rm \frac{ \sqrt{ln(9 - x)} + ln \sqrt{(x + 3)} }{ \sqrt{ln(9 - x)} + \sqrt{ln(x + 3)}}dx \)

\(\rm :\longmapsto\:2I = \displaystyle\int_{2}^{4}\rm 1dx \)

\(\rm :\longmapsto\:2I = \bigg|x\bigg| _{2}^{4}\rm \)

\(\rm :\longmapsto\:2I = 4 - 2\)

\(\rm :\longmapsto\:2I = 2\)

\(\rm :\longmapsto\:I = 1\)

Hence,

\(\boxed{\tt{ \displaystyle\int_{2}^{4}\rm \frac{ \sqrt{ln(9 - x)} }{ \sqrt{ln(9 - x)} + \sqrt{ln(x + 3)} } \: dx = 1}}\)

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

\(\rm :\longmapsto\:\boxed{\tt{ \displaystyle\int_{a}^{b}\rm f(x) \: dx \: = \: \displaystyle\int_{a}^{b}\rm f(y) \: dy \: }}\)

\(\rm :\longmapsto\:\boxed{\tt{ \displaystyle\int_{a}^{b}\rm f(x) \: dx \: = \: - \: \displaystyle\int_{b}^{a}\rm f(x) \: dx \: }}\)

\(\rm :\longmapsto\:\boxed{\tt{ \displaystyle\int_{0}^{a}\rm f(x) \: dx \: = \: \displaystyle\int_{0}^{a}\rm f(a - x) \: dx \: }}\)

\(\rm :\longmapsto\:\boxed{\tt{ \displaystyle\int_{0}^{2a}\rm f(x) \: dx \: = \:2 \displaystyle\int_{0}^{a}\rm f(x) \: dx \: if \: f(2a - x) = f(x) \: }}\)

\(\rm :\longmapsto\:\boxed{\tt{ \displaystyle\int_{0}^{2a}\rm f(x) \: dx \: = 0 \: if \: f(2a - x) = - f(x) \: }}\)

\(\rm :\longmapsto\:\boxed{\tt{ \displaystyle\int_{ - a}^{a}\rm f(x) \: dx \: = 0 \: if \: f(- x) = - f(x) \: }}\)

\(\rm :\longmapsto\:\boxed{\tt{ \displaystyle\int_{ - a}^{a}\rm f(x) \: dx \: = \:2 \displaystyle\int_{0}^{a}\rm f(x) \: dx \: if \: f( - x) = f(x) \: }}\)

The cost of the apples is 2.9 dollars.

The cost of the bananas is 5.7 dollars.

The total cost is 6 dollars, each apple cost $1.50 each banana cost $.30 and there’s two more bananas then apples.

Therefore,

let

x = number of apples

y = 2x

where

Therefore, using equations,

1.5(x) + y(0.30) = 6

Hence,

where

y = 2x

1.5(x) + 2x(0.30) = 6

1.5x + 0.6x = 6

2.1x = 6

divide both sides by 2.1

x = 6 / 2.1

x = 2.9 dollars

y = 2(2.9) = 5.7 dollars

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The equation in Standard Form. b) Identify P(x). c) Identify Q(x). d) Evaluate Integrating Factor. e) Solve for the general solution are given below:

a) Rewrite the equation in Standard Form:

To rewrite the equation in standard form, divide the entire equation by x⁴:

dy/dx + 2y = e^(-x)

b) Identify P(x):

In standard form, the coefficient of the y term is 2, which is the function P(x). So, P(x) = 2.

c) Identify Q(x):

In standard form, the right-hand side of the equation is e^(-x), which is the function Q(x). So, Q(x) = e^(-x).

d) Evaluate the Integrating Factor:

The integrating factor (IF) is given by the exponential of the integral of P(x) with respect to x. In this case, the integrating factor is:

IF = e^(∫P(x)dx) = e^(∫2dx) = e^(2x)

e) Solve for the general solution:

Multiply the entire equation by the integrating factor (IF = e^(2x)):

e^(2x) * (dy/dx + 2y) = e^(2x) * e^(-x)

Simplify the left side by applying the product rule of exponents:

(e^(2x) * dy/dx) + 2y * e^(2x) = e^(x)

Notice that the left side is now in the form (f(x)g(x))' = f'(x)g(x) + f(x)g'(x), where f(x) = y and g(x) = e^(2x). Apply the product rule and simplify further:

(d/dx)(y * e^(2x)) = e^(x)

Integrate both sides with respect to x:

∫(d/dx)(y * e^(2x)) dx = ∫e^(x) dx

Integrating the left side gives:

y * e^(2x) = ∫e^(x) dx = e^(x) + C₁, where C₁ is the constant of integration.

Finally, solve for y by dividing both sides by e^(2x):

y = (e^(x) + C₁) / e^(2x)

This is the general solution to the given differential equation using the Integrating Factor Method.

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The probability mass function of W is P(W=-3) = 1/27, P(W=-1) = 6/27, P(W=1) = 12/27, and P(W=3) = 8/27.

Let us consider the possible outcomes of three tosses of the biased coin. There are a total of 8 possible outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, and TTT.

Since a head is twice as likely to occur as a tail, the probability of getting a head is 2/3 and the probability of getting a tail is 1/3.

Let W be a random variable giving the number of heads minus the number of tails in three tosses of the coin. Then, W can take on any value between -3 and 3.

To find the probability mass function (PMF) of W, we need to calculate the probability of each possible outcome. When all three coins come up heads (HHH), W = 3 - 0 = 3. The probability of this outcome is:

P(HHH) = (2/3)^3 = 8/27

When two coins come up heads and one comes up tails (HHT, HTH, THH), W = 2 - 1 = 1. The probability of each of these outcomes is:

P(HHT) = (2/3)^2 × (1/3) = 4/27

P(HTH) = (2/3)^2 × (1/3) = 4/27

P(THH) = (2/3)^2 × (1/3) = 4/27

So, P(W=1) = P(HHT) + P(HTH) + P(THH) = 12/27

When one coin comes up heads and two come up tails (HTT, THT, TTH), W = 1 - 2 = -1. The probability of each of these outcomes is:

P(HTT) = (2/3) × (1/3)^2 = 2/27

P(THT) = (2/3) × (1/3)^2 = 2/27

P(TTH) = (2/3) × (1/3)^2 = 2/27

So, P(W=-1) = P(HTT) + P(THT) + P(TTH) = 6/27

When all three coins come up tails (TTT), W = 0 - 3 = -3. The probability of this outcome is:

P(TTT) = (1/3)^3 = 1/27

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Answer:

46\(\sqrt{2}\)

Step-by-step explanation:

4\(\sqrt{16} \sqrt{2} =4\sqrt{32}\)

\(\sqrt{16} =4\)

4x4=16

16\(\sqrt{2}\)

\(6\sqrt{25} \sqrt{2} =6\sqrt{50}\)

\(\sqrt{25} =5\)

6x5=30

30\(\sqrt{2}\)+16\(\sqrt{2}\)

=\(46\sqrt{2}\)

Answer:

s=8

Step-by-step explanation:

Answer:

S=8

Step-by-step explanation:

4(5-s)=-12

20-4s=-12

20-20-4s=-12-20

-4s=-32

s=8

The test statistic for this hypothesis test is approximately -2.748. Americans spend less than 7 hours a week answering their email.

To find the test statistic, we need to perform a hypothesis test to determine if the sample data supports the researcher's suspicion that Americans spend less than 7 hours a week answering their email.

Let's set up the null and alternative hypotheses:

Null hypothesis (H₀): The population mean number of hours Americans spend answering their email per week is 7 or more

Alternative hypothesis (H₁): The population mean number of hours Americans spend answering their email per week is less than 7

Next, we can calculate the test statistic, which is the standardized value that measures the distance between the sample mean and the hypothesized population mean, considering the sample size and variability.

The test statistic formula for a one-sample t-test is given by:

t = (sample mean - hypothesized mean) / (sample standard deviation / √sample size)

Given the information from the study:

Sample mean = 6.01

Sample standard deviation (s) = 8.96

Sample size (n) = 617

Hypothesized mean  = 7

Substituting these values into the formula, we get:

t = (6.01 - 7) / (8.96 / √617)

Calculating this expression gives us the test statistic.

t = (-0.99) / (8.96 / √617)

t ≈ -0.99 / (8.96 / 24.81)

t ≈ -0.99 / 0.3602

t ≈ -2.748

Therefore, the test statistic for this hypothesis test is approximately -2.748.

The test statistic provides a measure of how far the sample mean is from the hypothesized mean in terms of standard deviations. In this case, since the test statistic is negative, it suggests that the sample mean is less than the hypothesized mean, supporting the researcher's suspicion that Americans spend less than 7 hours a week answering their email.

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We can learn a lot about a population if we select a subset of it.

One kind of set is a sample space. It is a clear listing of every event that could occur in a statistical experiment. A statistical experiment's events are a subset of the sample space.

A subset is a smaller group of results that are part of the bigger group.

Subsets are events, and events are subsets. A subset is an event of a sample space, and an event is a potential result of an experiment. A random experiment's sample space is a set (S) that contains all of the experiment's potential outcomes.

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The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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Correct option is C, the correct equation is Y - 2 = -1/3 (x + 6).

Y=mx+b, where m is the slope and b is the y-intercept, is the slope intercept form. The graph of the linear equation can be drawn on the x-y coordinate plane using this form of the equation. Y = m x + b y=mx+b y=mx+by, equals, m, x, plus, b, where m is the slope and b is the y-intercept, is the slope intercept form.

Given points are (-6,2)

The required line should be perpendicular to y=3x-8.

When two lines are perpendicular,

their slopes are such that,

m1 = - 1/m2                    [1]

⇒ slope of line 2 =

⇒ -1/3    [using (1) relationship ]

Now substituting the points are slope in the equation of line -

y - y₀ = m (x - x₀)

⇒ y - 2 = -1/3 (x + 6)

⇒ 3y - 6 = -x - 6

⇒ 3y + x = 0

⇒ x = -3y

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Answer:

Step-by-step explanation:

For the sequence {3, 4, 5, 6, 7, ...}, we can observe that each term is obtained by adding 1 to the previous term. Therefore, we can find the general term (an) using the formula:

an = a1 + (n - 1)

Here, a1 represents the first term of the sequence, and n represents the position of the term in the sequence.

In this case, the first term is 3, so we have:

an = 3 + (n - 1)

= 2 + n

Therefore, the formula for the general term of the sequence is:

an = 2 + n

Expanding the expression (4x - 3)⁵ using the Binomial Theorem:

The Binomial Theorem states that for any positive integer n, the expansion of (a + b)ⁿ can be written as:

(a + b)ⁿ = C(n, 0)aⁿb⁰ + C(n, 1)aⁿ⁻¹b¹ + C(n, 2)aⁿ⁻²b² + ... + C(n, n-1)abⁿ⁻¹ + C(n, n)a⁰bⁿ

Where C(n, k) represents the binomial coefficient, given by C(n, k) = n! / (k!(n-k)!).

Applying the Binomial Theorem to (4x - 3)⁵:

(4x - 3)⁵ = C(5, 0)(4x)⁵(-3)⁰ + C(5, 1)(4x)⁴(-3)¹ + C(5, 2)(4x)³(-3)² + C(5, 3)(4x)²(-3)³ + C(5, 4)(4x)¹(-3)⁴ + C(5, 5)(4x)⁰(-3)⁵

Simplifying and expanding each term, we have:

(4x - 3)⁵ = 1(4x)⁵ - 5(4x)⁴(3) + 10(4x)³(9) - 10(4x)²(27) + 5(4x)(81) - 1(243)

(4x - 3)⁵ = 1024x⁵ - 2560x⁴ + 2880x³ - 1728x² + 405x - 243

Therefore, the expansion of (4x - 3)⁵ is:

1024x⁵ - 2560x⁴ + 2880x³ - 1728x² + 405x - 243

To find term number 5 in the expansion of (2x + 5)⁵, we need to determine the coefficient and the variable part for that term.

The expansion of (2x + 5)⁵ will have six terms, labeled from term number 0 to term number 5. The coefficient for term number 5 will be the binomial coefficient C(5, 5), which is equal to 1.

The variable part for term number 5 will be the product of the variable part of (2x) raised to the power of (5 - 5) and the variable part of (5) raised to the power of 5. In this case, since (2x) raised to the power of 0 is 1, and (5) raised to the power of 5 is 312

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The given function f(x) can be expressed as (x-2)(x^4+2x^3+12x^2+24x+32)/(x-1)(x-2)(x+4). As f(2)=-3.6667, it means that the numerator (x-2)(x^4+2x^3+12x^2+24x+32) evaluates to a negative value and the denominator (x-1)(x-2)(x+4) evaluates to a positive value at x=2. This implies that (x-2) term in both numerator and denominator cancel out leaving the sign of f(x) to be solely determined by the remaining terms. Hence, we can conclude that at x=2, f(x) is negative because the numerator is negative and denominator is positive.

To understand the meaning of f(2)=-3.6667, we first need to evaluate the given function f(x) at x=2. So, we have f(2) = 2^2 - 5(2) + 8(2) - 8 = -3.6667. This means that at x=2, the function f(x) has a negative value. However, this doesn't give us any information about the numerator and denominator of f. To find out more about the numerator and denominator, we need to factorize the given function as shown above.

Now, we can see that the numerator has a factor of (x-2) which cancels out with the (x-2) factor in the denominator. Hence, at x=2, we can ignore this factor and look at the remaining terms. As the numerator evaluates to a negative value and the denominator evaluates to a positive value at x=2, we can conclude that f(x) is negative at x=2.

In conclusion, the value of f(2)=-3.6667 tells us that at x=2, the function f(x) has a negative value. Further analysis of the function by factorizing it reveals that at x=2, the numerator of f(x) is negative and the denominator is positive. Hence, we can conclude that the function f(x) is negative at x=2 because the numerator is negative and the denominator is positive.

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lets take number one for example,

When subtracting negative numbers, the (-) in the number (-20) cancels out the original minus sign, therefore, to answer the equation:

10 - (-20)

you would need to turn the equation into an addition problem, getting the equation:

10 + 20

and from there you can get the simple answer of:

30

(brainliest please)

The number of rounds that Kate has to run along the perimeter of town to complete  12 miles is 4 rounds.

What is the perimeter of a triangle?

Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape. The perimeter of any polygon is equal to the sum of its side lengths. Considering a triangle, the sum of the three sides equals the perimeter.

Given the town is the shape of a triangle.

The distance covered after running one round around town is equal to the perimeter of the triangle.

The sides of the triangle are 0.7 miles, 1.4 miles and 0.9 miles.

Perimeter = 0.7+0.9+1.4 = 3 miles.

The distance covered in one round = 3 miles.

So the number of rounds required to complete 12 miles = 1/3 * 12 = 4 rounds.

Therefore the number of rounds that Kate has to run along the perimeter of town to complete  12 miles is 4 rounds.

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Question 13

\({12x+2}=\frac{18+34}{2}\\\\12x+2=26\\\\12x=24\\\\x=\boxed{2}\)

Question 14

Base angles of an isosceles trapezoid are congruent, so:

\(73x+1=74\\73x=73\\x=\boxed{1}\)