In the expansion of (1 + ax)24 where a > 0, the coefficient of x² is 1104. Find the value of a.​

The mean absolute deviation (MAD) for the given data is 1/20. This means that, on average, each data point in the set differs from the mean by 1/20.

To find the mean absolute deviation (MAD) of a set of data, we need to calculate the average difference between each data point and the mean of the data set. Here's how we can calculate it for the given data:

Step 1: Find the mean (average) of the data set.

Mean = (1/4 + 5/8 + 3/8 + 3/4 + 1/2) / 5 = 2/5

Step 2: Calculate the difference between each data point and the mean.

Differences: |1/4 - 2/5|, |5/8 - 2/5|, |3/8 - 2/5|, |3/4 - 2/5|, |1/2 - 2/5|

Step 3: Calculate the absolute value of each difference.

Absolute Differences: 1/20, 1/40, 1/40, 1/20, 1/10

Step 4: Find the average of the absolute differences.

MAD = (1/20 + 1/40 + 1/40 + 1/20 + 1/10) / 5 = 1/20

The MAD provides a measure of the average amount of variation or dispersion in the data set. In this case, a MAD of 1/20 indicates that the data points are relatively close to the mean, with most values falling within 1/20 of the mean value.

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Answer:

Lets suppose total number of tickets=X

so, 45= 60/100× X

X = 75

so total number of tickets are 75 therefore 75-67.5= 7 tickets have been sold

Answer:

1.1 x 10^4 km

Step-by-step explanation:

Its which ever that says 1.1 x 10^4 km

The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:

\(c^2 = a^2 + b^2 - 2ab*cos(C)\)

In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:

\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)

49 = 16 + 25 - 40*cos(C)

49 = 41 - 40*cos(C)

40*cos(C) = 41 - 49

40*cos(C) = -8

cos(C) = -8/40

cos(C) = -0.2

To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:

C = arccos(-0.2)

Using a calculator, we find that C ≈ 101.54 degrees.

Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.

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Answer:

Since 1/3 and -1/3 have the exact same denominators and numerators they will divide into 1. But since one of the number are negative, that means your answer switches to be negative 1

-1 is the answer

Step-by-step explanation:

The solutions to the inequalities are given as follows:

The first inequality is given as follows:

\(2^{x^2 - 5x - 4} < 4\)

We have that 4 = 2², hence:

\(2^{x^2 - 5x - 4} < 2^2\)

As the exponential function is increasing over it's entire domain, the inequality can be represented as follows:

x² - 5x - 4 < 2

x² - 5x - 6 < 0.

The quadratic equation x² - 5x - 6 is concave up, hence it's negative between it's roots, obtained as follows:

(x - 2)(x - 3) = 0.

Applying the Factor Theorem:

Hence the solution to the inequality is of:

2 < x < 3.

The second inequality is given as follows:

\(\log_{0.3}{(x^2 + 3)} \geq \log_{0.3}{4x}\)

The logarithm function is also increasing over it's entire domain, hence the inequality is simplified as follows:

x² + 3 ≥ 4x

x² - 4x + 3 ≥ 0.

Another concave up quadratic equation, which is non-negative to the left of the smallest root and to the right of the highest root.

The roots are obtained by factoring as follows:>

(x - 3)(x - 1) = 0.

Hence:

Then the solution is given as follows:

x ≤ 1 or x ≥ 3.

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Answer:

I have completed the answers and attached them to the explanation.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The question asks for a subtraction expression:

length is always a positive number so bigger number first here.

OB = 4-(-1)              >only moves in x direction so subtract x's

AB = 4-(-2)             >only moves in y direction so subtract y's

Answer:

Use the following Financial Ratios to measure financial performance against standards. In addition, analysts compare these ratios to industry averages (benchmarking), industry standards or rules of thumbs and against internal trends (trends analysis). Furthermore the most useful comparison when performing financial ratio analysis is trend analysis They are derived from thethree following financial

statements:

⚫Balance Sheet

•Income Statement

⚫Statement of Cash Flows

.5 Categories

The five (5) major categori in the financial ratios list include the following:

•Liquidity Ratios

•Activity Ratios

•Debt Ratios

•Profitability Ratios

•Market Ratios

Step-by-step explanation:

Sana makatulong

Ratios dealing with short-term debts are Liquidity Ratios; those gauging efficiency in using assets for sales are Activity Ratios, and those scrutinizing long-term debt handling are Leverage Ratios. Along with the calculations, observations and identification of trends and their driving factors are also necessary.

In finance and business, ratio analysis is a tool used for conducting quantitative analysis on a company's financial statements. It involves the calculation and interpretation of various financial ratios. The following are the answers to the question's blanks:

However, only calculating ratios is not enough; you must also observe and identify trends suggested by the analysis, as well as identify the factors that drive these trends. These additional steps provide context and deeper insights into the company's financial performance.

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Answer:

10 root 2

Step-by-step explanation:

root 200 = root 2 × root 100 = 10 root 2

Ansewern

I think you forgot the stament and please add it so i can helpyou out with it.

Step-by-step explanation:

Answer:

22 feet

Step-by-step explanation:

As the given measurements are not all in the same units, convert all measurements to inches using the conversion 1 ft = 12 inches:

Therefore:

Draw a diagram using the given information (see attachment).

From the diagram, we can see that the flagpole and the person are parallel.  Therefore, the two triangles are similar.

In similar triangles, corresponding sides are always in the same ratio.

Therefore, set up a ratio of height to shadow length and solve for h:

\(\implies \sf Flagpole\;height:Flagpole:shadow=Person\;height:Person\;shadow\)

\(\implies \sf h:168=66:42\)

\(\implies \sf \dfrac{h}{168}=\dfrac{66}{42}\)

\(\implies \sf h=\dfrac{66}{42} \cdot 168\)

\(\implies \sf h=\dfrac{11088}{42}\)

\(\implies \sf h=264\;inches\)

Convert the height into feet by dividing by 12:

\(\implies \sf h=\dfrac{264}{12}=22\;feet\)

Therefore, the height of the flagpole is 22 feet.

Answer:

835.865333

Step-by-step explanation:

16.6×16.6=275.56

275.56×9.1=2507.596

2507.596÷3=835.865333

A. The total value of the loan with quarterly compounded interest is $52,400.

B. The total value of the loan with monthly compounded interest is $52,010.04

Part A: Total value of the loan with the quarterly compounded interest

To find the total value of the loan, we'll use the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A = final amount (loan + interest)

P = principal amount (initial loan) = $20,000

r = interest rate = 7% = 0.07

n = number of times compounded per year = 4 (quarterly)

t = number of years = 10

Plugging in the values, we get:

A = $20,000 * (1 + 0.07/4)^(4 * 10)

A = $20,000 * (1.0175)^40

A = $20,000 * 2.620075

A = $52,401.51

Rounding to the nearest hundred, the total value of the loan with quarterly compounded interest is $52,400.

Part B: Total value of the loan with the monthly compounded interest

To find the total value of the loan with monthly compounded interest, we'll use the same formula with a different value of n:

A = P * (1 + r/n)^(nt)

Where:

n = number of times compounded per year = 12 (monthly)

Plugging in the values, we get:

A = $20,000 * (1 + 0.07/12)^(12 * 10)

A = $20,000 * (1.005833)^120

A = $20,000 * 2.600502

A = $52,010.04

Rounding to the nearest hundredth, the total value of the loan with monthly compounded interest is $52,010.04

The difference between the two loans is $52,401.51 - $52,010.04 = $391.47

The difference between the two loans is due to the higher frequency of compounding in the monthly compounded interest loan. The interest is compounded more times per year, so the interest is accumulating on the interest more quickly, leading to a higher overall interest charge.

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Answer:11

Step-by-step explanation:

Below, you'll find a list of all the answers to the questions which are solved by using proportional relationship.

The general equation for a straight line is y=mx + c, where m represents the line's slope and expresses the rate of change of y per unit time with respect to x.

The point where the graph crosses the y-axis is called the y-intercept, or c.

Direct proportionality is also represented by y = mx. We can express m as follows: m = y/x

OR

y₁/x₁ = y₂/x₂

In our cafeteria, lemonade is made using a powdered drink mix. The quantity of water required to manufacture a certain amount of powdered drink mix is proportional to the number of scoops required. For every 2 scoops of mix, 1/2 gallon of water is required, and for every 5 scoops,

1 1/4 gallons of water are required.

The proportional formula is written as y = k x.

Using the information provided, we can now write: 2 scoops require 0.5 gallon of water.

1.25 gallon of water is required for 6 scoops.

This means that k = 2/0.5

k = 2/(1/2)

k = 2 x 2

k= 4

Equations describing the relationship can be expressed as y = 4x + c.

0.5 gallon of water is now required for 2 scoops.

2=4(1/2)+c

2=2+c

c=0

Therefore, the formula will be y = 4x.

The end includes a graph for y = 4x.

12 scoops of water:

12=4x

x=3 gallons of water is needed.

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Considering the given figure angle 1 is calculated to be 26

The solution of angle 1 is gotten from the knowledge of adjacent angles

angle 1 and angle 2 are adjacent angles and the total angle is given to be x + 38

therefore  we have

x + 38 = angle 1 + angle 2

x + 38 = angle 1 + x + 12

angle 1 = x + 38 - x - 12

angle 1 = 38 - 12

angle 1 = 26

we can therefore say that angle 1 is 26

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I believe the answer would be yes. Since your dealing with Ratios it would be simple to understand that they are proportional. I'll explain a little better.

This means that if you double this ratio, it will still be equivalent to 1:3

1:3

This is also proportional because this number will always be equivalent to itself.

7:21

-----------------------------------------------------------------------------------------------------------------Hope this helps

-Miri

An unbiased statistic is one in which the average value of the statistic is equal to the population parameter. Hence, option d is the correct answer.

When a statistic does not overestimate or underestimate a population parameter, it is considered to be an unbiased estimator. To put it another way, a value is considered unbiased if it accurately represents the value of a certain parameter. There are various factors that can affect how biassed a statistic from a specific sample is. The possibility of bias can rise depending on the sample methods utilised.

According to the definition of the unbiased estimator we know that an unbiased statistic is one in which the average value of the statistic is equal to the population parameter.

Hence, option d is the correct answer.

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The area of the parking lot, given the dimensions of the lot can be found to be 9, 600 meters ².

To find the area of the parking lot, you need to divide the given shape into smaller shapes such that the area of these shapes can be found.

The area of the top rectangle would be:

= Length x Width

= 100 x 40

= 4, 000 meters ²

The area of the other rectangle :

= 40 x 140

= 5, 600 meters ²

The area of the parking lot is:

= 4, 000 + 5, 600

= 9, 600 meters ²

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Answer:

4/x-8=8/2

4/x-8=4

4=4(x-8)

4=4x-32

4+32=4x

36=4x

dividing through by 4

x=9

converting to the nearest tenth will be 9.0

therefore x=9.0

SOLUTION;

Step 1:

Answer:

548 > 373

Step-by-step explanation:

548 is greater than 373 because when we compare the digits from left to right, we find that the first digit of 548 (5) is greater than the first digit of 373 (3). Therefore, we can conclude that 548 is greater than 373.

The ">" symbol is used to represent "greater than" in mathematical comparisons.

Hope this helps!

Answer:

\(V=20.52\ in^3\)

Step-by-step explanation:

Given that,

The radius and the height of the cylindrical soup can are 1.1 inch and 5.4 inch.

We need to find the volume of the can.

The formula for the volume of the can is given by :

\(V=\pi r^2 h\\\\V=\pi \times (1.1)^2 \times 5.4\\\\V=20.52\ in^3\)

So, the volume of the can is equal to \(20.52\ in^3\).

Step-by-step explanation: Well to begin, you take 15$ and multiply it by 4, since he wants to buy 4 of those tickets, which is 60$. Then, take the 10$ and multiply it by 2 since he wants 2 of those tickets, which is 20$, you then apply 10% to 60 and 20 by taking 10 percent of 60, then adding  it to 60 once have that, which is 66, you take the 3% and find 3% of 66, then add the answer of that to 66, which is 67.98$, you then do the same thing to the 20$.

Sorry if this didnt help, im sure it didnt because im a very bad explainer, but i tried..

Step-by-step explanation:

The absolute value function is a well known piecewise function (a function defined by multiple subfunctions) that is described mathematically as

                                 \(f(x) \ = \ |x| \ = \ \left\{\left\begin{array}{ccc}x, \ \text{if} \ x \ \geq \ 0 \\ \\ -x, \ \text{if} \ x \ < \ 0\end{array}\right\}\).

This definition of the absolute function can be explained geometrically to be similar to the straight line   \(\textbf{\textit{y}} \ = \ \textbf{\textit{x}}\)  , however, when the value of x is negative, the range of the function remains positive. In other words, the segment of the line  \(\textbf{\textit{y}} \ = \ \textbf{\textit{x}}\)  where \(\textbf{\textit{x}} \ < \ 0\) (shown as the orange dotted line), the segment of the line is reflected across the x-axis.

First, we simplify the expression.

                                             \(3\left|x \ + \ 1 \right| \ < \ 9 \\ \\ \\\-\hspace{0.2cm} \left|x \ + \ 1 \right| \ < \ 3\).

We, now, can simply visualise the straight line,  \(y \ = \ x \ + \ 1\) , as a line having its y-intercept at the point  \((0, \ 1)\) and its x-intercept at the point \((-1, \ 0)\). Then, imagine that the segment of the line where \(x \ < \ 0\) to be reflected along the x-axis, and you get the graph of the absolute function \(y \ = \ \left|x \ + \ 1 \right|\).

Consider the inequality

                                                    \(\left|x \ + \ 1 \right| \ < \ 3\),

this statement can actually be conceptualise as the question

            \(``\text{For what \textbf{values of \textit{x}} will the absolute function \textbf{be less than 3}}"\).

Algebraically, we can solve this inequality by breaking the function into two different subfunctions (according to the definition above).

                                                \(x \ + \ 1 \ < \ 3 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 3 \ - \ 1 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 2\)

                                            \(-(x \ + \ 1) \ < \ 3 \\ \\ \\ \-\hspace{0.15cm} -x \ - \ 1 \ < \ 3 \\ \\ \\ \-\hspace{1cm} -x \ < \ 3 \ + \ 1 \\ \\ \\ \-\hspace{1cm} -x \ < \ 4 \\ \\ \\ \-\hspace{1.5cm} x \ > \ -4\)

           *remember to flip the inequality sign when multiplying or dividing by

            negative numbers on both sides of the statement.

Therefore, the values of x that satisfy this inequality lie within the interval

                                                     \(-4 \ < \ x \ < \ 2\).

Similarly, on the real number line, the interval is shown below.

The use of open circles (as in the graph) indicates that the interval highlighted on the number line does not include its boundary value (-4 and 2) since the inequality is expressed as "less than", but not "less than or equal to". Contrastingly, close circles (circles that are coloured) show the inclusivity of the boundary values of the inequality.