What number can you divide 1/2 by to get an answer smaller than 1/2

The standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

\(\rm SD = \sqrt{\dfrac{ \sum (x_i-X)^2}{N}\)

SD is the standard deviation

xi is each value from the data set

X is the mean of the data set

N is the number of observations in the data set.

It is given that:

The data set:

45, 76, 30, 22, 51, 40, 63, 66, 41

From the formula:

∑(x(i) - X)² = 2463.55

N = 9

SD = √(2463.55/9)

SD = 16.54

Thus, the standard deviation is 16.54 if the population of customers ages is 45, 76, 30, 22, 51, 40, 63, 66, and 41.

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Answer:

multipacation

Step-by-step explanation:

Answer:

-9x+5

Step-by-step explanation:

-6*x = -6x

-6*2 = -12

-6x-12+-3x+17

-6x+-3x = -9x

-12+17 = 5

-9x+5

Answer:

-9x+5

Step-by-step explanation:

Distribute:

-6x-12-3x+17

Combine like terms:

-9x+5

Final answer:

-9x+5

Hope this helps plz hit the crown :D

Answer:

There are 1,883 calories in 2 pounds

The question refers to the plot of the plate's function of the angle of inclination. When the hot side is tilted both upward and downward over the range of +90°, the discontinuous formulas must be used in different ranges of 0.

It refers to the plot of the function of the angle of inclination of a plate. It is a graph that shows the relationship between the angle of inclination and the plate's function. A plate is tilted on its hot side both upward and downward over a range of +90°. The graph shows that different discontinuous formulas are needed for different ranges of 0. A discontinuous formula refers to a formula that consists of two or more parts, each with a different equation. The two or more parts of a discontinuous formula have different ranges, such that each range requires a different equation. These formulas are used in cases where the same equation cannot be applied throughout the entire range.

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Answer: B

Step-by-step explanation: Hope this helps :)

Answer:

B

Step-by-step explanation:

It b because in the first columb it has the ordered pair (0,-2) the -2 is your y intercept and be has -2 in the equation.

Answer:

B

Step-by-step explanation:

Given :

Han says that we can wrap a 5 foot rope around a wheel with a 2 foot rope.

To Find :

It this true or false.

Solution :

Radius of wheel, r = 1 foot.

Circumference of wheel is given by :

\(C = 2\pi r\\\\C = 2\times 3.14\times 1\\\\C = 6.28 \ foot\)

Since, circumference is greater than 5 foot, therefore, we cannot wrap a  5-foot rope around a wheel with a 2-foot diameter.

Hence, this is the required solution.

agree Step-by-step explanation:

The second line of the solution in the given exercise is using the commutative property of multiplication to change the order of the factors for simplification.

In the given solution, the step where it says "By commutativity" is referring to the commutative property of multiplication. The commutative property states that the order of multiplication can be changed without affecting the result.

In this case, the expression is rearranged by changing the order of the factors. Instead of multiplying 3/5 and -2/3, it multiplies -2/3 and 3/5. This rearrangement is allowed because multiplication is commutative.

So, in the second line of the solution, the order of multiplication is changed using the commutative property to facilitate the simplification of the expression.

I hope this clarifies the use of the term "commutativity" in the solution. If you have any further questions, feel free to ask!

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Answer:

2.56

Step-by-step explanation:

I'm pretty sure, I'm sorry if its wrong

Answer:

0.5

Step-by-step explanation:

→ Find the difference in y

7 - 3 = 4

→ Find the difference in x

9 - 1 = 8

→ Divide the results

4 ÷ 8 = 0.5

Answer:

The slope is 1/2 (m=1/2)

Step-by-step explanation:

Use the slope formula: \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\) to solve for the slope. y2 is 7, y1 is 3, x2 is 1, x1 is 9. \(\frac{7-3}{9-1}=\frac{4}{8} = \frac{1}{2}\)

\( \frac{ - 9 - 8}{8 - 6} = \frac{ - 17}{2} = - 8.5 \)

The three positive integer that has mean of 5 and range of 10 will be 0, 5, 10.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Let the three positive number be (a – d), (a), and (a + d).

Then the mean of the number will be 5. Then we have

5 = (a – d + a + a + d) / 3

5 = (3a) / 3

a = 5

Then the range will be 10. Then we have

(a + d) – (a – d) = 10

   a + d – a + d = 10

                   2d = 10

                     d = 5

Then the three positive integer that has mean of 5 and range of 10 will be 0, 5, 10.

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Answer:

             i) TRUE

             ii) TRUE

             iii) TRUE

Step-by-step explanation:

\((ab+bc)(ab-bc)+(bc+ca)(bc-ca)+(ca+ab)(ca-ab)=\\\\=\underline{(ab)^2}-(bc)^2\ \,+\ \,(bc)^2-(ca)^2\ \,+\ \,(ca)^2-\,\underline{(ab)^2}=\\\\=0+0+0=0\)

\((a+b+c)(a^2+b^2+c^2-ab-bc-ca)=\\\\=a^3\,\underline{\,+ab^2}\ \underline{\underline{+\,ac^2}}\,-a^2b\ -\,abc\ \underline{\underline{\underline{-\,a^2c}}}+a^2b+b^3+bc^2\,\underline{-\,ab^2}\ \underline{\underline{\underline{ \underline{-\,b^2c}}}}\,-\,abc+\\{}\qquad\qquad\qquad\qquad\qquad\qquad \qquad\qquad \underline{\underline{ \underline{+\,a^2c}}}\ \underline{\underline{\underline{\underline{+\,b^2c}}}}+c^3\,-\,abc-bc^2\ \underline{\underline{-c^2a}}=\)

\(=a^3\ \underline{-\,a^2b}\ \underline{\underline{-\,abc}}\ \underline{+\,a^2b}+b^3\ \underline{\underline{\underline{+\,bc^2}}}\ \underline{\underline{-\,abc}}+c^3\ \underline{\underline{-\,abc}}\ \underline{\underline{\underline{-\,bc^2}}}=\\\\=a^3+b^3+c^3-3abc\)

\((p-q)(p^2+pq+q^2)=\\\\=p^3\ \underline{+\,p^2q}\ \underline{\underline{+\,pq^2}}\ \underline{-\,p^2q}\ \underline{\underline{-\,pq^2}}-q^3=\\\\=p^3-q^3\)

Answer:  see proofs below

Step-by-step explanation:

7i)  (ab + bc)(ab - bc) = a²b² - ab²c + ab²c - b²c²  →  a²b² - b²c²

  + (bc + ca)(bc - ca) = b²c² - abc² +abc² - a²c²   →             b²c²  - a²c²

  + (ca + ab)(ca - ab) = a²c² - a²bc + a²bc - a²b²  →                      a²c² - a²b²

                                                                             =   a²b² +  0   +   0   - a²b²

                                                                             = 0

7ii) a(a² + b² + c² - ab - bc - ca) = a³ + ab² + ac²           - a²b - abc - a²c

  + b(a² + b² + c² - ab - bc - ca) = b³ - ab²          + bc² + a²b - abc           - b²c

  + c(a² + b² + c² - ab - bc - ca) = c³           - ac² - bc²           - abc  + a²c + b²c

                                 =  a³ + b³ + c³  + 0     + 0   + 0     + 0   - 3abc + 0   + 0

                                  = a³ + b³ + c³ - 3abc

7iii) p(p² + pq + q²) = p³ + p²q + pq²

    -q(p² + pq + q²) =     - p²q  -  pq² - q³

                              = p³   + 0    + 0    - q³

                              = p³ - q³

Answer:

4

Step-by-step explanation:

Using the rule of exponents

\(a^{0}\) = 1

Then

4\((57ab)^{0}\) = 1 and

4\((57ab)^{0}\) = 4 × 1 = 4

Answer:

4

Step-by-step explanation:

since 57ab has power 0 it is equal to 1

1×4 is 4

Positive curve graphs will be upward-sloping.

Negative curve graphs will be downward-sloping.

Both graphs in the first image attached below, show curves sloping upward from left to right. As with upward-sloping straight lines, we can say that generally the slope of the curve is positive. While the slope will differ at each point on the curve, it will always be positive.

In the graphs in the second image attached, both of the curves are downward sloping. Straight lines that are downward sloping have negative slopes; curves that are downward sloping also have negative slopes. The slopes change from point to point on a curve, but all of the slopes along these two curves will be negative.

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Straight lines that are downward sloping have negative slopes; curves that are downward sloping also have negative slopes. The slopes change from point to point on a curve, but all of the slopes along these two curves will be negative.

The given p, α, and i using the exponentiation by squaring algorithm.

To prove that 2 is a primitive root of 11, to show that every integer a with 1 ≤ a ≤ 10 can be expressed as a ≡ 2²i (mod 11) for a unique i with 0 ≤ i ≤ 9.

verify this by checking the powers of 2 modulo 11:

2² ≡ 1 (mod 11)

2²≡ 2 (mod 11)

2² ≡ 4 (mod 11)

2³ ≡ 8 (mod 11)

2² ≡ 5 (mod 11)

2³ ≡ 10 (mod 11)

2³ ≡ 9 (mod 11)

2³ ≡ 7 (mod 11)

2² ≡ 3 (mod 11)

2³ ≡ 6 (mod 11)

The remainders obtained from the powers of 2 cover all the integers from 1 to 10 modulo 11. Additionally, each remainder is unique, express any integer between 1 and 10 as a power of 2 modulo 11.

To find log₂(9), to determine the exponent i such that 9 (mod 11). From the list of powers of 2 above, that 2³= 9 (mod 11). Therefore, log₂(9) = 6.

A given p, α, and i, where α is a primitive root of p and i is the discrete logarithm or index use the algorithm of exponentiation by squaring.

The algorithm for computing a given p, α, and i is as follows:

Set result = 1.

Initialize a binary representation of i, e.g., i = b[m]b[m-1]...b[1]b[0].

For j from m to 0:

a. Square the current result: result = result × result (mod p).

b. If bj = 1, multiply the current result by α: result = result × α (mod p).

Return the final result.

This algorithm takes advantage of the binary representation of i to compute a efficiently. By squaring the current result and multiplying by α only when necessary, compute a in logarithmic time complexity with respect to i.

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If you conclude that a soda filling machine is not filling bottles completely based on the results of a sample, it means that the sample of bottles you tested showed evidence of incomplete filling.

However, it is important to note that this conclusion is based on a sample and may not represent the behavior of the entire population of filled bottles.

To make a more reliable conclusion about the filling machine's performance, you would need to conduct a statistical analysis to determine the significance of the observed incomplete filling. This analysis could involve hypothesis testing or confidence interval estimation.

Hypothesis testing allows you to assess whether the observed incomplete filling is statistically significant or could have occurred by chance. You would formulate a null hypothesis, such as "the filling machine fills bottles completely," and an alternative hypothesis, such as "the filling machine does not fill bottles completely." By comparing the sample data to the expected behavior under the null hypothesis, you can determine if there is sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

The statistical analysis would involve calculating a test statistic, such as a t-test or a z-test, and determining the associated p-value. The p-value represents the probability of observing the sample data or more extreme data if the null hypothesis is true. If the p-value is below a predetermined significance level (e.g., 0.05), you would reject the null hypothesis and conclude that the filling machine is not filling bottles completely.

Additionally, you could also estimate a confidence interval for the proportion of bottles that are filled completely. This would provide a range of values within which the true proportion of completely filled bottles is likely to fall. If the lower limit of the confidence interval is below a desired threshold (e.g., 100%), it would provide further evidence that the filling machine is not consistently filling bottles completely.

It is crucial to note that drawing conclusions based on a sample has inherent limitations. The sample may not accurately represent the entire population of filled bottles, and there is always a margin of error associated with any statistical analysis. Therefore, it is recommended to conduct a larger-scale study or perform ongoing monitoring to obtain more reliable and comprehensive evidence about the filling machine's performance.

In summary, if you conclude that a soda filling machine is not filling bottles completely based on the results of a sample, it is an indication of potential issues with the machine. However, to make a more robust conclusion, you would need to conduct a statistical analysis, such as hypothesis testing or confidence interval estimation, to determine the significance of the observed incomplete filling. This analysis helps account for sampling variability and provides a more reliable assessment of the machine's performance.

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The conclusion which we get after analyzing the data given is that there aren't outliers in the displayed data set.

We will calculate the interquartile range and us the rule 1.5 .

The formula to calculate  interquartile range is to subtract the value of first quartile by the value of second quartile.

IQR = Q3 - Q1

Therefore, interquartile range becomes,

IQR = 17 - 13

IQR = 4

Now , we will apply rule 1.5 and for that we will multiply 4 by 1.5 first

4 * 1.5 = 6

and then,

17 + 6 = 23

on applying the rue we will get ,

13 - 6 = 7 .

This value means that there is no outlier in the displayed data set.

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The coordinates 73.355°N and 101.476°E can be converted from decimal degrees (DD) to degrees, minutes, and seconds (DMS) format. The rounded values in DMS are 73°21'18" N and 101°28'34" E.

To convert 73.355°N from DD to DMS, we start by extracting the whole number of degrees, which is 73°. Next, we need to convert the decimal part into minutes and seconds. Multiply the decimal by 60 to get the number of minutes. In this case, 0.355 * 60 = 21.3 minutes. Rounding to the nearest whole number, we have 21 minutes. Finally, to convert the remaining decimal part into seconds, we multiply by 60. 0.3 * 60 = 18 seconds. Rounding to the nearest whole second, we get 18 seconds. Combining all the values, we have 73°21'18" N.

For the coordinates 101.476°E, we follow the same steps. The whole number of degrees is 101°. Multiplying the decimal part, 0.476, by 60 gives us 28.56 minutes. Rounding to the nearest whole number, we have 29 minutes. The remaining decimal part, 0.56, multiplied by 60 gives us 33.6 seconds. Rounding to the whole second, we get 34 seconds. Combining all the values, we have 101°28'34" E.

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Using degree of freedom,

Two degrees of freedom would we report when we report the results of our study is (2,24).

Degree of freedom:

The statistical degrees of freedom (DF) indicate the number of independent values that can be changed in the analysis without violating the constraints.

degrees of freedom is the number of independent values that can be estimated in a statistical analysis. It can also be thought of as the number of values that are free to vary when estimating the parameters

DF = N – P

Where:

N = sample size

P = the number of relationships

We given that,

Number of groups , k = 3

Number of total participants, n = 27

Degrees of freedom for F-test is F(k-1,n-k)

= F(3-1 , 27-3)

= F(2,24)

Hence, (2,24,) are required two degrees of freedom.

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Answer:

I.4

ii.13

Step-by-step explanation:

....ur welcome........

To provide Logical Proofs with line-by-line justifications for the following arguments,

Let's use the first 4 rules of inference.

Given below is the justification for each step of the proof with the applicable rule of Inference.

E > M1. A > (E > ~F) Premise2. H v (~F > M) Premise3. A Premise4. ~H  Premise5. A > E > ~F 1, Hypothetical syllogism6.

E > ~F 5,3 Modus Ponens 7 .

~F > M 2,3 Disjunctive Syllogism 8.

E > M 6,7 Hypothetical SyllogismIf

A is true, then E must be true because A > E > ~F.

Also, if ~H is true, then ~F must be true because H v (~F > M). And if ~F is true,

Then M must be true because ~F > M. Therefore, E > M is a valid  based on the given premises using the first four rules of inference.

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Answer:

3 is the gradient ryt?

Step-by-step explanation:

so Ummm C?

Answer:

B cause it same

Step-by-step explanation:

If am wrong correct me thanks

\(n^{m}\) - \((n-1)^{m}\) * m + \((n-2)^{m}\) * (m choose 2) - \((n-1)^{m}\) * (m choose 3) + ... + \((-1)^{(n-1)}\) * \(1^{m}\) * (m choose n-1)

This formula gives the total number of ways to assign m jobs to n employees so that each employee is assigned at least one job.

What is combinatorics?

Combinatorics is a branch of mathematics that deals with counting and arranging the possible outcomes of different arrangements and selections of objects. It is concerned with the study of discrete structures, such as graphs, hypergraphs, and matroids, and their properties.

This problem is a classic example of applying the principle of inclusion-exclusion.

Let's start by assuming that we can assign any number of jobs to each employee, without the constraint that each employee must receive at least one job. In this case, the number of ways to assign m jobs to n employees would be n^m, since each job has n choices of employee to assign it to.

However, we need to subtract the number of cases where at least one employee is left without a job. This can happen in m different ways, since we can choose any of the m jobs to be unassigned. For each of these cases, there are \((n-1)^{m}\) ways to assign the remaining jobs to the n-1 remaining employees.

However, we have now "overcorrected" for cases where more than one employee is left without a job, since we have subtracted those cases twice (once for each pair of employees that are left out). To correct for this, we need to add back in the number of cases where at least two employees are left without a job. This can happen in (m choose 2) ways, since we can choose any pair of jobs to be unassigned. For each of these cases, there are \((n-1)^{m}\) ways to assign the remaining jobs to the remaining n-2 employees.

We continue this process of alternating subtraction and addition for all possible numbers of employees left without a job, up to n-1. The final answer is:

\(n^{m}\) - \((n-1)^{m}\) * m + \((n-2)^{m}\) * (m choose 2) - \((n-1)^{m}\) * (m choose 3) + ... + \((-1)^{(n-1)}\) * \(1^{m}\) * (m choose n-1)

This formula gives the total number of ways to assign m jobs to n employees so that each employee is assigned at least one job.

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Answer:

\(tan \: q = \sqrt{5} \div 2\)

Answer:

√5/2 or 1 (exact value is 2.2360679775/2)

Step-by-step explanation:

Q=2/OP

To find OP the equation will be like this:

2^2+b^2=3^2

4+b^2=9

b=√5

Q=√5/2

Answer:

B

Step-by-step explanation:

just did it

Answer:

\(\huge\boxed{Option \ B: 5\sqrt[3]{10} + 4\sqrt[3]{10} }\)

Step-by-step explanation:

\(\sf 9\sqrt[3]{10} \\We \ can \ split \ 9 \ into\ 5 \ and \ 4\\(5 + 4)\sqrt[3]{10} \\Applying distributive property\\5\sqrt[3]{10} + 4\sqrt[3]{10}\)