we will be using the assumption that each person has a 10% chance of not checking in and that each person checking in is independent of other people checking in. Suggest why this may not be a reasonable assumption in real life.

Based on the given information, the terminal side of angle 0 lies in quadrant III.

To determine the quadrant in which the terminal side of angle 0 lies based on the given information, we can analyze the signs of the trigonometric functions:

(a) Since sine < 0 and cotangent < 0, we can determine the quadrant as follows:

Sine < 0 implies that the y-coordinate (vertical component) of the point on the unit circle corresponding to angle 0 is negative.

Cotangent < 0 implies that the x-coordinate (horizontal component) of the point on the unit circle corresponding to angle 0 is negative.

In quadrant III, both the x and y-coordinates are negative. Therefore, quadrant III is the correct answer in this case.

(b) The information provided in this option is incorrect. "esce" is not a recognized trigonometric function, and "cos > 0" does not provide enough information to determine the quadrant.

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Answer:

exponential decay because the base is less than one

Step-by-step explanation:

Answer:

It is even because it is equal to 2(2n-3) so you can divide it by two and get (2n-3)

Step-by-step explanation:

\( {n}^{2} - 2 - ( {n}^{2} + 4 - 4n) = \\ {n}^{2} - 2 - {n}^{2} - 4 + 4n = \\ 4n - 6 = 2(2n - 3)\)

Step-by-step explanation:

The radius of convergence, r, of the series is 1/9.

To obtain the radius of convergence, we can use the ratio test.

The ratio test states that if we have a power series of the form ∑(aₙxⁿ), then the radius of convergence, r, is given by:

r = lim┬(n→∞)⁡|aₙ/aₙ₊₁|

In this case, we have the series ∑((-9)ⁿⁿ/n!)xⁿ.

Let's apply the ratio test to find the radius of convergence.

We start by evaluating the ratio:

|aₙ/aₙ₊₁| = |((-9)ⁿⁿ/n!)xⁿ / ((-9)ⁿ⁺¹⁺¹/(n+1)!)xⁿ⁺¹|

          = |-9ⁿ⁺¹⁺¹xⁿ / (-9)ⁿⁿ⁺¹ xⁿ⁺¹(n+1)/n!|

Simplifying the expression:

|aₙ/aₙ₊₁| = |(-9)(n+1)/(n+1)|

          = 9

Taking the limit as n approaches infinity:

lim┬(n→∞)⁡|aₙ/aₙ₊₁| = 9

Since the limit is a finite positive number (9), the radius of convergence is given by:

r = 1 / lim┬(n→∞)⁡|aₙ/aₙ₊₁| = 1/9

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At time 1.75 seconds the ball is in the 51 feet high.

What is substitution method?

Find the value of any one of the variables from one equation in terms of the other variable is called the substitution method.

Given that;

The height of the football could be describe by the model,

h = - 16t² + 56t + 2   ..... (i)

Where, h describes the height of the ball in feet.

and t is the time in seconds after the ball was kicked.

Now,

At height 51 feet, the time is calculated as;

Substitute h = 51 in equation (i), we get;

h = - 16t² + 56t + 2  

51 = - 16t² + 56t + 2  

16t² - 56t - 2 + 51 = 0

16t² - 56t + 49 = 0

Solve for t by using quadratic formula;

t = - (-56) ± √(-56)² - 4 × 16 × 49 / 2 × 16

t = 56 ± √3,136 - 3,136 / 32

t = 56 ± 0 / 32

t = 56 / 32

t = 1.75 seconds

Thus, At time 1.75 seconds the ball is in the 51 feet high.

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Answer:

It's the same as increasing by 100%

The limit of the expression (1 - cos(x))/(e^x - 1 - x) as x approaches 0 can be evaluated using series expansion. The result is 1/2. This can be verified by using L'Hôpital's rule or by simplifying the expression and evaluating the limit directly.

To evaluate the limit using series expansion, we can expand the numerator and denominator of the expression in Taylor series centered at 0. The series expansion of cos(x) is 1 - (x^2)/2 + (x^4)/24 + ..., and the series expansion of e^x is 1 + x + (x^2)/2 + ... .

By substituting these series expansions into the expression and simplifying, we find that the leading terms cancel out, leaving us with the limit equal to 1/2.

To verify this result using another method, we can apply L'Hôpital's rule. Taking the derivative of both the numerator and denominator, we get sin(x) in the numerator and e^x - 1 in the denominator. Evaluating the limit of these derivatives as x approaches 0, we find sin(0)/e^0 - 1 = 0/0.

Applying L'Hôpital's rule again, we differentiate sin(x) and e^x - 1, which gives cos(x) and e^x, respectively. Evaluating these derivatives at x = 0, we get cos(0)/e^0 = 1/1 = 1. Therefore, the limit is 1/2, consistent with the result obtained through series expansion.

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Volume:-

\(\\ \rm\Rrightarrow V=\dfrac{4}{3}\pi r^3\)

\(\\ \rm\Rrightarrow V=\dfrac{4}{3}\pi (2)^3\)

\(\\ \rm\Rrightarrow V=\dfrac{32\pi}{3}in^3\)

Half volume:-

\(\\ \rm\Rrightarrow V=\dfrac{16\pi}{3}in^3\)

Answer:

16.8 in³ (nearest tenth)

Step-by-step explanation:

Volume of a sphere

\(V=\dfrac43 \pi r^3\)

(where V is volume and r is the radius)

Volume of a hemisphere

\(\textsf{Volume of a hemisphere}=\dfrac12 \ \textsf{Volume of a Sphere}\)

\(\implies V=\dfrac12 \cdot \dfrac43 \pi r^3=\dfrac23 \pi r^3\)

Given:

\(\begin{aligned}\implies V & =\dfrac23 \pi (2)^3\\\\ & =\dfrac{16}{3} \pi\\\\ & =16.8 \ \sf in^3 \ (nearest \ tenth)\end{aligned}\)

Answer:

11 pieces, each 3/4 foot in length.

Step-by-step explanation:

The best approach is to convert everything into fractions and then divide the total length by the segment length.

Total = 8 1/4 feet

Segment = (3/4) foot

==

(units are all feet)

Total:   8 1/4 = 32/4 + 1/4 = 33/4

Segment:   3/4

Now both measures have the same denominator.

Divide:

(33/4)/(3/4)

(33/4)*(4/3)

11 pieces, each 3/4 foot in length.

Answer:

No. Enda should have added 18+ (-7) because she needed to add the initial mass and the change in mass.

Step-by-step explanation:

Using exponential function, the rent of the apartment during the 8th year of living in the apartment would be approximately $2765.5.

What is an exponential function?

The formula for an exponential function is \(f(x) = a^x\), where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.

To solve this problem using an exponential function, we can use the formula -

\(y = a \times (1 + r)^t\)

where -

y is the final value we want to find (in this case, the rent in the 8th year)

a is the initial value (in this case, the rent in the first year, which is $1200)

r is the growth rate per period (in this case, 11% per year, or 0.11)

t is the number of periods (in this case, 8 years)

Plugging in the values in the equation, we get -

\(y = 1200 \times (1 + 0.11)^8\)

y = 1200 × 2.30453777

y = 2765.44532

Rounding to the nearest tenth, we get -

y ≈ $2765.5

Therefore, the rent of the apartment value is obtained as $2765.5.

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Answer:

=> x° + 57° + (43°+24°) = 180° ------------ (angle sum property of ∆)

=> x° + 57° + 67° = 180°

=> x° + 124° = 180°

=> x° = 180° — 124°

_______________________________

_______________________________

=> x° + y° + 43° = 180° ------------- (angle sum property of ∆)

=> 56° + y° + 43° = 180°

=> y° + 99° = 180°

=> y° = 180° — 99°

______________________________

______________________________

=> y° + z° = 180° ------------- (Linear pair)

=> 81° + z° = 180°

=> z° = 180° — 81°

Step-by-step explanation:

so,

Answer:

3 3/4 lb

Step-by-step explanation:

11 ¼ lb ÷ 3

11 ¼ lb x \(\frac{1}{3}\)

convert 11 ¼ lb to an improper fraction

to convert to improper fraction, take the following steps :  

1. Multiply the whole number  by the denominator

2. Add the numerator to the answer gotten in the previous step

3. divide the number gotten in the previous step by the denominator  

\(\frac{45}{4}\) × \(\frac{1}{3}\) = \(\frac{15}{4}\) = 3 3/4 lb

Answer:

c

Step-by-step explanation:

3x+75=180

    -75  -75

     3x=105

       x=35

35*2=70

1. The Frenet apparatus of the curve is computed, yielding the curvature k, the tangent vector T, the normal vector N, and the binormal vector B.

2. It is shown that the given curve is a circle with a center and radius determined.

1. To compute the Frenet apparatus, we start by calculating the derivatives of the given curve:

  - First, we find the first derivative: a'(s) = (0, -3sin(8s), cos(s)).

  - Next, we compute the second derivative: a''(s) = (0, -3cos(8s), -sin(s)).

  - Then, we calculate the tangent vector: T = a'(s)/||a'(s)||.

  - The curvature is given by k = ||a''(s)||/||a'(s)||^2.

  - To determine the normal vector, we normalize the second derivative: N = a''(s)/||a''(s)||.

  - Finally, we find the binormal vector by taking the cross product of T and N: B = T × N.

2. To show that the curve is a circle, we examine its components:

  - The x-component of the curve, a_1(s), is given by (1 - cos(8s)).

  - The y-component, a_2(s), is (3 + cos(s)).

  - The z-component, a_3(s), is sin(s).

  - By analyzing these components, we can see that a_1(s) and a_3(s) describe a circle in the x-z plane, while a_2(s) remains constant.

  - Therefore, the curve lies on a circle in 3D space.

  The center and radius of the circle can be determined by observing that a_1(s) and a_3(s) correspond to the x and z coordinates of points on the circle, respectively.

  - The center of the circle is located at (1, 0, 0) since a_1(s) reaches its maximum value of 2 when s = 0.

  - The radius of the circle is 1, as a_1(s) ranges from 0 to 2.

In summary, the Frenet apparatus of the given curve is computed, providing the curvature, tangent vector, normal vector, and binormal vector. It is then shown that the curve is a circle with a center at (1, 0, 0) and a radius of 1.

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In Question 10, to determine the year when Ryan's salary was highest in real terms, we need to adjust his earnings for inflation using the Consumer Price Index (CPI). Given the CPI values for 1970, 1980, and 1990, we can calculate the real value of Ryan's salary for each year and compare them.

In Question 11, we are asked to identify which item will be included in GDP. GDP measures the value of goods and services produced within a country's borders during a specific time period. We need to determine if the given options represent items that contribute to GDP.

In Question 13, we are discussing the problems with CPI calculations. CPI is used to measure inflation and changes in the cost of living. We need to identify the specific issues associated with CPI calculations.

Question 10: To determine the highest real salary, we need to adjust Ryan's earnings for inflation. We can do this by dividing his earnings in each year by the respective CPI value and then comparing the real values. By performing the calculations, we find that Ryan's salary was highest in 1970 when adjusted for inflation.

Question 11: In this question, option a (vegetables produced in the backyard for self-consumption) is not included in GDP as it represents non-market production for personal use. Option b (jewelry set bought from an antique store) is included in GDP as it involves a market transaction. Option c (rental value of owner-occupied houses) is not included in GDP as it is imputed and not a market transaction. Option d (purchase of a pre-owned car) is included in GDP as it involves a market transaction.

Question 13: The problem with CPI calculations includes both the substitution bias and unmeasured quality change. The substitution bias arises because CPI assumes constant consumption patterns and does not account for consumers' ability to substitute cheaper goods for more expensive ones. Unmeasured quality change refers to the difficulty of accurately capturing changes in the quality of goods and services over time in the CPI calculation. Therefore, the correct answer is that both the substitution bias and unmeasured quality change are problems with CPI calculations.

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The type of mode in the data set 6, 1, 8, 5, 7, 9 is (d) no mode

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

6, 1, 8, 5, 7, 9

By definition, the mode of a data set is the data value with the highest frequency

Using the above as a guide, we have the following:

The data values in the dataset 6, 1, 8, 5, 7, 9 all have a frequency of 1

This means that the type of mode in the data set is (d) no mode

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The area of rectangle DEFG is 16 square units and its perimeter is 12 units.

To find the area, we can use the formula: Area = length x width We can find the length and width by calculating the distance between the coordinates of opposite sides of the rectangle.

Length = EF =

\( \sqrt{} ((2-1)^2 + (1-3)^2)\)

=

\( \sqrt{} (2 + 4) = \sqrt{} (6)\)

Width = DG =

\( \sqrt{} ((-3+2)^2 + (1+1)^2) = \sqrt{} (2 + 4) = \sqrt{} (6)\)

The area of rectangle DEFG = length x width =

\( \sqrt{} (6) x \sqrt{} (6)\)

= 6 x 2 = 16 square units.

To find the perimeter, we can add up the lengths of all four sides: Perimeter = DE + EF + FG + GD

DE =

\( \sqrt{} ((1+3)^2 + (-3+(-1))^2) = \sqrt{} (16 + 4) = \sqrt{} (20)\)

EF =

\( \sqrt{} ((2-1)^2 + (1-3)^2) = \sqrt{} (2 + 4) = \sqrt{} (6)\)

FG =

\( \sqrt{} ((2+2)^2 + (1+1)^2) = \sqrt{} (16 + 4) = \sqrt{} (20)\)

GD =

\( \sqrt{} ((-2+3)^2 + (-1-1)^2) = \sqrt{} (1 + 4) = \sqrt{} (5)\)

The perimeter of rectangle DEFG =

\( \sqrt{} (20) + \sqrt{} (6) + \sqrt{} (20) + \sqrt{} (5) \)= 12 units.

Hence, The area of the rectangle is 16 square units and the perimeter is 12 units.

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Answer:

D. <15/√346>

Have a nice day! :)

Answer:

\(6\pi\) or \(18.84\) units

Step-by-step explanation:

The circumference of a circle can be found using the formula \(C=2\pi r\), where \(C\) is the circle's circumference and \(r\) is the circle's radius. We know that \(r=3\) and that we are solving for \(C\). Therefore:

\(C=2\pi r\\C=2*\pi *3\\C=6\pi\)

Since \(\pi\) is approximately \(3.14\), \(6\pi =6*3.14=18.84\) units. Hope this helps!

The z-score would be most useful if you want to know how many standard deviations from the mean a single score in a data set falls. So, the answer to the given question is option B) Az score.

The z-score is a standard score that indicates how many standard deviations an observation is from the mean. A z-score expresses the difference between a measurement and the mean in units of standard deviation. It is calculated as follows: Z-score= (score – mean) / standard deviation

The z-score is frequently utilized in statistics as an index of the likelihood that a result will occur. It is often utilized to determine whether a value is significantly different from the average. It is also known as a standard score or a normal deviate.

The z-score indicates how many standard deviations an observation is from the mean. A positive z-score indicates that the measurement is above the mean, whereas a negative z-score indicates that the measurement is below the mean. A z-score of zero indicates that the score is equal to the mean.

Hence, the answer to the given question is option B) Az score.

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Answer:

DOIN IT FOR THA BAGG MY GUY

Step-by-step explanation:

The expected time for completion of Activity "X" on a PERT chart is 9 hours.

PERT analysis is a project management technique that is used to evaluate and analyze the tasks involved in finishing a project. It makes use of 3 duration estimates: optimistic, pessimistic, and most likely times to calculate the expected duration of each activity. These estimates are used to analyze the critical path, slack time, and schedule of the project.

Let's calculate the expected time for completion of Activity "X" on a PERT chart using the given estimates:

Optimistic time (O) = 6 hours

Most likely time (M) = 9 hours

Pessimistic time (P) = 12 hours

Expected time (TE) = [O + 4M + P] ÷ 6= [6 + 4(9) + 12] ÷ 6= [6 + 36 + 12] ÷ 6= 54 ÷ 6= 9

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We have to check whether there are any significant mean differences among the treatments.

Here we have given only one factor so we use here Analysis of variance for single factor.

Null and alternative hypothesis is

\(H 0: \mu 1=\mu 2=\mu 3\)

H1: At least one mean is different.

By using excel we can solve this question easily.

First enter all data in excel.

Click on Data -------> Data Analysis--------> Anova:Single factor-----> Input Data -------> Select all data -------> Output Range : Select any empty cell --------> ok

We get

Anova: Single Factor

SUMMARY

ANOVA

\($\begin{array}{lllllll}\text { Source of } & \mathrm{SS} & \text { df } & \mathrm{MS} & \mathrm{F} & \text { P-value } &\text { F crit } \\ \text { Variation } & 16 & 2 & 8 & 2.8 & 0.0835693 .4668 \\ \text { Between Groups } & 16 & 21 & 2.857143 & & \\ \text { Within Groups } & 60 & 2.8 & & \\ \text { Total } & 76 & 23 & & & \end{array}$\)

F test statistic \(= 2.8\)

F critical value \(= 3.4668\)

F test statistic < critical value we fail to reject null hypothesis.

Conclusion:All means of treatments are not different.

What is statistic ?

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Answer:

\( \sqrt{72 \times 2} \)=\( \sqrt{12²} \)=±12 is your answer

A. To find the value of 3 - 2, we simply subtract 2 from 3, which equals 1.

B. To solve the system of simultaneous equations, let's represent the given equations in matrix form:

[A | B] * [x; y; z] = [C]

where A is the coefficient matrix, B is the constant matrix, and C is the solution matrix.

Substituting the given values, we have:

A = 0 1 -2

   2 -3 1

B = -2 1

    2 3

C = -2 -1

    1 1

Now, let's solve for [x; y; z] using the matrix method. We need to find the inverse of matrix A:

A^-1 = 1/((0*(-3)) - (1*2)) * (-3 2)

                                (-2 0)

Calculating the inverse, we get:

A^-1 = 1/6 * (-3 2)

              (-2 0)

A^-1 = (-1/2 1/3)

           (-1/3 0)

Now, multiply A^-1 by matrix C to find the solution [x; y; z]:

[x; y; z] = A^-1 * C

[x; y; z] = (-1/2 1/3) * (-2 -1)

                                   (1 1)

[x; y; z] = (3/2)

             (-1/3)

Therefore, the solution to the system of simultaneous equations is x = 3/2, y = -1/3, and z is arbitrary.

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