Question 25?Find the inverse of the given function. Graph both functions on the same set of axes and show the line Y=x as a dotted line on the graph?

The interquartile range (IQR) of the data is 2, meaning that the middle 50% of the data falls within a range of 2 units.

To find the interquartile range, we first need to find the median of the data set. The median is the middle value when the data is arranged in numerical order. In this case, there are 16 data points, so the median is the average of the two middle values, which are 6 and 6. Therefore, the median is 6.

Next, we need to find the first and third quartiles of the data set. The first quartile (Q1) is the value below which 25% of the data falls, and the third quartile (Q3) is the value below which 75% of the data falls. To find these values, we first need to arrange the data in numerical order:

{3, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9}

To find Q1, we take the median of the lower half of the data set, which is {3, 4, 5, 5, 5, 6, 6, 6}, giving us a value of 5. To find Q3, we take the median of the upper half of the data set, which is {7, 7, 8, 8, 8, 8, 9, 9}, giving us a value of 8.

Finally, we can find the interquartile range (IQR) by subtracting Q1 from Q3. In this case, IQR = 8 - 5 = 3. However, the question asks for the answer to the nearest unit, so we round to the nearest whole number and report the IQR as 2. This means that the middle 50% of the data falls within a range of 2 units, from 5 to 7.

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The area of the given sector above would be = 33.5un²

To determine the area of the sector given above, the formula for the area of a sector needs to be used such as follows;

Area of a sector = πr²× ∅/360

where;

radius = 8

∅ = 60°

Area of sector = 3.14×8×8×60/360

= 12057.6/360

= 33.5un²

Therefore, the area of the given sector of the circle = 33.5un²

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Answer:

93.75 boxes

25/2 = 12.5 per hour

12.5*7.5 = 93.75

Answer:

To create a matrix for this linear system, we can arrange the coefficients of the variables and the constants into a matrix as follows:

| 1 3 2 | | x | | 26 |

| 1 -3 4 | x | y | = | 2 |

| 2 1 1 | | z | | 8 |

To solve the system using row reduction, we can perform elementary row operations to transform the matrix into row echelon form or reduced row echelon form. I will use the latter approach for simplicity:

| 1 0 0 | | x | | 6 |

| 0 1 0 | x | y | = | 5 |

| 0 0 1 | | z | | -1 |

Therefore, the solution to the system is x = 6, y = 5, and z = -1.

To evaluate the triple integral ∭ √(x^2 + y^2) dV using cylindrical coordinates, we need to express the integrand and the volume element in terms of cylindrical coordinates.

In cylindrical coordinates, we have:

x = ρcos(θ)

y = ρsin(θ)

z = z

The volume element in cylindrical coordinates is given by:

dV = ρ dz dρ dθ

Now let's substitute these expressions into the integrand:

√(x^2 + y^2) = √((ρcos(θ))^2 + (ρsin(θ))^2) = √(ρ^2(cos^2(θ) + sin^2(θ))) = ρ

Therefore, the triple integral becomes:

∭ ρ ρ dz dρ dθ

To evaluate this integral, we need to determine the limits of integration for each variable.

For ρ, it depends on the region of integration. Let's assume the region is bounded by ρ = a and ρ = b, where a and b are constants.

For θ, it typically ranges from 0 to 2π (a full revolution).

For z, it depends on the height of the region, so let's assume the limits are from z = c to z = d, where c and d are constants.

The integral becomes:

∫∫∫ ρ ρ dz dρ dθ

Integrating with respect to z first:

∫(c to d) ∫(a to b) ∫(0 to 2π) ρ ρ dθ dρ dz

Integrating with respect to θ:

∫(c to d) ∫(a to b) [(1/2)ρ^2] (2π) dρ dz

Simplifying:

2π ∫(c to d) ∫(a to b) (1/2)ρ^2 dρ dz

Integrating with respect to ρ:

2π ∫(c to d) [(1/6)ρ^3] (a to b) dz

Simplifying:

(2π/6) ∫(c to d) [(b^3 - a^3)] dz

(π/3) ∫(c to d) [(b^3 - a^3)] dz

Evaluating the integral with respect to z:

(π/3) [(b^3 - a^3)] (d - c)

So, the value of the triple integral ∭ √(x^2 + y^2) dV using cylindrical coordinates is (π/3) [(b^3 - a^3)] (d - c).

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Given an AR(1) process with drift X = α + βX_{t-1} + ε_t, where α = 2, β = 0.7, and ε_t ~ N(0, 1).To find the mean of the process, we note that the AR(1) process has a mean of μ = α / (1 - β).

So, the mean is 6.67, the variance is 5.41, the first three ACF are 0.68, 0.326, and 0.161, and the first three PACF are 0.7, -0.131, and 0.003.

So, substituting α = 2 and β = 0.7,

we have:μ = α / (1 - β)

= 2 / (1 - 0.7)

= 6.67

To find the variance, we note that the AR(1) process has a variance of σ^2 = (1 / (1 - β^2)).

So, substituting β = 0.7,

we have:σ^2 = (1 / (1 - β^2))

= (1 / (1 - 0.7^2))

= 5.41

To find the first three autocorrelation functions (ACF) and the first 3 partial autocorrelation functions (PACF), we can use the formulas:ρ(k) = β^kρ(1)and

ϕ(k) = β^k for k ≥ 1 and

ρ(0) = 1andϕ(0) = 1

To find the first three ACF, we can substitute k = 1, k = 2, and k = 3 into the formula:

ρ(k) = β^kρ(1) and use the fact that

ρ(1) = β / (1 - β^2).

So, we have:ρ(1) = β / (1 - β^2)

= 0.68ρ(2) = β^2ρ(1)

= (0.7)^2(0.68) = 0.326ρ(3)

= β^3ρ(1) = (0.7)^3(0.68)

= 0.161

To find the first three PACF, we can use the Durbin-Levinson algorithm: ϕ(1) = β = 0.7

ϕ(2) = (ρ(2) - ϕ(1)ρ(1)) / (1 - ϕ(1)^2)

= (0.326 - 0.7(0.68)) / (1 - 0.7^2) = -0.131

ϕ(3) = (ρ(3) - ϕ(1)ρ(2) - ϕ(2)ρ(1)) / (1 - ϕ(1)^2 - ϕ(2)^2)

= (0.161 - 0.7(0.326) - (-0.131)(0.68)) / (1 - 0.7^2 - (-0.131)^2) = 0.003

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Answer: 2/9

Step-by-step explanation:

Simplify the expression.

Answer:

1) 80+(-20)

2) -13+9

3) -5+(8)

I don't quite know how to explain

Just think about 1) 60 is the new temperature, in order to have an addition problem we're going to have to use negative numbers. Since we had to subtract 20, in order to use addition it would be 80+(-20).

Yes, it would be appropriate to use these values to carry out a two-sample z-test to evaluate whether the difference between doctors and pharmacists is real.  

Here are the steps to perform the two-sample z-test:
1. Define the null and alternative hypotheses:
  - Null hypothesis (H0): There is no significant difference between the proportions of respondents who rate medical doctors .
 
2. Calculate the standard error (SE) for the difference in proportions using the formula:
  SE = sqrt(p1*(1-p1)/n1 + p2*(1-p2)/n2)
  where p1 and p2 are the proportions of respondents who rated doctors and pharmacists as .

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The given values from the Gallup poll are not sufficient to carry out a two-sample z test and determine whether the difference between doctors and pharmacists is statistically significant.

Based on the information provided, it would not be appropriate to use these values to carry out a two-sample z test to evaluate whether the difference between doctors and pharmacists is real.

Here's why: The Gallup poll asked respondents to rate the honesty and ethical standards of people in different fields. The ratings for medical doctors and pharmacists were "very high or high" for 65% and 67% of respondents, respectively. However, these percentages alone do not provide enough information to carry out a statistical test.

To conduct a two-sample z test, we would need to know the sample sizes for both doctors and pharmacists, as well as the actual number of respondents who rated them "very high or high." We would also need to assume that the samples were randomly selected and independent.

Without this additional information, we cannot calculate the necessary statistics for a two-sample z test.

Therefore, the given values from the Gallup poll are not sufficient to carry out a two-sample z test and determine whether the difference between doctors and pharmacists is statistically significant.

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A pivot table is a table of grouped values that aggregates the individual items of a more extensive table within one or more discrete categories. This summary might include sums, averages, or other statistics, which the pivot table groups together using a chosen aggregation function applied to the grouped values.

To display the two key averages from the pivot table on the Summary sheet, follow these steps:
1. Open the Summary sheet.
2. In cell B2, insert the GETPIVOTDATA function. This function retrieves data from a pivot table based on specified criteria.
3. The function in cell B2 should reference cell C4 on the Pivot Table in the Sold Out sheet. This means the formula in B2 should be: =GETPIVOTDATA(C4, Sold Out'!$A$1).
  - The first argument of the function (C4) specifies the value or field you want to retrieve from the pivot table.
  - The second argument ('Sold Out) specifies the location of the pivot table. 'Sold Out' refers to the name of the sheet where the Pivot Table is located, and A is the cell reference of the top-left cell of the pivot table.
4. In cell B3, insert another GETPIVOTDATA function. This time, the function should reference cell C9 on the pivot table in the Sold Out sheet. The formula in B3 should be: =GETPIVOTDATA(C9,'Sold Out'!$A$1).
  - Similar to the previous step, the first argument (C9) specifies the value or field you want to retrieve from the pivot table.
  - The second argument ('Sold Out'!$A$1) again specifies the location of the PivotTable.

By using the GETPIVOTDATA function with the appropriate cell references, you can display the desired averages from Pivot Table on the Summary sheet.

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Answer:

The mean will be 420 without round of and after round of it will be 400

The value of mean absolute deviation of the numbers is,

⇒ 4.3

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

The numbers below represent the speeds of the last 6 vehicles that a police officer recorded:

⇒ 68, 72, 78, 59, 73, 70

Hence, Mean of data set is,

= (68 + 72 + 78 + 59 + 73 + 70)/ 6

= 70

So, The value of mean absolute deviation of the numbers is,

⇒ |68- 70| + |72 - 70| + |59 - 70| + |73 - 70| + |70 - 70| / 6

⇒ 13 / 3

⇒ 4.3

Thus, The value of mean absolute deviation of the numbers is,

⇒ 4.3

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The algebraic equation corresponding to the given initial value problem is:

Y(s) = 8/(s^2(s^2+4)) + (8s+5)/(s^2+4)

To create the corresponding algebraic equation for the given initial value problem, we need to take the Laplace transform of both sides of the differential equation.

Given differential equation is y"+4y=8t, y(0)=8, y'(0)=5.

Taking the Laplace transform of both sides of the differential equation, we get:

L(y") + 4L(y) = 8L(t)

Using the Laplace transform property L(y") = s^2 Y(s) - s y(0) - y'(0), where Y(s) is the Laplace transform of y(t), we can rewrite the above equation as:

s^2 Y(s) - s y(0) - y'(0) + 4Y(s) = 8/s^2

Substituting y(0) = 8 and y'(0) = 5, we get:

s^2 Y(s) - 8s - 5 + 4Y(s) = 8/s^2

Simplifying the above equation, we get:

Y(s) = 8/(s^2(s^2+4)) + (8s+5)/(s^2+4)

Therefore, the algebraic equation corresponding to the given initial value problem is:

Y(s) = 8/(s^2(s^2+4)) + (8s+5)/(s^2+4)

where Y(s) is the Laplace transform of y(t).

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Degree of h(x) is 5 because there are 5 x intercepts

Given :

The function h(x) has a zero of x = 2 + 7i with a multiplicity of one.

Every x intercept has multiplicity 1

Explanation

x intercept x=2+7i has multiplicity one

For complex intercepts occurs in pairs

So another x intercept is x=2-7i

From the given table , when h(x) is 0 then x is the x intercepts

other x intercepts from the given table are  -5, 4,10

There are 5 x intercepts with multiplicity one

h(x) has 5 x intercepts . so , the degree of h(x) is 5

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Answer:

5

Step-by-step explanation:

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Journal articles and research reports are widely recognized as the most common types of secondary sources used in education. In the field of education, secondary sources play a crucial role in providing researchers and educators with valuable information and scholarly insights.

Among the various types of secondary sources, journal articles and research reports hold a prominent position. These sources are often peer-reviewed and published in reputable academic journals or research institutions. They provide detailed accounts of research studies, experiments, analyses, and findings conducted by experts in the field. Journal articles and research reports serve as reliable references for educators and researchers, offering up-to-date information and contributing to the advancement of knowledge in the education domain. Their prevalence and credibility make them highly valued and frequently consulted secondary sources in educational settings.

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The probability that both Rachel and Robert are in the picture is 3/16.

The terms probability and possibility are interchangeable. It is a mathematical branch concerned with the occurrence of a random event. The value is between 0 and 1. In mathematics, the probability was introduced to predict the likelihood of events occurring.

Given that

Rachel and Robert both begin at the same point

Rachel completes a lap every 90 seconds.

Robert completes a lap every 80 seconds.

The photographer captures 1/4th of the track, centered on the starting line.

As a result, the photo captures 1/8th of the track on either side of the starting line.

The photographer captures it between 10 and 11 minutes, or 600 and 660 seconds.

Let us calculate the time interval between 600 and 660 seconds during which Rachel and Robert will be running in the quarter-length region of the track centered on the starting line. Specifically, 1/8th of the track length on each side of the starting line.

Robert will complete 1/8th of a lap in 10 seconds. So, between 630 and 650 seconds, Robert will be in the area of the ground captured by the photographer.

Rachel finishes one lap in 90 seconds. As a result, Rachel will take the starting line at the 630th second (after 7 laps).

Rachel will complete 1/8th of a lap in 90/8 seconds. So, Rachel will be in the area of the ground captured by the photographer from (630 - 90/80) seconds to (630 + 90/80) seconds.

i.e., for a duration of 90/80 seconds out of the 60 seconds both of them are in the frame captured by the photographer.

Required probability = {time window in which both Rachel and Robert are in the favorable zone}/{time window in which the photographer captures the picture}

= {90/8}/60

= 3/16

Therefore the probability that both Rachel and Robert are in the picture is 3/16

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Answer:

I believe the answer is 18/1

Answer:

x^(4+2/3)=x^a

a=4+2/3=(12/3)+(2/3)=14/3

Step-by-step explanation:

Answer:

For the equation given:

\(x + 2y = 16 \\ 2y = - x + 16 \\ y = - \frac{1}{2} x + 8\)

for perpendicular lines, the relationship between their slopes is given by:

\(m _{1} \times m _{2} = - 1\)

m1 is slope for one line, and m2 is slope for another line.

\( - \frac{1}{2} \times m_{2} = - 1 \\ \\ m_{2} = - 1 \times - 2 \\ { \underline{ \: \: m_{2} = 2 \: \: }}\)

Therefore, equation is;

\({ \boxed{ \boxed{y = 2x - 2}}}\)

The probability that  is more likely between selecting a tube of blue or yellow paint, OR selecting a tube of green or red paint id; Both are equally lilkely.

We are given;

Number of blue tubes = 7

Number of red tubes = 4

Number of yellow tubes = 3

Number of green tubes = 6

Thus;

Total number of painted tubes = 7 + 4 + 3 + 6 = 20

Probability of selecting a blue tube = 7/20

Probability of selecting a red tube = 4/20

Probability of selecting a yellow tube = 3/20

Probability of selecting a green tube = 6/20

Thus;

P(selecting a tube of blue or yellow paint) = (7/20) + (3/20) = 10/20

P(selecting a tube of green or red paint) = (6/20) + (4/20) = 10/20

Thus, they are equally likely.

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During that hour, the cola bottling facility increased their efficiency more compared to the water bottling facility.To determine which facility increased their efficiency more during that hour, we need to calculate the deviation from the mean for each facility.

For the water bottling facility, the deviation is calculated as:
(37.4 - 35.2) / 2.04 = 1.08
For the cola bottling facility, the deviation is calculated as:
(28.8 - 26.9) / 1.51 = 1.26
Since the deviation for the cola bottling facility is higher, this means that they had a larger increase in efficiency during that hour compared to the water bottling facility.
To determine which facility increased their efficiency more during that hour, we will calculate the number of standard deviations away from the mean for each facility's performance.
1. Calculate the deviations for each facility:
Water bottling facility:
Deviation = (Actual bottles - Mean bottles) / Standard deviation
Deviation = (37.4 - 35.2) / 2.04
Deviation ≈ 1.08
Cola bottling facility:
Deviation = (Actual bottles - Mean bottles) / Standard deviation
Deviation = (28.8 - 26.9) / 1.51
Deviation ≈ 1.26
2. Compare the deviations:
The cola bottling facility has a higher deviation (1.26) than the water bottling facility (1.08).
Conclusion:
During that hour, the cola bottling facility increased their efficiency more compared to the water bottling facility.

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Answer:

D

Step-by-step explanation:

Given

x³ + 2x² + 7x + 14 ( factor the first/second and third/fourth terms )

= x²(x + 2) + 7(x + 2) ← factor out (x + 2) from each term

= (x² + 7)(x + 2) → D

Step-by-step explanation:

p^(-5)  =  1 / p^5  =  1/14^5  = 1.859 x 10^-6

Answer: A

Step-by-step explanation:

Answer:

The diameter of the sphere with the given volume is 24.268 units

Step-by-step explanation:

Volume of a sphere is given by the equation:

\(V=4/3\pi r^3\)

Plug in your volume and solve for r

\(7483=4/3\pi r^3\)

\(7483(3/4)=\pi r^3\)

\(5612.25=\pi r^3\)

\(5612.25/\pi =r^3\)

\(1786.43=r^3\)

\(\sqrt[3]{1786.43}=r\)

\(r = 12.134\) units

\(d = 2r\)

\(d = 2(12.134)\)

\(d = 24.268\) units

Answer:

4 grams in 2/3 liter of soda.

Answer:

$1551 needed to cover the costs and 141 shirts will be sold.

Step-by-step explanation:

If a shirt costs $10 and the council is selling the shirt for $1 more ($11), after selling 141 shirts, they would have made a profit of $1*141=$141. Since there is also a setup fee of $141, the profit would actually be $0. This is when the costs are covered.

C = 10s + 141 (C is cost and s in no. of shirts sold)

s = 141

C = 141*10 + 141 = 1551

Hope this helps!