In a multiple regression model, the error term `e’ is assumed to be a random variable with a mean ofA)zero.B)-1.C)1.D)any value.

Answer:

<BAC = 78

<ABC = 68

Step-by-step explanation:

The remote angles theorem states that when one extends a side of a triangle, the angle formed between the extension and one of the sides of the triangle is equal to the sum of the two non-adjacent angles inside the triangle. One can apply this theorem here and state the following,

<BAC + <ABC = <ACD

Substitute,

(5y + 3) + (4y + 8) = (146)

Simplify,

9y + 11 = 146

Inverse operations,

9y + 11 = 146

     -11     -11

9y = 135

/9      /9

y = 15

Now substitute this value back into the expressions to find the numerical measurement of (<BAC) and (<ABC),

<BAC = 5y + 3

5(15) + 3

78

<ABC = 4y + 8

4(15) + 8

68

Answer:

Given that the garden is a right triangle with base 25m start and height 30 m The length of the hypothenus can be achieved by using pythagorean theorem. Please find the attached file for the diagram. I made a large unit for the sake of clarity.

Answer:

6.0 on the left side 5.0 at the bottom 7.8 on the right side

Step-by-step explanation:

To evaluate the indefinite integral ∫(44 / (1 + x²)) dx, we can use the trigonometric substitution method. Let's substitute x = tanθ, then dx = sec²θ dθ.

Substituting these values into the integral, we have:

∫(44 / (1 + x²)) dx = ∫(44 / (1 + tan²θ)) sec²θ dθ

Simplifying the denominator using the trigonometric identity: 1 + tan²θ = sec²θ, we get:

∫(44 / sec²θ) sec²θ dθ = ∫44 dθ

Integrating 44 with respect to θ, we obtain:

44θ + C

Now, we need to convert back to the original variable x. Since x = tanθ, we can use the inverse tangent function to find θ. Therefore, θ = arctan(x).

Substituting θ = arctan(x) into the previous result, we have:

44θ + C = 44arctan(x) + C

Therefore, the indefinite integral of (44 / (1 + x²)) dx is 44arctan(x) + C, where C is the constant of integration.

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Answer:

scalene triangle

Step-by-step explanation:

hshavsgtsusbevebbeush

Answer:

180

Step-by-step explanation:

V=lwh

3=10·9·6

3=180

The probability of getting stuck in traffic on any given day when leaving the city is 70%. When considering two separate days, we can use the multiplication rule of probability to find the probability of getting stuck in traffic on both days.

The multiplication rule of probability states that the probability of two independent events occurring together is the product of their individual probabilities. In this case, the events of getting stuck in traffic on two separate days are independent, meaning that the occurrence of one does not affect the probability of the other.

To find the probability of getting stuck in traffic on both days, we can multiply the probability of getting stuck on the first day (0.7) by the probability of getting stuck on the second day (also 0.7):

P(getting stuck on both days) = P(getting stuck on day 1) x P(getting stuck on day 2)
P(getting stuck on both days) = 0.7 x 0.7
P(getting stuck on both days) = 0.49 or 49%

Therefore, the probability of getting stuck in traffic on both days is 49%. This means that there is a less than 50% chance of getting stuck in traffic on both days, despite the 70% chance of getting stuck on each individual day.

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The given statement "Using p-value rule for a population proportion or mean, if the level of significance is less than p-value, null hypothesis is rejected." is True because the hypothesis is rejected in this case.

In hypothesis testing, the p-value is the probability of observing a test statistic as extreme as, or more extreme than, the observed test statistic, assuming that the null hypothesis is true. The level of significance, denoted by alpha, is the maximum probability of rejecting the null hypothesis when it is actually true.

If the p-value is less than the level of significance, it means that the observed test statistic is unlikely to have occurred by chance alone, assuming the null hypothesis is true. Therefore, we reject the null hypothesis in favor of the alternative hypothesis at the given level of significance.

For example, suppose we are testing the hypothesis that the population mean is equal to a certain value. If the p-value is 0.02 and the level of significance is 0.05, we would reject the null hypothesis because the p-value is less than the level of significance.

This means that there is strong evidence against the null hypothesis and we can conclude that the population mean is likely different from the hypothesized value.

In summary, if the level of significance is less than the p-value, we reject the null hypothesis in favor of the alternative hypothesis at the given level of significance.

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Answer:

Step-by-step explanation:

To answer this we need only know that negative parabolas are upside down, so by definition, it has a max point at the vertex. To find the vertex (h, k), the easy way to do this is to fill in the following expressions for h and k and solve:

\(h=\frac{-b}{2a}\)  and  \(k=c-\frac{b^2}{4a}\) (These are derived from the quadratic formula). Filling in knowing our a = -1, b = -7, c = 12:

\(h=\frac{-(-7)}{2(-1)}=\frac{7}{-2}=-\frac{7}{2}\)  and

\(k=12-\frac{(-7)^2}{4(-1)}=12-(\frac{49}{-4})=12+\frac{49}{4}=\frac{97}{4}\) so the vertex (aka max height occurs at \((-\frac{7}{2},\frac{97}{4})\). Depending upon what is meant by stating the max value, we may only need to state the k value (which is the same as the y coordinate, which is an up or down thing as opposed to the x value which is a side to side thing). The domain is all real numbers, as is the case for all x-squared parabolas, and the range is

R = {y | y ≤ 97/4}

I can't see your choices so match them up from these answers to the ones in the list of choices.

Answer:

y = 5

Step-by-step explanation:

-4(2y) +11y = 15

-8y + 11y = 15

3y = 15

y = 5

The Solution:

Given:

By Z-statistic formula:

Substitute:

From the Z-scores tables:

Converting to percentage, multiply by 100 to get:

Therefore, the correct answer is 8.08%

Answer:

20 and 24

Step-by-step explanation:

You can write 5:6 as 5x:6x. You know that 5x+8=7x or that 6x+8=8x. You can solve either one and then you get x=4. Then you can plug it in. I hope this is helpful!

The measure of angle BDC and angle BAC in the given circle is 58 degrees and 29 degrees respectively.

An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.

The relationship between an inscribed angle and an intercepted arc is expressed as:

Inscribed angle = 1/2 × intercepted arc.

From the diagram:

Central angle BDC =?

Inscribed angle BAC =?

Measure of arc BC = 58 degrees

a)

Measure of central angle BDC:

From the angle-arc relationship, the central angle of a circle is equal to its intercepted arc.

Since the measure of arc BC = 58 degrees

Central angle BDC = 58°

b)

Inscribed angle BAC:

Inscribed angle = 1/2 × intercepted arc.

Plug in the values:

Inscribed angle BAC = 1/2 × 58°

Inscribed angle BAC = 29°

Therefore, the measure of angle BAC is 29 degrees.

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the error bound for the mean U.S. household income is +/- $234, while the point estimate is $63179.

A yearly census identical to the one performed every ten years is conducted by the American Community Survey (ACS), a division of the United States Census Bureau, but with a lower participation rate. Since the most recent poll has high confidence that the mean household income in the United States is between, the point estimate for that income is $63179, and the error bound is +/- $234.

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Answer:

A

Step-by-step explanation:

The formula distance = speed x time must be used to calculate the duration of a marathon as a function of the runner's average speed.

 1: List the known data. For example, a marathon is 13.1 miles long, and an average runner moves at s miles per hour.

2 :Rearrange the equation to solve for time in Step 2: Time = Speed/Distance

3: Enter the known numbers for distance and speed into the equation: time = 13.1 miles per second.

4: If necessary, simplify the equation. The units of miles will cancel out because the time is measured in hours and the speed in miles per hour, therefore the ultimate unit of time will be hours.

  The final answer  is t = 13.1/s, which expresses the duration of a marathon (in hours) as a function of the runner's average speed (in miles per hour).

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The limit of (-8)^n / n^2 as n approaches infinity is -infinity.

To apply the ratio test to the series ∑(n=1 to infinity) (-8)^n / n^2, we need to compute the limit of the absolute value of the ratio of consecutive terms:

|(-8)^(n+1) / (n+1)^2|    |-8 / (n+1)^2|

lim -------------------- = lim ------------ = 0

n → infinity   |(-8)^n / n^2|   |(-8) / n^2|

Since the limit of this ratio is 0, which is less than 1, the series ∑(n=1 to infinity) (-8)^n / n^2 converges by the ratio test.

To identify the nth term, we can observe that the general term of the series is given by:

an = (-8)^n / n^2

To evaluate the limit, we need to use L'Hopital's rule:

lim n → infinity (-8)^n / n^2 = lim n → infinity (ln(-8))^n / (2n)

Now we can apply L'Hopital's rule again:

lim n → infinity (ln(-8))^n / (2n) = lim n → infinity [(ln(-8))^n * ln(-8)] / 2 = -infinity

Therefore, the limit of (-8)^n / n^2 as n approaches infinity is -infinity.

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Answer: One newton-meter is equal to 8.8507457676 inch pounds.

Step-by-step explanation:

As a simple example, if you wish to convert 5 newton-meters into inch pounds, you should multiply 5 by 8.8507457676 to give you a total of 44.253728838 inch pounds (or 44.254 rounded to 3 decimal places).

One newton-meter is equal to 8.8507457676 inch pounds.

What is nanometer ?

A nanometer (NM) is a unit of size this is equal to at least one billionth of a meter. it's miles extensively used as a scale for building tiny, complex, and atomic scale computing and digital additives - mainly in nanotechnology

As a simple example, if you wish to convert 5 newton-meters into inch pounds,

you should multiply 5 by 8.8507457676 to give you a total of 44.253728838 inch pounds (or 44.254 rounded to 3 decimal places).

Therefore, One newton-meter is equal to 8.8507457676 inch pounds.

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On a number line, an absolute value equation that has the given solution set is |m - 4| = 2.

By critically observing the given question, we can infer and logically deduce that the solution sets for this absolute value equation is given by:

m = {2, 6}

Next, we would calculate the mean of the solution sets as follows:

m₁ = (2 + 6)/2

m₁ = 8/2

m₁ = 4.

Also, we would calculate the difference in the solution sets as follows:

m₂ = (6 - 2)/2

m₂ = 4/2

m₂ = 2.

Mathematically, the absolute value equation is given by:

|m - m₁| - m₂ = 0

|m - 4| - 2 = 0

|m - 4| = 2.

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Answer:

0

Step-by-step explanation:

Combine like terms, combining 5x^2 and - 5x^2, -3x and 3x, etc. to get:

5x^2 - 5x^2 - 3x + 3x - 7 + 7.

These numbers are opposites, so they cancel out, and what we are left with is just 0.

In a 4x3x2x2 factorial experiment, you have 4 independent variables and potentially 4 main effect hypotheses.

The 4 independent variables are represented by the four numbers in the experimental design

(i.e., 4 levels of variable A, 3 levels of variable B, 2 levels of variable C, and 2 levels of variable D).

The potentially 4 main effect hypotheses are one for each independent variable, which states that there is a significant effect of that independent variable on the outcome variable.

A factorial experiment includes multiple factors simultaneously, each consisting of two or more

levels. Many factors simultaneously influence what is studied in a factorial experiment, and

experimenters consider the main effects and interactions between factors.

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Answer:

No

Step-by-step explanation:

They are not equivalent fractions

Answer:

No, they are not equivalent

Step-by-step explanation:

Setting the widths of divs within a div to equal 90% of the page allows each div to take up 90% of its parent div's width, while setting just one div to be 90% of the page causes that div to take up 90% of the width of the entire webpage.

The difference between setting the widths of the divs that are within a div to equal 90% of the page and setting just one div to be 90% of the page is the way the divs will be displayed on the webpage.

When you set the widths of the divs that are within a div to equal 90% of the page, each individual div will take up 90% of the width of its parent div. This means that if you have multiple divs within the parent div, they will each take up 90% of the available space, but will still be contained within the boundaries of the parent div.

On the other hand, when you set just one div to be 90% of the page, that div will take up 90% of the width of the entire webpage, not just its parent div. This means that the div will expand to take up most of the available space, potentially pushing other elements on the webpage to the side.

In summary, setting the widths of divs within a div to equal 90% of the page allows each div to take up 90% of its parent div's width, while setting just one div to be 90% of the page causes that div to take up 90% of the width of the entire webpage.

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(a) To find the mean and variance of the service times, we can use the given discrete distribution.

The mean can be calculated by taking the weighted average of the service times: Mean = (1 * 0.3) + (2 * 0.3) + (3 * 0.4) = 0.3 + 0.6 + 1.2 = 2.1 minutes
To find the variance, we need to calculate the squared deviations from the mean and then take the weighted average: Variance = [(1 - 2.1)^2 * 0.3] + [(2 - 2.1)^2 * 0.3] + [(3 - 2.1)^2 * 0.4]
      = [(-1.1)^2 * 0.3] + [(-0.1)^2 * 0.3] + [(0.9)^2 * 0.4]
      = 0.363 + 0.003 + 0.324
      = 0.69

(b) The traffic intensity (ρ) is the ratio of the mean service time to the mean interarrival time. In this case, the mean service time is 2.1 minutes, and the mean interarrival time is given as 2.2 minutes. Therefore:

Traffic Intensity (ρ) = Mean Service Time / Mean Interarrival Time
                    = 2.1 / 2.2
                    = 0.9545

(e) The system throughput is the average number of customers served per unit of time. Since the interarrival times are exponentially distributed, the system throughput can be calculated as the reciprocal of the mean interarrival time:

System Throughput = 1 / Mean Interarrival Time
                 = 1 / 2.2
                 ≈ 0.4545 customers per minute

(a) The long-run average waiting time (excluding service time) for each customer can be calculated using Little's Law. Little's Law states that the long-run average number of customers in a stable system is equal to the product of the long-run average arrival rate and the long-run average waiting time. Since the system is single-server, the arrival rate is the same as the throughput. Therefore:

Long-run Average Waiting Time = Average Number of Customers / Throughput
                            = 1 / System Throughput
                            ≈ 1 / 0.4545
                            ≈ 2.2 minutes

(e) The long-run average number of customers in the system can also be calculated using Little's Law. It is equal to the product of the long-run average arrival rate and the long-run average time a customer spends in the system. Since the arrival rate is the same as the throughput, and the service time includes both waiting time and service time, we can subtract the waiting time from the total service time to find the time spent in the system:

Long-run Average Number of Customers = Throughput * (Mean Service Time - Waiting Time)
                                   ≈ 0.4545 * (2.1 - 2.2)
                                   ≈ -0.0454

The negative value indicates that, on average, there are no customers in the system, which suggests that the system is underutilized or not operating at its full potential.

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the answer is 144 square inches

The z score associated with the highest 10% is closest to: option (c) 1.28

-To find the z score associated with the highest 10%, first determine the percentage that corresponds to the lower 90%, since the z score table typically represents the area to the left of the z score.

- Look up the 0.90 (90%) in a standard normal distribution  (z score) table, which will give you the corresponding z score.

-The z score closest to 0.90 in the table is 1.28, which corresponds to the highest 10% of values.

Therefore, the z score associated with the highest 10% is closest to 1.28.

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Answer:

795 toys

Step-by-step explanation:

if she gives away 25 toys each week for 22 weeks, that will be a total of 550 toys in 22 weeks

And now we simply minus 550 from 1345 to get 795 toys remaining after 22 weeks

Answer:

(-3,2) & (0,6)       4/3

(3,-5) & (-5,1)       -3/4

(0,0) & (-4,-3)     3/4

(5,6) & (8,2)      -4/3

(6,-2) & (7,-3)    -1

(8,-3) & (10,1)      2

(-8,-4) & (-6,-5)    -1/2

(-8,-4) & (-10,-5)    1/2

Step-by-step explanation:

Answer:

5. Slope: 2

y-intercept:(0,-6)

y=2x-6

6. Slope:1

y-intercept:(0,-1)

y=x-1