Let f(x) = x² + 2. Approximate the area bounded by the curve y = f(x), the x-axis, and the vertical lines x = 4 and x = 8 using a Riemann sum (right-point rule) with four rectangles.

Based on the fact that Saudi Arabia can either produce 45 barrels or 70 bushels, their opportunity cost for one barrel is 1.56 bushels

The opportunity cost for producing one barrel can be found by the formula:

= Number of bushels capable / Number of barrels

Solving gives:

= 70 / 45

= 1.56 bushels

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The relationship between the correlation coefficient, that is r and the closeness of the points on a scatter plot to the regression line or the coefficient of correlation is the measure of closeness of association.

Correlation coefficient

Correlation coefficient is a statistical measure of how much a change in the value of one variable predicts a change in the value of another variable. For variables with positive correlation, the values ​​increase or decrease together.

Scatter Plot:

A scatterplot (also called a scatterplot or scatterplot) uses points to plot the values ​​of two different numeric variables. The position of each point on the horizontal and vertical axes represents the value of one data point. Scatter plots are used to observe relationships between variables.

Measure of closeness of Association:

In statistics, any of several factors or coefficients used to quantify the relationship between two or more variables. Measures of association include Pearson's correlation coefficient, Spearman's rank correlation coefficient, and the chi-square test. Association measures are used in a variety of research fields, but they are most widely used in the fields of epidemiology and psychology, where they are often used to quantify the relationship between exposure and disease or behavior. Measures of association can be determined by any of several different analyzes, including correlation analysis and regression analysis. (The terms correlation and association are often used interchangeably, but in the narrower sense correlation refers to linear correlation and association for any relationship between variables.) Used to determine strength of association.

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All the measures of central tendency are, The median, The mode, and The mean.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are some measures,

A. The median

B. A sample statistic

C. The mode

D. The lowest value

E. The mean

We know that;

The four measures of central tendency are mean, median, mode and the midrange.

Here, mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set.

Hence, All the measures of central tendency are, The median, The mode, and The mean.

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For the hypotheses H₀ : π ≤ 0.81; H₁ : π > 0.81

(a) Decision-Rule is "if test-statistic is greater than 2.33, we reject the null hypothesis"

(b) The test-statistic is 3.19,

(c) As test-statistic value of 3.16 is greater than critical-value (2.33), we reject the null-hypothesis.

To determine if the null hypothesis can be rejected at the 0.01 significance level, we perform a one-sample proportion hypothesis test.

H₀: π ≤ 0.81 (null-hypothesis)

H₁: π > 0.81 (alternative hypothesis)

Sample size (n) = 80

Sample proportion (p) = 0.95

Part (a) State the decision rule:

Since the alternative-hypothesis is one-sided (π > 0.81), we need to find the z-value that corresponds to a 0.99 cumulative probability.

The critical-value is approximately 2.33. So, if the test-statistic is greater than 2.33, we reject the null hypothesis.

Part (b) : The test-statistic for a one-sample proportion test is calculated using the formula : z = (p - π₀)/ √(π₀ × (1 - π₀) / n),

Where π₀ = value specified in null hypothesis,

In this case, π₀ = 0.81, p = 0.95, and n = 80.

Substituting the values,

We get,

z = (0.95 - 0.81) /√(0.81 × (1 - 0.81) / 80)

z ≈ 3.19

Part (c) : The test-statistic value (3.16) is greater than the critical-value (2.33) at the 0.01 significance level.

Therefore, we reject the null hypothesis.

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The given question is incomplete, the complete question is

The following hypotheses are given.

H₀ : π ≤ 0.81

H₁ : π > 0.81

A sample of 80 observations revealed that p = 0.95. At the 0.01 significance level, can the null hypothesis be rejected?

(a) State the decision rule.

(b) Compute the value of the test statistic.

(c) What is your decision regarding the null hypothesis?

Answer:

4.5

Step-by-step explanation:

180/40 is 4.5. 40x4.5=180

Answer: I don’t think you can

Step-by-step explanation: ??????????????????

For 1st year percentage increase is 100%

For 2nd Year percentage increase is 50%

In essence, percentages are fractions with a 100 as the denominator. We place the percent sign (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 of 100 questions correctly on a test (75/100).

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

A percentage is a ratio or fraction where the full value is always 100. Sam, for instance, would have received 30 out of a possible 100 points if he had received 30% on his arithmetic test. In ratio form, it is expressed as 30:100 and in fraction form as 30/100.

Population function is

P(x) = 40000 * 1.2x

Population in 2015 , x = 1

P(1) = 40000*1.2 = 48000

Population in 2016 , x = 2

P(2) = 40000*1.2*2 = 96000

Population in 2017 , x = 3

P(3) = 40000*1.2*3 = 144000

So for 1st year percentage increase = (96000-48000)/48000 *100 = 100%

For 2nd Year percentage increase = (144000-96000)/96000 *100 = 50%

Similarly it will reduce at a rate of 0.5.

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Answer: d. 5/9v -5/9

Step-by-step explanation:  

2/9v +1/3v -5/9

2/9v + 3/9v-5/9

5/9v -5/9

Answer:

B.) and C.)

Step-by-step explanation:

Figure can be cut in half = reflection symmetry

Figure can be flipped = 180 rotational symmetry

(if those four choices in the picture are the only choices)

The values for the  quadratic equation,

x₁ + x₂ = -5 and x₁ × x₂ = 3.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. They are also known as quadratic equations.

Given equation,

3x² + 15x + 9 = 0

and given x₁ and x₂ are the solution of the equation or roots or zeros of the equation.

for any quadratic equation, the sum of the roots is equal to the -b/a

here x₁ + x₂ = -15/3 = -5

and the product of the roots is equal to the product of c/a

x₁ × x₂ = 9/3

x₁ × x₂ = 3

Hence x₁ + x₂ = -5,

x₁ × x₂ = 3.

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For each pairwise comparison, you would compare the p-value against an adjusted significance level of approximately 0.00167 to determine if the difference between the treatments is statistically significant after applying the Bonferroni correction.

The Bonferroni method is a statistical procedure used to adjust the significance level for multiple comparisons in order to control the familywise error rate. To perform multiple comparisons using the Bonferroni method at the 0.01 level, you would divide the desired overall significance level (0.01) by the number of pairwise comparisons being made.

If you have four levels of treatments and want to compare each pair of treatments, you would have a total of six pairwise comparisons: A vs. B, A vs. C, A vs. D, B vs. C, B vs. D, and C vs. D.

To apply the Bonferroni correction, divide the desired overall significance level of 0.01 by the number of comparisons (6):

Adjusted significance level = 0.01 / 6

The adjusted significance level for each individual comparison would then be:

Adjusted significance level = 0.01 / 6 ≈ 0.00167

So, for each pairwise comparison, you would compare the p-value against an adjusted significance level of approximately 0.00167 to determine if the difference between the treatments is statistically significant after applying the Bonferroni correction.

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The limit of f(x) as x goes to 2 is given by:

C. 0.

A limit is given by the value of function f(x) as x tends to a value a, that is, we have to look to the left of x = a and to the right of x = a, and if these values are equal, this is the limit of the function.

In this problem, we have that:

Since the lateral limits are equal, the limit of the function as x approaches 2 is of 0 and option C is correct.

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The equation that best represents the data in the scatter plot is y = -5x + 102.(Option-d)

To determine which equation best represents the data given in the scatter plot, we need to examine the general trend of the data. We can see that the data points roughly follow a downward sloping line from left to right. This suggests a negative correlation between the two variables, meaning that as the value of x increases, the value of y tends to decrease.

Now let us evaluate the given equations based on the trend of the scatter plot.

y = -3x + 100 represents a negative slope, but it is not as steep as the trend line in the scatter plot. Hence, it is not the best fit for the data.

y = -6x - 20 also has a negative slope which is steeper than the trendline of the scatter plot. Therefore, it is not the correct equation that best represents the given data.

y = -5x + 105 and y = -5x + 102 both have a negative slope that is similar to the trend line in the scatter plot. Since they differ in the vertical intercept, let us examine the scatter plot to determine which equation fits better. The cluster of data points is closer to the line represented by the equation y = -5x + 102, which best represents the trend line. Moreover, y = -5x + 102 cuts across the y-axis at 102, which is closer to the actual values of y near x = 0 in the scatter plot.(Option-d)

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Answer:

to find surface area of cylinder

A=2πrh+2πr²

Step-by-step explanation:

In the graph of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

The simple linear regression equation represents a linear relationship between a dependent variable and an independent variable. It can be written as y = ß0 + ß1x, where ß0 is the intercept and ß1 is the slope of the regression line.

The slope (ß1) determines the rate of change in the dependent variable (y) for each unit change in the independent variable (x). It represents the steepness or inclination of the regression line. The sign of ß1 indicates whether the line has a positive or negative slope, indicating the direction of the relationship between the variables.

Thus, in the context of the simple linear regression equation, the parameter ß1 is the slope of the true regression line.

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Answer:

318

Step-by-step explanation:

we can fill the corner in to form whole rectangle which would mean it has an area if 19*18=342 then we subtract the filled in triangle which we can find by doing (19-11)*(18-12)/2 then subtract it from the original we get 342-24=318 Hope it helps!!

Answer:

Step-by-step explanation:

I dont know the answer but all you have to do is make a rectangle with the 11mm,18mm,and 19mm then multiply them all together then you'll multiply 10mm,12mm,and 19mm then you add them or multiply i believe and boom you got your answer

Total stockholders’ equity 7,800,000

Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000

Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000

Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000

Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000

To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.

The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.

Calculations:Opening balance of common stock = $100,000

Opening balance of additional paid-in capital = $4,100,000

Opening balance of retained earnings = $3,000,000

Net Income for the year ended December 31, 2012 = $800,000

Retained earnings (Opening Balance) = $3,000,000

Add: Net Income for the year ended December 31, 2012 = $800,000

Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000

Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000

Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000

Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
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Answer:

550 sit-ups

Step-by-step explanation:

Given

See attachment for chart

Required

Number of sit-ups on March 11

Represent the number of sit-ups with x and the days with y.

So:

\((x_1, y_1) = (1,50)\) --- May 1

\((x_2, y_2) = (2,100)\) --- May 2

First, we calculate the slope of the line chart.

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

\(m = \frac{100 - 50}{2-1}\)

\(m = \frac{50}{1}\)

\(m = 50\)

Next, we calculate the equation using:

\(y = m(x - x_1) + y_1\)

This gives:

\(y = 50(x - 1) + 50\)

\(y = 50x - 50 + 50\)

\(y = 50x\)

So, on May 11.

\(x= 11\)

Substitute 11 for x

\(y = 50 * 11\)

\(y = 550\)

Answer:

mperpendicular = 5/2

Step-by-step explanation:

Answer:

I'm not smart at this stuff

(a) Approximated velocity of the object when t = 2 is (2.4,4,0) m/s.

(b) Approximated acceleration of the object when t = - 2.75 is (-4,-4,4) m/s^2.

(c) Approximated position of the object when t = 3.25 is (6,3,4) m.

(a) To approximate the velocity of the object when t = 2, we can use the data for t = 2.0 and t = 2.25. The change in time is 0.25 seconds.

To find the change in position, we subtract the coordinates of r(1) at t = 2.0 from those at t = 2.25, which gives us:

(3,2,0) - (2.4,1,0) = (0.6,1,0).

To find the velocity, we divide the change in position by the change in time, which gives us:

(0.6,1,0) / 0.25 = (2.4,4,0) m/s.

Therefore, the approximate velocity of the object when t = 2 is (2.4,4,0) m/s.

(b) To approximate the acceleration of the object when t = -2.75, we can use the data for t = 2.5 and t = 2.75. The change in time is 0.25 seconds.

To find the change in velocity, we subtract the coordinates of v(1) at t = 2.5 from those at t = 2.75, which gives us:

(1,1,2) - (2,2,1) = (-1,-1,1).

To find the acceleration, we divide the change in velocity by the change in time, which gives us:

(-1,-1,1) / 0.25 = (-4,-4,4) m/s^2.

Therefore, the approximate acceleration of the object when t = -2.75 is (-4,-4,4) m/s^2.

(c) To approximate the position of the object when t = 3.25, we can use the data for t = 3.0 and t = 3.25. The change in time is 0.25 seconds.

To find the change in position, we subtract the coordinates of r(1) at t = 3.0 from those at t = 3.25, which gives us:

(6,3,4) - (3,2,0) = (3,1,4).

To find the position, we add the change in position to the coordinates of r(1) at t = 3.0, which gives us:

(3,2,0) + (3,1,4) = (6,3,4).

Therefore, the approximate position of the object when t = 3.25 is (6,3,4) m.

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133.3333333333% (increase) is percent of increase 70%.

What is the percentage formula?

Use the formula percent change

Percent change = \(\frac{New - old}{old} * 100\)

                           = 70- 30/30 * 100

                           = 40/30 * 100

                           = 133.3333333333% (increase)

Where: 30 is the old value and 70 is the new value.

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The remainder theorem says that a polynomial f(x) has a remainder of f(c) upon getting divided by x - c. So if

f(x) = x⁴ + p x³ + q x² + r x + 6

is divisible by x - 1, x - 2, and x - 3, then we have

f (1) = 7 + p + q + r = 0

f (2) = 22 + 8p + 4q + 2r = 0

f (3) = 87 + 27p + 9q + 3r = 0

Solve the system for p, q, r. You can eliminate r by substituting the first equation into the other two:

p + q + r = -7

8p + 4q + 2r = -22   →   6p + 2q - 14 = -22   →   3p + q = -4

27p + 9q + 3r = -87   →   24p + 6q - 21 = -87   →   4p + q = -11

Eliminate q by adding (-1) times the first equation to the second one, then solve for p :

- (3p + q) + (4p + q) = - (-4) + (-11)

-3p - q + 4p + q = 4 - 11

p = -7

Solve for q :

3p + q = -4   →   3 (-7) + q = -4   →   q = 17

Solve for r :

p + q + r = -7   →   -7 + 17 + r = -7   →   r = -17

There is ONLY ONE __ line parallel to the provided line that passes through a certain point that is not contained in the supplied line.

Parallel lines are any two or more lines that are in the same plane but never cross one another ( never intersect). Both have the same slope and are equally far from one another.

We have a line and a point outside the line;

from that point, we can generate many lines, but only one of those lines will be parallel to the line as it is. From a point, we can make many lines, but that point can only create one line that will be parallel to a given line.

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Answer:

No Solution

Step-by-step explanation:

0.3(6y+15)=1.8y+4.5

Step 1: Simplify both sides of the equation.

0.3(6y+15)=1.8y+4.5

(0.3)(6y)+(0.3)(15)=1.8y+4.5(Distribute)

1.8y+4.5=1.8y+4.5

Step 2: Subtract 1.8y from both sides.

1.8y+4.5−1.8y=1.8y+4.5−1.8y

0y+4.5=4.5

Step 3: Subtract 4.5 from both sides.

0y+4.5−4.5=4.5−4.5

0y=0

Step 4: Divide both sides by 0.

0y/0 = 0/0

y=0

Answer:

x=16/3

Step-by-step explanation:

5x−2(x+1)=14

Distribute

5x -2x -2 =14

Combine like terms

3x -2 =14

Add 2 to each side

3x-2+2 =14+2

3x=16

Divide each side by 3

3x/3 = 16/3

x=16/3

Answer:

x = 16/3

Step-by-step explanation:

5x - 2(x + 1) = 14

~Simplify

5x - 2x - 2 = 14

~Combine like terms

3x - 2 = 14

~Add 2 to both sides

3x = 16

~Divide 3 to both sides

x = 16/3

Best of Luck!

Answer:

The answer is 52 cm

Step-by-step explanation:

Answer: 52 cm

Step-by-step explanation:

The 12th term of the geometric sequence is a₁₂ = -244140625.

Define Geometric Progression

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value. Its general term is,

aₙ = a₁ · rⁿ⁻¹.

The geometric sequence,

5, -25, 125 ....

from here,we know

a₁ = 5

Calculate the ratios of all the adjacent terms ,

r = aₙ₊₁ / aₙ

r = -25/5 = -5

r = 125/-25 = -5

We know, the formula for geometric sequence is

aₙ = a₁ · rⁿ⁻¹

Where, a₁ = initial term

r = common ratio

Now, we need to find 12th term so for that n = 12

Now, plug in the values

aₙ = a₁ · rⁿ⁻¹

a₁₂ = 5 * (-5) ¹²⁻¹

     = 5 * -5¹¹

After calculation we get,

a₁₂ = -244140625

Hence, the 12th term of the geometric sequence is a₁₂ = -244140625.

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The estimated cost of producing the 15th unit is $10.30.

Given the following information about a process that makes high-end boards that get mounted on skateboards:Process starts with a unit cost of $13 for the first unit. Learning rate of LR = 0.90.

Solution :Let's use the learning curve formula to calculate the estimated cost of producing the 15th unit.C = a * N^b .Where:

C = cost per unit ,N = cumulative production volume, a = the unit cost of the first unit, b = log(LR) / log(2) = log(0.90) / log(2) = -0.152N = 15a = 13 (given)

Now, b = -0.152

Therefore ,C = 13 * (15)^(-0.152)C = 13 * 0.789C = 10.3 dollars.

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Answer:

Answer: -3n^9

Step-by-step explanation:

cube root of -27 is -3 and divide 27 with 3 you'll get 9 so the answer is -3n^9