How would the real number 1/2 be written as a complex number?
1+2i
1/2i
1/2+0i
1\2

Answer:

108π mm.

Step-by-step explanation:

The hour hand makes a full circle of 12 hr, in 45 min=0.75 hours it will will have made 0.75/12 of a full circle. Given that the tip of the hour hand travels along the circumference of a circle, the radius of circle will be equal to the lenth of the hand.  

But:

circumference is given by:

C=2*π*radius

The distance traveled by the hand in 12 hours will be:

2**36=76π mm

The distance traveled in 45 min will be:

0.75/12 *72π=4.5π mm

in 45min, the min hand will make 45/60=3/4 of a full circle. If the min hand is 150% of the hour hand, then its length is 150/100*36=54 mm.

Thus the tip of the minute will travel along the entire circuference of a circle with a 54 mm radius, this implies that for a full circle we shall have:

2*π*54mm=108π mm.

Hence;

in 45 min, the tip of the minute hand will have traveled 108*3/4*π=81π mm

Answer:

D

Step-by-step explanation:

The equation of the line is y = 2x + 8

To find the y intercept we make x=0

When x=0 y=8

if y is total cost and x is number of visits then at zero visits (x=0) the total cost is 8, which is what you would find using choice D

Answer:

--------------------------------

It represents the cost with zero visits, likely the membership cost, therefore the correct choice is D.

Answer:-397x+-5

Step-by-step explanation:

-52x-345x-5

=-52x+-345x+-5

=(-52x+-345x)+(-5)

=-397x+-5

Answer:

this is a required answer.

Answer:

2827.4

Step-by-step explanation:

Answer:

9.78

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

The OLS estimator b in the presence of measurement error will be unbiased if certain conditions are met. The variance of b|X is larger than the variance of b*|X due to the additional measurement error.

i) The least squares problem for equation (3) is formulated as follows: minimize the sum of squared residuals, SSR(b) = (y - Xb)'(y - Xb). The first-order conditions give ∂SSR(b)/∂b = -2X'y + 2X'Xb = 0. Solving for b, we get b = (X'X)^(-1)X'y, which is the OLS estimator.

ii) The OLS estimator b will be unbiased if E(ν|X) = 0 and X is of full rank. Additionally, the error term ε should satisfy the classical linear model assumptions, including E(ε|X) = 0, var(ε|X) = σε^2In, and ε being uncorrelated with X.

iii) The variance of b|X is given by var(b|X) = σε^2(X'X)^(-1). Comparing it to var(b*|X), we find that var(b|X) is larger due to the presence of measurement error. The additional error term η introduces more variability into the estimated coefficients, leading to a larger variance compared to the scenario where y* is observed directly.

Therefore, The OLS estimator b in the presence of measurement error will be unbiased if certain conditions are met. The variance of b|X is larger than the variance of b*|X due to the additional measurement error.

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Answer:

Step-by-step explanation:

Given the inequality −14x+6≥14, we are to find the range of x that will make the inequality true.

Given −14x+6≥14

Subtract 6 from both sides.

−14x+6-6≥14-6

-14x≥8

-7x≥4

Multiply both sides by -1

-(-7)x≤-4

7x ≤ -4

x≤-4/7

This shows that the values of x is always less than or equal to -0.57

Hence the values less tan the value of x in the inequality are -36, -32 and -16

Option b accurately interprets the slope coefficient in the context of the regression equation provided. b. As x increases by 1 unit, y is predicted to decrease by 17 units.

In the given sample regression equation, the slope coefficient (-17) represents the rate of change in the predicted value of y (y-hat) for each one-unit increase in x. Since the coefficient is negative, it indicates a negative relationship between x and y.

Specifically, for every one-unit increase in x, the predicted value of y is expected to decrease by 17 units. Therefore, option b accurately interprets the slope coefficient in the context of the regression equation provided.

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Answer:

1.5 hours

As a general rule, 1,000 square feet of the house should take 1.5 hours to clean, according to Cleaning 4 Profit. So a 3,000 square feet home should take 3 hours to clean, and so on.

Answer:

70%

Step-by-step explanation:

you could use the 70° and see if the same size and it it is then you have the correct answer that's how I've been doing it it will help you alot more.

The formula for Average Fixed Cost (AFC) is: AFC = FC / Q. Where FC represents the total fixed costs incurred by a firm and Q represents the quantity of output produced by the firm.

AFC is a per-unit measure of the fixed cost of production, and represents the amount of fixed cost that is attributed to each unit of output. As the quantity of output increases, the AFC decreases, since the fixed costs are spread out over a larger number of units. AFC is an important concept in economics and business, as it is used to calculate other cost measures such as average total cost and average variable cost.

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Answer:

Simplify the expression.

−16x

Step-by-step explanation:

Answer:

20 maybe

Step-by-step explanation:

Answer:

20 because you have to cross multiple

All parties involved in the supply chain must work together to reduce losses and improve the supply chain's efficiency.

The supply chain is responsible for moving materials through various parties. Each party is accompanied by a loss or defect rate that can have a significant impact on the overall supply chain. The loss or defect rate associated with each party of the supply chain is listed below:

A. Suppliers: 1.0% of all materials delivered are unacceptable for use. This means that the suppliers are responsible for the quality and delivery of raw materials. Suppliers should ensure that the materials provided are of the required standard, meet the manufacturer's specifications, and are delivered on time.

B. Manufacturing: 0.9% of items produced are defective and are thus not shipped. The manufacturer should ensure that products are manufactured to meet quality specifications, and that product defects are identified and corrected.

C. Distribution: 1.1% of the items shipped are lost, stolen, or damaged in transit. The distribution parties are responsible for moving the products from the manufacturing plant to the retail stores. They are responsible for ensuring that the product is delivered to the right location at the right time, and that it is in the right condition.

D. Retail Store: 1.2% of items are stolen/damaged and thus unavailable for sale. Retailers are responsible for ensuring that products are on the shelves and in the right condition, with the right pricing, in the right quantity, at the right time. They must ensure that products are protected from damage or theft.

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Answer:

See below

Step-by-step explanation:

Question 1:

For polynomial:

\( x^2 + 11x + 24\)

add upto 11 x

multiply to 24

Question 2:

For polynomial:

\( x^2 - 12x + 20\)

add upto - 12 x

multiply to 20

It is important to choose the appropriate statistical test that takes into account the nature of the data and the study design to minimize the risk of making a type II error.

Using a t-test for two independent samples instead of a paired t-test when the samples are related (i.e., paired or dependent) can increase the probability of a type II error.

In a paired sample design, each individual or object in one sample is matched or related to a corresponding individual or object in the other sample. Because of this pairing, the observations in the two samples are not independent of each other, and using a t test for independent samples may not account for the dependency between the samples.

By ignoring the relatedness of the samples, the investigator may be introducing additional variability and error into the analysis, which can reduce the statistical power of the test and increase the probability of a type II error (i.e., failing to reject a null hypothesis that is actually false).

Therefore, it is important to choose the appropriate statistical test that takes into account the nature of the data and the study design to minimize the risk of making a type II error.

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x = number of hours

want to find probability (P) x >= 13

x is N(14,1) transform to N(0,1) using z = (x - mean) / standard deviation so can look up probability using standard normal probability table.

P(x >= 13) = P( z > (13 - 14)/1) = P(z > -1) = 1 - P(z < -1) = 1 - 0.1587 = 0.8413

To convert that to percentage, multiply 100, to get 84.13%

To calculate the number of possible sequences that can be studied when considering all possible orderings of the tasks, we can use the concept of permutations.

Since there are five tasks to be performed and each task can be arranged in any order, the number of possible sequences can be calculated using the formula for permutations of n objects, which is n!

In this case, n = 5, so the number of possible sequences is:

5! = 5 x 4 x 3 x 2 x 1 = 120

Therefore, 120 sequences will be studied when considering all possible task orderings.

Answer:

  A, C, E

Step-by-step explanation:

You want the values from the list that are included in the solution set of -6(1 + 2x) ≥ 6(2x - 1) + 2x.

Simplifying the inequality, we get ...

  -6 -12x ≥ 12x -6 +2x

  0 ≥ 26x . . . . . . . . . . . . . add 12x+6

  x ≤ 0 . . . . . . . . . . . . divide by 26

The solution set includes 0 (choice C) and all negative values (choices A and E).

The approximate volume of the larger candle is 244 cubic centimeters.

To find the volume of the larger candle, we need to compare the side lengths of the smaller and larger candles. Let's denote the side length of the smaller candle as "s."

According to the information given, the side length of the larger candle is five-fourths (5/4) as long as the side length of the smaller candle. Therefore, the side length of the larger candle can be calculated as (5/4) * s.

The volume of a square pyramid is given by the formula V = (1/3) * s^2 * h, where s is the side length of the base and h is the height.

Since both the smaller and larger candles have the same shape, their volume ratios will be equal to the ratios of their side lengths cubed.

Let's substitute the values into the volume ratio equation:

(125 / V_larger) = (s_larger / s_smaller)^3

Given that V_smaller = 125 cubic centimeters, we can rewrite the equation as:

(125 / V_larger) = ((5/4) * s_smaller / s_smaller)^3

Simplifying the equation:

(125 / V_larger) = (5/4)^3

Calculating (5/4)^3:

(125 / V_larger) = (125 / 64)

Cross-multiplying the equation:

125 * 64 = V_larger * 125

Solving for V_larger:

V_larger = (125 * 64) / 125

Approximating the value:

V_larger ≈ 64 cubic centimeters

The approximate volume of the larger candle is 244 cubic centimeters, rounded to the nearest cubic centimeter

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Tessa has been training for a marathon by running 13 km per day for 333 consecutive days.

Tessa regularly ran 13 km every day for an incredible 333 days, demonstrating her commitment to her marathon training. Her dedication displays her perseverance and discipline, two qualities essential for training for a marathon.

Tessa is likely to get a variety of physical and mental advantages by keeping up such a demanding training plan. Her physical stamina, cardiovascular fitness, and endurance will all greatly increase, preparing her for the demands of a complete marathon. Tessa will become more focused, determined, and resilient as a result of her consistency, which will help her mentally prepare for the challenges of finishing a lengthy marathon. Tessa's daily regimen of consistently running 13 km demonstrates her great commitment and positions her for success in her marathon endeavour.

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Complete Question: Tessa is getting ready to run a marathon. For 333 days, she runs 13 text kilometres (start text, space, k, m, finish text).

How far did Tessa run overall, in metres?

\((\stackrel{x_1}{-5}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-3}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-3}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{(-5)}}} \implies \cfrac{-3 +5}{1 +5} \implies \cfrac{ 2 }{ 6 } \implies \cfrac{1 }{ 3 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{ \cfrac{1 }{ 3 }}(x-\stackrel{x_1}{(-5)}) \implies y +5 = \cfrac{1 }{ 3 } ( x +5)\)

Answer:

Ishaan is currently 15 years old.

Step-by-step explanation:

Let B represent Ben's current age and I represent Ishann's current age.

Ben is four times as old as Ishaan. In other words:

\(B=4I\)

Six years ago, Ben was six times as old as Ishaan. In other words:

\(B-6=6(I-6)\)

Solve for I. Substitute:

\((4I)-6=6(I-6)\)

Distribute:

\(4I-6=6I-36\)

Subtract 4I from both sides and add 36 to both sides:

\(2I=30\)

And divide both sides by two. Hence:

\(I=15\)

Ishaan is currently 15 years old.

Answer:

Age of Ishaan = 15 years

Step-by-step explanation:

Let Ishaan's age = x years

Age of Ben = 4 * x = 4x years

6Years ago:

Age of Ishaan = x - 6

Age of Ben = 4x - 6

6 years ago, Ben was 6 times as old as Ishaan

So, Age of Ben = 6 * Ishaan's age

     4x - 6 = 6 *(x-6)

4x - 6 = 6x - 36

Add 36 to both sides

4x - 6 + 36  = 6x  

4x + 30 = 6x

Subtract '4x' from both sides

30 = 6x - 4x  

30 = 2x

2x = 30

Divide both by 2 sides

x = 30/2

x = 15

In general, to evaluate the function f(x) at a specific value of x, we substitute that value into the expression for f(x) and simplify.

In mathematics, a function is a relation between two sets, where for every element in the first set (called the domain), there is exactly one element in the second set (called the range) that the function maps to. In simpler terms, a function is a rule that assigns each input value from the domain to exactly one output value in the range. Functions are usually represented by a formula or equation that describes the relationship between the input and output values. For example, the function f(x) = 2x + 1 maps every input value of x to an output value that is twice the input value plus 1.

Here,

To evaluate the function f(x) = 4x - 6, we substitute the given values of the independent variable into the expression for f(x) and simplify.

For example:

f(0) = 4(0) - 6 = -6

f(1) = 4(1) - 6 = -2

f(2) = 4(2) - 6 = 2

f(-1) = 4(-1) - 6 = -10

f(3a) = 4(3a) - 6 = 12a - 6

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Answer:

\(2\sqrt{3}+3\)

Step-by-step explanation:

\($\frac{3}{2 \sqrt 3 - 3}$\)

Rationalize the fraction.

\($\frac{3}{2 \sqrt 3 - 3}\cdot \frac{2 \sqrt 3 + 3}{2 \sqrt 3 + 3} =\frac{6\sqrt{3}+9 }{12-9} =\frac{6\sqrt{3}+9 }{3} =2\sqrt{3}+3 $\)

Note that I used the positive signal because we would have a difference of squares.

The error involved in making a certain measurement is a continuous rv X with CDF if x < -3 F(x)= +(9x-x¹), if-3≤x≤3 if x > 3 (a) Compute PIX 0.5]

(d) Find the pdf of X

(e) Find the median, i.e., in order to answer the provided question, let's first solve the cumulative distribution function, F(x), which is provided as follows:

If x  -3, then F(x) = 0, as x  -3, and if x  -3. if -3 ≤ x ≤ 3, then

F(x) = (9x - x2)/18 + 1/2, as x2 - 9x  0 and x  -3 and x  3. if x > 3, then

F(x) = 1, as x  3.Since we have the CDF, we can calculate the probability as follows:

P(-2 < X ≤ 0.5) = F(0.5) - F(-2)

= (9(0.5) - (0.5)²)/18 + 1/2 - [(9(-2) - (-2)²)/18 + 1/2]

= (9/36 + 1/2) - (36/18 - 1/2)

= 7/12.

The probability of -2  X  0.5 is 7/12. Next, we need to find the PDF of X, which can be derived from the CDF using the following:

f(x) = F'(x), where F'(x) is the derivative of the CDF. For -3 < x < 3, the derivative is:f'(x) = (9 - 2x)/18

For x  -3, f(x) = 0, and for x  3, f(x) = 0.

Therefore, the PDF of X is given as: f(x) = { (9 - 2x)/18 for -3 < x < 3, 0 elsewhere }

The median is the value of X such that F (X) = 1/2. So, we need to solve for X in the following equation: (9x - x2)/18 + 1/2 = 1/2. Simplifying this, we get: x2 + 9x = 0.

Factoring this in, we get:x(x - 9) = 0. Therefore, the median is X = 9/2. Thus, the correct option is

(a) P(-2 < X ≤ 0.5) = 7/12,

(d) f(x) = { (9 - 2x)/18 for -3 < x < 3, 0 elsewhere } and

(e) Median = 9/2

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Answer:

5/9.

Step-by-step explanation:

Theoretical probability = number of outcomes with1 or 2 blues

                                         -------------------------------------------------------

                                             number of all possible outcomes

= 5/9