Describe all unit vectors orthogonal to both of the given vectors. 41 – 8j + 7k, -8i + 16j – 14k . a) Any unit vector in the opposite direction as 4i – 8j + 7k. b) Any unit vector in the same direction as – 8i + 163 – 14k. c) Any unit vector orthogonal to - 8i + 16) – 14k. d) Any unit vector in the same direction as 4i– 8j + Zk. e) Any unit vector.

Drake uses 9/4 cup of sugar to make 9 mug of brownie. Then the amount of sugar needed to make one brownie is 1/4 cup of sugar.

Determine how much sugar is needed

These are the specified parameters:

9/4 cup of sugar to make 9 mug of brownie.

Determine much sugar to make one brownie

Lots of sugar = cup of sugar : mug of brownie

                      = 9/4 : 9

                      = 9/4 × 1/9

                       = 1/4

So the amount of sugar needed to make one brownie is 1/4 cup of sugar.

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Arithmetic average return of the company is 2.57%.Geometric average return of the company is 13%.Variance of the company is 56.Standard deviation of the company is 7.48%.

Given, Returns of the company for the last few years are 5%, 10%, -15%, 20%, -12%, 22%, 8%
Arithmetic Average return:
Arithmetic Average return = (sum of all returns) / (total number of returns)
Arithmetic Average return = (5 + 10 - 15 + 20 - 12 + 22 + 8) / 7= 18 / 7= 2.57
Therefore, the arithmetic average return of the company is 2.57%.
Geometric average return:
Geometric average return = [(1+R1) * (1+R2) * (1+R3) * …….. * (1+Rn)]1/n - 1
Geometric average return = [(1.05) * (1.1) * (0.85) * (1.2) * (0.88) * (1.22) * (1.08)]1/7 - 1= 0.13
Therefore, the geometric average return of the company is 13%.
Variance:
Variance = (sum of (return - mean return)2) / (total number of returns)
Mean return = (5 + 10 - 15 + 20 - 12 + 22 + 8) / 7= 18 / 7= 2.57
Variance = [(5-2.57)2 + (10-2.57)2 + (-15-2.57)2 + (20-2.57)2 + (-12-2.57)2 + (22-2.57)2 + (8-2.57)2] / 7= 392.12 / 7= 56
Therefore, the variance of the company is 56.
Standard Deviation:
Standard Deviation = Square root of Variance
Standard Deviation = √56= 7.48
Therefore, the standard deviation of the company is 7.48%.

Thus, Arithmetic average return of the company is 2.57%.Geometric average return of the company is 13%.Variance of the company is 56.Standard deviation of the company is 7.48%.

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Answer:

a. -2 b. -2 c. -1 d. 4 e. -3 f. 0

Step-by-step explanation:

The average rate of change formula is:

\(\frac{y_{2}- y_{1}}{x_{2}-x_{1}}\)

a.  

We need to find the rate of change for x = -3 to x = -2 so we look on the graph to find y.

At x = -3 it look like y = 0  so

\(x_{1} = -3\)

\(y_{1} = 0\)

At x = -2 it looks like y = 2

\(x_{2} = -2\)

\(y_{2} = 2\)

Now we can just plug everything in to the rate of change formula.

\(\frac{y_{2}- y_{1}}{x_{2}-x_{1}} = \frac{2- 0}{-3-(-2)} = \frac{2- 0}{-3+2} = \frac{2}{-1}\) = -2

So for a. our rate of chage for the given interval is -2

b.

Now that you have the formula we don't need to explain each time.

\(x_{1} =\) -2

\(y_{1} =\) 2

\(x_{2} =\) 1

\(y_{2} =\) - 4

\(\frac{y_{2}- y_{1}}{x_{2}-x_{1}} = \frac{-4- 2}{1-(-2)} = \frac{-4-2}{1+2} = \frac{-6}{3}\) = -2

c.

\(x_{1} =\) 0

\(y_{1} =\) -3

\(x_{2} =\) 1

\(y_{2} =\) - 4

\(\frac{y_{2}- y_{1}}{x_{2}-x_{1}} = \frac{-4-(-3)}{1-0} = \frac{-4 + 3}{1-0} = \frac{-1}{1}\) = -1

d.

\(x_{1} =\) 1

\(y_{1} =\) -4

\(x_{2} =\) 2

\(y_{2} =\) 0

\(\frac{y_{2}- y_{1}}{x_{2}-x_{1}} = \frac{0 - (-4)}{2-1} = \frac{0 + 4}{2-1} = \frac{4}{1}\) = 4

e.

\(x_{1} =\) -1

\(y_{1} =\) 0

\(x_{2} =\) 0

\(y_{2} =\) -3

\(\frac{y_{2}- y_{1}}{x_{2}-x_{1}} = \frac{-3- 0}{0-(-1)} = \frac{-3- 0}{0+1} = \frac{-3}{1}\) = -3

f.

\(x_{1} =\) -1

\(y_{1} =\) 0

\(x_{2} =\) 2

\(y_{2} =\) 0

\(\frac{y_{2}- y_{1}}{x_{2}-x_{1}} = \frac{0- 0}{2-(-1)} = \frac{0- 0}{2+1} = \frac{0}{3}\) = 0

Answer:

8.64

Step-by-step explanation:

12% = 0.12

72(0.12) = 8.64

The numerical value of side length x to the nearest thundredth is 7.21.

Pythagorean theorem states that the "square on the hypotenuse of a right-angled triangle is equal in area to the sum of the squares on the other two sides.

It is expressed as;

c² = a² + b²

The figure in the image is a right triangle.

Given that;

Plug the given values into the above formula and solve for x.

c² = a² + b²

b² = c² - a²

b = √( c² - a² )

b = √( 14² - 12² )

b = √( 196 - 144 )

b = √52

b = 7.21

Therefore, the value of x is 7.21.

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Answer:

12.5

Step-by-step explanation:

Answer:

$12.50

Step-by-step explanation:

so u do revers math 4 x ?? = 50

so i took the time and found out 4 x 12= 48 but 4 x 13= 52 so i did the math and added .5 so i then times 4 x 12.5 witch ended up = 50 so every one got 12 dollars and 50 cents

Answer: a

Step-by-step explanation:

u do 1+1

Using the Lagrange method, the optimal choice is therefore (x1, x2) = (20/9, 4/3).

The optimal choice when pı = 3, P2 = 5 and I = 20 and utility is u(x1, x2) = min{2x1, x2} can be found using the Lagrange method .Lagrange method: This method involves formulating a function (the Lagrange function) which should be optimized with constraints, i.e. the optimal result should be produced while adhering to the constraints provided. The Lagrange function is given by: L(x1, x2, λ) = u(x1, x2) - λ(I - p1x1 - p2x2)

Where L is the Lagrange function, λ is the Lagrange multiplier, I is the budget, p1 is the price of good 1, p2 is the price of good 2.The optimal choice can be determined by the partial derivatives of L with respect to x1, x2, and λ, and setting them to zero to get the critical points. Then, the second partial derivative test is used to determine if the critical points are maxima, minima, or saddle points. The critical points of the Lagrange function L are:

∂L/∂x1 = 2λ - 2p1 = 0 ∂L/∂x2 = λ - p2 = 0 ∂L/∂λ = I - p1x1 - p2x2 = 0

Substitute the first equation into the second equation to get:λ = p2,2λ = 2p1 ⇒ p2 = 2p1,

Substitute the first two equations into the third equation to get: x1 = I/3p1,x2 = I/5p2

Substitute p2 = 2p1 into the above to get:x1 = I/3p1,x2 = I/10p1.Substitute the values of p1, p2 and I into the above to get:x1 = 20/9,x2 = 4/3.The optimal choice is therefore (x1, x2) = (20/9, 4/3).

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Answer:

For f (x):

f (x) = (x + 3) ^ 2 - 2

For x = -1

f (-1) = (-1 + 3) ^ 2 - 2

f (-1) = (2) ^ 2 - 2

f (-1) = 4 - 2

f (-1) = 2

For x = 3

f (3) = (3 + 3) ^ 2 - 2

f (3) = (6) ^ 2 - 2

f (3) = 36 - 2

f (3) = 34

AVR = ((34) - (2)) / ((3) - (- 1))

AVR = 8

For g (x):

linear graph with and intercept of negative 3 over 2 and x intercept of 3

y = mx + b

b = -3/2

For me we have:

0 = m (3) - 3/2

3m = 3/2

m = 1/2

The function g (x) is:

g (x) = (1/2) x - 3/2

For x = -1

g (-1) = (1/2) (- 1) - 3/2

g (-1) = -1/2 - 3/2

g (-1) = -4/2

g (-1) = -2

For x = 3

g (3) = (1/2) (3) - 3/2

g (3) = 3/2 - 3/2

g (3) = 0

AVR = ((0) - (- 2)) / ((3) - (- 1))

AVR = 1/2

For h (x):

Using the table we have:

AVR = ((62) - (14)) / ((3) - (- 1))

AVR = 12

Step-by-step explanation:

Answer:

from least to greatest:

1) g (x)

2) f (x)

3) h (x)

Step-by-step explanation:

The correct answer is option b. 1/36 is the expected value (Lesson 8.3: Unbiased Point Estimation. If X1, of the sample variance S2.

In unbiased point estimation, the expected value of the sample variance S2 is a crucial idea. When a sample is drawn from a population repeatedly, an average value of S2 is what is anticipated.

The population variance divided by the sample size represents the expected value of S2. It is, in other words, the population variance divided by n-1, where n is the sample size.

As a result, the expected value of the sample variance S2 for a sample size of 6 is equal to 1/36.

As a result, when a sample is drawn from a population repeatedly, the average value of S2 will be equal to 1/36 of the variance in the population.

Complete Question:

What is the expected value (Lesson 8.3: Unbiased Point Estimation. If X1, of the sample variance S2?

a. 1/6

b. 1/36

c. 6

d. 36

e.60

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Answer:

d

Step-by-step explanation:

Answer:

$20

Step-by-step explanation:

start with an equation. 15-(-5)=x. double negatives make positive so it becomes 15+5=x. therefore 20=x (x being the number kyle deposited).

Answer:

A radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length

Step-by-step explanation:

Using the concept of percentages the total earning of Cara can be found to be $4200.

Percentage is a number expressed as a fraction of 100. The % sign means to divide the number by 100.

Cara's earning = commission + basic salary

basic salary = $1800 (this is constant)

commission = 6% of $40000

= (6/100)*40000

= $2400

Cara's earning = 1800 + 2400

Hence, her earning is $4200

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According to the dimensions given, the volume of paper in the recycling bin is of 6800 cubic inches.

It is given by the multiplication of the base area by the height, that is:

\(V = S_bh\)

In this problem, we have that the measures in square inches and inches, respectively, are given by:

\(S_b = 400, h = 17\)

Hence:

\(V = 400 \times 17 = 6800\)

The volume of paper in the recycling bin is of 6800 cubic inches.

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Answer:

6800

Step-by-step explanation:

a. The expected value of profit associated with the medium-scale expansion is $105,400 and with the large-scale expansion is $94,000. Therefore, the preferred decision for maximizing the expected profit is the medium-scale expansion.

b. The variance of profit associated with the medium-scale expansion is $9,013,640 and with the large-scale expansion is $23,880,800. Therefore, the preferred decision for minimizing the risk or uncertainty is the medium-scale expansion.

a. The expected value of profit associated with the medium-scale expansion is

Expected profit = (0.32 x $50,000) + (0.5 x $150,000) + (0.18 x $200,000) = $105,400

The expected value of profit associated with the large-scale expansion is:

Expected profit = (0.32 x $0) + (0.5 x $100,000) + (0.18 x $300,000) = $94,000

Based on maximizing the expected profit, the preferred decision is the medium-scale expansion with an expected profit of $105,400.

b. The variance of profit associated with the medium-scale expansion is

Variance = (0.32 x ($50,000 - $105,400)^2) + (0.5 x ($150,000 - $105,400)^2) + (0.18 x ($200,000 - $105,400)^2) = $9,013,640

The variance of profit associated with the large-scale expansion is:

Variance = (0.32 x ($0 - $94,000)^2) + (0.5 x ($100,000 - $94,000)^2) + (0.18 x ($300,000 - $94,000)^2) = $23,880,800

Based on minimizing the risk or uncertainty, the preferred decision is the medium-scale expansion with a lower variance of $9,013,640.

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Answer:

Step-by-step explanation:

Given:

\(a_1=-4\) and \(a_n=a_{n-1}+9\) where \(n\geq 2\).

To find:

The explicit formula for the given recursive formula.

Solution:

We know that recursive formula of an AP is:

\(a_n=a_{n-1}+d\)

Where, d is the common difference.

We have,

\(a_n=a_{n-1}+9\)

Here, d=9.

The first term of the AP is \(a_1=-4\).

The explicit formula for an AP is:

\(a_n=a_1+(n-1)d\)

Substituting \(a_1=-4\) and \(d=9\), we get

\(a_n=-4+(n-1)9\)

\(a_n=-4+9n-9\)

\(a_n=-13+9n\)

Therefore, the required explicit formula for the given sequence is \(a_n=-13+9n\).

Thus, the Inequality effectively depicts how much somebody can spend provided his monthly savings goal is between 5% and 10%.: $55.75 < s < $111.50.

In mathematics, a percentage is a number or ratio that may be expressed as a fraction of 100.

When a number is expressed in decimal form, you can calculate its percentage by multiplying it by 100. For instance, multiplying 0.5 by 100 gives you the percentage 50%.

Given data:

Terrance's average bi-weekly net pay  = $1,115.00.

monthly budget savings - 5% to  10%.

Let s be the savings:

Then,

5% of 1,115.00.  < s < 10% of 1,115.00.  (both not included)

5 *1,115.00 / 100  < s < 10*1,115.00/100

55.75 < s < 111.50

Thus, the Inequality effectively depicts how much somebody can spend provided his monthly savings goal is between 5% and 10%.: $55.75 < s < $111.50.

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Answer: No

Is this 3/(2/3)?  I'll assume it is.

Step-by-step explanation:

3/(2/3) can be rewritten as 3*(3/2)

3*(3/2) = 9/2 or 4 1/2

Four groups of 2/3 would make 8/3 or 2 2/3, not 4 and 1/3.  

Answer:

ANS: 1 - D

ANS: 2 - B

ANS: 3 - A

ANS: 4 - D

Step-by-step explanation:

Step 1. Find the center

Step two

Graph a circle

Remember the radius is 3.5 units in order to know that, we need to have a point of 3.5 units of the center to the left, to the right, up and down and then we can obtain the graph of the circle

The specific value that the mean reading speed of a random sample of second-grade students will exceed cannot be determined solely based on the given information.

The statement mentions a "chance" but does not provide any specific information about the distribution or standard deviation of the reading speeds. Without knowing the variability of the data, it is not possible to determine a precise value that the mean reading speed will exceed.

To estimate the value, we would need additional information such as the standard deviation or a confidence interval. With this information, statistical techniques such as hypothesis testing or confidence intervals could be used to determine the likelihood of the mean reading speed exceeding a particular value.

Therefore, without more information, we cannot determine the exact value that the mean reading speed of a random sample of second-grade students will exceed. The statement implies that there is a possibility, but without additional data or assumptions, it is not possible to provide a specific value.

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If the speed "v" of train is 68 km/h, then the inequality that shows the error interval is  67.5 ≤ v < 68.5.

The speed of train being reported as 68 km/h, correct to the nearest km/h, the possible error interval for the true speed of the train can be expressed as : 67.5 ≤ v < 68.5,

The lower bound of interval, 67.5 km/h, is obtained by rounding down the true speed of the train to the nearest km/h.

The upper bound of interval, 68.5 km/h, is obtained by rounding up the true speed of the train to the nearest km/h.

Therefore, the error interval inequality is 67.5 ≤ v < 68.5.

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Answer: Where’s the question?

Step-by-step explanation: Bye, Have a Great Day!  :)

Answer:

385

Step-by-step explanation:

Answer:

The lines are straight the lines are at a 385 angle

Step-by-step explanation:

The reason they are straight lines is they are at a perfectly straight not curving to the side or bending like E and F how they have a 45 dgree angle I assume.

I not really sure if its right but umm if I am I hope this helps you out.

Answer:

Is Square Root of 25 Rational or Irrational?  

Step-by-step explanation:

A rational number can be expressed in the form of p/q. Because √25 = 5 and 5 can be written in the form of a fraction 5/1. It proves that √25 is rational.

The answer is:

Work/explanation:

What are rational numbers?

Rational numbers are integers and fractions.

Irrational numbers are numbers that cannot be expressed as fractions, such as π.

Now, \(\bf{\sqrt{25}}\) can be simplified to 5 or -5; both of which are rational numbers.

Using the information of the factors f ( x ) are

The term function as used n math refers to a relation consisting of variables. the variables are of two major types which include

The given function is substituted in the several equations given but the equations that yielded the desirable result of f ( x ) = 0 are:

Therefore they are the correct choice

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