3D Rotation (30 points) Suppose we have a coordinate system A that can be mapped to a coordinate system B in two steps: 1) R 1
​
: rotate π around X axes; 2) R 2
​
: rotate π/2 around Z axes. The rotation follows right hand rule. The overall rotation R carries out this mapping from A to B. - Give the 3x3 matrix R ′
carries out mapping from B to A. (5 points) - Given a point whose coordinate is [10,0,20] in B, calculate its coordinates A. (5 points)

Equity is generally defined as the difference between the value of a company’s assets and its liabilities, and is typically expressed as a dollar amount.

The formula for equity is: Equity = Assets - Liabilities To calculate equity, you would first need to calculate the value of all of the company’s assets, such as cash, investments, inventory, property, and equipment. Then, you would need to calculate the value of all of the company’s liabilities, such as accounts payable, short and long-term debt, and any other financial obligations. Once the value of the assets and liabilities have been calculated, the difference between them is the company’s equity. For example, if a company has total assets of $4,000 and total liabilities of $2,500, the equity can be calculated as follows :Equity = Assets - Liabilities Equity = $4,000 - $2,500  Equity = $1,500

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Answer:

C

Step-by-step explanation:

a parameter is a number describing a whole population (e.g., population mean), while a (sample) statistic is a number describing a sample (e.g., sample mean).

so, everything involving all 700,000 people creates parameters.

therefore, C is correct.

(12, 5)

equations:

To solve with elimination, either the x or y coefficient should be similar.

Then,

\(\sf 3x-5y=11\)

\(\sf 3x-12y=-24\)

==============       [ subtract equation 2 from equation 1 ]

\(\sf 7y = 35\)

\(\sf y = 5\)

For x,

\(\sf 3x-5(5)=11\)

\(\sf 3x-25=11\)

\(\sf 3x=11+25\)

\(\sf x=\dfrac{36}{3}\)

\(\sf x=12\)

In ordered pair: (x,y) → (12, 5)

To find P(A | B),  first we use the formula P(A | B) = P(A ∩ B) / P(B).To find P(B | A), we use the formula P(B | A) = P(A ∩ B) / P(A).  To determine if A and B are independent, we need to compare P(A ∩ B) with P(A)P(B). If P(A ∩ B) = P(A)P(B), then A and B are independent. If P(A ∩ B) ≠ P(A)P(B), then A and B are dependent.

a. Plugging in the given values, we have:
P(A | B) = 0.20 / 0.50 = 0.40
So, P(A | B) = 0.4000 (to 4 decimals).

b. Plugging in the given values, we have:
P(B | A) = 0.20 / 0.50 = 0.40
So, P(B | A) = 0.4000 (to 4 decimals).

c. Given values are:
P(A) = 0.50
P(B) = 0.50
P(A ∩ B) = 0.20
Calculating P(A) * P(B):
0.50 * 0.50 = 0.25

Since P(A ∩ B) ≠ P(A) * P(B), events A and B are not independent. The occurrence of one event affects the probability of the other event occurring.

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Answer: See attached image

Step-by-step explanation:

The two column proof is written as follows

Statement                                                           Reason

MA = XR                                           given (opposite sides of rectangle)

MK = AR                                           given (opposite sides of rectangle)

arc MA = arc RK                               Equal chords have equal arcs

arc MK = arc AK                               Equal chords have equal arcs

An arc is a portion of the circumference of a circle, and a chord is a line segment that connects two points on the circumference.

If two chords in a circle are equal in length, then they will cut off equal arcs on the circumference. This is because the arcs that the chords cut off are subtended by the same central angle.

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Answer:

10 years

Step-by-step explanation:

The number of vats to be used is 8

Given: Weight of material used per day = 196 pounds

Weight of each vat = 26 pounds

Cycle time for each vat = 2.5 hours

Inefficiency factor assigned by manager = 25%

Time available for each day = 8 hours

To calculate the number of vats to be used, we need to calculate the time required to transport the total material by the available vats.

So, the number of vats required = Total material weight / Weight of each vat

To calculate the total material weight transported in 8 hours, we need to calculate the time required to transport the weight of one vat.

Total time to transport one vat = Cycle time for each vat / Inefficiency factor

Time to transport one vat = 2.5 / 1.25

(25% inefficiency = 1 - 0.25 = 0.75 efficiency factor)

Time to transport one vat = 2 hours

Total number of vats required = Total material weight / Weight of each vat

Total number of vats required = 196 / 26 = 7.54 (approximately)

Therefore, the number of vats to be used is 8 (rounded up to the next whole number).

Answer: 8 vats will be used.

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a) The general equation is:

y = m*(x - h) + k

b) The slope is -3

c) the point-slope form is: y = -3*(x - 6) + 1

d) The standard form is: y + 3x = 19

We will write a linear equation that relates two variables x and y, and the slope-point form is given by:

y = m*(x - h) + k

Where m is the slope, and (h, k) is a point on the line.

Particularly, if a line passes through two points (a, b) and (c, d), then the slope of that line is:

m = (d - b)/(c - a)

In this case, the line passes through (6, 1) and (5, 4), then the slope is:

m  = (4 - 1)/(5 - 6) = 3/-1 = -3

Now  we can use one of the given points to write the line in the point-slope form, I will use (6, 1) to get:

y = -3*(x - 6) + 1

Now we want to write this in standard form.

Expanding the right side we get:

y = -3x + 18 + 1

y = -3x + 19

Adding 3x in both sides we get:

y + 3x = 19

This is the standard form.

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The irrational number for this problem are given as follows:

pi/2.

Rational numbers are numbers that can be represented by fractions, such as numbers that have no decimal parts, or numbers in which the decimal parts are terminating or repeating.

Irrational numbers are numbers that cannot be represented by fractions, being non-terminating and non-repeating decimals, such as non-exact square roots.

For this problem, we have that the number pi/2 is irrational, as pi is a non-terminating decimal, and the division of an irrational by a rational results in an irrational.

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Answer:

child tickets: 115

adult tickets: 175

Step-by-step explanation:

number of child tickets = x

number of adult tickets = y

(value of child ticket [8] * number of child tickets [x]) + (value of adult ticket [8.5] * number of adult ticket [y]) = total value (2407.50)

8x + 8.5y= 2407.50

290 (total number of tickets) = x (number of child tickets) + y (number of adult tickets)

290 = x+y

system of equations: 8x + 8.5y= 2407.50

290 = x + y

solve equation:

x = 115

y = 175

For data at the interval​ level, we cannot calculate meaningful differences between data entries. The statement is false.

Interval:

The interval of a numerical value generally represents the maximum and minimum value between which the numerical value belongs, it is the amount of time that has passed between the beginning and end of the event which is also known as elapsed time.

The various ways of showing intervals are Inequalities, interval notations, and number lines, the amount of time between two given times is known as the time interval.

Data at the ordinal level can be qualitative or quantitative.  A true statement is​ "For data at the interval​ level, you can calculate meaningful differences between data​ entries."

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The slope of the function represents the change in height per day. In the given function, h = 3d, the slope is 3. This means that for every 1 unit increase in the number of days, the height of the corn plant increases by 3 units (in this case, centimeters).

Therefore, the correct answer is (C) The change in height per day.

Slope of Function represents the change in height per day.(Option C)

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.

Consequently, the formula for the change in y-coordinate with respect to the change in x-coordinate is

\(m=\frac{dy}{dx}\) = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line can be shown as

tan θ = Δy/Δx

So, the slope of a line is tanΘ.

So as slope represents change in y per change in x, in the given question as y is height and x is days, slope is change in height per day.

Slope of Function represents the change in height per day.(Option C)

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Answer:

the red cup contains the highest amount of tomato juice

the blue and yellow cup contain the same amount of juice

the difference between the highest amount and the lowest is 10 ounces

Step-by-step explanation:

convert all the other measurements to ounces

i cup = 8 ounces

6 x 8 = 42

1 p = 16 ounces

16 x 2 = 32

Answer:oh tough one! iwould help but i cant see the pic :(

Step-by-step explanation:

Answer:

5 feet times the ratio of the lengths of the two grasshoppers

Step-by-step explanation:

\(5( \frac{1.5}{1.2} ) = 6.25\)

hope this helps

P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

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Answer:

1.x=0, –10

2.x=3, 4

Step-by-step explanation:

1.

x(x+10)=0===> x=0, –10

2.

x²–3x–4x+12===> x²–7x+12=0

(x–3)(x‐4)=0====> x=3, 4

Answer:

4 Hours & 30 Minutes

Step-by-step explanation:

The only thing you have to do is divide 27 by 6 and you get 4.5 which is your answer. This is because each 6 you have is 1 hour so when you have 4.5 it equals 4.5 hours.

Answer:6

Step-by-step explanation:Four ounces of oregano and 2 ounces of garlic powder are mixed to create a poultry seasoning. Oregano costs $4 per ounce, and garlic powder costs $3 per ounce.

Answer:

the point where the two lines intersect is (-8, 4)

Answer:

can u show me a picture of this problem.

Step-by-step explanation:

Answer:

17x1-4+183

Step-by-step explanation:

Answer:

8.73 Ounces

Step-by-step explanation:

8.73 + 8.86 = 17.59

17.59 - 0.23 = 17.36

17.36 divide by 4 = 8.73

Each bowl has 4.46 ounces of fruit.

The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication.

Now it is given that,

ounces of strawberries = 8.73 ounces

ounces of blueberries = 8.86 ounces

So, total ounces of fruits = 8.73 ounces + 8.86 ounces

⇒  total ounces of fruits = 17.59 ounces

Left over fruit = 0.23 ounces

So, total ounces of fruit in all bowls = 17.59 ounces - 0.23 ounces

⇒ total ounces of fruit in all bowls = 17.82 ounces

Since there are 4 bowls.

Thus, ounces of fruit in each bowl = 17.82/4 ounces

⇒ ounces of fruit in each bowl = 4.46 ounces

Thus, Each bowl has 4.46 ounces of fruit.

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Answer:

c

Step-by-step explanation:

Explanation

In the question, we are given that the millet seeds and the sunflowers seed are packaged in 5 pounds back.

We can assume that the pounds of millet seeds be x and the pounds of sunflower seeds be y. We can therefore create the equation;

Next, we know that a pound of sunflower seed cost $1.75 and a pound of millet seed cost $2.50 and the mixture is sold for $11.60. This will imply;

We will then solve the above equation simultaneously.

Insert equation 3 in equation 2

Since the weight of the sunflower seed is represented by y, therefore the answer is;

Answer: 1.2 pounds

The root of the function \(\(f(x) = 5\cos(x) - \sqrt{x^2 + 1} + 2^{x-1}\)\) lies within the interval \(\([-1, 0]\)\).

To find the interval where the root of the given function lies, we need to analyze the behavior of the function within certain intervals. Let's consider the interval  \(\([-1, 0]\)\).. For \(\(x = -1\)\), we have \(\(f(-1) = 5\cos(-1) - \sqrt{(-1)^2 + 1} + 2^{-2}\)\). Since \(\(\cos(-1)\)\) is positive and the other terms are also positive, the value of \(\(f(-1)\)\) is positive.

Now, for \(\(x = 0\)\), we have \(\(f(0) = 5\cos(0) - \sqrt{0^2 + 1} + 2^{-1}\)\). Since \(\(\cos(0)\)\) is positive and the other terms are positive, the value of \(\(f(0)\)\) is positive.

As the function is continuous, and it changes sign from positive to negative within the interval  \(\([-1, 0]\)\) (as \(\(f(-1)\)\) and \(\(f(0)\)\) have different signs), by the Intermediate Value Theorem, there exists at least one root of the function within this interval. Therefore, we can conclude that the root of \(\(f(x)\)\) lies within the interval  \(\([-1, 0]\)\).

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