complete the orthogonal matrix for an unknown scalar α so its determinant is 1.

The larger radius of Cylinder P, which produces a lower the height per unit volume, compared to the smaller radius of Cylinder Q, indicates;

Graph a, matches the graph of Cylinder Q

Graph b, matches the graph of Cylinder P

The volume of water in a cylinder can be found using the formula;

V = π·r²·h

The volume of water is therefore, directly proportional to the volume, therefore, we get;

V ∝ h

V = k·h

Where; k = The constant of proportionality = The slope of the graph of the proportional relation

The equation, V = π·r²·h, indicates that we get;

k = π·r²

The value of the radius for P, r₁ is larger than the value of the radius for Q, r₂

Therefore, k₁ = π·r₁² > k₂ = π·r₂²

h = V/(π·r²)

Therefore, for a specified volume, V, V/π·r₁² < V/π·r₂², h₁ < h₂, and as the water is added, the height of the water in Cylinder Q increases more than the height of the water in Cylinder P, which indicates that we get;

Graph a corresponds to the graph of Cylinder Q, and graph b corresponds to the graph of Cylinder P.

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Answer:

A. To find out how many eggs were in the flat, you need to use the information that 5 eggs were cracked, which is 1/6 of the total number of eggs in the flat.

If 5 eggs is 1/6 of the total number of eggs in the flat, then you can set up an equation to find the total number of eggs:

5 eggs = (1/6) * x

Where x is the total number of eggs in the flat.

To solve for x, you can cross-multiply to get:

5 eggs * 6 = 1 * x

Which gives:

x = 30

So there were 30 eggs in the flat.

B. To find out what percent of the eggs in the flat were not cracked, you need to know how many eggs were not cracked and divide that number by the total number of eggs in the flat, and then multiply by 100 to get the percentage.

Since 5 eggs were cracked and there were 30 eggs in the flat, you can find the number of eggs that were not cracked by subtracting the number of cracked eggs from the total number of eggs:

30 eggs - 5 eggs = 25 eggs

So 25 eggs were not cracked.

To find the percentage, you can divide the number of eggs that were not cracked by the total number of eggs in the flat and multiply by 100:

(25 eggs / 30 eggs) * 100 = 83.33%

So, 83.33% of the eggs in the flat were not cracked.

The distance Brett covered was 12 km, but his displacement was 8.6 km.

Displacement is a vector quantity that is measured as a change in an object's position, so the length of the position from the object's initial point to the object's end point.

Distance is a scalar quantity which is defined as the length of the entire path traveled by an object.

Given:

Distance = S₁ + S₂

Distance = 7 + 5

Distance = 12 km

The distance Brett has covered is 12 km.

Starting position = A

Final position = C

Displacement = AC

The displacement in this case is calculated by the Pythagorean theorem.

AC² = AB² + BC²

Displacement² = S₁² + S₂²

Displacement² = 7² + 5²

Displacement² = 49 + 25

Displacement² = 74

Displacement = [tex]\sqrt{74}[/tex]

Displacement = 8.6 km

The displacement that Brett has covered is 8.6 km.

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Answer:

The value of o is 0.13.

Step-by-step explanation:

No, (x - 2) is not a factor of f(x) = x³ - 2x² + 2x + 3.

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

Given that;

The expression is,

⇒ f (x) = x³ - 2x² + 2x + 3

And, The factor is (x - 2)

Now, If (x - 2) is factor of function then x = 2 satisfy the function.

Hence, We can check as,

⇒ f (x) = x³ - 2x² + 2x + 3

Put x = 2

⇒ f (2) = 2³ - 2 (2)² + 2 × 2 + 3

⇒ f (2) = 8 - 8 + 4 + 3

⇒ f (2) = 7 ≠ 0

Hence, (x - 2) is not a factor of f(x) = x³ - 2x² + 2x + 3.

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y(t) = 3u(t) is a constant function that is equal to 3 for t >= 0 and equal to 0 for t < 0.

The function x(t) = 3tu(t) is a product of a scalar 3 and a unit step function u(t). Here, u(t) is defined as:

u(t) = 0 for t < 0

u(t) = 1 for t >= 0

So, x(t) is equal to 3t for t >= 0 and equal to 0 for t < 0.

The function y(t) is the derivative of x(t) with respect to t. To find the derivative of x(t), we use the power rule for differentiation, which states that the derivative of tx(t) is x(t) + t × dx(t)/dt.

So, we have:

y(t) = dx(t)/dt = d(3tu(t))/dt = 3u(t) + 3tu'(t) = 3u(t)

Here, u'(t) is the derivative of u(t) with respect to t, which is equal to the Dirac delta function δ(t).

So, we have:

y(t) = 3u(t) = 3 for t >= 0

y(t) = 0 for t < 0

Hence, y(t) = 3u(t) is a constant function that is equal to 3 for t >= 0 and equal to 0 for t < 0.

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The fourth term of the arithmetic sequence will be negative 10.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The first term (a₁) is 2. And the common difference is given as,

aₙ = aₙ₋₁ - 4

aₙ - aₙ₋₁ = - 4

d = - 4

The fourth term of the arithmetic sequence is given as,

a₄ = 2 + (4 - 1)(-4)

a₄ = 2 + 3 x (-4)

a₄ = 2 - 12

a₄ = - 10

The fourth term of the arithmetic sequence will be negative 10.

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The critical chi-square value for a chi-square test with seven classes and a p-value of 0.05 is 12.59.

A hypothesis is an educated guess or prediction about a relationship between variables. The critical chi-square value is the value that is used to make a decision about the hypothesis.

If the calculated chi-square value is greater than the critical chi-square value, we reject the null hypothesis, which states that there is no significant difference between the expected and observed frequencies.

For a chi-square test with seven classes, the critical chi-square value can be found by looking at the critical chi-square values for a p-value of 0.05, as shown in Table 1.

The degrees of freedom (df) is equal to the number of classes minus 1, so in this case, df = 7 - 1 = 6.

Therefore, the critical chi-square value for a chi-square test with seven classes and a p-value of 0.05 is 12.59.

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The distance between any two raisins will not change when the bread doubles its size.

This is because the proportion of the raisins to the size of the dough remains constant. Mathematically, this can be expressed as:

Let d = the original distance between any two raisins

Let n = the new (doubled) size of the bread

d/n = constant

This means that when the size of the bread (n) doubles, the distance between the two raisins (d) remains unchanged. For example, if the original size of the bread was 10cm, and the distance between two raisins was 2cm, then when the bread is doubled to 20cm, the distance between the two raisins will still be 2cm.

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The equation for the given scenario is -1.5+1.5 =0.

Temperature is a degree of hotness or coldness the can be measured using a thermometer. It's also a measure of how fast the atoms and molecules of a substance are moving. Temperature is measured in degrees on the Fahrenheit, Celsius, and Kelvin scales.

Given that, the temperature in a city is -1.5° C

Now,

The temperature needs to rise -1.5° C to reach 0° C.

Then, the equation is

-1.5+1.5 =0

0 = 0

Therefore, the equation is -1.5+1.5 =0.

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Answer:

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

Area of circle with radius r is:

We have r = 8.5 m and using 3.14 for π to find the area:

The discontinuity as x is  -3 is removable by defining f(-3) is -1/8.

Factoring the function's denominator and numerator first is the recommended approach.When a number has zeros in both the numerator and denominator, a point of discontinuity is reached.

There is a point of discontinuity there since the denominator and numerator are both zeros.If x is between 0 and 1, we say that the function is discontinuous.

This function has 3 asymptotes, which are lines that the curve approaches but doesn't cross.The vertical line x=1 is one of them, along with the x-axis, y-axis, and (denoted by a dashed line in the graph above).

Maybe you have

f ( x) = x+ 3/x²- 2x -15

= x+3/(x+3)(x-5)

= 1/x- 5

x infinite  -3

This will have discontinuities (points where the function is undefined) at .

   x = -3

   x = 5

The discontinuity as x = -3 is removable by defining f(-3) = -1/8.

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each sitcom is 33 minutes long

each drama is 19 minutes long.

Let x be the length in minutes of a sitcom and y be the length in minutes of a drama.

We can write the following system of equations to represent the situation:

6x + y = 179

6x + 4y = 302

To solve the system using elimination, we can multiply the first equation by 4 to make the coefficients of y equal, and then subtract the second equation from the first:

24x + 4y = 716

6x - 4y = -123

18x = 593

Finally, we can divide both sides of the equation by 18 to find x:

x = 33

So, each sitcom is 33 minutes long. To find the length of each drama, we can substitute the value of x into either of the original equations:

6x + y = 179

6 * 33 + y = 179

198 + y = 179

y = 19

So, each drama is 19 minutes long.

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The surface areas of the regular solids are;

1. a. 150 ft²

b. 216 ft²

c. 894 mm²

2. a. 118 square units

b. 892 in²

3. a. 576·π square units

b. 1024·π square units

c. 100·π square units

4. a. 216·π square units

b. 48·π square units

c. 48·π square units

5. To complete the task, two circles of 1 ft radius should be cut from the carpet, followed by cutting a rectangular shape of width 4 ft and length of 2·π ft

The surface area of a solid is the sum of the areas that form a boundary around the outer part of the solid.

1 The surface area of a cube is A = 6·s²

a. When s = 5, A = 6 × 5² = 150

b. When s = 6 ft, A = 6 × 6² = 216

c. When s = 12 mm, A = 6 × 12² = 864

2. The surface area of a rectangular prism is; S.A. = 2·l·w + 2·h·w + 2·l·h

a. l = 2, w = 5, h = 7

Surface area = 2 × (2 × 5 + 5 × 7 + 2 × 7) = 118

b. l = 16 in, w = 11 in, h = 10 in

The surface area = 2 × (16 × 11 + 16 × 10 + 10 × 11) = 892

3. The surface area of a sphere, A  = 4·π·r²

a. The radius of the sphere, r = 12

A = 4 × π × 12² = 576·π

b. r = 16, therefore;

A = 4 × π × 16² = 1024·π

c. When the diameter, d = 10, we get;

A = 4·π·r² =  4·π·(d/2)² =  4·π·d²/4

A = 4·π·d²/4 = π·d²

4. The surface area of a cylinder, A = 2·π·r·h + 2·π·r²

a. r = 6, h = 12, therefore;

A = 2×π×6×12 + 2×π×6² = 216·π

b. r = 2, h = 10, therefore;

A = 2×π×2×10 + 2×π×2² = 48·π

c. r = 3, h = 5, therefore;

A = 2×π×3×5 + 2×π×3² = 48·π

5. The diameter of the cylinder = 1 ft

Height of the cylinder = 4 ft

The area for the carpet to cover the each of the top and bottom = π×1² ft² = π ft²

The area to cover the curved surface = 2 × π × r × h

Therefore, area of the curved surface = 2 × π × 1 × 4 = 8·π

Area of the curved surface = 8·π ft²

Two circular shapes of radius 1 ft should be cut, followed by a rectangle of side length, 4 ft, and width 8·π/4 ft = 2·π ft

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The Three V's of Big Data are Volume, Velocity, and Variety. While "Volume" is an important characteristic of big data, it is not considered one of the Three V's because it is not unique to big data. So option (4) is correct.

There are many other characteristics of big data that have been proposed, but the Three V's are the most widely recognized and used

The "Three V's of Big Data" is a well-known concept that refers to the defining characteristics of big data. These three V's are Volume, Velocity, and Variety. They describe the main challenges that organizations face when dealing with big data, and how they can be overcome.

A common misconception is that there are only three V's of big data, but in reality, there are more than three. Some additional V's that have been proposed include Veracity, Value, Variability, and others.

However, there is one common concept that is often mentioned in discussions of big data, but is not considered one of the V's. This concept is "Volume." While "Volume" is certainly a key characteristic of big data, it is not considered one of the Three V's because it is not unique to big data. All types of data, whether big or small, can be large in volume.

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Complete Question:

which is not one of the three v's of big data?

Answer:

-26.25 - 15.5x = -15.5x - 11.78

collect the like term

-15.5x + 15.5x = -11.78 + 26.25

= 14.48

Answer:

no solution

Step-by-step explanation:

- 5(5.25 + 3.1x) = - 6.2(2.5x + 1.9) ← distribute parenthesis on both sides

- 26.25 - 15.5x = - 15.5x - 11.78 ( add 26.25 to both sides )

- 15.5x = - 15.5x + 14.47 ( add 15.5x to both sides )

0 = 14.47 ← False

this false statement indicates the equation has no solution

The linear equation representing Mia's situation is y = 3x + 12.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The two points given are - (4,24) and (6,30)

The slope-intercept form of a linear equation is - y = mx + b, where m is the slope and b is the y-intercept.

To find the slope use the formula -

m = (y2 - y1)/(x2 - x1)

m = (30 - 24)/(6 - 4)

m = 6/2

m = 3

So, now the equation becomes - y = 3x + b

To find the y-intercept substitute the equation with x and y values -

24 = 3(4) + b

24 = 12 + b

b = 24 - 12

b = 12

So, now the equation becomes - y = 3x + 12.

Therefore, the linear equation y = 3x + 12.

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A bathtub has some water in it. Mia turns on the faucet and add more water. The total amount of water in gallons, y, is a function of the time in minutes since Mia turned on the faucet, x. The graph of a linear function passes through the points (4,24) and (6,30) What is the equation of the function?

The correct reaction profile is it applies to both SN1 and E1 reactions.

The term reaction is defined as a process in which one or more substances, also called reactants, are converted to one or more different substances, known as products

Here we have know that in a chemical reaction and then a transition state is a state that exists between reactants and intermediates or products directly,

Here in which bonds are concurrently breaking and forming new ones.

And it is extremely unstable and highly energetic.

We know that both intermediates and transition states are the states that are present between the reactants and the reaction's end products, on the other hand they differ in that intermediates have full bonds, are more stable than the substrate and therefore have a lower energy and have a discrete lifetime,

Here we know that instead of a transition state has only partial bonds and is least unstable, thus making it the state with the highest energy at the reaction profile.

Therefore the correct option is (a).

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Matching the transactions to their relevant posting in the ledger are;

Business purchases furniture: furniture account debited

Business sells furniture: furniture account credited

Business takes a loan from the bank: loan account debited

Business pays off the loan: loan account credited

The ledger transactions are simply defined as a summary of transactions made as journal entries to sub-ledger accounts.

Now, the three main types of ledgers are;

1) General ledger: This  contains accounts that correspond to the income statement and balance sheet for which they are destined.

2) Sales ledger or debtor's ledger: This shows  at any given time how much your customers owe you and your company.

3) Purchase ledger or creditor's ledger: This shows a record of a company's purchases of goods and services showing the amounts that have been paid and remain to be paid.

From the above, we can classify the transactions as;

Business purchases furniture: furniture account debited

Business sells furniture: furniture account credited

Business takes a loan from the bank: loan account debited

Business pays off the loan: loan account credited

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Answer:

tally 4 which has 19 points

Step-by-step explanation:

22+19=41

41/2 = 20.5, divided by two because the team is involved in only two game tournament

this is the least she should have in average to win the MVP award.

since more then 20 means not including 20 but more than of it.

The period of the function based on the information will be D. 2π.

The period of the function is the interval between repetitions of any function. A trigonometric function's period is the length of one whole cycle.

One cycle of the sine curve's length is referred to as its period. The period of the function is the minimum value of the dependent variable x after which the function will repeat itself.

f(x + k) = f(x).

-2sin(k + x) + 2 = 2sinx + 1

sin(k + x) = sin(2π + x)

k + x = 2π + x

k = 2π

The period is 2π.

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The table provides various values, including all minimums and maximums, of a cosine function f (x) on the interval [0, 2π].

Angle 0 pi over 6 pi over 2 5 pi over 6 3 times pi over 2 2π

f (x) 1 0 –1 0 3 1

What is the period of the function?

A) 2 times pi over 3

B) pi over 2

C) π

D) 2π

A: Average speed of the car is 50 km per hour,

B: speed in miles per hour is 34.068 miles per hour,

C: The distance covered by a cheetah in 5 seconds is 75 meters,

D: distance covered by a cheetah in 1 minute is 1500 meters.

The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other terms, it is a measurement of an object's motion's speed without direction The term "velocity" refers to the combination of direction and speed.

Given the distance covered in half-hour = 25 km

speed = distance/time

speed = 25/.5

speed = 50 km per hour

av. speed =  50 km per hour

B: we know,

1 km = 0.621371 mile

50 km = 50*0.621371

50 km = 31.068 miles

av. speed = 34.068 miles per hour

C: speed of cheetah = 25 m/s

distance covered in 5 seconds = 25* 5

distance covered in 5 seconds = 75 meters

D: distance covered in 60 seconds = 25*60

distance covered in 60 seconds = 1500 meters

Hence average speed is  50 km per hour,

speed in mph is 34.068 miles per hour,

distance covered in 5 seconds is 75 meters,

distance covered in 60 seconds is 1500 meters.

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Observing the options we see that the graph the corresponds to the given coordinates is option B. The function is increasing in the function (1, infinity).

What is first derivative of a function?

The rate of change of one variable with respect to another variable is represented by a function's first order derivative. For instance, in physics, we define a body's velocity as the rate at which its location changes in relation to time.

Given that the function is: f(x) = √x -1.

Substitute the value of x = 1:

f(x) = √ 1 -1

f(x) = 0

The first coordinate is (1, 0).

Substitute the value of f(x) = 0:

f(x) = √ x -1

0 = x -1

x = 1

The second coordinate is (1, 0).

Observing the options we see that the graph the corresponds to the given coordinates is option B.

a. Find the first derivative of the equation f(x) = √x -1.

f'(x) = (1/2)(x - 1)^(1/2)

Equate the value to 0:

(1/2)(x - 1)^(1/2)  = 0

x - 1 = 0

x = 1

Hence, the function is increasing in the function (1, infinity).

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to get the equation of any straight line, we simply need two points off of it, let's use the provided values

[tex]\begin{array}{|cc|ll} \cline{1-2} \stackrel{x}{years}&\stackrel{y}{value}\\ \cline{1-2} 3&15000\\ 5&11000\\ \cline{1-2} \end{array}\hspace{5em} (\stackrel{x_1}{3}~,~\stackrel{y_1}{15000})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{11000})[/tex]

[tex]\stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{11000}-\stackrel{y1}{15000}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{3}}} \implies \cfrac{ -4000 }{ 2 } \implies - 2000 \\\\\\ \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}{15000}=\stackrel{m}{- 2000}(x-\stackrel{x_1}{3})[/tex]

[tex]y-15000=-2000x+6000\implies {\Large \begin{array}{llll} y=-2000x+21000 \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{after 8 years, x = 8}}{y = -2000(8)+21000}\implies \boxed{y=5000}[/tex]

The above answer is better

Answer:

The length of the ramp can be found using the tangent function:

tan(21°) = height/length

length = height / tan(21°)

length = 16 inches / tan(21°)

Note: make sure to convert the height from inches to the same unit used in the tangent function, usually radians.

After 7 weeks, the plant's approximate height is 8.7 cm.

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the connection between two expressions on opposite sides of the sign. It generally consists of one variable and one equal to symbol.

Here,

You are given a a graph titled Plant Height that shows Number of Weeks on x axis and Height of Plant in cm on y axis. Plotting this and you will get an equation of y = 1.2792x - 0.1665 (I used excel using the given points from the above problem).

y = 1.2792x - 0.1665

y = 1.2792 (7) - 0.1665

y = 8.78 centimeters.

The most likely approximate height of the plant after 7 weeks is 8.7 centimeters.

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The probability that exactly two tails will come up in three tosses of this coin is given as follows:

0.288 = 28.8%.

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The parameter values for this problem are given as follows:

n = 3, p = 0.4.

The probability that exactly two tails will come up in three tosses of this coin is P(X = 2), hence:

P(X = 2) = 3 x 0.4² x 0.6

P(X = 2) = 0.288.

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If your car gets 29 miles per gallon, then it cost to drive 410 when gasoline costs $3.30 per gallon is $46.662.

Your car gets 29 miles per gallon.

It drive 410 miles.

Now determining how much gallon you used to drive 410 miles.

Total Gallon = Total Distance that you covered/Miles per gallon

Total Gallon = 410/29

Total Gallon = 14.14

The costs of per gallon = $3.30

Now we finding the total cost by multiplying the total gallon by the cost of per gallon. After multiplying we get how much it cost to drive 410 when gasoline costs $3.30 per gallon.

So, the cost of 14.14 gallon = 14.14 × $3.30

The cost of 14.14 gallon = $46.662

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Answer:

+, x, -

Step-by-step explanation:

8 + 6 x 4 - 2

8 + 24 - 2

32 - 2

30