Rewrite each of the following expressions using either a generic rectangle or the Distributive Property

Answer:

d) 2m+1

Step-by-step explanation:

for example:

m be 2 then. 2×2+1=5

m be 3 then. 2×3+1=7

The equation of the circle is (x-6)² + (y-11)² = 121. This is the standard form of the equation of the circle. The equation of a circle can be defined in the standard form as follows:(x-a)² + (y-b)² = r², where (a,b) is the center of the circle, and r is the radius of the circle.

The equation of a circle can be defined in the standard form as follows:(x-a)² + (y-b)² = r²where (a,b) is the center of the circle, and r is the radius of the circle. A circle is said to be tangent to the x-axis if its center lies on the x-axis. Here, the center is given to be (6,11) and is tangent to the x-axis. Hence, the equation of the circle can be written as (x-6)² + (y-11)² = r².

The radius of the circle can be determined by noting that it is a tangent to the x-axis, which means that the distance from the center (6,11) to the x-axis is equal to the radius of the circle. Since the x-axis is perpendicular to the y-axis, the distance between the center (6,11) and the x-axis is simply the distance between (6,11) and (6,0). Therefore, r = 11 - 0 = 11

Thus, the equation of the circle is (x-6)² + (y-11)² = 121. This is the standard form of the equation of the circle.

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Answer: 36.2

Step-by-step explanation:

To find the mean, you add up all the values then divide by the number of values present. So, 45+35+35+30+36= 181. 181 divided by 5 is 36.2

Sand is leaving at the rate of 3528 cm³/s when Sand collects in a conical pile with a radius that is always three times.

Given that,

Sand collects in a conical pile with a radius that is always three times its height as it falls from an overhead container. When the pile is 14 cm high, assume that the height of the pile is growing at a rate of 2 cm/s.

We have to find how quickly is the sand currently leaving the bin. Let V and h represent the cone's volume and height, respectively. Create an equation that connects V and h but leaves out the cone's radius.

We know that,

From given  r = 3 × h

Get an equation for the cone's volume in terms of height first.

v = 1/3 × π × r² × h

v = 1/3 × π × (3 × h)² × h

v = 1/3 × π × 9 × h³

Take derivative of both sides

d/dt { v = 3 × π × h }

dv/dt = 9 × pi × h² × dh/dt

In your problem,

dh/dt =2cm/sd

h = 14 cm

Plug in and solve for dh/dt

dv/dt = 9× π × 196 m² × 2

dv/dt = 3528 π cm³/s

Therefore, Sand is leaving at the rate of 3528 cm³/s when Sand collects in a conical pile with a radius that is always three times.

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The length of the microorganism that measure 5μm is equivalent to 0.005 mm

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

To solve this problem the we have to convert the units with the given information.

1mm is equal to 1000 μm

5μm * (1 mm/1000μm) = (5*1) / 1000 = 5/1000 = 0.005 mm = 5x10^-3 mm

The length of the microorganism that measure 5μm is equivalent to 0.005 mm

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Oberon's plan to gain the changeling boy from Titania reflects his character as he is willing to use devious means to get what he wants.

Oberon's plan to gain the changeling boy from Titania reflects his character as he is willing to use devious means to get what he wants. Oberon is portrayed as a manipulative character in A Midsummer Night's Dream. He tries to obtain what he wants from other characters without revealing his true intentions. In Act II, Scene 1, he becomes jealous when he sees Titania fawning over an Indian boy whom she has taken as a companion and wishes to possess him. In his efforts to gain the boy, Oberon concocts a plan to force Titania to give him up. He orders Puck to seek a love potion to sprinkle on Titania's eyes that will make her fall in love with a beast, so he can take the Indian boy without being hindered.

Oberon's desire to manipulate Titania into relinquishing the Indian boy exposes his character as being unscrupulous and selfish. He is willing to use any means to get what he wants without concern for other's feelings. Therefore, Oberon's plan to gain the changeling boy from Titania reflects his character as he is willing to use devious means to get what he wants.

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Answer:

9°

Step-by-step explanation:

m / sin L M = o / sin L O

41/sin L M = 98/sin 22°

=> sin L M = 41×sin 22°/98

= 41×0,3746 / 98

= 0,1567

so, L M = sin~¹ 0,1567 = 9°

Answer:

The answer is 4/45 lbs

Step-by-step explanation:

To solve, simply divide 2/3 by 7 1/2.

(2/3)/ (15/2)

When you divide fractions, you need to flip the second one, then multiply.

(2/3)*(2/15)

Multiply across.

4/45

The weight of Samantha's purchase is 4/45 pounds

Answer:

Step-by-step explanation:

Kate should deposit $46,158.28 monthly into an account

In this question, we have been given the amount A = $50,000,

interest rate R = 1.6%

period t = 5 years

We need to find the principal amount (P)

First, convert R as a percent to decimal

r = 1.6/100

r = 0.016

Using the formula of compound interest for P,

P = A / (1 + r/n)nt

P = 50,000.00 / (1 + 0.016/12)(12)(5)

P = $46,158.28

Therefore, Kate should deposit $46,158.28

Answer:

A. 29

Step-by-step explanation:

Set 5x - 11 = to 3x + 5, and then solve for X, and substitute the x value (8) back into the equation to get 29.

~theLocoCoco

Answer:

8 wristbands

Step-by-step explanation:

Let us assume that both of the company were ordered to deliver w wristbands.

The amount of money charged by company 1 who sells at $2 and offers free shipping is given as:

2w

The amount of money charged by company 2 who sells at $1.25 and $6 for shipping per order given as:

1.25w + 6

If both companies charge the same amount, hence:

2w = 1.25w + 6

2w - 1.25w = 6

0.75w = 6

w = 6/0.75

w = 8

The two companies charge the same amount for 8 wristbands

The sum of the two complex numbers will give:

(-4 + i) + (10 - 5i) = 6 - 4i

So the correct option is the third one.

Let's assume we have two complex numbers which are:

A = a + bi

B = c + di

The sum between these two complex numbers is:

A + B = (a + bi) + (c + di)

Taking i as a common factor we can rewrite:

(a + bi) + (c + di) = a + c + (b + d)i

And that is the general sum.

Here we want to solve:

(-4 + i) + (10 - 5i)

Again, if we take i as a common factor we can rewrite:

-4 + 10 + (1 - 5)*i

6 - 4i

So the correct option is the third one.

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Answer:

plot $30 on the line above one and plot $50 on the line above two and keep doing the same thing

Step-by-step explanation:

Plot the data first using the results above, so u can draw the line,

Then u can answer the questions, if the line goes through all the points its proportional, vice versa

No. of ways of selecting the 5 member committee by combination= 1981

What are the number of ways of selecting the 5 member committee ?

No. of women faculty in the mathematics department = 7

No. of men faculty in the mathematics department = 7

Total number of faculty members = 14

Condition - at least one woman must be on the committee

No. of ways of selection = C (14, 5) - C (7, 5)

We know that combination C(n , r) = \(\frac{n!}{(n-r)!r!}\)

Consider the total combination C (14, 5),

\(C (14, 5)=\frac{14!}{9!5!} \\\\=\frac{14 *13* 12 *11 *10 *9!}{9!* 5!} \\\\=\frac{14 *13* 12 *11 *10}{120} \\\\= \frac{240240}{120} \\\\= 2002\)              

Consider the combination of men C (7, 5) ,

\(C (7, 5)=\frac{7!}{2!5!} \\\\=\frac{7*6*5!}{2!* 5!} \\\\=\frac{7*6}{2} \\\\= 7*3\\\\=21\)

No. of ways of selection = C (14, 5) - C (7, 5)

                                        = 2002 - 21

                                        =1981

No. of ways of selecting the 5 member committee of the department with least one woman by combination= 1981

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Using mathematical operations, we can say that the extra pink sand avaliable to each girl is 1/16.

So, more pink sand is available to each girl:

Sand available to each girl:

Pink sand more to each girl:

Therefore, using mathematical operations, we can say that the extra pink sand avaliable to each girl is 1/16.

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The closest point to y in the subspace w spanned by u1 and u2 is [14/9, 46/9, 5/3], which is closest to option B.

The closest point to y in the subspace w spanned by u1 and u2 can be found using the formula:

proj_w(y) = [(y dot u1)/(u1 dot u1)]u1 + [(y dot u2)/(u2 dot u2)]u2

where dot denotes the dot product.

Substituting the given values, we get:

proj_w(y) = [(112 + 92 - 22*(-1))/(22 + 22 + (-1)(-1))] [2 2 -1] + [(11(-1) + 93 + 224)/(11 + 33 + 4*4)] [-1 3 4]

= [14/9, 14/9, -7/9] + [0, 16/3, 14/3]

= [14/9, 46/9, 5/3]

Therefore, the closest point to y in the subspace w spanned by u1 and u2 is [14/9, 46/9, 5/3], which is closest to option B.

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The multiplicative property of equality states that the same number can be added to or multiplied by both sides of an equation to obtain an equivalent equation. In this case, dividing both sides by 6 gives us u = 78/6 = 13.

The multiplicative property of equality states that if two numbers are equal, then multiplying both sides of the equation by the same number will also result in an equation that is still equal. In other words, if a=b, then ac=bc. We can use this property to solve for the variable u in the equation 78=6u.

To isolate the variable on one side of the equation, we can divide both sides by 6. This will give us:

78/6 = 6u/6

Simplifying the equation gives us:

13 = u

So the solution for u is 13.

In conclusion, the multiplicative property of equality with whole numbers was used to solve for the variable u in the equation 78=6u. The solution is u=13.

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Answer:

168

Step-by-step explanation:

We would like to multiply these two expressions together and then substitute -2 in for x to solve.

f(x) * g(x) = (8 - 10x) * (5x + 4)

We will use FOIL (first, outer, inner last):

(8 - 10x) * (5x + 4) = 8 * 5x + 8 * 4 + (-10x) * 5x + (-10x) * 4

Combining terms, we get:

f(x) * g(x) = 32 - 50x²

Plug -2 in for x:

32 - 50 * (-2)² = 32 - 50 * 4 = 32 - 200 = -168

The answer is thus 168.

~ an aesthetics lover

The given function is: f(x, y) = { 47122 * exp(-27), x > 0, y > 0

0, otherwise }

To check if it is a valid joint probability density function (PDF), we need to verify two conditions:

Non-negativity: The function should always be non-negative.

Integration: The integral of the function over the entire range should equal 1. Let's analyze each condition:

Non-negativity:

The function f(x, y) is defined as 47122 * exp(-27) for x > 0 and y > 0. Since both conditions are specified, the function is non-negative for valid values of x and y. Outside this range, the function is defined as 0, which is also non-negative.

Integration:

To check the integration, we need to evaluate the double integral of f(x, y) over the entire range. Since the function is defined as 0 outside the region where x > 0 and y > 0, we only need to integrate over this region.

∫∫ f(x, y) dx dy = ∫∫ 47122 * exp(-27) dx dy

Integrating with respect to x and y over their valid ranges, we have:

∫(0 to ∞) ∫(0 to ∞) 47122 * exp(-27) dx dy

This integral can be simplified as follows:

∫(0 to ∞) 47122 * exp(-27) dx * ∫(0 to ∞) 1 dy

The first integral evaluates to a constant, and the second integral evaluates to infinity. Therefore, the overall integration of the function is not finite.

Since the integral of the function does not equal 1, the given function f(x, y) does not satisfy the condition for a valid joint probability density function.

In conclusion, the given function is not a valid joint probability density function.

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Answer:

4 miles per hour

Step-by-step explanation:

\(\frac{\frac{1}{2} }{\frac{}{8} }\)  Which can be written

\(\frac{1}{2}\) ÷ \(\frac{1}{8}\)  There are a couple of ways to do this.  I think that the most intuitive way is to get a common denominator and then divide.

\(\frac{1}{2}\) x \(\frac{4}{4}\) = \(\frac{4}{8}\)    Anther name for \(\frac{4}{4}\) is one.  I used that to make an equivalent fraction

\(\frac{4}{8}\) ÷ \(\frac{1}{8}\) = \(\frac{\frac{4}{1} }{\frac{8}{8} }\) = \(\frac{4}{1}\) = 4

Answer:

k = - 4

Step-by-step explanation:

Given

y = 16 - x²

The point (k, 0 ) is a zero. To find the zero let y = 0, that is

16 - x² = 0 ( add x² to both sides )

16 = x² ( take the square root of both sides )

x = ± \(\sqrt{16}\) = ± 4

The zeros are x = - 4 and x = 4

Since (k, 0 ) is to the left of the origin, then k = - 4

To estimate the conditional probabilities for Pr(A = 1|+), Pr(B = 1|+), and Pr(C = 1|+), we need to calculate the probabilities of each event occurring given that the class is positive (+).

Let's analyze the given data and calculate the conditional probabilities:

Out of the 8 instances provided, there are 4 instances where the class is positive (+). Let's denote these instances as +1, +2, +5, and +6.

For Pr(A = 1|+), we calculate the proportion of instances among the positive class where A = 1. Out of the four positive instances, +2 and +5 have A = 1. Therefore, Pr(A = 1|+) = 2/4 = 0.5.

For Pr(B = 1|+), we calculate the proportion of instances among the positive class where B = 1. Out of the four positive instances, +5 has B = 1. Therefore, Pr(B = 1|+) = 1/4 = 0.25.

For Pr(C = 1|+), we calculate the proportion of instances among the positive class where C = 1. Out of the four positive instances, +5 and +6 have C = 1. Therefore, Pr(C = 1|+) = 2/4 = 0.5.

To summarize:

- Pr(A = 1|+) = 0.5

- Pr(B = 1|+) = 0.25

- Pr(C = 1|+) = 0.5

It's important to note that these probabilities are estimated based on the given data. Depending on the context and the underlying distribution of the data, these probabilities might not be accurate representations in other scenarios.

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Answer:

There are 68,640 different ways the runners can finish first, second, and third in the race.

Concept of Permutations

The number of different ways the runners can finish first, second, and third in a race can be calculated using the concept of permutations.

Brief Overview

Since there are 42 runners competing for the top three positions, we have 42 choices for the first-place finisher. Once the first-place finisher is determined, there are 41 remaining runners to choose from for the second-place finisher. Similarly, once the first two positions are determined, there are 40 runners left to choose from for the third-place finisher.

Calculations

To calculate the total number of different ways, we multiply the number of choices for each position:

42 choices for the first-place finisher × 41 choices for the second-place finisher × 40 choices for the third-place finisher = 68,640 different ways.

Concluding Sentence

Therefore, there are 68,640 different ways the runners can finish first, second, and third in the race.

The inverse function of f is denoted by f ⁻¹.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

The function is,

⇒ f

Now,

Since, The function is,

⇒ f

Hence, The inverse function of f = f ⁻¹.

Thus,  The inverse function of f is denoted by f ⁻¹.

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The critical point of f at z = 1 is a local minimum.

To find the critical points of the function f(z, 3) = 4z^2 - 8z + 1, we need to find the values of z where the first partial derivatives with respect to z are equal to zero. Let's solve it step by step.

Take the partial derivative of f with respect to z:

∂f/∂z = 8z - 8

Set the derivative equal to zero and solve for z:

8z - 8 = 0

8z = 8

z = 1

The critical point of f occurs when z = 1.

To determine whether the critical point is a local minimum, local maximum, or a saddle point, we can use the second partial derivative test. We need to calculate the second partial derivative ∂²f/∂z² and evaluate it at the critical point (z = 1).

Taking the second partial derivative of f with respect to z:

∂²f/∂z² = 8

Evaluate the second derivative at the critical point:

∂²f/∂z² at z = 1 is 8.

Analyzing the second derivative:

Since the second derivative ∂²f/∂z² = 8 is positive, the critical point (z = 1) corresponds to a local minimum.

Therefore, the critical point of f at z = 1 is a local minimum.

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The difference quotient of the function f(x) = 4x² - 5x is 8x + 4h - 5.

The formula for difference quotient is expressed as:

\(\frac{f(x+h)-f(x)}{h}\)

Given the function in the question:

f(x) = 4x² - 5x

To solve for the difference quotient, we evaluate the function at x = x+h:

First;

f(x + h) = 4(x + h)² - 5(x + h)

Simplifying, we gt:

f(x + h) = 4x² + 8hx + 4h² - 5x - 5h

f(x + h) = 4h² + 8hx + 4x² - 5h - 5x

Next, plug in the components into the difference quotient formula:

\(\frac{f(x+h)-f(x)}{h}\\\\\frac{(4h^2 + 8hx + 4x^2 - 5h - 5x - (4x^2 - 5x)}{h}\\\\Simplify\\\\\frac{(4h^2 + 8hx + 4x^2 - 5h - 5x - 4x^2 + 5x)}{h}\\\\\frac{(4h^2 + 8hx - 5h)}{h}\\\\\frac{h(4h + 8x - 5)}{h}\\\\8x + 4h -5\)

Therefore, the difference quotient is 8x + 4h - 5.

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Answer:

−

7

9

÷

(

−

2

5

8

)

Convert

2

5

8

to an improper fraction.

Tap for more steps...

−

7

9

÷

(

−

21

8

)

To divide by a fraction, multiply by its reciprocal.

−

7

9

(

−

8

21

)

Cancel the common factor of

7

.

Tap for more steps...

−

1

9

⋅

−

8

3

Multiply

−

1

9

by

−

8

3

.

−

−

8

9

⋅

3

Multiply.

Tap for more steps...

8

27

The result can be shown in multiple forms.

Exact Form:

8

27

Decimal Form:

0.

¯¯¯¯¯¯

296−

7

9

÷

(

−

2

5

8

)

Convert

2

5

8

to an improper fraction.

Tap for more steps...

−

7

9

÷

(

−

21

8

)

To divide by a fraction, multiply by its reciprocal.

−

7

9

(

−

8

21

)

Cancel the common factor of

7

.

Tap for more steps...

−

1

9

⋅

−

8

3

Multiply

−

1

9

by

−

8

3

.

−

−

8

9

⋅

3

Multiply.

Tap for more steps...

8

27

The result can be shown in multiple forms.

Exact Form:

8

27

Decimal Form:

0.

¯¯¯¯¯¯

296−

7

9

÷

(

−

2

5

8

)

Convert

2

5

8

to an improper fraction.

Tap for more steps...

−

7

9

÷

(

−

21

8

)

To divide by a fraction, multiply by its reciprocal.

−

7

9

(

−

8

21

)

Cancel the common factor of

7

.

Tap for more steps...

−

1

9

⋅

−

8

3

Multiply

−

1

9

by

−

8

3

.

−

−

8

9

⋅

3

Multiply.

Tap for more steps...

8

27

The result can be shown in multiple forms.

Exact Form:

8

27

Decimal Form:

0.

¯¯¯¯¯¯

296

Step-by-step explanation: