2. Use powers to rewrite these problems:
Example: 5 x 5 = 5^2
a. 4 * 4 * 4 * y * y * y
b. 7 * 7 * 7
c. 3 * 3 * 3 * x * x * x

The inequality that represents the heaviest the packaging can be without exceeding the 50-pound weight limit is 21 + x ≤ 50 and weight of the packaging is less than or equal to 29 pounds.

Let x be the weight of the packaging in pounds. Then the total weight of the item and its packaging is 21 + x pounds. To ensure that the total weight does not exceed the 50-pound weight limit, we can set up the following inequality:

21 + x ≤ 50

We subtract 21 from both sides to isolate x and obtain:

x ≤ 50 - 21

x ≤ 29

Therefore, the weight of the packaging cannot be greater than 29 pounds without exceeding the 50-pound weight limit. To ensure that the item can be mailed by parcel post, the weight of the packaging must be less than or equal to 29 pounds.

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Answer:

63 because 4×15 is 60 and 0.25 of 15 is 3.75 you cant have 0.75 of a lizard

Answer:

It would take 9 years for the population to fall below 10000.

Answer:

16π or 50.3 units

Step-by-step explanation:

the formula for the surface area of a sphere (as you mentioned) is:

4πr²

So if we plug in the given value (2) for r:

4π×2²=16π

Answer:

16

Step-by-step explanation:

I got it right

Answer:

Brainliest!

Step-by-step explanation:

30+8

=38

16/2 = 8

Answer:

38

Step-by-step explanation:

16/2 = 8

30 + 8 = 38

Answer:

0

Step-by-step explanation:

A rational number is a number that can be expressed as a fraction of two integers q/p where p, the denominator is not a 0. Therefore if a is 0 then it isn't a rational number

Answer:

0 must be the value of 'a' the number 7/a is not a rational number

Step-by-step explanation:

7/0=infinity

The perimeter of the television screen is 54 inches.

To find the perimeter of a television screen, we need to add up all four sides. In this case, the two shorter sides are 11 inches tall and the two longer sides are 16 inches wide. So, the perimeter would be:

P = 2(11) + 2(16)
P = 22 + 32
P = 54 inches

To calculate the perimeter of the television screen, you'll need to add up the lengths of all four sides. Since the screen has a rectangular shape, it has two pairs of equal sides: one pair measuring 16 inches wide and the other measuring 11 inches tall.

To find the perimeter, you can use the formula P = 2(L + W), where P represents the perimeter, L is the length (or height), and W is the width. In this case, L equals 11 inches and W equals 16 inches. Plugging these values into the formula, we get:

P = 2(11 + 16)
P = 2(27)
P = 54

So, the perimeter of the television screen is 54 inches.

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In 2D, tt can be extended on other side to any length you deserve. But if you talk of sub tangent, then it has particular length.

In 3D, on the surface talking of size of tangent plane it has no particular size. It can be extended on either side to any extent you desire.

In 2D:

At a particular point P(h,k) to a curve y=f(y). Tangent vector is given by equation y(k) = f(h,k)*(x-k) which is unique for that point on the curve. Taking of length a tangent has no particular length. It can be extended on other side to any length you deserve. But if you talk of sub tangent, then it has particular length.

In 3D:

As a particular point P(h,k,1) to a surface f(x,y,z) = 0. Tangent plain is given by equation F(x)(x-h)+F(y)(y-k)+F(z)(z.1)=0 which is unique. For that point on the surface talking of size of tangent plane it has no particular size. It can be extended on either side to any extent you desire.

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Answer:

Look below

Step-by-step explanation:

Well, earthquakes do really shake things up, don't they?

Answer:

Step-by-step explanation:

1. Vertical angles are complementary

2. Vertical angles are adjacent

3. The complement of an acute angle is an acute angle

4. The supplement of an obtuse angle is an obtuse angle

Answer:

Step-by-step explanation:

\((x-4) (3x^{3} -6x+2)\)

= \(3x^{4} -6x^{2} +2x -12x^{3} +24x-8\)

= \(3x^{4} -12x^{3} -6x^{2} +26x-8\)

I hope this helps and the working out is clear.  :)

The variable data refers to the list [10, 20, 30]. After the statement data[1] = 5, data evaluates to [10, 5, 30]. A list is one of the compound data types that Python provides. Lists can contain items of different types, but they are usually all the same type.

Lists are mutable sequences, meaning that their elements can be changed after they have been created. Lists can be defined in several ways, including by enclosing a comma-separated sequence of values in square brackets ([ ]).

The elements of a list can be accessed using indexing, with the first element having an index of 0. The second element has an index of 1, the third element has an index of 2, and so on. To change the value of an element in a list, you can use indexing with an assignment statement.

For example, the statement `data[1] = 5` changes the second element of the `data` list to 5. Therefore, after this statement, the `data` list will be `[10, 5, 30]`.

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Explanation:

The figure preserves its size in certain transformations and only its location is changed. Examples of this kind of transformation are: translations, rotations, and reflections. The size of the figure can change with other transformations, such as dilations.

A translation is a transition that slides through a plane or through space through a figure. Both points of a diagram travel the same distance and the same direction as a translation. A TRANSLATION IS A CHANGE IN LOCATION. A translation is usually specified by a direction and a distance.

A rotation is a move that transforms a figure around a point or a line (around). Rotation involves simply rotating a shape. The center of rotation is called the point at which a figure revolves. The rotation center may be on or outside of the shape. What seems like a rotation? Rotation Core A ROTATION Implies TO Transform A FIGURE.

A transformation that flips a figure over a line is a mirror. A REFLECTION IS FLIPPED OVER A LINE. Note, it's the same but it looks like a mirror image of itself when a shape is mirrored. Remember, the line that forms a shape is flipped precisely over the same distance that is considered a line from the reflection. Reflection line on both ends. It is possible to reflect on the outline or it may be outside the shape.

Without modifying the shape, dilation shifts the scale of the shape. When you go to the eye specialist, your pupils are dilated. Let's try it by shutting the lights off. Dilations are created as you enlarge a photograph or use a copy machine to minimize a map. To render a shape larger, Widen means. Reducing involves having a shape smaller.

The scale factor shows you how much you enlarge or decrease something.

Hope this helps :D (paraphrased; no plagiarism)

Infer means to guess or reach a conclusion, especially based on an indirect hint.

The passage suggests that the main reason the narrator considers Great Expectations to be the best gift he ever received is that reading the book convinced him that he wanted to be a writer.

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Answer:

Step-by-step explanation:

average=(sum of numbers)/number of numbers

15=(sum of numbers)/3

sum of numbers=15×3=45

Therefore, the correct option is 39.364.

When conducting a test at the 5% significance level, the critical value of\( χ2df is 39.364\).

The χ2 distribution is a continuous probability distribution that is commonly used in statistics to determine the variance of a population or the goodness of fit of a sample to an anticipated distribution. In the given question, we have to calculate the critical value of χ2df when conducting the test at the 5% significance level.The formula for calculating χ2 is:χ2=(n−1)s2σ2

Where, n is the sample size, s2 is the sample variance, and σ2 is the population variance .The null hypothesis H0 of this test is:H0:σ2=50The alternative hypothesis Ha of this test is:Ha:σ2≠50So, the degrees of freedom are:\(df=n−1=25−1=24\)The χ2 critical value with 24 degrees of freedom at the 5% significance level is:χ2df=39.364

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You have the following function:

As you can notice, the function does not have exponentials, logarithms, denominators and roots. Then there are no restrictions to the domain of the function neither the range of the function.

The range are all real numbers. In interval notation is:

(-∞,∞)

answer: (-∞,∞)

the standard form of the equation -9x²+25y²-100y = 125 is x²/25 + (y-2)²/9 = 1

Add 125 to both sides of the equation.

-9x²+25y²-100y = 125

Complete the square for 25y²-100y

25(y-2)²-100

Substitute 25(y-2)²-100 for 25y²-100y in the equation

-9x²+25y²-100y = 125

-9x²+25(y-2)²-100 = 125

Move −100 to the right side of the equation by adding 100 to both sides.

-9x²+25(y-2)² = 125 +100 = 225

Divide each term by 225 to make the right side equal to one.

-9x²/225 +25(y-2)²/225 = 225/225

Simplify each term in the equation in order to set the right side equal to 1. The standard form of an ellipse or hyperbola requires the right side of the equation to be 1.

x²/25 + (y-2)²/9 = 1

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The required white effective interest rate is 0.71% more than his nominal interest rate.

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
\(R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=\)
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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Option B. Information. Information links the present to the future in financial markets.

Financial markets are driven by expectations of future events and conditions, and the actions of market participants are based on their assessment of available information about those events and conditions. As new information becomes available, it can change market participants' expectations and lead to changes in market prices and behavior.

Risk, interest rates, and stability are also important factors in financial markets, but they do not directly link the present to the future. Risk refers to the possibility of losing money or not achieving expected returns, and it affects investment decisions in the present. Interest rates are the cost of borrowing or the return on lending money, and they reflect current market conditions rather than future expectations. Stability refers to the absence of significant changes or disruptions in the market, which can be important for maintaining confidence and preventing panic, but it does not necessarily provide a link between the present and the future.

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Answer:

3

Step-by-step explanation:

Given

y = mx ( m is the constant of proportionality )

Given y = 12 when x = 4 , then

12 = 4m ( divide both sides by 4 )

3 = m ← constant of proportionality

Answer:

m = 3

Step-by-step explanation:

Find the constant of proportionality by plugging in x and y into the equation, and solving for m

y = mx

12 = m(4)

Divide each side by 4

3 = m

So, the constant of proportionality is 3

The statement, When two events are disjoint, they are also independent is false.

In a sample space, we can use probability laws to determine the probabilities of these events and how they relate to each other. Disjoint Events: Two events are non-overlapping or mutually exclusive if they have no common outcome. Mathematically, this can be written as, P(B ∩ A) = 0 --(1)

Independent Events: Events are independent when they do not "affect" the probability of another event occurring. Mathematically written as:

P(B/A) = P(B) P(A and B)

=> P(B ∩ A) = P(B) × P(A) --(2)

(1) ) and (2) events cannot be independent unless they overlap. That is, if events do not overlap, they are also dependent. Hence, disjoint events are not independent that means the above statement is false.

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The unit tangent vector is \(\(T(t) = \left(\frac{2}{\sqrt{13}}, \frac{-3\sin(t)}{\sqrt{13}}, \frac{3\cos(t)}{\sqrt{13}}\right)\)\), and the unit normal vector is\(\(N(t) = \left(0, -\frac{\cos(t)}{\sqrt{13}}, -\frac{\sin(t)}{\sqrt{13}}\right)\).\)

To find the unit tangent vector\(\(T(t)\)\) and unit normal vector \(\(N(t)\)\)for the given vector function \(\(r(t) = 2t, 3\cos(t), 3\sin(t)\)\), we can follow these steps:

Step 1: Compute the first derivative of \(r(t)\) with respect to \(t\) to obtain the velocity vector:

\(\(v(t) = r'(t) = 2, -3\sin(t), 3\cos(t)\).\)

Step 2: Calculate the magnitude of the velocity vector:

\(\(|v(t)| = \sqrt{(2)^2 + (-3\sin(t))^2 + (3\cos(t))^2} = \sqrt{4 + 9\sin^2(t) + 9\cos^2(t)} = \sqrt{13}\).\)

Step 3: Compute the unit tangent vector \(T(t)\) by dividing the velocity vector by its magnitude:

\(\(T(t) = \frac{v(t)}{|v(t)|} = \left(\frac{2}{\sqrt{13}}, \frac{-3\sin(t)}{\sqrt{13}}, \frac{3\cos(t)}{\sqrt{13}}\right)\).\)

Step 4: Calculate the derivative of the unit tangent vector with respect to \(\(t\)\) to obtain the curvature vector:

\(\(T'(t) = \left(0, -\frac{3\cos(t)}{\sqrt{13}}, -\frac{3\sin(t)}{\sqrt{13}}\right)\).\)

Step 5: Compute the magnitude of the curvature vector:

\(\(|T'(t)| = \sqrt{\left(-\frac{3\cos(t)}{\sqrt{13}}\right)^2 + \left(-\frac{3\sin(t)}{\sqrt{13}}\right)^2} = \frac{3}{\sqrt{13}}\).\)

Step 6: Calculate the unit normal vector \(N(t)\) by dividing the curvature vector by its magnitude:

\(\(N(t) = \frac{T'(t)}{|T'(t)|} = \left(0, -\frac{\cos(t)}{\sqrt{13}}, -\frac{\sin(t)}{\sqrt{13}}\right)\).\)

Therefore, the unit tangent vector is \(\(T(t) = \left(\frac{2}{\sqrt{13}}, \frac{-3\sin(t)}{\sqrt{13}}, \frac{3\cos(t)}{\sqrt{13}}\right)\),\) and the unit normal vector is \(\(N(t) = \left(0, -\frac{\cos(t)}{\sqrt{13}}, -\frac{\sin(t)}{\sqrt{13}}\right)\).\)

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Answer:

Step-by-step explanation:4/3 inch increase per year

The transformation of System A into System B is:

Equation [A2]+ Equation [A 1] → Equation [B 1]"

The correct answer choice is option D

How can we transform System A into System B?

To transform System A into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

System A:

-3x + 4y = -23 [A1]

7x - 2y = -5 [A2]

Multiply equation [A2] by 2

14x - 4y = -10

Add the equation to equation [A1]

14x - 4y = -10

-3x + 4y = -23 [A1]

11x = -33 [B1]

Multiply equation [A2] by 1

7x - 2y = -5 ....[B2]

So therefore, it can be deduced from the step-by-step explanation above that System A is ultimately transformed into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

The complete image is attached.

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Answer:

\((xy)^{7}\)

 ↓

\(x^{7} y^{7}\)

So the answer is \(x^{7} y^{7}\).

Answer:

Step-by-step explanation:

Just divide 17.25 by 1.83 and you will get the answer. You'd get 9.4 but you can't have .4 of something so it is just 9.

The solution of the given equation is x = 4i-3.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given equation is  x² + 6x + 13 = 0. The solution of the equation will be done as,

x² + 6x + 13 = 0

( x + 3 )² - 3² + 13 = 0

( x + 3 )² - 9 + 13 = 0

( x + 3 )² = -4

( x + 3 ) = √-4

( x + 3 )²  = 4i

x = 4i - 3

Therefore, the solution of the given equation is x = 4i-3.

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