A book store sells used graphic novels in packages of 5 and new graphic novels in packages of 3.
If Amy buys a total of 16 graphic novels, how many packages of used, and how many packages of new graphic novels did she buy?

Answer:

73 apples

Step-by-step explanation:

Step-by-step explanation:

remember, i = sqrt(-1)

you know what an exponent means, right ?

it means you multiply the enclosed term that many times with itself.

when you envision this as a long chain of (1+i)/(1-i) multiplications, you can see you can group them into pairs, and then multiply these pairs - just half the times than for the single terms.

so,

((1+i)/(1-i))²⁰²⁰ = ((1+i)/(1-i))² ^ 1010

to get an idea what the result of the long chain of multiplications might be, let's start with the square and see, if we can find a pattern, that we then can use to come to a conclusion about the total result.

((1+i)/(1-i))² = (1+i)²/(1-i)²

(1+i)² = 1×1 + 1×i + 1×i + i² = 1 + 2i - 1 = 2i

(1-i)² = 1×1 - 1×i - 1×i + i² = 1 - 2i - 1 = -2i

so,

((1+i)/(1-i))² = 2i/-2i = -1

aha !

so,

((1+i)/(1-i))² ^ 1010 = (-1)¹⁰¹⁰

just to be sure you understand, we use the same trick again

(-1)¹⁰¹⁰ = (-1)² ^ 505 = 1⁵⁰⁵ = 1

as 1 to any power is always 1.

so, the right answer is A.

remember, a negative number to an even power results always in a positive number. and to an uneven/odd power in a negative number.

again, because such an exponent is only the summary of many multiplications.

Answer:

Step-by-step explanation:

I am planning to take an upper division mathematics class starting this Fall 2021 at a four-year college/university right now. In my spare time, I like to come here at https://brainly.com and help out others who struggle with mathematics.

Answer:

Math is essential in day in day out activities.

Step-by-step explanation:

Mathematics covers extensive areas within your comfort zone or the outside world. Just to mention a few making your budgets, running a restaurant, kiosk, calculating time you take rest etc. Mathematics is also done or essential in careers or subjects or units you are undertaking. It has helped me a lot for sure.

Volume of the napkin ring is: \(V=\frac{343\pi h^3}{6}\)

Consider the napkin ring of height 7h created by drilling a hole of radius r through the center of a sphere of radius R.

Based on the fig. in bottom representing the cross- section of the ring using the xy-plane, the napkin ring can be generated by rotating the right-half of this cross-section represented as the region D about the y - axis.

First, define the equation of the upper and lower boundary of the region D, which is defined on the interval \(r\leq x\leq R\)

\(x^{2} +y^2=R^2 \, [Equation \, of \, a \, circle \, centered \, at (0,0)\, with \, radius R]\\ \\= > y^2=R^2-x^{2} \\\\= > y =\sqrt{R^2-x^{2}} [Equation \, of \, the \, upper \, boundary \, of\, region \, D]\\\\y =-\sqrt{R^2-x^{2}} [Equation \, of \, the \, lower \, boundary \, of\, region \, D]\)

Therefore , since we are revolving the region D about the vertical y -axis, the thin slices of the region that will be used as heights of the thin cylindrical shells must also be vertical and equal to:

\(h =(\sqrt{R^2-x^2} )-(-\sqrt{R^2-x^2})\\\\h = 2\sqrt{R^2-x^2}\)

Additionally, the radius of the thin cylindrical shells represented by the distances of the thin vertical slices of D from the y - axis is equal to

r = x ∈ [r, R]

Therefore, the volume of the napkin ring using the Cylindrical Shell Method is equal to:

\(V=\int\limits {2\pi \,r \, h} \, dt\\ V = \int\limits^R_r 2\pi x (2\sqrt{R^2-x^2}) \, dx \\\\ V= \int\limits^R_r 4\pi x \sqrt{R^2-x^2} \, dx\)

Let \(u = R^2-x^2\)

such that : du = -2x dx,

\(u(r) =R^2-r^2 \, and \, u(R) =0\)

\(V=\int\limits^0_\\R^2-r^2\)   -2\(\pi \sqrt{u}du\)

V= \(\int\limits\)(limit takes \(R^2-r^2\, to\, 0\)) \(2\pi u^\frac{1}{2}du\)

V= \(\frac{4\pi }{3}u^\frac{3}{2} |_0^\\R^2-r^2\)

\(V=\frac{4\pi }{3}[(R^2-r^2)^\frac{3}{2} -0]\\ \\V= \frac{4\pi }{3}((R^2-r^2)^\frac{3}{2})\)

However, based on the fig. the radius R of the sphere can be expressed in terms of h using the Pythagorean Theorem as \(R^2=r^2+(\frac{7h}{2} )^2\)

Therefore, the volume of the napkin ring can be expressed as:

\(V= \frac{4\pi }{3}((R^2-r^2)^\frac{3}{2})\)

Substitute \(R^2=r^2+(\frac{7h}{2} )^2\)

\(V= \frac{4\pi }{3}[r^2+(\frac{7h}{2} )^2-r^2]^\frac{3}{2})\)

\(V=\frac{4\pi }{3}[(\frac{7h}{2} )^2]^\frac{3}{2}\)

\(V=\frac{343\pi h^3}{6}\)

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Complete question is:

Suppose you make napkin rings by drilling holes with different diameters through two wooden balls (which also have different diameters). You discover that both napkin rings have the same height 7h, as shown in the figure. (Let a = 7.)

Use cylindrical shells to compute the volume V of a napkin ring of height 7h created by drilling a hole with radius r through the center of a sphere of radius R and express the answer in terms of h.

Answer:

The value of 6(2b-4) is 36.

Step-by-step explanation:

Given expression: 6(2b-4)

To find the value of 6(2b-4) at b=5, we need to substitute the b=5 in the expression, we get

6(2(5)-4)

= 6(10-4)

=6(6)

= 6x6=36

⇒ 6(2(5)-4)=36

Answer:

The value of 6(2b-4) when b=5 is 36.

Step-by-step explanation:

Given expression: 6(2b-4). To find the value of 6(2b-4) at b= 5, we need to substitute the b=5 in the expression, we get….Therefore, the value of 6(2b-4) is 36, when b=5.

Answer:

If there are 2 quarters for every 3 nickels,

then there are \(45*\frac{2}{3} =30\) quarters.

If there are 2 dimes for every quarter,

then there are \(30*2=60\) dimes.

If the number of pennies and nickels together are equal to the number of dimes, then there are \(60-45=15\) pennies.

There are two points that satisfy the system of equations:

(0.79, 0.37)

(-3.79, -12.37)

The system of equations is:

y = 3x - 3

y = -x^2

To determine which point from a specified set satisfies the system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

Substituting y = 3x - 3 into the second equation, we get:

3x - 3 = -x^2

Rearranging this equation, we get:

x^2 + 3x - 3 = 0

Using the quadratic formula, we can solve for x:

x = (-3 ± sqrt(3^2 - 41(-3))) / (2*1) = (-3 ± sqrt(21)) / 2

Therefore, there are two possible values of x that satisfy the system of equations:

x = (-3 + sqrt(21)) / 2 ≈ 0.79

x = (-3 - sqrt(21)) / 2 ≈ -3.79

To find the corresponding values of y, we can substitute these values of x into either equation. For example, if we use y = 3x - 3, we get:

y ≈ 0.37 (when x ≈ 0.79)

y ≈ -12.37 (when x ≈ -3.79)

Therefore, there are two points that satisfy the system of equations:

(0.79, 0.37)

(-3.79, -12.37)

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The  graph shows a function and its is the graph in option A.

The original path is reflected on the line y = x. The two functions are said to be inverses of one another if the graphs of both functions are symmetric with respect to the line y = x. This is due to the fact that (y, x) lies on the inverse function of the function if (x, y) lies on the original function.

The inverse function is shown on a graph with the use of a vertical line test. The line has a slope and travels through the origin.

Instance is the  f(x) = 2x + 5 = y. Then, is the inverse of \(g(y) = \frac{ (y-5)}{2} = x\) f(x).Reflecting over the y and x gives us the function of the inverse.

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Answer:

\(\frac{xa}{28}\)

Step-by-step explanation:

   \(\frac{4x^2}{y7a^3} * \frac{a^4}{16+8x}\)

= \(\frac{2x(2+x)}{7a^3} * \frac{a^4}{8(2+x)}\)

= \(\frac{xa}{28}\)

\(\frac{x^{2}a }{28}\)

Explination:

Factor the numerator and the denominator and cancel the common factors

Answer:

A

Step-by-step explanation:

the length of the arc is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × \(\frac{120}{360}\)

     = 2π × 8 × \(\frac{1}{3}\)

    = 16π × \(\frac{1}{3}\) = \(\frac{16\pi }{3}\) m

Answer:

Therefore, the coordinates of the vertices of ΔA'B'C' after the dilation with a scale factor of 2.5.

Step-by-step explanation:

Given the vertices of ΔABC

Given that ΔA'B'C' is a dilation of ΔABC with a scale factor of 2.5 and the center of dilation (0, 0).

We know that when the scale factor > 1, then the image is enlarged.

The formula to determine the dilation with a scale factor of 2.5.

P(x, y) → P'(2.5x, 2.5y)

Here, P' is the image of P, and the vertices of the image is dilated by a scale factor of 2.5.

In other words, the vertices of the image can be obtained by multiplying the vertices of the original triangle with 2.5.

Thus,

P(x, y) → P'(2.5x, 2.5y)

A(-2, -1) → P'(2.5(-2), 2.5(-1)) = A'(-5, -2.5)

B(1, 2) → B'(2.5(1), 2.5(2)) = B'(2.5, 5)

C(2, -4) → C'(2.5(2), 2.5(-4)) = C'(5, -10)

Therefore, the coordinates of the vertices of ΔA'B'C' after the dilation with a scale factor of 2.5.

Answer: 80 Fluid Oz

Step-by-step explanation:

I first have to find out how many fluid Oz there are in one bottle. If there are 16 Oz in 2 bottles, I have to divide 16/2=8. Now I know there are 8 Oz in each bottle. Now I have to multiply 8 by 10. 10*8=80. There is 80 Oz all together.

Hope this helps! :)

Answer:

the question is not clear

Step-by-step explanation:

wdym by this 2 ÷3 × 6 whole number 3 on 4, into bracket 2 whole number 4 on 15 - 1 whole number 2 on 3

Product of the given expression -2.8 (-1.7) is equal to 4.76.

As given in the question,

Given expression is equal to :

-2.8 (-1.7)

There are two numbers -2.8 and -1.7.

Both the numbers are negative.

Multiply negative to a negative number is positive number.

Result of -2.8 and -1.7 is positive number.

Required product of the given expression is equal to :

-2.8 (-1.7)

= (-1) × (2.8) × (-1) × (1.7)

Multiply (-1) to (-1) is equal to positive (1) :

= 2.8 × 1.7

= 4.76

Therefore, product of the given expression -2.8 (-1.7) is equal to 4.76.

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Answer:

972

Step-by-step explanation:

\( {6}^{2} \times {3}^{3} \\ = 36 \times 27 \\ = 972\)

Answer:

16/22, 24/33, and 40/55

or

72.7272...% = Percentage form

0.7272... = Decimal form

Hope this helps :)

Pls brainliest...

Given:

Joey had 26 game cards.

His friend Richard gave him some more, and now Joey has 100 cards.

To find:

How many cards did Richard give to Joey?

Solution:

Let x be the number of cards that Richard give to Joey.

Joey had 26 game cards.

Now, the total cards joey has \(=26+x\)

Joey has total 100 cards.

\(26+x=100\)

\(x=100-26\)

\(x=74\)

Therefore, Richard gave him 74 cards.

We find the slope(m) by replacing the values in the following expression:

That is:

So, the slope equals -7/3.

Answer:

(18-4+5)+(2/7 j-6/7 j)=

19 +(-4/7 j)=

Answer:          IQR = 16

Step-by-step explanation:

The given data is 25 th percentile is 64, 50th percentile is 74 and 75 th percentile is 80.

percentage : 25    50   75

 score        : 64    74    80

Median:- The median is obtained by first arranging the data in ascending or descending order and applying the following rule.

If the number of observations is odd, then the median is  observation

term

If the number of observations is even, then the median is  observation and  observations.

given n=3, middle term is '74'

In this given data the median is (M) = 74

Interquartile range IQR = median of upper half-median of lower half

                                      = 80-64

                                      = 16

                           IQR = 16

The variable P0 represents the initial amount.

In the exponential growth model, P(t) represents the population at time t, P0 represents the initial population at time t=0, k represents the growth rate, and e is the mathematical constant, approximately equal to 2.71828. Therefore, P0 represents the initial amount or the starting point of the population.

The correct answer is B, the variable P0 represents the initial amount.

B. The variable P0 represents the initial amount.

In the exponential growth model P(t) = P0 * e^(kt), the variables are defined as follows:
- P(t): The population size at time 't'
- P0: The initial population size (i.e., the population size at the beginning, when t=0)
- e: The base of the natural logarithm (approximately 2.71828)
- k: The growth rate constant
- t: Time

In this model, P0 is the population size at the beginning of the observed period (when t=0). Therefore, it represents the initial amount.


The variable P0 in the exponential growth model P(t) = P0 * e^(kt) represents the initial amount of the population or quantity being studied.

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Answer:

a. x = 7.07  b. x = 10

Step-by-step explanation:

a is a 45-45-90 pythagorean triple and b is a 30-60-90 pythagorean triple

When the separation between the plates of a parallel-plate capacitor is doubled while the battery remains connected, the second proton released from rest will reach the negative plate with a speed that is half of the initial speed.

When the separation is increased to 2d, the electric field strength between the plates is reduced by half. However, the potential difference (V) across the capacitor remains the same because the battery is still connected.

When the second proton is released from rest from the positive plate after the separation is doubled, it experiences the same electric field as the first proton.

As a result, the second proton will take longer to reach the negative plate compared to the first proton. Since both protons experience the same potential difference (V), the second proton will continue to accelerate until it reaches the negative plate. However, due to the reduced acceleration, its final speed will be less than v0.

Since the acceleration experienced by the second proton is halved and the time taken is four times longer, we can conclude that the final speed (v1) of the second proton when it reaches the negative plate will be v0/2.

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Answer: 20.8

Step-by-step explanation:

Since it is an equilateral triangle, we know the bottom is also 24. We also know that line E is bisecting the base. So using the smaller right triangle we know that the hypotenuse is 24 and one leg is 12. So use the Pythagorean theorem.

\(a^{2} +b^{2} =c^{2} \\12^{2} +b^{2} =24^{2} \\144+b^{2} =576\\b^{2} = 432\\b= 20.8\)

This estimate suggests that there are approximately 912,000 drones in the wild. This is much smaller than the ten million drones we imagined earlier.

It is unreasonable to imagine that there are ten million drones in the wild because the serial numbers we observed do not suggest such a large number. If the drones were numbered sequentially starting from 1, the highest serial number we observed was 912. Even if we assume that we only observed a small fraction of the total number of drones in the wild, it is unlikely that the highest serial number we observed is only a tiny fraction of the total number of drones.  

For example, if we assume that we observed 0.1% of the total number of drones in the wild, then we can estimate the total number of drones as follows:

Total number of drones = (Highest serial number observed) / (Observed fraction)

= 912 / 0.001

= 912,000

This estimate suggests that there are approximately 912,000 drones in the wild. This is much smaller than the ten million drones we imagined earlier. Therefore, based on the limited information we have, it is unreasonable to imagine that there are ten million drones in the wild.

In general, when making estimates based on limited data, it is important to consider the range of possible values and the assumptions underlying the estimate. It is also important to update the estimate as new data becomes available.

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Answer:

2/9

Step-by-step explanation:

hope this helps. have a good day.

With the survey, the following statements are true;

1. 11th graders and 12th graders equally likely to prefer soccer

2. A 12th grade student is less likely to prefer soccer to a 11th grade student and

3 A 11th grade student is more likely to prefer basketball than a 12th grade student.

4. The data suggests there is an association between what grade the student are in and their preference of soccer or basketball

A statement is true if what it asserts is the case, and it is false if what it asserts is not the case. For instance, the statement “The trains are always late” is only true if what it describes is the case, i.e., if it is actually the case that the trains are always late.

The true statement of a data are the positive facts that can be derived from the data. For example, with the survey of 84 students, 48, 11th graders and 36, 12th graders. The following facts can be obtained:

A. 11th graders and 12th graders equally likely to prefer soccer

B. . A 12th grade student is less likely to prefer soccer to a 11th grade student and

C. A 11th grade student is more likely to prefer basketball than a 12th grade student.

d . The data suggests there is an association between what grade the student are in and their preference of soccer or basketball.

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Answer:

-3 ( x + 4) = -3x-3 (4) it's option D