Which expeession can be simplified as 1/n¹⁸ ?

(n²)⁹

\(( {n}^{ - 9}) ^{ - 2} \)
\((n^{ - 6}) ^{ - 3} \)
\((n^{ - 3}) ^{6} \)
​

Answer:

7 quarters, 15 dimes. :)

Answer:

the answer become 5 dolars

Answer:

11

Step-by-step explanation:

Sum of all angles = 180

Right angle = 90

Acute  angle = 79

90+79 =169

   180 -169 = 11

Answer:

11 degrees

Step-by-step explanation:

a right angle = 90 degrees

90-79=11 degrees

Answer:

Volume of sphere A

= (4/3)π(3^3) = 36π cubic units

Volume of sphere B

= (4/3)π((3/2)^3) = (4/3)π(27/8) = (9/2)π = 4.5π cubic units

The ratio of the volume of sphere A to sphere B is 4.5:36 = 1:8.

Answer:

49th term = 225

Step-by-step explanation:

The following sequence: -15, -10, -5, 0, -5... is an example of an arithmetic progression.

An arithmetic progression or AP for short, is a sequence in which the difference between successive terms is constant. This difference is known as the common difference, and can be found by subtracting a term by its preceding term.

The general formula, for the nth term of an arithmetic progression, is thus:

Tn = a + (n - 1)d, where a = first term, and d = common difference.

In the sequence: -15, -10, -5, 0, 5...,

a = -15, and d = -10--15 = 5

T49 = -15 + (49 - 1)5 = 225

∴ 49th term = 225

Answer:

centroid

Step-by-step explanation:

Answer:

x = pm - pn

Step-by-step explanation:

m = n + \(\frac{x}{p}\)  Subtract n from both sides

m - n = n - n + \(\frac{x}{p}\)

m-n = \(\frac{x}{p}\)   Multiply both sides by p

p(m - n) = (\(\frac{p}{1}\)) \(\frac{x}{p}\)          \(\frac{p}{1}\) means the same as p

pm - pn = x             Distribute the p

x = pm - pn

Answer:

3d^2-9d

=3d(d-3)

Therefore,GCF IS 3d

Answer:

the answer to this question is 19.2 meters per minute

(-2, 5) Minimum

Step-by-step explanation:

y-5=(1/3)(x + 2)²

y-5=(1/3)(x²+4x+4))

y-5=1/3x²+4/3x+4/3

y=1/3x²+4/3x+4/3+5

y=1/3x²+4/3x+4/3+15/3

y=1/3x²+4/3x+19/3

graph is attached

x= -b/2a

x= (-4/3)/2(1/3)

x= (-4/3)/(2/3)

x= (-4/3)*(3/2)

3's cancel

x= (-4/1)*(1/2)

x = -4/2

x = -2

plug -2 back into

y=1/3x²+4/3x+19/3

y=1/3*4+4/3*-2+19/3

y=4/3-8/3+19/3

y=15/3

y=5

(-2,5)

if a is positive

graph looks like a smile

so minimum

if a is negative

graph looks like a frown

so maximum

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The inverse of the function f(x) = 1/3x-2 is f^-1(x) = (1 + 2x)/3x.

A function f is has an inverse if it is both one-to-one and onto.

Given the function f(x) = 1/3x-2

we replace f(x) with y and make x the subject of the formula to derive the inverse function f^-1(x) as follows ;

y = 1/3x - 2

by cross multiplication

3x - 2 = 1/y

add 2 to both sides of the equation

3x = 1/y + 2

3x = (1 + 2y)/y

divide both sides of the equation by 3

x = (1 + 2y)/y ÷ 3

x = (1 + 2y)/3y

So, f^-1(x) = (1 + 2x)/3x

Therefore, the inverse of the function f is derived by interchanging the value of x for y and vice versa, that is f^-1(x) = (1 + 2x)/3x.

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Answer:

When we add 23°, 145°, 23° and 69° we get 260°

And 260° does not have defined number of sides

Step-by-step explanation:

These are the polygons with the number of sides and angles

Polygon Name  |  Number of Interior Angles  |  Sum of Interior Angles

Triangle                                     3                                    180°

Quadrilateral                            4                                    360°

Pentagon                                  5                                    540°

Hexagon                                   6                                    720°

Septagon                                  7                                    900°

Octagon                                    8                                   1080°

Nonagon                                   9                                   1260°

Decagon                                   10                                  1440°

The probability that a randomly selected Christian living in the United States would identify as Catholic can be calculated by dividing the number of Catholics in the US by the total number of Christians in the US.

To do this calculation, we need to know the accurate data on the number of Catholics and the total number of Christians in the US. Let's assume that there are X Catholics and Y total Christians in the US.

The probability of a randomly selected Christian being Catholic would be:

P(Catholic) = X/Y

Without the accurate data on the number of Catholics and total Christians in the US, it is not possible to calculate the exact probability. However, if we assume that the data provided is accurate and stable, we can use the formula above to calculate the probability.

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Based on the mean and standard deviation of men's heights at that time, the tallest living man had a more extreme height compared to the shortest living man.

The question asks which of the two men, the tallest living man or the shortest living man at that time, had a height that was more extreme.

To determine this, we need to compare their heights to the mean and standard deviation of men's heights at that time.

The mean height of men at that time was 177.71 cm, and the standard deviation was 6.03 cm.

The tallest living man had a height of 237 cm, which is 59.29 cm above the mean (237 - 177.71 = 59.29).

The shortest living man had a height of 139.5 cm, which is 38.21 cm below the mean (177.71 - 139.5 = 38.21).

To determine which height is more extreme, we can compare the distance from each height to the mean.

The distance from the tallest man's height to the mean is 59.29 cm, while the distance from the shortest man's height to the mean is 38.21 cm.

Since the distance from the tallest man's height to the mean is greater than the distance from the shortest man's height to the mean,  we can conclude that the tallest living man had the height that was more extreme.

In summary, based on the mean and standard deviation of men's heights at that time, the tallest living man had a more extreme height compared to the shortest living man.

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The volume of the composite solid round to the nearest tenth is 83.7 inches³.

Volume of a three dimensional shape is the space occupied by the shape.

There are 2 hemispheres and a cylinder in the given composite solid.

Volume of hemisphere =  \(\frac{2}{3}\) π r³, where r is the radius.

Volume of the cylinder = π r² h, where r is the radius and h is the height.

Here r = 2 inches and

h = 8 - 4 = 4 inches

Volume of hemisphere = \(\frac{2}{3}\) π × 2³

                                      = \(\frac{16}{3}\) π

There are two hemispheres.

Volume of two hemispheres = 2 × \(\frac{16}{3}\) π =  \(\frac{32}{3}\) π

Volume of the cylinder = π r² h

                                      = π × 2² × 4

                                      = 16 π

Volume of the composite Solid = \(\frac{32}{3}\) π + 16 π

                                                    = \(\frac{80}{3}\) π

                                                    = 83.7 inches³

Hence the volume of the composite solid is 83.7 inches³.

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The distribution of Z = -log(Y/X) can be described as a mixture of exponential distributions for Z ≤ 0 and a shifted exponential distribution for Z > 0.

The distribution (density) of Z = -log(Y/X) can be described as follows:

For Z ≤ 0, the probability density function (PDF) is fZ(z) = 2e^z / (2c), where c is a constant.

For Z > 0, the PDF is\(fZ(z) = e^(-z) / (2c).\)

The probability distribution is split into two regions based on the relationship between X and Y. When X is less than or equal to Y, the PDF follows an exponential distribution. When X is greater than Y, the PDF follows a shifted exponential distribution.

The constant c is determined by normalizing the joint density function over its support.

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The given statement "To change the contents of a macro, you must use the Record Macro button to step into the macro" is false because one can use other options such open the Visual Basic Editor .

To change the contents of a macro,

It is not necessary we have to use the Record Macro button to step into the macro.

Here one can also open the Visual Basic Editor instead of record Macro button.

In the Visual Basic Editor Project Explorer window.

First we have to open the project folder

And then in the Modules folder we have to select Recorded.

Finally select the module that has the name of the macro.

Here the recorded macro code is going to displayed in the code window.

First one can find the macro in the project window, and then edit the code directly.

Alternatively, one can use the Macro dialog box to have a view and to edit the macro.

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Answer:

f(1)= 5

so x=1

f(5)= 5(5-1) = 20

The value of f(5) is 3125.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(1) = 5 and f(n) = 5f(n − 1)

Now, for finding the the 5 th term we have to find the remaining four term before the 5th term.

So, n=2

f(2) = 5f(1)

f(2)=  5(5)

f(2)=  25

Now, n=3

f(3) = 5f(2)

f(3)=  5(25)

f(3)=  125

Now, n=4

f(4) = 5f(3)

f(4)=  5(125)

f(4)=  625

Now, n=5

f(5) = 5f(4)

f(5)=  5(625)

f(5)=  3125

Hence, the value of f(5) is 3125.

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Answer:  1 and 1/3 or 1 and 2/6

Step-by-step explanation: 1/2 x 3 = 3/6

3/6+5/6= 1 and 2/6 or 1 and 1/3

Considering that she does not know the population standard deviation, the hypothesis test that she should use is given by:

c. one-sample, left-tailed t-test for a mean.

First, we consider that she does not know the population standard deviation, hence a t-test should be used instead of a z-test.

Then, we consider that she suspects that the mean weight is less than 15 lb, and less is associated with a left-tailed test, instead of a right-tailed(associated with more) or a two-tailed(associated with different).

Hence option c is correct.

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The probability that none of the packs are defective is 0.478. The probability that five packs are defective is 0.000455.The probability that all the packs are defective is 2.8243e-14.The probability that 7 or more packs are defective is 0.00416 (approx).

A shipment of 10,000 Karak tea packs is produced by the company Chai Karak. If 7% of the packs are defective, what is the probability that: none of the packs are defective, five packs are defective, all the packs are defective, and seven or more packs are defective?  The number of trials, n, is 10 and the probability of a defective tea pack is 0.07. Therefore, the number of successful trials, X, follows a binomial distribution. Formula for binomial distribution: P(X = k) = nCk × pk × (1 − p)n−kWhere nCk = number of combinations of n things taken k at a time = n! / (k! (n-k)!)a. The probability that none of the packs are defective P(X = 0):P(X = 0) = nC0 * p0 * (1-p)n-0= 10C0 * 0.07^0 * (1-0.07)^10= 1 * 1 * 0.478= 0.478Therefore, the probability that none of the packs are defective is 0.478.

The probability that 5 packs are defective:P(X = 5) = nC5 * p^5 * (1-p)n-5= 10C5 * 0.07^5 * (1-0.07)^5= 252 * 0.0000028 * 0.649= 0.000455Therefore, the probability that five packs are defective is 0.000455.

The probability that all the packs are defective:P(X = 10) = nC10 * p^10 * (1-p)n-10= 10C10 * 0.07^10 * (1-0.07)^0= 1 * 2.8243e-14 * 1= 2.8243e-14Therefore, the probability that all the packs are defective is 2.8243e-14.

The probability that 7 or more packs are defective: P(X ≥ 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)P(X = 7) = nC7 * p^7 * (1-p)n-7= 10C7 * 0.07^7 * (1-0.07)^3= 120 * 0.0000953677 * 0.657= 0.00416P(X = 8) = nC8 * p^8 * (1-p)n-8= 10C8 * 0.07^8 * (1-0.07)^2= 45 * 0.0000024969 * 0.859= 0.000011P(X = 9) = nC9 * p^9 * (1-p)n-9= 10C9 * 0.07^9 * (1-0.07)^1= 10 * 0.00000005 * 0.93= 4.65e-7P(X = 10) = nC10 * p^10 * (1-p)n-10= 10C10 * 0.07^10 * (1-0.07)^0= 1 * 2.8243e-14 * 1= 2.8243e-14P(X ≥ 7) = 0.00416 + 0.000011 + 4.65e-7 + 2.8243e-14= 0.00416Therefore, the probability that 7 or more packs are defective is 0.00416 (approx).

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Total stockholders’ equity 7,800,000

Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000

Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000

Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000

Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000

To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.

The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.

Calculations:Opening balance of common stock = $100,000

Opening balance of additional paid-in capital = $4,100,000

Opening balance of retained earnings = $3,000,000

Net Income for the year ended December 31, 2012 = $800,000

Retained earnings (Opening Balance) = $3,000,000

Add: Net Income for the year ended December 31, 2012 = $800,000

Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000

Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000

Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000

Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
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Answer:

\(27^{\frac{1}{3}} \quad 125^{\frac{2}{3}} \quad 9^{\frac{3}{2}}\)

Step-by-step explanation:

Rewrite 9 as 3²:

\(\implies 9^{\frac{3}{2}}=\left(3^2\right)^{\frac{3}{2}}\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies 3^{(2 \cdot \frac{3}{2})}=3^3\)

Therefore:

\(\implies 3^3= 3 \cdot 3 \cdot 3=27\)

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

Rewrite 27 as 3³:

\(\implies 27^{\frac{1}{3}}=\left(3^3\right)^{\frac{1}{3}}\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies 3^{(3 \cdot \frac{1}{3})}=3^1\)

Therefore:

\(\implies 3^1=3\)

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

Rewrite 125 as 5³:

\(\implies 125^{\frac{2}{3}}=\left(5^3\right)^{\frac{2}{3}}\)

\(\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:\)

\(\implies 5^{(3 \cdot \frac{2}{3})}=5^2\)

Therefore:

\(\implies 5^2=5 \cdot 5=25\)

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

Solution

In order, from smallest to largest:

\(27^{\frac{1}{3}} \quad 125^{\frac{2}{3}} \quad 9^{\frac{3}{2}}\)

Answer:

Lying outside the cirlce.

Step-by-step explanation:

         (x - h)² + (y - k)²= r²

         Here, (h ,k) is the center of the circle and r is the radius.

       (x + 10)² + (y - 1)² = 25

         r² = 25

         r = √25

        r = 5 units

       LHS = (-20 + 10)² + (6 - 1)²

               = (-10)² + 5²

               = 100+25

              = 125 > 25

      As 125 is greater than 25, the point (-20 ,6 ) is lying outside the circle.

Answer:

D: PUR and SUR

Step-by-step explanation:

A linear par is made of two angle's whoes measure add to 180, or it forms a line. PUR and SUR form a line so therefore they are a linear pair.

The answer is D) <PUR and <SUR

A linear pair is when a pair of angles add up to 180 degrees. The angles must share 2 points and should be next to each other. They are adjacent angles  formed by two intersecting lines.

Luke charged an amount of $37.18 in sales tax which is determined by the evaluation of 6.25% of 595.

The percentage is defined as a ratio expressed as a fraction of 100.

For example, If Saima obtained a score of 57% on her exam, that corresponds to 67 out of 100. It is expressed as 57/100 in fractional form and as 57:100 in ratio form.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

Luke bought a computer for $525 and two computer games for $34.99 each. The sales tax rate was 6.25%.

⇒ 525 + 2×34.99 = 595

We have to determine the evaluation of 6.25% of 595.

⇒ 6.25% of 595

6.25%  is expressed as 6.25/100 in fractional form

⇒ (6.25/100)(595)

6.25/100  is expressed as 0.0625 in decimal form

⇒ (0.0625 )(595)

Apply the multiplication operation, and we get

⇒ 37.18

Therefore, Luke charged an amount of $37.18 in sales tax.

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The total cost of student ticket in the class of Ms. Green is $210 and the cost of student ticket in the class of Ms. White is $165.

In the given question, we have to find how much the student tickets for both classes cost in total.

Ms. Green and Mr. White took their science classes to the museum.

Let the cost of student ticket is x.

Let the cost of adult ticket is y.

Ms. Green spent $262 to buy 28 student tickets and 4 adult tickets for her class.

So the required equation is:

28x + 4y = 262...(1)

Mr. White spent $191 for 22 student tickets and 2 adult tickets for his class.

So the required equation is:

22x + 2y = 191...(2)

Multiply equation 2 by 2 then subtract by 1

44x + 4y - (28x + 4y) = 382 - 262

16x = 120

Divide by 16 on both side, we get

x = 7.5

Now putting the value of x in equation 1, we get

28(7.5) + 4y = 262

210 + 4y = 262

Subtract 210 on both side, we get

4y = 52

Divide by 4 on both side, we get

y = 13

Hence, the cost of student ticket is $7.5 and the cost of adult ticket is $13.

Now we have to find the total cost of student tickets in both classes.

The cost of student ticket in the class of Ms. Green = 28x

The cost of student ticket in the class of Ms. Green = 28×7.5

The cost of student ticket in the class of Ms. Green = $210

The cost of student ticket in the class of Ms. White = 22x

The cost of student ticket in the class of Ms. White = 22×7.5

The cost of student ticket in the class of Ms. White = $165

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Answer:

b. Complementary gas masks

Step-by-step explanation:

Adjacent means that the two angles are right next to each other and touching. The two angels in the photo are touching. Supplementary means that the two angels can for together to make a 180 degree line. The two angels in the photo make a 180 degree line. Complementary means that the two angels make a 90 degree angel. Since the two angels already make a 180 degree angels then, they cannot make a 90 degree angel. The question is asking for what it is not so, complements would be the answer.

Answer:

A

Step-by-step explanation:

6 friends

Mean - 10

Median - 9.5

Range - 14

3 friends watched 12, 13, and 18 movies.

Let's find the sum, this will help us find the total number of movies the other 3 friends watched.

12 + 13 + 18 = 43

The mean is all their movies added toether, divided by the number of friends.

m = number of movies the other friends watched.

(43 + m) / 6 = 10        Multiply each side by 6

43 + m = 10 * 6

43 + m = 60          Subtract 43 from each side

m = 60 - 43

m = 17

So we know the total movies the other friends watched is 3.

A. 4+6+7 = 17

B. 4+4+7 = 15

C. 5+8+9 = 22

D. 2+3+5 = 10

We know the answer is A.

We can check it by looking at the Median, the median is the middle number, if there are an even number of samples, you add the 2 middle numbers together and divide by 2.

4, 6, 7, 12, 13, 18

So 7+12 = 19

19/2 = 9.5

So we know for sure A is correct!