Find a formula for the nth term of the sequence.

1, −8, 27, −64, 125

Determine the sequence's formula in terms of n.
a_n= _____, n ≥ 1

Answer:

x=-9

Step-by-step explanation:

x=36/-4=-9

Answer:

-9

Step-by-step explanation:

-4x=36

36/-4=-9

x = -9

-4(-9)=36

Answer: no

Step-by-step explanation:

The total deposits of Ella Bell based on the information is $ 7,107.38

From the information, Ella Bell operates a company that buys and sells tickets to sporting events. She deposits the day's receipts into her savings account.

In bills, she had 52 one hundreds, 21 fifties, 19 tens, 71 fives, and 63 ones. Change included 6 one-dollar coins, 60 fifty-cent pieces, 32 quarters, 121 dimes, and 165 pennies. She also deposited checks for $29.44, $125.65, and $45.94. She wants to receive 5 two-dollar bills in cash.

This will be:

= Currency + Coins + Checks - Cash received

= 6858 + 57.75 + 201.63 - 10

= 7107.38

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Answer:

C, E and F

Step-by-step explanation:

As,

C. - 3/4 m + 8m + m. [Like terms of m]

= 29/4 m + m

= 33/4 m

E. 5. 75t + 7.75 t - t. [Like terms of t]

= 13.5t - t

= 12 . 5t

F. 8xy - 6xy. [Like terms of xy]

= 2xy

The density is:

D = 10g/2mL = 5 g/mL

The correct option is the first one.

Remember that density is defined as the quotient between mass and volume.

We know that the mass of the solid is 10.0 grams.

And the volume of the solid is given by the difference between the volume of the water alone (15.0 mL) and the water with the solid (17 mL).

V = 17mL - 15mL = 2mL

Then the density is:

D = 10g/2mL = 5 g/mL

The correct option is the first one.

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The value of natural logarithm of the given complex number is ln(-1.386 ob i21 + 1.386 oc ir + 1.386 Od 1.386) = ln(2.4) + i(54.74°).

The value of natural logarithm of -4 in the complex number system can be found by expressing -4 in polar form. We can write -4 as 4cis(π), where cis(π) is the complex number cos(π) + i sin(π). Now, applying the properties of logarithms, we can write:

ln(-4) = ln(4) + ln(cis(π)) = ln(4) + iπ

Therefore, the value of natural logarithm of -4 in the complex number system is ln(-4) = ln(4) + iπ.

It is important to note that the natural logarithm is not defined for negative real numbers, as it is a real-valued function. However, in the complex number system, we can still define the logarithm for all non-zero complex numbers.

In the given expression, we have -1.386 ob i21 + 1.386 oc ir + 1.386 Od 1.386. To find the value of natural logarithm of this complex number, we need to first express it in polar form. Using the Pythagorean theorem, we can find the magnitude of the complex number to be approximately 2.4. To find the angle, we can use the inverse tangent function, which gives us an angle of approximately 54.74 degrees.

Therefore, the complex number can be expressed as 2.4cis(54.74°). Now, using the properties of logarithms, we can write:

ln(-1.386 ob i21 + 1.386 oc ir + 1.386 Od 1.386) = ln(2.4) + ln(cis(54.74°)) = ln(2.4) + i(54.74°)

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The probability of the word MATH being found in one of the two piles is approximately 0.0000242, which is a very small probability.

This is a probability question that requires a bit of combinatorics. There are 26 letters in the alphabet, and they are separated into two equal piles, each containing 13 letters.

To calculate the probability of the word MATH being found in one of the piles, we need to first determine the number of ways that the letters can be arranged in each pile.

For the first pile, there are 13 letters to choose from, so we have 13 choices for the first letter, 12 choices for the second letter, 11 choices for the third letter, and 10 choices for the fourth letter.

This gives us a total of 13 x 12 x 11 x 10 = 15,120 possible arrangements.

The same is true for the second pile, so we have a total of 15,120 x 15,120 = 228,614,400 possible arrangements for the two piles combined.

To calculate the probability of the word MATH being found in one of the piles, we need to determine how many of these arrangements contain the letters M, A, T, and H in the same pile.

To do this, we can fix the position of the first letter, which must be one of the letters in MATH.

There are four choices for this letter. We can then fix the position of the second letter, which must be one of the remaining three letters in MATH. There are three choices for this letter.

We can then fix the positions of the remaining two letters, which must be two of the 22 remaining letters in the pile. There are 22 x 21 = 462 possible arrangements for these two letters.

Multiplying these choices together gives us a total of 4 x 3 x 462 = 5,544 possible arrangements that contain the letters M, A, T, and H in the same pile.

Finally, we can calculate the probability of the word MATH being found in one of the piles by dividing the number of arrangements that contain the letters M, A, T, and H in the same pile by the total number of possible arrangements. This gives us:

Probability = 5,544 / 228,614,400 = 0.0000242

So the probability of the word MATH being found in one of the two piles is approximately 0.0000242, which is a very small probability.

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There are probability (6 choose 3) = 20 possible ways to select 3 or more students from 6 students, since the order in which the students are selected is not important.

If 3 or more students must be selected from 6 students, and the order in which the students are selected is not important, then this is an example of a combination problem. Combination problems are used to calculate the number of ways a certain number of objects can be selected from a larger group of objects. To calculate this, the formula that is used is (n choose r) = n!/(r!(n-r)!), where n is the total number of objects, and r is the number of objects that must be selected. In this case, n = 6 and r = 3, so the answer is (6 choose 3) = 6!/(3!(6-3)!) = 20. This means that there are 20 possible ways to select 3 or more students from 6 students, since the order in which the students are selected is not important.

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The following are the solution to the given inequalities;

-13 < 4x + 7 ; -5 < x

-2x + 7 < 19 ; x > -6

-45 < 5(p - 2) ; -7 < p

21 < -7(x - 2) ; -1 > x

-9x + 10 > -8 ; x < 2

2 - 6 < 3 ; -4 < 3

-13 < 4x + 7

combine like terms

-13 - 7 < 4x

-20 < 4x

divide both sides by 4

-5 < x

-2x + 7 < 19

combine like terms

-2x < 19 - 7

-2x < 12

x < 12/-2

x > -6

When dividing inequality with negative, the inequality sign will flip.

-45 < 5(p - 2)

open parenthesis

-45 < 5p - 10

-45 + 10 < 5p

-35 < 5p

-7 < p

21 < -7(x - 2)

21 < -7x + 14

21 - 14 < -7x

7 < -7x

divide both sides by -7.

-1 > x

-9x + 10 > -8

-9x > -8 - 10

-9x > -18

x > -18/-9

x < 2

2 - 6 < 3

-4 < 3

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Answer:

Freds car is the cheapest to run.

Step-by-step explanation:

Fred is not correct. He is wrong, each car uses different amounts of fuel.

The results generated in the map phase are combined in the _reduce_ phase.

In maps, the "reduced phase" refers to a technique used to remove the phase ambiguity present in interferometric synthetic aperture radar (InSAR) data. InSAR uses radar to measure the distance between a satellite or aircraft and the ground and can be used to create detailed maps of changes in the surface of the earth over time.

However, because InSAR data is collected using radar waves, which are sensitive to the phase of the signal, the data can be affected by phase ambiguities. The reduced phase technique is used to remove these ambiguities and create more accurate maps.

Therefore, The results generated in the map phase are combined in the _reduce_ phase.

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Answer:

Choice a : $96,600

Step-by-step explanation:

The net worth of a person is computed as total assets - total liabilities in money terms

Ben's assets are as follows:

Townhome: $195,000

Savings: $5000

Car: $38,000

Total Assets: 195000 + 5000 + 38000 = $238,000

Ben's liabilities

Home Loan: $120,000

Credit Card: $1,400

Car Loan: $20,000

Total Liabilities = 120000 + 1400 + 20000 = $141,400

Net Worth = 238000 - 141400 = $96,600   (Answer is choice a)

Answer:

A

Step-by-step explanation:

The values of x and y could be 25 and 113

What are parallel lines ?

parallel lines can be stated as , they both are equi distant from each other and which never intersect.

From the given figure,

y+12 = 3x + 50

as both are parallel to each other.

y-3x = 38

and 5x  = y + 12

as vertically opposites are always equal .

y = 3x + 38

y = 5x - 12

hence,

5x - 12 = 3x +38

2x = 50

x = 25

put x = 25 in y = 3x + 38

y = 3 * 25 + 38

y = 113

hence the values of x and y are 25 and 113 respectively.

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The shape of the sample as the sample size increases is  the sample becomes more and more like the population distribution

A given set a data is considered to be normally distributed if it appears to take on a bell-shaped, symmetrical curve. Both skew (i.e. a lack of symmetry) and kurtosis (i.e. a more dramatically flattened or peaked curve) can be present in a distribution. If skew or kurtosis is present in a set of data, it cannot be said to be normally distributed.

A positively skewed (or right-skewed) distribution is a type of distribution in which most values are clustered around the left tail of the distribution while the right tail of the distribution is longer. The positively skewed distribution is the direct opposite of the negatively skewed distribution.

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Shelly was 1km from her camp. Since her initial direction is in the North-West direction, hence the quadrant  bearing will be at the 3rd quadrant

If Shelly walks 2  kilometers N30°W from her camp and then walks 2  kilometers directly east, then the distance of Shelly from the starting point can be gotten using the trigonometry identity as shown:

Let x be the required distance, hence;

\(x = 2 sin \theta\\x = 2sin 30^0\\x = 2(0.5)\\x=1km\)

Hence Shelly was 1km from her camp. Since her initial direction is in the North-West direction, hence the quadrant  bearing will be at the 3rd quadrant

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A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).

Answer:

\(m\angle FGC =101\degree \)

Step-by-step explanation:

\(m\angle CBF = 46\degree\) (Given)

\(m\angle FIG = 55\degree\) (Given)

\(m\angle IFG = m\angle CBF\) (Corresponding angles)

\(\implies m\angle IFG = 46\degree\)

\(m\angle FGC =m\angle IFG+ m\angle FIG\)

(By exterior angle theorem)

\(m\angle FGC =46\degree+ 55\degree \)

\(m\angle FGC =101\degree\)

Here

Using the formula

sum of interiors=external

The correct answer to the given question about chi-square distribution and sampling distribution is a. 5 or higher.

The chi-square distribution provides a good approximation to the sampling distribution of the chi-square statistic only if the sample size is large. Generally, a sample size of 5 or higher is considered large enough for this approximation. This is because the chi-square distribution approaches a normal distribution as the degrees of freedom increase, and a sample size of 5 or more provides enough degrees of freedom for the approximation to be valid. However, if any expected count is less than 5, then the approximation may not be reliable, and alternative methods should be considered (such as Fisher's exact test or the Monte Carlo method).

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Answer:

The chef cooked 1/3 pound of potatoes and

1/4 pound of green beans for

each customer.

so. Sum of all vegetables for one customer = 1/3 pound of potatoes + 1/4 pound of green beans

                                                                        = 1/3 + 1/4 pound

                                                                        = 7/12 pound

so. Sum of all vegetables for 22 customer = (7/12 pound ) 22

                                                                      = 22/12 pound

                                                                      = 11/6 pound

Step-by-step explanation:

Answer:divideing by the whole number

Step-by-step explanation:

To solve for the diameter and radius of a cone with a volume of 8 and a height of 6, we need to use the formulas for the volume and surface area of a cone.

The volume of a cone is given by the formula:

V = 1/3 * π * r^2 * h

where V is the volume, r is the radius, h is the height, and π is the mathematical constant pi (approximately 3.14).

We know that the volume is 8 and the height is 6, so we can plug these values into the formula and solve for the radius:

8 = 1/3 * π * r^2 * 6

r^2 = 8/(π*6/3)

r^2 = 4/π

r = √(4/π)

r ≈ 0.798

The radius is approximately 0.798.

To find the diameter, we simply multiply the radius by 2:

d = 2 * r

d ≈ 1.596

Therefore, the diameter is approximately 1.596 and the radius is approximately 0.798.

Answer:

8 frogs

Step-by-step explanation:

10 - 2 = 8

Answer:

91%

Step-by-step explanation:

The first step is to calculate the increase

= 1635-858

= 777

Therefore the percent increase can be calculated as follows

= 777/858 × 100

= 0.905× 100

= 90.5 %

= 91%

Hence the percentage increase is 91%

The volume of the square pyramid will be 108 cm³.

What is volume of square pyramids?  

A square pyramid's volume is the space contained between its five sides. The volume of a square pyramid = one-third of the product of the base area and the height of  pyramid. As a result, volume = (1/3) (Base Area) (Height). The volume of a square pyramid is expressed in "cubic units" as the number of unit cubes that can fit inside it. It is commonly stated as m3, cm3, in3, and so forth.

A square pyramid is a five-sided three-dimensional shape. A square pyramid is a polyhedron (pentahedron) made out of a square base and four triangles joined at the vertex. It has a square base and triangular side faces with a shared vertex.

Now,

As given that

side of square=9 cm and height of pyramid= 4cm

then volume of pyramid=1/3*area of square*height of pyramid

=1/3*9*9*4

=3*9*4

=108 cm³

Hence,

         The volume of the square pyramid will be 108 cm³.

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This question is incomplete

Complete Question

You are in a bike race. When you get to the first checkpoint, you are 2/5 of the distance to the second checkpoint. When you get to the second check point, you are 1/4 of the distance to the finish. If the entire race is 40 miles, what is the distance between the start and the first check point?

Answer:

4 miles

Step-by-step explanation:

When you get to the first checkpoint, you are 2/5 of the distance to the second checkpoint. When you get to the second check point, you are 1/4 of the distance to the finish.

Hence, the distance between the start and the first check point is given by the fraction:

2/5 × 1/4

= 2/20 = 1/10

We are told that the: entire race = 40 miles

Hence, 1/10 × 40 miles

= 4 miles.

The distance between the start and the first check point is 4 miles

The expression represented by the mathematical sentence is 3/5a - 7 = –36

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

"The difference between three-fifths of a number and 7 is –36."

Three-fifths of a number a means multiply 3/5 and the number i.e. 3/5 * a

So, we have

The difference between three-fifths of a number and 7 is –36 ⇒ The difference between 3/5a and 7 is –36

difference means subtraction

So, we have

The difference between three-fifths of a number and 7 is –36 ⇒ 3/5a - 7 is –36

"is" means =

So, we have

The difference between three-fifths of a number and 7 is –36 ⇒ 3/5a - 7 = –36

Hence, the expression represented by the difference between three-fifths of a number and 7 is –36 is 3/5a - 7 = –36

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Answer:

<5 = 30

<6 = 60

<BFD = 120

Step-by-step explanation:

The Sum of the first six terms of the progression is 14706

What is Geometric Progression?

A geometric progression, also known as a geometric sequence, is a non-zero numerical series in which each term after the first is determined by multiplying the preceding one by a fixed, non-zero value known as the common ratio.

Solution:

On carefully observing

We can state that, the Common Ratio is -7

Sum(n) = a(\(r^{n}\) - 1) / r - 1

Sum(6) = -1 (-7^6 - 1) / -7-1

Sum(6) = -1(117648)/-8

Sum(6) = 14706

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Therefore, the value of x that satisfies the equation √x = 14i√3 is -588. The answer is (a). The only value of x that satisfies this equation is option (b): which is -2i.

We can start by squaring both sides of the equation to eliminate the square root:

We have to apply the knowledge of multiplying or squaring a complex number will give us a negative value.

(√x)^2 = (14i√3)^2

x = (14i)^2 x (√3)^2

We have to take the square of the complex number and the square root of 3.

x = -196 x 3

Multiply the value

x = -588

The value of x in the equation is -588.

2. We can factor out x from the expression as follows:

x(x^4 + 6x^2 + 8)

Now, we need to find the value(s) of x that make the expression equal to 0.

We can see that one solution is x = 0, since anything multiplied by 0 is 0.

To find the other solution(s), we can solve the quadratic equation inside the parentheses:

x^4 + 6x^2 + 8 = 0

Substitute y = x^2:

y^2 + 6y + 8 = 0

Factor the quadratic equation:

(y + 4)(y + 2) = 0

Therefore, the possible values of y are -4 and -2. Substituting back y = x^2, we get:

x^2 = -4 or x^2 = -2

Since x^2 cannot be negative for real numbers, there are no real solutions to this equation. However, if we allow complex numbers, we can find the solutions by taking the square roots of -4 and -2:

x = ±2i or x = ±sqrt(2)i

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