I will give BRAINILEST

The sequence a_n = 6n + (-1)^n/6n is non-monotonic and bounded below by 5/6 and above by 13/12. So, the correct answer is A).

We observe that the sequence can be written as\($a_n = \frac{6n}{|6n|} + \frac{(-1)^n}{6n} = \frac{6n}{|6n|} + \frac{(-1)^n}{6|n|}.$\)

We have \($a_{2n} = \frac{12n}{6n} + \frac{1}{6n} = \frac{13}{6} \leq \frac{13}{6}$\) and \($a_{2n+1} = \frac{-12n-6}{6n+3} - \frac{1}{6n+3} = -\frac{13}{12} \geq -\frac{13}{12}.$\)Therefore, the sequence is increasing and bounded below by 5/6 and above by 13/12.

We have\($a_{2n} = \frac{12n}{6n} + \frac{1}{6n} = \frac{13}{6} \geq \frac{0}{1}$\)and

\($a_{2n+1} = \frac{-12n-6}{6n+3} - \frac{1}{6n+3} = -\frac{13}{12} \geq -\frac{13}{12}.$\) Therefore, the sequence is non-increasing and bounded below by 0 and above by 6.

From above part, we see that the sequence is not monotonic.

We have \($a_{2n} = \frac{12n}{6n} + \frac{1}{6n} = \frac{13}{6} \geq 1$\) and\($a_{2n+1} = \frac{-12n-6}{6n+3} - \frac{1}{6n+3} = -\frac{13}{12} \leq \frac{13}{12}.$\) Therefore, the sequence is decreasing and bounded below by 1 and above by 6.

We have \($a_{2n} = \frac{12n}{6n} + \frac{1}{6n} = \frac{13}{6} \geq 1$\) and \($a_{2n+1} = \frac{-12n-6}{6n+3} - \frac{1}{6n+3} = -\frac{13}{12} \geq \frac{-11}{12}.$\)Therefore, the sequence is not monotonic and bounded below by 1 and above by 11/12.

Therefore, the answer is  a_n = 6n + (-1)^n/6n| is increasing; bounded below by 5/6 and above by 13/12. So, the correct option is A).

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Answer:

Step-by-step explanation:

To maintain an average of 79, Aldo must obtain a score of 82 in his upcoming exam.

To get the solution, let's calculate the total of the first five scores.

Total of the first five scores = 77 + 88 + 77 + 87 + 63 = 392

Now we know that there are a total of six scores, so to get the mean, we will divide the total by six.

Mean = Total/Number of ScoresTherefore, 79 = 392 + x/6

We need to find the value of x that will satisfy the above equation.

Now we will solve for x.79 = 392 + x/6

(Multiply both sides by 6) 6 * 79 = 6 * 392 + x6 * 79 = 2352 + xx = 6 * 79 - 392x = 474 - 392x = 82

Therefore, Aldo needs to score 82 on his next test to achieve an average of 79.


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Answer:

i forgot how to do this

Step-by-step explanation:

We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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Based on the information, the percentage increase for the area s greater as it is 600% greater

Here, we have a square of side length 3 cm

The area of the square is 3² = 9 cm²

Perimeter of the square = 4L = 4 * 3 = 12 cm

When we triple the length of the square, its new length becomes 3 ,× 3 = 9 cm

Area here will be 9 * 9 = 81 cm²

Perimeter = 4 L = 4 * 9 = 36cm

To calculate percentage change, we use the formula;

(new value - old value)/old value * 100%

For the perimeter;

(36-12)/12 * 100% = 24/12 * 100% = 2 * 100% = 200%

For the area;

(81-9)/9 * 100% = 72/9 * 100% = 8 * 100% = 800%

The percentage increase of the area is greater by: 800% - 200% = 600%

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The side length of the square shown is tripled.

3 cm

Which percent of increase is greater the percent of increase for the perimeter of the square or the percent of increase for the area

Answer: square root of 9

Step-by-step explanation:

The answer is the square root of 9, which is 3.

Answer:

i cant do dat because im broke sorry

Step-by-step explanation:

the data derived from a sample statistic will show that the two variables that are being researched are related or that the relationship is not large enough for the variables to be related is true

Current statistical studies are modern and have a wealth of analysis tools and software to understand the data. Statistics has a wide range of objectives, which aim not only to understand the variability of the data, but also its origin and motivation. For example, if an election poll shows a variation from a previous poll, statisticians will seek to understand the causes of these variability and not just present the variation in the data.

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Function rule describes the translation OT_1-9(x, y)

A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation.

A square on a coordinate plane is translated 9 units down and 1 unit to the right.

Let's (x, y) be the coordinate.

where x be the horizontal move and y be the vertical move.

As, it is translated 9 units down and 1 unit right.

then

(x, y) = (x +1, y - 9)

and the translation be

(x, y ) = (x+1, y-9)

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Using proportions, it is found that both patterns have the same number of ovals.

For Phil:

1 oval - 2 shapes

x oval - 96 shapes

Applying cross multiplication:

\(2x = 96\)

\(x = \frac{96}{2}\)

\(x = 48\)

For Stacy:

2 oval - 4 shapes

x oval - 96 shapes

Applying cross multiplication:

\(4x = 192\)

\(x = \frac{192}{4}\)

\(x = 48\)

Both patterns have the same number of ovals.

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The volume in a pyramid is given by the next formula:

Where:

Ab is the area of the base

h is the heigh of the pyramid.

The area of the base is:

where l is length and w is the width

l=49cm

w=36cm

Then, the volume of the figue is:

Answer:

so the Domain:

{5, -5, 6,−6}

Range:  {1,4,2,8,3}

functon no

Since x=−5 produces y=4 and y=3, the relation (5,1),(−5,4),(6,2),(−6,8),(−5,3)is not function.

Step-by-step explanation:

domain is normally x and range in most the time y, this is what i was taught and i hope it helps and is right

Answer:

1.) You my add any positive or negative number to both sides of an inequality.

2.) You may multiply or divided both sides of an inequality by any positive number.

Step-by-step explanation:

*Hope this helped*

The procedure is summarized in three steps: 1) Write expressions, 2) Simplify/reduce expressions, 3) Solve for each variable.

The procedure of Writing and Solving Equations and Inequalities: is described below:

1) Write a number of Equations with same quantity of Variables, in order to solve the System.

2) Use Algebra properties to Simplify and Reduce the number of Expressions.

3) Solve for each reduced Expression.

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You are designing a 5 kilometer course for charity run. The design now has been covers 4,908.5 meters, hence, you need to add more 91.5 meters on the course.

The conversion from yard to meter is:

1 yard = 0.9144 meters

The course streets and the distances after converted into meters are:

main street to 6th ave.  781 yards = 714.15 meters

6th ave. to pleasant road 1,250 yards = 1143 meters.

pleasant road to city park 275 yards = 251.46 meters

route through city park 2,337 yards = 2,136.95 meters

city park to main street 725 yards = 662.94 meters

Total course = 714.15 + 1143 + 251.46 +  2,136.95 +  662.94

Total course = 4,908.5 meters

The design is 5 km = 5000 meters. Therefore, you still need to add:

5000 - 4,908.5 = 91.5 meters more course.

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Given data:

The given number is a=0.09.

The given nummber can be written as,

a=0.09

=9x10^(-2)

=9/100

Thus, the given nummber can be written infraction form as 9/100.

Answer:

15 answers

Step-by-step explanation:

To solve this question we need to set up an equation.

Let's name the number of incorrect answers x.

We can set up an equation that's essentially:

(Points for correct answer)*(number of correct answers)+(points for incorrect answer)*(number of incorrect answers)=final score

When we plug in our numbers and variables it looks like this:

5(3)+(-2x)=-15

Simplify

15-2x=-15

Subtract 15 from both sides

-2x=-30

Divide both sides by -2

x=15

This means Smitha attempted 15 wrong answers, and that there were 18 questions in total.

DNE in each coordinate of the ordered triplet are y is -7 , DNE ,y is-2.

1.) 2+3 = y + 12

Make y the formula's subject after adding the LHS.

5 = y + 12

Y = 5 - 12

Y = - 7

The answer to the equation is -7

2.) 2 + 13 = 1 +8

The equation cannot have a solution since there is no unknown variable and the sum of the numbers on the left hand side (LHS) does not equal the sum of the numbers on the right hand side (RHS).

3.) y - 7 = 2 - 11

RHS is added, and y is become the formula's subject.

Y - 7 = -9

Y = -9 + 7

Y = -2

The equation's answer is -2.

The complete question is:Solve the following system of equations. If there is no solution, write DNE in each coordinate of theordered triplet. If there are an infinite number of solution, write each coordinate in terms of z.2+3 = y + 12

2 + 13 = 1 +8

y - 7 = 2 - 11

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The dimensions of the rectangular metal tank that requires the least material to build are approximately 7.58 feet by 7.58 feet by 7.58 feet.

Let the length, width, and height of the tank be L, W, and H, respectively. Since the tank has an open top, its volume is given by V = LWH. We are given that V = 364.5 cubic feet. We want to minimize the surface area of the tank, which is given by A = 2LW + 2LH + 2WH.

To minimize A, we can use the volume constraint to eliminate one of the variables. Solving for one of the variables, say H, we get H = V/LW. Substituting this into the equation for A, we get A(L,W) = 2LW + 2V/L + 2V/W. To minimize A, we take partial derivatives with respect to L and W and set them equal to zero. This gives us the system of equations:

2 + 2V/L^2 = 0

2 + 2V/W^2 = 0

Solving for L and W, we get L = W = sqrt(V/2) = 7.58 (rounded to two decimal places). Substituting these values into the equation for H, we get H = V/LW = 7.58. Therefore, the dimensions of the tank that require the least amount of material to build are approximately 7.58 feet by 7.58 feet by 7.58 feet.

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The tank that requires the least amount of material to build has Length = 1 ft. Width = 1 ft. Height = 364.5 ft

To find the dimensions of the tank that require the least amount of material to build, we need to minimize the surface area of the tank while keeping its volume constant.

Let's denote the length, width, and height of the tank as L, W, and H, respectively.

The volume of a rectangular tank is given by:

Volume = Length × Width × Height

In this case, the volume is given as 364.5 cubic feet:

364.5 = L × W × H

The surface area of a rectangular tank can be calculated by considering the four sides and the bottom:

Surface Area = 2(LW + LH + WH)

We need to minimize the surface area while keeping the volume constant. To achieve this, we can express one of the dimensions in terms of the other two using the volume equation and substitute it into the surface area equation.

From the volume equation, we can express H in terms of L and W:

H = 364.5 / (LW)

Substituting this value of H into the surface area equation, we have:

Surface Area = 2(LW + L(364.5 / (LW)) + W(364.5 / (LW)))

Simplifying further:

Surface Area = 2(LW + 2 * 364.5 / W + 2 * 364.5 / L)

To find the dimensions that minimize the surface area, we need to differentiate the surface area equation with respect to L and W and set the derivatives equal to zero.

Differentiating with respect to L:

d(Surface Area) / dL = 2W - (2 * 364.5 / L^2) = 0

Differentiating with respect to W:

d(Surface Area) / dW = 2L - (2 * 364.5 / W^2) = 0

Solving these equations will give us the values of L and W that minimize the surface area.

2W - (2 * 364.5 / L^2) = 0

2L - (2 * 364.5 / W^2) = 0

Simplifying:

W = 364.5 / L^2

L = 364.5 / W^2

Substituting these expressions into the volume equation:

364.5 = (364.5 / L^2) * L * W

364.5 = 364.5 / L * W

Simplifying:

L * W = 1

This implies that the product of the length and width is equal to 1.

Since we want to minimize the amount of material used, we can set one of the dimensions to 1 and solve for the other dimension.

Let's set W = 1:

L * 1 = 1

L = 1

Therefore, the dimensions that require the least amount of material to build the tank are:

Length = 1 ft

Width = 1 ft

Height = 364.5 ft

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Becky would need to invest approximately $11,621.14 in a sinking fund paying a 7% interest rate compounded over 45 years to accumulate $100,000.

To calculate the amount Becky needs to invest in the sinking fund, we can use the future value formula for compound interest. The formula is:

FV = PV *\((1 + r)^n\)

Where:

FV is the future value (desired amount),

PV is the present value (amount to be invested),

r is the interest rate per period (7% in this case), and

n is the number of compounding periods (45 years).

Rearranging the formula to solve for PV:

PV = FV /\((1 + r)^n\)

Plugging in the given values:

PV = 100,000 / \((1 + 0.07)^45\)

PV ≈ 100,000 /\((1.07)^45\)

PV ≈ 100,000 / 13.237797

Therefore, Becky would need to invest approximately $11,621.14 in the sinking fund to accumulate $100,000 in 45 years. This assumes that the interest rate remains constant, and the interest is compounded annually.

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Answer:

-3 < x

Step-by-step explanation:

first of all get the positive x on one side, so we have

12 < 18 + 2x ( positive x is easier to work with)

then, get only x on one side

-6 < 2x

simplify

-3 < x

The equation of the line is y = -2x + 16 which passes through the point (4, 8) and has a slope of -2.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The line that passes through the point (4, 8) and has a slope of -2.

On comparing the standard equation:

y = mx + c

Here m is the slope of the line and c is the y-intercept.

m = -2

y = -2x + c

Plug x = 4 and y = 8

8 = -2(4) + c

c = 16

y = -2x + 16

Thus, the equation of the line is y = -2x + 16 which passes through the point (4, 8) and has a slope of -2.

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The characteristic displayed by the graph by virtue of the number of turning points and end behaviour is; Odd function.

It follows from the task content that the characteristic displayed by the graph is to be determined.

By observation, first, the graph has a odd number of zeroes and also has 2 turning points; it most likely indicates that the graph is of degree 3 and it's end behaviours suggest an odd function.

On this note, it can be inferred that the given graoh is an odd function.

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Answer:

lost 120

Step-by-step explanation:

10% of 1200 is 120 so you subtract 120 from 1200

Answer:

120

Step-by-step explanation:

Loss = (Loss%)(C.P)

Loss = (10%)(1200)

Loss = (10/100)(1200)

Loss = 120

In an observational study, the statement that a cause and effect can be determined is false.

Observational studies simply establish associations between predictor and outcome variables. Observational studies cannot confirm that an association contemplates cause and effect.

In observational studies, confounding variables may explain an observed relationship between predictor and outcome variables.

In an observational study, a cause and effect cannot be determined. Observational studies are used to gather data about a particular population or phenomenon, but they do not allow for the determination of cause-and-effect relationships.

This is because observational studies do not control the variables that are being studied and, therefore, cannot determine the relationship between two variables.

In order to determine cause and effect, a controlled experiment is needed in which the variables are manipulated, and their effects are observed.

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The length of the deep end is 12 feet of the swimming pool.

Given: Area of the swimming pool is 210 square feet

Width of the pool = 10 feet

The length of the shallow end is 9 feet and the length of the deep end is d.

To find the value of d.

Let's solve the problem.    

The area of the swimming pool is 210

The width is 10

The deep end length is d

The shallow end length is 9

The total length of the swimming pool = The length of the deep end + The length of the shallow end

=> d + 9

Therefore, the total length of the swimming pool is d + 9

The surface of the swimming pool is rectangular, so

The area of rectangle = width × length

Therefore,

area of swimming pool = width of the pool × length of the swimming pool

=> 210 = 10 × (9 + d)

or 10 × (9 + d) = 210

Dividing both sides by 10:

10 × (9 + d) / 10 = 210 / 10

9 + d = 21

Subtracting 9 on both sides:

9 + d - 9 = 21 - 9

d = 12

Therefore the length of the deep end is 12 feet

Hence the length of the deep end is 12 feet of the swimming pool.

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The length of the deep end of the swimming pool is 12 feet.

We are given that:

The Area of the swimming pool = 210 square feet

width of the swimming pool = 10 feet

Length of shallow end = 9 feet

Let the length of the deep end be d.

Total length of the swimming pool = length of deep end + length of shallow end =  d + 9

Area of swimming pool = width × length

Substituting the values, we get that:

210 = 10 × (9 + d)

9 + d = 21

d = 12

Therefore the length of the deep end of the swimming pool is 12 feet.

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Answer:

  6

Step-by-step explanation:

You want to know the number of uphill integers divisible by 15, where an uphill integer is one that has its digits strictly increasing.

An integer will be divisible by 15 if and only if it is divisible by 3 and 5. An integer is divisible by 5 if it ends in 5 or 0. An uphill integer cannot end in 0, so must end in 5.

An integer is divisible by 3 if the sum of its digits is divisible by 3

An uphill integer will have differences between successive digits that are positive integers. In order for the final digit to be 5, the sum of these differences must be 5. Hence we can find uphill integers by considering the "integer partitions" of 5: the sets of positive integers whose total is 5. Those sets would be ...

  {5}, {4, 1}, {3, 1, 1}, {2, 2, 1}, {2, 1, 1, 1}, {1, 1, 1, 1, 1}

Uphill integers will also have digit differences that are some permutation of each of these sets. For example, the digit differences may be {4, 1} or {1, 4}, corresponding to the numbers 45 or 15.

The uphill integers that end in 5 are ...

  5, 45, 15, 35, 25, 345, 145, 125, 245, 235, 135, 2345, 1345, 1245, 1235, 12345

We already know each of these is divisible by 5. The ones that have a digit total that is a multiple of 3 are ...

  15, 45, 135, 345, 1245, 12345

There are 6 uphill integers divisible by 15.

Answer:

0/121 and 144