given the geometric sequence where a1=3 and the common ratio is -1, what is the domain for n?

All integers where >_0
all integers where n>_0
all integers where n<_0
all integers where n>_1​

a) The amount after 2 years with continuous compounding is approximately $6539.48.

b) It will take approximately 2.32 years for the amount to reach $8000 with continuous compounding.

a) To calculate the amount after 2 years with continuous compounding, you can use the formula:

[tex]A = P \times e^{rt}[/tex]

Where:

A = the amount after time 't'

P = the principal amount (initial investment)

e = Euler's number (approximately 2.71828)

r = the interest rate (as a decimal)

t = the time in years

Given that P = $5800, r = 6% (0.06 as a decimal), and t = 2 years, we can now calculate the amount (A):

[tex]A = 5800 \times e^{0.06 \times 2}[/tex]

[tex]A=5800 \times e^{0.12}[/tex]

[tex]A=5800 \times 1.1275[/tex]

A=6539.48

Hence,  the amount after 2 years is approximately $6539.48.

b) To find how long it takes for the amount to be $8000, we need to solve for 't' in the formula:

[tex]A = P \times e^{rt}[/tex]

Given that A = $8000 and P = $5800, we can rearrange the formula:

[tex]e^{rt}=\frac{A}{P}[/tex]

[tex]e^{0.06t}=\frac{8000}{5800}[/tex]

Take logarithms on both sides:

[tex]0.006t=log(\frac{8000}{5800})[/tex]

[tex]0.006t=0.139[/tex]

t=0.139/0.06

t=2.327

Hence, it takes 2.32 years for the amount to be $8000.

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After 2 years, the investment grows to approximately $6498.78. It will take around 5.37 years for the investment to grow to $8000.

We can use the formula for continuously compounded interest, which is A = Pe^(rt), where P is the principal amount ($5800), r is the interest rate (6% or 0.06), t is the time, and e is the mathematical constant approximated as 2.71828.

a) To find the amount after 2 years, sub in $5800 for P, 0.06 for r, and 2 for t to get: A = $5800 * e^(0.06*2). Evaluating this gives approximately $6498.78.

b) To find out when the amount will be $8000, we set A to $8000 and solve for t, getting: t = ln($8000 / $5800) / 0.06. Evaluating this gives approximately 5.37 years.

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I believe the answer is d. 156,029

I think the answer is D

Answer:

B. Data set X is not linear, and data set Y is linear.

Step-by-step explanation:

We assume here that "form a pattern" means "roughly forms a line"... because a pattern doesn't necessarily equal a line, it would be a curve that would easily be interpreted too, but it wouldn't be linear.

Since you cannot form a pattern, and based on your choices for answer, we have have to say that data set X is NOT linear.

On the opposite, since the data set Y produces a pattern, it has to be linear.

So, X = NOT linear, Y = linear.

Answer:

(Data set x is linear, and data set y is not linear.) This is the correct answer 100%...

When i put the answer in from the other person which was (x is not linear, and y is linear) it said incorrect and gave me this answer x is linear, and y is not linear. So be careful what you put down.

Step-by-step explanation:

Answer:

  68

Step-by-step explanation:

[tex]a_2=2a_1+4=2\cdot 5+4=14\\\\a_3=2a_2+4=2\cdot 14+4=32\\\\a_4=2\cdot 32+4=68[/tex]

  a₄ = 68

_____

The explicit formula is

  an = 9·2^(n-1) -4

Answer:

11.6 cm²

Step-by-step explanation:

The area (A) of the shaded region is

A = area of sector - area of triangle

area of sector = area of circle × fraction of circle

                       = π × 9.28² ×[tex]\frac{68.9}{360}[/tex] ≈ 51.78 cm²

area of triangle = [tex]\frac{1}{2}[/tex] × 9.28 × 9.28 × sin68.9°

                         = 0.5 × 9.28² × sin68.9 ≈ 40.17 cm²

Area of shaded region = 51.78 - 40.17 ≈ 11.6 cm²

Answer: 8 2/3

Step-by-step explanation:

Answer:

sandals costed $32.55

Step-by-step explanation:

Final answer:

To find the cost of the sandals, subtract the cost of the T-shirt from the total cost. The equation 8.95 + c = 41.50 leads to c = 32.55, meaning the sandals cost $32.55.

Explanation:

The question asks us to find the cost of sandals that Tina bought, given the total cost of a T-shirt and the sandals combined, and the cost of the T-shirt alone. To solve for the cost c of the sandals, we start with the equation 8.95 + c = 41.50. We then isolate c by subtracting 8.95 from both sides of the equation:

c = 41.50 - 8.95

c = 32.55

Therefore, the cost of the sandals was $32.55.

[tex]

f(4)=5\times(\frac{1}{2})^4 \\

f(4)=\frac{5\times1^4}{2^4} \\

f(4)=\boxed{\frac{5}{16}}

[/tex]

Hope this helps.

Brainliest would be great.

For this case we have a function of the form[tex]y = f (x)[/tex]

Where:

[tex]f (x) = 5 * (\frac {1} {2}) ^ x[/tex]

We must find the value of the function when x = 4, that is, f (4):

Substituting we have:

[tex]f (x) = 5 * (\frac {1} {2}) ^ 4\\f (x) = 5 * \frac {1} {2} * \frac {1} {2} * \frac {1} {2} * \frac {1} {2}\\f (x) = 5 * \frac {1} {16}\\f (x) = \frac {5} {16}\\f (x) = 0.3125[/tex]

ANswer:

[tex]f (x) = \frac {5} {16}\\f (x) = 0.3125[/tex]

Answer:

True

Step-by-step explanation:

The area of a regular polygon is found by multiplying 1/2 times the apothem times the perimeter.  The area for a single triangle is 1/2 times the height (which is the same as the apothem of a regular polygon) times the base (which is one of the sides of the regular polygon which you are multiplying by  to find the perimeter of the polygon).

Answer:

The given statement is true.

Step-by-step explanation:

The area of a regular heptagon can be found by breaking the heptagon into seven congruent triangles and then taking the sum of their areas.

This is true.

Breaking down in 7 triangles and adding separately the areas of these triangles, will give the complete area of the heptagon. We can also find the area of one triangle and multiply that by 7 to get the same result.

Answer:

Your salary will be $62,500.

Step-by-step explanation:

This is an arithmetic sequence with first term $45,000 and common difference $2,500.

The appropriate formula is a(n) = a(1) + (n-1)d, where a(1) is the first term, n is a counter and d is the common difference.

In this particular case, a(8) = $45,000 + (8-1)($2,500) = $62,500

Your salary will be $62,500.

A function assigns the values. Your salary after completing the 8th year within the company will be $62,500.

A function assigns the value of each element of one set to the other specific element of another set.

Given that the starting salary will be $45,000 while the salary will increase every year by $2,500. Therefore, the function that can represent the salary after (n-1) years can be written as,

y = $45,000 + $2,500(n-1)

Now, the salary after 8th year will be,

y = $45,000 + $2,500(n-1)

y = $45,000 + $2,500(8-1)

y = $62,500

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Answer:

The answer is B

Step-by-step explanation:

just took the answer on e2020

Answer:

B:

Yes, a translation mapping vertex Q to vertex T and a reflection across the line containing QS will map  △QRS to △TUV.

Answer:

The fourth graph (last graph)

Step-by-step explanation:

Remember that the zeros of a function are the x-intercepts of the graph. To find the zeros we just need to set the function equal to zero and solve for x:

[tex]f(x)=(x-1)(x+4)[/tex]

[tex](x-1)(x+4)=0[/tex]

[tex]x-1=0,x+4=0[/tex]

[tex]x=1,x=-4[/tex]

Now we know that the graph or our function intersects the x-axis at x = 1 and x = -4.

Since both x values inside the parenthesis are positive, our parabola is opening upwards.

The only graph opening upwards whose x-intercepts are x = 1 and x = -4 is the fourth one.

We can conclude that the graph of [tex]f(x)=(x-1)(x+4)[/tex] is the fourth one.

ANSWER

See attachment.

EXPLANATION

The given function is

f(x) = (x – 1)(x + 4).

This parabola will open upwards because the leading coefficient is positive.

The x-intercepts can be found by equating the function to zero.

[tex](x - 1)(x + 4) = 0[/tex]

By the zero product property;

[tex]x - 1 = 0 \: or \: x + 4 = 0[/tex]

This implies that,

[tex]x = 1 \: or \: x = - 4[/tex]

The graph that touches the x-axis at -4 and 1, and opens upwards is the last graph.

The correct choice is D.

Answer:

d. a=1. b=2, c=3

multiply by the Reciprocal.

Answer:

D

Step-by-step explanation:

(5/8) / (3/8)

(5/8) * (8/3)

5/3

1 ⅔

a = 1, b = 2, c = 3

Answer D.

Answer:

the correct choice is marked

Step-by-step explanation:

The red line has intercept -3 and slope 1/3, so is ...

y = 1/3x -3

The blue line has intercept +1 and slope -1, so is ...

y = -x +1

The graph solves this system of equations, which can also be written as the single equation ...

y = y

1/3x -3 = -x +1

Answer:

There were 40 student tickets sold.

Step-by-step explanation:

First I set up equations to represent this situation.

4x+3y=380

x+y=105

x represents the adult tickets and y represents the student tickets.

I can solve this with the elimination method. I want to cancel out the x so I will multiply every term in equation 2 by -4.

4x+3y=380

-4x-4y=-420

Now I combine like terms.

-y=-40

I can divide the negative one from both sides.

y=40

40 Tickets sold.

Thank me later.

Answer:

Second Option

[tex]a=1.46[/tex]

Step-by-step explanation:

The triangle of the figure is a straight triangle.

We know the length of the hypotenuse, h = 2, and we know the angle A = 43°. We need to find the length a. Side a is the side adjacent to the 43° angle

By definition we know that

[tex]cosx = \frac{adjacent}{hypotenuse}[/tex]

Then

adjacent = a

hypotenuse  =2

x =43°

[tex]cos(43\°) = \frac{a}{2}[/tex]

[tex]a= 2cos(43\°)[/tex]

[tex]a= 1.46[/tex]

Answer:

it is the third one (from left to right)

Step-by-step explanation:

no explation

Answer:

y = 2 x - 1

Hope this helps :)

Have a great day !

5INGH

Step-by-step explanation:

When x = 1 , y= 1

x = 2 , y=3

The answer is:

The missing step is the step shown in the last option:

D. [tex]324=0.042x+16[/tex]

To find which is the missing step, we need to remember that to cancel a square root, we need to elevate it, so:

Starting from the last step before the missing step, we have:

[tex]-18=-\sqrt{0.042x+16}[/tex]

In order to calculate the value of the variable (x) we need to square both sides of the equation, since squaring a root will cancel the root.

We must remember the following properties:

[tex]\sqrt{a^{m} }=a^{\frac{m}{2}}\\\\(a^{b})^{c}=a^{b*c}[/tex]

Now, finding the missing step, we need to find what to do in order to get the expression of the following step.

So, squaring both sides of the equation in order to cancel the square root and isolate the variable, we have:

[tex]-18=-\sqrt{0.042x+16}\\\\(-18)^{2} =(-\sqrt{0.042x+16})^{2} \\324=0.042x+16\\324-16=0.042x\\\\x=\frac{304}{0.042}=7333[/tex]

Hence, we found the the missing step is:

D. [tex]324=0.042x+16[/tex]

Have a nice day!

Answer: Permutation; number of ways = 120

Step-by-step explanation:

Answer with explanation:

Number of runner= 5

Number of Distinct Medal = 5

First Medal can be Awarded in 5 ways, second Medal can be awarded in 4 ways and third Medal can be awarded in 3 ways , fourth medal can be awarded in 2 ways and fifth Medal can be awarded in one way.

So, total number of ways =5 × 4×3×2×1=120 way

⇒We will use the concept of Permutation as there are five distinct medal and five different runners

So, Five distinct places can be filled in 5! or [tex]_{5}^{5}\textrm{P}[/tex] ways as order of arrangement is Important because any of the five candidates can win first second, third , fourth or fifth Prize.  

= 5!=5×4×3×2×1=120 ways

Because, n!=n×(n-1)×(n-2)×........1.

Answer:

The right answer is 3a - 11 ≤ 7 ⇒ 4th answer

Step-by-step explanation:

* Lets study the problem

- From the figure

# The blue line started from 6 and the point is bold that means

   the inequality sign is ≤ or ≥

# The blue line started from 6 and moved to the negative numbers

   that means the inequality is less than or equal

∴ a ≤ 6

* Now lets look to the answers

- There is only one answer has the sign ≤ , the last answer

* Now lets solve it to be sure

∵ 3a - 11 ≤ 7 ⇒ add 11 to the both sides

∴ 3a ≤ 18 ⇒ divide the both sides by 3

∴ a ≤ 6

* The right answer is 3a - 11 ≤ 7

Answer:

The three integers are 13,14,15

Step-by-step explanation:

Let x be the first integer

x+1 be the second integer

x+2 be the third integer

The sum of the three integers is 42

x+ (x+1) + (x+2) = 42

Combine like terms

3x+3 = 42

Subtract 3 from each side

3x+3-3 = 42-3

3x= 39

Divide by 3

3x/3 = 39/3

x = 13

x+1 = 14

x+2 = 15

The three integers are 13,14,15

Answer:

$1615.00

Step-by-step explanation:

Without more information, we cannot give a specific numerical answer for the total interest on a 20-year loan. As a rule, total interest paid will be less on a shorter loan, despite higher monthly payments.

The question is asking how much total interest would Misty pay on a 20-year loan, given she knows the total interest paid on a 25-year loan to be $57,810. We're not given enough information to provide a specific numerical answer for this - the loan interest for a 20-year loan and a 25-year loan involve different payment schedules and amounts - so we can't directly compare or convert the total interest paid.

However, generally speaking, the total interest paid over a shorter loan term (i.e. 20 years) is expected to be less than that of a longer term (i.e. 25 years), assuming all else (loan amount, interest rate) remains equal - this is because the principal balance is being paid down more rapidly, leaving less time for interest to accrue. The trade-off is that monthly payments would be higher on the shorter term loan.

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ANSWER

The solution is (2,1)

EXPLANATION

The given equations are:

2x+4y=8...(1)

3x-5y=1...(2)

We make x the subject in the first equation to get:

2x=8-4y

This means that,

x=4-2y...(3)

Put equation (3) into equation (2)

3(4-2y)-5y=1

Expand:

12-6y-5y=1

-6y-5y=1-12

-11y=-11

y=1

Put y=1 into equation (3).

x=4-2(1)=2

The solution is (2,1)

The total surface area for the figures aee;

1) 128 m²

2) 714 in²

1) To find the surface area, we need to find the area of each surface that makes up the object and add together.

Thus:

T.S.A = 4(4 * 4) + (4 * 4) + 4(½ * 4 * 6)

T.S.A = 128 m²

2) The total surface area here is;

T.S.A = 2(15 * 10) + 2(10 * 7) + 2(15 * 7) + 4(4 * 4)

T.S.A = 714 in²

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Answer: 3421.19

Step-by-step explanation:

look up cylinder formula and r= radius which is just the diameter cut in half

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The volume of the cylinder is 3421.1944 cm³.

A cylinder is a three-dimensional structure formed by two parallel circular bases connected by a curving surface. The circular bases' centers overlap each other to form a right cylinder.

Given the diameter of the cylinder is 22 cm, therefore, the radius of the cylinder is 11cm, Also, given the height of the cylinder is 9 cm.

The volume of the cylinder = πR² × H

                                             = π × (11cm)² × 9cm

                                             = 1089π cm³

                                             = 3421.1944 cm³

Hence, the volume of the cylinder is 3421.1944 cm³.

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Answer:

Step-by-step explanation:

This is a special die.  Its six sides bear the numbers {9, 10, 11, 12, 13, 14}.

There are three possibilities for getting a multiple of two:  {10, 12, 14}, and

there is only one possibilities for getting a multiple of ten:  {10, 12, 14}

The probability here of getting a multiple of two is 3/6, and that of getting a multiple of ten is 1/6.  But one of the outcomes is found in both result sets:  10.  Getting a multiple of 10 is already included in the event that the outcome is a multiple of two.  My answer here would be 3/6, or 1/2.

the probability of rolling a multiple of two or ten is 4/6, which simplifies to 2/3.

The probability of rolling a multiple of two or ten on a die numbered 9 through 14 can be calculated as follows:

\

Answer:

x^2 + y^2 + 6x - 8y + 21= 0.

Step-by-step explanation:

The center of this circle is (-3, 4) and the radius id 2.

So in Standard form, the equation is:

(x + 3)^2 + ( y - 4)^2 = 2^2

Converting to General form we have:

x^2 + 6x + 9  + y^2 - 8y + 16 = 4

x^2 + y^2 + 6x - 8y + 9 + 16 - 4 = 0

x^2 + y^2 + 6x - 8y + 21= 0.

Answer:

[tex]-4[/tex]

Step-by-step explanation:

The given logarithmic equation is:

[tex]\log_7(x+1)+\log_7x=\log_712[/tex]

Recall and apply product rule of logarithms.

[tex]\log_aM+\log_aN=\log_aMN[/tex]

We apply this property to the left side of the equation to get;

[tex]\log_7x(x+1)=\log_712[/tex]

We take the antilogarithm of both sides to get:

[tex]x(x+1)=12[/tex]

We expand to obtain:

[tex]x^2+x=12[/tex]

We rewrite in the standard quadratic form:

[tex]x^2+x-12=0[/tex]

We factor to obtain:

[tex](x-3)(x+4)=0[/tex]

Either [tex](x-3)=0[/tex] or [tex](x+4)=0[/tex]

Either [tex]x=3[/tex] or [tex]x=-4[/tex]

But the domain is[tex]x\:>\:0[/tex].

Hence [tex]x=-4[/tex] is an extraneous solution.