I know that these answers are correct, but I don't understand how to get it using the De Moivere Theorem. Can someone please explain in detail? Thank you so much!

Answer:

Step-by-step explanation:

looks like it's about 1/2

Looks approximately like x = 0.6 ish

are there MCQ choices?

Answer:

  TRUE

Step-by-step explanation:

Changing the mean by adding the same number to every data value does not change the differences those values have from the new mean. Hence the standard deviation remains unchanged. If it was 6, it will be 6.

Answer:

True because standard divination stays the same

Step-by-step explanation:

Answer:

a) 103, b) No

Step-by-step explanation:

a) We need to multiply the probability by the amount of the sample to get:

200 × 51.6% = 103.2, rounded down to 103

b) As we have selected the people randomly, we have no control over the type of people we are given - this is theoretical and the estimate is not definite - all of the sample could have murdered by firearm or even none (even though it is highly unlikely).

Answer:

0.034

Step-by-step explanation:

Data:

Let the standard deviation be : [tex]\sigma = 2[/tex]

The mean be: [tex]\mu = 6[/tex]

Therefore, P (x>4) which is  the probability that a person will wait for more than 4 minutes is given by:

[tex]z = \frac{X- \mu }{\sigma }[/tex]

 = [tex]\frac{4-6}{2} \\= -1[/tex]

Therefore,

P(x > 4)  = P (z > -1)

             = P (z < -1)

From the z-tables, we find 0.034

To find the probability that a person will wait for more than 4 minutes, calculate the z-score and use a standard normal distribution table or calculator. The probability is approximately 0.8413 or 84.13%.

To find the probability that a person will wait for more than 4 minutes, we need to calculate the z-score for the value 4 using the given mean and standard deviation. The z-score formula is z = (x - mean) / standard deviation. Plugging in the values, we get z = (4 - 6) / 2 = -1. Now, we can use a standard normal distribution table or a calculator to find the probability associated with this z-score.

Using a standard normal distribution table, the probability of a z-score less than -1 is approximately 0.1587.

Therefore, the probability of a person waiting for more than 4 minutes is approximately

1 - 0.1587 = 0.8413 or 84.13%.

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Answer:

2/9

Step-by-step explanation:

Because there's 2 blue marbles and 9 in total

Answer:

6 units

Step-by-step explanation:

A rectangle's width is one-fourth of its length.

w = 1/4 l

area is 9 square units

A = l*w = 9

  Replacing w with 1/4l

  l * (1/4l) = 9

1/4 l^2 = 9

Multiply each side by 4 to clear the fraction

4 * 1/4 l^2 = 4*9

l^2 = 36

Take the square root of each side

sqrt (l^2) = sqrt(36)

l =6

Answer:

6 units

Step-by-step explanation:

Let the length = L

Then the width = L/4

area = length * width

area = L * L/4 = 9

L^2/4 = 9

L^2 = 36

L = 6 or L = -6

Since we are dealing with a length, we eliminate the negative answer.

Answer: 6 units

P.S. Your equation is incorrect. L(L) = 9 would work for a square with 4 congruent sides and area 9. Here the sides have different lengths. The equation is L(L/4) = 9.

Answer:

y = 2

Step-by-step explanation:

r tan θ / sec θ = 2

First, simplify tan θ / sec θ:

r (sin θ / cos θ) / (1 / cos θ) = 2

r sin θ = 2

Remember that r cos θ = x and r sin θ = y:

y = 2

Answer:

Answer is A hope that helped

Step-by-step explanation:

Answer:

  142°

Step-by-step explanation:

∠3 is an alternate exterior angle with ∠7, so is congruent to ∠7. ∠7 is supplementary to 38°, so has measure 180° -38° = 142°.

The measure of ∠3 is 142°.

Answer:

y intercept equals 1

Step-by-step explanation:

y= -1/2x+1

the slope is -1/2

the y intercept is 1

The  probability that all selected transistors are defective is approximately 0.0014, while the probability that none of the selected transistors are defective is 0.1762.

Given:

Transistors = 13

Defective = 4

a. The number of ways to choose 4 defective transistors from the 4 available = [tex]^4C_4[/tex]

               = [tex]\dfrac{4!}{4! 0!}[/tex]

               = 1

and, the total number of ways to choose 4 transistors from the 13 available

[tex]^{13}C_4= \dfrac{13!}{4! * (13-4)!}[/tex]

    = [tex]\dfrac{(13 * 12 * 11 * 10)}{(4 * 3 * 2 * 1)}[/tex]

    = 715

Therefore, the probability of selecting all defective transistors is:

Probability = Number of favorable outcomes / Total number of possible outcomes

                  = 1 / 715

                  = 0.0014

b. The number of ways to choose 4 non-defective transistors from the 9 available is

[tex]^{9}C_4= \dfrac{9!}{4! * (9-4)!}[/tex]

      = [tex]\dfrac{(9 * 8* 7* 6)}{(4 * 3 * 2 * 1)}[/tex]

      = 126

So, the probability of selecting none defective transistors is:

Probability = Number of favorable outcomes / Total number of possible outcomes

                  = 126 / 715

                  = 0.1762

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Final answer:

The probabilities are calculated using combinations: the probability all selected transistors are defective is 1/C(13,4) or 0.13%, and the probability none are defective is C(9,4)/C(13,4) = 17.6%.

Explanation:

The student's question about probabilities can be answered using combinations and the basic principles of probability. We need to calculate the probability that out of 13 transistors, all 4 selected are defective, and then the probability that none are defective.

Probability All Are Defective

To find the probability that all 4 transistors selected are defective, we calculate the number of ways to pick 4 defective ones out of 4 (which is 1 way, since we only have 4 defective ones), and divide it by the number of ways to pick any 4 out of 13. Using combinations, we calculate:

Probability(all defective) = C(4,4) / C(13,4) = 0.13%.

Probability None Are Defective

To find the probability that none of the 4 selected transistors are defective, we calculate the number of ways to pick 4 non-defective ones out of 9 (since 13 total minus 4 defective leaves 9 non-defective), and divide it by the number of ways to pick any 4 out of 13:

Probability(none defective) = C(9,4) / C(13,4) = 17.6%

Answer:

a. x-intercept = 3 , y-intercept = 9.

Step-by-step explanation:

-6x - 2y = -18

Convert to slope-intercept form:

-2y = 6x - 18

y = -3x + 9

So the y-intercept  (when x = 0) is  when y = 9..

Solving for x to find the x-intercept:

0 = -3x + 9

3x = 9

x = 3.

Step-by-step explanation:

Tree A's heights are less spread out than tree B's heights. Tree A has a lower average height than tree Bs

Answer:

1. [tex]\dfrac{AD}{DB}+1=\dfrac{CE}{EB}+1[/tex]

2. Addition property of equality

Step-by-step explanation:

In triangle ABC,

[tex]\dfrac{AD}{DB}=\dfrac{CE}{EB}.[/tex]

The addition property of equality states that if the same amount is added to both sides of an equation, then the equality is still true.

Use addition property of equality, add 1 to both sides of previouse equality:

[tex]\dfrac{AD}{DB}=\dfrac{CE}{EB}\\ \\\dfrac{AD}{DB}+1=\dfrac{CE}{EB}+1\\ \\\dfrac{AD+DB}{DB}=\dfrac{CE+EB}{EB}[/tex]

Answer:

(AD/DB) +1 = (CE/EB) +1 -----> Addition Property of Equality

Answer:

[tex]m =-\frac{1}{2}[/tex]

Step-by-step explanation:

The equation of a line in the pending intersection form is:

[tex]y = mx + b[/tex]

Where m is the slope of the line and b is the intersection with the y axis.

In this case we have the following equation

[tex]y-3=-\frac{1}{2}(x-2)[/tex]

To find the slope of this line you must rewrite it in the form

[tex]y = mx + b[/tex]

Then we solve the equation for y.

[tex]y-3=-\frac{1}{2}(x-2)[/tex]

[tex]y=-\frac{1}{2}(x-2)+3[/tex]

[tex]y=-\frac{1}{2}x-2*(-\frac{1}{2})+3[/tex]

[tex]y=-\frac{1}{2}x+1+3[/tex]

[tex]y=-\frac{1}{2}x+4[/tex]

Note that [tex]m =-\frac{1}{2}[/tex]

Finally the slope is: [tex]m =-\frac{1}{2}[/tex]

The slope of the line with equation; y-3 = -1/2(x-2) is; slope, m = -1/2.

According to the question, the equation of the line in discuss is; y-3 = -1/2(x-2).

To determine the slope of the line, we need to rearrange the equation such that it resembles the slope-intercept form of the equation of a straight line as follows;

The equation of a straight line; y = mx + c.

Now, we expand the equation of the line and rearrange as follows;

By comparison, the slope of the line given bey the equation, y-3=-1/2(x-2) is; slope, m = -1/2.

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Answer:

She needs 11374 cm to buy

Step-by-step explanation:

* Lets explain how to solve the problem

- The dimensions of the first rectangle is 1809 cm and 2891 cm

- The dimensions of the first rectangle is 738 cm and 249 cm

- Elly wants to put a fence around both

- To find the length of the fence calculate the perimeters of the two

 rectangles

- The perimeter of the rectangle = 2(b + h), where b , h are the

 dimensions of the rectangle

# First rectangle

∵ The dimensions are 1809 cm and 2891 cm

∵ P = 2(b + h)

∴ P = 2(1809 + 2891) = 2(4700) = 9400 cm

# Second rectangle

∵ The dimensions are 738 cm and 249 cm

∵ P = 2(b + h)

∴ P = 2(738 + 249) = 2(987) = 1974 cm

∵ The length of the fence = the sum of the perimeters of the two

  rectangles

∴ The length of the fence = 9400 + 1974 = 11374 cm

* She needs 11374 cm to buy

Answer:

She needs to purchase 11374

The difference i the length of her and her brother's fence is 8442

Step-by-step explanation:

First you need to find the perimeter by adding the lengths and widths all together.

1809+2891+738+249=5687

But you need to times it by 2 because it says Elly has 2 gardens.

5687 x 2=11374.

If you are confused on the second question the answer is down below ( The person who ask this question did have to ask the second question but on my math test this question has 2 parts).

The question is Elly's brother also wants to put up a fence around his garden that is 1034 centimeters by 432 centimeters. What is the difference in the length of fence that each will purchase?

First you have to find the perimeter of Elly's brother garden.

1034+432+1034+432=2932

Last we have to find out what is the difference in the length of fence that each will purchase.

To do that you will have to subtract Elly's perimeter and Elly's brothers perimeter.

11374-2932=8442

So Elly difference in the length of the fence is 8,442.

Answer with explanation:

To find the common multiple of 45 and 95,we will find HCF of 45 and 95.

45=3 × 3× 5

95=5 × 19

⇒H CF(45,95)

=3 × 3×5×19

=855

→Common multiple of 45 and 95 =855

→There are infinite number of multiple of 855 which are 855, 1710, 2565,.....

You have not written between which two numbers.So, you should write multiple of 855 such that it is smaller than the greater number.

Answer:

Attached

Step-by-step explanation:

The conic section you can chose is a parabola

A parabola is a curve where any point on the curve is equidistant from the focus and from a directrix

When you have the vertex and focus points, you can write the equation of the parabola then graph it on a graph tool to visualize the curve.

Assume the vertex is at (3,1) and focus is at (3,5), then you notice here the x-coordinate for vertex and focus is the same , to mean one is top of the other.

This is a regular vertical parabola the x part is squared.

Vertex and focus are 4 units apart. This is by checking the difference in values of y-axis of vertex and focus.This is your p

The equation of the parabola will be

(x-h)²=4p(y-k)

but p=4

(x-3)²=4(4)(y-1)

(x-3)²=16(y-1)

x²-6x+9=16y-16

x²-6x-16y+25=0-----------------equation of the parabola

It is a right-side up parabola

Answer:

I only know question number one; the answer is

A parabola is a curve where any point on the curve is equidistant from the focus and from a directrix.

Step-by-step explanation:

Answer:

  15.542%

Step-by-step explanation:

For uneven cash flows such as those in this problem, there is no formula for "internal rate of return" (IRR). It must be computed graphically or iteratively. Spreadsheets and financial calculators are equipped to do this calculation. Attached is the result of the calculation done by a graphing calculator.

The sum of "present value" of each of the cash flows is zero when the discount rate is the IRR.

Answer:

  168 km

Step-by-step explanation:

Let x represent the distance Tyler drives at the slower speed, and let y represent the distance at the higher speed. Using time = distance/speed, we can write equations for the total travel time:

  x/42 +y/105 = 2.5

  x/28 +y/60 = 4.0 . . . . . 1.5 hours more than the usual 2.5 hours

Multiplying the first equation by 210, we have ...

  5x +2y = 525

Multiplying the second equation by 420, we get ...

  15x +7y = 1680

Subtracting 3 times the first of these equations from the second, we have ...

  (15x +7y) -3(5x +2y) = (1680) -3(525)

  y = 105

Putting this into the very first equation, we get ...

  x/42 + 105/105 = 2.5

  x/42 = 1.5 . . . . . . subtract 1

  x = 63 . . . . . . . . .multiply by 42.

The total distance to Tyler's parents' house is ...

  63 km + 105 km = 168 km

Tyler's total travel distance is approximately 168 km.

Calculating Total Distance Traveled

To determine the total distance Tyler traveled, let du be the distance through urban areas and dm be the distance on the motorway.

→ The total distance is:

[tex]D = d_u + d_m[/tex]

First, using the normal journey:

→ Urban Area:

Speed = 42 km/h

Time = [tex]t_u[/tex] / 42,

→ Motorway:

Speed = 105 km/h

Time = [tex]t_m[/tex] / 105,

→ Total time for normal journey:

→ [tex]t_u/42 + t_m/105 = 2.5\ hours[/tex]

We have:

→ [tex]d_u[/tex] = 42 * [tex]t_u[/tex]

→ [tex]d_m[/tex] = 105 * [tex]t_m[/tex]

When there is fog:

→ Urban Area:

Speed = 28 km/h

Time = [tex]t__uf}[/tex] / 28

→ Motorway:

Speed = 60 km/h

Time = [tex]t_{um[/tex] / 60

Total time for foggy journey:

→ [tex]t_{uf[/tex] /28 + [tex]t_{mf[/tex] /60

Given that he leaves 1 hour early and arrives 30 minutes late, the total journey time in foggy conditions is:

→ 2.5+1+0.5=4 hours

Thus,

→  [tex]t_{uf[/tex] /28 + [tex]t_{mf[/tex] /60 = 4

Solving the Equations

We now have two equations:

→ [tex]t_u/42 + t_m/105 = 2.5\ hours[/tex]

→ [tex]t_{uf}\ /\ 28\ + t_{mf} \ /\ 60 = 4 hours[/tex]

Let's solve these equations step-by-step.

First, let's multiply the first equation by 210 (the least common multiple of 42 and 105):

→ [tex]210(t_u/42 + t_m/105) = 210*2.5[/tex]

→ [tex]5t_u+2t_m=525[/tex] (eq. 1)

Next, let's multiply the second equation by 420 (the least common multiple of 28 and 60):

→ [tex]420( t_u/28+ t_m /60)=420*4[/tex]

→ [tex]15t_u +7t_m =1680[/tex] (eq. 2)

We now solve these two linear equations:

→ [tex]5t_u+2t_m=525[/tex]

→ [tex]15t_u +7t_m =1680[/tex]

First, let's solve Equation 1 for [tex]t_m[/tex] in terms of  [tex]t_u[/tex]:

→ [tex]d_m=(525-5d_u)/2[/tex]

Substitute this expression into Equation 2:

→ [tex]15t_u+7((525-5d_u)/2)=1680[/tex]

Multiply through by 2 to clear the fraction:

→ [tex]30t_u +7(525-5t_u )=3360[/tex]

→ [tex]30t_u +3675-35t_u =3360[/tex]

→ [tex]-5t_ u +3675=3360[/tex]

→ [tex]-5t_u=3360-3675[/tex]

→ [tex]-5t _u=-315[/tex]

→ [tex]t_u=63[/tex]

Now substitute [tex]t_u=63[/tex] back into Equation 1 to find [tex]t_m[/tex]:

→ [tex]5(63)+2t_m =525[/tex]

→ [tex]315+2t_m =525[/tex]

→ [tex]2t_m =210[/tex]

→ [tex]t_m=105[/tex]

Thus, the total distance Tyler travels is:

[tex]= t _u +t_m[/tex]

[tex]=63+105[/tex]

[tex]=168\ kilometers[/tex]

Answer: 0.25

Step-by-step explanation:

Given : The  future lifetime of Gary is uniformly distributed with interval [0 years , 60 years].

Then the probability density function for Gary's future lifetime will be:-

[tex]f(x)=\dfrac{1}{60-0}=\dfrac{1}{60}[/tex]

The future lifetime of Eric is uniformly distributed with interval [0 years , 40 years].

Then the probability density function for Erin's future lifetime will be:-

[tex]f(x)=\dfrac{1}{40-0}=\dfrac{1}{40}[/tex]

Now, the joint density function for Gary and Eric's future lifetime :-

[tex]f(x,y)=f(x)f(y)=\dfrac{1}{40\times60}=\dfrac{1}{2400}[/tex]  [∵Their future lifetimes are independent. ]

Now, the probability that Gary dies first is given by :-

[tex]\int^{60}_{0}\int^{40}_{x}f(x,y)\ dy\ dx\\\\=\int^{60}_{0}\int^{40}_{x}\dfrac{1}{2400}\ dy\ dx\\\\=\int^{60}_{0}\dfrac{40-x}{2400}\ dx\\\\=\dfrac{1}{2400}[40x-\dfrac{x^2}{2}]^{60}_{0}\\\\=\dfrac{1}{2400}(2400-\dfrac{3600}{2})=0.25[/tex]

Hence, the probability that Gary dies first =0.25

Answer:

D.

Step-by-step explanation:

You could find the 8 terms and then add them up.

Let's do that.

Luckily we have the common ratio which is -5.   Common ratio means it is telling us what we are multiplying over and over to get the next term.

The first term is -11.

The second term is -5(-11)=55.

The third term is -5(55)=-275.

The fourth term is -5(-275)=1375.

The fifth term is -5(1375)=-6875.

The sixth term is -5(-6875)=34375.

The seventh terms is -5(34375)=-171875.

The eighth term is -5(-171875)=859375.

We get add these now. (That is what sum means.)

-11+55+-275+1375+-6875+34375+-171875+859375

=716144 which is choice D.

Now there is also a formula.

If you have a geometric series, where each term of the series is in the form [tex]a_1 \cdot r^{n-1}[/tex], then you can use the following formula to compute it's sum (if it is finite):

[tex]a_1\cdot \frac{1-r^{n}}{1-r}}[/tex]

where [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio. n is the number of terms you are adding.

We have all of those. Let's plug them in:

[tex]a_1=-11[/tex], [tex]r=-5[/tex], and [tex]n=8[/tex]

[tex]-11 \cdot \frac{1-(-5)^{8}}{1-(-5)}[/tex]

[tex]-11\cdot \frac{1-(-5)^{8}}{6}[/tex]

[tex]-11 \cdot \frac{1-390625)}{6}[/tex]

[tex]-11 \cdot \frac{-390624}{6}[/tex]

[tex]-11 \cdot -65104[/tex]

[tex]716144[/tex]

Either way you go, you should get the same answer.

Final answer:

The sum of the 8-term geometric series with the given first term and common ratio is calculated using the geometric series sum formula, resulting in a sum of 716,144, Which is option D.

Explanation:

The sum of a geometric series is determined by the formula Sₙ = a(1 - rⁿ)/(1 - r), where Sₙ is the sum of the first N terms, a is the first term, r is the common ratio, and N is the number of terms. Since we have an 8-term geometric series with a first term of -11 and a common ratio of -5, we can calculate the last term (-11 x (-5)⁷) to ensure it is indeed 859,375, confirming the ratio and the number of terms.

The sum can then be calculated as follows: S₈ = -11 x (1 - (-5)⁸) / (1 - (-5)) = -11 x (1 - 390625) / (1 + 5) = -11 x (-390624) / 6 = -11 x -65104 = 716,144, which corresponds to option D.

Answer:

  Yes

Step-by-step explanation:

One way to tell is to look at the remainder from division by x-1, which is the value of f(1).

  1³ -1² +1 -1 = 0

so (x -1) is a factor of f(x).

  f(x) = (x -1)(x^2 +1) = h(x)(x^2 +1)

Final answer:

To maximize profit, the hotel management should determine the rate at which the difference in revenue gained from increasing the rate and the cost to service fewer rooms is maximized. By analyzing different rate increases and subtracting the cost of servicing fewer rooms, the management can identify the rate that will generate the highest profit. For example, by increasing the rate to $42 per room, the hotel could maximize profit at $1940.

Explanation:

To determine the price at which the hotel management should charge per room to maximize profit, the management needs to consider the relationship between the price, the number of rented rooms, and the cost to service each room.

First, let's establish the initial conditions:

60 rooms are rented at a rate of $40 per room.

Each rented room costs $8 per day to service.

Next, management determines that for each $2 increase in the nightly rate, five fewer rooms will be rented. To maximize profit, the management should find the rate at which the difference in revenue gained from increasing the rate and the cost to service fewer rooms is maximized.

Here is the step-by-step calculation:

Calculate the initial revenue: $40/room * 60 rooms = $2400

Calculate the initial cost: $8/room * 60 rooms = $480

Calculate the initial profit: $2400 - $480 = $1920

Calculate the new revenue: ($40 + $2)/room * (60 - 5) rooms = $2280

Calculate the new cost: $8/room * (60 - 5) rooms = $440

Calculate the new profit: $2280 - $440 = $1840

Repeat steps 4-6 for different rate increases until the profit is maximized.

Based on this analysis, the management should charge a rate that allows them to profit the most, such as $42/room, which would result in a profit of $1940.

Management should charge $44 per room to maximize profit.

To determine the optimal room rate to maximize profit, we'll utilize concepts from algebra and profit modeling. Let's define the variables:

The revenue, R, can be calculated as:

R = (40 + 2x)(60 - 5x)

The cost, C, of servicing the rooms can be calculated as:

C = 8(60 - 5x)

The profit, P, is given by:

P = R - C

Substituting the revenue and cost formulas:

P = (40 + 2x)(60 - 5x) - 8(60 - 5x)

Let's expand and simplify this equation:

P = (40 + 2x)(60 - 5x) - 8(60 - 5x)

[tex]P = 2400 - 200x + 120x - 10x^2 - 480 + 40x[/tex]

[tex]P = -10x^2 - 40x + 1920[/tex]

To find the value of x that maximizes the profit, we need to find the vertex of the quadratic function. The vertex form of a parabola given by [tex]ax^2 + bx + c[/tex] is at:

[tex]x = \frac{-b}{2a}[/tex]

Substituting a = -10 and b = -40:

[tex]x = -\frac{-40}{2 \times -10} = 40/20 = 2[/tex]

Thus, the management should increase the rate by 2 increments of $2, or $4. Therefore, the optimal room charge is:

$40 + $4 = $44

Answer:

  a.  F(x) = 1.2(2.5)^(x – 1)

Step-by-step explanation:

The sequence is geometric with first term 1.2 and common ratio 3/1.2 = 2.5. The explicit formula for such a sequence is ...

  a[n] = a[1]·r^(n-1)

For a[1] = 1.2 and r = 2.5, and using x as the term number, the formula is ...

  F(x) = 1.2·2.5^(x-1) . . . . . matches selection A

The formula that could be used for showing the sequence is option A.[tex]F(x) = 1.2(2.5)^{(x - 1)}[/tex]

The sequence should be geometric which means the first term 1.2 and the common ratio is [tex]3\div 1.2[/tex] = 2.5.

Now The explicit formula should be

[tex]a[n] = a[1].r^{(n-1)}[/tex]

Now

Here a[1] = 1.2

and r = 2.5,

So, the formula is

[tex]F(x) = 1.2\times 2.5^{(x-1)[/tex]

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Answer:

No, it is not a linear function. It is an exponential function.

Step-by-step explanation:

You have a secret that you tell to one person.

Every hour, each of the people that know the secret tells one person.

Let N be the people who know the secret.

Let t be the number of hours since you told the first person.

Now, when only you know the secret, means 1 person.

N(0) = 1

Next hour, there are now 2 people that know the secret.  

N(1) = 2

After the next hour, these 2 people will tell 2 more people, so people doubled to 4.

N(2) = 4

One hour later it will be N(3) = 8

We can see the pattern as following.

[tex]N(t)=2^{t}[/tex]

Therefore, the function is exponential not linear.

Answer:

$98.47

Step-by-step explanation:

1. 2(9.5) + 3 (7.95) + 49.95 = $92.80

6% • $92.80 = $5.57

$92.80 + $5.57 = $98.47

Answer:

Step-by-step explanation:

The problem statement tells you that x represents the horizontal distance in feet that the airplane is from the building. The domain is the set of useful values of x, which will be from 0 to 50 feet. Values of x less than 0 or more than 50 make no sense in this scenario.

[tex]6x[/tex]

............................................

Answer:

1, 2, 3, 6, 7, 14, 21, 42 [start from the outer ends, then come inner, placing negative symbols on either or]

Step-by-step explanation:

Just like what "dashabo123" said, you can hand each number a negative one at a time before moving to the next set of factors.

I am joyous to assist you anytime.

Answer:

1st problem:

Converges to 6

2nd problem:

Converges to 504

Step-by-step explanation:

You are comparing to [tex]\sum_{k=1}^{\infty} a_1(r)^{k-1}[/tex]

You want the ratio r to be between -1 and 1.

Both of these problem are so that means they both have a sum and the series converges to that sum.

The formula for computing a geometric series in our form is [tex]\frac{a_1}{1-r}[/tex] where [tex]a_1[/tex] is the first term.

The first term of your first series is 3 so your answer will be given by:

[tex]\frac{a_1}{1-r}=\frac{3}{1-\frac{1}{2}}=\frac{3}{\frac{1}{2}=6[/tex]

The second series has r=1/6 and a_1=420 giving me:

[tex]\frac{420}{1-\frac{1}{6}}=\frac{420}{\frac{5}{6}}=420(\frac{6}{5})=504[/tex].