Use the given information to determine if the geometric series converges or
diverges. If it converges, find the sum.
ai = 0.75; r = 5
a) The series converges to 3.75.
b) The series converges to 0.15.
c) The series diverges. There is no sum.
d) The series converges to 20.

Answer:

1 hour and 50 minutes

Step-by-step explanation:

Time Connie takes to clean the house: 210 minutes

Time takes for both of them at the same time: 100 minutes.
210 - 100 = 110 minutes

Therefore, Alvaro takes one hour and 50 minutes to clean the house by himself.

Answer:Alvaro can clean the house alone in approximately 3.89 hours.

Step-by-step explanation:

If Connie can clean her house in 3.5 hours, then her rate of work is 1/3.5 of the house per hour. Together, Connie and Alvaro can clean the house in 1 hour and 40 minutes, or 1.67 hours.

To find how long it would take Alvaro to clean the house alone, we can use the formula:

combined rate of work = sum of individual rates of work

So, (1/3.5 + 1/a) * 5/3 = 1, where "a" is the time it takes Alvaro to clean the house alone.

Simplifying the equation, we get 1/a = 9/35, which means that Alvaro can clean the house alone in approximately 3.89 hours (or 3 hours and 53 minutes).

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{ 6(x+y)+y-(x+3)} \end{gathered}$}\)

Put the parentheses using: - (a + b)(= -a -b).

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{-\left(x+3\right)=-x-3 } \end{gathered}$}\)

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{=6\left(x+y\right)+y-x-3 } \end{gathered}$}\)

Expand 6(x+y): 6x+6y.

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{=6x+6y+y-x-3 } \end{gathered}$}\)

Add like elements 6y+y=7y

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{=6x+7y-x-3 } \end{gathered}$}\)

Group Like Terms

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{=6x-x+7y-3 } \end{gathered}$}\)

Add like elements 6x-x=5x.

\(\large\displaystyle\text{$\begin{gathered}\sf \bf{\red{=5x+7y-3 \ \ \Rightarrow \ \ \ Answers }} \end{gathered}$}\)

Answer:

R35625

Step-by-step explanation:

(R30,000×.125×18/12)+R30000

=R35625

The top five percent of the distribution's lowest weight as calculated from the given data  for a bag is 246.

Average population = 240

Standard deviation for the population; 3

Z-score can be calculated as ,

z = (x' - μ)/σ

Now, in order to determine which of the top 5 values in the distribution has the least weight, we will use the significance threshold of 1 - 0.05/2 = 0.025.

Z-score is 1.96 at significance level 0.025.

Thus;

1.96 = (x' - 240)/3

3 × 1.96 = x' - 240

x' = 240 + 5.88

x' = 245.88

Getting close to a whole number results ,

x' = 246

The two z-score tables are as follows:

Positive Z Score Table: The observed value is greater than the average of all values.

An observed value that is below the mean of all values is shown by a negative Z score table.

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Answer:

Linear

Step-by-step explanation:

If its linear it fits into the y=mx+b, and this on does so its linear

Answer: 28 yards

You just have to multiple the 7 by the 4. :)

Answer:

They run at the same speed

Step-by-step explanation:

First, you have to find a way seeing how fast both animals run in the same amount of time. You can find out how fast they both run in one second.

60 feet in 6 seconds is how many feet in one second? Well, you can do 60/6 (60 divided by 6) and you will see that in one second, the cheetah can run 10 feet

100 feet in 10 seconds is how many feet in one second? Same thing, you can do 100/10 (100 divided by 10) and you will see that the gazelle can run 10 feet in one second.

Finally, you compare the two answers from the two animals. For the cheetah, we learned that it can run 10 feet in one second, and for the gazelle, we learned that it can run 10 feet in one second. So, we know that they run at the same speed.

Thank you! Please let me know if this was helpful!

Answer:

Cheeta's speed = 10 feet per second

Gazelle's speed = 10 feet per second

Hence, They run at the same speed.

Step-by-step explanation:

Determining the Cheeta's speed:

Covered distance = 60 feet

Time taken = 6 seconds

Speed = Covered distance / Time taken

           = 60 / 6

           = 10 feet per second

Therefore, Cheeta's speed is 10 feet per second.

Determining the Gazelle's speed:

Covered distance = 100 feet

Time taken = 10 seconds

Speed = Covered distance / Time taken

           = 100 / 10

           = 10 feet per second

Therefore, Gazelle's speed is 10 feet per second.

Conclusion:

Cheeta's speed = 10 feet per second

Gazelle's speed = 10 feet per second

Hence, They run at the same speed.

Step-by-step explanation:

31 + 6x + x + 16 = 180

7x + 47 = 180

7x = 180 - 47

x = 133/7

x = 19

Answer:

11x-6+(19x+6)=180°

11x+19x-6+6=180°

30x=180

x=180/30

x=6

it means that

19x+6=19*6+6=114+6=120°

The value of x is -3 and y is 7 for equilateral triangle having x+1, 2x+4 and 3x+y sides.

We can use the fact that an equilateral triangle has equal lengths on each of its three sides to determine the values of x and y.

Given:

First side=x+y

second side= 2x+4

third side=3x+y

An equilateral triangle has three equal sides, hence the following equations can be constructed:

x + 1 = 2x + 4

2x + 4 = 3x + y

Let's tackle each of these equations separately:

x + 1 = 2x + 4

We will subtract x from both sides and subtract 4 from both sides in order to solve this equation:

x + 1 - x = 2x + 4 - x

1 = x + 4

By taking 4 away from both sides, we arrive at:

1 - 4 = x + 4 - 4 , -3 = x

Therefore, x has been determined to be -3.

Now, substitute the value of x in the second equation:

2x + 4 = 3x + y

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

-6 + 4 = -9 + y

-2 = -9 + y

y = -2 + 9

y = 7

So, we determined that y has a value of 7.

As a result, the values of x and y are, respectively, x=-3 and y=7

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Answer:

Step-by-step explanation:

In an equilateral triangle all sides are equal.

So each of these sides (and their equations are equal to each other.)

To find x - set the first two (as they only involve x) equal to each other and solve.

x + 1 = 2x + 4

x -x + 1 = 2x - x + 4

1 = x + 4

1- 4 = x + 4 - 4

-3 = x

Then substitute -3 for x in the last equation to find y, also setting it equal to one of the other equations.

3(x) + y = x + 1

3(-3) + y = -3 + 1

-9 + y = -2

-9 + 9 + y = -2 + 9

y = 7

so x = -3 and y equal 7

The angle measure explained in the solution.

Given that, a || b, we need to find the missing angles,

∠1 = 42° [vertically opposite angles]

∠3 = 62° [vertically opposite angles]

∠2 = 180°-(∠1+62°) [angle in a straight line]

∠2 = 76°

∠4 = ∠2 [vertically opposite angle]

∠4 = 76°

∠4 = ∠9 = 76° [alternate angles]

∠9 = ∠12 = 76° [vertically opposite angle]

∠3 = ∠ 6 = 62° [alternate angles]

∠ 6 = ∠7 = 62° [vertically opposite angle]

∠3 + ∠5 = 180° [consecutive angles]

∠5 = 118°

∠5 = ∠8 = 118° [vertically opposite angle]

∠4 + ∠10 = 180° [consecutive angles]

∠10 = 104°

∠10 = ∠11 [vertically opposite angle]

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Answer:

78

Step-by-step explanation:

You need to do inverse operations

13 x 6 = 78

D = 78

78 divided by 6 = 13

:)

The shape represented by the net, which consists of five plane surfaces is a triangular prism. The correct option ii therefore;

A net is obtained by unfolding a three dimensional shape. Three dimensional shapes can be made by folding a net after drawing the model.

The shape in the figure consists of five faces, which includes;

The figure is in the shape of a triangular prism

A prism is a solid consisting of plane surfaces on its sides. The faces of the prism (top and bottom faces), which are identical, defines the name of the prism.

A triangular prism is a prism that has a top and bottom face that are both shaped as identical triangles. The top and bottom faces of the triangular prism are joined together by rectangular side faces that have a width, equivalent to the side length of the triangle.

The shape of a triangular prism is in the shape of a tent, with the entrances shaped as a triangle.

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Answer:

Step-by-step explanation:

it would be "c" because the question asks for the number that makes the inequality true

4x≤ x+3

the graph in c is saying that every number that is 1 or less than 1 makes the inequality true. so lets take -7 as an example

4 x -7=-28

-28+3=-25

-25 is greater than -28 so the inequality is true. the reason why graph d doesnt work is because if we plug in 2 into the equation, then 4x =8 and x+3=5

5 is not greater than 8 so it doesnt work

Step-by-step explanation:

Given equation is:-

Dividing both sides by 4, we get

By doing simply, we get

Hence, the value of c will be ¾.

Answer: 8.20 miles I believe

Answer:

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation:

Answer:

y = 1/2x

Step-by-step explanation:

Slope: 1/2

y = 1/2x

Answer:

Step-by-step explanation:

-3≤ x = graph 6

-3 > x = graph 3

x≥ 3 = graph 2

x ≤ 3 = graph 4

3 > x = graph 1

x > 3 = graph 5

the closed circles means greater/less than or equal to

the open circle means greater/less than

the direction of the arrow tells you if the number is greater than x or less than x

Answer:

15

Step-by-step explanation:

180-15

Hello!

the sum of the angles in the triangle = 180°

so the 3rd angle = 180° - 165° = 15°

In order to find when the ball will be 18 ft above the moon's surface, we need to equal the expression to 18

then, solve the associated quadratic expression

answer:

after 0.40 seconds the ball will be 18 ft above the surface

Answer: 66%

Step-by-step explanation: To convert a fraction to a percentage, divide the top number by the bottom number. For example, \(\frac{1}{4}\) is 25% because if divide them, (1÷4=0.25) then we get 25%. So, for this problem, we solve 2÷3, which equals 0.66, or 66%.

hope this helps!

please give brainliest!

Answer: 15x^2+6xy

Step-by-step explanation: 3x(6y−4y+5x)

(3x)(6y+−4y+5x)

(3x)(6y)+(3x)(−4y)+(3x)(5x)

18xy−12xy+15x^2

15x^2+6xy

\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies SA=4\pi (4)^2\implies SA\approx 201.1~in^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3}\implies V\approx 268.1~in^3\)

Answer:

Below

Step-by-step explanation:

The equation to use for CONTINUOUS compounding is :

FV = PV e^(it)

18532.08 = 8327 * e^( i*10)        where i is the interest in decimal form

18532.08/8327  = e^(10i)

2.225541 = e^(10i)             now take natural log  (ln) of both sides to get

.8000 = 10i

i = .08     or 8% interest

Answer:

the answer is 15% but there's none of the above

hope this helps