Mathematics College

Find the sum of the first 10 terms for the sequence {21, 63, 189, . . . }.

5.2 × 1010

620,004

206,661

2730

Answers

Answer 1
The sum of n terms of a geometric sequence with first term "a" and common ratio "r" is given by
[tex]S_{n}=a\dfrac{r^{n}-1}{r-1}[/tex]
You have a=21, r=3, so the sum of 10 terms is
[tex]S_{10}=21\cdot \dfrac{3^{10}-1}{3-1}=620004[/tex]

The appropriate choice is the 2nd one:
   620,004
Answer 2

The sum of the first 10 terms for the sequence given is 620,004.

What is Geometric sequence?

A geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

Given is a geometric sequence, 21, 63, 189, . . . we need to find the sum of the first 10 terms,

Sum of n terms of GP = aₙ = arⁿ-1 / r-1,

a₁ = 21

r = 3

So,

a₁₀ = 21 × 3¹⁰-1 / 3-1

a₁₀ = 21 × 29,524

a₁₀ = 620,004

Hence the sum is 620,004.

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Related Questions

When two births are randomly selected, the sample space for genders is bb, bg, gb and gg. assume that those four outcomes are equally likely. does the mean of the sample proportions equal the population proportion of girls in two births?

Answers

The answer is No. The mean of the sample and that of the population can not be equal. As the sample moves closer to the population, the mean of sample moves closer to the mean of the population

PLEASE HELP ME WITH THIS MATH QUESTION

Answers

The general formula of an Arithmetic sequence is:

[tex] a_{n}= a_{1}+(n-1)*d [/tex]

Comparing this formula with the given formula, we can write:

Common Difference = d = 5

Since, every term of an Arithmetic sequence can be obtained by adding the common difference to the previous term, so we can write the recursive formula as: 

[tex] a_{n} = a_{n-1} +d[/tex]

For the given sequence we can write:

[tex] x_{n} = x_{n-1} +5[/tex]

So, the answer to this question is 5

Rectangle QRST is shown.

What would be a reason to claim that QRST is NOT a square?

SECOND PICTURE ARE THE FOLLOWING SOLUTIONS.

WILL MARK BRAINLIEST!!!

Answers

That would be QT ≠ QR because then QT and QR is not same which makes it impossible for QRST to be square. Square needs all side lengths to be equal.

(4+8r^5) - (4r^5 + 2)

Answers

(4+8r^5) - (4r^5 + 2)

= 4+8r^5 - 4r^5 - 2
=  4r^5 +2
= 2(2r^5 + 1)

The simplest form of the equation is 2(2r^5 + 1)

Can the figure below tessellate a plane? Explain your answer.

Answers

No. The only curve on the figure that can align with the inner radius is the inner radius itself. To tessellate a plane with a figure, all sides of the figure must align with a non-corresponding side.

Answer:

Step-by-step explanation:

A tessellation is created when a shape is repeated over and over again covering a plane without leaving any gaps or overlaps. Tessellation is also known as tiling. Triangles, squares and hexagon are perfect examples of figures that can create tessellation.

The figure below cannot, because there will be gaps.

I hope it helps, Regards.

hey can you please help me posted picture of question

Answers

The parent reciprocal function is represented in the table.

As you can see, increasing the value of x, decreases the value of y as both are inversely related as:

[tex]y= \frac{1}{x} [/tex]

We can also write this equation as:

yx = 1

This means, the product of each x and y value must be 1 for parent reciprocal function. If you observe the table, the product of each pair is 1.

So the correct answer is option A
The pairs of values of x and y above represent that of the equation, 

   y = 1/x.

If we are to substitute the given values of x to determine the values of y for checking, the results are as shown below.

1.   y = 1/-2 = -0.5
2.   y = 1/-1 = -1
3.   y = 1/2 = 0.5
4.   y = 1/3 = 0.33

Thus, the answer to this item is the first option, y = 1/x. 

Suppose angle A is complementary to angle B, and angle B is supplementary to angle C. If measure of angle A is 21 degree, find measure of angle C.

Answers

C = 111 degrees

Since A and B are complementary they add to 90. So we know that B must be 69 degrees. 

Since B and C are supplementary they add to 180. So we know that C must be 111. 
Final answer:

In solving this problem, we first identify that angle B is 69 degrees as it is complementary to 21-degree angle A (adding to 90 degrees). Then, we find angle C to be 111 degrees as it is supplementary to angle B (adding to 180 degrees).

Explanation:

In this problem, we are told that angle A (measuring 21 degrees) is complementary to angle B. Complementary angles are angles that add up to 90 degrees. So, we can find the measurement of angle B by subtracting the measurement of angle A from 90 degrees, which gives us 90 - 21 = 69 degrees for angle B.

Next, we are told angle B is supplementary to angle C. Supplementary angles are angles that add up to 180 degrees. So, we can find the measurement of angle C by subtracting the measurement of angle B from 180 degrees, which results in 180 - 69 = 111 degrees for angle C.

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Find the volume of the given prism round to the nearest 10th if necessary

Answers

we know that
volume of the prism=area of the base*height
height=24 yd

area of the base
is a equilateral triangle
so
the internal angles are 60 degrees
with the law of sine calculate the area
Area=(1/2)*a*b*sin C-----> (1/2)*13*13*sin 60-----> (1/2)*13*13*√3/2
Area=73.18 yd²

volume of the prism=73.18*24-----> 1756.30 yd³

the answer is
1756.3 yd³

Approximately how many boxes that are 2 ft. by 2 ft. by 3.5 ft. fit inside of the back of a tractor trailer box truck whose dimensions are 28 ft. by 8 ft. by 9 ft.?

26 Boxes

87 Boxes

144 Boxes

216 Boxes

Answers

144 is the correct answer

Approximately how many boxes that are 2 ft. by 2 ft. by 3.5 ft. fit inside of the back of a tractor trailer box truck whose dimensions are 28 ft. by 8 ft. by 9 ft.?

Solution:

Volume of trailer box= Number of boxes * Volume of Box

Volume of Trailer Box=Length*Width*Height

Dimensions of Trailer Box are 28 ft. by 8 ft. by 9 ft.

Volume of Trailer Box=28*8*9ft³=2016ft³

Dimensions of box are 2 ft. by 2 ft. by 3.5 ft.

Volume of Box=2*2*3.5ft³=14ft³

Volume of Trailer Box=Number of Boxes *Volume of Box

2016=Number of Boxes*14

To get, Number of Boxes, Let us divide by 14

2016/14=Number of Boxes=144

Number of Boxes=144

Answer: Option C:144 boxes

hey can you please help me posted picture of question

Answers

G(x) can be obtained from F(x) by shifting F(x) 4 units to the right and 1 unit upwards.

Shift towards right can be obtained by subtracting 4 from the x in the function and the upward shift can be obtained by adding 1 to the function.

So,

G(x) = F(x-4) + 1

Thus,

G(x) = (x-4)² + 1

So, the correct answer to this question is option B

What is the area of the trapezoid?


56 square inches

240 square inches

108 square inches

120 square inches

Answers

You'd add the bases then multiply by the height to get, 
120
Take care ^-^

Answer:

120

Step-by-step explanation:

Any figure that has line symmetry must also have rotational symmetry. true or false

Answers

A figure that has line symmetry MUST also have a rotational symmetry.

 Answer is TRUE.

Jay stores hay in cubic stacks on his farm. If the length of each stack is 2/3 yards, what is the volume of hay in each stack? 1/3 cubic yards, 4/9 cubic yards, 1/9 cubic yards, 8/27 cubic yards

Answers

[tex]\left( \dfrac{2}{3}\,yd\right)^{3}=\dfrac{8}{27}\,yd^{3}[/tex]

The 4th selection is appropriate.

Answer: The volume of hay in each stack is 8/27 yards

Step-by-step explanation:

Since, the volume of a cube = (side)³

Here, the side of the a cubic stack = [tex]\frac{2}{3}[/tex] yards,

Hence, the volume of a cubic stack,

[tex]V=(\frac{2}{3})^3[/tex]

[tex]=\frac{8}{27}[/tex] cube yard.

⇒ The volume of hay in each stack is 8/27 yards

Martha is making a scarf for her sister. Each day she knits 1/6 of a scarf....#1 what fraction of the scarf will be complete after 3 day...#2 What fraction will be complete after 6 days....#3 How can you use a number line to prove that your answers are correct?

Answers

You can use the number line to count up by 1/6s like day 1: 1/6 day 2:2/6 and so on. After three days 3/6s of the scarf will be done which is equivalent to 1/2 and on day 6: 6/6 of the scarf will be done which is equivalent to 1.
Hope I could help!
-Montana

A rectangular picture has dimensions 2 1/2 by 1 1/2. It is to be enlarged so that it is still similar to the original rectangle. If the longer dimension is now 10 , how much longer than the original is the perimeter now

Answers

The original perimeter is:
 p = 2 (w) +2 (l)
 First we look for the scale factor of the longest dimension, which is given by:
 k = (10) / (2 1/2)
 k = 4
 Then, the perimeter is given by:
 p '= 2 (4w) +2 (4l)
 Rewriting:
 p '= 4 (2 (w) +2 (l))
 p '= 4p
 Answer:
 the perimeter now is 4 times longer than the original

Ivanova has a healthcare plan with $25 co-pays to see doctors, $10 co-pays for prescription drugs, and an annual deductible of $1,500. In February she has a broken ankle which costs $2,300 in hospital treatment. As a follow-up in March she sees three doctors who bill $657, $134, and $232 and buys two prescriptions which cost $12 and $27. What is Ivanova's share of the costs for March?

Answers

1842 I think ,hope this helps :D

Ok, so let's start with the hospital bill. The total is $2,300, but she has a $1,500 deductible. So subtract $1,500 from $2,300. You should get $800. Now the doctor's visits. She has a $25 co-pay, and she saw three doctors. Multiply $25 by 3. You should have $75. Lastly, the prescriptions. She has a $10 co-pay, and there are 2 prescriptions, so multiply 2 and $10. You get $20. Now add the hospital bill, the doctor's bills, and the prescriptions.

$800+$75+$20=$895.

The number of acres of wetland infested by an invasive plant species after t Years is given by u(t)=12•2^t/3. Solve the equation u(t)=50. What does your answer tell you about the wetland?

Answers

For this case we have the following equation:
 u (t) = 12 • 2 ^ t / 3
 We equate the equation for u (t) = 50.
 We have then:
 12 • 2 ^ t / 3 = 50
 We clear the value of t:
 2 ^ t / 3 = 50/12
 log2 (2 ^ t / 3) = log2 (50/12)
 t / 3 = log2 (50/12)
 t = 3 * log2 (50/12)
 t = 6.2 years
 Answer:
 After 6.2 years 50 acres of wetland are infested by an invasive plant species

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What are the benefits and limitations to each method? When is it best to use each method?
1) graphing 2) substitution method 3) elimination method

Answers

With graphs on paper you can visually see intersecting lines(one solution), identical lines
(infinite solutions), or parallel lines(no solutions).
This method works best for lines that have integers for solutions. The task of determining rational or irrational solutions from graphs is difficult.

The substitution method usually must be used for equations with higher exponents. The deawback of this method is having to work with fractions.

The elimination method is often the method of choice.
This method however requires that you learn to recognize when the systems produce parallel lines or have equations that represent the same lines.

Answer:

don't copy exactly, this is my answer to the question.

Step-by-step explanation:

Find the shaded area of the basketball court to the nearest foot.

Answers

So the image consists of 1 rectangle and half a circle.

Rectangle - 12*19 = 228
Half a circle - [tex]\pi r^2 = \pi 6^2 = 36 \pi/2 = 18 \pi [/tex]

In the end there are 2 rectangles (2*228 = 456) and 1 full circle (18*2 = 36), which makes the shaded area 456 ft and 36[tex] \pi [/tex]
First, find the area of the rectangle, which is just 12•19=228 ft.

Then find the area of the semi-circle above it, which is pi times the radius squared. The diameter is 12ft, and we know the radius is half of the diameter, so the radius is 6ft. Our equation is pi times 6^2, or pi times 36.
We’ll just make pi 3.14, so 36•3.14=113.04 feet.

Add the area of the semi-circle and the rectangle together to get one of the shaded areas. 228+113.04= 341.04.

Now that we know the full area of one shaded region, we multiply it by two because there’s two of them. 341.04•2= 682.02.

Since we round it to the nearest foot, our final answer is that the shaded area of the basketball court is 682 square feet.

what is the next number in this pattern 0.54,0.6,0.66,0.72

Answers

This is a linear pattern. In this case, every next number goes up by 0.06.
So, add 0.06 to 0.72.
0.06+0.72=0.78.
So, your answer is 0.78.
Have a nice day! ♪

Andy is 2 years older than Jeff. In 5 years the sum of their ages will be 40.find their ages now? Explain your answer using algebra

Answers

Hello!

You can make two equations based on what you know

let x stand for andy's age
let y stand for Jeff's age

x = 2 + y
5 + x + 5 + y = 40

Put x into the second equation

5 + (2 + y) + 5 + y = 40

Combine like terms

12 + 2y = 40

Subtract 12 from both sides

2y = 28

Divide both sides by 2

y = 14

Put y into the first equation

x = 2 + (14)

x = 16

Andy is 16 and Jeff is 14

Hope this helps!

square root 2x -5 =11

Answers

Add five to 11 it’ll give you 16 then divide that by 2 it’ll give you 8 than plug it in x=8

Hey can you please help me posted picture of question

Answers

possible outcome

3 x 6 x 4 = 72

answer A. 72
3*6*4=72. Since we did this we have just found out how many possible combinations there are! That means your answer should be A.

Explanation:
There is 3 flavors
6 cookie add ins
4 flavors of syrup
We multiply these answers using multiplication and we get 72!

:D
Good Day! 

Answer:72


How do you determine if two probabilities are conditional to each other?
Please help

Answers

if they are conditional

Final answer:

You can determine if two probabilities are conditional by checking if the occurrence of one affects the probability of the other. If it does, the probability is conditional, represented by P(A|B), otherwise, the events are independent.

Explanation:

Determining Conditional Probabilities

To determine if two probabilities are conditional to each other, you consider if the occurrence of one event affects the probability of the other event happening. The conditional probability of event A given event B is denoted by P(A|B). This is calculated by dividing the probability of both events A and B occurring together (P(A AND B)) by the probability of event B:

P(A|B) = P(A AND B) / P(B)

This formula is applicable only when P(B) is greater than zero, meaning event B must have a chance of occurring. If the probability of A happening does NOT change whether B occurs or not, then A and B are independent events. Conversely, if the probability of A does depend on the occurrence of B, then A and B are dependent, and the probability P(A|B) is a conditional probability.

Independence is defined as the situation where the probability of A and B occurring together is the product of their individual probabilities (P(A) * P(B)). If this is true, P(A|B) would simply be P(A), as B's occurrence doesn't affect A's probability.

At a​ school, 129 students play at least one sport. This is 60​% of the students at the school. How many students are at the​ school?

Answers

(portion of school) = (1.00-portion) x (whole of group)
129 = (1.00-.60) x (whole school)
129 = .4 x (whole school)
129/.4 = Whole school
School size = about 323 students

the surface area of a polyhedron can be found by

Answers

It can be found by summing the areas of its faces

The surface area of a polyhedron is equal to the sum of the area of all of its faces. Said another way, the surface area is the total area covered by the net of a polyhedron.

Answer:

the surface area of a polyhedron can be found by sum of the area of all its sides.

Step-by-step explanation:

The surface area is nothing find the area of each faces and add them together.

Surface area = Sum of area of each faces.

Polyhedron is a three dimensional figure.

For instance, cube a polyhedron which has 6 square faces.

Surface area of a cube = [tex]a^{2} + a^2 + a^2 + a^2 + a^2 + a^2 = 6a^2[/tex], where "a" is the side of the square.

Therefore, the surface area of a polyhedron can be found by sum of the area of all its faces.

Find the slope and y-intercept fotv

Answers

Look at the picture.

[tex]A(3;\ 2)\\\\the\ slope:\ m=\dfrac{2}{3}\\\\B(0; 0):\ y-intercept[/tex]

The diameter of a circle is 18 cm. What is its area in terms of π.

Answers

The area of the circle would be 81π.

Answer:

Area, [tex]A=(81\pi )\ cm^2[/tex]

Step-by-step explanation:

Given that,

The diameter of the circle, d = 18 cm

The radius of a circle is half of its diameter, r = 9 cm

The formula to find the area of a circle is given by :

[tex]A=\pi r^2[/tex]

When r = 9 cm

[tex]A=\pi (9\ cm)^2[/tex]

[tex]A=(81\pi )\ cm^2[/tex]

So, the area of the circle is [tex](81\pi )\ cm^2[/tex]. Hence, this is the required solution.

Solve x^2 +14x = -24 by completing the square. Which is the solution set of the equation?

Answers

Start with x^2 +14x = -24,

Find HALF the value of 14:  7
Square this:  49
Add 49, and then subtract 49:        x^2 + 14x + 49 - 49 = -24  We have a
                                                                                             perfect square
Rewrite the quadratic as the sq. of a binomial:                    trinomial on
                                                                                              the left
                                                         (x+7)^2 = 25

Take the sqrt of both sides:  x+7 = plus or minus 5

Then x = -2 and x = -12

Answer:

{−12, −2}

Step-by-step explanation:

Jamal states that ax + b = a(x + c), given a, b, and c are not equal to 0.

What must be the value of c for Jamal’s statement to be true?

Answers

To answer the question, we must find c of the equation:
 ax + b = a (x + c)
 If we divide by "a" on both sides we have to:
 x + b / a = x + c
 For values of "a" other than zero.
 So:
 c = b / a.
 So that the affirmation of Jamal Be true c = b / a

Answer:

[tex]c=\frac{b}{a}[/tex]

Step-by-step explanation:

We have been given an equation [tex]ax+b=a(x+c)[/tex], given that a, b and c are not equal to 0.    

Let us solve for the value of c that will make Jamal's statement true.

Upon dividing both sides of our equation by a we will get,

[tex]\frac{ax+b}{a}=\frac{a(x+c)}{a}[/tex]

[tex]\frac{ax+b}{a}=x+c[/tex]

[tex]\frac{ax}{a}+\frac{b}{a}=x+c[/tex]

[tex]x+\frac{b}{a}=x+c[/tex]

Now, we will subtract x from both sides of our equation.

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

[tex]\frac{b}{a}=c[/tex]

Therefore, the value of [tex]c=\frac{b}{a}[/tex] will make Jamal’s statement true.

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The naturalist also comes to the conclusion that most mutations occurring today are harmful because he and the theist both assume that by now, the living thing is a collection of highly inter-related, well "crafted" systems. so most mutations occurring today would not contribute to the process of ___________. Which one of the following scenarios accurately describes a condition in which resonance can occur? A. A column of air has a height equal to 18 of the wavelength of the sound waves produced by a tuning fork vibrating over the column of air in an open pipe that's partially immersed in water. B. A person is holding a tuning fork on one end of a football field and another person is holding a separate tuning fork on the opposite end of the field. C. A pipe's length is equal to 12 of the wavelength of the sound waves produced by a tuning fork vibrating over one end of the pipe that's open to the air at both ends. D. A vibrating tuning fork is struck and begins to vibrate as the object used to strike it is placed away from the tuning fork. What is the value of x?a. 6b. 63c. 12d. 123 Name and describe the three Cs used in determining a persons willingness and ability to repay debts. How did philosophers spread knowledge to different parts of society? what is the atomic number z of 73li? Which is a function of nephrons? they release urine from the body. they filter perspiration from sweat glands. they release adh into the blood. they filter water and solutes from blood? The federalist party disappeared forever as a result of ________. a. jefferson's election in 1800 b. the war of 1812 c. alexander hamilton being killed by aaron burr d. the civil war e. the louisiana purchase According to sternberg's theory, the elements of successful intelligence are __________. emotional intelligence, interpersonal intelligence, and general intelligence emotional intelligence, creative intelligence, and interpersonal intelligence general intelligence, linguistic intelligence, and practical intelligence analytic intelligence, creative intelligence, and practical intelligence Had they ______ arrived when you got there? A: after B: before C: still D: already E: yet State five different ways in which SATourism promote tourism development and growth in south Africa as a destination of promotion of tourism in south Africa for questions 1 - 2, what are the excluded functions of the function? 1.) y= 4/9x-452.) y= 7/2x+48 What type of triangle has 3 sides that are the same length? What most determines the entropy of a solid? A. The mobility of electrons in the solid B. The crystalline structure of the solid C. The specific heat capacity of the solid D. The enthalpy of formation of the solid A person or group dissatisfied with the decision of the Florida Supreme Court A) could appeal the case to their U.S. District Court B) could appeal the case to the U.S. Supreme Court C) has no recourse because each state's supreme court is a court of last resort D) has no recourse because each state's supreme court is an appeals court This room has an oil stain on the floor. Tyler wants to rotate the rug so that it covers the stain. What kind of rotation should be performed on the kite-shaped rug? Be sure to specify the center of rotation and the direction (clockwise or counter-clockwise). Puedes vivir en filadelfia aunque no seas mononita o indegena de Paraguay. True or False What is the y-intercept of the quadratic y=-2x^2-4x-5 ?(-5,0)(0,-2)(-1,3)(0,-5) What is the best estimate of the mean price of all the sunglasses on the rack? Which of the following equations can be used to determine the change in enthalpy of a system?