Mathematics High School

What is the sum of the geometric series: 
3
∑5(-2/3)^i
i=0

Answers

Answer 1
We use the law of the sum of the 3 first terms of the geometric sequence:
[tex]\sum_{i=0}^35\left(\dfrac{-2}{3}\right)^i=5\dfrac{1-\left(\dfrac{-2}{3}\right)^4}{1-\left(\dfrac{-2}{3}\right)}\\=5\dfrac{\left(\dfrac{3^4-2^4}{3^4}\right)}{\left(\dfrac{5}{3}\right)}\\=3\left(\dfrac{65}{81}\right)=\dfrac{65}{27}[/tex]

Related Questions

A quarter circle is attached to the side of a square as shown.

What is the best approximation for the area of this figure?

Use 3.14 to approximate pi.


28.6 m²

41.1 m²

66.24 m²

116.5 m²



Answers

The area of the square is s×s
 = 4×4 = 16 m²
The area of a quarter circle is (πr²)/4
    = 3.14 × 16/4
    = 3.14 ×4
    = 12.56 m²
Therefore, the total area is;
     = 16 +12.56
     = 28.56 m²
     ≈ 28.6 m²
-TalibShaheed
The area of the square is YxY
 = 4×4 = 16 m²
The area of a quarter circle is (πr²)/4
    = 3.14 × 16/4
    = 3.14 ×4
    = 12.56 m²
That means, the total area is:
     = 28.56 m²
Or it will be about:
     ≈ 28.6 m²
Hope it helped!
-Gabrielle



Daria walked 1 2/5 miles this morning and 2 3/10 miles this afternoon. How many miles did Daria walk in all?

Answers

the answer is 3 7/10 miles 

In all, means add up
1 2/5 + 2 3/10
rewrite into improper fractions
7/5 + 23/10
To add, you must have the same denominator
in this case, multiply the first fraction by 2 to get the denominator to 10
7*2/5*2
14/10

now solve
14/10 + 23/10
37/10

Now you can rewrite this to a mixed number
3  7/10

She walked 3  7/10 miles total of the day.

Hope this helps

A regular pyramid has a _____ base and a vertex over the center of the base.

Answers

A regular pyramid has a regular polygon base and vertex over the center of the base.

Regular Polygon~~~~ APEX

Part A) Julio makes a scale drawing of the kitchen floor to determine how many square feet of flooring he needs to buy . The scale of his drawing is 1 inch:4 feet. (The length is 4 1/2 and the width is 3 3/8)

What is the actual are of Julio's kitchen floor?

Part B) Julio makes a scale drawing of part of the kitchen wall to design a tile pattern. He will use gray tiles and white tiles to form the pattern shown. The length of each square in the drawing represents 1/2 foot on the actual kitchen wall. (There are 14 gray tiles and 10 white tiles)

If Julio uses 2-inch by 2-inch tiles, how many tiles of each color will he need?

Answers

part A) 
we know that
scale ---------->  inch/4 feet=0.25 in/ft

[scale]=[scale drawing]/[actual]
[actual]=[scale drawing]/[scale]

for length --------> 4 1/2 in ---------> 4.5 in  (scale drawing)
[actual]=[4.5]/[0.25]=18 ft

for width ---------> 3 3/8 in ---> (3*8+3)/8 ---> 27/8 in  (scale drawing)
[actual]=[27/8]/[0.25]=13.5 ft

the answer part A is
length actual kitchen floor is 18 ft
width actual kitchen floor is 13.5 ft

Part B)  
the area of one square in the actual=(1/2)*(1/2)=0.25 ft²
total area gray tiles=0.25*14=3.5 ft²
total area white tiles=0.25*10=2.5 ft²

find how many tiles 2 in by 2 in of each color will he need
1ft²-------------> 144 in²
gray tiles
3.5 ft²---------------> 3.5*144=504 in²
[tiles 2 in by 2 in gray]=504/(2*2)=126 gray tiles 

white tiles
2.5 ft²---------------> 2.5*144=360 in²
[tiles 2 in by 2 in white]=360/(2*2)=90 white tiles 

the answer Part B) is
126 gray tiles
90 white tiles 



Answer:

Sample response: Julio divided 6 whole parts into groups of 2 instead of dividing them into groups of  

1

2

which would make the quotient 12, not 3.

Step-by-step explanation:

If two polygons are similar then the corresponding sides are equal and the corresponding angles are proportional. True or False?

Answers

We can say that two polygons are similar if they have the same shape as the other but they are jut different in size. Even when the other polygon is flipped over or rotated, the shape still remains similar. Two polygons are considered similar only if their corresponding sides are proportional and their angles must be congruent. 

If the question is phrased like that however, your answer would be false because the sides are not equal, they are proportional. The angles are not proportional, they should be congruent or equal.

The percent of the discount in the problem above is 15%. What percent of the original bill is Chumani's bill? How could you solve the problem using this percent?

Answers

15%= 0.15

That’s all I know about this problem but was there something else? Like the actual total of Chumani’s bill?

Chumani's bill represents 85% of the original bill after a 15% discount is applied. The discounted amount can be found by multiplying the original bill by 0.85.

If the discount on an item is 15%, and Chumani is paying after this discount has been applied, we want to find out what percent of the original bill Chumani's bill is. To do this, we subtract the discount rate from 100%. So, 100% - 15% = 85%. Thus, Chumani's bill is 85% of the original bill.

To calculate the discounted bill, you multiply the original bill amount by 0.85 (which represents 85%). If the original bill was, for example, $100, the calculation would be $100 x 0.85 = $85. So, Chumani would pay $85, which is 85% of the original bill amount.

Which expression is equivalent to (b^n)^m

Answers

C
When the exponents are set up like that you multiply them. 

Answer:

C. [tex]b^{n\cdot m}[/tex]

Step-by-step explanation:

We have been given an expression [tex](b^n)^m[/tex]. We are asked to find the equivalent expression to our given expression.

Using exponent property [tex](a^b)^c=a^{b\cdot c}[/tex], we can write our given expression as:

[tex](b^n)^m=b^{n\cdot m}[/tex]

Therefore, option C is the correct choice.

a fair cube is used in a game . the face of the cube are labeled 1 through 6 . what is the probability of a player rolling a number grater than 4 ?

Answers

There are six equally possible outcomes to get: 1, 2, 3, 4, 5, 6. The probability to roll a number greater than 4 is equal to the probability to get 5 or 6, two of the six possible outcomes. Thus the probability is 2/6=1/3.

Can someone please explain this to me? I keep getting -infinity as the answer.

Answers

There is an indeterminate form: infinity/infinity. To solve it, you can use the infinite comparison method. First, you have to identify which has the highest degree term: whether the numerator or the denominator. In this case, it is the numerator, which has the negative term of degree 4: -7x ^ 4. Then, the result is -∞.

 Therefore, the answer is the last option: Does not exist.

Which term can be combined in the expression below? check all that apply. 5/6a - 2b - 16.3 + b/12 + c - 0.9b

Answers

the answers are options 2, 4, and 6.

Answer:

Option 2nd , 4th and 6th correct

[tex]-2b[/tex], [tex]\frac{b}{12}[/tex] and [tex]-0.9b[/tex]

Step-by-step explanation:

Like terms are those terms which have same variable to the same power.

Given the expression:

[tex]\frac{5}{6}a-2b-16.3+\frac{b}{12}+c-0.9b[/tex]

Combine like terms;

[tex]\frac{5}{6}a+b(-2+\frac{1}{12}-0.9}-16.3+c[/tex]

Simplify:

[tex]\frac{5}{6}a-2.81666667b-16.3+c[/tex]

Therefore, the  term can be combined in the given expression is,

[tex]-2b[/tex], [tex]\frac{b}{12}[/tex] and [tex]-0.9b[/tex]

HELPHELPHELPHELPHELPHELPHELPHELPHELPHELPHELPHELPHELPHELPHELP

Answers

Your answer would be 37.5%

Carson’s estimate for the cost of tiling his bathroom floor is $25 plus $5 per square foot. He says that he can model the cost with a linear function. Is Carson correct? Why or why not?

Answers

Carson is correct.
 Let's write the variables first.
 Let:
 x = number of square feet of the bathroom floor.
 y = total cost in $.
 The function that best suits the problem is:
 y = 5x + 25
 Answer:
 Carson is correct.
 y = 5x + 25

solve proportion 12/p = 36/45

Answers

12 x 45 / 36 is 15. p=15

Sara has 20 sweets.
12 liquorice, 5 mint, 3 humbug.
Sara is going to take at random two sweets.
work out the probability that the two sweets will not be the same type. Give your answer as a fraction

Answers

Answer:

111/190

Step-by-step explanation:i know you dont want to see explanation so yeah...

Probabilities are used to determine the chances of an event.

The probability that the two selected sweet will not be of the same type is [tex]\frac{111}{190}[/tex]

The given parameters are:

[tex]n = 20[/tex] --- number of sweet

[tex]L = 12[/tex]

[tex]M = 5[/tex]

[tex]H = 3[/tex]

First, we calculate the probability that the two selected sweet will be of the same type.

This is calculated as:

[tex]P(Same) =P(L\ and\ L) + P(M\ and\ M) + P(H\ and\ H)[/tex]

Because the selection is without replacement, the equation becomes

[tex]P(Same) = \frac{12 \times 11}{20 \times 19} +\frac{5 \times 4}{20 \times 19} + \frac{3 \times 2}{20 \times 19}[/tex]

[tex]P(Same) = \frac{132}{380} +\frac{20}{380} + \frac{6}{380}[/tex]

Add fractions

[tex]P(Same) = \frac{132+20+6}{380}[/tex]

[tex]P(Same) = \frac{158}{380}[/tex]

Using the complement rule, the probability that the two selected sweet will not be of the same type is:

[tex]P(Not\ same) = 1 - P(Same)[/tex]

This gives

[tex]P(Not\ same) = 1 - \frac{158}{380}[/tex]

Take LCM

[tex]P(Not\ same) = \frac{380 - 158}{380}[/tex]

[tex]P(Not\ same) = \frac{222}{380}[/tex]

Simplify

[tex]P(Not\ same) = \frac{111}{190}[/tex]

Hence, the required probability is: [tex]\frac{111}{190}[/tex]

Read more about probabilities at:

https://brainly.com/question/11234923

There is an old riddle about a frog at the bottom of a 20-foot well. if he climbs up 3 feet each day and slips back 2 feet each night, how many days will it take him to reach the 20-foot mark and climb out of the well?

Answers

For this case what we are going to do is write step by step the equation of the line
 f (x) = mx + b
 We have:
 20-foot well:
 f (x) = mx + 20
 if he climbs up 3 feet each day and slips back 2 feet each night:
 f (x) = - 3x + 2x + 20
 f (x) = - x + 20
 When it reaches 20 feet we have f (x) = 0:
 f (x) = - x + 20
 0 = -x + 20
 x = 20 days.
 Answer: 
 It will take him 20 days to reach the 20-foot mark and climb out of the well

In a plane, if a line is perpendicular to one of two blank lines, then it is also perpendicular to the other

Answers

check the picture below.

if the black lines are parallel, and the red one is perpendicular to one of them, well, you know the rest.

Which equation is equivalent to

Answers

It is the last equation. You square both sides. 
the last equation is correct

helppppppppppppppppppppp

Answers

What you should keep in mind in this case is:
 1) Trigonometric functions.
 2) rewrite the expression
 3) Cancel similar terms.
 Note: See attached image.
 Answer:
 Cot(x)
 option 2

The angle of depression from the top of a flag stick to a golf ball on the ground is 24 degrees. If the flagstick is 6 feet tall, how far away is the golf ball from the base of the flag stick?

A. 13.5 ft
B. 12.3 ft
C. 9.8 ft
D. 14.6 ft
E. 15.1 ft

Answers

check the picture below.

make sure your calculator is in Degree mode.

Answer:

The Golf ball from the base of the flag stick is 13.5 ft

A is correct.

Step-by-step explanation:

Please see the attachment for figure.

Let AB is height of flag stick. AB=6 ft

BC is distance of golf ball from base of the flag stick.

In ΔABC, ∠B=90°

[tex]\dfrac{AB}{BC}=\tan 24^\circ[/tex]

[tex]\dfrac{6}{BC}=0.4452[/tex]

[tex]BC=13.5[/tex] ft

Hence, The Golf ball from the base of the flag stick is 13.5 ft

ALGEBRAIC PROOF PLEASE HELP IT IS MY LAST QUESTION I AM STUMPED
Use the following problem to answer the question below:

Given: 3(x – 4) = 33
Prove: x = 15

3(x – 4) = 33 Given

3x – 12 = 33 A

3x – 12 + 12 = 33 + 12 B

3x + 0 = 45 C

3x = 45 D

x = 15 Division Property of Equality

What is the reason for D?

Answers

3x +0 can be replaced by 3x because of "the additive identity property of real numbers: anything plus zero is that thing."

what is the solution to the proportion 3/m=12/15

Answers

b 3.75 it is simple it is easy 
the answer 3.75 i think 

COULD U PLEASE PLEASE HELP ME !!!!!!!!!!!
BRAINLIEST AVAILABLE

Answers

The first one is correct

2/5 of the children in a club are girls,if there are 24 boys,how many children are there altogether?how many more boys than girls are there

Answers

2/5 are girls, therefore 3/5 are boys

3/5 = 24
1/5 = 24 ÷ 3 = 8
2/5 = 8 x 2 = 16

Altogether = 16 + 24 = 40 

24  - 1 6 = 8

There are 40 children altogether
There are 8 more boys than girls.


8 More Boys

2/5 = 16/40
24 = 3/5

24 - 16 = 8

Therefore, There Are 8 More Boys Than Girls.

How many possible outcomes would there be if three coins were each tossed once?

Answers

the answer is 6 because there is only 2sides to a coin and there are three coins so you would times 3by 2

The price of a share of stock started theday at $37. During the day it went down $3, up $1, down $7, and up $4.What was the price of a share at the end of the day?

Answers

$32  because 37-4+1-7+4=32
it went up $5 total but went down $10 so you take the base number and subtract 5 from it
(because 10-5=5)
so the answer is $32

A chord divides a circle into two segments true or false?

Answers

True so happy to help have a nice day 

True, it has its start and finish

Select the correct product.

(2x + 9)(x + 1)

2x2 + 11x + 9
3x2 + 11x + 9
2x2 - 7x + 9
2x2 + 11x + 10

Answers

We can simplify this by multiplying all the terms together.

2x * x + 2x * 1 + 9 * x + 9 * 1
= 2x^2 + 2x + 9x + 9
= 2x^2 + 11x + 9

Hope this helped!

The sum of three consecutive numbers is greater than 40. The inequality that represents this is x + x + 1 + x + 2 > 40. Which values of x hold true for the inequality?

choices are 8,10,12,13,9,15,7

Answers

3x ＞ 37
x ＞ 12.333
Thus, 13 and 15 satisfy

Answer:

15

Step-by-step explanation:

which term describes the red curve of the figure below?

Answers

A. Hyperbola
Hyperbola is where there are two curves (one up, one down)

Answer:

A) Hyperbola.

Step-by-step explanation:

Given : Figure .

To find : Which term describes the red curve of the figure below.

Solution : We can see from the given figure two red curve  up and down .

Hyperbola : A hyperbola is two curves that are like infinite bows.

Therefore, A) Hyperbola.

Choose the right answer. If the distance on a map from point R to point T measures 3.0 inches and the scale is 1 inch = 0.5 miles, what is the distance in miles from point R to point T? ______ miles
A. 6.0
B. 3.0
C. 1.5

Answers

The answer is c because when you multiply 3.0 by 0.5 I️t gives you 1.5

Answer: The distance from point R to point T is 1.5 miles.

Step-by-step explanation:

In the map, the scale is,

1 inches = 0.5 miles,

3 inches = 3 × 0.5 = 1.5 miles,

Thus, in the map 3 inches shows 1.5 miles,

Since, in the map, the distance from point R to point P = 3 inches,

Thus, the actual distance from point R to point P = 1.5 miles.

⇒ Option C is correct.

Other Questions
Kim rode her bicycle 135 miles in 9 weeks riding the same distance each week. Eric rode his bicycle 102 miles in 6 weeks, riding the same distance each week. Which statement correctly compares the number of miles per week they rode? A.) Eric rode 2 more miles per week than Kim rode B.)Kim rode 3 more miles per week than Erick rode C.) Kim rode 11 more miles per week than Erick rode D.) Eric rode 17 more miles per week than Kim rode Write 4.4 as a reduced mixed number A restaurant owner spends 892 for 65 pounds of produce. Which equation could you use to find the price per pound The geological processes that shape earths features today i need help asap please Which description best describes the effect of Queen Victorias reign on the middle class in Great Britain?The growth of the empire continued to increase their confidence.They felt squeezed between the wealthy and the rising working class.They heard silence in return for their demand for suffrage and other basic rights.They felt disenfranchised and fought for reform. He wants to know why she peers over her glasses at him like that. Based on the context, to peer is to do which of the following? Talks Walks Look Fear Which role did the United Nations have, according to its charter? A. to determine the consequences for Germany and Japan at the end of World War II B. to ratify the Treaty of Versailles C. to formalize the plan to prevent the dropping of the atomic bomb on Japan in August 1945 D. to maintain international peace Write a short paragraph to answer the following question. How are these four types of transformation similar to each other? How do they differ? In particular, what is one major difference between dilations and the other three types of transformations? How many molecules of SO2 are in 2.45 g of SO2? (molar mass=64.06 g/mol). (Hint: you need to use your entire stoichiometry flow chart!)0.0382 molecules9.45 x10^25 molecules2.30 x 10^22 molecules6.35 x 10^-26 molecules A person is eligible to have their name on the peace officer memorial, if the person was killed in the line of duty and was _______. miss Roberts simplified this ratio 2:6 explain how you know she is incorrect can you tell where she might have made a mistake Which statements are correct steps in finding the linear equation of a line that passes through the points (1, 7) and (2, 4) using the point-slope form method? Select all that apply. Why did allied leaders reject many of president wilson's ideas at the paris peace conference? describe dwarf planets and their orbits in the solar system Describe a real-world situation that the graph could represent You are dropped off by helicopter at a site on the land. you are told that it is a plate boundary. almost immediately, you feel an earthquake. you look around and note the absence of volcanoes, but you notice an offset stream channel, and find a vertical fault with two kinds of rock on either side of it. what sort of plate boundary are you most likely on? Social cognitive theory is closely aligned with which major theoretical perspective? Then I'd throw big Asia in one giant Load & wash out the blood & Agent Orange, Dump the whole mess of Russia and China in the wringer, squeeze out the tattletail Gray of U.S. Central American police state. . . . How do the allusions in this excerpt reinforce the meaning of the poem? A. The allusions clarify specific geographic orientation. B. The allusions emphasize historical achievements. C. The allusions recall troublesome international issues. D. The allusions recount specific battles from recent wars. by creating optical sensations with the repetition of line and shape and the manipulation of high-contrast values and complementary colors, _________ truly is in the eye of the beholder. Let f(x)=4x^2+5.The g(x) is f(x) translated up 4 units.What is the equation of g(x)