Find the sum of the first 6 terms of the following sequence. Round to the nearest
hundredth if necessary.
324,
54,
9….
Answers
Answer:
388.79 (nearest hundredth)
Step-by-step explanation:
Given sequence: 324, 54, 9, ...
Therefore:
[tex]a_1=324[/tex]
[tex]r=\textsf{common ratio}=\dfrac{54}{324}=\dfrac16[/tex]
Sum of a finite geometric series:
[tex]S_n=\dfrac{a_1-a_1r^n}{1-r}[/tex]
Sum of the first 6 terms → n= 6:
[tex]\begin{aligned}S_6 & =\dfrac{324-324(\frac16)^6}{1-\frac16}\\ & =\dfrac{324-\frac{1}{144}}{1-\frac16}\\ & =\dfrac{9331}{24}\\ & = 388.79\:\textsf{(nearest hundredth)}\end{aligned}[/tex]
So
[tex]\\ \rm\Rrightarrow S_n=\dfrac{a-ar^n}{1-r}[/tex]
[tex]\\ \rm\Rrightarrow S_6=\dfrac{324-324(1/6)^6}{1-1/6}[/tex]
[tex]\\ \rm\Rrightarrow S_6=\dfrac{324-\dfrac{1}{12^2}}{\dfrac{5}{6}}[/tex]
[tex]\\ \rm\Rrightarrow S_6=\dfrac{9331}{24}=388.79[/tex]
Related Questions
what is the solution to the exponential equation 8x = 1/4
Answers
Divide each term in
8x=1/4 by 8 and simplify.
Exact Form: x=1/32
Decimal Form: x=0.03125
[tex]~~~8^x = \dfrac 14\\\\\implies 2^{3x} = 2^{-2}\\\\\implies 3x = -2 \\\\\implies x = -\dfrac 23[/tex]
please help im so confused (need asap)
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \tt \dashrightarrow \:10 {x}^{2} - 25x + 15 = 0[/tex]
[tex]\qquad \tt \dashrightarrow \:5(2x {}^{2} - 5x + 3) = 0[/tex]
[tex]\qquad \tt \dashrightarrow \:2x {}^{2} - 5x + 3 = 0[/tex]
[tex]\qquad \tt \dashrightarrow \:2x {}^{2} - 3x - 2x + 3 = 0[/tex]
[tex]\qquad \tt \dashrightarrow \:x(2x - 3) - 1(2x - 3) = 0[/tex]
[tex]\qquad \tt \dashrightarrow \:(x - 1)(2x - 3) = 0[/tex]
Therefore, the required factors are ~ (x - 1) and (2x - 3)
So, correct choice is B
Select the correct answer from each drop-down menu.
When a figure is translated, its orlentation
and the measures of its angles
Answers
Answer:
Not sure wha the options are, but is it "When a figure is translated, its orientation changes and the measure of its angles stays the same"
there isnt the word bank because you did not take a photo with the dropdown menu
The ellipse with the equation 9x2 + 16y2 = 144 ________.
a. is in Position II
b. has no symmetry
c. is in Position I
d. has no foci
Please help me figure out how to determine this!!
Answers
The ellipse with the equation stated above is:
Position I (Option C )
An ellipse is a circle that has been extended in one direction such that it is no longer a circle but an oval.
Solution
In order to determine the position of the ellipse with the above equation, we can start by simplifying the equation.
Hence, 9x² + 16y = 144 becomes
x²/16 + y²/9 = 1 (We arrive at this by dividing both sides of the equation by 144);
The x-axis is the major axis because the biggest denominator is under the x² term.
Thus the coordinates of the vertices are as follows:
(± a, 0); (0, ± b)
Hence:
a² = 16 → a = 4
b² = 4 → b = 2
Hence the coordinates are:
(± 4, 0); (0, ± 2)
Given the above, the eccentricity is given as:
e = √(1 - (3/4)^2 = (√7)/4 = 0.6614378
Hence the ellipse is: 0.66
Learn more about Ellipse at:
https://brainly.com/question/2284093
Solve this equation. Enter your answer in the box.
-24 + 12d= 2(d-3)+22
Answers
[tex]-24 + 12d= 2(d-3)+22\\\\\implies -24 +12d = 2d-6 +22\\\\\implies 12d-2d-24+6-22 = 0\\\\\implies 10d -40=0 \\\\\implies d = \dfrac{40}{10} = 4\\\\[/tex]
Answer:
[tex]\boxed{\sf{d=4}}[/tex]Step-by-step explanation:
In order to solve this equation, you must isolate it on one side of the equation.
Use the distributive property.
Distributive property:
⇒ A(B+C)=AB+AC⇒ -24+12d=2(d-3)+22
Multiply.
⇒ 2(d-3)+22
⇒ 2d-2*3
⇒ 2*3=6
⇒ 2d-6
Rewrite the problem down.
⇒ 2d-6+22
⇒ -6+22=16
⇒ 2d+16
⇒ -24+12d=2d+16
Then, you add by 24 from both sides.
⇒ -24+12d+24=2d+16+24
Solve.
⇒ 12d=2d+40
Subtract by 2d from both sides.
⇒ 12d-2d=2d+40-2d
Solve.
⇒ 12d-2d=10d
⇒ 10d=40
Divide by 10 from both sides.
⇒ 10d/10=40/10
Solve.
Divide the numbers from left to right.
⇒ 40/10=4
[tex]\Longrightarrow:\boxed{\sf{d=4}}[/tex]
Therefore, the correct answer is d=4.I hope this helps! Let me know if you have any questions.
Express cos S as a fraction in simplest terms.
Answers
Answer:
cos S = 7/25
Step-by-step explanation:
cosine is the ratio of the side adjacent to angle S and the hypotenuse.
use the pythagorean Theorem to or a Pythagorean triple to find the third side of the triangle It is a 7-24-25 triple or
b²=c²-a²
b=√c²-a²
b=√625-196
b=√49=7
cos S = 7/25
At approximately what time on the next day does the depth first reach 4 meters? 3:00 am 4:00 am 5:00 pm 10:00 am
Answers
Answer:
the answer is B, 4:00 am
Step-by-step explanation:
Answer:
At approximately what time on the next day does the depth first reach 4 meters?
3:00 am
4:00 am
5:00 pm
10:00 am
The correct answer is B. 4:00 am
In need of help, please help before tomorrow
Answers
Answer:
D
Step-by-step explanation:
A rubber bouncy ball is dropped from a height
of 177.00 cm onto a hard flat floor. After each
bounce, the ball returns to a height that is 19%
less than the previous maximum height. What
is the maximum height reached after the 9th
bounce?
Answers
Answer:
0.0000571
Step-by-step explanation:
Height after 9th bounce = Initial height * (19/100)^9
= 177*(0.19)^9
= 0.00005711572
Consider the following regular octagon below
Answers
Answer:
The answer is given in the picture
PLEASE MARK ME BRAINLIEST IF MY ANSWER IS CORRECT PLEASE
The formula for interior angle of any polygon is (n-2) x 180 / n where n is the number of sides.
An octagon has 8 sides:
Part A.
interior angle = (8-2) x 180 /8
Interior angle = 135 degrees
Part B.
3x -57 = 135
Add 57 to both sides:
3x = 192
Divide both sides by 3:
X = 64
Half of the product of two consecutive numbers is 105. which equation can be used to solve for n, the smaller of the two numbers? n2 n – 210 = 0 n2 n – 105 = 0 2n2 2n 210 = 0 2n2 2n 105 = 0
Answers
The equation that can be used to solve for n, the smaller of the two numbers would be n² + n - 210 = 0.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
If we use n to be the smaller number of two integer numbers, then the next consecutive number is n + 1.
The product of those two numbers would become n × (n + 1) = n (n + 1).
Half of that product is n (n + 1) / 2.
And the question states that the equation is equal to 105, so the equation becomes,
n (n + 1) / 2 = 105
Now we have to simplify that equation until we get an expression equal to one of the choices,
Multiply both sides by 2
n (n + 1) = 210
n² + n = 210
Subtract 210 from both sides
n² + n - 210 = 0
Thus, the equation formed is the quadratic equation.
Learn more about quadratic equations;
brainly.com/question/13197897
Answer:
n² + n - 210 = 0 is your answer! hope it helps!
Step-by-step explanation:
Real world problem for quadratic using square root property?
please help
Answers
Answer:
Example:
Sri Rangaman's flower garden is now a square. If she enlarges it by increasing the width 1 meter and the length 3 meters, the area will be 19 square meters more than the present area. What is the length of a side now?
Another Example how to solve it:
1. Solve the quadraticsa) (2x + 5)2 = 10b) x2 - 2x + 1 = 52. Given the formula HF = -16t2 + HI. How long does it take a ball to fall from a roof to the ground 25 feet below1. Solve the quadraticsa) (2x + 5)2 = 10b) x2 - 2x + 1 = 52. Given the formula HF = -16t2 + HI. How long does it take a ball to fall from a roof to the ground 25 feet below
How to use the square root function in word problems?Examples: 1. The floor of a square room is covered with square-foot floor tiles. If 81 tiles cover the floor, how long is each side of the room?2. Mr. Dase found a square digital image of a famous painting on a Web site. The image contained 490,000 pixels. How many pixels high is the image?
par
-
129
2 A stew recipe calls for 3.75 pounds of meat. Jack wants to make 5 batches of stew.
How many pounds of meat does he need? Show your work.
Answers
Answer:
18.75 pounds
Step-by-step explanation:
3.75 pounds per 5 batches
batch 1 : 3.75 7.5
add them + + 7.5
batch 2: 3.75 = 15
= +3.75
7.5 = 18.75
hope this helped
batch 3: 3.75
add them +
batch 4 3.75
= 7.5
batch 5 3.75
Someone solve number 8 pleaseeeee
Answers
Answer:
2 cats
Step-by-step explanation:
12% of 24 = 2.88
Answer:
2 cats were adopted.
Step-by-step explanation:
When finding a percentage of something, heres a trick. Just take the number you taking the perccentage of, and mutiply it by the percentage. In this case, 24*12.
24*12 = 288.
Now take that new number and divide it by 100. Now you have your answer. In this case,
288/100 = 2.88.
Becuase these are cats, we can't have or adopt half of one XD. You can't adopt half of a cat, so we round it down to 2. Meaning, 2 cats were adopted.
Write a rule for the nth term of the geometric sequence for which a1=11 and a4=88
Answers
Answer:
[tex]a_{n}[/tex] = 11 [tex](2)^{n-1}[/tex]
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
given a₁ = 11 and a₄ = 88 , then
11 r³ = 88 ( divide both sides by 8 )
r³ = 8 ( take cube root of both sides )
r = [tex]\sqrt[3]{8}[/tex] = 2 , then the nth term is
[tex]a_{n}[/tex] = 11 [tex](2)^{n-1}[/tex]
Hakeem buys a two-gallon bottle of juice for $25.60. What is the unit rate of the cost
of the juice per fluid ounce?
1 gallon = 4 quarts
1 quart = 2 pints
1 pint = 2 cups
1 cup=8 fluid ounces
-
Before you try that problem, answer the question below.
How many fluid ounces of juice did Hakeem buy?
try
Answers
Answer:
256 fluid ounces
Step-by-step explanation:
2 gallons = 8 quarts
8 quarts = 18 pints
18 pints = 32 cups
32 cups = 256 fluid ounces
1 gallon = 4 quarts x 2 that's 2 gallons = 8 quarts
1 quarts = 2 pints x 8 that's 8 quarts = 16 pints
1 pints = 2 cups x 16 that's 16 pints = 32 cups
1 cup = 8 fluid ounces x 32 that's 32 cups = 256 fluid ounces
The community center organizers want to buy 600 hot dogs. What will the cost be if they purchased the packages with the best buy? The best buy is 50 for 12 dollars
Answers
Answer:
144
Step-by-step explanation:
do 5 into 600 and u get 12 have a good day!!!
Answer:
$144
Step-by-step explanation:
first, we need to divide 600 by 50, to get them organized for the best packages. 600/50 = 12.
then, we multiply that (the 12) by the cost ($12/ea) so 12*12 which is $144 if they use the bundling.
I NEED THIS ASAP
five doctors are selected at random from a hospital employing 27 doctors to fill out a question
*WILL GIVE BRAINLIEST
Answers
Answer:
See below
Step-by-step explanation:
There are 27 C 5 ways to choose 5 doctors from 27
= 27 ! /(22! 5!) = 80730 ways to choose 5
This is a COMBINATION.
Answer: Combination
Step-by-step explanation: It has no order of selection. It is random and can't be paired like permutation.
Compare with another response
What is the vertex of g(x) = 3x2 − 12x 7? (−6, −5) (−2, −5) (2, −5) (6, −5)
Answers
The vertex of g(x) = [tex]\rm 3x^2 - 12x + 7[/tex] is (2, -5), the correct option is C.
What is the vertex of the parabola?The vertex of a parabola is the highest or lowest point, also known as the maximum or minimum of a parabola.
The standard equation of the vertex of the parabola is;
[tex]\rm a(x - h)^2 + k[/tex]
Where h and k are the coordinates of the vertex of the parabola.
The given expression is;
[tex]\rm =3x^2 - 12x + 7\\\\= 3(x^2 - 4x) + 7\\\\ = 3[ (x - 2)^2 - 4)] + 7\\\\= 3(x - 2)^2 - 12 + 7\\\\= 3(x - 2)^2 - 5[/tex]
On comparing with the standard form of vertex of the parabola
h = 2 and k = -5
Hence, the vertex of g(x) = [tex]\rm 3x^2 - 12x + 7[/tex] is (2, -5).
To know more about parabola click the link given below.
https://brainly.com/question/20333425
Please help
I need the lateral surface area
Answers
Answer:
[tex]la = 588 \: \: {cm}^{2} [/tex]
Step-by-step explanation:
Lateral area for trapezoidal prism:
- Is the sum of all the areas excluding the base area.
la - Lateral area
[tex]a = 20\\ b = 10 \\ c = 10 \\ d = 9 \\ l = 12[/tex]
[tex]la = al + \: bl + \: cl + \: dl[/tex]
[tex]la = l(a + \: b + \: c + \: d)[/tex]
[tex]la = 12(20 + 10 + 10 + 9)[/tex]
[tex]la = 588 \: \: {cm}^{2} [/tex]
can you answer it pls and by the way i am in 5th grade
Answers
Step-by-step explanation:
3×3 = 9, so it's greater than 3
3×4/3 = 4, so it's greater than 3
3×5/5 = 3, so it's equal to 3
3x4/9 = 4/3, so it's less than 3
3x5/6 = 5/2, so it's less than 3
help please im in class rn
Answers
Answer:
https://brainly.com/question/27407610
Step-by-step explanation:
What is the determinant of the coefficient matrix of the system?
Answers
Answer:
0Step-by-step explanation:
the explanation is in the picture
Tyler swam for 230 minutes during his first week of vacation. In his two weeks of vacation, he swam for a total of 539 minutes. How many more minutes did he swim for in the second week than in the first week?
Answers
Answer:
79 minutes.
Step-by-step explanation:
Look below me for a further explanation he/she is correct.
Answer:
79 minutes.
Step-by-step explanation:
539 - 230 is 309. Tyler swam 309 inutes the 2nd week and 230 minutes the first week.309 - 230 is 79 minutes. Tyler swam 79 minutes more in the 2nd week than in the first week.
find the height of the equilateral triangle
Answers
Answer:
height of the equilateral triangle is 5cm
by the use of Pythagoras
Step-by-step explanation:
H^2 = A^2 + O^2devide the base of the triangle i.e 3 as A and 6 as HO is Same as height hby substitution6^2 = 3^2 + O^236 = 9 + O^2O^2 = 36-9O = √27O or h = 5.197 The scouts are collecting canned food to donate to the food bank. Their goal is to
collect 550 cans of food. By the end of the first hour, they had collected 13 bags with
16 cans of food in each bag. By the end of the second hour, they had collected 12
more bags with 15 cans of food in each bag. How many more cans of food do they
need to collect to meet their goal of 550? Show all your work.
The scouts need to collect
more cans of food to meet their goal of 550.
Answers
Answer:
162 Cans more to reach goal of 550 cans.
Step-by-step explanation:
See attached image for the calculations
HELPPPP HEL-P MEE ME
Answers
Answer:
208
Step-by-step explanation:
the formula is:
2*(width*lenght+height*lenght+height*width)
2*(6*8+4*8+4*6)
208
Answer:
208 m²[tex] \: [/tex]
Step-by-step explanation:
In the given figure, it is given a net of cuboid where, the length is 8m, the breadth is 6m and the height is 4m and we have to find the surface area of the cuboid.
So, the formula for finding the surface area is ;
[tex]\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: Surface\: area_{(cuboid)}=2(lb + bh + lh )}}}}}} \: \: \bigstar \\ \\[/tex]
Now, we'll substitute the values in the formula :
[tex]\\{ \longrightarrow \qquad{ {{ \sf{ { \: Surface\: area_{(cuboid)}=2(8.6 + 6.4 + 8.4 }}}}}}) \: \: \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ {{ \sf{ { \: Surface\: area_{(cuboid)}=2(48 + 24 + 32 }}}}}}) \: \: \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ {{ \sf{ { \: Surface\: area_{(cuboid)}=2(104 }}}}}}) \: \: \\ \\[/tex]
[tex]{ \longrightarrow \qquad{ { \pmb{ \frak{ { \: Surface\: area_{(cuboid)}=208 }}}}}}\: \: \\ \\[/tex]
Therefore,
The surface area of the cuboid is 208m²Can someone help me with this problem
Answers
d(4.4)
hope it really helps ...!!!
.............................................
Answers
Answer:
90 degrees
Step-by-step explanation:
it is a right angle
A trail mix contains raisin, peanut, and chocolate.
The ratio of raisin to peanut is 2:3 and the ratio
of peanut to chocolate is 5:8. What is the ratio
of raisin to chocolate?
Answers
2: 13.333 or 2: 13
multiply the 8 by 5/3 to combine the terms