Answer:
[tex]a_{n} = \frac{8}{2^{n-1} }[/tex]
Step-by-step explanation:
A geometric sequence has a constant ratio (r) and is defined by:
[tex]a_n=a_1r^{n-1}[/tex]
Since the first value is 8, [tex]a_{1}[/tex] = 8.
[tex]a_n=8r^{n-1}[/tex]
We can also see that a_n is double that of the next value in the sequence [tex](a_{n} = 2a_{n+1}})[/tex], hence r = 1/2
[tex]a_n=8\left(\frac{1}{2}\right)^{n-1}[/tex] or
[tex]a_{n} = \frac{8}{2^{n-1} }[/tex]
If it takes one man three days to dig a hole, how long does it take two men to dig half a hole?
Answer: This is wrong. It takes 4 men to dig a hole and you cannot dig half a hole.
Step-by-step explanation:
Answer:
u have to be kidding me 2 Men can not dig a hole it takes like 4 or 5 men
How much greater is 16x² + 7x + 5 than-18x² - 13x + 8?
Answer:
34x² + 20x - 3Step-by-step explanation:
Given
1st Polynomial : 16x² + 7x + 52nd Polynomial : -18x² - 13x + 8We need to subtract the 2nd polynomial from the 1st.
16x² + 7x + 5 - [-18x² - 13x + 8]16x² + 7x + 5 + 18x² + 13x - 834x² + 20x - 3Concerns about climate change and CO2 reduction have initiated the commercial production of blends of biodiesel and petrodiesel. Random samples of 38 blended fuels are tested in a lab to ascertain the bio/total carbon ratio. (a) If the true mean is .9350 with a standard deviation of 0.0090, within what interval will 90 percent of yhe sample means fall? Round your answers to 4 decimal places.
Answer:
10 men can complete work l in 120 doy . In how many days does 30 me can complete it.
-
PLEASE HURRY DUE TODAY
3. Leo designs a stand for the new statue on display at the local library. The stand is in the shape of a right trapezoidal prism. The base of the prism has an area of 4 ft^2 and the prism stands 2.4 feet high. As Leo paints the stand, he calculates the surface area of the stand to be 32 ft^2. (a) Leo is asked to purchase roping that will be used to close off the area around the statue. He purchases a length that is five times the perimeter of the stand in roping. How much roping does he purchase? (b) Leo plans to add gold leaf to the sides of the stand but not to the two bases. What percent of the area of the stand will have gold leaf? Round your answer to the nearest whole number
Answer A: 45 5/16
B: The present of the area as 83%
Step-by-step explanation:
(a)
35= 3+3+3.2x+3.2x+3.2x+3.2x
35= 6 + 12.8
29/12.8 +12.8x/12.8
X=2.265625 = 2/12/64
1x = 2 17/64 * 4 + 9 1/16
P = 45 5/16
(b)
The present of the area as 83%
35 – the bases or 6 = 29
29/35 + 0.82857142857
0.82857142857 * 100 = 82.8571428571
Rounded to the nearest whole number is 83%
If y=x+4 then what is (x-y)^3
Answer:
64
Step-by-step explanation:
y = x + 4
y - x = 4
4^3 = 64
The net of the figure shown is made of which set of
shapes?
O 3 triangles and 1 square
O 3 triangles and 1 rectangle that is not a square
О 4 triangles and 1 square
O4 triangles and 1 rectangle that is not a square
Step-by-step explanation:
It's not 3 triangles and 1 square because you need four triangles to make the siding and the square wont go anywhere because of how it's going to look.
It's not 3 triangles and 1 rectangle because still you need four to make the sides and a rectangle is too long.
4 triangles and 1 rectangle is still not correct because the rectangle on the bottom of the net is going to mess it up fir the whole shape.
So in conclusion, 4 triangles and 1 squares is the correct answer.
Determine the longest distance inside a rectangular prism with dimensions of 8 ft x 3 ft by 9 ft
Answer:
8*3*9 = 216 sq. ft³.Step-by-step explanation:
This is like volume!
Equation:
8 * 3 * 9Solve:
8 * 3 * 9= 24 * 9= 216Simplify:
8 * 3 * 9= (8 * 3) * 9= 24 * 9= 216.Answer is 216 sq. ft³.
Solving Trig. Equations
In each solution, n is an arbitrary integer.
1. Nothing fancy, just take the inverse tangent.
tan(x) = -5
x = arctan(-5) + nπ
x = -arctan(5) + nπ
2. Recall the identity cos(2x) = 2 cos²(x) - 1, then factorize:
cos(2x) - 3 cos(x) + 2 = 0
(2 cos²(x) - 1) - 3 cos(x) + 2 = 0
2 cos²(x) - 3 cos(x) + 1 = 0
(2 cos(x) - 1) (cos(x) - 1) = 0
2 cos(x) - 1 = 0 or cos(x) - 1 = 0
cos(x) = 1/2 or cos(x) = 1
[x = arccos(1/2) + 2nπ or x = -arccos(1/2) + 2nπ]
… or x = arccos(1) + 2nπ
x = π/3 + 2nπ or x = -π/3 + 2nπ or x = 2nπ
3. By definition, csc(x) = 1/sin(x) :
csc(2x) + √2 = 0
csc(2x) = -√2
1/sin(2x) = -√2
sin(2x) = -1/√2
2x = arcsin(-1/√2) + 2nπ or 2x = π - arcsin(-1/√2) + 2nπ
2x = -π/4 + 2nπ or 2x = 5π/4 + 2nπ
x = -π/8 + nπ or x = 5π/8 + nπ
4. More factorization:
2 sin²(x) - sin(x) = 0
sin(x) (2 sin(x) - 1) = 0
sin(x) = 0 or 2 sin(x) - 1 = 0
sin(x) = 0 or sin(x) = 1/2
x = arcsin(0) + 2nπ
… or [x = arcsin(1/2) + 2nπ or x = π - arcsin(1/2) + 2nπ]
x = 2nπ or x = π/6 + 2nπ or x = 5π/6 + 2nπ
5. Yet more factorization. Also recall that |cos(x)| ≤ 1 for all x.
4 cos²(x) - 8 cos(x) + 3 = 0
(2 cos(x) - 3) (2 cos(x) - 1) = 0
2 cos(x) - 3 = 0 or 2 cos(x) - 1 = 0
cos(x) = 3/2 or cos(x) = 1/2
The first case gives no solution since 3/2 > 1.
x = arccos(1/2) + 2nπ or x = -arccos(1/2) + 2nπ
x = π/3 + 2nπ or x = -π/3 + 2nπ
6. Recall the identity sin(a - b) = sin(a) cos(b) - cos(a) sin(b).
sin(2x) cos(x) - cos(2x) sin(x) = -√3/2
sin(2x - x) = -√3/2
sin(x) = -√3/2
x = arcsin(-√3/2) + 2nπ or x = π - arcsin(-√3/2) + 2nπ
x = -π/3 + 2nπ or x = 4π/3 + 2nπ
Question 3
1 pts
Use the diagram to answer the question. Find the measure of the
arc in degrees, type in a number only.
180° hope it's correct and really helps....!!!!
A men's department store sells 14 different suit jackets, 6 different shirts, 10 different ties, and
8 different pairs of pants. How many different suits consisting of a jacket, shirt, tie, and pants are
possible? *
Answer:
The total number of different suits consisting of a jacket, shirt, tie, and pants are possible is 576 ways and this can be determined by using the given data.
Given :
A men's department store sells 3 different suit jackets, 6 different shirts, 8 different ties, and 4 different pairs of pants.
The following steps can be used in order to determine the total number of different suits consisting of a jacket, shirt, tie, and pants are possible:
Step 1 - The arithmetic operations can be used in order to determine the total number of different suits consisting of a jacket, shirt, tie, and pants are possible.
Step 2 - According to the given data, the total number of shirts is 6, ties is 8, suit jackets is 3, and pants is 4.
Step 3 - So, the total number of different suits consisting of a jacket, shirt, tie, and pants are possible is:
= 576 ways
Step-by-step explanation:
Emily recently started a part time job. She is saving for a car, which she will need when she attends college next year. She plans to deposit $400 at the end of each month into an account that 3.6% per year, compounded monthly . How much will Emily have saved at the end of six months? pays
Answer:
$2418.07
Step-by-step explanation:
Problems involving the time-value of money are conveniently solved using a TVM app on a suitable calculator or spreadsheet. The result of doing that is shown in the attachment.
__
If you would like to compute the value of Emily's account by hand, the annuity formula is the one you want.
A = Pn((1 +r/n)^(nt) -1)/r . . . . where r is the annual interest rate, n is the number of times per year it is compounded (12), t is the number of years (1/2), and P is the periodic payment into the acccount (400).
Using the given values in the formula, we have ...
A = 400(12)((1 +0.036/12)^(12/2) -1)/0.036 = 4800×(1.003^6 -1)/0.036
A ≈ 2418.07
At the end of 6 months, Emily will have saved $2418.07.
Solve: (x + 4)2 – 4 = 16
O x= - 4+2V5
O
O x= – 4 + 20
O x= 4 + V20
O x= +4
Answer:
[tex] {x} = - 4 \pm \: 2\sqrt{5} [/tex]
Step-by-step explanation:
[tex] {(x + 4)}^{2} - 4 = 16 \\ \\ \implies \: {(x + 4)}^{2} = 16 + 4 \\ \\ \implies \: {(x + 4)}^{2} = 20 \\ \\ \implies \: {(x + 4)} = \pm \: \sqrt{20} \\ \\ \implies \: {x + 4} = \pm \: 2\sqrt{5} \\ \\ \implies \: {x} = - 4 \pm \: 2\sqrt{5} [/tex]
What is the inverse of f(x)=3-x/7
Answer:
I got f^-1 (x) = -7x + 21
Step-by-step explanation:
A grocery store sells a bag of 6 oranges for $3.24. How much does one orange cost
20. Which value of x makes the inequality
3x 27 true?
A. x=8
B. x =10
C. X=12
D. x 14
Hey there!
3x = 27
DIVIDE 3 to BOTH SIDES
3x/3 = 27/3
CANCEL: 3/3 because it give you 1
KEEP: 27/3 because it help solve for the x-value
NEW EQUATION: x = 27/3
SIMPLIFY IT!
x = 9
Good luck on assignment & enjoy your day!
~Amphitrite1040:)
can some one solve this for me
Answer:
x = 2
Step-by-step explanation:
24 - 7x = 10
Rearrange terms,
-7x + 24 = 10
Subtract 24 from both sides,
-7x + 24 - 24 = 10 - 24
-7x = 10 - 24
-7x = -14
Divide by sides by -7,
[tex]\frac{-7x}{-7}=\frac{-14}{-7}[/tex]
[tex]x=\frac{-14}{-7}[/tex]
x = 2
A sample of students is taken from the school's A honor roll. The school estimates that there are 360 students on the A honor roll. Using this sample how many students on the A honor roll are 8th graders. There are 14 8th graders on the A honor roll.
Answer:
Number of 7th grade = 360 - X
Step-by-step explanation:
As you can see this question is not complete and lacks the essential data. But we will try to create a mathematical expression to calculate the number of students on the A honor roll which are from &th grade. As we know: Total number of students on the A honor roll = 360 We are asked to calculate, number of students from 7th grade on the A honor roll. So, let's assume that "X" represents the all the students who are on the A honor roll except 7th grade. Mathematical Expression: Number of 7th Graders = Total number of students on the A honor roll - X Number of 7th Graders = 360 - X So, if you know the value of X, you can easily calculate the number of students which are from 7th grade on the A honor roll.
Answer:
There are 126 8th grade A honor roll students.
Step-by-step explanation:
Since there are 14 8th grade A honor roll students out of 40 A honor roll students. That means that the fraction is 14/40. After that we do 14/40x360 which results in 126.
What is the image point of (3,8)(3,8) after a translation right 4 units and up 1 unit?
Answer:
The point [tex](3,8)[/tex] will transform into [tex](7,9)[/tex]
Step-by-step explanation:
When you move the unit right, you make the number larger. right and left deal with the X value. you add 4 to 3, and you get 7. Now you move 1 point up, which is just 8+1, which is 9. You get your answer, [tex](7,9)[/tex].
Hope This Helps! :)
Graph the function. f(x)=3/5x-5
y=x^2-6x+7 write equation in vertex form
Answer:
y=(x−3)2−2
Step-by-step explanation:
The vertex form of a quadratic function isy=x^2-6x+7 , where x, y, are constants. of the parabola is at (x, y).
Determine the shaded area.
9 ft
(
The shaded area is
(Round to two decimal places as needed.)
Shaded area = area of square - area of a circle.
[tex] \\ \\ [/tex]
For this we have to find area of both square and circle which is visible in the picture.
[tex] \\ [/tex]
Part one :
In this part we'll find area of circle.
Given :
radius = 9ftTo find :
Area of circleSolution:
We know :
[tex] \boxed{ \rm Area \: of \: circle =\pi {r}^{2} }[/tex]
Steps :
[tex] \dashrightarrow\sf Area \: of \: circle =\pi {r}^{2}[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times {9}^{2} [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times 9 \times 9[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22}{7} \times 81[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{22\times 81}{7}[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Area \: of \: circle = \dfrac{1782}{7}[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\bf Area \: of \: circle =254.57 \: ft {}^{2} \\ [/tex]
[tex] \\ [/tex]
Part 2
As it's visible diameter of circle = side of square.
So we have to find diameter of circle.
We know :-
[tex] \boxed{ \rm Diameter \: of \: circle =2 \: radius}[/tex]
[tex] \\ [/tex]
Steps:-
[tex] \dashrightarrow\sf Diameter \: of \: circle =2 \: radius \\ [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Diameter \: of \: circle =2 \times 9\\ [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\bf Diameter \: of \: circle =18 \: ft[/tex]
We have :
side of square = 18 ftTo find:
Area of squareSolution:
We know :
[tex] \boxed{ \rm Area \: of \: square= {side}^{2} }[/tex]
Steps :
[tex] \dashrightarrow\sf Area \: of \: square= {side}^{2}[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Area \: of \: square= {18}^{2}[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\sf Area \: of \: square= {18} \times 18[/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\bf Area \: of \: square= 324 \: {ft}^{2} [/tex]
Part three:
Remember the first line of answer ? :)
So let's insert here:-
[tex] \boxed{ \text{Shaded area = area of square - area of a circle}}[/tex]
Steps :-
[tex] \dashrightarrow\textsf{Shaded area = area of square - area of a circle} \\ [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\textsf{Shaded area = 324 - 254.57} \\ [/tex]
[tex] \\ [/tex]
[tex] \dashrightarrow\textbf{Shaded area = 69.43 }\bf {ft}^{2} \\ [/tex]
Help please!!!!! Asap!!!
Answer:
Step-by-step explanation:
[tex]\sqrt{3}[/tex] =1.73205 In between 1 and 2 closer to 2
[tex]\sqrt{8}[/tex]=2.82842 In between 2 and 3 closer to 3
[tex]\sqrt{23}[/tex]=4.7958 In between 4 and 5 closer to 5
A laptop computer is purchased for $2600. Each year, its value is 80% of its value the year before. After how many years will the laptop computer be worth
$500 or less?
the will he worth less because 80% a year is a 10% so 2600-500=2100 so 2100÷10=210
Which of the following numbers must be added to complete the square in the equation below? x^2 +16x=5 27
O A. 64
O B. 25
O C. 16
O D. 8
Answer:
A) 64
Step-by-step explanation:
16/2=8
8^2= 64
x^2 +16x +64= 69
(x +8)^2= 69
solve for x ~
[tex]x {}^{2} - 36 = 0[/tex]
thankyou ~
Answer:
[tex]x {}^{2} - 36 = 0 \\ \\ x {}^{2} = 36 \\ \\ x = \sqrt{36} \\ \\ x = + 36 \: \: or \: \: - 36[/tex]
hope helpful -,-
M log_5(8) rewrite to log _?(?)
Answer:
[tex]\log_5 8^{M}[/tex]
Step-by-step explanation:
[tex]\text{We know that,}~ b\log_a c = \log_a c^b[/tex]
Find the circumcenter of the triangle with vertices at A(2,4),
B(8, 4), and C(6, 10).
Please help me with this math problem
Answer:
P1:40% P2:47500 P3:10%
Step-by-step explanation:
2/5 = 0.4 =40%
5/8= .625
.625 x 76000 =
47500
Help please I have a d in this class
Answer:
2. Elana's Family. Elana's Family.
3. 8 minutes 4 seconds
4. Elena's family will have driven 2.76 miles while Andre's family will have driven which is farther.
Step-by-step explanation:
Five members of a mystery-book club each read a 1,296-page book. Nine members of a fantasy-book club each read a 398-page book. How many more pages did the mystery-book club read than the fantasy-book club? Select all the correct equations or set of equations that could be used to solve the problem.
Answer:
2898
Step-by-step explanation:
number of people * number of pages in each book they read =total
mystery bookclub:
5 * 1,296 = 6480
fantasy bookclub:
9 * 398 = 3582
mystery - fantasy = difference in books between the two groups
6480 - 3582 = 2898
possible equation:
(1296 x 5) - (398 x 9) = x
x = answer
Answer:
Step-by-step explanation:
hey i got a couple (10) calculus questions in my profile and im pretty desperate right now
can u pls help