Answer:
The answer is C
Sn=3(1-1/2^n)
Step-by-step explanation:
The expression which defines [tex]S_{n}[/tex] is option c which is [tex]S_{n} =3(1-1/2){n}[/tex].
What is geometric progression?A geometric progression is basically a sequence in which all the terms have a common ratio. It is also known as G.P.
How to find sum of G.P.?We have been given a sequence as 3/2+3/4+3/8+3/16+.....
If we carefully see the sequence then we will find that this sequence is a Geometric progression because there is a common ratio between all the terms that is 1/2.
Ratio of first and second term=3/4/3/2=1/2
We know that Sum of GP when n<1 is [tex]a(1-r^{n} )/1-r[/tex]
we have to just put the value of =3/2 and r=1/2 in the above formula.
[tex]S_{n}[/tex]=3/2(1-[tex]1/2^{n}[/tex])/1-1/2
=3/2(1-[tex]1/2^{n}[/tex])/1/2
=3*2/2(1-[tex]1/2^{n}[/tex])
=3(1-[tex]1/2^{n}[/tex])
Hence the expression which denotes [tex]S_{n}[/tex] is 3(1-[tex]1/2^{n}[/tex]).
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Can anyone help me ASAP please
You pick a card at random, put it back, and then pick another card at random. 3 4 5 6 What is the probability of picking a 5 and then picking a 3?
Answer:
1/16
Explanation:
You have a 1/4 chance both times but in probability you multiply when in a sequence of events. 1/4*1/4= 1/16
g if we want to calculate a confidence interval of the difference of two proportions what is the standard error (do not pool for this answer)
Answer:
The standard error is [tex]s = \sqrt{\frac{\pi_1(1-\pi_1)}{n_1}+\frac{\pi_2(1-\pi_2)}{n_2}}[/tex], in which [tex]p_1,p_2[/tex] are the proportions and [tex]n_1,n_2[/tex] are the sample sizes.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The standard error is:
[tex]s = \sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
For the difference of proportions:
For proportion 1, the standard error is:
[tex]s_1 = \sqrt{\frac{\pi_1(1-\pi_1)}{n_1}}[/tex]
For proportion 2, the standard error is:
[tex]s_2 = \sqrt{\frac{\pi_2(1-\pi_2)}{n_2}}[/tex]
For the difference:
The standard error is the square root of the sum of the squares of each separate standard error. So
[tex]s = \sqrt{(\sqrt{\frac{\pi_1(1-\pi_1)}{n_1}})+(\sqrt{\frac{\pi_2(1-\pi_2)}{n_2}})^2} = \sqrt{\frac{\pi_1(1-\pi_1)}{n_1}+\frac{\pi_2(1-\pi_2)}{n_2}}[/tex]
The standard error is [tex]s = \sqrt{\frac{\pi_1(1-\pi_1)}{n_1}+\frac{\pi_2(1-\pi_2)}{n_2}}[/tex], in which [tex]p_1,p_2[/tex] are the proportions and [tex]n_1,n_2[/tex] are the sample sizes.
how many 1/8 cups are in 4/4
Answer:8
is the answer
Find the value of x. If necessary, write your answer in simplest radical form.
12
9
Answer:
3√7
Step-by-step explanation:
9²+B²=12²
simplify
81+B²=144
minus the 81
B²= 63
HELP! PLEASEE I’ve been stuck!! I WILL GIVE BRAINLY,,, THANK YOU SM
Answer:
$119
Step-by-step explanation:
08:00 - 12:15 = 4hrs 15mins
13:00 - 17:15 = 4hrs 15mins
Total hours worked = 8hrs 30 mins
$14/hr
14 × 8 = 112
30 mins is half of an hour so 14/2 = 7
$7 for 30 mins
112 + 7 = 119
$119
hope this helps ^^
Complete the blanks:
Horizontal lines have _____
slope and vertical lines have slope.
Horizontal lines have _______ equations that say __= any number.
Vertical lines have equations that say __= any number.
Answer:
Horizontal lines have __zero___
slope and vertical lines have undefined slope.
Horizontal lines have ___linear____ equations that say _y_= any number.
Vertical lines have equations that say _x_= any number.
Answer:
To write the equation of a horizontal line, we only need to specify where it intersects with the y-axis. This will look like y=k, where k is where the line crosses the y-axis.
The equation of a vertical line always takes the form x = k, where k is any number and k is also the x-intercept .
Step-by-step explanation:
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Your neighbor's are building a dog pen in the shape of a right triangle. The legs of the triangular pen measures 9 meters and 12 meters. Find the perimeter of the enclosed space
Find the distance between the two points rounding to the nearest tenth (if necessary).
(-6, 6) and (3, -6)
Answer:
[tex]\displaystyle d = 15[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Coordinates (x, y)Algebra II
Distance Formula: [tex]\displaystyle d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Step-by-step explanation:
Step 1: Define
Point (-6, 6)
Point (3, -6)
Step 2: Identify
(-6, 6) → x₁ = -6, y₁ = 6
(3, -6) → x₂ = 3, y₂ = -6
Step 3: Find distance d
Simply plug in the 2 coordinates into the distance formula to find distance d
Substitute in points [Distance Formula]: [tex]\displaystyle d = \sqrt{(3--6)^2+(-6-6)^2}[/tex][√Radical] (Parenthesis) Subtract/Add: [tex]\displaystyle d = \sqrt{(9)^2+(-12)^2}[/tex][√Radical] Evaluate exponents: [tex]\displaystyle d = \sqrt{81+144}[/tex][√Radical] Add: [tex]\displaystyle d = \sqrt{225}[/tex][√Radical] Evaluate: [tex]\displaystyle d = 15[/tex]I NEED HELP PLEASEeeee
Answer:
All false jhgffyyhvfftuhvgfy
Find the 12th term of the geometric sequence 5, 20, 80, ...5,20,80
Answer:
a₁₂ = 20971520
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
Here a₁ = 5 and r = a₂ ÷ a₁ = 20 ÷ 5 = 4 , then
a₁₂ = 5 × [tex]4^{11}[/tex] = 5 × 4194304 = 20971520
which polygon matches this set of ordered pairs?
A (1,3),B(1,9),c(4,9),d(4,3)
Answer:
B
Step-by-step explanation:
if 7x - 9 equals 15, what is the value of 7x +1
Answer:
25Step-by-step explanation:
First,
7x - 9 = 15
=> 7x = 15 + 9
=> 7x = 24
[tex] = > x = \frac{24}{7} [/tex]
Now putting its value in 7x + 1,
= 7x + 1
[tex] = 7 (\frac{24}{7} ) + 1[/tex]
[tex] = 7 \times \frac{24}{7} + 1[/tex]
= 24 + 1
= 25 (Ans)
Name the postulate, if possible, that makes the triangles congruent. *
Answer:
answer is ASA
Step-by-step explanation:
two triangles are congruent by angle side angle theorem.
What clockwise rotation is equivalent to a 90° counterclockwise rotation?
Answer: 270°
Step-by-step explanation:
A full rotation is 360° so to find out the clockwise equivalent of a 90° counterclockwise rotation, deduct the counterclockwise rotation from 360°:
= 360 - 90
= 270°
If you rotated 90° counterclockwise, you would get to the same point as if you rotated 270° clockwise.
What is the equation of the line that is parallel to y minus 3 x = 2 and that passes through (6,1)?
Answer:
y = 3x - 17
Step-by-step explanation:
y - 3x = 2
y = 3x + 2
Parallel slope (m) = 3
Passes through (6, 1)
Slope-intercept:
y - y1 = m(x - x1)
y - 1 = 3(x - 6)
y - 1 = 3x - 18
y = 3x - 17
Find the value of the variable. Round decimal to nearest tenth if necessary.
Given:
In a right angle triangle,
Length of legs are x and 7.
Length of hypotenuse = y
Measure of angle between leg 7 and hypotenuse = 33 degrees.
To find:
The value of x and y.
Solution:
In a right angle,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
[tex]\tan (33^\circ)=\dfrac{x}{7}[/tex]
[tex]7\times \tan (33^\circ)=x[/tex]
[tex]7\times 0.6494=x[/tex]
[tex]4.5458=x[/tex]
Approximate the value to the nearest tenth.
[tex]x\approx 4.5[/tex]
In a right angle triangle,
[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]
[tex]\cos (33^\circ)=\dfrac{7}{y}[/tex]
[tex]y=\dfrac{7}{\cos (33^\circ)}[/tex]
[tex]y=\dfrac{7}{0.83867}[/tex]
[tex]y=8.34655[/tex]
Approximate the value to the nearest tenth.
[tex]y\approx 8.3[/tex]
Therefore, the correct option is D.
1 gold plate weight 30 mg if the weight of some plates is 450 ml mg find the number of plates
Answer:
15 plates
Step-by-step explanation:
450 divided by 30 = 15, meaning 30 x 15 would be 450 mg. This also means that if the weight of some plates was 450 mg, there would be 15 plates.
Answer:
15
Step-by-step explanation:
Your units are a little confused.
The mass (total ) is 450 mg
1 plate weighs 30 mg
1 plate / 30 mg = x plates / 450 mg Cross multiply
1 * 450 = 30x Divide by 30
450 / 30 = x
x = 15
There are 15 gold plates.
Sove for X choose one. Pls
100 POINTS !!!! Let f(x)=√3x and g(x)=x-6 What's the smallest number that is in the domain of fog?
Answer:
6
Step-by-step explanation:
fog(x) = √3(x-6)
Domain => 3(x-6) ≥ 0
<=> x-6≥ 0
=> x ≥ 6
so, the smallest number is 6
As
(fog)(x)=f(g(x))
g(x)=x-6f(g(x))
f(x-6)√3(x-6)So
x-6≥0x≥6Smallest no is 6
The table shows the number of gallons of water
Answer:
Hello! answer: 360
Step-by-step explanation:
The rule is multiply by 30 I found this out by using the info shown in the table like...
120 ÷ 4 = 30 90 ÷ 30 = 3 60 ÷ 30 = 2 and so on matching up with the chart! so what I did was 12 × 30 to get the final answer to follow the pattern so... 12 × 30 = 360 therefore the answer is 360 HOPE THAT HELPS!
The first day of a water polo tournament the total value of tickets sold was $1540. One-day passes sold for $10
and tournament passes sold for $20. The number of tournament passes sold was 23 more than the number of day
passes sold. How many day passes and tournament passes were sold?
Answer:
59 tournament passes and 36 one-day passes were sold.
Step-by-step explanation:
Since the first day of a water polo tournament the total value of tickets sold was $ 1540, and one-day passes sold for $ 10 and tournament passes sold for $ 20, and the number of tournament passes sold was 23 more than the number of day passes. sold, to determine how many day passes and tournament passes were sold, the following calculation must be performed:
20 x 33 + 10 x 10 = 760
20 x 63 + 10 x 40 = 1,660
20 x 58 + 10 x 35 = 1,510
20 x 59 + 10 x 36 = 1,540
Thus, 59 tournament passes and 36 one-day passes were sold.
Sam is practicing speed skating at an ice rink.The distance around the rink is 150 yards. He skated around the rink 5 times. How many feet did Sam skate
Let BC=CD=12cm, and the length of arc BD=15cm. Find the area, in square centimeters, of sector BCD.
Answer:
option b : 90 sq. cm
Step-by-step explanation:
1) Area of circle with radius = 12cm
Area = π r^2
= 3.14 * (12) (12)
= 3.14 * 144
= approx 452.4
2) Circumference of circle with radius = 12cm
Circumference = 2πr
= 2 * 3.14 * 12
= approx 75 .4
3) Arc length = 15cm ......(given)
[tex] \frac{area \: of \: sector}{total \: area} = \frac{arc \: length}{circumference} [/tex]
[tex] \frac{area \: of \: sector}{452.4} = \frac{15}{75.4} [/tex]
[tex]area \: of \: sector \: = \frac{15 \times 452.4}{75.4} [/tex]
[tex] = \frac{6786}{75.4} [/tex]
[tex] = 90 {cm}^{2} [/tex]
The x-intercept is the point on the x-axis where the line crosses it. The
y-coordinate of the line's x-intercept is always zero. The x-coordinate of the
x-intercept is the number where it crosses the x-axis. A line with an x-
intercept of (5,0) crosses the x-axis at the number 5. A line with an x-
intercept of (-5,0) crosses the x-axis at -5.
Which of these coordinates could be a line's x-intercept?
A
(3,1)
B
(0,-12)
С
(-5,4)
(-7,0)
Answer:
D
Step-by-step explanation:
In desperate need. for answer 11 and 12.
Question 11 has to have an answer with explanation and
Question 12 has 3 parts. I need answers to all three with explanations for all three.
Hence, Solve the equation
X Х
1- x
4x=
Solve for r.
K=4r-7s
r=
Answer:
[tex]r=\frac{k+7s}{4}[/tex]
Step-by-step explanation:
HELPP!!! ALMOST OUT OF TIME
Answer:
option 2 is correct
Step-by-step explanation:
Another 2 btc please
Determine if lines AB and CD are parallel, perpendicular, or neither. A(-3,8), B(3,2), C(7,1), D(5,-1)
Answer:
Step-by-step explanation:
The slope of line AB is
[tex]\frac{2-8}{3-(-3)} = \frac{-6}{6} = -1[/tex]
The slope of line CD is
[tex]\frac{-1-1}{5-7} = \frac{-2}{-2} = 1[/tex]
Since the slopes multiply to [tex]-1[/tex], these lines are perpendicular to one another.
The lines AB and CD are perpendicular to one another.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.
let (x₁, y₁ ) = A(-3,8), and (x₂, y₂ ) = B(3,2)
The slope of line AB is;
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( 2 - 8) / ( 3 +3 )
m = -1
let (x₁, y₁ ) = C(7,1) and (x₂, y₂ ) = D(5,-1)
The the slope of line CD is;
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( -1 - 1) / ( 5 - 7 )
m = 1
Since slope of AB and CD are not equal the lines are not parallel therefore, these lines are perpendicular to one another.
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