Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Here's the solution ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{2 {}^{n} - 1}{ {4}^{n} - 1} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{2 {}^{n} - 1}{ {( {2}^{2}) }^{n} - 1} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{2 {}^{n} - 1}{ {( {2}^{n}) }^{2} - 1} [/tex]
Now we will use this identity in denominator
[ a² - b² = (a + b)(a - b) ]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ \cancel{(2 {}^{n} - 1)}}{ {( {2}^{n} }^{} + 1) \cancel{( {2}^{n} - 1)}} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{ 1}{ {( {2}^{n} }^{} + 1) } [/tex]
Answer:
[tex]\sf \dfrac{1}{2^n+1}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sf \dfrac{2^n-1}{4^n-1}[/tex]
Rewrite [tex]\sf 4^n[/tex]: [tex]\sf 4^n=(2^2)^n=2^{2n}=(2^n)^2[/tex]
Rewrite 1: 1 = 1²
[tex]\sf \implies \dfrac{2^n-1}{(2^n)^2-1^2}[/tex]
Apply difference of two square formula to the denominator
[tex]\sf a^2-b^2=(a+b)(a-b)[/tex]
[tex]\sf \implies \dfrac{2^n-1}{(2^n+1)(2^n-1)}[/tex]
Cancel out the common factor [tex]\sf 2^n-1[/tex] :
[tex]\sf \implies \dfrac{1}{2^n+1}[/tex]
Related Questions
Find the length of the third side. If necessary, round to the nearest tenth. 10 24
Answers
Answer:
26 units
Step-by-step explanation:
Pythagoras' Theorem: [tex]\sf a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Given
a = 10b = 24Substitute the given values into the formula and solve for c:
[tex]\sf \implies 10^2+24^2=c^2[/tex]
[tex]\sf \implies c^2=676[/tex]
[tex]\sf \implies c=\pm\sqrt{676}[/tex]
[tex]\sf \implies c=\pm26[/tex]
Since length is positive, c = 26 only
Answer:
26 units
Step-by-step explanation:
To find the missing side length, we need to use Pythagoras theorem, as this triangle is a right triangle.
Formula: h² = x² + y² [h = hypotenuse, x and y = legs]
Legs: 10 units and 24 units (Stated in comments)
Finding the third side of the triangle (h):
⇒ h² = 10² + 24²
Simplify the LHS:
⇒ h² = 100 + 576
⇒ h² = 676
Take a square root both sides:
⇒ √h² = √676
⇒ h = ±26
⇒ h = 26 (Side lengths can never be negative)
Thus, the length of the third side is 26 units.
1. What number, when substituted for x in the following problem, will make the problem true?
6X + 8% = 107
Answers
Answer:
x = 17.82
Step-by-step explanation:
6x + 8% = 107
-8% -8%
or
107 - 0.08 = 106.92
-----------------------------------
6x = 106.92
÷6 ÷6
x = 17.82
------------------------------------
I hope this helps!
The graph shows △ABC and the midpoints for each segment.
What statements showing the medians of a triangle meet at a point are TRUE?
A.
The equation of the lines of the medians are x=0, y=−x+8, and y=x.
The ordered pair solution of each pair of system of equation is (0,8).
B
The equation of the lines of the medians are x=0, y=−x+8, and y=x.
The medians do not meet at one point for this triangle because one equation is a vertical line.
C
The equation of the lines of the medians are y=3x, y=4, and y=−3x+8.
The ordered pair solution of each pair of system of equation is (43,4).
D
The equation of the lines of the medians are y=3x, y=4, and y=−3x+8.
The medians do not meet at one point for this triangle because two equations have opposite slopes.
Answers
Answer: C
Step-by-step explanation:
A cylinder has a base diameter of 20ft and a height of 5ft. What is its volume in cubic ft, to the nearest tenths place?
Answers
Answer:
Formula for volume of cylinder;
V = π[tex]r^{2}[/tex]h
Where 'π' represents pi(22/7 or 3.14), 'r' represents the radius which is 1/2 x diameter (half of diameter = radius) which is squared, and 'h' which represents the height.
To find the radius of the diameter 5, we must find 1/2 of 5:
1/2 x 5
5/2 = 2.5 is our radius.
Now we plug these into our equation:-
V = π[tex]r^{2}[/tex]h
V = 3.14(2.5^2) x 20
V = 3.14(6.25) x 20
V = 19.625 x 20
V = 392.5 cubic feet.
During his first 20 picks from a bag of marbles, mike chose 8 yellow marbles, 9 green marbles, and 3 blue marbles. What is the experimental probability that mark will choose a green marble on his next pick? Write the probability as a percent.
Answers
Answer:
Step-by-step explanation:
All you have to do for this problem is take 3, over the 20, and then turn into a percent. Your final answer is D. 15%, because if you multiply 3/20 by 5, you get 15/100, which is easier to turn into a percent, leaving you with 15%
help with q7 please !!
Answers
Step-by-step explanation:
[tex] \frac{dA}{dx} = 3 {(x - 1)}^{2} \\A = ∫3 {(x - 1)}^{2}dx \\ = ∫3 {x}^{2} - 6x + 3 \: dx \\ = \frac{3 {x}^{3} }{3} - \frac{6 {x}^{2} }{2} + 3x + c \\ = {x}^{3} - 3 {x}^{2} + 3 + c[/tex]
Now substitute in A=10 and X=3, to find the value of c
[tex]10 = {3}^{3} - 3 {(3)}^{2} + 3(3) + c \\ c = 1[/tex]
Hence,
[tex]A = {x}^{3} - 3 {x}^{2} + 3x + 1[/tex]
The table shows information about town a in illinois and town b in florida. a 3-column table has 2 rows. the first column has entries town a, town b. the second column is labeled population with entries 54,016, question mark. the third column is labeled area (miles squared) with entries 3.89, 0.37. if the two towns have the same population density, which must also be true? town b has the same population as town a. town b has a greater population than town a. town b has a population of approximately 5,138. town b has a population of approximately 37,530.
Answers
Answer:
c. Town B has a population of approximately 5,138.
Step-by-step explanation:
sorry its late
Based on the population density, town B has a population of approximately 5138; option C
What is population density?Population density is the ratio of the total population of a place and the area of the place.
Population density = population/areaPopulation density of A = 54016/3.89 = 138885.86 per square miles
Population density of B = 138885.86 per square miles
Population of B = 138885.86 × 0.37 = 5138
Therefore, town B has a population of approximately 5138.
Learn more about population density at: https://brainly.com/question/13902749
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A baker needs 500 cupcake wrappers for this month's orders.
He has 365 cupcake wrappers in his store.
He buys an additional 250 cupcake wrappers.
He wants to see if he has enough cupcake wrappers.
Complete the statements. Answer All
1. Should the baker round the wrappers up or down?
2. Estimate the total number for wrappers.
3. The baker has or doesn't have enough cupcake wrappers.
(I kinda forgot how to round and estimate
Answers
Answer:
the Baker should round up.
365=400 250=300 400+300=700. the Baker does have enough. and even if you add 365+ 250 you get 615 over 500.
The total number of wrappers is 615 wrappers, which implies bakes has enough cupcake wrappers.
Given that,
A baker needs 500 cupcake wrappers for this month's orders, he has 365 cupcake wrappers in his store. He buys an additional 250 cupcake wrappers.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Total number of wrappers = 365 + 250 = 615
But according to the condition, a baker needs 500 cupcake wrappers for this month's orders. So the number of wrappers exceeds 15.
Thus, the total number of wrappers is 615 wrappers, which implies bakes has enough cupcake wrappers.
Learn more about arithmetic here:
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What is the formula of the curved surface of a cylinder?
Answers
Answer:
2πr × h = 2πrh
Step-by-step explanation:
that is the formula for a curved surface of a cylinder 2πr × h = 2πrh.
PLS HELP QUICK
Rachel designs a small flower garden for her new home. The garden is the shape of a rectangle, with a quarter circle added to each of the shorter sides of the rectangle. The shorter sides of the rectangle each measure 4 feet. The area of the garden is 73.12 ft2. What is the length of the other dimension rectangular portion of the garden?
Use 3.14 as an approximation for pi.
Answers
The length of the other dimension rectangular portion of the garden is 12 feet.
What is area?Area is the amount of space occupied by a two dimensional shape or object.
The area of each semicircle = (1/4) * π * radius² = (1/4) * π * 4² = 12.56 ft²
Let x represent the other side of the rectangle, hence:
Area of garden = 2(12.56) + 4x = 4x + 25.12
Hence:
73.12 = 4x + 25.12
x = 12 feet
The length of the other dimension rectangular portion of the garden is 12 feet.
Find out more on area at: https://brainly.com/question/25292087
Find the equation of the line that passes through (1,4) and is parallel to 3x+y+2=0. Leave your answer in the form y=mx+c.
Answers
Answer:
y = -3x + 7.
Step-by-step explanation:
First find the slope of the given line by converting to intercept form:
3x + y + 2 = 0
y = -3x - 2
So the slope is -3.
Then the line we want has a slope of -3 also (as it is parallel).
y - y1 = m(x - x1) where m is the slope and (x1, y1) is a point on the line:
m = -3, x1 = 1 and y1 = 4, so we have:
y - 4 = -3(x - 1)
y = -3x + 3 + 4
y = -3x + 7.
What percent of the values represented in this box-and-whisker plot are between 20 and 30?
5
20
25
30
45
about 10%
about 25%
about 50%
about 75%
pls answer i will give brainliest
Answers
Answer:
10%
Step-by-step explanation:
I took the test on K12 and I know that's the answer.
For my quiz the answer is 50%
I need help desperately lol
Answers
Answer:
Step-by-step explanation:
First find the shaded area. Ignore the fact that something is missing.
L = 16
w = 8
Area = L*w Substitute the givens
Area = 16*8
Area = 128
Now consider the white area. It has a "length" of 4 and a width of 8
L = 4
w = 8
Area = 32
Now subtract 32 from 128
Area of shaded part = 128 - 32
Answer: 96 mm^2
Destiny performs a hypothesis test on a population with µ = 115 and Sigma = 30. Her sample size is 25 with a mean of 120. 4. Which of the following correctly depicts the z-statistic for this data? 0. 04 0. 90 3. 53 3. 93.
Answers
The correct answer which refers to the z-statistic for this data is b)0.90.
What is a Hypothesis Test?The hypothesis Test refers to the statistical approach where the test is applied to an assumption regarding a population parameter.
It is given that µ = 115 and Sigma = 30.
sample size is 25 with a mean of 120.4
The formular for z-statistic is
z = (x – u) / (σ / sqrt n)
Therefore, we input the values and we get
z = (120.4 – 115) / (30 / sqrt 25)
We calculate further and we get
z = 0.90
Therefore, the correct answer is option b.
Learn more about the hypothesis test here:
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Write an expression equivalent to 6 — 2.2 +5+ 4. that only has two
terms.
Answers
Answer:
3.8 + 9?
Step-by-step explanation:
A plastic alphabet cube is 7 cm on each side. What is the surface area of the cube?
Answers
Answer:
In a cube, the length and width are the same, so both sides will be 7 cm, yielding an area of 49 square centimeters.
Step-by-step explanation:
Answer:
Cube's features;
6 sides to a cubeAll side lengths are equal, so all areas are the sameGiven this information, we must find the area of one side and multiply that area by 6 since there are 6 equal sides of the same area.
Formula for area of square:-
A = a^2
or
A = a · a
Where 'a' represents the length of one side.
Plug in values;
A = a^2
A = 7^2
A = 49 centimetres is the area of one side.
Now we find the areas of all sides (6 sides in total);
49(6)
= 294 is the surface area of the cube.
Solve for x please and round
Answers
Answer:
[tex]\displaystyle 74,4[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{x}{67} = cot\:42 \hookrightarrow 67cot\:42 = x \hookrightarrow 74,411038494... = x \\ \\ 74,4 ≈ x[/tex]
OR
[tex]\displaystyle \frac{67}{x} = tan\:42 \hookrightarrow xtan\:42 = 67 \hookrightarrow \frac{67}{tan\:47} = x \hookrightarrow 74,411038494... = x \\ \\ 74,4 ≈ x[/tex]
Information on trigonometric ratios
[tex]\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOCITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:θ \\ \frac{ADJACENT}{OPPOCITE} = cot\:θ[/tex]
I am joyous to assist you at any time.
Which expression is equivalent to 16 4 6 ax?
Answers
Answer:
i believe the correct answer is a
Identify the center and the radius of a circle that has a diameter with endpoints at (−5, 9) and (3, 5)
Answers
Check the picture below, so the circle looks more or less like that one.
well, the center of it is simply the Midpoint of those two points, and its radius is simply half-the-distance between them.
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 3 -5}{2}~~~ ,~~~ \cfrac{ 5 + 9}{2} \right)\implies \left( \cfrac{-2}{2}~~,~~\cfrac{14}{2} \right)\implies \stackrel{center}{(-1~~,~~7)} \\\\[-0.35em] ~\dotfill[/tex]
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{diameter}{d}=\sqrt{[3 - (-5)]^2 + [5 - 9]^2}\implies d=\sqrt{(3+5)^2+(-4)^2} \\\\\\ d=\sqrt{8^2+16}\implies d=\sqrt{80}\implies d=4\sqrt{5}~\hfill \stackrel{\textit{half the diameter}}{\cfrac{4\sqrt{5}}{2}\implies \underset{radius}{2\sqrt{5}}}[/tex]
Write the equation in spherical coordinates. (a) x2 y2 z2 = 64
Answers
The equation in spherical coordinates will be a constant, as we are describing a spherical shell.
r(φ, θ) = 8 units.
How to rewrite the equation in spherical coordinates?The equation:
x^2 + y^2 + z^2 = R^2
Defines a sphere of radius R.
Then the equation:
x^2 + y^2 + z^2 = 64
Defines a sphere of radius √64 = 8.
Then we will have that the radius is a constant for any given angle, then we can write r, the radius, as a constant function of θ and φ, the equation will be:
r(φ, θ) = 8 units.
If you want to learn more about spheres, you can read:
https://brainly.com/question/10171109
The equation in spherical coordinates is r(φ, θ) = 8 units.
What are the spherical coordinates?Spherical coordinates of the system denoted as (r, θ, Φ) is the coordinate system mainly used in three-dimensional systems.
The equation of the spherical coordinates is written as;
[tex]\rm x^2 + y^2 + z^2 = R^2[/tex]
Where R is the sphere of radius.
The given equation of the spherical coordinates is;
[tex]\rm x^2 + y^2 + z^2 = 64^2[/tex]
Here 8 is the sphere of radius.
Hence, the equation in spherical coordinates is r(φ, θ) = 8 units.
Learn more about spheres here;
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The following scatter plot represents the relationship between a person's weight and the number of calories the person burns in one minute of jump roping. Using the line of best fit, about how many calories per minute could you expect a 100-pound person to burn while jump roping?
a. 6
b. 8
c. 7
d. 6.5
Please answer!
Answers
Answer:
b. 8
Step-by-step explanation:
the point asked has coordinates (100;8) (weight;calories)
How many liters are in 950mL
Answers
Answer:
0.950 L
Step-by-step explanation:
ml/1000 = L
Find the size of angle x.
Answers
Answer:
x = 115°
Explanation:
x + 81° + 164° = 360°x + 245° = 360°x = 360° - 245°x = 115°Answer:
x=115°
Step-by-step explanation:
whole thing is supposed to = 360° so
164+81+x=360
245+x=360
x=115
What is
|Ay|
in the system of linear equations below?
-8x+y=-6
3x-2y=-1
Answers
Considering the given system of equations, it is found that:
[tex]|Ay| = \left|\begin{array}{cc}-8&1\\-6&-1\end{array}\right|[/tex]
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the system is:
-8x+y=-6
3x-2y=-1
In matrix form, it is given by:
[tex]\left[\begin{array}{cc}-8&1\\3&-2\end{array}\right]\left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}-6\\-1\end{array}\right][/tex]
To find the matrix |Ay|, we replace the y coefficients of 1 and -2 by the results of -6 and -1, hence:
[tex]|Ay| = \left|\begin{array}{cc}-8&1\\-6&-1\end{array}\right|[/tex]
More can be learned about a system of equations at https://brainly.com/question/24342899
Answer:
C. (-8 -6 3 -1)
Step-by-step explanation:
EDG
There are 24 crayons in a box. How many boxes will be needed for 15 children if each child gets 12 crayons
Answers
Answer:
7.5
Step-by-step explanation:
15×12=180
180÷24(crayons per box)=7.5 boxes
complementary
supplementary
neither
Answers
Answer:
Two angles are called complementary if their measures add to 90 degrees, and called supplementary if their measures add to 180 degrees. Note that in these definitions, it does not matter whether or not the angles are adjacent; only their measures matter.
Step-by-step explanation:
hope its help po
correct me if im wrong
Two angles say x and y, are said to be complementary iff the sum of both angles x and y is 90° , while on the another hand, if their sum is 180°, they're called supplementary angles. So, here 75° + 105° = 180°, so both the angles are supplementary.
Hence, the required answer is supplementary
What is the scale factor from square ABC to square DEF
Answers
Answer:
the scale factor is 6
scale factor:
length of image ÷ length of original
Here:
24 ÷ 4 = 624 ÷ 4 = 612 ÷ 2 = 6the volume of a cylinder is 411π in^3. The height of the cylinder is 9 in. Calculate the diameter of the cylinder to the nearest tenth of a centimeter.
Answers
Answer:
13.5 in, or 34.3 cm.
Step-by-step explanation:
First, use the formula volume = pi * r^2 * height- you have the volume, so just solve the equation 411pi = pi * 9 * r^2 for r, and you get that r = 6.75. Since diameter is equal to 2r, multiply 6.75 by 2 to get your answer of 13.5 inches. The questions asks for the diameter in centimeters though, which makes it 34.3 cm.
Hopefully this helps- let me know if you have any questions!
I need to know 219.8 x 0.48.
Answers
Answer:
105.504
Step-by-step explanation:
I really need help to understand this problem for my end of course exam!!!!
Answers
Answer:
D. [tex]13(2.81)^n[/tex]
Step-by-step explanation:
[tex]13(1.09)^{12n} < ==exponents\ first\(PEMDAS)\\\\13(2.8126)^n < ==approximate\\\\13(2.81)^n[/tex]
Hope this helps!