We happen to have
[tex]\dfrac17 = \dfrac18 + \dfrac1{8^2} + \dfrac1{8^3} + \cdots[/tex]
which is to say, the base-8 representation of 1/7 is
[tex]\dfrac17 \equiv 0.111\ldots_8[/tex]
This follows from the well-known result on geometric series,
[tex]\displaystyle \sum_{n=1}^\infty ar^{n-1} = \frac a{1-r}[/tex]
if [tex]|r|<1[/tex]. With [tex]a=1[/tex] and [tex]r=\frac18[/tex], we have
[tex]\displaystyle \sum_{n=1}^\infty \frac1{8^{n-1}} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac1{1-\frac18} = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac87 = 1 + \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots \\\\ \implies \frac17 = \frac18 + \frac1{8^2} + \frac1{8^3} + \cdots[/tex]
Uniformly multiplying each term on the right by an appropriate power of 2, we have
[tex]\dfrac17 = \dfrac2{16} + \dfrac{2^2}{16^2} + \dfrac{2^3}{16^3} + \dfrac{2^4}{16^4} + \dfrac{2^5}{16^5} + \dfrac{2^6}{16^6} + \cdots[/tex]
Now observe that for [tex]n\ge4[/tex], each numerator on the right side side will contain a factor of 16 that can be eliminated.
[tex]\dfrac{2^n}{16^n} = \dfrac{2^4\times2^{n-4}}{16^n} = \dfrac{2^{n-4}}{16^{n-1}}[/tex]
That is,
[tex]\dfrac{2^4}{16^4} = \dfrac1{16^3}[/tex]
[tex]\dfrac{2^5}{16^5} = \dfrac2{16^4}[/tex]
[tex]\dfrac{2^6}{16^6} = \dfrac4{16^5}[/tex]
etc. so that
[tex]\dfrac17 = \dfrac2{16} + \dfrac4{16^2} + \dfrac9{16^3} + \dfrac2{16^4} + \dfrac4{16^5} + \dfrac9{16^6} + \cdots[/tex]
and thus the base-16 representation of 1/7 is
[tex]\dfrac17 \equiv 0.249249249\ldots_{16}[/tex]
and the first 10 digits after the (hexa)decimal point are {2, 4, 9, 2, 4, 9, 2, 4, 9, 2}.
If f(x) = 2x^2+3 and g(x)= 5x, evaluate the following: a. f(g(x)) b. g(g(3)) c. g(f(-2))
Answer:
A = 50x^2+3
B = 75
C = 55
Step-by-step explanation:
[tex]f(x)=2x^2+3\\g(x)=5x[/tex]
A. f(g(x))
[tex]2(5x)^2+3\\2(25x^2)+3\\=50x^2+3[/tex]
B. g(g(3))
[tex]5(5(3))\\5(15)\\=75[/tex]
C. g(f(-2))
[tex]g(2(-2)^2+3)\\g(8+3)\\g(11)\\5(11)\\=55[/tex]
How many dogs were in the sample?
each number under the leaves section would be a dog
answer: 11
Answer:
11
Step-by-step explanation:
The presence of a midpoint will result in what type of segments?
Answer: two congruent segments.
Step-by-step explanation:
idlk im not smart
Z varies directly as x and y, z=6 when x=2 and y=6 find the value of z when x=3 and y=8
Answer:
12
Step-by-step explanation:
Direct Variation. I think it's gonna be like this.
SInce Z is not inversely to y , its varies directly to both.
Then it's,
Z=kxy, where k is constant.
subst. Z=6,x=2 and y=6.
6=k×2×6
6=k×12=12k
6=12k=½
the formula connecting them is
Z=½xy
Z=½×3×8
Z= 1×3×8÷2
Z=24÷2
Z=12.
That's my solution.
Help anyone? Simple problem
Answer:x>7
Step-by-step explanation:
Its saying a nuber greater than 7 and 3 plus 8 would be 11
Let a population consist of the values cigarettes, cigarettes, and cigarettes smoked in a day. Show that when samples of size 2 are randomly selected with replacement, the samples have mean absolute deviations that do not center about the value of the mean absolute deviation of the population. What does this indicate about a sample mean absolute deviation being used as an estimator of the mean absolute deviation of a population?.
Based on the given mean absolute deviations, the sample mean absolute deviation will be 2 and the population mean absolute deviation will be 3.8.
What is the sample mean absolute deviation?= Sum of sample mean absolute deviation / Number
= (0 + 0.5 + 4.5 + 0.5 + 0 + 4 + 4.5 + 4 + 0) / 9
= 2
What is the population mean absolute deviation:First find the population mean:
= (10 + 11 + 19) / 3
= 13.3
Population mean absolute deviation:
= 1/3 x ( (10 - 13.67) + (11 - 13.3) + (19 - 13.3))
= 3.8
We can therefore see that the sample mean deviations is a biased estimate of the population mean absolute deviation.
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What number were both the numerator and denominator multiplied by to arrive at the equivalent fraction? What number were both the numerator and denominator multiplied by to arrive at the equivalent fraction ?
Answer:
Both the numerator and denominator should be multiplied by the same number to arrive at the equivalent fraction.
Step-by-step explanation:
Equivalent fractions = two or more than two fractions are said to be equal if both results the same fraction after simplification.
For example, consider the fraction 1/3
Multiplying numerator and denominator with 2, we get 1/3 × 2/2 = 2/6
Multiplying numerator and denominator with 3, we get 1/3 × 3/3 = 3/9
Multiplying numerator and denominator with 4, we get 1/3 × 4/4 = 4/12
Therefore, we can conclude that,
1/3 = 2/6 = 3/9 = 4/12 these are equivalent fractions.
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Answer: 2 and 6/8
Step-by-step explanation:
How do you write an effective explanation to explain this problem?
The error happens in the last line.
The relevant log rule is ln(A) - ln(B) = ln(A/B)
The issue is that the 0 isn't ln(0), so that 0 cannot be thrown into the natural log like that.
What we can do is this set of steps
ln(3x) - 0
ln(3x) - ln(1)
ln(3x/1) ... applying the log rule mentioned
ln(3x)
But these steps are a needlessly overcomplicating things. We can simply go from ln(3x)-0 to ln(3x) in one step. Subtracting off zero doesn't change ln(3x) at all.
--------------------------
Let's continue the steps to solve for x.
ln(x^2) = ln(3x)
x^2 = 3x
x^2-3x = 0
x(x-3) = 0
x = 0 or x-3 = 0
x = 0 or x = 3
Those are the two possible solutions.
However, x = 0 isn't valid because it's not in the domain of ln(x^2). In other words, ln(0) isn't defined. The domain of y = ln(x) is x > 0
This means that x = 3 is the only solution.
if 13n-6 = 98 what is the value of n
Answer:
n = 8
Step-by-step explanation:
13n-6 = 98
Solution:
13n = 98+613n = 104n = 104/13n = 8Hence the value of n is 8.
13n - 6 = 98
13n = 98 + 6
13n = 104
n = 104/13
n = 8
1. At which point do Line CF and Line GF intersect? They intersect at point?
2. Look at Line AD and Like BE. Do these lines intersect?
(a) yes they will intersect at Point F?
(b) no they will never intersect?
(c) yes they will point at Point G
(d) yes they will intersect at Point F?
3. Look at Line BG and Line AC. Where do they intersect? They intersect at Point?
(Please hurry giving 50 points!)
Answer: i think no?
Step-by-step explanation:
AD and BE are both parallel lines (they are parallel to eachother), so they will never intersect
CF and GF intersect at point F (i think)
Bg and Ac intersect at point B (i think)
i dont want to give a definite answer in the event im wrong bc I just learned this like a few weeks ago-
A car travels ¹/4 mile in ³ minutes, what 4 is its speed in terms of miles per minutes? A car travels ¹ / 4 mile in ³ minutes , what 4 is its speed in terms of miles per minutes ?
Answer:
1/12 mile per minute
Step-by-step explanation:
1/4 mile in 3 minutes
then miles per minute is 1/4 mile / 3 min = 1/12 mile/min
Fraction
Puja Limbu did 8 out of 10 math problems and Raju lama did 11 out of 15 similar maths problems.Express the number of problems solved by each of them in fractions and identify who did better performance.
Using percentages, we have that Puja Limbu did 80% of the problems and Raju Lama did 73.3%, hence Puja Limbu had the better performance.
What is a percentage?The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:
[tex]P = \frac{a}{b} \times 100\%[/tex]
The percentage for Puja Limbu is:
[tex]P = \frac{8}{10} \times 100\% = 80\%[/tex]
The percentage for Raju Lama is:
[tex]P = \frac{11}{15} \times 100\% = 73.3\%[/tex]
80% > 73.3%, hence Puja Limbu had the better performance.
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Match each box plot to the data set it represents.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
{20,18,8,18,10,8,4}
{12,14,16,20,4,8,10}
{12,16,4,20,8,6,8}
An expression can either be an equation or an inequality.
The correct classification of the terms are:
Expression; 4x+20
Inequality: 4x+20>40
Equation: 4x+20=40
We have given that,
{20,18,8,18,10,8,4}
{12,14,16,20,4,8,10}
{12,16,4,20,8,6,8}
How to determine the correct classification?To determine the correct classification, we make use of the following highlights
When an expression has the =, then the expression is an equation.
When an expression has any of the following signs>, <, >=, <= or != , then the expression is an inequality.
When the expression is neither an equation nor an inequality, then it is just an expression.
Hence, the correct classifications are:
Expression; 4x+20
Inequality: 4x+20>40
Equation: 4x+20=40
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In a market survey, 100 traders sell fruits, 40 sell apples, 46 oranges, 50 mangoes. 14 apples and oranges. 15 apples and mangoes, and 10 sell the three fruits. Each of the 100 traders sells at least one of the three fruits. Find the number that sell oranges and mangoes only.
The number of traders that sell oranges and mangoes only are 17.
How to determine the common differenceSince there are three sets, use the formula
n (A∪O∪M) = n(A) + n(O) + n(M) - n(A∩O) -n(O∩M) - n(A∩M) + n(A∩O∩M)
A represents apple traders = 40
O represents orange traders = 46
M represents mangoes traders = 50
A∪O∪M = total traders = 100
A∩O = 14
O∩M = ?
A∩M = 15
A∩O∩M = 10
Substitute values into the formula
100 = 40 + 46 + 50 - 14 - 15 - O∩M + 10
100 = 146 - 29 - O∩M
100 = 117 - O∩M
Make O∩M subject of formula
- O∩M = 100 -117
O∩M = 17 traders
Therefore, the number of traders that sell oranges and mangoes only are 17.
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which of the following are NOT classified as a trapezoid? Select all that apply
a) rhombuses
b) parallelograms
c) rectangles
d) squares
e) quadrilaterals
Answer:
[tex]\boxed {a, b, c, d}[/tex]
Step-by-step explanation:
Rhombuses, parallelograms, rectangles, and squares cannot be classified as trapezoids as they have 2 pairs of parallel sides each. But quadrilaterals can be classified as trapezoids if they have a pair of parallel sides and a pair of non-parallel sides.
a) rhombuses
b) parallelograms
c) rectangles
d) squares
We have two fractions, 1/6 3/8 and we want to rewrite them so that they have a common denominator (and whole number numerators). What numbers could we use for the denominator? Choose 2 answers:
Answer:
See below
Step-by-step explanation:
The denominator has to be divisible by 6 and 8
you could choose 24 48 72 96 etc
which of the following is a Monomail
Reason:
sorry but here is no options so I am giving you a example so that you can understand by your own!
Answer;
5r+3
2x-6
X4+10
4y-1
Step by step answer;
So the method of identifying the Monomail is if you see a variable in a constant so it is a Monomail !
Mark as brainlest answerWhat is the range of the given data set?
Answer:
6
Step-by-step explanation:
21 - 15 = 6
how many spherical balls of diameter 15cm can be covered by 40 square metres of material
Answer:
It's very simple: divide the 40 m² area by area of 1 one sphere
[tex] \frac{40 \: m {}^{2} }{3.41 \times 15m {}^{2} } = 565[/tex]
Simplify completely.
3 189x5y7
√/7x²y²
3
Answer:
[tex]\large \boxed{\sf 3x\sqrt[3]{y^5}}[/tex]
Explanation:
[tex]\rightarrow \dfrac{\sqrt[3]{\sf 189x^5y^7}}{\sqrt[3]{\sf 7x^2y^2}}[/tex]
applying radical rule[tex]\rightarrow \sf \sqrt[3]{\dfrac{\sf 189x^5y^7}{\sf 7x^2y^2}}[/tex]
simplify[tex]\rightarrow \sqrt[3]{\sf 27x^3y^5}[/tex]
put cubic root[tex]\rightarrow \sqrt[3]{\sf 27} \sqrt[3]{\sf {x^3} }\sqrt[3]{\sf y^5}}[/tex]
simplify[tex]\rightarrow \sf 3x\sqrt[3]{y^5}[/tex]
complete the square to rewrite y=x^2+8x+3 in vertex form and then identify the minimum y-value of the function
The vertex-form of the quadratic equation is given by y = (x + 4)² - 13, and the minimum value of y is of -13.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient. If a > 0, k is the minimum value of y, and if a < 0, it is the maximum value.
In this problem, the equation is:
y = x² + 8x + 3.
Completing the squares, the function is:
y = (x + 4)² - 13
13 is subtracted as (x + 4)² = x² + 8x + 16, hence for the equations to be equal 13 has to be subtracted. k = -13 is also the minimum value of y.
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The minimum y-value of the function for the parabolic equation is -13.
What is the vertex of a parabolic equation in quadratic form?The vertex for an up-down facing parabola of the form y = ax² + bx + c is [tex]\mathbf{x_v= -\dfrac{b}{2a}}[/tex]
From the given equation:
y = x² + 8x + 3
The parameters for the parabola are:
a = 1, b = 8, c = 3
[tex]\mathbf{x_v= -\dfrac{8}{2\times 1}}[/tex]
[tex]\mathbf{x_v= -4}[/tex]
If we replace the value of [tex]\mathbf{x_v= -4}[/tex] to find the minimum value of [tex]\mathbf{y_v}[/tex] value, we have:
[tex]\mathbf{y_v = -13}[/tex]
Thus, the parabola vertex is (-4,-13). If a< 0, the vertex is a maximum value and If a>0, the vertex is a minimum value.
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2. analyze the data you gathered about the number of births in the united states in 2011.
a. what do you observe about michigan and florida? justify your conclusion by using the cartogram. (5points)
b. there were 4,008,000 births in the united states during 2011. what proportion of all national births are accounted for by michigan? what proportion of all national births are accounted for by florida? (5 points)
c. suppose a person born during 2011 in the united states is chosen randomly. is the person more likely to have been born in florida or michigan? explain. (5 points)
d. the population of the united states was 308,745,538 in 2011. there were 18,801,310 people in florida and 9,883,640 people in michigan. compute the probability that a randomly selected us resident in 2011 was living in florida. do the same for michigan. which is greater? (5 points)
e. the number of births in a region depends mostly on population size. there are also random fluctuations and regional differences. consider your answers about populations and birth rates. are your answers consistent with this fact? (5 points)
The figures show that the number of births for Florida and Michigan reduced
How to compute the probability?From the data sourced, the number of births in Florida in 2010 was 214519 while in 2011, it was 213237. For Michigan, there was decrease from 114717 to 114159.
When a person born during 2011 in the United States is chosen randomly, the person is more likely to have been born in Florida.
The probability that a randomly selected us resident in 2011 was living in Florida will be:
= 18,801,310/308,745,538
= 0.061
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One lucky day, you meet a leprechaun who promises to give you fantastic wealth, but hands you only a penny before disappearing. You head home and place the
penny under your pillow. The next morning, to your surprise, you find two pennies under your pillow. The following morning, you find four pennies, and the morning after
that, eight pennies.
Suppose that you could keep making a single stack of the pennies. After how many days would the stack be long enough to reach a star that is about 3x10¹3 km
away? (Assume that 1 penny = 1.5 mm)
The number of days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days
How to find the number of days the penny would stack?Since from the question, we see that the number of pennies double with each day. It forms a geoemetric progression with
first term a = L and common ratio , r = 2.Since the number of pennies after n days equals N = 2ⁿ
Let
L = length of 1 penny = 1.5 mm = 1.5 × 10⁻³ mSo, after n days, the length of the stack of pennies is the geoemetric progression D = 2ⁿ × L
Number of days pennies would stack to reach starMaking n subject of the formula, we have
n = ㏒(D/L)/㏒2
Since D = the distance of the star = 3 × 10¹³ km = 3 × 10¹⁶ m, and L = length of 1 penny = 1.5 mm = 1.5 × 10⁻³ mSubstituting the values of the variables into the equation, we have
n = ㏒(D/L)/㏒2
n = ㏒(3 × 10¹⁶ m/1.5 × 10⁻³ m)/㏒2
n = ㏒(3/1.5 × 10¹⁹)/㏒2
n = ㏒(2 × 10¹⁹)/㏒2
n = ㏒2 + ㏒10¹⁹/㏒2
n = (19㏒10 + ㏒2)/㏒2
n = (19 + 0.3010)/0.3010
n = 19.3010/0.3010
n = 64.1
n ≅ 64 days
So, the number of days would the stack be long enough to reach a star that is about 3 × 10¹³ km away is 64 days
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simplify the equation ( 3(3) × 3 (4) ) ÷ 3 (2)
Answer:
(3(3) × 3(4) ) ÷ 3(2)
(9 × 12) ÷ 6
108 ÷ 6
18
On a coordinate plane, 2 parallelograms are shown. Parallelogram 1 has points (0, 2), (2, 6), (6, 4), and (4, 0). Parallelogram 2 has points (2, 0), (4, negative 6), (2, negative 8), and (0, negative 2). How do the areas of the parallelograms compare? The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2. The area of parallelogram 1 is 2 square units greater than the area of parallelogram 2. The area of parallelogram 1 is equal to the area of parallelogram 2. The area of parallelogram 1 is 2 square units less than the area of parallelogram 2
The area of parallelogram 1 is 4 square units greater than the area of parallelogram 2
How to compare the areas?The coordinates are given as:
Parallelogram 1: (0, 2), (2, 6), (6, 4), and (4, 0).
Parallelogram 2: (2, 0), (4, -6), (2, -8), and (0, -2)
Next, calculate the base and the height
For parallelogram 1, we have:
Base = (0, 2) and (2, 6)
Height = (6, 4), and (4, 0).
So, we have:
[tex]Base = \sqrt{(0 - 2)^2 + (2 -6)^2} = \sqrt{20}[/tex]
[tex]Height = \sqrt{(6 - 4)^2 + (4 -0)^2} = \sqrt{20}[/tex]
The area is:
Area = Base * Height
Area = √20 * √20
Area = 20
For parallelogram 2, we have:
Base = (0, -2) and (4, -6)
Height = (4, -6) and (2, -8)
So, we have:
[tex]Base = \sqrt{(0 -4)^2 + (-2 +6)^2} = \sqrt{32}[/tex]
[tex]Height = \sqrt{(4 - 2)^2 + (-6 +8)^2} = \sqrt{8}[/tex]
The area is:
Area = Base * Height
Area = √32 * √8
Area = 16
By comparing both areas, we have:
20 is greater than 16 by 4
This means that the area of parallelogram 1 is greater by 4 units
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Smallest to greatest 4/9, 4.9, 49%
Answer:
4/9, 49%, 4,9
Step-by-step explanation:
4/9=0,444444
49%=0,49
4,9=4,9
An equilateral triangle has the height BO= 80 cm. Considering, height BO splits the base (segment) AC into two equal segments of size x/2, find X.
Answer:
Given - an equilateral triangle
An equilateral triangle means all sides equal and all angle equal to 60°
In triangle BOA
sin 60° = OB/ AB
√3/2. = 80/AB
AB = 160√3/3
X = 160√3/3
If you receive a 25% DISCOUNT off an item costing $22.00, how much money do you save?
Answer:
The amount of money you saved by receiving a discount of 25% is $5.5
Step-by-step explanation:
Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price. Selling price is the actual price at which an article is sold after any reduction or discounts in the cost price.
discount is always calculated on the cost price of the article
formula to calculate the discount and discount %
Discount = List Price - Selling Price
Discount (%) = (Discount/cost price) × 100
here, in the question discount % is given = 25%
cost price of the item = $22
therefore using the above mentioned discount percentage formula:
25 = (Discount/22)×100
25/100 = Discount/ 22
0.25 × 22 = Discount
$5.5 = Discount
thus ,
the amount of many you saved by receiving a discount of 25% is $5.5
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please help, performance task: trigonometric identities
The solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)
How to solve the trigonometric equations?Equation 1: 1 - cos(x) = 2 - 2sin²(x) from (-π, π)
The equation can be split as follows:
y = 1 - cos(x)
y = 2 - 2sin²(x)
Next, we plot the graph of the above equations (see graph 1)
Under the domain interval (-π, π), the curves of the equations intersect at:
(-π/3, 0.5) and (π/3, 0.5)
Hence, the solutions to 1 - cos(x) = 2 - 2sin²(x) from (-π, π) are (-π/3, 0.5) and (π/3, 0.5)
Equation 2: 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π)
The equation can be split as follows:
y = 4cos⁴(x) - 5cos²(x) + 1
y = o
Next, we plot the graph of the above equations (see graph 2)
Under the domain interval [0, 2π), the curves of the equations intersect at:
(π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)
Hence, the solutions to 4cos⁴(x) - 5cos²(x) + 1 = 0 from [0, 2π) are (π/3, 0), (2π/3, 0), (π, 0), (4π/3, 0) and (5π/3, 0)
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This question was confusing 15 for whoever answers
Answer:
Refer to the attached image. I'm not clear on one point. Yes, it is confusing.
Step-by-step explanation:
See attached image.
