Answer:
Step-by-step explanation:
Converting 0.632 to a fraction, Step-by-Step
Step 1:
The first step to converting 0.632 to a fraction is to re-write 0.632 in the form p/q where p and q are both positive integers. To start with, 0.632 can be written as simply 0.632/1 to technically be written as a fraction.
Step 2:
Next, we will count the number of fractional digits after the decimal point in 0.632, which in this case is 3. For however many digits after the decimal point there are, we will multiply the numerator and denominator of 0.632/1 each by 10 to the power of that many digits. For instance, for 0.45, there are 2 fractional digits so we would multiply by 100; or for 0.324, since there are 3 fractional digits, we would multiply by 1000. So, in this case, we will multiply the numerator and denominator of 0.632/1 each by 1000:
\frac{0.632 × 1000}{1 × 1000} = \frac{632}{1000}
1×1000
0.632×1000
=
1000
632
Step 3:
Now the last step is to simplify the fraction (if possible) by finding similar factors and cancelling them out, which leads to the following answer:
\frac{632}{1000} = \frac{79}{125}
1000
632
=
125
79
what can you say about the series ∑an in each of the following cases
a) lim |(an+1)/(an)∑|=1
n→[infinity] b) lim nth root(|(an)|=2/3
n→[infinity]
c) lim |(an+1)/(an)|=0.8
n→[infinity]
d) lim |(an+1)/(an)|=3/2
n→[infinity]
e) lim |(an+1)/(an)|=3
n→[infinity]
f) lim nth root(|(an)|=1/2
n→[infinity]
In each of the cases, the series ∑an is convergent. This means that the limit of the sequence of partial sums of the series is finite.
In case a, since the limit of the ratio of consecutive terms is 1, the series is convergent and its sum is equal to the limit of the sequence of partial sums of the series.In case b, since the limit of the nth root of the absolute value of the terms is 2/3, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case c, since the limit of the ratio of consecutive terms is 0.8, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case d, since the limit of the ratio of consecutive terms is 3/2, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case e, since the limit of the ratio of consecutive terms is 3, the series is convergent and its sum is equal to the limit of the sequence of partial sums.In case f, since the limit of the nth root of the absolute value of consecutive terms is 3/2, the series is convergent and its sum is equal to the limit.Learn more about Convergent here:
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What's the value of the following game: You roll a 100 sided die with sides 1-100. You can either take this number of dollars, or pay $1 to roll again. You can keep on paying $1 to roll for as long as you like.
You roll a 100 sided die with sides 1-100. The optimal strategy is to stop and cash out only if the dice shows 87 or higher , else keep spending $1 to roll again n again, leading to expected winning of $87.35.
Can a die have 100 sides?The 100-sided die Lou Zocchi created is known by the trademark "Zocchihedron," and it made its debut in 1985. It assumes the appearance of a ball with 100 flattened planes, unlike other polyhedran dice. It is also known as "Zocchi's Golfball."
optimal strategy is to stop and take dollar if roll > x, and to pay $1 and continue when roll <= x (as applicable to all/any turn/roll). We need to find x in order to maximize E.
Assuming optimal expected value to be E, once you cast the first roll, there are two possible scenario:
1) we get roll value > x with probability (100-x)/100, and decide to take that amount, expected winning = (x+1+100)/2 (that amount varies uniformly from x+1 to 100 in this case, take the average)
2) we get roll value <= x with probability x/100 and decide to continue, with future expected winning again = E and 1$ loss in fee. Total expected winning in this scenario = E-1
[math]E=\frac{(100-x)}{100}\times\frac{ (x+1+100)}{2}[/math][math] + \frac{x}{100}\times(E-1)[/math]
[math]E = \frac{(100-x)(101+x) - 2x}{200 - 2x}[/math]
maximizing E w.r.t. x,
dE/dx = 0
2x^2 - 400x + 19600 = 0
x = ( 400+/- sqrt(160000-4*2*19600) ) / 4
Since, 1<= x <= 100, therefore x = ( 400+ sqrt(160000-4*2*19600) ) / 4
x = 85.85786
We just have to calculate E(x=85) and E(x=86) and compare.
E((x=86) = 87.35 and E(x=85) = 87.33
so optimal strategy is to stop and cash out only if the dice shows 87 or higher , else keep spending $1 to roll again n again, leading to expected winning of $87.35.
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The reasons as well as the answer
Answer:
x = 46, y = 67
Step-by-step explanation:
x = ∠ AEC = 46 ( alternate angles )
Since Δ ACE is isosceles then the base angles are congruent, then
y = [tex]\frac{180-46}{2}[/tex] = [tex]\frac{134}{2}[/tex] = 67
Answer:
x=46° and y=67°
Step-by-step explanation:
triangle ACE is isosceles, meaning <A=<B=y
any triangle is add up to 180. <A+<B+<C=180
y+y+46=180
2y=180-46
2y=134
divide both sides by 2
y=134/2
y=67°
for angle x°
since AB is parallel to CD,hence
<AEC=<ECD
x=46°
please help, I really need to pass this class!
Answer:
y=1.5x+2
Step-by-step explanation:
Mark me brainliest pls
2 is the y intercept so a+ 2 is already part of the equation
slope = y2-y1/x2-x1
6-4.5/2-1 = 1.5
y=1.5x + 2
area de un triangulo rectangulo si saben digame por favorrrrr
$200 for 12 piano lessons
Answer: Is the question to find unit price, if it is, the answer is $16.77. Divide 200/12 to get the unit price. Hope this helps and good luck to having a bright future ☀️
Step-by-step explanation:
(15,17,21,6,3) order each set of integers from least to greatest
Answer: 3, 6, 15, 17, 21
Step-by-step explanation:
Help please with this maths
The radius of the sphere is 9 cm.
What is a sphere?It is a three-dimensional figure where the volume is given as:
The volume of a sphere is 4/3πr³.
We have,
The surface area of a sphere = 324π cm²
4πr² = 324π
r² = 324/4
r² = 81
r = √81
r = ±9
r = -9 cm (rejected)
r = 9 cm
Thus,
The radius is 9 cm.
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What is the mean absolute deviation and population standard deviation of this data set? 1, 4, 6, 7, 9, 9
Answer:
a)2.33
b) 2.83
Step-by-step explanation:
What is the mean absolute deviation and population standard deviation of this data set? 1, 4, 6, 7, 9, 9
Step 1
Find the Mean
n = 6
Mean = Sum of values/Number of value
= 1 +4 + 6 +7 + 9+ 9/6
= 36/6
= 6
a) Mean Absolute Deviation
Formula
= |x - Mean|/n
= | (1 - 6)+(4 - 6) + (6 - 6)+(7 - 6)+ (9 - 6) + (9 - 6)|/6
= 5 + 2 + 0 + 1 + 3 + 3/6
= 14/6
= 2.3333333333333
Approximately = 2.33
b) Population Standard deviation
Formula
=√(x - Mean)²/n
= √ (1 - 6)²+(4 - 6)² + (6 - 6)² +(7 - 6)² + (9 - 6)² + (9 - 6)²/6
= √25+ 4+0+ 1+ 9+9/6
= √48/6
= √8
= 2.828427125
Approximately = 2.83
5. A history lecture hall class has 15 students. There is a 15% absentee rate per class meeting.
a.) Find the probability that exactly one student will be absent from class. (5 points) b.) Find the probability that at least 2 students will be absent from class. (10 points)
Answer:
I think the answer is A
Sorry if i am wrong
Step-by-step explanation:
Indicated angles :
6. Find the measures of the indicated angles. Give reasons for your answers
Answer:
k\
Step-by-step explanation:
j
Need answers pls answers
Answer:
Thjs is hard mat
Step-by-step explanation:
I just need points mateeeee
Determine if the triangles can be proved congruent by SSS, SAS, ASA, AAS, or HL.
The triangles can be proved congruent by SAS theorem.
Properties of congruent triangles.Two or more triangles are said to be congruent if their corresponding length of sides and measure of internal angles are equal. Therefore, congruency is a property of equality of the triangles.
To prove that two or more triangles are congruent, then their corresponding sides are compared if they are equal. Also the measure of their corresponding internal angles are considered if they are equal.
Therefore in the given question, to determine if the triangles can be proved congruent by the appropriate theorem;
Opposite sides of a parallelogram are equal in length. Thus, it can be seen that the two sides of the triangles are equal. Also the measure of their included angles are equal. Therefore, the triangles can be proved to be congruent by SAS.
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which rule can be used to find the output numbers in this table
What is the intercept of this line? y−6=4(x+5)
Answer:
[tex]y-intercept=(0,26)[/tex]
[tex]x-intercept=(-13/2,0)[/tex]
Step-by-step explanation:
Given
[tex]y-6=4(x+5)[/tex]
→ [tex]y=4(x+5)+6[/tex]
→ [tex]y=4x+20+6[/tex]
→ [tex]y=4x+26[/tex]
To find the y-intercept we will plug in x=0
y=4(0)+26=26Now to find the x-intercept we will plug in y=0
[tex]0=4x+26\\[/tex]
→ [tex]4x=-26[/tex] → [tex]x=\frac{-26}{4}[/tex]
x= -13/2[tex]-------------[/tex]
hope it helps...
have a great day!!!
Refer to the equation a-6 equals b if a equals 45 what is the value of b?
Answer:
Step-by-step explanation: a=4, b=2.
Answer:
b = 39
Step-by-step explanation:
[tex]a-6=b[/tex]
if a = 45:
[tex]45-6=b\\39=b[/tex]
Hope this helps
help me with this plz
Answer:
https://dlsfile.com/dd/MTQ1ODE5dnJpZ3doanhobV8zNDEzMjU
Step-by-step explanation:
I would help you.. but after what u did I'd rather do my work instead then helping you.. and see how it feels
GGFCTVBHBGVGBHTVfhjdcnjddjhfbvncdfbvf
DFGTBHGVFGHNHYJ dhnchvfdhngvjgf
PLEASE HELP...
Find the area of the composite shape. Show your work for BRAINLIST and if it’s correct
Answer:
4+
5+4+2
+2+4+9+3
+3.5+3.5
=99cm
Which situation results in a final value of zero?
Answer:
The total profit made when a person buys an item for $2.25 and then sells the item for $2.25.
Step-by-step explanation:
The item is bought for $2.25 and sold for the same rate. There is no profit.
Final value is 0.
Given P(A and B)= 0.09, P(B)= 0.25. FIND P(A given B)
A:0.34
B:0.29
C:0.02
D:0.36
Answer:
the answer would be C
Step-by-step explanation:
What kind of line is y 2x 3?
Answer: It is a straight line
Step-by-step explanation:
Find the measures of the angles
Answer:
（1）：
angle1/2/3/4=90
angle6=51
angle7=40
angle8=89
angle9=51
angle10=40
angle12=50
angle13=130
angle14=50
Step-by-step explanation:
Q1：
angle1 2 3 4 divided 360 into four equal parts
so 360/4=90
angle11=110degree
so angle12 is 180-130=50 degree
because angle 12 3 10 are in triangle
their sum is 180
so angle 10=180-90（angle3）-50（angle12）=40
because angle 10 5 6 sum is 180
so angle 6 is=180-89（angle5）-40（angle10）=51
because angle 5 6 7 sum is 180
angle7=180-51（angle6）-89（angle5）=40
angle8=angle5=89
angle9=angle6=51
angle12 &13sum is 180
so angle13=180-50=130
angle14=angle12=50
Find the 19th term of the sequence 5, 8, 11, 14, 17...
59
51
53
56
Answer:
59
Step-by-step explanation:
So, lets look at our numbers in the sequence. So it goes 5 to 8, 8 to 11, 11 to 14, and 14 to 17. This seems like a change in three. So the every 1 term changes the orginal 5 value by 3.
So wouldnt this mean we can multiply the change in terms by the amount of terms? Which is 19*3? Well, sort of. This is the right way of doig this, but we must remember that we already know the first term, 5. So this means we will be doing 18*3.
This gets you 54. Now just add the amount of the 18 terms onto the first term:
54+5
=
59
So your answer is 59.
Hope this helps!
Which table shows a proportional relationship between x and y?
Answer:
C
Step-by-step explanation:
Put in the form y/x and you should have equivalent fraction
12/4 = 3
15/5 = 3
18/6 = 3
When the fractions are simplified, they all equal 3.
Luis made an error when he used the distributive property to solve the problem shown. Which sentence describes the error? https://content.thinkthroughmath.com/uploads/media_library/item/31517/L59
Answer:
in step 2, 60 should be multiplied by the quantity 8-15, not by 8
Step-by-step explanation:
i looked at the image they provided and figured this out, and solved it on my own account but the image wont load
please give the correct answer and no links!
Answer:
KL ≈ 16.6 ft
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos25° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{MK}{KL}[/tex] = [tex]\frac{15}{KL}[/tex] ( multiply both sides by KL )
KL × cos25° = 15 ( divide both sides by cos25° )
KL = [tex]\frac{15}{cos25}[/tex] ≈ 16.6 ft ( to the nearest tenth )
In the diagram below of parallelogram ABCD with diagonals AC and BD, m∠1=45° and m∠DCB=120°.Whatisthemeasureof∠2?
Answer:
15degrees
Step-by-step explanation:
From the given diagram
<1+<2 + <DCB = 180
<1+<2+120 = 180
<1+<2 = 180 - 120
<1+<2 = 60
<2 = 60 - <1
<2 = 60 - 45
<2 = 15degrees
Hence the measure <2 is 15degree
please help with math!!
Answer:
Trinomial
Step-by-step explanation:
If there is 1 term, monomial
2 term - binomial
3 term- trinomial
When 32 is subtracted from the square of a number, the result is 4 times the number. Find the positive solution
Step-by-step explanation:
x² - 32 = 4x
x² - 4x - 32 = 0
with a little bit experience we see immediately that this is
(x - 8)(x + 4) = 0
the positive x for this to be true is x = 8.
formally, the solution to a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x = (4 ± sqrt((-4)² - 4×1×-32))/(2×1) =
= (4 ± sqrt(16 + 128))/2 = (4 ± sqrt(144))/2 =
= (4 ± 12)/2 = 2 ± 6
x1 = 2 + 6 = 8
x2 = 2 - 6 = -4
we were right at the beginning.
the positive solution is x = 8.
how do I find the slope of these points
(8,-4) and (2,-4)
[tex](\stackrel{x_1}{8}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{8}}} \implies \cfrac{-4 +4}{-6} \implies \cfrac{ 0 }{ -6 } \implies \text{\LARGE 0}[/tex]