The Egyptian fraction representation for 7/9 using Fibonacci's Greedy Algorithm is 1/8 + 1/5 + 1/3 + 1/1080 = 711/1080.
Let's find the Egyptian fraction representation for the fraction 7/9.
1. Begin by representing the fraction 7/9 visually with a rectangle. Divide the rectangle into 9 equal parts horizontally and mark 7 parts.
```
---------------
| | | | | | | |
---------------
```
2. Now, let's use Fibonacci's Greedy Algorithm to find the Egyptian fraction representation for 7/9.
a. Start with the largest Fibonacci number less than or equal to the denominator, which in this case is 8 (Fibonacci sequence: 1, 1, 2, 3, 5, 8).
b. Take one unit of this Fibonacci number and mark it as a fraction on the rectangle.
```
---------------
| | | | | | | |
----|----------
```
c. Subtract this fraction (1/8) from the original fraction (7/9) to get 7/9 - 1/8 = 41/72.
d. Repeat steps a-c with the remaining fraction (41/72) until the numerator becomes 1.
e. The sum of the fractions obtained in step b will be the Egyptian fraction representation of 7/9.
3. Applying the algorithm further:
a. The largest Fibonacci number less than or equal to the remaining fraction (41/72) is 5.
b. Take one unit of this Fibonacci number and mark it as a fraction on the rectangle.
```
---------------
| | | | | | | |
----|----|-----
```
c. Subtract this fraction (1/5) from the remaining fraction (41/72) to get 41/72 - 1/5 = 7/360.
d. Since the numerator is still greater than 1, we need to repeat steps a-c.
e. The largest Fibonacci number less than or equal to 7/360 is 3.
f. Take one unit of this Fibonacci number and mark it as a fraction on the rectangle.
```
---------------
| | | | | | | |
----|----|-----
|
```
g. Subtract this fraction (1/3) from the remaining fraction (7/360) to get 7/360 - 1/3 = 1/1080.
h. Since the numerator is now 1, we stop the algorithm.
4. The sum of the fractions obtained in step b is the Egyptian fraction representation of 7/9:
1/8 + 1/5 + 1/3 + 1/1080 = 135 + 216 + 360 + 1/1080 = 711/1080.
Therefore, the Egyptian fraction representation for 7/9 using Fibonacci's Greedy Algorithm is 1/8 + 1/5 + 1/3 + 1/1080 = 711/1080.
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Jess is having a private party at the bowling alley. The party costs $99 plus %3 per person who attends.
Answer:
Total cost= 99 + 2.97x
Step-by-step explanation:
Giving the following information:
Fixed cost= $99
Variable cost= 3% per person
First, we need to calculate the 3% of 99:
Unitary variable cost= 99*0.03= $2.97
Now, we establish the total cost structure:
Total cost= 99 + 2.97x
x= number of people in attendance
Finally, suppose 200 people attend the party:
Total cost= 99 + 2.97*200
Total cost= $693
The students in Mr. Andersen's science class counted the number of leaves on each of 11 different rose bushes. The data they collected is:
26, 54, 38, 65, 58, 35, 52, 43, 55, 41, 61
What is the range of the set of data?
Answer:
35
Step-by-step explanation:
subtract highest and lowest numbers
Answer this question
y is less than or equal to three more than the product of x and negative two thirds put it on standard form
Using the standard Normal distribution tables, what is the area under the standard Normal curve corresponding to Z<0.75? a.0.7223 b.0.7734 Oc 0.9127 d.0.6915 QUESTION 26 Given the least squares regression line y-3 x-3, which of the following is true? a. The relationship between x and y is positive. b. The relationship between x and y is negative. c. As x decreases, y increases. d. None of the answer options is correct.
The least squares regression line y-3 x-3 is (a) "The relationship between x and y is positive."
To get the area under the standard Normal curve corresponding to Z < 0.75, we can use the standard Normal distribution tables. The tables provide the cumulative probability up to a given Z-score.
Looking up the value of 0.75 in the standard Normal distribution table, we find that the corresponding area is approximately 0.7734.
Therefore, the answer is (b) 0.7734.
Regarding the least squares regression line y = 3x - 3, we can make the following observations:
a. The relationship between x and y is positive: This is true because the coefficient of x (3) is positive, indicating a positive relationship between x and y.
b. The relationship between x and y is negative: This is false because the coefficient of x (3) is positive, indicating a positive relationship between x and y.
c. As x decreases, y increases: This is false because as x decreases, y will also decrease based on the equation y = 3x - 3.
d. None of the answer options is correct: This is false because option (a) "The relationship between x and y is positive" is correct.
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In a particular region, 6% of the population is thought to have a certain disease. A standard diagnostic test has been found to correctly identify 91% of the people who have the disease. However, the test also incorrectly diagnoses 8% of those who do not have the disease as having the disease (in other words, the person does not have the disease but the test tells them that they do). A randomly selected person in the region is tested for the disease. (a) What is the probability the test comes back positive
Answer:
The positive predictive value ≈ 30.012%
Step-by-step explanation:
(a) The given percentage of the people in the region that have the disease, P(D) = 6% = 0.06
The percentage people correctly identified as having the disease by the standard diagnostic test = 91%
The percentage of people incorrectly identified as having the disease by the standard diagnostic test, P(T + |H) = 8%
Therefore, the sensitivity of the test, P(T + |D) = 0.91
The specificity of the test, P(T - |H) = 1 - 0.08 = 0.92
Therefore, the probability that a person is healthy, P(H) = 1 - 0.06 = 0.94
Therefore, in a population of 1,000 people, 60 people have the disease, with a sensitivity of 91%, the test will correctly pic 0.91×66 = 60.06 people correctly with the disease and 0.91 × 940 = 855.4 people without the disease
The number of non-diseased that test positive by the test is 0.08 × 1000 = 80 people which are false positives
Therefore, the number of diseased diagnosed as negative is 0.08 × 60 = 4.8
Therefore, we have;
[tex]\begin{array}{cccc}&Deseased&Non-diseased& Diseased + Non-diseased\\Test \ +ve&60.06&80& 140.06\\Test \ -ve&4.8&855.4&\end{array}[/tex]
The positive predictive value = Diseased +ve/(Diseased +ve + Non-diseased +ve)
[tex]The \ positive \ predictive \ value = \dfrac{Diseased +ve}{Diseased +ve + Non-diseased +ve} \times 100[/tex]
Therefore;
The positive predictive value = 60.06/(60.06 + 140.06) × 100 ≈ 30.012%
approximate the sum of the series correct to four decimal places. [infinity] (−1)n − 1n2 8n n = 1
To approximate the sum of the series [infinity] (−1)n−1n^2/(8n), we can use a numerical method such as the partial sum method.
Let's calculate the partial sums of the series and add up terms until the sum converges to a desired level of accuracy. We will stop adding terms once the absolute difference between two consecutive partial sums is less than the desired accuracy.
Let's start by calculating the partial sums:
S_1 = (-1)^1-1(1^2)/(81) = 1/8
S_2 = (-1)^2-1(1^2)/(82) + (-1)^1-1(2^2)/(82) = 1/8 - 1/16 = 1/16
S_3 = (-1)^3-1(1^2)/(83) + (-1)^2-1(2^2)/(83) + (-1)^1-1(3^2)/(83) = 1/8 - 1/16 - 1/24 = -1/24
We can observe that the partial sums alternate between positive and negative values. This indicates that the series does not converge to a specific value but oscillates between two values.
To approximate the sum, we will calculate partial sums until the difference between two consecutive partial sums is less than the desired accuracy. Let's say we want the accuracy to be 0.0001.
Let's continue calculating partial sums:
S_4 = (-1)^4-1(1^2)/(84) + (-1)^3-1(2^2)/(84) + (-1)^2-1(3^2)/(84) + (-1)^1-1(4^2)/(84) = 1/8 - 1/16 - 1/24 + 1/32 = -1/48
S_5 = (-1)^5-1(1^2)/(85) + (-1)^4-1(2^2)/(85) + (-1)^3-1(3^2)/(85) + (-1)^2-1(4^2)/(85) + (-1)^1-1(5^2)/(8*5) = 1/8 - 1/16 - 1/24 + 1/32 + 1/40 = 1/120
The difference between S_4 and S_5 is 1/120 - (-1/48) = 1/120 + 1/48 = 1/80, which is greater than 0.0001.
Therefore, we can approximate the sum of the series as -1/48, correct to four decimal places.
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A cylinder has been cut out of a solid. Find the volume of the remaining solid. Round answer to the nearest tenth.
Answer:
98.19
Step-by-step explanation:
Volume of whole cube minus volume of cylinder. volume of cylinder is pi x r^2 x h
The volume of remaining solid is 46.44 in³
What is Volume?Volume is the measure of the capacity that an object holds.
For example, if a cup can hold 100 ml of water up to the brim, its volume is said to be 100 ml. Volume can also be defined as the amount of space occupied by a 3-dimensional object. The volume of a solid like a cube or a cuboid is measured by counting the number of unit cubes it contains. The best way to visualize volume is to think of it in terms of the space.
How To Calculate the Volume?Here are the steps to calculate volume of any solid shape:
Identify all the given parameters that are useful and are required to substitute in the respective volume formula. Such as the radius to be 'r' and height to be 'h', the slant height, diameter, etc.Make sure all the parameters are of the same units.Substitute the values in the volume formula of the respective shapes.Write the units as cubic units.edge= 6
Volume of cube= l³
= 6*6*6
=216 in³
Now, Volume of cylinder
=πr²h
= 3.14 * 3 * 3 * 6
=169.56 in³
Volume of remaining solid= 216- 169.56
=46.44 in³
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Puzzle One
Determine the correct vocabulary word(s) in the questions below. To break the code of puzzle
one you will need to determine the third letter of the word in EACH space and then put those
letters in alphabetical order to break the code. For example, if the first blank was MODE the
letter you would use to help you break out would be D.
*Hint: Use the word bank to help you, some words may be used more than once and some may
not be used at all.
1) The
tells you how the data is spread out
of the data.
for
2) The might be a better representation of the data if there are
outliers that skew the data.
3) To find the
of
you add the numbers and
by the quantity
distance between
4) The Mean Absolute Deviation (MAD) is the
each
point and the
MODE
MEDIAN
MEAN
RANGE
NUMBERS
QUARTILE
Word Bank:
MULTIPLY
AVERAGE
DIVIDE
SUBTRACT
INNER
DATA
FIFTY
TWENTY
PERCENT
Code:
Math in the Mid 2019
MI
Answer:
Ошйжй Щ отдйдй шубу Ц дцдць о о
Step-by-step explanation:
corine in making potato salad for each bowl of potato salad she needs 1/4 cup of potatoes how many cups of potatoes will she use if she makes 32 bowls of potato salad ?
Answer:
8 cups of potatoes are needed
Step-by-step explanation:
One way of doing this work is to write out
1/4 cup 1 cup
------------- , which is equivalent to ------------ (a unit rate)
1 bowl 4 bowl
and then multiply this unit rate by 32 bowls:
(1/4)(32 bowls) = 8 cups of potatoes are needed
Draw a graph which has the following adjacency matrix: [2 1 1 0] 1 0 0 1 1 0 0 1 0 1 1 0 (b) Label the vertices of your graph A,B,C,D (in any order). (c) How many different paths of length 10 are there from the vertex you labelled A to the vertex you labeled D in the graph you draw in part (a)? Show your working.
In the drawing a graph is there with labeling of vertices A,B,C,D with matrix [tex]\begin{bmatrix}2 &1 & 1&0\\1 & 0 & 0&1\\1&0&0&1\\0&1&1&0\end{bmatrix}[/tex].
Given that,
a. We have to draw a graph which has the following adjacency matrix
[tex]\begin{bmatrix}2 &1 & 1&0\\1 & 0 & 0&1\\1&0&0&1\\0&1&1&0\end{bmatrix}[/tex]
Taking the matrix rows and column as A,B,C,D.
Therefore, In the drawing the graph is with matrix.
(b) We have to label the vertices of your graph A,B,C,D.
The drawing can be seen with the label of vertices A,B,C,D.
(c) We have to find how many different paths of length are there from the vertex you labelled A to D
A →A →B →A→A→B→A→C→D
A→A→A→A→A→C→D
A→A→A→A→A→B→D
Therefore, In the drawing a graph is there with labeling of vertices A,B,C,D with matrix [tex]\begin{bmatrix}2 &1 & 1&0\\1 & 0 & 0&1\\1&0&0&1\\0&1&1&0\end{bmatrix}[/tex].
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Help please the question is in the photo
PLEASE HELP I WILL GIVE BRAINLIEST IF YOU DO BOTH
please give me a real answer
Answer:
Q2. angle 5 +angle 6=90°
angle 5+ 6°=90°
angle 5=90°-6°
angle 5=84°
Q.3 angle 8+angle 9=90°
angle 8 + 11°=90°
angle 8=90°-11°
angle 8=79°
Glenn needs to cut pieces of ribbon that are each 1 meter long to make ribbon key chains. If he has 6 pieces of ribbon that are each 1 dekameter long, how many 1−meter pieces of ribbon can he cut?
Answer: 60
Step-by-step explanation:
1=10. x6=60
The product of 3 consecutive even integers is equal to the cube of the first plus the square of the second plus twice the square of the third. Find the integers. Please show work.
Answer:
6, 8 and 10 and -2, 0, 2
There are two roots x = -2 and 6,
but the since I don't believe 0 is an even number the answer is 6, 8 and 10
I was incorrect according to G0ggle zero is an even number so another answer is -2, 0, 2
Step-by-step explanation:
read the question and convert the English to mathematics
x, y and z even consecutive number
y = x+2
z = y+2 = x+4
and
xyz = x³ + y² + 2z² substitiute x terms in for y and z
x(x+2)(x+4) = x³ + (x+2)² + 2(x+4)² solve for x by graphing on DEMOS
x = -2, 6 solved algebraically below
x = -2 y=0 z=2
x = 6 y=8 z=10
Checked both answers
xyz = x³ + y² + 2z²
-2(0)2 = -8 + 0 + 8 when x = -2
0 = 0
and
6(8)(10) = 6³ + 8² +2(10)² when x = 6
480 = 216+64+200
= 480
x(x+2)(x+4) = x³ + (x+2)² + 2(x+4)² solved algebraically
(x²+2x)(x+4) = x³ + x² +4x +4 + 2x² + 16x + 32
x³ + 6x² + 8x = x³ + x² +4x +4 + 2x² + 16x + 32
x³ + 6x² + 8x = x³ + 3x² + 20x + 36
3x² - 12x - 36 = 0 factor out the 3
3[x² - 4x - 12] = 0
3(x+2)(x-6) = 0 x = -2 and -12
6th grade math plz help
Answer:
The question needs more information but you can see that all the numbers in the 1st column are multiplied by 6 to equal the number in column 2
Step-by-step explanation:
3 x6 =18
6 x 6= 36
9 x6= 54
12 x6 =72
Find m QRS? who can help me?
Answer:
m<PRS+m<PRQ=m<QRS.
17 + 17 = 34
m<QRS=34
Help ASAP 15 Points
The hot water heater in the Alvarez's home holds 70 gallons of water. Each shower taken uses 5.4 gallons
of water. How much water is left after 3 showers. (Hint: Write an equation relating the number of showers and
the number of gallons left in the tank)
Answer:
53.8 gallons
Step-by-step explanation:
5.4*3=16.2
5.4 (gallons used per shower) * 3 (number of showers) = 16.2 (gallons used in 3 showers)
70-16.2=53.8
70 (Water in tank) - 16.2 (gallons used in 3 showers) = 53.8 (gallons of water left)
Hope this helps! Please brainliest!!!
Answer:
A(3) = 53.8 gallons left after 3 showers
Step-by-step explanation:
A(x) = volume of water left in tank = 70 gallons - (5.4 gallons)x, where x is the number of showers already taken.
After 3 showers, the volume of water left is A(3) = 70 gal - (5.4 gallons)(3), or
A(3) = 53.8 gallons left after 3 showers
Can anyone solve these please, cos I'm nucklehead and my brain won't work
×-10=13
t+20=44
y
_ =7
5
Answer:
Hello There!!
Step-by-step explanation:
1.×-10=13. 13+10=23
2.t+20=44. 44-20=24
3.y/5=7. 5×7=35
You do the inverse operations to find the unknown number.For example if it is minus you do plus. e.g x-7=19 . 19+7=26
hope this helps,have a great
HELP
I WILL GIVE YOU BRAINLIEST
Give the solution to this quadratic.
y = 3(x-1)^2
Answer:
y=3x^2-6x+3
Step-by-step explanation:
give the slope of the line with equation 17x = -34; then graph the line
Answer:
Slope: Undefined
Step-by-step explanation:
Find the exact value of tan A in simplest radical form
Answer:
12.68 de
Step-by-step explanation:
Can we just get rid of math forever?
Answer:
I don't think so .... :(((
Can someone help me with this. Will Mark brainliest.
Answer:
(1.5, -4)
Step-by-step explanation:
( -1, -5) and (4, -3)
[tex](\frac{-1+4}{2} ,\frac{-5-3}{2} )\\\\(\frac{3}{2} ,\frac{-8}{2} )\\\\(1.5,-4)[/tex]
What is the area of the triangle in square yards?
6 yd.
15 3/4 yd.
Answer:
6x15 2/4 yd dividedby 2
Step-by-step explanation:
do the math and u get ur answer
HELP
Is x+7 a factor of p(x)
Answer:
No
Step-by-step explanation:
Because the remainder is not zero
Jimrgrant or Someone Answer this PLZ
Answer:
C and A
Step-by-step explanation:
For the triangle to be isosceles then the legs are congruent, that is
XZ = XY , substitute values
5x - 1 = 3x + 5 ( subtract 3x from both sides )
2x - 1 = 5 ( add 1 to both sides )
2x = 6 ( divide both sides by 2 )
x = 3 → C
(10)
The diagonals of a square bisect each other
Calculate PR using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2-y_{1})^2 }[/tex]
with (x₁, y₁ ) = P(0, 0) and (x₂, y₂ ) = R(6, - 8)
PR = [tex]\sqrt{(6-0)^2}+(-8-0)^2[/tex]
= [tex]\sqrt{6^2+(-8)^2}[/tex]
= [tex]\sqrt{36+64}[/tex]
= [tex]\sqrt{100}[/tex]
= 10
Then
PT = 0.5 × 10 = 5 → A
Factor the expression: 2x^2 +21x+49
Answer:
(2x+7)(x+7)
Step-by-step explanation:
CAN SOMEONE PLEASE HELP!!! I DONT UNDERSTAND. I WILL GIVE BRAINLIEST!!!
Answer:
586.76
Step-by-step explanation:
Take the area of the rectangular prism = 348
Find the area of the cylinder = 477.52
Divide the cylinder by 2 = 238.76
Add both together = 586.76
Michael wants to know if support for a local referendum on gay rights is related to political party affiliation. He conducts a survey of 200 local residents and asks them their political party affiliation and whether they intend to vote for or against the referendum. He learns that 16 people who say they are republican are for the referendum and 54 are against. Of those who say they are democrat, 72 people are for the referendum and 28 are against it. Some people identified as "other" and among that group, 3 were against the referendum and 27 were in favor of it. How would you represent the data in a table? Identify the null and alternative hypothesis. Conduct the appropriate analysis with a=.05. What should Michael conclude?
The answer is the test statistic (13.765) is greater than the critical value (5.991), we reject the null hypothesis. Therefore, we can conclude that there is a significant relationship between political party affiliation and support for the referendum on gay rights.
To represent the data in a table, we can create a contingency table:
For Against
Republican 16 54
Democrat 72 28
Other 27 3
Null hypothesis (H₀): There is no relationship between political party affiliation and support for the referendum on gay rights.
Alternative hypothesis (H₁): There is a relationship between political party affiliation and support for the referendum on gay rights.
To analyze the data, we can perform a chi-square test of independence. This test will determine if there is a significant association between political party affiliation and support for the referendum.
Applying the chi-square test at a significance level (α) of 0.05, we can calculate the test statistic and compare it to the critical value from the chi-square distribution with (rows - 1) × (columns - 1) degrees of freedom.
Let's calculate the expected frequencies for each cell assuming the null hypothesis is true:
For Against Total
Republican 27 43 70
Democrat 48 52 100
Other 12 18 30
Total 87 113 200
Now, we can calculate the chi-square statistic:
χ² = Σ[(O - E)² / E]
where O is the observed frequency and E is the expected frequency.
Performing the calculations, we find:
χ² ≈ 13.765
To determine the critical value, we need to find the degrees of freedom, which is equal to (rows - 1) × (columns - 1) = (3 - 1) × (2 - 1) = 2.
Using a chi-square distribution table or a statistical software, we find that the critical value for a significance level of 0.05 and 2 degrees of freedom is approximately 5.991.
Since the test statistic (13.765) is greater than the critical value (5.991), we reject the null hypothesis. Therefore, we can conclude that there is a significant relationship between political party affiliation and support for the referendum on gay rights.
In Michael's survey data, political party affiliation is related to the support for the referendum. Further analysis and interpretation of the results are needed to understand the nature and strength of this relationship.
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Suppose that y varies directly with x and y = 3 when x = 9. What is y when x = 18?
Answer:
y = 6
Step-by-step explanation:
Use the direct variation equation, y = kx
Plug in y = 3 and x = 9, and solve for k
y = kx
3 = k(9)
1/3 = k
So, the equation is y = 1/3x
Plug in 18 as x and solve for y
y = 1/3x
y = 1/3(18)
y = 6
So, when x = 18, y = 6