1.716762 is the correct solution up to 6 decimal places by using Newton's method.
What is Newton's method?The Newton's method is a potent tool, and in general, the convergence is quadratic: as the procedure approaches the root, the discrepancy between the root and the approximation squares, almost doubling the number of accurate digits at each step. The approach does, however, have significant drawbacks. The phrase "Newton's method" refers to Isaac Newton's explanation of a particular application of the method in his books De analysi per aequationes numero terminorum infinitas, which he wrote in 1669 and had William Jones publish in 1711, and De metodis fluxionum et serierum infinitarum (written in 1671, translated and published as Method of Fluxions in 1736 by John Colson).
Given,
f(x)=eˣ+2x-9
f'(x)=eˣ+2
ˣₙ₊₁=ˣₙ-f(ˣₙ)/f'(ˣₙ)
Let, n=1
x₂=1.9074740
x₃=1.7299338
x₄=1.716825
x₅=1.7167621
x₆=1.716762
x₅≈x₆
Therefore, 1.716762 is the correct solution up to 6 decimal places.
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choose each digit of a 5 digit number at random from digits 1, . . . , 9. compute the probability that no digit appears more than twice.
The probability that no digit appears more than twice is 0.648.
What is probability?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Here,
We will choose each digit of 5-digit numbers at random from digits 0,1,2,..,9.
We have to compute the probability that no digit appears more than twice.
So, we have to form a five-digit number say "abcde".
Now, for 'a' we have 10 choices.
For 'b' we have again 10 choices because a digit can appear at most two.
For 'c' we have 9 choices because the digit in 'a' can not be chosen as a digit can appear at most two.
For 'd' we have again 9 choices by a similar argument.
Finally, for 'e' we have 8 choices because the digit chosen previously can not be repeated more than twice.
The total number of such 5-digit numbers is = 10*10*9*9*8 = 64800.
Now, a total number of 5-digit numbers = 10*10*10*10*10 = 100000.
Hence, the probability that no digit appears more than twice is given by,
= 64800/ 100000
= 0.648
Hence, the probability that no digit appears more than twice is 0.648.
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What is the relationship between a 90% confidence interval around a mean and a 95% confidence interval around a mean?.
In determining a mean, the 90% C.I. is more accurate than the 95% C.I.
What is confidence interval mean ?A confidence interval is the mean of your estimate plus or minus the range of that estimate's variability.
You can reasonably anticipate that if you repeat the test, your estimate will fall within these values. In statistics , confidence is another name for probability
What does "confidence interval" actually mean?A statistician who declares that they have a 95% confidence level has basically seen one possible interval out of many possible ones, and 19 out of 20 of those intervals include the correct value of the parameter.
In determining a mean, the 90% C.I. is more accurate than the 95% C.I.
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According to a survey conducted by Independent Sector, the percent of their income that Americans give to charities is related to their household income. For families with an annual income of $100000 or less, the percent approximately given by P(x)=0.0014[tex]x^2[/tex] - 0.1529x + 5.855, 5≤x≤100 where P is the percent of annual income given and x is the annual income in thousands of dollars. According to this model , what income level corresponds to the minimum percent of charity contributions,to the nearest whole number?
According to given model income level corresponds to the minimum percent of charity contributions is 5%.
The given function is P(x)=0.0014x² - 0.1529x + 5.855, 5≤x≤10.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
Check the critical points and end points to test for any absolute extrema over the given interval.
Absolute Maximum: (5,5.1255)
Absolute Minimum: (10,4.466)
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex: (54.60714285,1.68028392)
Focus: (54.60714285,180.2517125)
Axis of Symmetry: x=54.60714285
Directrix: y=−176.89114464
Now, P(5)=0.0014(5)² - 0.1529(5)+5.855
= 5.1255
≈5%
Therefore, according to given model income level corresponds to the minimum percent of charity contributions is 5%.
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Find the surface area of a square pyramid with a side length of 5cm and slant height of 6cm.
Answer:
85 cm^2
Step-by-step explanation:
The surface area of a square pyramid is given by the formula:
Surface area = base area + 4 * (base edge length * slant height) / 2
In this case, the base area is 25 cm^2, because the side length of the base is 5 cm. The base edge length is also 5 cm, because it is a square pyramid. Plugging these values into the formula above, we get:
Surface area = 25 cm^2 + 4 * (5 cm * 6 cm) / 2
= 25 cm^2 + 60 cm^2
= 85 cm^2
So the surface area of the square pyramid is 85 cm^2.
f”(x)=1/x^3/2, f’(4)=2, f(4)=0 f(x)=?
The value of function f (x) will be;
⇒ [tex]f (x) = - 2 x^{1/2} * 2 + 3x - 4[/tex]
What is mathematical expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division
Given that;
The value of function is,
⇒ [tex]f '' (x) = \frac{1}{x^{3/2} }[/tex]
And, f ' (4) = 2 , f (4) = 0
Now,
Since, The value of function is,
⇒ [tex]f '' (x) = \frac{1}{x^{3/2} }[/tex]
After integration we get;
⇒ [tex]f '(x) = - 2 x^{- 1/2} + c[/tex]
Here, f ' (4) = 2
Put x = 4 in above function, we get;
⇒ [tex]f '(x) = - 2 x^{- 1/2} + c\\2 = - 2 * 4^{- 1/2} + c\\ 2 = - 2/2 + c\\c = 3[/tex]
Hence, We get;
⇒ [tex]f'(x) = - 2x^{- 1/2} + 3[/tex]
Again integrating, we get;
[tex]f (x) = - 2 x^{1/2} * 2 + 3x + b\\f (x) = - 4 x^{1/2} + 3x + b[/tex]
Here, f (4) = 0
Put x = 4 in above function, we get;
[tex]f (4) = - 4 * 4^{1/2} + 3*4 + b\\0 = - 4 * 2 + 12 + b\\b = - 4[/tex]
So, We get;
⇒ [tex]f (x) = - 2 x^{1/2} * 2 + 3x - 4[/tex]
Thus, The value of function f (x) is,
⇒ [tex]f (x) = - 2 x^{1/2} * 2 + 3x - 4[/tex]
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An amusement park says "You must be 40 inches tall to ride" What percentage of this height is:
a. 34 inches?
b. 54 inches?
Answer:85%, 135%
Step-by-step explanation:
2/40 is 5%. There is 17 2's in 34 so the percentage is 17x5=85.
There is 27 2's in 54 so the percentage is 27x5=135.
Erica read 4 pages on Wednesday, 20 pages on Thursday, 100 pages on Friday, and 500 pages on Saturday. What kind of sequence is this?
Answer:
Geometric sequence
Step-by-step explanation:
A geometric sequaence is when the term is multiplied or divided to get to the next term.
each term is being multiplied by 5
Match the linear equation to the correct graph.
Answer: y= -1x + 2
Step-by-step explanation:
The linear equation is y= mx + b
Y-intercept here is at (0,2), so b is 2
Let pick point (0,2) (2,0)
The slope is rise/run, and we see that the graph is going down by 2 and goes over by 2, so it is -2/2 = -1
So the equation is y=1x +2
If you can, please give me a Brainliest, I only need 1 more to become an Ace, thank you!
Consider the graph of equation y=mx+b
How does changing the value of b affect the graph of the equation?
Write an explicit formula for each sequence and find the 7th term for each
1. -4, 12, -36
2. 12, 3, 3/4
Answer:
a[n] = -4·(-3)^(n-1); -2916a[n] = 12·(1/4)^(n -1); 3/1024Step-by-step explanation:
You want the explicit formula for each of the geometric sequences, and the 7th term.
-4, 12, -36 12, 3, 3/4Explicit formulaThe explicit formula for a geometric sequence with first term a[1] and common ratio r is ...
a[n] = a[1]·r^(n-1)
1. a[1] = -4, r = -3The explicit formula is ...
a[n] = -4·(-3)^(n-1)
The 7th term is ...
a[7] = -4·(-3)^(7-1) = -2916
2. a[1] = 12, r = 1/4The explicit formula is ...
a[n] = 12·(1/4)^(n -1)
The 7th term is ...
a[7] = 12·(1/4)^(7-1) = 3/1024
A hockey coach recorded the number of shots taken by the home team and the number taken by the visiting team in 20 games
The inference from given boxplot is : The visiting team had more variability in the number of shots taken.
In this question we have been given two boxplots.
For the boxplots that the coach made,
for the home team:
Whiskers range is:16 to 32
So, the minimum value = 16
the maximum value = 32
the box ranges from 20 to 23. A line divides the box at 22.
so, the first quartile = 20
the third quartile = 23
the Median = 22
interquartile range(IQR) = 23 - 20
= 3
And for the visiting team
Whiskers range :14 to 32
This means, the minimum value is 14 and the maximum value = 32
As the box ranges from 16 to 24 and a line divides the box at 18,
the first quartile is 16, the third quartile = 24 and the median = 18
So, the interquartile range (IQR) = 24 - 16
= 8
From above data analysis the inference is that the visiting team had more variability in their shots, because their distribution has a higher interquartile range (8 > 3)
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Given question is incomplete.
The complete question is:
A hockey coach recorded the number of shots taken by the home team and the number taken by the visiting team in 20 games. He displayed the results in the box plots below.A box plot titled Number of Shots Taken by home team players. The number line goes from 10 to 32. The whiskers range from 16 to 32, and the box ranges from 20 to 23. A line divides the box at 22.
Number of Shots Taken by Home Team Players
A box plot titled Number of Shots Taken by visiting team players. The number line goes from 10 to 32. The whiskers range from 14 to 32, and the box ranges from 16 to 24. A line divides the box at 18.
Number of Shots Taken by Visiting Team Players
Which describes an inference that the coach might make after comparing the medians of the two data sets?
Jane received a $90 gift card for a coffee store. She used it in buying some coffee that cost $8.68 per pound. After buying the coffee, she had $37.92 left on
her card. How many pounds of coffee did she buy?
Kevin and Randy Muise have a jar containing 62 coins, all of which are either quarters or nickels. The total value of the coins in the jar is
$7.90. How many of each type of coin do they have?
Answer: 38 nickels, 24 quarters
Step-by-step explanation:
x=number of quarters
y=number of nickels
x + y = 62
$0.25x + $0.05y = $7.90
solve for x in terms of y, then substitute into the 2nd equation:
x = 62-y
.25(62-y) + .05y = 7.90
15.5 - .25y + .05y = 7.90
15.5 - .20y = 7.90
-.20y = -7.6
y = -7.6/-.20
y = 38
now solve for x:
x + 38 = 62
x = 62-38 = 24
x = 24
evaluate the expression 3^3
Answer:
27
Step-by-step explanation:
3*3*3 equals 27. I hope this helps.
Answer: The solution to this problem is 27.
a. Find SL
Explain your reasoning.
b. Explain how the captain can use a similar process to find the distance between the boat and the shoreline.
Answer:
SL = 2.1 miles
Step-by-step explanation:
Given ∆LRS with RS extended to point T, and angles R = 35° and exterior angle LST = 70°, you want the measure of SL. You want to apply the process to finding distance to shore.
a. Isosceles triangleThe exterior angle LST is the sum of interior angles SRL and SLR. In equation form, this is ...
∠LST = ∠SRL +∠SLR
70° = 35° +∠SLR
∠SLR = 35°
The angles at either end of segment LR are both 35°, so the triangle is isosceles. That means sides SR and SL are congruent:
SL = SR = 2.1 miles
b. Distance to shoreThe distance from the boat to the lighthouse has been found using an isosceles triangle. A similar method can be used to find the distance to shore. It requires the captain to be able to identify a point on shore, and measure the distance traveled parallel to the shore.
By using a 45° angle to start, and a 90° angle at the second measurement, the distance traveled between angle measurements will be exactly the (closest) distance to shore from the point of the second measurement.
Other angle measures can be used with trigonometric methods.
30 POINTS ANSWER ASAP!!!!
Determine the perimeter of the right triangle shown.
right triangle with vertices at negative 4 comma 4, 4 comma 4, and 4 comma negative 2
10 units
24 units
36 units
64 units
Answer: 24 units.
Step-by-step explanation: To find the perimeter of the right triangle, you need to add up the lengths of all three sides of the triangle.
The right triangle shown has a vertex at (-4, 4), another vertex at (4, 4), and a third vertex at (4, -2). The length of the side between the first two vertices can be calculated using the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((4 - (-4))^2 + (4 - 4)^2)
= sqrt(8^2 + 0)
= sqrt(64)
= 8
The length of the side between the second and third vertices can be calculated using the distance formula:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
= sqrt((4 - 4)^2 + (-2 - 4)^2)
= sqrt(0 + (-6)^2)
= sqrt(36)
= 6
The length of the hypotenuse of the right triangle can be calculated using the Pythagorean theorem:
c^2 = a^2 + b^2
c = sqrt(a^2 + b^2)
= sqrt(8^2 + 6^2)
= sqrt(64 + 36)
= sqrt(100)
= 10
To find the perimeter of the triangle, add up the lengths of all three sides: 8 + 6 + 10 = 24 units.
Therefore, the perimeter of the right triangle is 24 units.
At the gift shop, they sell small greeting cards and large greeting cards. The cost of a small greeting card is $1.80 and the cost of a large greeting card is $3.85. How much would it cost to get 4 small greeting cards and 3 large greeting cards? How much would it cost to get xx small greeting cards and yy large greeting cards?
To find the cost of x small greeting cards and y large greeting cards, use the equation: cost = x * $1.80 + y * $3.85.
What is the system of linear equations?
A system of linear equations is a group of one or more linear equations that can be solved by using a simultaneous equation or elimination method. Therefore, by using the substitution method and writing the solution of the system in terms of coordinate point (x, y) = (-1, 1).
The cost of 4 small greeting cards is 4 * $1.80 = 4 * 1.8 = $7.20.
The cost of 3 large greeting cards is 3 * $3.85 = 3 * 3.85 = 11.55.
The total cost of 4 small greeting cards and 3 large greeting cards is $7.20 + $11.55 = 7.2 + 11.55 = 18.75.
To find the cost of x small greeting cards and y large greeting cards, you can use the following equation:
cost = x * $1.80 + y * $3.85
Substituting the values of x and y into this equation will give you the total cost of the greeting cards.
Hence, to find the cost of x small greeting cards and y large greeting cards, use the equation: cost = x * $1.80 + y * $3.85.
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Please help I’ll give brainliest what is the slope of the line
-1/2
1/2
-2
2
Answer:
2
Step-by-step explanation:
Pick 2 coordinates on the line and do the formula for slope.
ex: (2,4) and 3,6)
4-6/2-3 = -2/-1 = 2
eternity greatful if you help me
Answer:
1) Associative
2) Distributive
3) Distributive
4) Associative
The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
Answer:
1 : 2
or
1/2
Step-by-step explanation:
The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
6 : 12
semplify
1 : 2
in fraction
1/2
Sebatian and zoey had 3068 button in all. Sebatian and Valeria had 2103 button in all. Valeria ha half a many button a zoey. How many button do they have in all
When Sebatian has 379.33 buttons, Zoey has 2688.73 buttons, and Valeria has 1344.36 buttons, there will be a total of 4412.42 buttons.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
Here,
Let Sebastian have x button and Zoey have y button and Valeria have z button.
x+y=3068
x+z=2103
z=y/2
x+y=3068
x+y/2=2103
4x+y=4206
x+y=3068
3x=4206-3068
3x=1138
x=1138/3
x=379.33
x+y=3068
379.33+y=3068
y=3068-379.33
y=2688.73
z=y/2
z=2688.73/2
z=1344.36
x+y+z=379.33+2688.73+1344.36
Total number of button=4412.42 buttons
The total number of buttons will be 4412.42 buttons when Sebatian have 379.33 buttons, Zoey have 2688.73 buttons, Valeria have 1344.36 buttons.
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A model car is 12 inches long. Using a scale of 3 inches : 4 feet ,how long is the actual car
Length of the car is 12 inches equal to 192 feet.
What is unit of length?Using measuring instruments like a ruler, measuring tape, etc., one can measure the length of any object. A ruler can be used to determine, for instance, how many inches a pencil is long. A feet scale can be used to gauge the height of each student in a class.
The inch, foot, yard, and mile are the fundamental units of length and distance measurement in the English system. The rod, furlong, and chain are additional length units.
Given ,
3 inches : 4 feet
3 inches : 4*12
3 inches :48
1 inches : 16 feet
Length of the car is 12 inches = 12 * 16
Length of the car is 12 inches = 192 feet
The measurement or size of something from end to end is referred to as its length. To put it another way, it is the greater of the higher two or three dimensions of a geometric shape or object. For instance, a rectangle's length and width are its dimensions.
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William buys a T.V that is on sale for 40% off the original price. The original price is $140 more than the sale price.
What is the original price of the T.V?
What is the square root of 81b^2?
Answer:
Step-by-step explanation:
9 bytes2
On a cale drawing of a hore, the cale i 1 in: 10 ft. If the real hore i 25 ft tall, how tall i the hore on the cale drawing?
If the scale of drawing is 1 inches : 10 feet and the real horse height is 25 feet, then the height of the horse in drawing is 2.5 inches
The scale of drawing the horse = 1 inch : 10 feet
Therefore in scale
The height of the horse in drawing = 1 inch
The height of the horse = 10 feet
The original height of the horse = 25 feet
The height in the picture = x inches
To find the height the horse in the picture, we have to use proportion
1 inch : 10 feet = x inches : 25 feet
1 / 10 = x / 25
1 × 25 = 10x
10x = 25
x = 25/10
x = 2.5 inches
Therefore, the height of the horse in drawing is 2.5 inches
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what is the answer for 3y2 + 4y2 =
Answer:
y^2(3+4)
7y^2
BTW isn't it too much to ask for high school level question?
The population of Browne County is represented by the function f(x)=87,000(0.9)x, where x is the number of years since 2010. The population of Orange County was 102,000 in 2010 and has decreased exponentially at a rate of 16% each year. How do the populations of these counties compare in 2015? In 2015, the population of Browne County was approximately and the population of Orange County was approximately. In 2015, which County was more populous?
Browne County shows a population bigger than Orange County in 2015.
How to compare two populations that change exponentially in time
Herein we find the case of two cities in the United States that changes exponentially in time, the population of Browne County decrease in time, while the population of Orange County decreases at a lower rate in time in time. Exponential model is introduced below:
p'(n) = p · (1 + r / 100)ⁿ
Where:
p - Initial population.p'(n) - Final population.r - Growth rate, in percentage.n - Period, in years.Now we proceed to build the equation that explain the growth of the two cities:
Browne County (p = 87,000, r = - 10)
p'(n) = 87,000 · 0.9ⁿ
Orange County (p = 102,000, r = 16)
p'(n) = 102,000 · 0.84ⁿ
Now we evaluate the two functions at n = 5:
Browne County
p'(5) = 87,000 · 0.9⁵
p'(5) = 51,372
Orange County
p'(5) = 102,000 · 0.84⁵
p'(5) = 42,657
Browne County has more population than Orange County.
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The points (-7, 3) and (9, r) lie on a line with slope 1/4
Find the missing coordinate r.
Answer:
Use the formula y-3= 1/4(x--7) ---> y-3= 1/4(x+7)
4.75 is the y intercept
whats the sum of 1 3/5 + 8 1/2
Answer: i hope this helps
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Step-by-step explanation:
Answer: 43 1/10
Step-by-step explanation:
I ordered some books online for myself and friends.
Each book costs $13 and the store charges a one-time shipping fee of $ 20
Write an expression for the cost of buying nn books.
The expression for the cost of buying n book will be 20 + 13n.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
It is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Numbers, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
In this case, the person some books online for myself and friends and each book costs $13 and the store charges a one-time shipping fee of $20.
The expression for the cost of buying n books is:
= 20 + (13 × n)
= 20 + 13n
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