The scatterplot of the given data points are attached herewith.
A scatter plot uses dots to speak to values for two different numeric factors. The position of each dot on the level and vertical axis shows values for an individual information point. Scatter plots are utilized to watch connections between variables, Scatter plots’ essential uses are to observe and show connections between two numeric variables. The dots in a scatter plot do not as it were report the values of personal information points, but moreover designs when the information is taken as a whole.
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On a given planet, the weight of an object varies directly with the mass of the object. Suppose that an object whose mass is 3 kg weighs 30 N. Find the weight of an object whose mass is 5 kg
Answer:
\(50 N\)
Step-by-step explanation:
To help us find our answer, we need to use Newton's Second law
\(F = m \times a\)
Where F is the force (N), m is the mass (Kg) and a is the acceleration (m/s^2, on a planet this would just be the gravity)
So if we know that a person has a mass of 3Kg and weighs 30N, the acceleration (or the gravity on that planet is)
\(30 = 3 \times a\\a = 10 m/s^2\)
Now that we know the acceleration we can easily find the weight of the person.
\(F = 5 * 10 = 50 N\)
HELP ME PLZZ THIS DUE TODAY!
Answer:
D.
Step-by-step explanation:
I think that the easiest one would be D, because even after you use the property, it will still have addition only.
a 'scooped' pyramid has a cross-sectional area of x 4 at a distance x from the tip. what is its volume if the distance from tip to base is 5?
The volume of the 'scooped' pyramid is approximately 26.6667 cubic units.
To find the volume of the 'scooped' pyramid, we first need to determine the area of its base. Since the cross-sectional area of the pyramid is x 4 at a distance x from the tip, we can assume that the area at the tip is zero. This means that the area of the base is 4 times the area at a distance of 5 from the tip (since the distance from tip to base is 5).
Therefore, the area of the base is 4x4 = 16 square units. To find the volume, we can use the formula for the volume of a pyramid, which is:
Volume = (1/3) x Base Area x Height
In this case, the height of the pyramid is 5 units. So, we can substitute the values we have:
Volume = (1/3) x 16 x 5
Volume = 26.6667 cubic units
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marking brainliest pls help
Answer:
2.7 The second question I am unsure of because side EF is clearly labeled 7, if they meant to ask for the value of x in the second question then your answer is 12
Step-by-step explanation:
Answer:
2 = 2.7
4 = D, 12
Step-by-step explanation:
2 is because 1.8 multiplied by 1 2/3 is 3, therefore you can take the same logic but just reverse it for 4.5
4.5 / 1 2/3 is 2.7
D, the same thing but 7 * 2 = 14, so the factor is 2 therefore 6 * 2 = 12
pls no scam I only need 2 more brainliest to get expert
A system of two linear equations in two variables has no solution. What statement is accurate about these two linear equations?
Responses
The two linear equations never intersect.
The two linear equations never intersect.
The two linear equations graph the same line.
The two linear equations graph the same line.
The two linear equations do not cross the x-axis.
The two linear equations do not cross the x-axis.
The two linear equations do not cross the y-axis.
The two linear equations do not cross the y-axis.
The two linear equations intersect at exactly one point.
The right response is that the two linear equation never intersect , because the graph of these two linear equation will be two parallel lines.
How many types of solution are there for two linear equations ?
There are 2 types of solution :
Consistent :
A consistent system is said to be an independent system if it has a single solution.
A consistent system is said to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide, so the equations represent the same line. Each point on the line represents a pair of coordinates that fits the system. So there are an infinite number of solutions.
Non-consistent :
Another type of system of linear equations is the inconsistent system, in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no common points for both lines; therefore, there is no solution to the system and if we draw the graph of these equations then the graphs of both equation becomes parallel to each other.
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The two linear equations never intersect.
When a system of two linear equations in two variables has no solution, it means that there is no set of values for the variables that satisfies both equations simultaneously. Geometrically, this corresponds to the two lines represented by the equations being parallel. Since parallel lines never intersect, the statement "The two linear equations never intersect" accurately describes the situation.
If the two linear equations were graphed on a coordinate plane, they would appear as two distinct lines that run parallel to each other without ever crossing or intersecting. This indicates that there is no common point of intersection between the lines, and therefore no solution exists for the system of equations.
It is important to note that this scenario is different from the case where the two linear equations represent the same line. In that case, the equations would be equivalent, and every point on the line would satisfy both equations. However, when there is no solution, it means that the lines do not share any common points and never intersect.
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a researcher took a random sample of 100 students from a large university. she computed a 95% confidence interval to estimate the average weight of the students at this university. the confidence interval was too wide to provide a precise estimate. true or false? the researcher could produce a narrower confidence interval by increasing the sample size to 150.
It's true that the researcher could produce a narrower confidence interval by increasing the sample size to 150.
A confidence interval is a range of values within which the true value of a population parameter is expected to fall with a certain degree of confidence. The width of a confidence interval depends on several factors, including the sample size, the level of confidence chosen, and the variability of the data.
If the confidence interval is too wide, it means that there is a lot of uncertainty about the true value of the population parameter. In other words, the sample size is not large enough or the data is too variable to provide a precise estimate.
Increasing the sample size can help to reduce the width of the confidence interval, as it provides more information about the population and can help to reduce the impact of random sampling error. Therefore, it is true that the researcher could produce a narrower confidence interval by increasing the sample size to 150.
However, it is important to note that other factors, such as the level of confidence chosen and the variability of the data, will also affect the width of the confidence interval.
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=-72\(x^{2}\)
On solving for (x), we get -
x = ±i√(a/72).
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.
Given is the equation as -
- 72x² = a
The given equation is -
- 72x² = a
x² = -a/72
x = ±i√(a/72)
Therefore, on solving for (x), we get -
x = ±i√(a/72).
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T Raiderlink Bb Blackboard SPC Blackboard TTU -/1 Points] DETAILS HARMATHAP12 9.4.011. Find the derivative of the function. w = 2? - 326 + 14 w= 1-/1 Points) DETAILS HARMATHAP12 9.4.014.MI. Find the derivative of the function. +(x) = 16x12 + 6x6 - 2x + 19x - 7 h'(x) = [-/1 Points] DETAILS HARMATHAP12 9.5.002.MI. Find the derivative and simplify. y = (8x + 5)(x2 – 3x).
The derivative of the function is
A) dw/dz=z^5 (7z-18)
B) dh/dx=192x^11+36x^5-6x^2+19
C) dy/dx=24x^2-38x-15
In mathematics, the derivative of a function measures the sensitivity to change of the function value with respect to a change in its argument. It is the rate of change of a function with respect to a variable.
A) w = z^7 – 3z^6 + 14
dw/dz=7z^6-18z^5
dw/dz=z^5 (7z-18)
B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7
dh/dx=192x^11+36x^5-6x^2+19
C) y = (8x + 5)(x^2 – 3x)
dy/dx= d/dx [8x+5]*〖(x〗^2-3x)+(8x+5)*d/dx[x^2-3x]
dy/dx=(8* d/dx [x}+d/dx[5])*〖(x〗^2-3x)+(8x+5)*(d/dx[x^2]-3 d/dx[x])
dy/dx=(8*1+0)(x^2-3x)+(8x+5)(2x-3*1)
dy/dx=8(x^2-3x)+(2x-3)(8x+5)
dy/dx=24x^2-38x-15
Note: The question is incomplete. The complete question probably is: Find the derivative of the following function: A) w = z^7 – 3z^6 + 14 B) h(x) = 16x^12 + 6x^6 – 2x^3 + 19x – 7 C) y = (8x + 5)(x^2 – 3x).
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what is the standard deviation of the data set? 6.5, 11.2, 13, 6.3, 7, 8.8, 7.4 enter your answer rounded to the nearest hundredth in the box.
The standard deviation of the data set 6.5, 11.2, 13, 6.3, 7, 8.8, and 7.4 is 2.98, rounded to the nearest hundredth.
To find the standard deviation of the given data set {6.5, 11.2, 13, 6.3, 7, 8.8, 7.4}, follow these steps:
1. Calculate the mean (average) of the data set:
(6.5 + 11.2 + 13 + 6.3 + 7 + 8.8 + 7.4) / 7 = 60.2 / 7 = 8.6
2. Find the difference between each data point and the mean, then square each difference:
(6.5 - 8.6)^2 = 4.41
(11.2 - 8.6)^2 = 6.76
(13 - 8.6)^2 = 19.36
(6.3 - 8.6)^2 = 5.29
(7 - 8.6)^2 = 2.56
(8.8 - 8.6)^2 = 0.04
(7.4 - 8.6)^2 = 1.44
3. Find the average of these squared differences:
(4.41 + 6.76 + 19.36 + 5.29 + 2.56 + 0.04 + 1.44) / 7 = 39.86 / 7 = 5.694
4. Take the square root of the average squared difference:
√5.694 = 2.39 (rounded to the nearest hundredth)
The standard deviation of the data set is approximately 2.39.
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Assume that the numbers of a data set are arranged in ascending order. Which statement about the third quartile is true?
75% of the numbers lie below or on the third quartile, and the remaining 25% lie on or above it.
In any data set, if arranged in ascending order, the mid value gives the median.
If there are even number of entries, the middle value of the mid two entries average would be the median.
I quartile is the entry below which 25% of the entries lie and III quartile is one above which 25% of the entries will lie
Hence out of 4 options given
the last one is the correct answer
75% of the numbers lie below or on the third quartile, and the remaining 25% lie on or above it.
Complete Question-
Assume that the numbers of a data set are arranged in ascending order. Which statement about the third quartile is true?
A. All of the numbers lie below the third quartile.
B. 50% of the numbers lie below or on the third quartile, and the remaining 50% lie above it.
C. 25% of the numbers lie below or on the third quartile, and the remaining 75% lie above it.
D. 75% of the numbers lie below or on the third quartile, and the remaining 25% lie on or above it.
In Cedarburg, the library is due south of the courthouse and due west of the community
swimming pool. If the distance between the library and the courthouse is 12 kilometers and
the distance between the courthouse and the city pool is 13 kilometers, how far is the library
from the community pool?
kilometers
The library is 5 kilometres far from the community pool.
According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides. Look at the triangle ABC, where BC² = AB² + AC² is present. The base is represented by AB, the altitude by AC, and the hypotenuse by BC in this equation.
The distance between the courthouse and the library is 12 kilometres and the distance between the courthouse and the city pool is 13 kilometres. Let the distance between the library and the community pool be x and it can be observed that the Courthouse, library and Community hall form a sort of right-angled triangle
So, using Pythagoras theorem, we get
\(13^2=x^2+12^2\\x^2=169-144\\x^2=25\\x=5 km\)
So, the library is 5 kilometres far from the community pool.
Therefore, the distance between the library and the community pool is 5 kilometres.
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What's the answer to this? brainliest if correct!
Answer:
Slope of dotted lines: 3/1 or 3
Slope of reflected line: 1/3
Step-by-step explanation:
Rise and run
From a horizontal distance of 80.0 m, the angle of elevation to the top of a flagpole is 18 degrees. Calculate the height of the flagpole to the nearest then of a meter.
Answer: 84.1m
Step-by-step explanation:
Let the height of the flagpole be represented by x.
First and foremost, we have to know that the cosine of 18° = 0.9511.
The equation to get the height will then be:
0.9511 = 80/x
Cross multiply
(0.9511 × x) = 80
0.9511x = 80
Divide both side by 0.9511
0.9511x/0.9511 = 80/0.9511
x = 84.1
The height of the flagpole is 84.1m
Jillian volunteered to work at the ticket booth for her school's Halloween carnival. The chart below gives the number of hours Gwen worked and the total amount of money she collected for the tickets she sold.
Tickets (t) Money (m)
10 $25.00
8 $20.00
6 $15.00
4 $10.00
Based on the table, write an equation for the relation between the number tickets Jillian sold and the amount of money she collected.
t= 2.50mt= 2.50m
t=m2.5t is equal to m over 2 point 5
tm = 25tm = 25
m=25tm is equal to 25 t
The equation for the relation between the number tickets Jillian sold and the amount of money she collected is m = 2.5t.
How to compute the equation?It should be noted that there's a constant relationship between the figures that are given.
This can be illustrated as:
= 25/10
= 2.5
Therefore, the equation for the relation between the number tickets Jillian sold and the amount of money she collected is m = 2.5t.
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What is the slope of the line shown?
Answer:
M=(-3)
Step-by-step explanation:
Take two points on the line
(5,1) and (2,2)
the equation to find M is y2-y1/x2-x1
2-5=(-3) 2-1=1
(-3)/1=(-3)
Hope this helps =3
Isaiah has $145 in his savings account. He earns $36 a week mowing lawns.
If Isaiah saves all of his earnings, after how many weeks will he have $433
saved?
Answer:
8 weeks
Step-by-step explanation:
Amount saved from mowing lawns = $433 - $145
= $288
Number of weeks to save $288 from $36 a week = 288/36 = 8 weeks
Solve for x. Round to the nearest tenth of a degree, if necessary.
Answer:
x ≈ 54.8°
Step-by-step explanation:
Using the tangent ratio in the right triangle
tan x = \(\frac{opposite}{adjacent}\) = \(\frac{PQ}{QR}\) = \(\frac{7.1}{5}\) , then
x = \(tan^{-1}\) (\(\frac{7.1}{5}\) ) ≈ 54.8° ( to the nearest tenth )
a family on a trip budgets $800 for sit-down restaurant meals and fast food. if the price of a fast food meal for the family is $20, how many such meals can the family buy if they do not eat at restaurants? group of answer choices 8 15 20 40 160
Answer:
If the family has $800 for sit-down restaurant meals and fast food and they budgeted all of it for fast food, then they can buy $800/$20 = 40 fast food meals.
Step-by-step explanation:
yw;)
Answer:
40
Step-by-step explanation:
No. Of Meal=Budget/price of Meal
=800/ 20
=40
how easy is it for you to apply algebra concepts when determining angle measures of a polygon?
To determine the measures of the angles of a polygon are necessary the concepts of algebra by using the formula of the sum of interior angles and creating equations and obtaining the measures of unknown angle.
First, it is important to remember the formula for the sum of interior angles of a polygon, which is (n-2) x 180°, where n is the number of sides of the polygon.
Next, you can use algebra concepts to solve for the unknown angle measures. For example, if you know the sum of the interior angles and the measures of some of the angles, you can create an equation and solve for the unknown angle measures.
Here is an example:
If a quadrilateral has interior angles of 70°, 110°, and 120°, you can use the formula (4-2) x 180° = 360° to find the sum of the interior angles. Then, you can create the equation 70° + 110° + 120° + x = 360° and solve for x to find the measure of the unknown angle.
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The statistical definition of Six Sigma allows for 3.4 defects per million. This is achieved by what Cpk index value
Answer:
2
Step-by-step explanation:
In general, the higher the Cpk, the better. A Cpk value less than 1.0 is considered poor and the process is not capable. A value between 1.0 and 1.33 is considered barely capable, and a value greater than 1.33 is considered capable. But, you should aim for a Cpk value of 2.00 or higher where possible.
f(x) = 4x^2 – 4x
Find f(-7)
Answer:
f(-7)=224
Step-by-step explanation:
\(f(x) = 4x^2 -4x\\f(-7)= 4(-7)^2 - 4(-7)\\= 4(49) -+28\\=196+28\\f(-7) = 224\)
You have a shuffled deck of thro cards: 2, 3, and 4, and you deal out the three cards. Let Er denote the event thitith card dealt is even numbered. (a) What is P(Ez E1), the probability the second card is even given that the firscard is even? b) What is the conditional probability that the first two cards are even givesthat the third card is even? (c) Let O; represent the event that the ith card dealt is odd numbered. What is P[E2 Oil, the conditional probability that the second card is even given thatthe first card is odd? (d) What is the conditional probability that the second card is odd given thatthe first card is odd?
There is only one possible outcome where the first card is odd and the second card is even: {3,2}.
We are dealing with a shuffled deck of three cards: 2, 3, and 4. There are three possible outcomes when dealing one card, and two possible outcomes when dealing the second card (since one card has already been dealt). Therefore, there are a total of 3x2=6 possible outcomes when dealing two cards, and 3x2x1=6 possible outcomes when dealing all three cards.
(a) What is P(E2 | E1), the probability the second card is even given that the first card is even?
There are two ways the first card can be even: 2 or 4. If the first card is 2, there are two possible outcomes for the second card: 3 or 4. If the first card is 4, there is only one possible outcome for the second card: 2. Therefore, there are three possible outcomes where the first card is even and the second card is even: {2,3}, {2,4}, and {4,2}. The probability of the second card being even given that the first card is even is therefore:
P(E2 | E1) = number of outcomes where E1 and E2 occur / number of outcomes where E1 occurs
P(E2 | E1) = 2 / 3
(b) What is the conditional probability that the first two cards are even given that the third card is even?
There is only one way the third card can be even: 2. If the third card is 2, there are two possible outcomes for the first card: 2 or 4. If the third card is 2 and the first card is 2, there is only one possible outcome for the second card: 4. If the third card is 2 and the first card is 4, there are two possible outcomes for the second card: 2 or 3. Therefore, there are three possible outcomes where the third card is even and the first two cards are even: {2,4,2}, {2,2,4}, and {4,2,4}. The probability that the first two cards are even given that the third card is even is therefore:
P(E1E2 | E3) = number of outcomes where E1 and E2 and E3 occur / number of outcomes where E3 occurs
P(E1E2 | E3) = 3 / 6 = 0.5
(c) Let Oi represent the event that the ith card dealt is odd numbered. What is P(E2 | O1), the conditional probability that the second card is even given that the first card is odd?
If the first card is odd, there is only one possible outcome: 3. If the first card is 3, there is only one possible outcome for the second card: 2. Therefore, there is only one possible outcome where the first card is odd and the second card is even: {3,2}. The probability that the second card is even given that the first card is odd is therefore:
P(E2 | O1) = number of outcomes where O1 and E2 occur / number of outcomes where O1 occurs
P(E2 | O1) = 1 / 3
(d) What is the conditional probability that the second card is odd given that the first card is odd?
If the first card is odd, there is only one possible outcome: 3. If the first card is 3, there is only one possible outcome for the second card: 2. Therefore, there is only one possible outcome where the first card is odd and the second card is even: {3,2}. Therefore, the conditional probability that the second.
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a+b/c=5. Solve for b
Answer:
b = c(5 - a)
Step-by-step explanation:
Given
a + \(\frac{b}{c}\) = 5 ( subtract a from both sides )
\(\frac{b}{c}\) = 5 - a ( multiply both sides by c to clear the fraction )
b = c(5 - a)
The value of b form the equation a + b/c = 5 will be b = c(5 - a)
How to evaluate a given mathematical expression with variables if values of the variables are known?We can simply replace those variables with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.
Given;
a + b/c = 5
subtract a from both sides;
b/c = 5 - a
multiply both sides by c to clear the fraction;
b = c(5 - a)
Hence, The value of b form the equation a + b/c = 5 will be b = c(5 - a)
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Find the third order maclaurin polynomial. Use it to estimate the value of sqrt1.3
You can use the well-known binomial series,
\(\displaystyle (1+x)^\alpha = \sum_{k=0}^\infty \binom \alpha k x^k\)
where
\(\dbinom \alpha k = \dfrac{\alpha(\alpha-1)(\alpha-2)\cdots(\alpha-(k-1))}{k!} \text{ and } \dbinom \alpha0 = 1\)
Let \(\alpha=\frac12\) and replace \(x\) with \(3x\); then the series expansion is
\(\displaystyle (1+3x)^{1/2} = \sum_{k=0}^\infty \binom{\frac12}k (3x)^k\)
and the first 4 terms in the expansion are
\(\sqrt{1+3x} \approx 1 + \dfrac{\frac12}{1!}(3x) + \dfrac{\frac12\cdot\left(-\frac12\right)}{2!}(3x)^2 + \dfrac{\frac12\cdot\left(-\frac12\right)\cdot\left(-\frac32\right)}{3!}(3x)^3\)
which simplify to
\(\sqrt{1+3x} \approx \boxed{1 + \dfrac32 x - \dfrac98 x^2 + \dfrac{27}{16} x^3}\)
You can also use the standard Maclaurin coefficient derivation by differentiating \(f\) a few times.
\(f(x) = (1+3x)^{1/2} \implies f(0) = 1\)
\(f'(x) = \dfrac32 (1+3x)^{-1/2} \implies f'(0) = \dfrac32\)
\(f''(x) = -\dfrac94 (1+3x)^{-3/2} \implies f''(0) = -\dfrac94\)
\(f'''(x) = \dfrac{81}8 (1+3x)^{-5/2} \implies f'''(0) = \dfrac{81}8\)
Then the 3rd order Maclaurin polynomial is the same as before,
\(\sqrt{1+3x} \approx f(0) + \dfrac{f'(0)}{1!} x + \dfrac{f''(0)}{2!} x^2 + \dfrac{f'''(0)}{3!} x^3 = 1 + \dfrac32 x - \dfrac98 x^2 + \dfrac{27}{16} x^3\)
Now,
\(\sqrt{1.3} = \sqrt{1+3x} \bigg|_{x=\frac1{10}} \\\\ ~~~~~~~~ \approx 1 + \dfrac32 \left(\dfrac1{10}\right) - \dfrac98 \left(\dfrac1{10}\right)^2 + \dfrac{27}{16} \left(\dfrac1{10}\right)^3 \\\\ ~~~~~~~~ = \dfrac{18,247}{16,000} \approx \boxed{1.14044}\)
Compare to the actual value which is closer to 1.14018.
\(\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}\) is the maclaurin polynomial and estimate value of \(\sqrt{1.3}\) is 1.14. This can be obtained by using the formula to find the maclaurin polynomial.
Find the third order maclaurin polynomial:Given the polynomial,
\(f(x)=\sqrt{1+3x}=(1+3x)^{\frac{1}{2} }\)
The formula to find the maclaurin polynomial,
\(f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} + \frac{f'''(0)}{3!}x^{3}\)
Next we have to find f'(x), f''(x) and f'''(x),
\(f'(x) = \frac{3}{2}(1+3x)^{-\frac{1}{2} }\) \(f''(x) =-\frac{9}{4}(1+3x)^{-\frac{3}{2} }\)\(f'''(x) = \frac{81}{8}(1+3x)^{-\frac{5}{2} }\)By putting x = 0 , we get,
\(f(0)=(1+3(0))^{\frac{1}{2} }=1\) \(f'(0) = \frac{3}{2}(1+3(0))^{-\frac{1}{2} }=\frac{3}{2}\)\(f''(0) =-\frac{9}{4}(1+3(0))^{-\frac{3}{2} }=-\frac{9}{4}\)\(f'''(0) = \frac{81}{8}(1+3(0))^{-\frac{5}{2} }=\frac{81}{8}\)Therefore the maclaurin polynomial by using the formula will be,
\(\sqrt{1+3x}=f(0)+\frac{f'(0)}{1!}x+\frac{f''(0)}{2!}x^{2} + \frac{f'''(0)}{3!}x^{3}\)
\(\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}\)
To find the value of \(\sqrt{1.3}\) we can use the maclaurin polynomial,
\(\sqrt{1.3}\) is \(\sqrt{1+3x}\) with x = 1/10,
\(\sqrt{1+3(1/10)}=1+\frac{3}{2} (1/10)-\frac{9}{8} (1/10)^{2} + \frac{81}{8}(1/10)^{3}\)
\(\sqrt{1+3(1/10)}=\frac{18247}{16000} = 1.14\)
Hence \(\sqrt{1+3x}=1+\frac{3}{2} x-\frac{9}{8} x^{2} + \frac{81}{8}x^{3}\) is the maclaurin polynomial and estimate value of \(\sqrt{1.3}\) is 1.14.
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Use the formula f'(x) = lim Z-X 3 X+7 f(z)-f(x) Z-X to find the derivative of the following function.
To find the derivative of a function using the given formula, we can apply the limit definition of the derivative. Let's use the formula f'(x) = lim┬(z→x)┬ (3z + 7 - f(x))/(z - x).
The derivative of the function can be found by substituting the given function into the formula. Let's denote the function as f(x):
f(x) = 3x + 7
Now, let's calculate the derivative using the formula:
f'(x) = lim┬(z→x)┬ (3z + 7 - (3x + 7))/(z - x)
Simplifying the expression:
f'(x) = lim┬(z→x)┬ (3z - 3x)/(z - x)
Now, we can simplify further by factoring out the common factor of (z - x):
f'(x) = lim┬(z→x)┬ 3(z - x)/(z - x)
Canceling out the common factor:
f'(x) = lim┬(z→x)┬ 3
Taking the limit as z approaches x, the value of the derivative is simply:
f'(x) = 3
Therefore, the derivative of the function f(x) = 3x + 7 is f'(x) = 3.
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Solve the following system by using substitute
x - 4y = 28
7y - 6x = - 15
Answer:
y = -9
x = -8
Step-by-step explanation:
x = 28 + 4y
7y - 6(28 + 4y) = -15
7y - 168 - 24y = - 15 ---> *distribute the -6, not positive 6*
-17y = 153
y = -9
x = 28 + 4(-9)
x = -8
Determine the length of the curve indicated by x = 4sin t, y = 4 cost-5,0 < t < phi/2
The length of the curve indicated by x = 4sin t, y = 4 cost-5,0 < t < phi/2 is 4*sqrt(2)*phi.The length of a curve is the distance between its starting point and its endpoint.
In this case, the starting point is (0, -5) and the endpoint is (4cos(phi/2), 4sin(phi/2)-5).To find the length of the curve, we can use the formula for the arc length of a parametric curve:
L = int_a^b sqrt(dx^2 + dy^2) dt
In this case, a = 0, b = phi/2, dx = 4cos(t), dy = 4sin(t), and dt = dt.
Substituting these values into the formula, we get:
L = int_0^{\phi/2} sqrt(16*cos^2(t) + 16*sin^2(t)) dt
We can simplify this expression as follows:
L = int_0^{\phi/2} sqrt(16) dt
The integral of sqrt(16) is simply 4*sqrt(2)*t, so the length of the curve is:
L = 4*sqrt(2)*int_0^{\phi/2} dt
Evaluating the integral, we get:
L = 4*sqrt(2)*phi
Therefore, the length of the curve is 4*sqrt(2)*phi.
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the life of an electric component has an exponential distribution with a mean of 10 years. what is the probability that a randomly selected one such component has a life more than 7 years?
The probability is 0.4647.
What is probability?Probability is the branch of mathematics that deals with numerical descriptions of the likelihood of an event occurring or the likelihood of a statement being true.The probability of an event is a number between 0 and 1, with approximately 0 indicating the improbability of the event and 1 indicating certainty. The higher the probability of an event, the more likely the event will occur. A simple example is tossing a fair coin. Both outcomes are equally likely because the coin is fair. The probability of heads or tails is 1/2. These concepts are an axiomatic mathematical formalization of probability theory that is widely used in research fields such as statistics, mathematics, science, finance, gambling, artificial intelligence, machine learning, computer science, game theory, and philosophy. Infer the expected frequency from the event. Probability theory is also used to explain the underlying dynamics and laws of complex systems.To learn more about probability from the given link :
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Mrs. Wong is researching what it would cost to order flower arrangements for a fancy party. She wants one large centerpiece for the head table, and smaller arrangements for the smaller tables. Lakeside Florist charges $19 for each smaller arrangement, plus $50 for the large centerpiece. Spencer's Flowers, in contrast, charges $42 for the large centerpiece and $23 per arrangement for the rest. If Mrs. Wong orders a certain number of small arrangements, the cost will be the same at either flower shop. How many small arrangements would that be? What would the total cost be?
Step-by-step explanation:
so, we have 2 cost functions. each consisting of 1 large centerpiece, and x smaller arrangements.
cost1(x) = 19x + 50
cost2(x) = 23x + 42
to get the value for x we know that the cost is the same either way.
that means
cost1(x) = cost2(x) = 19x + 50 = 23x + 42
19x + 50 = 23x + 42
50 = 4x + 42
8 = 4x
x = 2
so, she orders 2 small arrangements.
the total cost is
19×2 + 50 = 38 + 50 = $88
cross check with the other function :
23×2 + 42 = 46 + 42 = $88
correct
suppose a research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. a sample of 100 steady smokers revealed that the sample mean is $20. the population standard deviation is $5. what is the probability that a sample of 100 steady smokers spend between $19 and $21? 0.0228 0.4772 1.0000 0.9544
The required probability is 0.9544
A z-score is a quantitative measure obtained when a data point from a normal population with mean μ and standard deviation
σ is transformed. It describes the position of the data point representing its distance from the average value of the normal population measured in number of standard deviations. It is given by:
z =(X − μ)/σ
A standard normal table (z-score table) provides the probability to the left of the z-score so obtained.
Number of randomly selected steady smokers is, n=100.
Sample mean is, M=$20.
The population standard deviation is, σ = $5.
To compute the probability that a sample of 100 steady smokers spend between 19 and 21.
Using the definition of a z-score, computing the z-score for X =$19,
z =(X − μ)/σ /\(\sqrt{n}\)
\(z = \frac{19-20}{5}/\sqrt{100}\)
z = -2
Again using the definition of a z-score to compute the z-score for X = $21,
z =(X − μ)/σ /\(\sqrt{n}\)
\(z = \frac{21-20}{5}/\sqrt{100}\)
z = 2
The probability that a sample of 100 steady smokers spend between 19 and 21 is obtained as:
P(19< X < 21) = P(-2 < X < 2)
= P(z< 2) - P(z < -2)
= P(z < 2) − [1 − P (z < 2)]
= 0.9772 - (1 - 0.9772)
= 0.9772 - 0.0288
= 0.9544
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