Which statement is true about solving 8* = 256?
A
B
C
D
x = 2 because 4²x = 44.
x = 2 because 2³x = 26.
X =
X =
8
3
8
3
because 2³x = 28.
because 43x = 48.
Answers
The true statement about solving 8* = 256 is:
x = 2 because 2³x = 256. Option D
How to determine the true statement about solving 8* = 256To solve for x, we need to find the value that, when raised to the power of 3, equals 256. In this case, 2 raised to the power of 3 is 8, not 256.
The correct statement should be that x = 2 because 2³ (2 raised to the power of 3) equals 8, not 256.
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Related Questions
If AH=13mm, A F=15mm, and FC=37mm, what would be the distance between A and D? Round your answer to two decimal places if necessary.
Answers
The measure of segment AD in the similar triangle is 45.07 mm
What are similar triangles?Two triangles are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. Also, their corresponding angles are congruent.
Triangle FEA and triangle ABC are similar triangles by the angle angle similarity postulate, therefore:
13/AD = 15 / (15 + 37)
AD = 45.07 mm
The measure of segment AD in the similar triangle is 45.07 mm
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Shota invests $2000 in a certificate of deposit that earns 2, percent interest each year write a function that gives the total value v(t) in dollars, of the investment t years from now
Answers
V(t)=2000(1.02)^t function that gives the total value in dollars of the investment t years from now given that Shota invests $2000 in a certificate of deposit that earns 2 percent interest each year. This can be obtained by using the formula of compound interest formula.
What is the required function?Equation of compound interest compounded yearly,
A = P(1 + R/100)^t
where,
A = amount
P = principal amount
R = rate
t = number of years
Given that P = $2000, R = 2%, number of years = t,
V(t) = 2000(1+2/100)^t
V(t) = 2000(1+0.02)^t
V(t) = 2000(1.02)^t
Hence V(t)=2000(1.02)^t function that gives the total value in dollars of the investment t years from now given that Shota invests $2000 in a certificate of deposit that earns 2 percent interest each year.
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Which of the following correlation coefficients expresses the weakest relationship between two variables
Answers
The correct option is a) -0.15.
The weakest correlation relationship between two variables is given by -0.15.
What is correlation?With the aid of correlation, the strength of the relationship between two variables can be determined. We can tell from this study whether there is no correlation, weak correlation, or a strong correlation between the two variables.
Two different types of correlation exist:
positive correlation: Two variables that move together, or in the same direction, are said to have a positive correlation. When one variable rises while the other rises or when one variable falls while the other falls, there is a positive correlation.negative correlation: When two variables are correlated negatively, the other variable's value falls as the value of the first variable rises. The correlation coefficient, which expresses correlation on a scale from +1 to -1, is used. Values less than 0 indicate a negative connection.The correlation value (r) always lies between -1 and 1.
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The complete question is -
Which of the following is the weakest correlation relationship between two variables?
a) -0.15
b) 0.27
c) -0.70
d) 0.55
Charlotte is driving at 52.7 mi/h and receives a text message. She looks down at her phone and takes her eyes off the road for 4.99 s. How far has Charlotte traveled in feet during this time
Answers
Answer:
385.7 ft
Step-by-step explanation:
The relation between speed, distance, and time is ...
distance = speed × time
Compatible unitsThe speed is given in miles per hour, but the time is given in seconds and the distance is wanted in feet. This suggests a conversion of speed to feet per second is appropriate.
[tex]\dfrac{52.7\text{ mi}}{\text{h}}\times\dfrac{1\text{ h}}{3600\text{ s}}\times\dfrac{5280\text{ ft}}{1\text{ mi}}=\dfrac{52.7\cdot22\text{ ft}}{15\text{ s}}=77.29\overline{3}\text{ ft/s}[/tex]
DistanceThe distance traveled is the product of this speed and the time period.
[tex]\dfrac{77.29\overline{3}\text{ ft}}{1\text{ s}}\times4.99\text{ s}=385.6937\overline{3}\text{ ft}\approx\boxed{385.7\text{ ft}}[/tex]
Solve 3a
17
7
8
9
- (2² + 1)² + a
when a = 8
Answers
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Assuming the equation should be:}[/tex]
[tex]\mathbf{3a - (2^2 + 1)^2 + a}[/tex]
[tex]\huge\textbf{Simplify it: }[/tex]
[tex]\mathbf{3a - (2^2 + 1)^2 + a}[/tex]
[tex]\mathbf{= 3(8) - (2^2 + 1)^2 + 8}[/tex]
[tex]\mathbf{= 24 - (2^2 + 1)^2 + 8}[/tex]
[tex]\mathbf{= 24 - (4 + 1)^2 + 8}[/tex]
[tex]\mathbf{= 24 - 5^2 + 8}[/tex]
[tex]\mathbf{= 24 - 25 + 8}[/tex]
[tex]\mathbf{= -1 + 8}[/tex]
[tex]\mathbf{= 7}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\frak{Option\ B. 7}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphiitrite1040:)}[/tex]Which of the following shows the correct order of the numbers?
5/6, 12/13, 0.8
A.) 5/6 < 0.8 < 12/13
B.) 0.8 < 5/6 < 12/13
C.) 0.8 < 12/13 < 5/6
Answers
The correct order of the numbers is 0.8 < 5/6 < 12/13. The correct option is B.) 0.8 < 5/6 < 12/13
Magnitude of numbersFrom the question, we are to determine the correct order of the numbers
The given numbers are
5/6, 12/13, and 0.8
Convert the fractions to decimals
5/6 = 0.8333
12/13 = 0.923
Thus, the numbers are
0.8333, 0.923, and 0.8
Order the numbers from the smallest to the largest
0.8 < 0.8333 < 0.923
≡ 0.8 < 5/6 < 12/13
Hence, the correct order of the numbers is 0.8 < 5/6 < 12/13. The correct option is B.) 0.8 < 5/6 < 12/13
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Find the equation of a line through (3, 1) and perpendicular to 10x + 3y = 5
Answers
Answer:
y = (3/10)x + 1/10
Step-by-step explanation:
The general structure of an equation in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept. First, we need to rearrange the given equation to determine the slope of the original line.
10x + 3y = 5 <----- Original equation
3y = -10x + 5 <----- Subtract 10x from both sides
y = (-10/3)x + 5 <----- Divide both sides by 3
Now, we can tell that the slope of the original line is m = -10/3. The perpendicular line should have an opposite-signed, reciprocal slope to that of the original. Therefore, the new slope is m = 3/10.
We can find the value of "b" by plugging the new slope and values from the Point (3, 1) into slope-intercept form.
m = 3/10
x = 3
y = 1
y = mx + b <----- Slope-intercept form
1 = (3/10)(3) + b <----- Insert values
1 = 9/10 + b <----- Multiply 3/10 and 3
10/10 = 9/10 + b <----- Create common denominators
1/10 = b <----- Subtract 9/10 from both sides
Now that we know the values for "m" and "b", we can construct the equation of the perpendicular line.
y = (3/10)x + 1/10
A yard with a tree is to be concreted. The owner wants to concrete the whole yard, but keep the tree in place and so concretes around the tree to its circumference. The tree has a circular cross section, with a diameter of 1 m. The yard is a rectangle, with sides of length 3 m and 4 m. What is the area of concrete required (to 1 d.p.)?
Answers
Answer:
11.2 square meters
Step-by-step explanation:
This is a very simple question. Basically, it's the area of a rectangle with the area of a circle subtracted. The area of a circle is calculated with the following formula:
[tex]\pi \times r^{2} [/tex]
Where r is the radius. We know the diameter is 1m, so we can simply halve this value to find the radius of 0.5m. Substituting in this value, we find the area of the circle to be:
[tex]\pi \times {0.5}^{2} \approx0.78539816339744830961566[/tex]
Now let's calculate the area of the rectangle, which is simply 3x4=12. Subtracting our earlier value from 12, we are left with an answer of 11.2 (to 1 d.p)
Consider this quadratic equation.
x2 + 2x + 7 = 21
The number of positive solutions to this equation is
.
The approximate value of the greatest solution to the equation, rounded to the nearest hundredth, is
Answers
Answer:
1 positive solution (and 1 negative)
the greatest solution is about 2.87
Step-by-step explanation:
so, it is
x² + 2x + 7 = 21
x² + 2x - 14 = 0
the general solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 2
c = -14
x = (-2 ± sqrt(2² - 4×1×-14))/(2×1) =
= (-2 ± sqrt(4 + 56))/2 = (-2 ± sqrt(60))/2 =
= (-2 ± sqrt(4×15))/2 = (-2 ± 2×sqrt(15))/2 =
= -1 ± sqrt(15)
x1 = -1 + sqrt(15) = 2.872983346... ≈ 2.87
x2 = -1 - sqrt(15) = -4.872983346...
Which side lengths form a right triangle?
Choose all answers that apply:
A:
11,13,√290
B:
7, 24, 25
C: 2, 5, 7
Answers
Answer:
B
Step-by-step explanation:
Use the Pythagorean theorem, 7^2+24^2=25^2
49+576=625
625=625
All the other answers do not satisfy the Pythagorean theorem (a^2+b^2=c^2)
Answer: A, B
Step-by-step explanation:
A right triangle's sides have a special property that the sum of the squares of the two legs is equal to the square of the hypotenuse. This is also known as the Pythagorean Theorem.
Let's check if this theorem holds true for each triangle.
A[tex]11^2+13^2=(\sqrt{290})^2\\ 121 + 169=290\\ 290 = 290[/tex]
The Pythagorean Theorem holds true, so this is a right triangle.
B[tex]7^2+24^2=25^2\\ 49 + 576 = 625\\ 625=625[/tex]
The Pythagorean Theorem holds true, so this is a right triangle.
C[tex]2^2+5^2=7^2\\ 4+25=49\\ 29 = 49[/tex]
This is a false statement, which doesn't make this triangle a right triangle. We could have use the triangle inequality theorem to prove that this isn't a triangle at all, and therefore not a right triangle, but I encourage you to learn about it and try it yourself.
Use the function f(x) = 5x² + 2x-3 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)
Answers
A)f(x)=3/5 and -1.
B)f(x)=(3/5, 0) and (-1, 0).
C)f(x)=(-0.2, -3.2)
D)f(x)= = -0.2.
What is factorization and example?Factorization in mathematics is dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the division of a number into its factors or divisors.For instance, the factorization of the integer 12 might appear as 3 times 4.Function: f(x) = 5x² + 2x-3.
a) Completely factor f(x)
f(x) = 5x² + 2x-3.
= 5x² + 5x-3x − 3
= 5x(x+1)-3(x+1)
=(5x-3)(x+1)
f(x)=3/5 and -1.
b)The x-intercepts of the graph of f(x):
f(x) = 5x² + 2x-3.
At f(x) = 0, the x-intercepts are present.
Therefore, x-intercepts are (3/5, 0) and (-1, 0).
c) The end behavior of the graph of f(x):
f(x) = 5x² + 2x-3.
The middle of the zeros is the vertex's x-coordinate.
=-0.2
Find the y-coordinate of the vertex, and substitute the found value of x into the given equation:
f(-0.2)= 5(-0.2)² + 2(-0.2) − 3
=-3.2
d)The steps you would use to graph f(x):
The axis of symmetry is the x value of the vertex.
Therefore, the graph is symmetrical at about x = -0.2.
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Total slack is calculated by ____
Answers
Total slack is calculated by the late finish minus early finish and the late start minus the early start
What is the total slack?Total slack is simply the amount of time taken for a task to be delayed before the project finish date is delayed. It can be positive or negative.
It is calculated as the calculated as the value of the Late Finish minus the Early Finish field, and the Late Start minus the Early Start field.
Total slack = Late finish - early finish + late start - early start
Thus, the total slack is calculated by the late finish minus early finish and the late start minus the early start.
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A group of scientists is conducting an experiment on the effects of media on children. they randomly select 100 children and randomly assign each child to one of four treatment groups. each treatment group has a specific amount of screen time during a one-week time frame. the first group has no screen time, the second group has two hours of screen time, the third group has four hours of screen time, and the fourth group has six hours of screen time. after the first week, the scientists conduct the same experiment, with the same subject groups, for three more weeks so that each group experiences each of the four treatments. which statements about this study are true?
Answers
The statements that are true about this study are
This study uses random samplingThis study uses a control groupThis study uses a repeated measures designThis is further explained below.
What is an experiment?Generally, a scientific technique is used to create a discovery, test a theory or show an established truth.
In conclusion, The following are accurate claims concerning this study:
Random sampling is used in this investigation. In this investigation, a control group is used. Repeated measurements are employed in this investigation.
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The solution of the cubic function f(x) are −4,53, and 1. Identify a factor of this function.
Select one:
a. 3x+5
b. 5x+3
c. x+1
d. x+4
Answers
A factor of the polynomial function is (d) x + 4
How to determine the factor of the function?The solution of the cubic function f(x) are given as:
−4, 5/3, and 1.
This means that:
x = -4, x = 5/3 and x = 1
Set the above equations to 0
x + 4 = 0, x - 5/3 = 0 and x - 1 = 0
From the list of options, we have
(d) x + 4
Hence, a factor of the polynomial function is (d) x + 4
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f(x) 2 square root -x^2+10 x what’s the domain
Answers
The domain of the function are all real numbers greater than 10
Domain of a functionDomain are values of the independent variables for which the function exist.
Given the function below;
[tex]f(x)=2\sqrt{-x^2+10x}[/tex]
For the function to exist, then;
-x^2+10x = 0
-x^2 = -10x
x = 10
Hence the domain of the function are all real numbers greater than 10
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Alissa is analyzing an exponential growth function that has been reflected across the y-axis. She states that the domain of the reflected function will change because the input values will be the opposite sign from the reflected function. Simon disagrees with Alissa. He states that if an exponential function is reflected across the y-axis, the domain will still be all real numbers.
Which student is correct and why?
Alissa is correct because the domain will change from negative to positive x-values.
Alissa is correct because a reflection across the y-axis will change the possible input values of the reflected function.
Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input.
Neither student is correct.
Answers
Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input for an exponential growth function.
Verification of Choice
Let us consider the following exponential growth function.
y = Aeˣ ...........................(1)
This equation changes when it is reflected across the y axis and becomes,
y = Ae⁻ˣ ...........................(2)
Here, the set of all x values for which y is defined is known as the domain of this exponential growth function.
Therefore, the domain of exponential growth function 1 is the set of all real numbers, given by, x ∈ [-∞,∞]
The domain of function 2, which is a reflection of function 1, will also consist entirely of real numbers and will be given by x ∈ [-∞,∞ ]
Therefore, between Alissa and himself, Simon is right when he asserts that even if an exponential growth function is reflected across the y-axis, the domain will still consist only of real values.
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Which point is a solution to the inequality shown in this graph? (urgent)
Answers
Answer: D
Step-by-step explanation:
sorry if its wrong
A pile of cards contains 3 diamonds,
4 hearts, and 2 spades. Marianna randomly
selects two cards without replacing the
first. What is P(hearts, then spades)?
F. 8/81
G. 1/9
H. 2/3
J. 1/18
Answers
Answer:G
Step-by-step explanation:
4/9 times 2/8= 1/9
Answer:
G 1/9
Step-by-step explanation:
add all of the cards together that will get you 9 then you take the hearts overing it by total then times it by 2 overing by 8 or
4/9x2/8
Last year, nicholas started babysitting to earn extra spending money. over the summer, he tracked how much money he earned at each babysitting job. this box plot shows the results.
Answers
The percent of the time Nicholas earned is the percent of the time 25%
The 5 values of the given box plot are;
The minimum fee = 20
In the first quartile, the 25th percentile point, Q₁ = 25
In the median or second quartile, the fiftieth percentile factor, Q₂ = 30
The 1/3 quartile, the 75th percentile point, Q₃ = 40
The maximum value = 55
The range = The most value - The minimal fee
The range = 55 - 20 = 35
We are aware that Nicholas earned $25 or less from the minimum value up to the first quartile, Q₁, which is the 25th percentile point, in which we've got 25 percent of the statistics points.
Consequently, the percentage of the time Nicholas earned $25 or much less is 25 percent of the time.
In mathematics, a percentage is a variety of ratios that can be expressed as a fraction of 100. If we have to calculate the percent of various, divide the wide variety by way of the whole and multiply by way of a hundred. For this reason, the shared approach is a component in line with a hundred. The phrase according to cent means in keeping with one hundred.
A relative cost indicates the hundredth component of any amount. One percent (symbolized 1%) is the hundredth part; for this reason, a hundred percent represents the whole lot and two hundred percent specifies two times the given amount.
Multiply the entire number amount through the decimal equal to the proportion. The end result is the share portion quantity. (consequently, this answers the question “How a whole lot is 24 percentage of 500,” you examine that 24 percent of 500 is a hundred and twenty).
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On a sunny day, Andrew, who is 1.9 m tall, casts a shadow that is 3.5 m long. A nearby tree casts a shadow that is 28.0 m long. To the nearest tenth of a metre, how tall is the tree?
Answers
Answer:
15.2
Step-by-step explanation:
The explanation is in the photo.. but basically this question is about similar triangles and you need to find the scale factor to find the height.
Hope it helps
the height of the tree is approximately 15.2 meters.
To find the height of the tree, we can set up a proportion between Andrew's height and the height of the tree based on their respective shadow lengths.
Let's denote the height of the tree as "h" meters.
The proportion between the height and shadow lengths can be written as:
h / 28.0 = 1.9 / 3.5
Now, we can solve for "h":
h = (1.9 / 3.5) * 28.0
h ≈ 15.2 meters
To the nearest tenth of a meter, the height of the tree is approximately 15.2 meters.
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A set of 5 numbers has an average of 50. The largest element in the set is 5 greater than 3 times the smallest element in the set. If the median of the set equals the mean, what is the largest possible value in the set
Answers
Answer:
5×3=15
15×3=45
therefore the largest value is 45
The largest possible value in the set is 92. The set has an equal mean and median. So, the set is {29, 29, 50, 50, 92}.
What are the mean and median of a set of data?Mean:
For a set of data, the average of all the data values is said to be its mean.
Median:
When the set is arranged in ascending order, the middle term is said to be its median (if there are an odd number of data values in the set) or the average value of the two middle terms is the median (if there are an even number of data values in the set).
Calculation:It is given that,
there are 5 numbers in the set
Mean = 50 and Median = Mean
So, Median = 50
Since there are 5 numbers in the set (odd number), the median is the third(middle) number.
Consider the first or smallest number as 's'.
Then the largest number = 3s + 5
By minimizing each term we get,
first term = s
second term = s
third term = 50
fourth term = 50
fifth term = 3s+5
If the mean is 50, then the sum of all the terms = 50 × 5 = 250
So,
s + s + 50 + 50 + 3s + 5 = 250
⇒ 5s + 105 = 250
⇒ 5s = 145
∴ s = 29
Thus, the smallest number is 29
Then, the largest number = 3s + 5 = 3 × 29 + 5 = 92
Therefore, the largest number in the given set is 92.
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help im in a rush!!!!!!!
Answers
Answer:
Your answer should be 52!!
Step-by-step explanation:
Work included on the picture below.
The graph of F(x) shown below resembles the graph of G(x) = x4, but it has
been changed somewhat. Which of the following could be the equation of
F(x)?
Answers
Using translation concepts, the equation of F(x) is:
A. [tex]F(x) = \frac{1}{3}x^4 - 2[/tex]
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The parent function is:
[tex]G(x) = x^4[/tex]
For function F(x), we have that:
It was shifted down 2 units, hence F(x) = G(x) - 2.It was vertically compressed by a factor of 3, hence [tex]F(x) = \frac{1}{3}G(x) - 2[/tex]Then the equation is:
A. [tex]F(x) = \frac{1}{3}x^4 - 2[/tex]
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Pls help me !!! due today:(
Answers
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "equations, expressions". The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
Brian is 8 and his brother is twice his age. How old will his brother be when brian is 11?.
Answers
Hence, the age of his brother when brain is [tex]11[/tex] is [tex]19.[/tex]
What is the simplification?
Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
Here given that,
Brian is [tex]8[/tex] and his brother is twice his age.
As age of brain is [tex]8[/tex].
His brother is twices than his age is [tex]8(2)=16[/tex]
When the age of brain is [tex]11[/tex] then [tex]3[/tex] added to his present age.
Then the age of his brother is [tex]16+3=19[/tex]
Hence, the age of his brother when brain is [tex]11[/tex] is [tex]19.[/tex]
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Firm valuation schultz industries is considering the purchase of arras manufacturing. arras is currently a supplier for schultz, and the acquisition would allow schultz to better control its material supply. the current cash flow from assets for arras is $8 million. the cash flows are expected to grow at 9 percent for the next five years before leveling off to 6 percent for the indefinite future. the cost of capital for schultz and arras is 13 percent and 11 percent, respectively. arras currently has 3 million shares of stock outstanding and $25 million in debt outstanding. what is the maximum price per share schultz should pay for arras? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) price per share $
Answers
Based on the calculations, the maximum price per share that Schultz should pay for Arras is approximately equal to $53.00.
How to calculate the maximum price per share?First of all, we would determine the cash flows for the company until the growth rate changes at a constant perpetual rate:
Year 1: $8,000,000(1 + 0.09) = $8,720,000.
Year 2: $8,720,000(1 + 0.09) = $9,504,800.
Year 3: $9,504,800(1 + 0.09) = $10,360,232.
Year 4: $10,360,232(1 + 0.09) = $11,292,652.88.
Year 5: $11,292,652.88(1 + 0.09) = $12,308,991.6392.
Year 6: $12,308,991.6392(1 + 0.06) = $13,047,5311.137552.
Next, we would calculate the terminal value in Year 5:
TV₅ = CF₆/(RWACC - g)
TV₅ = CF₆/(0.11 - 0.06)
TV₅ = $12,308,991.6392/0.05
TV₅ = $246,179,832.784.
By using Arras' cost of capital, we would determine its present value:
V₀ = $8,720,000/(1 + 0.11) + $9,504,800/(1 + 0.11)² + $10,360,232/(1 + 0.11)³+ $11,292,652.88/(1 + 0.11)⁴+ ($12,308,991.6392 + $246,179,832.784)/(1 + 0.11)⁵.
V₀ = $8,720,000/(1.11) + $9,504,800/(1.11)² + $10,360,232/(1.11)³+ $11,292,652.88/(1.11)⁴+ ($12,308,991.6392 + $246,179,832.784)/(1.11)⁵.
V₀ = 7,855,855.8559 + 7,714,308.9035 + 7,575,312.3467 + 7,438,820.2323 + 153,400,536.1422.
V₀ = $183,984,855.4806.
For the market value of the equity, we have:
S = 183,984,855.4806 - 25,000,000
S = $158,984,855.4806.
Now, we can find the maximum price per share:
Maximum price per share = 158,984,855.4806/3,000,000
Maximum price per share = $52.9949 ≈ $53.00.
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The cost of a flight is related to the distance traveled:
Miles 225 1,100 1,375 1,675 1,950 2,250
Cost ($) 50.3 111 143 187 214 196
Find the linear regression equation that models this data.
Answers
The linear regression equation that models the cost of a flight in function of the distance traveled is given as follows:
C(m) = 0.08316m + 31.36331
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points (x,y) are given as follows:
(225, 50.3), (1100, 111), (1375, 143), (1675, 187), (1950, 214), (2250, 196).
Hence, inserting these points in the calculator, the linear regression equation that models the cost of a flight in function of the distance traveled is given as follows:
C(m) = 0.08316m + 31.36331
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If $2000 is invested at 4% per annum compounded semiannually, how much is in the account after 8 years?
Answers
final balance $2,745.57
a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. -1/1.06
Answers
The required answers are:
a. The linear approximating polynomial at a = 1: P₁(x) = x - 2
b. The quadratic approximating polynomial at a = 1: P₂(x) = -3 + 3x - x²
c. Appromating the given quantity -1/1.06 for P₁(x) and P₂(x): -3.06 and -7.30 respectively.
Using Taylor polynomial series, the required approximating polynomials are calculated.
What is the Taylor polynomial series?The Taylor polynomial series is
Pₙ(x) = ∑ [tex]\frac{f^n(a)}{n!}[/tex](x - a)ⁿ; limits from 0 to n
Where fⁿ(a) is the nth derivation of f(x) at a
The first order(linear) Taylor polynomial series is
P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹
The second order(quadratic) Taylor polynomial series is
P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) + [tex]\frac{f''(a)}{2!}[/tex](x - a)²
Calculation:The given function is f(x) = -1/x at a = 1
f(a) = f(1) = -1
f'(x) = -(-1/x²) = 1/x²; f'(a) = f'(1) = 1
f''(x) = -2/x³; f''(a) = f''(1) = -2
a. Linear approximating polynomial:
From the Taylor series, we have
P₁(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a)¹
On substituting,
P₁(x) = -1 + (1/1!)(x - 1)¹
= -1 + (x - 1)
= x - 2
b. Quadratic approximating polynomial:
From the Taylor series, we have
P₂(x) = f(a) + [tex]\frac{f'(a)}{1!}[/tex](x - a) + [tex]\frac{f''(a)}{2!}[/tex](x - a)²
On substituting,
P₂(x) = f(1) + (1/1!)(x - 1) + (-2/2!)(x - 1)²
= -1 + (x - 1) - (x - 1)²
= -1 + x - 1 - (x² - 2x + 1)
= x - 2 - x² + 2x - 1
= -3 + 3x - x²
c. Approximating the given quantity -1/1.06:
Substituting x = -1.06 in P₁(x) and P₂(x),
P₁(x) = x - 2
⇒ P₁(-1.06) = (-1.06) - 2 = -3.06
P₂(x) = -3 + 3x - x²
⇒ P₂(-1.06) = -3 + 3(-1.06) - (-1.06)² = -7.30
Therefore, the approximating polynomials are calculated by using Taylor polynomial series.
Disclaimer: The given question is incomplete. Here is the complete question.
Question:
a. Find the linear approximating polynomial for the following function centered at the given point a.
b. Find the quadratic approximating polynomial for the following function centered at the given point a.
c. Use the polynomials obtained in parts a. and b. to approximate the given quantity.
f(x) = -1/x , a = 1; approximate -1/1.06
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The table shows data from a survey about the number of times families eat at restaurants during a week. The families are either from Rome, Italy or New York, New York:
Maximum Minimum Q1 Q3 IQR Median Mean σ
Rome 16 0 3 13 10 8.5 8 5.4
New York 20 1 4.5 6 1.5 5.5 7.25 5.4
Which of the choices below best describes how to measure the center of this data? (5 points)
Group of answer choices
Both centers are best described with the mean.
Both centers are best described with the median.
The Rome data center is best described by the mean. The New York data center is best described by the median.
The Rome data center is best described by the median. The New York data center is best described by the mean.
It's NOT C "The Rome data center is best described by the mean. The New York data center is best described by the median." already tried, its incorrect.
Answers
The best description on measurement of the center of this data is; C. The Rome data center is best described by the mean. The New York data center is best described by the median.
How to find the center of the data?If we make the box and whisker plot of the Rome and New York data, we will see that there will clearly be an outlier in the New York data.
Thus;
Due to the fact that the data set for New York has an outlier and the mean is skewed, it means that we would use the median.
Finally, we see that the Rome data set is symmetrical because it has no outlier, and as such we can use the mean.
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