We can see that the linear approximation appears to be the best for function g since it is closer to g for a larger domain than it is to f and h. The approximation looks worst for function f since f moves away from Lf faster than g and h do. Hence, the linear approximation is the worst for function f.
Given that f(x) = (x - 1)^2, g(x) = e^(-2), and h(x) = ln(1+2x) - 2x.
(a) Find the linearizations of f, g, and h at a = 0.
The linearization of f at a = 0 is given by
Lf(x) = f(0) + f'(0)(x - 0)
= (0 - 1)^2 + 2(0 - 1)(x - 0)
= -x + 1
The linearization of g at a = 0 is given by
Lg(x) = g(0) + g'(0)(x - 0)
= e^(-2) + 0(x - 0)
= e^(-2)
The linearization of h at a = 0 is given by
Lh(x) = h(0) + h'(0)(x - 0)
= (ln(1 + 2(0)) - 2(0)) + [(1/(1 + 2(0)))2 - 2](x - 0)
= -2x
Graph f, g, and h and their linear approximations. For which function is the linear approximation best? For which is it worst? Explain.
The graphs of f(x) = (x - 1)^2, g(x) = e^(-2), h(x) = ln(1+2x) - 2x, and their respective linear approximations Lf(x) = -x + 1, Lg(x) = e^(-2), and Lh(x) = -2x.
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What will be the exponent of the product of 8.9 x 1012 and 4.7 x 10-2 in Scientific Notation?
the exponent of the product of 8.9 x 10¹² and 4.7 x 10⁻² in scientific notation is 11.
define exponentialExponential refers to a mathematical function or relationship in which a variable (such as x) is raised to a constant power (such as 2, 3, or e) to produce a result. The term "exponential" can also be used more broadly to describe any situation in which something grows or changes at an increasingly rapid rate over time, often with a compounding effect.
First, we multiply the two numbers:
(8.9 x 10¹²) x (4.7 x 10⁻²) = 41.83 x 10¹⁰
41.83 x 10¹⁰ = 4.183 x 10¹¹
Therefore, the exponent of the product of 8.9 x 10¹²and 4.7 x 10⁻² in scientific notation is 11.
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Let X1, X2,..., Xn be i.i.d. random variables from a double exponential distribution with density f(x) = 1/2*λ*exp(−λ|x|). Derive a likelihood ratio test of the hypothesis H0: λ=λ0 versus H1: λ=λ1, where λ0 and λ1 > λ0 are specified numbers. Is the test uniformly most powerful against the alternative H1: λ > λ0?
Which operation is used to convert 245 liters to milliliters?
O Multiply by 1,000
O Multiply by 10,000
O Divide by 1,000
O Divide by 10,000
How is multiplying by a fraction ( 1/2x 1/4 ) and dividing by a whole number ( 1/2÷ 4) related?
Answer:
same
Step-by-step explanation:
They are the same since
1/2÷4=1/2×1/4(reciprocal)
Answer:
dfgdfvdfvthtybg f cv v
Step-by-step explanation:
Question below pls help:
florian bought his first car for $6,040. he saved up $1,000 gor a down payment and takes out a loan for the rest.the loan will allow him to pay $140 per month for the remaining balance. how much will he own on his car for 3 months?
Florian has to pay $2,013.3, then he own on his car for 3 months
What is unitary method?"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value. For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
According to our question-
6040 is the total amount
he has to repay in 3 months
dividing the total amount/3
6040/3
$2,013.3
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Masons backyard deck is rectangular. The width is 12 feet less than the length. The perimeter is 64 feet. What is the length?
As Masons backyard deck is rectangular, the length of the deck is 22 feet.
Let's start by using algebra to solve for the length of the rectangular deck.
Let L be the length of the deck.
Then, the width of the deck is L - 12.
The perimeter is the sum of all four sides, so we have:
Perimeter = 2L + 2(L - 12) = 64
Simplifying the equation, we get:
2L + 2L - 24 = 64
Combining like terms, we get:
4L - 24 = 64
Adding 24 to both sides, we get:
4L = 88
Dividing both sides by 4, we get:
L = 22
Therefore, the length of the deck is 22 feet.
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Round the answer to the nearest hundredth
Using trigonometric functions, the value of the side AC = 2.85 units.
What are trigonometric functions?The right triangle's angle serves as the domain input value for the six fundamental trigonometric operations, and the output is a range of numbers.
The angle, given in degrees or radians, is the domain of the trigonometric function, sometimes referred to as the "trig function," of f(x) = sin, and the range is [-1, 1]. The other functions have a similar domain and scope. Trigonometric functions are widely used in algebra, geometry, and calculus.
Now in the given figure,
The angle is a right-angled triangle.
Now as per the trigonometric functions,
Sin 35° = AC/AB
⇒ 0.57 = x/5
⇒ x = 0.57 × 5
= 2.85.
The length of the opposite side AC is 2.85 units.
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the national center for heatlh has found that there is a 0.41% chance that an american citizen will die from falling. what is the probability that you will not die from a fall?
If the probability an American will die from falling is 0.41%, the probability a American will not die from falling is 100% - 0.41% = 99.59%.
Answer: 99.59%.
Liam has 62 dollars.he saves an equal amount of money each week for 6 weeks. now he was 110 dollars . how much money did Liam save each week?
Answer: $8
Step-by-step explanation:
To find how much he saved over the course of 6 weeks, subtract 62 from 110.
110 - 62 = 48
To find how much he saved each week, divide 48 by 6.
48 ÷ 6 = 8
Liam saved $8 each week.
You have five student groups to present in class one group cannot go first because they need additional set up time and how many orders can they present
They can present in 96 different orders. Given, there are five student groups to present in class and one group cannot go first because they need additional set-up time.
Permutation is to select an object then arrange it and it cares about the orders while Combination is about only selecting an object without caring the orders.
We have 5 positions to fill here.
First position: 4 ways (one of the rest 4 groups will present first)
Second position: 4 ways (one of the rest 3 groups and the group which could not present first, will present second)
Third position: 3 ways (one of the rest 3 groups will present third)
Fourth position: 2 ways (one of the rest 2 groups will present fourth)
Fifth position: 1 way (rest group will present last)
Total ways in which they can present = 4*4*3*2*1 = 96
Hence, the answer is 96.
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Triangle ABC is rotated 270 clockwise about the origin to produce Triangle A'B'C'. which rule best describes this rotation?
the best rule to describe this rotation is:
(x, y) → (-y, x)
Why it is?
The given rotation is a 270 degree clockwise rotation about the origin. This means that each point in Triangle ABC is rotated 270 degrees in a clockwise direction around the origin to produce the corresponding point in Triangle A'B'C'.
One possible rule to describe this rotation is:
(x, y) → (-y, x)
This rule represents a 90 degree clockwise rotation about the origin, which can be applied three times to achieve a 270 degree clockwise rotation.
So, if we apply this rule to each vertex of Triangle ABC, we get the corresponding vertices of Triangle A'B'C':
A = (a, b) → A' = (-b, a)
B = (c, d) → B' = (-d, c)
C = (e, f) → C' = (-f, e)
Therefore, the best rule to describe this rotation is:
(x, y) → (-y, x)
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approximately 10.5% of american high school students drop out of school before graduation. assume the variable is binomial. choose 15 students entering high school at random. find these probabilities. round intermediate calculations and final answers to three decimal places. part: 0 / 30 of 3 parts complete part 1 of 3 (a) at least 13 graduate
Probabilities (at least 13 graduates) = 0.29858
The variable is binomial, which means that it can only have two possible outcomes (in this case, either a student will graduate or they will drop out). The probability of at least 13 students out of 15 graduating is calculated by adding the probability of exactly 13 students graduating and the probability of exactly 14 students graduating:
P(at least 13 graduate) = P(exactly 13 graduate) + P(exactly 14 graduate)
To calculate the probability of exactly 13 students graduating, use the binomial formula:
P(X = 13) = (15 choose 13) * (0.105)13 * (0.895)2
The calculation for P(X = 13) is: (15 choose 13) * (0.105)13 * (0.895)2 = (15!/13!(15-13)!) * (0.105)13 * (0.895)2 = (15 * 14 / 1 * 1) * (0.00155) * (0.80505) = 0.16437
Similarly, to calculate the probability of exactly 14 students graduating, use the binomial formula:
P(X = 14) = (15 choose 14) * (0.105)14 * (0.895)1
The calculation for P(X = 14) is: (15 choose 14) * (0.105)14 * (0.895)1 = (15!/14!(15-14)!) * (0.105)14 * (0.895)1 = (15 / 1) * (0.01462) * (0.895) = 0.13421
Finally, add the probabilities together to find the probability of at least 13 students graduating.
P(at least 13 graduates) = P(exactly 13 graduate) + P(exactly 14 graduate)
P(at least 13 graduates) 0.16437 + 0.13421 = 0.29858, rounded to three decimal places.
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a restaurant bill before tax is 15.50 how much is 15% tip for this bill
Answer:
$2.235
Step-by-step explanation:
15% = 0.15
We Take
15.50 x 0.15 = $2.235
So, the tip for this bill is $2.235
5. Line 1 passes through the point D(2, 4) and has the same slope as the line segment joining
M(4, 5) and N(6, -19). Determine the equation of Line 1 in the form y = mx + b.
The equation of Line 1 in the form y=-12x+28
What is a Line Segment?A measurable path between two places is referred to as a line segment. Line segments may make up the sides of any polygon since they have a set length.
Coordinates of Line 2 M(4,5) and N(6,-19)
Slope of Line 2 is =(-19-5)/(6-4)
=-24/2=-12
Slope of line 1 and line 2 are same
Cordinate of Line 1 is D(2,4)
D(2,4) must pass through line 1, so it must satisfy the equation
y=mx+b
4=2(-12)+b
4+24=b
b=28
the equation of Line 1 in the form y=-12x+28
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Please help. Get more math
Step-by-step explanation:
since we can officially use only one point (the given point), we need to start with the point-slope form :
y - y1 = m(x - x1)
with m being the slope, (x1, y1) being the point.
sadly, to get the slope, we need a second point anyway, because the slope is the ratio
y coordinate difference / x coordinate difference
when going from one point on the line to another.
I recommend to use (0, 50) for the "other" point, as there seems to be the smallest error in the coordinates.
so, when going from (0, 50) to the given point (6, -40) :
x changes by +6 (from 0 to 6).
y changes by -90 (from 50 to -40).
the slope m = -90/+6 = -15/1 = -15
y - -40 = -15(x - 6) = -15x + 90
y + 40 = -15x + 90
y = -15x + 50
that is the slope-intercept form.
m = -15
b = 50
y = -242
-242 = -15x + 50
-292 = -15x
x = -292/-15 = 292/15 = 19.46666666... ≈ 19
MAthematics pls help
Answer:
x = 4
Step-by-step explanation:
6x + 21 = 5x + 25
Then, subtract 5x from both sides:
x + 21 = 25
Then, subtract 21 from both sides.
x = 4
Therefore, x is equal to 4 degrees
If the sum of two numbers is 10 and the product of the numbers is 15, then find the following:
(a) The difference of numbers.
(b) Sum of cube of the numbers.
Answer:
the numbers are
[tex] \sqrt{10} + 5 \\ - \sqrt{10} + 5[/tex]
Step-by-step explanation:
then there difference is
square root of 10 + 5 -(- square root of 10 +5)
=
[tex]2 \sqrt{10} [/tex]
and the cube of there sum is 15^3 = 15* 15* 15
= 3375
The Turners have purchased a house for $170,000. They made an initial down payment of $34,000 and secured a mortgage with interest charged at a rate of 3.5%/year on the unpaid balance. (Interest computations are made at the end of each month.) Assume that the loan is amortized over 15 years. (Round all answers to the nearest cent.)
(a) What monthly payment will the Turners be required to make?
$
(b) What will be their total interest payment?
$
(c) What will be their equity (disregard depreciation and inflation) after 10 years?
$
(a) The present value of an annuity formula can be used to calculate the monthly payment: Payment is equal to (PV x I / (1 - (1 + i)(-n)).
What monthly payment will the Turners be required to make?Where PV is the loan's present value, I is its monthly interest rate (0.035 / 12), and n is the number of payments (15 years multiplied by 12 months every year = 180 months).
Applying the values provided, we obtain:
(136,000 x 0.002917) / (1 - (1 + 0.002917)(-180)) is the amount to be paid.
Amount paid: $1,054.63
Hence, the installment will be $1,054.63 per month.
What will be their total interest payment?(b) By deducting the loan amount (PV) from the total amount paid over the loan's lifetime, it is possible to get the total interest payment:
Total interest equals PV minus (Payment x n)
Applying the values provided, we obtain:
$1,054.63 multiplied by 180 equals $136,000 in interest.
Interest totaled $88,833.40.
The total interest payment will therefore be $88,833.40.
What will be their equity (disregard depreciation and inflation) after 10 years?(c) The Turners will have paid 120 times over the course of 10 years (10 years x 12 months/year). To determine their equity, we can apply the formula for calculating a loan's remaining balance:
The remaining balance is calculated as follows: PV x (1 + i)n - Payment x (1 + i)n - 1)/i
Where n denotes how many payments are still due (180 - 120 = 60).
Applying the values provided, we obtain:
The remaining balance is calculated as follows: $136,000 x (1 + 0.002917)60 - $1,054.63 x (1 + 0.002917)60 - 0.002917
Balance remaining: $71,587.90
As a result, their equity will be $170,000 (the original purchase price) less $71,587.90 (the outstanding balance) = $98,412.10 after ten years.
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Which situation can be best modeled by a linear function?
A The amount of money in a savings account with an annual interest rate of 1.5%
B) The amount of radioactive material with a decay rate of 3% every day
C) The cost of a laptop that depreciates at the rate of 8% every year
D) The height of the water in a tank when drained at the rate of 0.3 gallons per minute
A The amount of money in a savings account with an annual interest rate of 1.5%
3. What is the value of x?
x + 5
X
05
02.5
07.5
O 10
x-2
x + 1
(1 point)
The value of x is equal to; A. 5.
What is the basic proportionality theorem?In Mathematics, the basic proportionality theorem states that when any of the two (2) sides of a triangle is intersected by a straight line which is parallel to the third (3rd) side of the triangle, then, the two (2) sides that are intersected would be divided proportionally and in the same ratio.
By applying the basic proportionality theorem to the given triangle, we have the following:
x/(x + 5) = (x - 2)/(x + 1)
By cross-multiplying, we have the following:
x(x + 1) = (x - 2)(x + 5)
x² + x = x² + 5x - 2x - 10
By rearranging and collecting like-terms, the value of x is given by:
2x - 10 = 0
2x = 10
x = 10/2
x = 5.
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Work out the compass directions that should replace A, B and C.
The compass directions that are given to A, B and C. are East, South-East and North-west respectively.
Explain about the compass directions?North, South, East, and West are the four cardinal directions. The sun's rising and setting serve as a point of reference for these instructions.
The sun seem to rise in the east then set in the west because the Earth revolves from west to east. Moreover, the North and South Poles serve as orientation markers.On the compass rose, the four cardinal directions are, from north (N), east (E), south (S), and west (W), at 90° angles. By slicing the aforementioned in half, the following directions result: northeast (NE), southwest (SW), southeast (SE), and northwest (NW)Thus, the compass directions that are given to A, B and C. are East, South-East and North-west respectively.
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a man allow 12% discount in a computer having marked price RS 32000. If he make Rs.1160 profit on it , Find the cost price of computer
Answer:
CP of computer = 27000 rs.
Step-by-step explanation:
D% = Dis/MP*100
12*32000/100 = Dis Dis = 3840 rs.We know, Dis = MP-SP
32000 - 3840 = SP28160 = SPGiven Profit= 1160 rs.
SP-CP = 1160CP = 28160-1160 = 27000So,CP = 27000 rs.
For f (0,1)4 10,1) f(x) is obtained by removing the second bit from x and placing the bit at the end of the string. For example, f(1011) 1110 Select the correct value for f (0101) 0101 1010 0110 0011 Let f: A A and g: A-A be one-to-one functions. Which of the following statements are true? (Check all that apply) f o g is onto f o g is one-to-one f o g is invertible If f, g are also onto, then f o g is invertible. g o f is one-to-one
The given example of f(1011) = 1110 illustrates how a one-to-one function operates, in that the same bitstring is not mapped to multiple elements in the range.
For the given functions f: A -> A and g: A -> A which are one-to-one functions, the following statements are true:
f o g is onto (also known as surjective), meaning that the range of f o g is equal to the codomain of f o g. This means that for any value in the codomain, there is at least one value In the domain that will produce it when operated on by f o g.for such more questions on function operates
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The measures of include mean and mode. The third of those measures is. Dividing the sum of all data values by the total frequency will give us the. Some data sets may have zero, one, or more than one. If there are 4999 values in a data set, then the will be located at the 2500th value, when those values are put into increasing order. If there are 4999 values in a data set, then the will be found by subtracting the first value from the 4999th value, when those values are put into increasing order. The measures of include variance and range. The third of those measures is. The is found by taking the square root of the. To approximate the variation of the data values from the mean, find the. In the excel function stdev. S, the last s stands for
The measures of central tendency include mean and mode, which include a third measure called median.
The three measures for determining central tendency are mean, median, and mode. The mean, also known as average, is the result of dividing the total number of observations by the number of observations. The mode is the value that occurs the most frequently, whereas the median is the midpoint value in the ordered set of observations.
The average or middle of a dataset can be discovered with the aid of central tendency measures. The most frequent value is the mode. The median is the midpoint of an ordered dataset. Mean: the product of the total number of values and their sum.
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Correct question is:
The measures of _________ include mean and mode. The third of those measures is ________.
Dividing the sum of all data values by the total frequency will give us the_____.
Which is the best estimate of the sum of 5 1/4 and 8 5/6
Answer:
Step-by-step explanation:
ur mom
Decide whether you can use the given information to prove that $\triangle ABC\cong\triangle DEF$ . Explain your reasoning.
$\angle A\cong\angle D,\ \angle C\cong\angle F,\ \overline{AC}\cong\overline{DF}$
Responses
Answer:
Yes, we can use the given information to prove that $\triangle ABC\cong\triangle DEF$ by the Angle-Side-Angle (ASA) congruence criterion.
We are given that $\angle A\cong\angle D$ and $\angle C\cong\angle F$, which satisfies the Angle-Angle (AA) criterion. Furthermore, we are given that $\overline{AC}\cong\overline{DF}$, which satisfies the Side-Side-Side (SSS) criterion. Therefore, by combining the AA and SSS criteria, we can conclude that $\triangle ABC\cong\triangle DEF$ by the ASA criterion.
In summary, the given information satisfies the necessary conditions for the ASA congruence criterion, and therefore we can prove that $\triangle ABC\cong\triangle DEF$.
please help me i really need it
a. the mean is 200.31 cm. b. The height of the new player is 210 cm.
What is mean?The mean, commonly referred to as the average, is a statistic that depicts the usual value of a group of data and measures central tendency. It is calculated by adding up all of the data set's values and dividing the result by the total number of values. Since it offers a single value that summarises the complete set of data, the mean is an effective statistical tool. It may, however, be vulnerable to outliers or extremely high or low values that affect the mean's value. As a result, while examining data, it is crucial to take additional measures of central tendency into account, such as the median or mode.
The mean or average is given as:
mean = (sum of all heights) / (number of players)
The total number of players are:
1 + 3 + 2 + 5 + 2 = 13
Sum of heights is:
(198 x 1) + (199 x 3) + (200 x 2) + (201 x 5) + (202 x 2) = 198 + 597 + 400 + 1005 + 404 = 2604
Thus,
mean = 2604 / 13 = 200.31 cm
b. For the new player the number of players are 14:
201 = (2604 + height of new player) / 14
201 x 14 = 2604 + height of new player
2814 = 2604 + height of new player
height of new player = 2814 - 2604 = 210 cm
Hence, a. the mean is 200.31 cm. b. The height of the new player is 210 cm.
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Five cars start out on a cross-country race. The probability that a car breaks down and drops out of the race is 0.2. Cars break down independently of each other.
(a) What is the probability that exactly two cars finish the race?
(b) What is the probability that at most two cars finish the race?
(c) What is the probability that at least three cars finish the race?
(a) The probability that exactly two cars finish the race is 0.0512.
(b) The probability that at most two cars finish the race is 0.05792.
(c) The probability that at least three cars finish the race is 0.94208.
(a) To determine the probability that exactly two cars finish the race, we have to use binomial distribution. In this case, we have n = 5 trials, and p = 0.8 is the probability that a car finishes the race (1 - 0.2). Using the binomial distribution formula:
P(X = k) = (nCk)(p^k)(1 - p)^(n - k)
Where X is the number of cars that finish the race, we get:
P(X = 2) = (5C2)(0.8²)(0.2)³= (10)(0.64)(0.008)= 0.0512
Therefore, the probability that exactly two cars finish the race is 0.0512.
(b) To determine the probability that at most two cars finish the race, we have to calculate the probabilities of 0, 1, and 2 cars finishing the race and add them up.
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)= (5C0)(0.8⁰)(0.2)⁵ + (5C1)(0.8¹)(0.2)⁴ + (5C2)(0.8²)(0.2)³= 0.00032 + 0.0064 + 0.0512= 0.05792
Therefore, the probability that at most two cars finish the race is 0.05792.
(c) To determine the probability that at least three cars finish the race, we can calculate the probability of 0, 1, and 2 cars finishing the race and subtract it from 1, which gives us the probability of at least three cars finishing the race.
P(X ≥ 3) = 1 - [P(X = 0) + P(X = 1) + P(X = 2)]= 1 - (0.00032 + 0.0064 + 0.0512)= 0.94208
Therefore, the probability that at least three cars finish the race is 0.94208.
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If point is slid(translated) 4 units to the right, what would the new coordinates be (3,-4)