The Taylor polynomial t3(x) for f(x) = cos(x) centered at a = pi/2 is t3(x) = -(x-pi/2) + (x-pi/2)³/3!.
How do we calculate?A polynomial is described as an expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
The Taylor polynomial of degree n for a function f(x) centered at a is given by the formula:
We get the derivatives :
pn(x)=f(c)+f′(c)(x−c)+f′′(c)2!....
f(x) = cos(x)
f'(x) = -sin(x)
f''(x) = -cos(x)
f'''(x) = sin(x)
We the evaluate these derivatives at x = pi/2:
f(pi/2) = cos(pi/2) = 0
f'(pi/2) = -sin(pi/2) = -1
f''(pi/2) = -cos(pi/2) = 0
f'''(pi/2) = sin(pi/2) = 1
We substitute these values into the formula for the Taylor polynomial, and simplify to get Taylor polynomial T3(x) for the function:
the Taylor polynomial t3(x) for f(x) = cos(x) centered at a = pi/2 is t3(x) = -(x-pi/2) + (x-pi/2)³/3!.
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CNNBC recently reported that the mean annual cost of auto insurance is 1016 dollars. Assume the standard deviation is 209 dollars. You take a simple random sample of 94 auto insurance policies. Assuming the original population forms a bell-shaped distribution, answer the following and round your answers to three decimals.
Find the probability that a single randomly selected value is more than 979 dollars.
P(X > 979) = ???
Find the probability that a sample of size
is randomly selected with a mean that is more than 979 dollars.
P(M > 979) = ???
1. The probability that P(X > 979) = 0.567
2. The probability that P(M > 979) = 0.956
How do you calculate probability?
To calculate the probability that a single randomly selected value is more than 979 dollars.
979-1016
= -37/209
= -0.177
P(X > -0.177) = 0.5675
Therefore P(X > 979) = 0.568
To calculate that a sample of size is randomly selected with a mean that is more than 979 dollars.
209 / √94 = 21.557
-37/ 21.557 = -1.7164
P(Z > -1.714) = 0.9564
therefore P(M > 979) = 0.956
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For two programs at a university, the type of student for two majors is as follows. find the probability a student is a graduate student, given they are a history major.
The probability that a student is a graduate student given they are a history major is approximately 0.16.
What is probability?The likelihood or chance that an event will occur is quantified by probability. A number between 0 and 1, where 0 denotes that the occurrence is impossible and 1, denotes that the event is certain, is generally used to express it.
According to question:We are given the following information:
Total number of students who are history major: 463
Total number of graduate students: 261
Number of graduate students who are history major: 73
We can use the formula for conditional probability to find the probability that a student is a graduate student given that they are a history major:
P(graduate | history) = P(graduate and history)/P(history)
P(graduate | history) = 73/463
P(graduate | history) ≈ 0.1575 (rounded to the nearest hundredth)
Therefore, the probability that a student is a graduate student given they are a history major is approximately 0.16.
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A box contains 16 transistors, 3 of which are defective. If 3 are selected at random, find the probability of the statements below.
a. All are defective
b. None are defective
a. The probability is.
(Type a fraction. Simplify your answer.)
***
The probability of selecting all defective transistors is 1/560.
To find the probability of the statementsThe probability of selecting all defective transistors can be calculated as:
P(all defective) = (number of ways to select 3 defective transistors) / (total number of ways to select 3 transistors)
The number of ways to select 3 defective transistors is simply the number of combinations of 3 defective transistors out of the total of 3, which is 1. The total number of ways to select 3 transistors out of 16 is:
total number of ways = number of combinations of 3 transistors out of 16
= (16 choose 3)
= 560
Therefore, the probability of selecting all defective transistors is:
P(all defective) = 1 / 560
To simplify the answer, we can write it as a fraction in lowest terms:
P(all defective) = 1 / 560 = 1/ (161514/321) = 1/560
Therefore, the probability of selecting all defective transistors is 1/560.
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I need the answers and a explanation if possible
Wwe can reject the null hypothesis and deduce that there is sufficient empirical evidence to validate the presumption that seatbelts are competent for mitigating fatalities.
How to explain the hypothesisNull Hypothesis: There is no discernible distinction between the proportion of fatalities among occupants wearing seat belts and those without.
Alternative Hypothesis: The portion of fatalities experienced by those in vehicles donning seatbelts will be demonstrably lower in comparison to individuals not utilizing them.
The z-value was computed, finding that (0.0113 - 0.0024) / √(0.0047 * (1 - 0.0047) * (1/2915 + 1/7848)) = 12.43.
For a two-tailed test at a 0.05 significance level with 2915 plus 7848 less 2 = 10761 degrees of freedom, the critical value range would be ±1.96. With the calculated z-value of 12.43 surpassing the critical threshold, we can reject the null hypothesis.
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0.0625 What is the equivalent percent? %
Answer:6.25%
Step-by-step explanation:
mathematics plssssssss help me!!!!
correct me
Answer:
let the children be x
let the dog be y
for the heads
x+y = 14 --- eqn 1
for the legs
2x + 4y = 40 ----- eqn2
since the children have 2 legs each and the dogs have 4 legs each
x + y = 14
2x+4y=40
through elimination method
multiply eqn1 by 2 and multiply eqn2 by 1
2x + 2y = 28
2x + 4y = 40 , then subtract
-2y = -12
to get y divide both sides by -2
y = 6
since in eqn 1
x+y=14
x = 14-y = 14-6 = 8
x = 8, y = 6
the children are 8 while the dogs are 6
Shirley returned from Canada with $23 445 and converted the dollars to kina at the Jacksons International Airport Calculate the amount in kina he received at rate of exchange of K1 (2 marks) CASO 4689 ?
what are the answers to these questions_
The general formula for f'(x) would be f' (x) = - 8 sin (x) + C.
The most general formula based on the first would be f(x) = 8 cos ( x ) + Cx + D.
How to find the general formula ?To find the most general formula for f ' ( x ), we need to integrate f'' ( x ) with respect to x:
f'' ( x ) = - 8 cos (x)
f' (x) = ∫ ( -8cos(x)) dx
f ' (x) = - 8 sin(x) + C, where C is an arbitrary constant.
We need to integrate f'( x ) with respect to x to find the most general formula for f ( x ):
f'(x) = - 8 sin(x) + C
f(x) = ∫ ( - 8sin ( x ) + C) dx
f(x) = 8 cos ( x ) + Cx + D, where D is another arbitrary constant.
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Surface area pls help
The surface area of the triangular pyramid is 147.6 cm².
What is surface area?The surface area of a three-dimensional object is the total area of all its faces.
To calculate the surface area of the triangular pyramid, we use the formula below
Formula:
S.A = (3bL/2)+(bh/2)...................... Equation 1Where:
S.A = Surface area of the Pyramidb = Length of the triangleL = Slant height of the pyramidh = Height of the triagular baseFrom the question,
Given:
b = 8 cmh = 6.9 cmL = 10 cmSubstitute these values into equation 1
S.A = (3×8×10/2)+(8×6.9/2)S.A = 120+27.6S.A = 147.6 cm²Learn more about surface area here: https://brainly.com/question/76387
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AC has endpoints A (3,6) and C (-2, 10). What is the length of AC ?
f(25) = 80 , find the value of f(2022) and give proper method and the final answer
The value of f(2020) is 39/100.
Given function is,
f(25) = 80
And f(xy) = f(x)/y² .....(i)
Since
f(25) = 80
Then we define function as
f(x) = x + 55 .....(ii)
Now we can write 2020 = 101 x 20
So f(2020) = f(101x20) = f(101)/20² from (i)
= (101 + 55)/400 from(ii)
= 156/400
= 39/100
Hence, f(2020) = 39/100
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HELP ME PLEASEEE!
Whoever answers right will get brainliest!
Answer:
last choice: 2b²/a³
Step-by-step explanation:
2a⁻³/b⁻² = 2·(1/a³) / (1/b²) = 2·(1/a³)(b²) = 2b²/a³
Solve.
13. A ferry shuttles from Seattle to Vancouver Island and back. Because of
head winds, the return trip is slower than the trip to the island. The
average speed of the, ferry, in miles per hour, is given by the
2d
expression:
What is the average speed of the ferry?
d
+
50 60
The average speed of the ferry is 54.54 miles per hour.
The expression for the average speed is given [tex]\frac{2d}{\frac{d}{50}+\frac{d}{60} }[/tex].
Now, the given expression can be solved as follows
2d÷ (6d/300 + 5d/300)
= 2d÷(11d/300)
= 2d×300/11d
= 600/11
= 54.54 miles per hour
Therefore, the average speed of the ferry is 54.54 miles per hour.
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What are the period and amplitude of the function?
Answer:
period : π ; amplitude : 2
Step-by-step explanation:
Correct me if I'm wrong!!
Each day for 47 days, Zara predicted whether or not it would snow.
The frequency tree below shows her predictions and whether it snowed or not.
On what fraction of the days when it snowed was Zara's prediction correct?
Give your answer in its simplest form.
Predicted weather
Snow
No snow
19
Actual weather
Snow 15
No snow
Snow
No snow
Elin chose C as the correct answer. Explain how she got her answer.
Answer:
Elin concluded that car B travels a distance of 265.8 km during the same time based on her interpretation of the given information.
Step-by-step explanation:
My apologies for the confusion. Let's analyze how Elin arrived at her answer.
According to the given information, car A travels 221.5 km at a given time. Elin interpreted the statement "car B travels 1.2 times the distance car A travels at the same time" to mean that the distance traveled by car B is 1.2 times the distance traveled by car A.
To calculate the distance traveled by car B, Elin multiplied the distance of car A (221.5 km) by 1.2:
Distance of Car B = 1.2 * Distance of Car A
Distance of Car B = 1.2 * 221.5 km
Distance of Car B = 265.8 km
Therefore, Elin concluded that car B travels a distance of 265.8 km during the same time based on her interpretation of the given information.
Can anyone help me answer this question?
1. What is the derivative of sin(x)cos(x)?
2. What is the derivative of sin2(x)cos2(x)?
Answer:
cos 2x
f(x)=4•sin(x)•cos(x)
Step-by-step explanation:
Please help me , I don't understand the question..
The test statistic z ≈ -2.59 falls into the rejection region (z < -1.96).
Therefore, we reject the null hypothesis (H₀) in favor of the alternative hypothesis (H₁).
How to solvea) Null and alternative hypothesis:
The null hypothesis (H₀) states that there is no significant difference between the claimed weekly production volume and the actual production volume.
The alternative hypothesis (H₁) states that there is a significant difference between the claimed weekly production volume and the actual production volume.
H₀: μ = 370 units (the claimed weekly production volume is true)
H₁: μ ≠ 370 units (the claimed weekly production volume is not true)
b) Critical value:
Since we're using a two-tailed test at α = 0.05 significance level, we'll look for the critical value (z-score) that corresponds to the 2.5% in each tail (5% total) of the standard normal distribution.
The critical value for a two-tailed test at α = 0.05 is ±1.96. The rejection region consists of the areas where the z-score is less than -1.96 or greater than 1.96.
c) Test statistic:
To calculate the test statistic, we will use the following formula:
z = (X - μ) / (σ / √n)
z = (355 - 370) / (19 / √30) = -15 / (19 / √30) ≈ -2.59
d) Conclusion:
The test statistic z ≈ -2.59 falls into the rejection region (z < -1.96).
Therefore, we reject the null hypothesis (H₀) in favor of the alternative hypothesis (H₁).
This means that there is significant evidence to suggest that the claimed weekly production volume of 370 units is not true.
The Vice President's suspicion about the statement appears to be correct, and further investigation should be conducted to determine the actual production volume.
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How to write 1/4 (x-12) in words
Answer:
To write 1/4 (x - 12) in words, you would say "one-fourth of the quantity obtained by subtracting 12 from x."
Rationalize the denominator and simplify:
4/4+√x
Answer: 16-4√x/16-x is the answer.
Step-by-step explanation:
=> 4/4+√x*4-√x/4-√x
=> 4(4-√x)/(4)²-(√x)² {using identity - (a+b) (a-b)=a² - b²}
=> 16-4√x/16-x
5. Find the area of the kite.
18 m
-21 m-
Answer: 189 m^2
Step-by-step explanation:
Area = (Diagonal 1 x Diagonal 2) ÷ 2
(a) In the figure below, two secants are drawn to a circle from exterior point H.
Suppose that HZ=16.8, HX-14, and HY=42. Find HW.
H
w
M
HW = 0
(b) In the figure below, two chords intersect inside the circle at point V.
Suppose that VJ-18, VM-36, and VK=27. Find MN.
MN = 0
Applying the intersecting secants and chords theorem, the indicated measures in the circle is: HW = 35 units; MN = 49.5 units.
How to Apply the Intersecting Secants and Chords Theorem?To find the measures indicated, we will apply the intersecting secants and chords theorem to form an equation, then solve.
a. HZ * HW = HX * HY [based on the intersecting secants theorem]
Plug in the values:
16.8 * HW = 14 * 42
HW = 588/16.8
HW = 35 units
b. VK * VJ = VM * VN [based on the intersecting chords theorem]
Plug in the values:
27 * 18 = 36 * VN
VN = 486/36
VN = 13.5 units
MN = VM + VN = 36 + 13.5
MN = 49.5 units
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Alicia took a friend for a birthday dinner. The total bill for dinner was $44.79 (including tax and a tip). If Alicia paid a 21.6% tip, what was her bill before adding the tip?
(Round your answer to the nearest cent.)
Answer: 27.33
Step-by-step explanation: If you use a calculator to do the hard stuff the rest is a breeze
Carl is buying a shirt that costs $24.00. It is on sale for 50% off. what will the price of the shirt be?
A. 19.00
B. 50.00
C. 12.00
D. 14.00
Please help I’ll give brainly if you explain :)
Answer: C
Step-by-step explanation:
We need to turn 50% into a fraction first to make it easier,
50% is equal to 1/2 because 50/100 is simplified to 1/2.
Now let's multiply!
24 x 1/2 = 24/2 = 12/1 = 12
2. Kyle submits a design for the contest, but his explanation was misplaced. How can Figure A be mapped onto Figure B? Can any other transformation be used to map Figure A onto Figure B?
help please i have 5 min
Note that in order to map A onto B, Kyle would have to dilate the given figure by a scale factor or 3.
What is dilation?A dilation is a function f from a metric space M into itself that fulfills the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real integer. Such a dilatation is a resemblance of space in Euclidean space.
The original point of figure A which has 4 points are
(0,02)
(-1, 2)
(0, 1)
(1, 2)
Multiply all th e points by 3, and you get,
(0,02) x 3 = (0, -6) =
(-1, 2) x 3 = (-3, 6)
(0, 1) x 3 = (0, 3)
(1, 2) x3 = (3, 6)
Plotting the new values will give us the transformation (dilation) required. See the attached image.
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Harrold is a dog walker. He walks 13 different dogs for the same distance around Greenpoint Park everyday. The park is a perfect square in shape. Harrold takes each dog for 1 full lap around the park. In one day Harrold will walk 6, 396ft all together. What is the length of 1 side of the park in yards.
Answer:
123 feet/41 yards
Step-by-step explanation:
When solving problems like this, we need to understand and note down what we already know to make our lives easier.
- He walks 13 different dogs
- the park is a perfect square
- he takes each dog for one full lap
- That day, he walked 6396ft
- He takes each dog the same distance
Now, let's find the unit value (how much ft does he walk if he takes JUST ONE dog around Greenpoint Park?)
Just divide: 6396 / 13 = 492 ft
Meaning, that when Harrold takes JUST ONE dog around the park, which is a perfect square, he walks 492 feet.
One full lap around the square shaped park is just 4 sides of the square.
So, he walks 492 ft every 4 sides.
However, the question specifically asked for one side.
Just divide again to get your answer:
492 / 4 = 123 ft
Therfore, the length of one side of the park is 123 feet, which is 41 yards.
use logb28
PLEASE HELP SOLVE!! 30 PTS!!
Answer:
logb28 ≈ 1.634.
Step-by-step explanation:
logb28 = (log428)/(log47)
We can then substitute the given values for logb4 and logb7:
logb28 = (log428)/(log47) = (log28)/(log24 + log27) = (log28)/(1.386 + 1.946)
1.386+1.946=3.332
logb28/3.332
logb28 ≈ 1.634.
Answer:
[tex]log_b28=3.332[/tex]--------------------
Given:
[tex]log_b 4 = 1.386\ and\ bog_b7=1.946[/tex]Use the following identity to find [tex]log_b28[/tex]:
[tex]log_a(bc)=log_ab+log_ac[/tex]Apply the identity to the given:
[tex]log_b28=log_b(4*7)=log_b4+log_b7=1.386+1.946=3.332[/tex]The sequence is geometric.
1, 6, 30, 60, . . .
The sequence 1, 6, 30, 60, . . . is not a geometric sequence
Checking if the sequence is geometricFrom the question, we have the following parameters that can be used in our computation:
1, 6, 30, 60, . . .
To check if the sequence is geometric, we calculae the common ratio of the sequence using
r = next term/previous term
Using the above as a guide, we have the following:
r = 6/1 = 6
r = 30/6 = 5
r = 60/30 = 2
The common ratios of the sequence calculated above are different
This means that the sequence is not geometric
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50 Points! Multiple choice algebra question. Find the domain and range of the function whose graph is shown. Photo attached. Thank you!
Answer:
"B". Domain is all real numbers, and the Range is all positive real numbers
Step-by-step explanation:
It is important to recognize that this function is an exponential function, either by the graph (observe a horizontal asymptote on the x-axis, and increasing exponentially), or more importantly by the equation which is in exponential form [tex]y=a*b^x[/tex] where "a" is a non-zero real number, and "b" is a positive real number not equal to 1.
Observe that for the given function, a=4 (a real number not equal to zero), and b=2 (a positive real number that is not 1).
The domain for all exponential functions is all real numbers, so this function's domain is all real numbers.
The Range for exponential functions depends on "a", where if "a" is a positive number the Range is positive numbers only, and if "a" is a negative number, the Range is negative numbers only.
Since "a" is positive, the Range is positive numbers only.
Writing the Domain in "set-builder notation" (since all of the choices are given using that notation), the Domain is "all real numbers" put into curly brackets, so {all real numbers}.
Writing the Range in "set-builder notation", recall that the Range is the outputs of the function, so the Range is "y values such that y is greater than zero". There is some shorthand used, where the phrase "such that" is symbolized using a short vertical line (common in set-builder notation), and the phrase "y is greater than zero" is shortened using inequality symbols "y>0". So, the Range is written as { y | y>0 }.
Further, the "Domain" and "Range" are abbreviated with "D" and "R" respectively.
Therefore, the final answer would be D = {all real numbers}; R = { y | y>0 }, which is answer "B"
Please help will give a lot of points
Answer:
how many points will you give?
Step-by-step explanation:
