Hi there!
[tex]\large\boxed{p(x) = 7x + 7x^2 + \frac{7}{2}x^3 + \frac{7}{6}x^4}[/tex]
Recall a Taylor series centered at x = 0:
[tex]p(x) = f(0) + f'(0)(x) + \frac{f''(0)}{2}x^{2} + \frac{f'''(0)}{3!}x^{3} + ...+ \frac{f^n}{n!}x^n[/tex]
Begin by finding the derivatives and evaluate at x = 0:
f(0) = 7(0)e⁰ = 0
f'(x) = 7eˣ + 7xeˣ f'(0) = 7e⁰ + 7(0)e⁰ = 7
f''(x) = 7eˣ + 7eˣ + 7xeˣ f''(0) = 7(1) + 7(1) + 0 = 14
f'''(x) = 7eˣ + 7eˣ + 7eˣ + 7xeˣ f'''(0) = 21
f⁴(x) = 7eˣ + 7eˣ + 7eˣ + 7eˣ + 7xeˣ f⁴(0) = 28
Now that we calculated 4 non-zero terms, we can write the Taylor series:
[tex]p(x) = 0 + 7x + \frac{14}{2}x^2 + \frac{21}{3!}x^3 + \frac{28}{4!}x^4[/tex]
Simplify:
[tex]p(x) = 7x + 7x^2 + \frac{7}{2}x^3 + \frac{7}{6}x^4[/tex]
¿Pueden ayudarme por favor?
find the length of side AB
Answer:
AB = 5.6 cm
Step-by-step explanation:
Reference angle (θ) = 62°
Hypotenuse = 12 cm
Adjacent = AB
Apply the trigonometric ratio formula, CAH, which is:
Cos θ = Adj/Hyp
Plug in the values
Cos 62° = AB/12
12*Cos 62° = AB
5.63365876 = AB
AB = 5.6 cm (1 decimal place)
A basketball team is to play two games in a tournament. The probability of winning the first game is .10.1 the first game is won, the probability of winning the second game is 15. If the first game is lost, the probability of winning the second game is 25. What is the probability the first game was won if the second game is lost? Express the answer with FOUR decimal points.
Answer:
[tex]P(\frac{A}{B'})[/tex]=0.111
Step-by-step explanation:
Given:
The probability of winning the first game is 10.1
The first game is won
The probability of winning the second game is 15
If the first is lost, the probability of winning the second game is 25
Solution:
[tex]P(B)=P(A)P(\frac{B}{A})+P(A')P(\frac{B}{A'})\\ =0.1(0.15)+(0.3)*0.25)\\P(B)=0.24 ------(1)\\P(\frac{A}{B})=\frac{P(\frac{B}{A})P(A) }{P(B)}\\ =\frac{0.15(0.1)}{0.24}\\ =0.0625 ------(2)\\P(B')=1-P(B)=0.76 ------(3)\\P(A)=P(B)P(\frac{A}{B})+P(B')P(\frac{A}{B'})\\0.1=0.24(0.0625)+0.76(p(\frac{A}{B'} ))\\P(\frac{A}{B'})=0.111[/tex]
Answer:
[tex]P(W_1/W_2')=0.1110[/tex]
Step-by-step explanation:
Probability of winning the first game be considering the given factors be, [tex]W_1=0.1[/tex]
Probability of winning the second game be considering the given factors be, [tex]W_2[/tex]= probability of winning the second game when the first game is won + probability of winning the second game when the first game is lost:
[tex]P(W_2)=P(W_1).P(W_2/W_1)+P(W_1').P(W_2/W_1')[/tex]
[tex]P(W_2)=0.1\times 0.15+0.9\times 0.25[/tex]
[tex]P(W_2)=0.24[/tex]
Hence the probability of losing the second game:
[tex]P(W_2')=1-P(W_2)[/tex]
[tex]P(W_2')=0.76[/tex]
Probability of winning the first game when the second game is won:
[tex]P(W_1/W_2)=\frac{P(W_2/W_1).P(W_1)}{P(W_2)}[/tex]
[tex]P(W_1/W_2)=\frac{0.15\times 0.1}{0.24}[/tex]
[tex]P(W_1/W_2)=0.0625[/tex]
Probability of winning the first game be considering the given factors, [tex]W_1[/tex]= probability of winning the first game when the second game is won + probability of winning the first game when the second game is lost:
[tex]P(W_1)=P(W_2).P(W_1/W_2)+P(W_2').P(W_1/W_2')[/tex]
[tex]0.1=0.24\times0.0625+0.76\times P(W_1/W_2')[/tex]
[tex]P(W_1/W_2')=0.1110[/tex]
If the actual price in this market were below
the equilibrium price, what would drive the
market toward the equilibrium?
Step-by-step explanation:
If the price is below the equilibrium level, then the quantity demanded will exceed the quantity supplied. Excess demand or a shortage will exist. If the price is above the equilibrium level, then the quantity supplied will exceed the quantity demanded. Excess supply or a surplus will exist.Whenever markets experience imbalances—creating disequilibrium prices, surpluses, and shortages—market forces drive prices toward equilibrium. A surplus exists when the price is above equilibrium, which encourages sellers to lower their prices to eliminate the surplus.
Can any one you help me with this ?
NUE is 30° LUN is 60° EUS is 30° LUE is 90° LUS is 120°
Step-by-step explanation:
NUE is given
LUN was from the 90° angle LUE but just minus 30°
EUS is honestly a guess :/
LUE is obviously 90° as we used it earlier
LUS was the 90° plus the EUS
SHOW PROCESS!!!
Will mark brainly!!
Thank you!
Answer:
Step-by-step explanation:
By applying cosine rule in the given triangle,
c² = a² + b²-2abcosC
c² = (5.6)² + (10.7)² - 2(5.6)(10.7)cos(109.3°)
c² = 185.46
c = 13.6 km
By applying sine rule in the given triangle ABC,
[tex]\frac{\text{sin}A}{a}= \frac{\text{sin}B}{b}= \frac{\text{sin}C}{c}[/tex]
[tex]\frac{\text{sin}A}{5.6}=\frac{\text{sin}B}{10.7}=\frac{\text{sin}109.3}{13.6}[/tex]
[tex]\frac{\text{sin}B}{10.7}=\frac{\text{sin}109.3}{13.6}[/tex]
sin(B) = [tex]\frac{10.7\times \text{sin}(109.30)}{13.6}[/tex]
= 0.7425
B = [tex]\text{sin}^{-1}(0.7425)[/tex]
B = 48.0°
[tex]\frac{\text{sin}A}{5.6}=\frac{\text{sin}109.3}{13.6}[/tex]
sin(A) = [tex]\frac{[\text{sin}(109.3)]\times (5.6)}{13.6}[/tex]
= 0.3886
A = [tex]\text{sin}^{-1}(0.3886)[/tex]
A = 22.9°
you have to find ABC and I'm not sure how to any help is appreciated
Hello,
Since (BD) bissects angle ABC,
18-x=26-3x
2x=8
x=4
18-x=18-4=14
m angle ABC=14°*2=28°
Need helpppppppppppppppppp
Answer:
-18
Step-by-step explanation:
B=-6 C=2 P.E.M.D.A.S.
b - 6(c)
-6 - 6(2)
-6 - 12 . The negatives cancel out, adding each other
-6 + -12
= -18 :)
Answer:
b - 6c
= -6 - 6x2
= -6 x( 1+2)
= -6x3
= -18
The graph of f(x)=x^2 is shown. Compare the graph of f(x) with the graph of g(x)=x^2+8
Answer:
D
Step-by-step explanation:
Number 8 is not related to the x, but is related to the the function. so g(x) is 8 units above f (x)
Answer:
D. 8 units above the graph
Step-by-step explanation:
y = mx + b
this formula is basically y = x^2 + 8
+8 part means where it is on the y axis
if it were y = (x+6)^2 + 8
it would also be on 6 places to the left on the x axis
need help asap!! (geometry)
Answer:
A. reflection.
Step-by-step explanation:
If you were to use the reflection rule, then your answer will be:
B' (Now D): (1 , 2)
A' (Now E): (4 , 2)
C' (Now F): (3 , 5)
In this case, the reflected triangle does not match the given points, therefore it cannot be reflection.
~
A radioactive substance decays exponentially: The mass at time t is m(t) = m(0)e^kt, where m(0) is the initial mass and k is a negative constant. The mean life M of an atom in the substance is
[infinity]
M = âk â« te^kt dt.
0
For the radioactive carbon isotope, 14C, used in radiocarbon dating, the value of k is -0.000121. Find the mean life of a 14C atom.
Answer:
mean life = 8264.5 s
Step-by-step explanation:
k = - 0.000121
The relation is given by
[tex]m = mo e^{kt}[/tex]
Now, the mean life is the life time for which the sample retains.
The mean life is the reciprocal of the decay constant.
The relation between the mean life and the decay constant is
[tex]\tau =\frac{1}{k}\\\\\tau = \frac{1}{0.000121} = 8264.5 seconds[/tex]
1 1/3 bushels of seed are needed to plant 1 acre of wheat. How many bushels of seed would be required to plant 30 acres?
An acre requires 1.33 bushels of seed.
Thirty acres thusly require 30 times 1.33 bushels of seed.
So we have, [tex]1.33\cdot30=\boxed{39.9}[/tex] bushels of seed.
Hope this helps.
What is the scare root of 85 roused to nearest tenth?
Answer:
9.2
Step-by-step explanation:
You can do this calculation with a calculator by taking the square root of 85.
Hi there!
»»————- ★ ————-««
I believe your answer is:
9.2
»»————- ★ ————-««
Here’s why:
Assuming that you mean "the square root of 85 rounded to the nearest tenth..."
⸻⸻⸻⸻
[tex]\boxed{\text{Calculating the Answer...}}\\\\\rightarrow \sqrt{85} = 9.21954445729....[/tex]
⸻⸻⸻⸻
Since the digit to the right of the tenth (the 1) is less than or equal to four, we round down.
⸻⸻⸻⸻
[tex]9.21954445729...\approx\boxed{9.2}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Okay, let's calculate the year end adjustment for overhead. Based on the data below, determine the amount of the year end adjustment to cost of goods sold due to over or under allocated manufacturing overhead during the year
Answer:
the adjustment made to the cost of goods sold is -$2,014
Step-by-step explanation:
The computation of the adjustment made to the cost of goods sold is given below:
Total actual overhead expenses $110,822
Less: Total overheads allocated -$112,836
Adjustment made to the cost of goods sold -$2,014
Hence, the adjustment made to the cost of goods sold is -$2,014
The same should be considered
If a translation of T.3. - 8(x, y) is applied to square
ABCD, what is the y-coordinate of B'?
4
3
0-12
A
В
-8
-E
5
2
3
4
0
D
C
Answer:
Its C. -6
Step-by-step explanation:
The coordinates of point B after translation are (-2, -6).
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
A translation T(-3, -8) follows the rule:
A translation is a movement of the graph either horizontally parallel to the -axis or vertically parallel to the -axis.
(x, y)--->(x-3, y-8)
From the diagram you can see that point B has coordinates (1,2).
(1, 2)--->(1-3, 2-8)
(1, 2)--->(-2, -6)
According to the previous rule this point will transform in point B' with coordinates (-2,-6),
Hence, the coordinates of point B after translation are (-2, -6).
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ7
PLEASE I NEED HELP!!!!!
Find the volume of this sphere.
Use 3 for TT.
L-r=3ft
V [?]ft3
V = Tr3
Answer:
113.1 =VOLUME , 4/3 X 3.14 (3) ^3 = 113.1
Solve for x. The triangles are similar.
Write an addition or a subtraction equation (your choice!) to describe the diagram. Pls help
Answer:
Addition equation = -4-0) + [(-13)-(-4)]
Answer = -13
Step-by-step explanation:
For the small arrow in the diagram, the expression is (-4 - 0)
For the bog arrow, the expression will be -13 - (-4)
Adding both expressions
Addition = (-4-0) + [(-13)-(-4)]
Addition = (-4) + (-13+4)
Addition = -4 + (-9)
Addition = -4-9
Addition = -13
to have batting average over 0.500. how many hits in 45 times at bat would raul or karen need?
What is the mean of this data? 7,5,5,3,2,2
Answer:
4
Step-by-step explanation:
The mean is the average of a data set. It can be found by adding up all of the values in a data set and then dividing it by the number of values in the data set.
The values in this data set;
[tex]7,5,5,3,2,2[/tex]
The number of values in this data set,
[tex]6[/tex]
Find the mean;
[tex]\frac{sum\ of\ vlaues}{number\ of\ values}[/tex]
[tex]=\frac{7+5+5+3+2+2}{6}\\\\=\frac{24}{6}\\\\=4[/tex]
If the bearing of A from B is 125.Find the bearing of B from A
Answer:
305°
Step-by-step explanation:
The bearing in the reverse direction is 180° plus the bearing in the forward direction, that is
bearing of B from A = 180° + 125° = 305°
Divide: (2n3+4n−9)÷(n+2).
Answer:
2n+2
_____
9 2n
1.055.
Determine whether the statement is true or false. If the statement is false, give a reason.
{5, 6, 7} = {5, 5, 6, 7, 7}
Given:
The statement is:
{5, 6, 7} = {5, 5, 6, 7, 7}
To find:
Whether the given statement is true or false.
Solution:
Two sets are equal if they have exactly the same elements.
The given set {5, 6, 7} has three elements and the set {5, 5, 6, 7, 7} has five elements but we known that all the elements of a set are distinct. It means, it has no repeated element.
Set {5, 5, 6, 7, 7} has three distinct elements 5, 6, 7. So,
{5, 5, 6, 7, 7} = {5, 6, 7}
Therefore, the given statement is true.
I don’t understand these problems
Both E and F are sets.
E = {w | w ≤ 2}
means that E is the set of all numbers w satisfying the condition that w ≤ 2. In other words, E contains all real numbers less than and including 2.
Similarly,
F = {w | w > 9}
is the set of all real numbers strictly greater than 9.
The intersection of E and F, denoted E ∩ F, is the set that contains the overlap of the two sets, or all the numbers that are common to both sets. In this case, E ∩ F is the empty set; this is because all numbers small than 2 cannot be larger than 9, so E ∩ F = ∅.
The union of E and F, written as E ∪ F, is the set containing all elements from both sets. In interval notation, E = (-∞, 2] and F = (9, ∞), so E ∪ F = (-∞, 2] ∪ (9, ∞).
A tree cast a shadow of 30m long and a 2m stick casts one that is 3m long. As show in the below diagram how tall is the tree?
Answer:
20 mStep-by-step explanation:
We have similar triangles here.
BC║DE, AB║AD and AC║AE ⇒ ΔADE ~ ΔABCThe ratio of corresponding sides of similar triangles is same:
BC/DE = AC/AEBC / 2 = 30/3BC / 2 = 10BC = 2*10BC = 20 mTake the similar triangles,
→ ∆ADE ≈ ∆ABC
Now we can find,
The height of the tree in meters,
→ BC/DE = AC/AE
In this equation BC is the height of tree,
→ BC/2 = 30/3
→ BC/2 = 10
→ BC = 10 × 2
→ BC = 20
Hence, the height of the tree is 20 m.
Pls solve the above question
Kindly don't spam+_+
Answer:
Step-by-step explanation:
Given expressions are,
[tex]p=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}+\sqrt{5}}[/tex] and [tex]q=\frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}-\sqrt{5}}[/tex]
Remove the radicals from the denominator from both the expressions.
[tex]p=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}+\sqrt{5}} \times \frac{\sqrt{10}-\sqrt{5}}{\sqrt{10}-\sqrt{5}}[/tex]
[tex]=\frac{(\sqrt{10}-\sqrt{5})^2}{(\sqrt{10})^2-(\sqrt{5})^2}[/tex]
[tex]=\frac{(\sqrt{10}-\sqrt{5})^2}{5}[/tex]
[tex]\sqrt{p}=\sqrt{\frac{(\sqrt{10}-\sqrt{5})^2}{5}}[/tex]
[tex]=\frac{\sqrt{10}-\sqrt{5}}{\sqrt{5}}[/tex]
[tex]q=\frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}-\sqrt{5}}[/tex]
[tex]=\frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}-\sqrt{5}}\times \frac{\sqrt{10}+\sqrt{5}}{\sqrt{10}+\sqrt{5}}[/tex]
[tex]=\frac{(\sqrt{10}+\sqrt{5})^2}{(\sqrt{10})^2-(\sqrt{5})^2}[/tex]
[tex]=\frac{(\sqrt{10}+\sqrt{5})^2}{5}[/tex]
[tex]\sqrt{q}=\sqrt{\frac{(\sqrt{10}+\sqrt{5})^2}{5}}[/tex]
[tex]=\frac{(\sqrt{10}+\sqrt{5})}{\sqrt{5}}[/tex]
[tex]\sqrt{q}-\sqrt{p}-2\sqrt{pq}=\frac{(\sqrt{10}+\sqrt{5})}{\sqrt{5}}-\frac{(\sqrt{10}-\sqrt{5})}{\sqrt{5}}-2(\frac{(\sqrt{10}+\sqrt{5})}{\sqrt{5}})(\frac{(\sqrt{10}-\sqrt{5})}{\sqrt{5}})[/tex]
[tex]=\frac{1}{\sqrt{5}}(\sqrt{10}+\sqrt{5}-\sqrt{10}+\sqrt{5})-\frac{2}{5}[(\sqrt{10})^2-(\sqrt{5})^2)][/tex]
[tex]=\frac{1}{\sqrt{5}}(2\sqrt{5})-\frac{2}{5}(10-5)[/tex]
[tex]=2-2[/tex]
[tex]=0[/tex]
A study is done to determine the average salary for all Santa Clara County teachers. If we were to randomly pick 15 schools in Santa Clara County and average together the salaries of all teachers, would this be a good sampling technique or a bad sampling technique
Answer:
Good sampling technique
Step-by-step explanation:
In other to determine the mean value for a population, it may be necessary to make inference from the a small subset of the population, called the sample, if it is impossible, difficult or inefficient to get all population data. Hence, in other to select a subset of the population, then the sample must be selected at random, such that all elements of the population have equal chances of being selected and hence, be representative of the population. Since, the sampling technique adopted above is done at random, hence, it is a good sampling technique.
Which of the following expressions is not equivalent to the others?
Answer:
Im going to guess the second one
Step-by-step explanation:
It's the only one that does not have more than one negative fraction.
HELP ME FAST WILL GIVE BRAINLY
A bag contains 16 white marbles, 10 blue marbles and 12 red marbles. Give each ratio as a reduced fraction.
A) The ratio of white marbles to blue marbles.
B) The ratio of red marbles to total marbles.
the total of marbles = 16 + 10 +12 =38
A) white : blue = 16/10 = 8/5
B) red : total = 12/38 = 6/19
Step-by-step explanation:
1. find the total of marbles
testing for a disease can be made more efficient by combining samples. If the samples from two people are combined and the mixture tests negative, then both samples are negative. On the other hand, one positive sample will always test positive, no matter how many negative samples it is mixed with. Assuming the probability of a single sample testing positive is 0.15, find the probability of a positive result for two samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely necessary?w./search?q=%E2%80%8B"At+least%E2%80%8B+one"+is+equivalent+to%E2%80%8B+_______.&oq=%E2%80%8B"At+least%E2%80%8B+one"+is+equivalent+to%E2%80%8B+_______.&aqs=chrome..69i57j0i22i30l3.409j0j4&sourceid=chrome&ie=UTF-8 The probability of a positive test result is nothing
Answer:
(a) [tex]P(Two\ Positive) = 0.2775[/tex]
(b) It is not too low
Step-by-step explanation:
Given
[tex]P(Single\ Positive) = 0.15[/tex]
[tex]n = 2[/tex]
Solving (a):
[tex]P(Two\ Positive)[/tex]
First, calculate the probability of single negative
[tex]P(Single\ Negative) =1 - P(Single\ Positive)[/tex] --- complement rule
[tex]P(Single\ Negative) =1 - 0.15[/tex]
[tex]P(Single\ Negative) =0.85[/tex]
The probability that two combined tests are negative is:
[tex]P(Two\ Negative) = P(Single\ Negative) *P(Single\ Negative)[/tex]
[tex]P(Two\ Negative) = 0.85 * 0.85[/tex]
[tex]P(Two\ Negative) = 0.7225[/tex]
Using the complement rule, we have:
[tex]P(Two\ Positive) = 1 - P(Two\ Negative)[/tex]
So, we have:
[tex]P(Two\ Positive) = 1 - 0.7225[/tex]
[tex]P(Two\ Positive) = 0.2775[/tex]
Solving (b): Is (a) low enough?
Generally, when a probability is less than or equal to 0.05; such probabilities are extremely not likely to occur
By comparison:
[tex]0.2775 > 0.05[/tex]
Hence, it is not too low
