The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer: x = 10
Step-by-step explanation:
The sum of interior angles in a triangle is equal to 180°.
(2x + 3) + (5x + 17) + 90 = 180
2x + 3 + 5x + 17 + 90 = 180
7x + 110 = 180
7x = 70
x = 10
The function f(x) = \frac{5}{(1 - 9 x)^2} is represented as a power series \displaystyle f(x) = \sum_{n=0}^\infty c_n x^n . Find the first few coefficients in the power series. c_0 = c_1 = c_2 = c_3 = c_4 = Find the radius of convergence R of the series.
[tex]c_0 = 9, c_1 = 2(9^2), c_2 = 3(9^3), c_3 = 4(9^4)[/tex]and [tex]c_4 = 5(9^5)[/tex]. The radius of convergence R is infinity.
To find the coefficients of the power series representation of the function f(x) = 5/(1 - 9x)², we can expand the function using the geometric series formula. The formula states that for |x| < 1, we have:
1/(1 - 9x) = 1 + 9x + (9x)² + (9x)³ + ...
Now, let's differentiate both sides of the equation with respect to x:
d/dx [1/(1 - 9x)] = d/dx [1 + 9x + (9x)² + (9x)³ + ...]
To differentiate the left side, we can use the power rule:
d/dx [1/(1 - 9x)] = (1 - 9x)⁻²
To differentiate the right side, we differentiate each term individually. Since the derivative of x^n with respect to x is nxⁿ⁻¹, the terms with powers of x become:
d/dx [1 + 9x + (9x)² + (9x)³ + ...] = 0 + 9 + 2(9²)x + 3(9³)x² + ...
Equating the derivatives, we have:
(1 - 9x)⁻² = 9 + 2(9²)x + 3(9³)x² + ...
To obtain the coefficients of the power series representation, we compare the terms on both sides of the equation. Since the expression on the right side is already in the desired form, we can read off the coefficients as follows:
[tex]c_0 = 9\\c_1 = 2(9^2)\\c_2 = 3(9^3)\\c_3 = 4(9^4)\\c_4 = 5(9^5)[/tex]
Now, let's find the radius of convergence R of the series. The radius of convergence can be determined using the ratio test. The ratio test states that if the limit of |[tex]c_{n+1} / c_n[/tex]| as n approaches infinity is L, then the series converges if L < 1 and diverges if L > 1.
Applying the ratio test to our series, we have:
|[tex]c_{n+1} / c_n[/tex]| = |[(n+1)(9ⁿ⁺¹)] / [n(9ⁿ)]| = 9((n+1)/n)
Taking the limit as n approaches infinity, we get:
lim(n->∞) |[tex]c_{n+1}/ c_n[/tex]| = lim(n->∞) 9((n+1)/n) = 9
Since the limit is 9, which is less than 1, the series converges for all values of x within a radius of convergence R. Therefore, the radius of convergence R is infinity (R = ∞).
Therefore,[tex]c_0 = 9, c_1 = 2(9^2), c_2 = 3(9^3), c_3 = 4(9^4)[/tex]and [tex]c_4 = 5(9^5)[/tex]. The radius of convergence R is infinity.
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Determine the domain and range in the function, f(x)=abx
f(x)=ab^x , when a =1/4 and b=16.
Assuming the sample was taken from a normal population, what type of test should be performed to test the following?
H_ọ: µ = 190
H_A: μ > 190
X = 186
s = 22
n = 14
To test the given hypothesis, where the null hypothesis (H_ọ) states that the population mean (µ) is equal to 190, and the alternative hypothesis (H_A) states that µ is greater than 190, a one-tailed test should be performed.
Given that the sample mean (X) is 186, the sample standard deviation (s) is 22, and the sample size (n) is 14, we can use the t-test for a single sample to test the hypothesis.
Calculate the test statistic:
t = (X - µ) / (s / √n)
t = (186 - 190) / (22 / √14)
t ≈ -0.8182
Determine the critical value for the given significance level and degrees of freedom.
Since the alternative hypothesis is one-tailed (µ > 190), we need to find the critical value corresponding to the desired significance level (α). Let's assume a significance level of α = 0.05 and degrees of freedom (df) = n - 1 = 14 - 1 = 13. Using a t-distribution table or calculator, the critical value for a one-tailed test at α = 0.05 and df = 13 is approximately 1.771.
Compare the test statistic to the critical value:
If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Since -0.8182 is less than 1.771, we fail to reject the null hypothesis.
Therefore, based on the given sample, assuming a normal population, and performing a one-tailed test at α = 0.05, we fail to reject the null hypothesis (H_ọ: µ = 190) in favor of the alternative hypothesis (H_A: μ > 190).
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Gary is 4 years less than three times his brothers age, \displaystyle bb. The sum of Gary and his brothers' age is 52. Write an equation to represent this relaitonship.
(PLS HELP ME WITH THAT QUESTION! IF YOU HELP ME I GIVE YOU BRAINLIEST I SWEAR)
If $120.99 is charged for 654 units of electricity used,find the cost of one unit of electricity
Answer:
$5.41
Step-by-step explanation:
654 divided by 120.99=5.405... therefore the answer is $5.41
can someone pls simplify this
[tex] \frac{105}{12} [/tex]
A rectangular hall is 55 feet long and 48 feet wide. How long is a walkway along the diagonal?
Answer:
[tex]73[/tex]
Step-by-step explanation:
[tex]73=\sqrt{55^{2} +48^{2} }[/tex]
Tell whether the angles are adjacent or vertical. Then find the value of X
Answer:
The angles are adjacent, and x=100
Step-by-step explanation:
The angles are adjacent because they share the same starting point. x=100 because x and the other angle are on a line, which has a measure of 180 degrees. We subtract 80 from 180 to get 100.
Hope this was helpful.
~cloud
Problem 8-28 The exponential distribution applies to lifetimes of a certain component. Its failure rate is unknown. Find the probability that the component will survive past 5 years assuming:
(a) lambda=.5
Pr=
(b) lambda=0.9
Pr=
(c) lambda=1.1
Pr=
The exponential distribution applies to the lifetimes of a certain component. Its failure rate is unknown. The probability that the component will survive the past 5 years assumes:
(a) lambda=.5
Pr= 0.082
(b) lambda=0.9
Pr= 0.082
(c) lambda=1.1
Pr= 0.036
In the exponential distribution, the failure rate is a degree of the way fast the factor is expected to fail. It is regularly denoted through the parameter lambda (λ).
The opportunity that a thing will continue to exist beyond a positive time may be calculated using the exponential survival function, which is given by:
[tex]Pr(X > t) = e^(-λt)[/tex]
where X represents the random variable denoting the life of the thing, t is the specific time, and e is the bottom of the herbal logarithm.
Now let's calculate the possibilities for each case:
(a) lambda = 0.5, t = 5
Pr(X > 5) = [tex]e^(-0.5 * 5)[/tex] ≈ 0.082
In this example, with a lambda of 0.5, the element has a notably low failure price. The opportunity of the thing surviving beyond 5 years is about 0.082, or 8.2%.
(b) lambda = 0.9, t =5
Pr(X > 5) = [tex]e^(-0.9 * 5)[/tex] ≈ 0.082
With a lambda of 0.9, the issue has a slightly higher failure rate as compared to the previous case. The probability of the aspect surviving beyond 5 years stays at about 0.082, or 8.2%.
(c) lambda = 1.1, t = 5
Pr(X > five) = [tex]e^(-1.1 * 5)[/tex]≈ 0.036
In this situation, with a lambda of one.1, the factor has a better failure fee. The possibility of the element surviving beyond 5 years decreases to approximately 0.036, or 3.6%.
In precis, the possibility of a component surviving the past five years in an exponential distribution relies upon the failure price parameter lambda.
A lower failure price ends in a higher chance of survival, at the same time as a higher failure price decreases the opportunity of survival. It is essential to don't forget these chances when assessing the reliability and toughness of additives in diverse packages.
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please help------------,
Answer:
600 cm²
Step-by-step explanation:
The shaded area (A) is calculated as
A = area of square - ( area of 3 unshaded triangles )
area of square = 40 × 40 = 1600 cm²
area of lower right triangle = [tex]\frac{1}{2}[/tex] × 20 × 40 = 10 × 40 = 400 cm²
area of upper left triangle = [tex]\frac{1}{2}[/tex] × 40 × 20 = 20 × 20 = 400 cm²
area of lower left triangle = [tex]\frac{1}{2}[/tex] × 20 × 20 = 10 × 20 = 200 cm²
Then
A = 1600 - (400 + 400 + 200 ) = 1600 - 1000 = 600 cm²
let W be the subspace of spanned by the vectors [3 1 1] and [15 11 -1]
find the projection matrix that projects vectors in R3 onto W.
P=
The projection matrix P is [1/√11 -1/√337].
To find the projection matrix that projects vectors in ℝ³ onto the subspace W spanned by the vectors [3 1 1] and [15 11 -1], we can follow these steps:
Let's start by normalizing the basis vectors of W. Normalizing means dividing each vector by its magnitude to obtain unit vectors.
First basis vector:
u₁ = [3 1 1]
Normalize: v₁ = u₁ / ||u₁||
Compute the magnitude: ||u₁|| = √(3² + 1² + 1²) = √11
Normalize: v₁ = [3/√11, 1/√11, 1/√11]
Second basis vector:
u₂ = [15 11 -1]
Normalize: v₂ = u₂ / ||u₂||
Compute the magnitude: ||u₂|| = √(15² + 11² + (-1)²) = √337
Normalize: v₂ = [15/√337, 11/√337, -1/√337]
Next, we construct a matrix P using the normalized basis vectors as columns.
P = [v₁ v₂]
P = [3/√11 15/√337]
[1/√11 11/√337]
[1/√11 -1/√337]
Therefore, the projection matrix P that projects vectors in ℝ³ onto the subspace W spanned by the vectors [3 1 1] and [15 11 -1] is:
P = [3/√11 15/√337]
[1/√11 11/√337]
[1/√11 -1/√337]
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Find the total surface area of this cone. Leave your answer in terms of pie.
Answer:
90[tex]\pi[/tex]
Step-by-step explanation:
if you want explanation say in comments
Find the perimeter of the window to the nearest hundredth.
perimeter: about
ft
What is the Median for the Box & Whisker Plot below?
HELP PLEASEE
Answer:
20
Step-by-step explanation:
13. What is the quadratic function that has a graph that contains the points
{(-1,8), (0,5),(1,0))?
A g(x) = -x2 - 4x + 5
B g(x) = -x2 +5
C g(x) = -x2 + 7x + 5
D g(x) = -x2 + 4x + 5
Answer: D, i am a hight school teacher names miss smell my butt, and i know that i am right
Write the equation of the line graphed at the right(please help I really need this)
the correct answer is X= -3
(50 POINTS) Write out each sum.
Step-by-step explanation:
12. n^2+2n
if you insert 1 for k and then work up by inserting 2 for k and adding those together and stoping at n.
13. 8-2(2^n)
if you insert 3 for k and then work up by inserting 4 for k and adding those together and keep on going but stopping at n.
Hope that helps :)
Event A: You roll a double. Event B: The sum of the two scores is even. Event C: The score on the blue die is greater than the score on the red die. Event D: You get a 6 on the red die. Complete the following as a group. Discuss each question together and enter your answers. When you are done, be sure to finish the last few steps of the meeting agenda ("reflect" and "share recording"). = 1. Circle the pairs of events for which PIX and Y) = P(X) x P(Y) A&B A&C A&D B&C B&D C&D
Among the pairs of events A&B, A&C, A&D, B&C, B&D, and C&D, the pairs A&C and B&D satisfy the condition P(A∩B) = P(A) × P(B), indicating that they are independent events.
To determine if two events are independent, we compare the product of their individual probabilities to the probability of their intersection. If the product of the individual probabilities is equal to the probability of the intersection, then the events are independent.
Let's examine each pair of events:
A&B: Rolling a double and getting a sum of even scores are not independent events. The occurrence of one event does not guarantee the occurrence of the other.
A&C: Rolling a double and having the score on the blue die greater than the score on the red die are independent events. The probability of rolling a double is solely dependent on the outcome of the dice roll, while the probability of the blue die having a greater score than the red die is independent of the outcome of rolling a double.
A&D: Rolling a double and getting a 6 on the red die are not independent events. The occurrence of rolling a double does not affect the probability of getting a 6 on the red die.
B&C: Getting a sum of even scores and having the score on the blue die greater than the score on the red die are not independent events. The occurrence of one event does not guarantee the occurrence of the other.
B&D: Getting a sum of even scores and getting a 6 on the red die are independent events. The probability of getting a sum of even scores is solely dependent on the outcome of the dice roll, while the probability of getting a 6 on the red die is independent of the sum of the scores.
C&D: Having the score on the blue die greater than the score on the red die and getting a 6 on the red die are not independent events. The occurrence of one event does not guarantee the occurrence of the other.
In summary, the pairs of events A&C and B&D are the only pairs that satisfy the condition P(A∩B) = P(A) × P(B), indicating that they are independent events.
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MARK BRAINLIESTTTTTT
Answer:
i think its c hope it helps
Step-by-step explanation:
What is the simple interest on $4,000 for 2 and a half years at 4 percent a year?
Answer:
Step-by-step explanation:
You can't receive money if you withdraw in the midst of a year.
So 4000 * 1/25 * 2 = $4320
Over which interval does f(t) have positive average rate of change?
A) -8,-2
B) -5,-1
C) -9,-8
D) 2,4
Answer:
D) 2,4
Step-by-step explanation:
The only answer with positive numbers
Answer:
D) 2,4
Step-by-step explanation:
A spinner has five equal sections labeled 1-5. In 60 spins, how often can you expect to spin a 3?
ok so lets say that you have a pizza cutted out in 5 sections and want to pick up only a certain piece, let's say pepperoni. If you took a piece at random, the chances of getting that certain piece of pepperoni in 60 spins is: 12 / 60
What is the best description of a food chain?
the competition among several species for the same food item
the transfer of energy from one organism to another
Answer:
the transfer of energy from one organism to another
Step-by-step explanation:
help me bros, this question is a big part of my grade!!
Answer:
6.
m1 : 61
m2 : 61
m3 : 29
7.
m1 : 87
m2 : 45
m3 : 45
m4 : 52
Solve the system using substitution: x = -4y and x + 5y = 2
Please and thank you.
Answer:
x = - 8, y = 2
Step-by-step explanation:
[tex]x = - 4y......(1) \\ x + 5y = 2....(2) \\ plug \: x = - 4y \: in \: equation \: (2) \\ - 4y + 5y = 2 \\ y = 2 \\ plug \: y = 2 \: in \: equation \: (1) \\ x = - 4(2) \\ x = - 8\\[/tex]
Combine the like terms to create an equivalent expression for 4z−(−3z)
Answer:
7z
Step-by-step explanation:
Answer: 7z
Step-by-step explanation:
two negatives cancel into a positive, so -(-3z) is +3z. 4z + 3z = 7z
4th grade math helplolll
Answer:
175 dollars
Step-by-step explanation:
from that word problem the equation that i was able to get out of it was
1225/ 7
^ the travel allowance and how much days they are going to be there
i dont know if you are allowed to use a calculator in your class but puting 1225/ 7 does give you a answer of a positive number of 175 dollars
meaning that they can only use 175 dollars a day so they dont go over the allowance
i hope this helps you! please stay safe and have a good day :)
Answer:
Um, the answer for that is 175.
Step-by-step explanation:
all you need to do is divide $1,225 by 7 which is 175.
Calculate each value for ⊙P. Use 3.14 for π and round to the nearest tenth.
please help!! will mark brainliest!!
Answer:
226.19 inches
Step-by-step explanation:
Find the volume of an oblique circular cylinder that has a radius of five feet and a height
of three feet
Answer:
235.5 cubic feet
Step-by-step explanation:
The volume v of a circular cylinder whose base radius is r and height h is given as
v = πr^2h
where π is 22/7 or 3.14
Given that the radius is five feet and the height is three feet
the volume v = 3.14 *5^2 * 3
= 235.5 cubic feet
The volume of the oblique circular cylinder is 235.5 cubic feet