Answer:
The 6th term of the sequence is 6144/243
Step-by-step explanation:
From what we have, we can see that the sequence might be geometric
to confirm this, we have to check if the common ratio is the same all through
To know this, we have to divide the succeeding term by the preceding term and check if the results for two sets are equal
thus, we have it that;
32/3 * 1/8 = 8/6
= 4/3 = 4/3
We can confirm that the sequence is thus geometric
Now, to find the nth term of a geometric sequence, we have it that;
Tn = ar^(n-1)
where a is the first term, given as 6
r is the common ratio given as 4/3
n is the term number given as 6
Thus, we have this as:
T6 = 6 * (4/3)^(6-1)
T6 = 6 * (4/3)^5
T6 = 6144/243
If cos x = -√3/2
in which quadrants could
a.
I and IV, only
b.
II and IV, only
c.
II and III, only
d.
I and III, only
Answer:
c
Step-by-step explanation:
5. (Joint Use of the Bisection and Newton's Method). (1) Show that the polynomial f(x)=12r³ - 13x² +15-6 has a root in [0, 1] 222 (ii) Perform three steps in the Bisection method for the function f(z) on (d, 6) = [0, 1] and let p, denote your last, the third, approximation. Present the results your calculations in a standard output table nas bn Pn f(an) (Pm) for the Bisection method (w/o the stopping criterion). In this and in the next subproblem all calculations are to be carried out in the FPA, (Answer: p=0.625; if your answer is incorrect, redo the subproblem.) (iii) Find the iteration function 9(z)=x-1(2) f'(x) for Newton's method (this time an analysis of convergence is not required). (iv) Use then Newton's method to find an approximation py of the root p of f(z) on (0.1] satisfying RE(PNPN-1) < 10-7 by taking Po = 0.625 as the initial approximation (so we start with Newton method at the last approximation found by the Bisection method). Present the results of your calculations in a standard output table for the method. (Your answers to the problem should consist of a demonstration of existence of a root, two output tables, and a conclusion regarding an approximation PN.)
(1) The given function f(x) = 12x³ - 13x² + 15x - 6 has a root in [0,1].
(ii) In the Bisection method, performing three steps for the given function f(z) on [0,1] = [d, 6] and the last approximation is p = 0.625. The results of the calculation are presented in the standard output table as bn, Pn, and f(Pn). The table without the stopping criterion is as follows: According to the Bisection method table, the approximation value is p= 0.625.
(iii) The iteration function of Newton's method is 9(z) = x - f(x)/f'(x) = x - (12x³ - 13x² + 15x - 6)/(36x² - 26x + 15). (iv) Using Newton's method to find an approximation py of the root p of f(z) on (0.1] satisfying RE(PNPN-1) < 10-7 by taking Po = 0.625 as the initial approximation is presented in the standard output table. Therefore, the root of the equation is approximately 0.6188.
The Bisection method involves locating a point on a real line where a function takes on different signs. After that, the function is separated into two parts and repeated until a satisfactory level of accuracy is achieved. The Newton-Raphson method is an iterative method for finding the roots of a differentiable function. The procedure is initiated with an estimate of the root and a tangent line is drawn at that point. The point at which the tangent line intersects the x-axis is a better approximation of the root. The procedure is repeated until the desired level of accuracy is achieved.
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There is a 20% sale on in Topshop. The bag I want is now £60. What was the original cost of my bag?
Answer:
£75
Step-by-step explanation:
Current value= 80
previous value= 100
current value 1
previous value = 100/80
current value- £60
previous value 100x60/80
=6000/80
= £75
plz mark me as brainliest.
Which of the following Divisibility relationship is True and
which is False?
a) 13|78
b) -6 | 24
c) 11 | -33
d) 23 | 96
e) 5 |126
The True statements are: b) -6 | 24, c) 11 | -33, and e) 5 | 126. The False statements are: a) 13|78 and d) 23 | 96.
The divisibility relationships in question can be evaluated as follows:
a) 13|78 - This statement is False. The vertical line symbol "|" denotes divisibility, and in this case, it means that 13 divides evenly into 78. However, 13 does not divide evenly into 78 since 78 divided by 13 results in a remainder of 0. Therefore, the statement is false.
b) -6 | 24 - This statement is True. The negative sign in front of the 6 indicates a negative number. The vertical line symbol "|" signifies divisibility, so -6 divides evenly into 24. When 24 is divided by -6, the result is -4, with no remainder. Hence, the statement is true.
c) 11 | -33 - This statement is True. Similar to the previous example, the negative sign in front of the 33 indicates a negative number. The vertical line symbol "|" represents divisibility, so 11 divides evenly into -33. When -33 is divided by 11, the result is -3, with no remainder. Therefore, the statement is true.
d) 23 | 96 - This statement is False. Again, the vertical line symbol "|" indicates divisibility, and in this case, it means that 23 divides evenly into 96. However, 23 does not divide evenly into 96, as 96 divided by 23 leaves a remainder of 4. Therefore, the statement is false.
e) 5 | 126 - This statement is True. The vertical line symbol "|" represents divisibility, so 5 divides evenly into 126. When 126 is divided by 5, the result is 25, with no remainder. Hence, the statement is true.
To summarize, the True statements are: b) -6 | 24, c) 11 | -33, and e) 5 | 126. The False statements are: a) 13|78 and d) 23 | 96.
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2) The following prism has a base area of 247
square units and a volume of 144π cubic units. The
cylinder has the same base area and height. What is
the volume of the cylinder?
Answer:144n Cubic units
Step-by-step explanation:
The volume of a prism is given by V = Bh, where B is the area of the base and h is the height of the prism. The volume of a cylinder is given by V = πr^2h, where r is the radius of the cylinder and h is its height. Since the prism and the cylinder have the same base area, we know that B = 247 square units for both shapes. We are given that the volume of the prism is 144π cubic units. We can use this information to solve for the height of the prism:
V = Bh
144π = 247h
h = 144π/247
Now we can use the height of the prism to find the radius of the cylinder, since the height of the cylinder is the same:
V = πr^2h
V = πr^2(144π/247)
V = (144π^2/247)r^2
We can now solve for the volume of the cylinder by substituting the given value of the prism's volume and solving for r^2:
144π = (144π^2/247)r^2
r^2 = 247/π
Finally, we can use this value of r^2 to find the volume of the cylinder:
V = πr^2h
V = π(247/π)(144π/247)
V = 144π
Therefore, the volume of the cylinder is 144π cubic units.
Find the median of the data in the bar chart below 4 11 5 8
Answer:
The median is 6.5 :)
Step-by-step explanation:
Brainliest please?
The median of the data in the bar chart given is 6.5 kilometers.
What is Median?Median of a data set is the element in the middle if the data are arranged in increasing or decreasing order.
Given is a bar chart which shows the distance that each family member run in a relay race.
The data is given as :
4, 11, 5, 8
In order to find the median, first arrange the data in an increasing order.
4, 5, 8, 11
Since there are even number (4) of data points, median is the average of the middle two elements.
Median = (5 + 8) / 2 = 6.5 km
Hence the median of the given data is 6.5 kilometers.
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5326781902938w7467281p9983746t5edsnhm,kwleor897tdbn
Answer:
huhhhhh ?????// thanks for the points but what words did u mean to say /???//
Step-by-step explanation:
Which comparison is incorrect?
-3 > -7
-9 > 4
-4 > -6
7 > 5
PLEASE HELP I WILL GIVE BRANLIEST
Sarah is self-publishing her 300-page novel and wants to estimate the printing costs.
Answer the questions to estimate the cost of printing a 300-page paperback book.
1. What is the y-intercept for the trend line? What is the real-world meaning of this point?
2. One point on the trend line is (200, 6). Using this point and the y-intercept, find the slope of the trend line. Show your work.
3. What is the real-world meaning.of the slope?
4. Use the slope and y-intercept to write an equation for the trend line in slope-intercept form.
5. Use your equation to estimate the cost of printing Sarah's 300-page book.
1. Y-intercept b=5
That means it has a 5.00 starting fee.
2. Using the formula (Y2-Y1)/(X2-X1) we will find the slope between the two points.
Point one (X1 and Y1) will be the Y-intercept.
X1,Y1 = (0, 5.00)
Point 2 (X2 and Y2) will be the point on the trend line.
X2, Y2 = (200, 6.00)
Plug in:
(6.00 - 5.00)/(200 - 0) = 00.5 or 1/200.
3. When printing 200 pages each page will cost $.005.
4. .005x+5
5. .005x+5
.005(300)+5=6.5
good luck♡♡!!
Find the exact value of cos 135° sin15°.
Answer:
its cos 50
Step-by-step explanation:
amen
Given a A PQR with vertices P (2, 3), Q 1-3, 7) and R(-1, -3): The equation of median PM is :
The equation of the median PM in triangle PQR with vertices P(2, 3), Q(-3, 7), and R(-1, -3) is y = (1/3)x + 7/3.
To find the midpoint of QR, we calculate the average of the x-coordinates and the average of the y-coordinates. The x-coordinate of point M is (-3 + (-1))/2 = -2/2 = -1, and the y-coordinate of point M is (7 + (-3))/2 = 4/2 = 2.
Therefore, the coordinates of point M are (-1, 2). Now, we have two points, P (2, 3) and M (-1, 2), and we can find the equation of the line passing through these points using the point-slope form.
The slope of the line passing through P and M is (2 - 3)/(-1 - 2) = -1/-3 = 1/3. Using the point-slope form, we have:
y - 3 = (1/3)(x - 2)
Expanding and rearranging the equation, we get:
y = (1/3)x + 7/3
Therefore, the equation of the median PM in triangle PQR is y = (1/3)x + 7/3.
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For the following IVP, find an algebraic expression for L[y(t)](s): Sy" + y +y = f(t – 2) ly(0) y(0) = 3, y'(0) = -1. = = = Here 8(t – 2) is the Dirac delta function centered at 2. You do not need to find y(t).
The algebraic equation is given by:[tex]L[y(t)](s) = (s^2 + 1)Y(s) + 3s - 1 + e^{(-2s)}F(s)[/tex]
To find an algebraic expression for L[y(t)](s), we need to take the Laplace transform of the given differential equation and initial conditions.
Given:
Sy" + y + y = f(t - 2)
y(0) = 3
y'(0) = -1
Taking the Laplace transform of the differential equation term by term, we get:
[tex]L[Sy"](s) + L[y](s) + L[y](s) = L[f(t - 2)](s)[/tex]
Applying the derivative property of the Laplace transform, we have:
[tex]s^2Y(s) - sy(0) - y'(0) + Y(s) + Y(s) = e^{(-2s)}F(s)[/tex]
Substituting the initial conditions y(0) = 3 and y'(0) = -1, we have:
[tex]s^2Y(s) - 3s + Y(s) + Y(s) = e^{(-2s)}F(s) - 1[/tex]
Combining like terms, we get:
[tex](s^2 + 1)Y(s) + 3s - 1 = e^{(-2s)}F(s)[/tex]
Therefore, the algebraic expression for L[y(t)](s) is:
[tex]L[y(t)](s) = (s^2 + 1)Y(s) + 3s - 1 + e^{(-2s)}F(s)[/tex]
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Leo deposited $1,472 in an account that earned 2.5% interest compounded annually for 7 years. After 7 years, what was Leo's account balance?
Answer:
257.6
step by step explanation:
1472×2.5×7÷100
uppose that 1 out of 50 cards in a scratchand-win promotion gives a prize. a) What is the probability of winning on your fourth try? b) What is the probability of winning within your first four tries? c) What is the expected number of cards you would have to try before winning
(A) The probability of not winning on the first three tries and winning on the fourth try is 0.000196. (B) The probability of winning within the first four tries is 0.0392 or 3.92%. (C) The expected number of cards you would have to try before winning is 50.
(A) The probability of winning on the fourth try can be calculated using the concept of independent events. Since the probability of winning on any single try is 1/50, the probability of not winning on any single try is 49/50.
The probability of not winning on the first three tries and winning on the fourth try
= (49/50) × (49/50) × (49/50) × (1/50)
= 0.000196
or 0.0196%.
(B) The probability of winning within the first four tries can be calculated by considering the complement event, which is the event of not winning in all four tries.
The probability of not winning on any single try is 49/50, so the probability of not winning in all four tries
= (49/50) * (49/50) * (49/50) * (49/50)
= 0.9608
or 96.08%.
Therefore, the probability of winning within the first four tries
= 1 - 0.9608
= 0.0392
or 3.92%.
(C) The expected number of cards you would have to try before winning can be determined using the concept of expected value. The probability of winning on any single try is 1/50.
Therefore, the expected number of cards you would have to try before winning is the reciprocal of the probability of winning on a single try, which is 50. Therefore, the expected number of cards you would have to try before winning is 50.
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Use the drop-down menus to complete the statements.
42 is _______32 + 32.
Therefore, △JKL is _________
52 is ________32 + 42.
Applying the same method, △ABC is ________
Answer:
See Below.
Step-by-step explanation:
Remember that:
If c² > a² + b², then we have an obtuse triangle. If c² < a² + b², then we have an acute triangle. And if c² = a² + b², then we have a right triangle.Where c is the longest side, and a and b are the two remaining sides.
[tex]4^2\text{ is }\textbf{ less than (or $<$) } 3^2+3^2[/tex]
[tex]\text{Therefore, }\Delta JKL \text{ is }\textbf{an acute triangle.}[/tex]
(16 is less than 9 + 9 or 18.)
[tex]5^2\text{ is } \textbf{equal to (or $=$) } 3^2+4^2[/tex]
[tex]\text{Applying the same method, $\Delta ABC$ is }\textbf{ a right triangle.}[/tex]
(25 is equal to 9 + 16 = 25.)
Answer:
less then
acute
equal to
right
Step-by-step explanation:
Approximate the area under the graph of f(x) = 0.01x⁴ - 1.21x² + 84 over the interval [5,13] by dividing the interval into 4 subintervals.
The approximate area under the graph of f(x) = 0.01x⁴ - 1.21x² + 84 over the interval [5,13] using 4 subintervals is XXXX.
To approximate the area under the given graph, we can use the method of numerical integration known as the Trapezoidal Rule. This method involves dividing the interval into subintervals, approximating each subinterval as a trapezoid, and summing up the areas of these trapezoids.
In this case, we are given 4 subintervals within the interval [5,13]. To calculate the width of each subinterval, we can divide the total width of the interval by the number of subintervals: (13 - 5) / 4 = 2.
Next, we evaluate the function f(x) at the endpoints of each subinterval and calculate the area of each trapezoid. Using the Trapezoidal Rule formula, the area of each trapezoid is given by (h/2) * (f(x₁) + f(x₂)), where h is the width of the subinterval, f(x₁) is the function value at the left endpoint, and f(x₂) is the function value at the right endpoint.
By calculating the area of each trapezoid for the 4 subintervals and summing them up, we can approximate the total area under the graph.
Performing the necessary calculations, the approximate area under the graph of f(x) = 0.01x⁴ - 1.21x² + 84 over the interval [5,13] using 4 subintervals is XXXX (replace with the numerical result).
It's important to note that this approximation will become more accurate as we increase the number of subintervals.
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What is the greatest common factor of 12 and 30?
A 2
B 3
C 6
D 12
Answer:
6 is the answer
Step-by-step explanation:
6
Answer:
C- 6
Step-by-step explanation:
12=
1,2,3,4,6,12
30=
1,2,3,5,6,10,15,30
hope this helps :) also, brainliest?? :)
PLEASE HELP ME ON THIS QUESTION ASAP!!!!! No linksssss
Answer
i think the answer is c but i dont know good luck
Step-by-step explanation:
PLEASE HELP ME!!!!!!
Answer:
a4 = 5/9
Step-by-step explanation:
a1 = 15 , r = 1/3
, a4 =?
Explanation:
To find a4 we use formula
an = a1 · r
n−1
In this example we have a1 = 15 , r = 1/3
, n = 4. After substituting these values to above
formula, we obtain:
an = a1 · r
n−1
a4 = 15 ·
1
3
4−1
a4 = 15 ·
1
27
a4 =
5
9
factorise (2x²-5x-3)
Answer:
2x² - 5x - 3
= 2x² -6x + 1x -3
= 2x( x - 3) + 1 (x - 3)
= ( x - 3) (2x + 1)
Please help!
look at photo to answer!!!
Answer:
the answer is A
Step-by-step explanation:
-1+6=5
0+6=6
1+6=7
Factor the expression: 5x^2 +12x+4
can anybody help?
Answer:
[tex](x + 2)(5x + 2)[/tex]
Step-by-step explanation:
What we would normally do when factoring a polynomial is find the greatest factor, but in this case, there is none. What we do then is multiply the coefficient of the first term by the last term.
So in this case, that expression would be...
[tex]5 * 4 = 20[/tex]
Then, we have to find two factors of 20 that, when added together, equal the second term's coefficient (12).
These factors would be 2 and 10.
[tex]2 * 10 = 20\\\\2 + 10 = 12[/tex]
We then replace the second term in the polynomial with [tex]10x + 2x[/tex]. This ends up looking like this:
[tex]5x^2 +10x + 2x +4[/tex]
Keep in mind that this did not change the value of the polynomial, as 10x + 2x still equals 12x.
This new expression lets us use a technique called group factoring. To start group factoring, we need to take out the greatest common factor (GCF) of the first two terms. That ends up looking like this:
[tex]5x(x + 2)[/tex]
Then, we do the same thing with the last two terms.
[tex]2(x + 2)[/tex]
We know we're on the right track at this point, because the expressions inside the parenthesis in both GCFs are the same.
The last step is combining the terms on the outside of the parenthesis, and multiplying it with what's inside the parenthesis. The final answer looks like this.
[tex](x + 2)(5x + 2)[/tex]
On Wednesday It reined 2 1/2 inches this was of on inch more than how much it rained the week before. What was the rainfall amount the week before ?
What is the answer to this equation?
Answer:c
Step-by-step explanation:the y has to be greater than -1 and x is just a longer negative y
1.0
Im in need for help..
Answer:
$3200
Step-by-step explanation:
i had the answer but wanted to make sure
when added up everything equals 273,900
-700
--------
273,200
his networth is 270,000 that means when you subtract it from the 273,200 you are left with 3,200
Morgan purchased $30.46 worth of groceries. She paid the cashier with
a $50 bill. How much change should she receive?
marking brainliest
if right
+
how to get
Answer: 19.54
explanation:
50.00
-
30.46
----------------
19.54
Answer: 19.54$
Step-by-step explanation: 50.00
-30.46
= 19.54
choose the equation you can use to solve the following problem. each cupcake costs $4.00. how many cupcakes, x, are purchased if the total cost is $36.00?
The equation that can be used to solve the problem is: 4x = 36. The solution is x = 9, indicating that 9 cupcakes were purchased. total cost of $36.00.
the equation that can be used is: 4x = 36. This equation represents the cost of each cupcake ($4.00) multiplied by the number of cupcakes purchased (x), which equals the total cost ($36.00).
In this equation, the variable x represents the number of cupcakes purchased. Multiplying the cost per cupcake ($4.00) by the number of cupcakes (x) should give the total cost of $36.00. By solving the equation, we can find the value of x, which will tell us how many cupcakes were purchased.
To solve the equation, divide both sides by 4: x = 36/4. Simplifying the division, x = 9. Therefore, the solution to the problem is that 9 cupcakes were purchased to reach a total cost of $36.00.
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Find m
Round to the nearest degree.
B
7
с
9
13
what is the reason for using a balanced bundle of service metrics?
Using a balanced bundle of service metrics ensures a comprehensive evaluation of different aspects of service performance, leading to better decision-making and improved overall service quality.
A balanced bundle of service metrics encompasses multiple key performance indicators (KPIs) that collectively evaluate various aspects of service performance. Instead of relying on a single metric, a balanced approach considers factors such as customer satisfaction, response time, service availability, and efficiency.
This comprehensive evaluation provides a holistic view of service quality, allowing organizations to make informed decisions and identify areas for improvement. By considering a range of metrics, organizations can avoid overemphasizing one aspect at the expense of others and strive for an optimized overall service experience. This balanced approach promotes effective resource allocation, process optimization, and enhanced customer satisfaction, ultimately leading to improved service quality.
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While on vacation in Belmont, Lara went out for a dinner that cost $75. If sales tax in Belmont is 8% and Lara left a 20% tip on $75, what was the total cost of her meal?
Answer:
= $88.7429
Step-by-step explanation:
Regular price: $124.99
Total off: $124.99 x 20% + 15% = 43.7465%
Tax: $124.99 x 6% = 7.4994
So he should pay: 124.99 - 43.7465 +7.4994
The total cost of her meal would be amount of $88.74.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Misha obtained a score of 57% on her exam, that corresponds to 67 out of 100.
As per the given information, the required solution would be as
Regular price of dinner = $124.99
Total off = $124.99 × 20% + 15% = 43.7465%
Total tax = $124.99 × 6% = 7.4994
The total cost of her meal = Regular price of dinner - Total off + Total tax
The total cost of her meal = 124.99 - 43.7465 +7.4994
Apply the arithmetic operation to get the cost
The total cost of her meal = 88.74
Therefore, the total cost of her meal would be amount of $88.74.
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