Answer:
45
hope this helps
Answer:
45
Step-by-step explanation:
9x5=45
Find a power series for the function, centered at c, and determine the interval of convergence. f(x) = 9 3x + 2 , c = 6
Answer:
[tex]\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ........[/tex]
The interval of convergence is:[tex](-\frac{2}{3},\frac{16}{3})[/tex]
Step-by-step explanation:
Given
[tex]f(x)= \frac{9}{3x+ 2}[/tex]
[tex]c = 6[/tex]
The geometric series centered at c is of the form:
[tex]\frac{a}{1 - (r - c)} = \sum\limits^{\infty}_{n=0}a(r - c)^n, |r - c| < 1.[/tex]
Where:
[tex]a \to[/tex] first term
[tex]r - c \to[/tex] common ratio
We have to write
[tex]f(x)= \frac{9}{3x+ 2}[/tex]
In the following form:
[tex]\frac{a}{1 - r}[/tex]
So, we have:
[tex]f(x)= \frac{9}{3x+ 2}[/tex]
Rewrite as:
[tex]f(x) = \frac{9}{3x - 18 + 18 +2}[/tex]
[tex]f(x) = \frac{9}{3x - 18 + 20}[/tex]
Factorize
[tex]f(x) = \frac{1}{\frac{1}{9}(3x + 2)}[/tex]
Open bracket
[tex]f(x) = \frac{1}{\frac{1}{3}x + \frac{2}{9}}[/tex]
Rewrite as:
[tex]f(x) = \frac{1}{1- 1 + \frac{1}{3}x + \frac{2}{9}}[/tex]
Collect like terms
[tex]f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2}{9}- 1}[/tex]
Take LCM
[tex]f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2-9}{9}}[/tex]
[tex]f(x) = \frac{1}{1 + \frac{1}{3}x - \frac{7}{9}}[/tex]
So, we have:
[tex]f(x) = \frac{1}{1 -(- \frac{1}{3}x + \frac{7}{9})}[/tex]
By comparison with: [tex]\frac{a}{1 - r}[/tex]
[tex]a = 1[/tex]
[tex]r = -\frac{1}{3}x + \frac{7}{9}[/tex]
[tex]r = -\frac{1}{3}(x - \frac{7}{3})[/tex]
At c = 6, we have:
[tex]r = -\frac{1}{3}(x - \frac{7}{3}+6-6)[/tex]
Take LCM
[tex]r = -\frac{1}{3}(x + \frac{-7+18}{3}+6-6)[/tex]
r = -\frac{1}{3}(x + \frac{11}{3}+6-6)
So, the power series becomes:
[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}ar^n[/tex]
Substitute 1 for a
[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}1*r^n[/tex]
[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}r^n[/tex]
Substitute the expression for r
[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}(-\frac{1}{3}(x - \frac{7}{3}))^n[/tex]
Expand
[tex]\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}[(-\frac{1}{3})^n* (x - \frac{7}{3})^n][/tex]
Further expand:
[tex]\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ................[/tex]
The power series converges when:
[tex]\frac{1}{3}|x - \frac{7}{3}| < 1[/tex]
Multiply both sides by 3
[tex]|x - \frac{7}{3}| <3[/tex]
Expand the absolute inequality
[tex]-3 < x - \frac{7}{3} <3[/tex]
Solve for x
[tex]\frac{7}{3} -3 < x <3+\frac{7}{3}[/tex]
Take LCM
[tex]\frac{7-9}{3} < x <\frac{9+7}{3}[/tex]
[tex]-\frac{2}{3} < x <\frac{16}{3}[/tex]
The interval of convergence is:[tex](-\frac{2}{3},\frac{16}{3})[/tex]
Which answer describes the pattern in this sequence?
2, 1, 12, 14, ...
multiply by 2
subtract 1
add 12
multiply by 12
Find the missing side or angle.
Round to the nearest tenth.
A=60°
b=50
C=48
a=[?]
The missing side 'a' of the triangle ABC is 96.80 units.
What is a triangle?
A triangle is a flat geometric figure that has three sides and three angles. The sum of the interior angles of a triangle is equal to 180°. The exterior angles sum up to 360°.
For the given situation,
Let ABC be the triangle and a,b,c be the respective sides of the triangle.
The diagram below shows that the triangle with their dimensions.
The dimensions are
A=60°, b=50, c=48.
The two sides and one angle of the triangle are given.
The missing side a can be found by using the law of cosines,
[tex]a=\sqrt{b^{2}+c^{2} -2abcosA }[/tex]
Substitute the above values,
⇒ [tex]a=\sqrt{50^{2}+48^{2} -2(50)(48)cos60 }[/tex]
⇒ [tex]a=\sqrt{2500+2304-4800(-0.9524)}[/tex]
⇒ [tex]a=\sqrt{2500+2304+4571.58}[/tex]
⇒ [tex]a=\sqrt{9375.58}[/tex]
⇒ [tex]a=96.82[/tex] ≈ [tex]96.80[/tex]
Hence we can conclude that the missing side 'a' of the triangle ABC is 96.80 units.
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One number is 5 times as large as another. The sum of their reciprocals is
[tex] \frac{36}{5} [/tex]
. Find the two numbers.
Answer:
[tex]The \ two \ numbers \ are \ \frac{1}{6} \ and \ \frac{5}{6}[/tex]
Step-by-step explanation:
Let the two numbers be = x , y
Given:
One of the number is 5 times other number, that is y = 5x ----- ( 1 )
The sum of their reciprocals is 36/5 , that is
[tex]\frac{1}{x} + \frac{1}{y} = \frac{36}{5}[/tex] ------ ( 2 )
Substitute y in the second equation.
[tex]\frac{1}{x} + \frac{1}{5x} = \frac{36}{5}\\\\\frac{1 \times 5}{5 \times x} + \frac{1}{5x} = \frac{36}{5}\\\\\frac{5}{5x} + \frac{1}{5x} = \frac{36}{5}\\\\\frac{5+1}{5x} = \frac{36}{5}\\\\\frac{6}{5x} =\frac{36}{5}\\\\36 \times 5x = 6 \times 5\\\\x = \frac{6 \times 5}{36 \times 5} = \frac{1}{6}[/tex]
Substitute x in first equation.
[tex]y = 5x\\\\y = 5 \times \frac{1}{6} \\\\y = \frac{5}{6}[/tex]
When is 9+10 really equal to 21
Answer:
it's equal to 21 when I say it's equal to 21
If you vertically compress the square root parent function by a factor of 1/3, what is the equation of the new function?
9514 1404 393
Answer:
y = (1/3)√x
Step-by-step explanation:
Vertical scaling of a function is accomplished by multiplying the function by the scale factor. If you want to scale the square root function by a factor of 1/3, then the scaled function is ...
y = (1/3)√x
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate for the data below. Types of restaurants (fast food, organic food, sea food, etc.)A. The ratio level of measurement is most appropriate because the data can be ordered, differences (obtained by subtraction) can be found and are meaningful, and there is a natural starting point. B. The nominal level of measurement is most appropriate because the data cannot be ordered. C. The interval level of measurement is most appropriate because the data can be ordered, differences (obtained by subtraction) can be found and are meaningful, and there is no natural starting point. D. The ordinal level of measurement is most appropriate because the data can be ordered, but differences (obtained by subtraction) cannot be found or are meaningless.
Answer:
B. The nominal level of measurement is most appropriate because data cannot be ordered.
Step-by-step explanation:
Nominal scale is used when there is no specific order scale and data can be arranged according to name. Ordinal scale requires variables to be arranged in specific order. For fast food restaurant the best scale used is nominal scale as variables can be arranged according to their name without specific order.
please step by step with formula.
Suppose that you deposit $3,850 in an account paying 4.65% simple interest. How long will it take to earn $150 in interest?
Answer:
0.837
Step-by-step explanation:
3850*4.65%=179.025
150/179.025=0.837
0.837
Mathematics text book for class vi has 320 pages the chapter symmetry runs from page 261 to 272. The ratio of the number of pages of this chapter to the total number of pages of the book
Answer:
Step-by-step explanation:
No
To solve the equation 6x + 3 = 9 for x, what operations must be
performed on both sides of the equation in order to isolate the variable
x?
Answer:
Subtraction, and then division.
Step-by-step explanation:
We would subtract 3 on each side to undo the '3', and then divide by 6 on both sides to isolate 'x'.
[tex]6x+3 = 9\\\\6x + 3 - 3 = 9 - 3\\\\ 6x = 6\\\\\frac{6x=6}{6}\\\\\boxed{x=1}[/tex]
Hope this helps.
To solve the equation 6x + 3 = 9 for x, the operations that must be performed on both sides of the equation in order to isolate the variable x are subtraction and then division.
What is a linear equation?A linear equation in one variable has the standard form Px + Q = 0. In this equation, x is a variable, P is a coefficient, and Q is constant.
How to solve this problem?Given that 6x + 3 = 9.
First, we have to separate variable and constants. So, we have to subtract 3 from both sides.
6x + 3 - 3 = 9 - 3
i.e. 6x = 6
Now, to solve this equation, we use division.
x = 6/6 = 1
i.e. x = 1
Therefore, to solve the equation 6x + 3 = 9 for x, the operations that must be performed on both sides of the equation in order to isolate the variable x are subtraction and then division.
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The number of visits to public libraries increased from 1.3 billion in 1993 to 1.7 billion in 1997. Find the average rate of change in the number of public library visits from 1993 to 1997.
Answer:
The average rate of change in the number of public library visits from 1993 to 1997 was of 0.1 billion an year.
Step-by-step explanation:
Average rate of change:
Division of the subtraction of the final value by the initial value, divided by the length of time.
The number of visits to public libraries increased from 1.3 billion in 1993 to 1.7 billion in 1997.
Initial value: 1.3 billion
Final value: 1.7 billion
1997 - 1993 = 4 years.
Thus:
[tex]A = \frac{1.7 - 1.3}{4} = \frac{0.4}{4} = 0.1[/tex]
The average rate of change in the number of public library visits from 1993 to 1997 was of 0.1 billion an year.
A, B, and C are collinear points:
C is between A and B.
If AC = 2x + 1, CB = 3x - 1, and AB = 35, findX.
Answer:
X = 7
Step-by-step explanation:
Calculate the interest rate with a deposit $27,580.00 in an interest-bearing account. After one year, your accrued interest is $1,442.43.
Answer:
5.23%
Step-by-step explanation:
See Image below:)
∫▒〖e^2x dx〗= ???? thanks
Answer:
Step-by-step explanation:
I=∫e^2x dx
put 2x=t
2dx=dt
dx=dt/2
I=1/2∫e^t dt
=1/2 e^t+c
=1/2 e^{2x}+c
At an assembly plant for light trucks, routine monitoring of the quality of welds yields the following data:
Number of Welds
High Moderate Low
Quality Quality Quality
Day Shift
Evening Shift
Night Shift 467 191 42
445 171 34
254 129 17
Can you conclude that the quality varies among shifts?
a. State the appropriate null hypothesis.
b. Compute the expected values under the null hypothesis.
c. Compute the value of the chi-square statistic.
d. Find the P-value. What do you conclude?
Answer:
Kindly check explanation
Step-by-step explanation:
H0 : quality does not vary among shift
H1 : quality varies among shift
The expected values :
(Row * column) / grand total
Given the data:
Observed values :
_________________total
_______467 191 42 __700
_______445 171 34 __650
_______254 129 17 _ 400
Total __ 1166 491 93 _ 1750
Expected value count using the formula :.
Expected Values:
466.4 ____196.4 ______37.2
433.086 _182.371___ 34.5429
266.514_ 112.229____ 21.2571
The Chisquare statistic (χ²) :
χ² = (observed - Expected)²/ observed
χ² = 5.76045
The degree of freedom = (row - 1) * (column - 1)
Degree of freedom = (3-1)*(3-1) = 2*2 = 4
Pvalue = 0.2178
Pvalue > α ; We foal to reject H0 ; Hence, we conclude that quality does not vary among shift
Tìm căn bậc hai của số phức z=1+i√3
Write z in polar form:
z = 1 + √3 i = 2 exp(i π/3)
Taking the square root gives two possible complex numbers,
√z = √2 exp(i (π/3 + 2kπ)/2)
with k = 0 and k = 1, so that
√z = √2 exp(i π/6) = √(3/2) + √(1/2) i
and
√z = √2 exp(i 7π/6) = -√(3/2) - √(1/2) i
how do you find contribution margin %?
Answer:
Contribution margin = Revenue − Variable costs
Step-by-Step Explanation
For example, if the price of your product is $20 and the unit variable cost is $4, then the unit contribution margin is $16.
The first step in doing the calculation is to take a traditional income statement and recategorize all costs as fixed or variable. This is not as straightforward as it sounds, because it’s not always clear which costs fall into each category.
Hope this helps and if it does, don't be afraid to rate my answer as well as maybe give it a "Thanks"? (Or even better a "Brainliest"). And if it’s not correct, I am sorry for wasting your time, and good luck finding the correct answer :)
-6c< -12
what will the answear be
Answer:c>2
Step-by-step explanation:
-6c (divide) (-6) > -12 (divide) (-6)
c>-12 (divide) (-6)
c>12 (divide) 6
c> 2
what is a bank statement
Answer:
A statement that shows current balance of an account and all transactions that occurred on that account since the last statement.
Transactions such as deposits, withdrawals, checks written, debt card uses...
There are other examples of bank statements for things like home loans, business loans, and investments.
Help pls ASAP this need to be done
D
Because slope of section D is greater than the others and hence speed is highest.
Use the substitution method to solve the system of equations. Choose the correct ordered pair. 4(x + 4) = 8(y + 2); 18y - 22 = 3x + 2
x = 30
y = 2
Get the explanation from the image I have shared.
Hope it helps you
this image may be the result of the ___. if mRQS is 75, then mTPU is ____.
Answer:
B for first one.
75 for second.
Hope this helps !
Step-by-step explanation:
Which of the following correctly describes the symmetry of the cubic parent
function?
^
A. It is symmetric about the x-axis.
B. It is symmetric about the y-axis.
C. It is symmetric about the origin.
D. It is not symmetric about any point or line.
The statement that correctly describes the symmetry of the cubic parent function is 'It is symmetric about the origin.'
The correct answer is option (c)
What is the symmetry of the function about the X-axis?"The graph of the function is said to be symmetric about X-axis if whenever (a, b) is on the graph then so is (a, -b) "
What is the symmetry of the function about the Y-axis?"The graph of the function is said to be symmetric about Y-axis if whenever (a, b) is on the graph then so is (-a, b) "
What is the symmetry of the function about the origin?"The graph of the function is said to be symmetric about X-axis if whenever (a, b) is on the graph then so is (-a, -b) "
For given question,
The parent cubic function is [tex]f(x)=x^3[/tex]
The graph of the function [tex]f(x)=x^3[/tex] is as shown below.
From graph we can observe that, point (x, y) as well as (-x, -y) is on the graph.
This means, the graph of the function [tex]f(x)=x^3[/tex] is symmetric about the origin.
Therefore, the statement that correctly describes the symmetry of the cubic parent function is 'It is symmetric about the origin.'
The correct answer is option (c)
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What is sin(C)? Please explain.
Answer:
sin(C) = opposite side / hypotenuse
= 15/17
Answer:
[tex] \small \sf \: Sin ( C ) = \blue{ \frac{15}{17}} \\ [/tex]
Step-by-step explanation:
[tex] \small \sf \: Sin ( C ) = \frac {Opposite \: side }{Hypotenuse} \\ [/tex]
Where we have given :-
Opposite side = 15Hypotenuse = 17substitute the values, we get
[tex] \small \sf \: Sin ( C ) = \blue{ \frac{15}{17}} \\ [/tex]
Solve the system of equations??
Answer:2921
Step-by-step explanation: Add the two equations together to get (x+y)+(x-y)=3500+2342. Simplify and get 2x=5842. Divide 5842 by 2 and get 2921.
Complete parts (a) through (c) below
a. A storage pod has a rectangular floor that measures 22 feet by 13 feet and a flat ceiling that is 7 feet above the floor. Find the area of the floor and the volume of the pod.
Alap pool has a length of 28 yards, a width of 20 yards, and a depth of 3 yards Find the poof's surface area (the water surface) and the total volume of water that the pool holds Raised flower bed is 30 feet long. 5 feet wide, and 1.2 feet deep. Find the area of the bed and the volume of soil it holds
The area of the floor of the pod is (Type an integer or a decimal)
The volume of the pod is (Type an integer or a decimal
b. The pool's surface area is (Type an integer or a decimal)
The total volume of the water that the pool holds (Type an integer or a decimal)
c. The area of the flower bed is (Type an integer or a decimal)
The volume of the soil that the flower bed holds is (Type an integer or a decimal)
Answer:
Kindly check explanation
Step-by-step explanation:
Given :
Pool dimension :
rectangular floor that measures 22 feet by 13 feet and a flat ceiling that is 7 feet above the floor
Floor area = length * width
Floor area = 22 * 13 = 286 ft²
Volume of the pod :
Floor area * height = 286ft² * 7ft = 2002 ft³
2.)
Surface area = length * width
Surface area = 28 * 20 = 560 ft²
Volume of the pool :
Surface area * deptb = 560ft² * 7ft = 2002 ft³
3.)
Area of flower bed = length * width
Floor area = 30 * 5 = 150 ft²
Volume of the soil flowerbed holds :
Depth = 1.1 m
Area of flowerbed * depth =150ft² * 1.2ft = 180 ft³
(Y = 179x
(Y = 105x + 2046
Graph pls
9514 1404 393
Answer:
see attached
Step-by-step explanation:
A graphing calculator does a nice job of graphing these equations.
__
The very steep slope suggests the graph will need somewhat different vertical and horizontal scales in order to show anything useful.
A piece of office equipment purchased for dollar-sign 67,500 depreciates in value each year. Suppose that each year the value of the equipment is StartFraction 1 Over 15 EndFraction less than its value the preceding year.
Calculate the value of the equipment after 2 years.
The value of the equipment after 2 years is dollar-sign
9514 1404 393
Answer:
$58,800
Step-by-step explanation:
Each year, the value is multiplied by 1-1/15 = 14/15. Then after 2 years, the initial value has been multiplied by (14/15)^2 = 196/225. The value after 2 years is ...
$67,500×196/225 = $58,800
what is the square root of 15
Step-by-step explanation:
[tex] \sqrt{15} = 3.872983346 = 3.88[/tex]
Find the distance from (4,2) to the line defined
by y = -2x + 5. Express as a radical or a number
rounded to the nearest hundredth.
Answer:
The desired distance is √5
Step-by-step explanation:
Recall that the distance from a point to a line is measured along a path perpendicular to the line. Thus, given the line y = -2x + 5, the slope of any line perpendicular to it is the negative reciprocal of -2: +1/2.
The line perpendicular to y = -2x + 5 and passing through (4, 2) is
y - 2 = (1/2)(x - 4), or
2y - 4 = x - 4, or 2y = x, or y = (1/2)x.
Now our problem becomes "find the length of the line connecting (4, 2) and the intersection of y = -2x + 5 and y = (1/2)x."
Equating these, we get (1/2)x = -2x + 5, which, if multiplied through by 2, becomes x = -4x + 10, or 5x = 10, or x = 2. If x = 2, then y = (1/2)(2) = 1.
Finally, find the distance between (2, 1) and (4, 2):
Using the Pythagorean Theorem, d = √(2^2 + 1^2) = √5
The distance from (4, 2) to the line y = -2x + 5 is √5