Write the sum using summation notation, assuming the suggested pattern continues. 6, -18, 54, -162, +… Is this sequence arithmetic or geometric? Explain your answer.
Answer:
Hello,
This sequence is geometric with a ratio of -3
the first term is 6
Step-by-step explanation:
[tex]u_1=6\\u_2=-18=6*(-3)=u_1*(-3)\\u_3=54=-18*(-3)=u_2*(-3)=u_1*(-3)^2\\u_4=-162=u_3*(-3)=u_1*(-3)^3\\\\...\\u_{n+1}=u_1*(-3)^n\\\\\displaystyle \sum\limits^\infty _{i=1}u_i = \lim_{n \to \infty} \sum\limits^n _{i=1}u_1*(-3)^{i-1}\\=6*\lim_{n \to \infty} \sum\limits^\infty _{i=1}(-3)^{i-1}\\=6*\frac{1-(-3)^n}{1-(-3)} \\=\dfrac{3}{2} *({1-(-3)^n)\\[/tex]
serie does not converge.
there are 40 marbles in an urn: 14 are green and 26 are yellow. you reach into the urn and randomly select 4 marbles without replacement. what is the probability that at least one of the marbles is green
Answer:
p=0,83641536
Step-by-step explanation:
Let's calculate the probability that all 4 marbles are yellow:
p=26/40*25/39*24/38*23/37 ( no replacement)
=0,1635846372688....
probability that at least one of the marbles is green= 1-p
=0,83641536...
HELP PLEASE WILL MARK BRAINLIEST
Answer:
C.
Step-by-step explanation:
since x=1 it should be -1 so C. is correct
Which of the following is a solution to 6x - 5y=4?
(2,7)
(-1, -2)
(-2, -1)
(2, -7)
Answer:
2,7
Step-by-step explanation:
Answer:
(-1,-2)
Step-by-step explanation:
(6 x -1) -(-2 x 5) = 4
-6 + 10 = 4
X>70
y<45
What is the smallest whole number value of x - y?
Answer:
27
Step-by-step explanation:
x-y
We are subtracting and we want the smallest number
We want the smallest number for x and the largest number for y
The smallest number for x is 71
The largest number for y is 44
71-44
27
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y = f(x + 3)
b. y = f(x – 3)
c. y + 3 = f(x)
d. y - 3 = f(x)
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Answer:
b. y = f(x -3)
Step-by-step explanation:
The translation right h and up k units is ...
y -k = f(x -h)
Here, the red graph is translated right 3 and up 0, so the translated function is ...
y = f(x -3)
_____
Additional comment
You can check this if you like by listing a couple of corresponding points:
y = f(x)
1 = f(-3) . . . . left-most point on black graph.
The corresponding point on the red graph is (0, 1). Putting this into the equation (b), we get ...
1 = f(0 -3) = f(-3) . . . . . correct value for f(-3)
15. (x - 3)
If f(x) = 2x2 – 5, find the following.
16.fly-2)
17. f(a+h)-f(a)
Answer:
16. f(y-2) = 2(y-2)²-5
= 2(y²-4y+4)-5
= 2y²-8y+8-5
= 2y²-8y+3
17. f(a+h)-f(a) = 2(a+h)²-5-(2a²-5)
= 2(a²+2ah+h²)-5-2a²+5
= 2a²+4ah+h²-2a²
= h²+4ah
If a drawing of a house is 12 inches tall and the scale ratio is 1 inch:6 feet, how tall is the house?
А
6 feet
B
18 feet
C
72 feet
D
82 feet
Answer:
72 ft
Step-by-step explanation:
We can use a ratio to solve
1 inch 12 inches
---------- = -----------
6 ft x ft
Using cross products
1 * x = 6*12
x = 72 ft
A right cylinder has a radius of 3 and a height of 12. What is its surface area?
O A. 9077 units2
B. 72 units2
O C. 10877 units
D. 457 units2
Answer:
Option A, [tex]90\pi[/tex] [tex]units^{2}[/tex], is correct.
Step-by-step explanation:
The formula for the surface area of a cylinder is as follows:
A= [tex]2\pi rh+2\pi r^{2}[/tex]
We know that the radius, r, is 3, and the height, h, is 12.
r=3
h=12
Pi will be rounded to 3.14.
Thus, applying the known values to the formula:
A=[tex]2(3.14)(3)(12)+2(3.14)(3)^{2}[/tex]
A=226.08+56.52
A=282.6 [tex]units^{2}[/tex]
In accord with the given options, we must determine which one has a product of around 282.6:
A. [tex]90\pi =282.7433388[/tex]
B.[tex]72\pi =226.1946711[/tex]
C.[tex]108\pi =339.2920066[/tex]
D.[tex]45\pi =141.3716694[/tex]
Therefore, option A, [tex]90\pi units^{2}[/tex], is correct.
WHAT GRAPH BEAST REPRESENTS THE FOLLOWING SITUATION? aS X INCREASES, Y DECREASES R=-0.41
Answer:
there is no graph here
Step-by-step explanation:
The weight of an object above the surface of the Earth varies inversely with the square of the
distance from the center of the Earth. If a body weighs 50 pounds when it is 3,960 miles from
Earth's center, what would it weigh if it were 4,015 miles from Earth's center?
Answer:
weight =48.71228786pounds
Step-by-step explanation:
[tex]w = \frac{k}{ {d}^{2} } \\ 50 = \frac{k}{ {3960}^{2} } \\ \\ k = 50 \times {3960}^{2} \\ k = 50 \times 15681600 \\ k = 784080000 \\ \\ w = \frac{784080000}{ {d}^{2} } \\ w = \frac{784080000}{16120225} \\ \\ w = 48.71228786 \\ w = 48.7pounds[/tex]
If a body weighs 50 pounds when it is 3,960 miles from Earth's center, it would weigh approximately 48.547 pounds if it were 4,015 miles from Earth's center, according to the inverse square law formula.
We know the inverse square law formula:
W₁ / W₂ = D²₂ / D²₁
Where W₁ is the weight of the body at the initial distance D₁, and W₂ is the weight at the final distance D₂.
So we have,
W₁ = 50
D₁ = 3,960
D₂ = 4015
We know that the body weighs 50 pounds when it is 3,960 miles from Earth's center,
So we can plug in those values as follows:
50 / W₂ = (4,015)²/ (3,960)²
To solve for W₂, we can cross-multiply and simplify as follows:
W₂ = 50 x (3,960)² / (4,015)²
W₂ = 50 x 15,681,600 / 16,120,225
W₂ = 48.547 pounds (rounded to three decimal places)
Therefore, if the body were 4,015 miles from Earth's center, it would weigh approximately 48.547 pounds.
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sin2A + cos4A = cos2A + sin4A
Answer:
Hello,
Step-by-step explanation:
I suppose the question is to solve the equation.
[tex]Remember:\\\\sin(a)-sin(b)=2cos(\dfrac{a+b}{2} )*sin(\dfrac{a-b}{2} )\\cos(a)-cos(b)=2sin(\dfrac{a+b}{2} )*cos(\dfrac{b-a}{2} )\\\\\\sin(2a)+cos(4a)=cos(2a)+sin(4a)\\\\\Longleftrightarrow sin(4a)-sin(2a)=cos(4a)-cos(2a)\\\\\Longleftrightarrow 2cos(\dfrac{4a+2a}{2})*sin(\dfrac{4a-2a}{2})=2cos(\dfrac{4a+2a}{2})*sin(\dfrac{2a-4a}{2})\\\\\Longleftrightarrow cos(3a)*sin(a)=cos(3a)*(-sin(a))\\\\\Longleftrightarrow 2cos(3a)*sin(a)=0\\\\[/tex]
[tex]sin (a)=0\ or\ cos(3a)=0\\\\\boxed{k\in\ \mathbb{Z}\ : a=k*\pi\ or\ a=\dfrac{(2k+1)*\pi}{2} }\\[/tex]
Triangles are worth 3 points. Quadrilaterals are worth 4 points. Parallelograms are worth 5 points. Each student identifies and names as many of each shape as they can then calculate their total score. Ryan says the greatest possible score is 156, but Janice says she can score more. Who do you agree with and why?
Answer:
I agree on janice because if is reliable and brilliant,she can score more than that
Michigan and Michigan State play each other this Saturday in football. Based on data from ESPN, Michigan averages 38.1 points per game with a SD of 8.4 and average 424 yards gained per game with a SD of 72. The correlation between points scored and yards gained is 0.68. Thus:
Average points = 38.1, SD= 8.4
Average yards gained = 424, SD= 72, r = 0.68
Required:
a. Find the slope of the regression equation for predicting number of points scored based on average yards gained per game). Report your answer to 4 decimal places.
b. If Michigan gains 500 yards in the game against Michigan State, what is Michigan's predicted points scored? Round to the nearest whole number.
Answer:
200000
by 10009
Step-by-step explanation:
nbebsbsbsbbsbsbsbsbBz
(2f-1)^2, please help, also tell me how to give you brainlyist, or what ever it’s called
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Answer:
4f^2 -4f +1
Step-by-step explanation:
It can be useful to memorize the form of the square of a binomial:
(a +b)^2 = a^2 +2ab +b^2
Here, you have a=2f and b=-1. Then the square is ...
(2f)^2 +2(2f)(-1) +(-1)^2 = 4f^2 -4f +1
__
More generally, the distributive property applies.
(2f -1)^2 = (2f -1)(2f -1) = 2f(2f -1) -1(2f -1)
= (2f)(2f) +(2f)(-1) +(-1)(2f) +(-1)(-1) = 4f^2 -2f -2f +1 = 4f^2 -4f +1
Payton took a friend for a birthday dinner. The total bill for dinner was $44.85 (including tax and a tip). If Payton paid a 19.5% tip, what was his bill before adding the tip?
(Round your answer to the nearest cent.)
$
Number
Answer:
The answer closest to 36.10425. So 36.10 or 36.1
Step-by-step explanation:
x = 44.85 ( 1 - 0.195) = 36.10425
If this helps, it would be nice if 5 stars are given, and a brainliest :)
The amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
For this case, we can assume the amount of bill without tip being A.
Then, as given, Payton gave 19.5% tip (tip is given assumingly on A), then:
Total price of the bill = Bill amount before tip + Tip
44.85 = A + (19.5 % of A)
(we don't write symbols like of currency generally in equations, and understand it from context(which is dollars here))
44.85 = A + (19.5 % of A)
or
[tex]44.85 = A + \dfrac{A}{100} \times 19.5\\\\\text{Multiplying 100 on both the sides}\\\\4485 = 100A + 19.5A\\4485 = 119.5A\\\\\text{Dividing both the sides by 119.5}\\\\\dfrac{4485}{119.5} = A\\\\37.53 \approx A\\\\A \approx 37.53 \: \rm \text{(in dollars)}[/tex]
Thus, the amount of the bill before adding the amount of tip is evaluated being of $37.53 approx.
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What function type does the table of values represent?
A) Linear
B) Exponential
C) Quadratic
D) Can't be determined
Answer:
Hello,
answer C
Step-by-step explanation:
[tex]\begin{array}{|c|c|c|c|}x&y&x^2&3x^2\\---&---&---&---\\1&3&1^2&3*1^2=3\\2&12&2^2&3*2^2=12\\3&27&3^2&3*3^2=27\\4&48&14^2&3*4^2=48\\5&75&5^2&3*5^2=75\\\end{array}\\\\\\\boxed{y=3x^2\ the\ function\ is\ quadratic.}[/tex]
Twice a number is equal to five more than five times the number.
Write that into an equation
Answer:
2x=5y+5
Step-by-step explanation:
Let one number be x, other y
Twice a number(2x) is five more(+5) than 5 times the other number(5y),
It means 2x > 5y
By 5 more, so
2x=5y+5
(d) (8x2 + 7y2 – z2 + 2yz + 3xz – 5xy) * (2x – 3y) vertical method
Answer:
(8x²+7y²–z²+2yz+3xz–5xy) × ( 2x–3y)
= (16x³+14xy²–2z²x+4yzx+6x²z–10x²y –24yx²–21y³+3z²y–6y²z–9xzy+15xy²)
=( 16x³+29xy²–2z²x–5xyz+6x²z–34x²y–21y³+3z²y–6y²z)
[tex] = 16 {x}^{3} - 21 {y}^{3} - 2 {z}^{2}x + 3 {z}^{2} y - 5xyz - 6 {y}^{2} z + 6 {x}^{2} z - 34 {x}^{2} y+ 29x {y}^{2} [/tex]
I hope I helped you^_^
d is the same as k less than 372
(How can I write this as an equation)
I thought it would be d=k-372
Answer:
d = 372 -k
Step-by-step explanation:
is means equals
less than means subtract from
d = 372 -k
1101001÷11 i am really confused
Answer:
100091
Step-by-step explanation:
A 26 foot ladder is lowered down a vertical wall at a rate of 3 feet per minute. The base of the ladder is sliding away from the wall. A. At what rate is the ladder sliding away from the wall when the base of the ladder is 10 feet from the wall
[tex]7.2\:\text{ft/s}[/tex]
Step-by-step explanation:
We can apply the Pythagorean theorem here:
[tex]26^2 = x^2 + y^2\:\:\:\:\:\:\:\:\:(1)[/tex]
where x is the distance of the ladder base from the wall and y is the distance of the ladder top from the ground. Taking the time derivative of the expression above, we get
[tex]0 = 2x\dfrac{dx}{dt} + 2y\dfrac{dy}{dt}[/tex]
Solving for [tex]\frac{dx}{dt},[/tex] we get
[tex]\dfrac{dx}{dt} = -\dfrac{y}{x}\dfrac{dy}{dt}[/tex]
We can replace y by rearranging Eqn(1) such that
[tex]y = \sqrt{26^2 - x^2}[/tex]
Therefore,
[tex]\dfrac{dx}{dt} = - \dfrac{\sqrt{26^2 - x^2}}{x}\dfrac{dy}{dt}[/tex]
Since y is decreasing as the ladder is being lowered, we will assign a negative sign to [tex]\frac{dy}{dt}[/tex]. Hence,
[tex]\dfrac{dx}{dt} = - \dfrac{\sqrt{26^2 - (10)^2}}{10}(-3\:\text{ft/min})[/tex]
[tex]\:\:\:\:\:\:\:= 7.2\:\text{ft/min}[/tex]
I don't know how to do this ? can someone help me please
please mark this answer as brainlist
Type an equation for the
following pattern.
X
Y
1
5
N
2
3
-1
y=[? ]x+[ ]
4
Answer:
Does the answer help you?
please mark this question as brainliest answer.Cause it take a few mins to solve your question.Tq
(a + b + c)(a + b - c)
Answer:
[tex]a^{2} + 2ab + b^{2} - c^{2}[/tex]
Step-by-step explanation:
A B C
A a^2 ab -ac
B ab b^2 -bc
C ac bc -c^2
The angle between a chord and a targent is equal to the angle in the alternate segment
that's the diagram above
if <BAD =19°
find <ACB
Answer:
19
Step-by-step explanation:
The angle between a chord and a targent is equal to the angle in the alternate segment
if <BAD =19°
<ACB=19
Look at the image for the question
Answer:
Does the answer help you?
Find the distance between the pair of points.
(-6/11, -3)
and (-6/11, 2/3)
The distance between the pair of points is
Type an integer or a simplified fraction.)
Answer:
3 2/3
Step-by-step explanation:
The x value is the same for both points. So we're only trying to figure out the difference in the y values. One y value is three steps down from zero and one y value is 2/3 of a step up from zero. So the total vertical distance between the two points is 3 and 2/3.
how many bit strings of length 10 contain exactly six 1s?
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Answer:
210
Step-by-step explanation:
The number of combinations of 10 things taken 6 at a time is ...
10!/(6!(10-6)!) = 210
210 bit strings of length 10 will have 6 1-bits.
Using combination
[tex]\\ \sf\longmapsto {}^{10}C_6[/tex]
We know
[tex]\boxed{\sf {}^nC_r=\dfrac{n!}{r!(n-r)!}}[/tex]
[tex]\\ \sf\longmapsto \dfrac{10!}{6!(10-6)!}[/tex]
[tex]\\ \sf\longmapsto \dfrac{10!}{6!(4!)}[/tex]
[tex]\\ \sf\longmapsto 210[/tex]
If the largest of 89 consecutive integers is 324, what is the smallest?
Answer:
Step-by-step explanation:
If the larger of 2 consecutive integers is 324, then 324-(2-1) = 323 is the smaller.
If the largest of 89 consecutive integers is 324, then 324 - (89-1) = 236 is the smallest.
Hence, the smallest consecutive integer is [tex]237[/tex].
What is the smallest consecutive integer?
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers.
Here given that,
The largest of [tex]89[/tex] consecutive integers is [tex]324[/tex]
So, it is of the form
[tex]324-89=237[/tex]
Hence, the smallest consecutive integer is [tex]237[/tex].
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