Answer:
Please see the Step-by-step explanation for the answers
Step-by-step explanation:
1)
∑[tex]\left \ {{5} \atop {j=1}} \right.[/tex] 2j
The sum of series from j=1 to j=5 is:
∑ = 2(1) + 2(2) + 2(3) + 2(4) + 2(5)
= 2 + 4 + 6 + 8 + 10
∑ = 30
2)
This question is not given clearly so i assume the following series that will give you an idea how to solve this:
∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] 2k²
The sum of series from k=1 to j=4 is:
∑ = 2(1)² + 2(2)² + 2(3)² + 2(4)²
= 2(1) + 2(4) + 2(9) + 2(16)
= 2 + 8 + 18 + 32
∑ = 60
∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] (2k)²
∑ = (2*1)² + (2*2)² + (2*3)² + (2*4)²
= (2)² + (4)² + (6)² + (8)²
= 4 + 16 + 36 + 64
∑ = 120
∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] (2k)²- 4
∑ = (2*1)²-4 + (2*2)²-4 + (2*3)²-4 + (2*4)²-4
= (2)²-4 + (4)²-4 + (6)²-4 + (8)²-4
= (4-4) + (16-4) + (36-4) + (64-4)
= 0 + 12 + 32 + 60
∑ = 104
∑[tex]\left \ {{4} \atop {k=1}} \right.[/tex] 2k²- 4
∑ = 2(1)²-4 + 2(2)²-4 + 2(3)²-4 + 2(4)²-4
= 2(1)-4 + 2(4)-4 + 2(9)-4 + 2(16)-4
= (2-4) + (8-4) + (18-4) + (32-4)
= -2 + 4 + 14 + 28
∑ = 44
3)
∑[tex]\left \ {{6} \atop {k=3}} \right.[/tex] (2k-10)
∑ = (2×3−10) + (2×4−10) + (2×5−10) + (2×6−10)
= (6-10) + (8-10) + (10-10) + (12-10)
= -4 + -2 + 0 + 2
∑ = -4
4)
1+1/2+1/4+1/8+1/16+1/32+1/64
This is a geometric sequence where first term is 1 and the common ratio is 1/2 So
a = 1
This can be derived as
1/2/1 = 1/2 * 1 = 1/2
1/4/1/2 = 1/4 * 2/1 = 1/2
1/8/1/4 = 1/8 * 4/1 = 1/2
1/16/1/8 = 1/16 * 8/1 = 1/2
1/32/1/16 = 1/32 * 16/1 = 1/2
1/64/1/32 = 1/64 * 32/1 = 1/2
Hence the common ratio is r = 1/2
So n-th term is:
[tex]ar^{n-1}[/tex] = [tex]1(\frac{1}{2})^{n-1}[/tex]
So the answer that represents the series in sigma notation is:
∑[tex]\left \ {{7} \atop {j=1}} \right.[/tex] [tex](\frac{1}{2})^{j-1}[/tex]
5)
−3+(−1)+1+3+5
This is an arithmetic sequence where the first term is -3 and the common difference is 2. So
a = 1
This can be derived as
-1 - (-3) = -1 + 3 = 2
1 - (-1) = 1 + 1 = 2
3 - 1 = 2
5 - 3 = 2
Hence the common difference d = 2
The nth term is:
a + (n - 1) d
= -3 + (n−1)2
= -3 + 2(n−1)
= -3 + 2n - 2
= 2n - 5
So the answer that represents the series in sigma notation is:
∑[tex]\left \ {{5} \atop {j=1}} \right.[/tex] (2j−5)
For (1) the sum is 30, for (2) the sum is 90, for (3) the sum is -4, for(4) the sigma notation is [tex]\rm \sum j = 1(\frac{1}{2})^{j-1}\\[/tex] where j = 1 to j = 7, and for (5) the sigma notation is [tex]\rm\sum j = (2j-5)[/tex] where j = 1 to j = 5.
We have different series in the question.
It is required to find the sum of all series.
What is a series?In mathematics, a series can be defined as a group of data that followed certain rules of arithmetic.
1) We have:
[tex]\rm \sum j=2j[/tex] where j = 1 to j = 5
After expanding the series, we get:
= 2(1)+2(2)+2(3)+2(4)+2(5)
=2(1+2+3+4+5)
= 2(15)
=30
2) We have:
[tex]\rm \sum k=(2k^2-4)[/tex] where k = 1 to k = 4
After expanding the series, we get:
[tex]\rm = (2(1)^2-4)+(2(2)^2-4)+(2(3)^2-4)+(2(4)^2-4)+(2(5)^2-4)\\[/tex]
[tex]\rm = 2[1^2+2^2+3^2+4^2+5^2]-4\times5\\\\\rm=2[55]-20\\\\\rm = 90[/tex]
3) We have:
[tex]\rm \sum k= (2k-10)[/tex] where k = 3 to k = 6
After expanding the series, we get:
[tex]= (2(3)-10)+(2(4)-10)+(2(5)-10)+(2(6)-10)\\\\=2[3+4+5+6] - 10\times4\\\\=2[18] - 40\\\\= -4[/tex]
4) The series given below:
[tex]1, \frac{1}{2} ,\frac{1}{4},\frac{1}{8},\frac{1}{16},\frac{1}{32},\frac{1}{64}[/tex]
It is a geometric progression:
[tex]\rm n^t^h[/tex] for the geometric progression is given by:
[tex]\rm a_n = ar^{n-1}[/tex]
[tex]\rm a_n = 1(\frac{1}{2})^{n-1}\\\\\rm a_n = (\frac{1}{2})^{n-1}\\[/tex]
In sigma notation we can write:
[tex]\rm \sum j = 1(\frac{1}{2})^{j-1}\\[/tex] where j = 1 to j = 7
5) The given series:
−3+(−1)+1+3+5, it is arithmetic series.
[tex]\rm n^t^h[/tex] for the arithmetic progression is given by:
[tex]\rm a_n = a+(n-1)d[/tex]
[tex]\rm a_n = -3+(n-1)(2)\\\\\rm a_n = 2n-5[/tex]
In sigma notation we can write:
[tex]\rm\sum j = (2j-5)[/tex] where j = 1 to j = 5
Thus, for (1) the sum is 30, for (2) the sum is 90, for (3) the sum is -4, for(4) the sigma notation is [tex]\rm \sum j = 1(\frac{1}{2})^{j-1}\\[/tex] where j = 1 to j = 7, and for (5) the sigma notation is [tex]\rm\sum j = (2j-5)[/tex] where j = 1 to j = 5.
Learn more about the series here:
https://brainly.com/question/10813422
helpppppppppppppppppppppppppppp give bralienst
Answer:
Brainliest! Hope I helped!
Step-by-step explanation:
you know its greater than 1cm and less than 2cm,
1 and 7hundreths cm is = 1.07 cm
thats not right because you know it is greater than that for sure!
so the only answer left is 1.7 cm
You answer is 1.7 cm
another way...
read the ruler and see the answer
Answer:
1.7 cm.
Step-by-step explanation:
The midpoint of 1 - 2 is 5 so count the lines after 5 and you get .7 to add to one cm.
Hope this helps, have a good day :)
Please help. I’ll mark you as brainliest if correct
Answer:
32 20 17 -57 13
-24 15 -31 31 -28
27 10 -7 18 22
Step-by-step explanation:
solve 27 to the power of (2/3)
Answer:
9Step-by-step explanation:
[tex]27^{\frac{2}{3}}\\\mathrm{Factor\:the\:number:\:}\:27=3^3\\=\left(3^3\right)^{\frac{2}{3}}\\\mathrm{Apply\:exponent\:rule}:\\\\\quad \left(a^b\right)^c=a^{bc},\:\quad \:a\ge 0\\\\\left(3^3\right)^{\frac{2}{3}}=3^{3}\times \frac{2}{3}}\\\\3\=times \frac{2}{3}=2\\\\=3^2 \\\\=9[/tex]
[tex]27^{2/3}=(3^3)^{2/3}=3^2=9[/tex]
Which is the simplified form of (StartFraction 2 a b Over a Superscript negative 5 Baseline b squared EndFraction) Superscript negative 3? Assume a not-equals 0, b not-equals 0. StartFraction b cubed Over 8 a Superscript 18 Baseline EndFraction StartFraction b squared Over 8 a Superscript 45 Baseline EndFraction StartFraction a Superscript 6 Baseline Over 4 b EndFraction StartFraction 2 a Superscript 6 Baseline Over b Superscript 5 Baseline EndFraction
Answer:
[tex]\dfrac{b^3}{8a^{18}}[/tex] matches the first choice
Step-by-step explanation:
[tex]\left(\dfrac{2 a b}{a^{-5}b^2}\right)^{-3}=(2a^{1-(-5)}b^{1-2})^{-3}=(2a^6b^{-1})^{-3}\\\\=2^{-3}a^{6(-3)}b^{-1(-3)}=8^{-1}a^{-18}b^3=\boxed{\dfrac{b^3}{8a^{18}}}[/tex]
__
The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
(a^b)^c = a^(bc)
a^-b = 1/a^b
Answer:
A
Step-by-step explanation:
just took the pretest! good luck!
If mL DOC = 44º and m2 COB = 80°,
find the measure of the indicated arc
in circle o.
С
o
B.
mDEB = ?
Answer:
236°
Step-by-step explanation:
The circumference of a circle is 360° since <DOC is given as 44° and <COB is given as 80° and the center angles are equal to the arc it sees the the measure of arc DEB would be 360 - 44 - 80 = 236°
Chris wanted to know how likely he is to win at his favorite carnival game. He conducted 50 tests and won 15 times. What is the probability that he will win next time he plays? All answers are rounded to the nearest hundredth. a.) 0.15 b.) 0.30 c.) 0.50 d.) 0.35 SUBMIT MY ANSWER g
Answer:
b.) 0.30
Step-by-step explanation:
15/50 = 0.3
Raul tried to evaluate an expression step by step.
Answer:
(B) Step 2
Step-by-step explanation:
In step 2, Raul should have had one of these results:
8 -7 . . . . according to the order of operations
or
3 -2 . . . . properly adding 5 -7
Raul's step 2 is not either of these (or 5-4), so is incorrect.
Answer:
step 2 i did it on khan yall
Step-by-step explanation:
in a class of 40 students, 30 students read chemistry, 40 students read physics, if all students read at least one of the subject, find the probability a students is selected at random will read only chemistry
Answer: 0%
Step-by-step explanation:
There's 40 students, and 40 students read physics. That means that every student reads physics. So, no student could read only chemistry.
What is f(0) given f(x) = 5(x + 2)2 – 10?
Answer:
10
Step-by-step explanation:
f(o) is given when x= 0 in f(x)
f(0) = 5 ( 0 + 2 ) 2 - 10
= 20 - 10
= 10
Answer:
[tex] \boxed{ \bold{ \huge{ \sf{f{(0) = 10}}}}}[/tex]
Step-by-step explanation:
Given, f ( x ) = 5 ( x + 2 )² - 10
Let's find f ( 0 ) :
[tex] \sf{f(0) = 5( {0 + 2)}^{2} - 10}[/tex]
Add the numbers
⇒[tex] \sf{f(0) = 5( {2)}^{2} - 10}[/tex]
Evaluate the power
⇒[tex] \sf{f(0) = 5 \times 4 - 10}[/tex]
Multiply the numbers
⇒[tex] \sf{ 20 - 10}[/tex]
Subtract 10 from 20
⇒[tex] \sf{10}[/tex]
Hope I helped !
Best regards !!
Find the area of the composite figure in terms of the figure (use 3.14 for pi)
Answer:
105.12 ft²
Step-by-step explanation:
Let's first find the area of the rectangle.
[tex]10\cdot8=80[/tex] ft², so the rectangle has an area of 80ft².
To find the area of the semi-circle, we find the area of a whole circle and divide by two.
The formula to find the area of a circle is [tex]\pi r^2[/tex]. The radius is 4, as the diameter is 8.
[tex]3.14\cdot4^2[/tex]
[tex]3.14\cdot16[/tex]
[tex]50.24\div2=25.12[/tex]
Add 80 and 25.12:
[tex]80+25.12=105.12[/tex]
Hope this helped!
Find the minimum and maximum values of 3 sin^2x – 2 cos^2x + 9
Mr Gomez wants to put a ceramic Tile border along for all four sides of his kitchen wall mr. Gomez has measured and knows he needs enough tiles to make three rows with 63 tiles in each row on each of his for how many tiles is mr. Goma's need to make the border tiles are sold in boxes with 14 tiles in each box how many boxes of tile does mr. Gomez need to buy show all your mathematical thinking please explain step by step
Answer:
14 boxes
Step-by-step explanation:
We are given that he needs 3 rows with 63 tiles per row.
Hence total number of tiles needed:
= 3 rows x 63 tiles per row
= 189 tiles
we are also given that tiles come in boxes of 14 tiles.
Hence the number of boxes of tiles needed,
= 189 tiles ÷ 14 tiles per box
= 13.5 boxes
but because he cannot just buy 0.5 of a box (i.e he needs to buy whole boxes), we must round this number up to the next whole box
hence
13.5 boxes rounded up to next whole box = 14 boxes.
Use the graph of f to estimate the local maximum and local minimum. Local maximum: (0,1); local minimum: three pi over two, negative 1 and negative pi, negative 1 Local maximum: (0,0) and approx (0,1); local minimum: negative three pi over two, negative 1 Local maximum: (0,0); local minimum: three pi over two, negative 1 Local maximum: (0,1); local minimum: approx. (0,0) and three pi over two, negative 1
Answer:
The answer is A.
Step-by-step explanation:
Local maximums are whenever the graph reaches it's highest y value.
Local minimums are whenever the graph reaches it's lowest y value.
From the graph, we can see that the maximum y-value the graph reaches is y=1. And this happens when x=0.
This only happens once (from the graph shown). Thus, the local maximum would be:
[tex](0,1)[/tex]
The minimum values we can see from the graph is at y=-1. This happens twice from the graph, once at -π and again at 3π/2.
Thus, the local minimums are:
[tex](-\pi,-1), (3\pi/2,-1)[/tex]
Which system of linear inequalities has the point (3, –2) in its solution set?
Answer:
see below
Step-by-step explanation:
We want where both inequalities are true
y > -3
-2 >-3 this is true
y ≥ 2/3x -4
-2≥ 2/3*3 -4
-2 ≥ 2 -4
-2≥ -2
This is true
This is is the graph
Answer:
[tex]\boxed{\sf Option \ 3}[/tex]
Step-by-step explanation:
[tex]\sf The \ values \ must \ be \ true \ for \ both \ inequalities.[/tex]
[tex]x = 3\\y = -2[/tex]
[tex]y>-3\\-2>-3\\ \sf True[/tex]
[tex]y\geq \frac{2}{3}x-4 \\ -2\geq \frac{2}{3}(3)-4\\2\geq 2-4\\-2\geq-2 \\ \sf True[/tex]
Describe all numbers x that are at a distance of 2 from the number 8. Express this using absolute value notation.
Answer:
The numbers that are at a distance of 2 from the number 8 can be expressed using absolute value notation as:
|x - 8| = 2
Step-by-step explanation:
The numbers that are at a distance of 2 from the number 8 are the numbers that are satisfied by the equation:
|x - 8| = 2
The equation is written in the notation of absolute value as required.
Please please help :((((
Answer:
y = x-4
Step-by-step explanation:
The y intercept is -4
We have 2 points so we can find the slope
( 0,-4) and(4,0)
m = ( y2-y1)/(x2-x1)
= ( 0- -4)/ (4-0)
= 4/4
=1
The slope intercept form is
y = mx+b
y = 1x-4
y = x-4
Sharvay spends $15 to buy 17 pieces of candy. M&M’s cost $0.75 and candy bars cost $1. How many M&M’s and candy bars did Sharvay buy?
Answer:
8 M&Ms and 9 Candy Bars
Step-by-step explanation:
$15 dollars could buy 15 candy bars, and there are 17 pieces of candy total.
Prioritizing the number of bars:
0.75 * 2 = 1.50
1.50 * 2 = 3
At least $3 were spend on M&Ms, meaning 4 M&Ms and 12 candy bars, which is only 16 candy pieces...
8 M&Ms and 9 candy bars is equivalent to 17 total candy pieces.
Heidi bought a machine that throws tennis balls for her dog to fetch. The height of each ball thrown by the machine, in feet, is modeled by the function f(x) = –x2 + x + 2, where x represents time in seconds. How many seconds after the machine throws the ball does it hit the ground?
Answer:
2 seconds
Step-by-step explanation:
Given the equation:
[tex]f(x) = -x^2 + x + 2[/tex]
Where f(x) represents the height of each ball thrown by machine.
and x represents the time in seconds.
To find:
The number of seconds after which the machine throws the balls hits the ground = ?
Solution:
In other words, we have to find the value of [tex]x[/tex] after which the [tex]f(x) = 0[/tex]
(Because when the ball hits the ground, the height becomes 0).
Let us put [tex]f(x) = 0[/tex] and solve for [tex]x[/tex]
[tex]f(x) = -x^2 + x + 2 =0\\\Rightarrow -x^2 + x + 2 =0\\\Rightarrow x^2 - x - 2 =0\\\Rightarrow x^2 - 2x+x - 2 =0\\\Rightarrow x(x - 2)+1(x - 2) =0\\\Rightarrow (x+1)(x - 2) =0\\\Rightarrow x =-1, 2[/tex]
[tex]x=-1[/tex] sec is not a valid answer because time can not be negative.
So, the answer is after 2 seconds, the ball hits the ground.
What is the slope of the line shown below?
A. -13/6
B. 6/13
C. 13/6
D. -6/13
-
Answer:
13/6
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= (6 - -7)/(1 - -5)
= ( 6+7)/ (1+ 5)
= 13/6
nolan completely fills a glass with water and then pours the water into a bowl. he does this until the bowl is completely filled with water. The full glass holds 1 1/3 cups of water the full bowl holds 4 2/3 cups of water How many full glasses of water does the bowl hold
Answer:
[tex]\bold{3\dfrac{1}{2 }}[/tex] full glasses of water the bowl holds.
Step-by-step explanation:
Full glass of water holds [tex]1\frac{1}{3}[/tex] cups of water.
Full bowl of water holds [tex]4\frac{2}{3}[/tex] cups of water.
To find:
How many full glasses of water does the bowl hold ?
Solution:
Let us convert the unit of cups of water to glass of water.
Given that
[tex]1\frac{1}{3}[/tex] or [tex]\frac{4}{3}[/tex] cups of water is equivalent to 1 full glass of water
Now, let us use unitary method to find the answer.
[tex]\frac{4}{3}[/tex] cups of water is equivalent to 1 full glass of water
1 cups of water is equivalent to [tex]\frac{3}{4}[/tex] full glass of water
[tex]4\frac{2}{3}[/tex] or [tex]\frac{14}{4}[/tex] cups of water is equivalent to [tex]\frac{3}{4}\times \frac{14}3 = \frac{14}{4}[/tex] full glass of water
[tex]\dfrac{14}{4} = \dfrac{7}{2} = \bold{3\dfrac{1}{2}}[/tex] full glass of water is the quantity the bowl holds.
which of the following is equal to 5^-3?
Answer:
5⁻³ = 1/5³ = 1/125
Answer: 1/125
Step-by-step explanation:
Ellen is making jewelry sets that contain a bracelet and a pair of earrings. Each bracelet uses 3 times as many beads as one earring. Each bracelet uses 3 as times as many beads as one earring . Ellen uses 13 beads for each earring. How many beads does Ellen need to make one jewelry set?
It's given that the Bracelet uses 3 times the number of beads that's used in making a single earring.
It's also given that one single earing has 13 beads. So a single bracelet would have (3×13) beads .... and that's equal to 39.
Making a single set of jewellery needs a pair of earrings and a Bracelet.
So total number of required beads will be =
39 + 13 + 13 = 65Given the trinomial, what is the value of the coefficient B in the factored form?
2x2 + 4xy − 48y2 = 2(x + By)(x − 4y)
Answer:
B = 6
Step-by-step explanation:
2x^2 + 4xy − 48y^2
Factor out 2
2(x^2 + 2xy − 24y^2)
What 2 numbers multiply to -24 and add to 2
-4 *6 = -24
-4+6 = 2
2 ( x+6y)( x-4y)
Answer:
[tex]\huge\boxed{B=6}[/tex]
Step-by-step explanation:
They are two way to solution.
METHOD 1:Factor the polynomial on the left side of the equation:
[tex]2x^2+4xy-48y^2=2(x^2+2xy-24y^2)=2(x^2+6xy-4xy-24y^2)\\\\=2\bigg(x(x+6y)-4y(x+6y)\bigg)=2(x+6y)(x-4y)[/tex]
Therefore:
[tex]2x^2+4xy-48y^2=2(x+By)(x-4y)\\\Downarrow\\2(x+6y)(x-4y)=2(x+By)(x-4y)\to\boxed{\bold{B=6}}[/tex]
METHOD 2:Multiply everything on the right side of the equation using the distributive property and FOIL:
[tex]2(x+By)(x-4y)=\bigg((2)(x)+(2)(By)\bigg)(x-4y)\\\\=(2x+2By)(x-4y)=(2x)(x)+(2x)(-4y)+(2By)(x)+(2By)(-4y)\\\\=2x^2-8xy+2Bxy-8By^2=2x^2+(2B-8)xy-8By^2[/tex]
Compare polynomials:
[tex]2x^2+4xy-48y^2=2x^2+(2B-8)xy-8By^2[/tex]
From here we have two equations:
[tex]2B-8=4\ \text{and}\ -8B=-48[/tex]
[tex]1)\\2B-8=4[/tex] add 8 to both sides
[tex]2B=12[/tex] divide both sides by 2
[tex]B=6[/tex]
[tex]2)\\-8B=-48[/tex] divide both sides by (-8)
[tex]B=6[/tex]
The results are the same. Therefore B = 6.
I NEED HELP ASAP PLEASE
Answer:
3 and 2
Step-by-step explanation:
I can't see your orginal equation. But it's probably 3 cos x . Which the amplitude is 3 then. Vertical translation would be how I move this graph up or down compared to the y axis. So if I were to add a +2 to the end of 3cos(x) I will move the graph up 2 spaces. So my final equation is 3cos (x)+2.
14. Find the distance between (7,217pi/180 ) and (5,-23pi/36 ) on the polar plane.
Answer: the distance is 3.49 units
Step-by-step explanation:
There are some ways to find the exact distance, i will calculate the distance in rectangular coordinates.
When we have a point (R, θ) in polar coordinates, we can transform it into rectangular coordinates as:
x = R*cos(θ)
y = R*sin(θ)
Then we have:
(7,217pi/180 )
R = 7
θ = (217/180)*pi
x = 7*cos( (217/180)*pi) = -5.59
y = 7*sin( (217/180)*pi) = -4.21
So this point is (-5.59, -4.21) in rectangular coordinates.
And the other point is (5,-23pi/36 )
R = 5
θ = -(23/36)*pi
x = 5*cos( -(23/36)*pi ) = -2.11
y = 5*sin( -(23/36)*pi ) = -4.53
So this point is (-2.11, - 4.53)
Then the point distance between those points is:
D = I (-2.11, -4.53) - (-5.59, -4.21) I
D = I (-2.11 + 5.59, -4.53 + 4.21) I
D = I (3.48, -0.32) I = √( (3.48)^2 + (-0.32)^2) = 3.49
A research worker gave a scholastic aptitude test to a sample of eighth graders. Then he correlated the aptitude test scores with the chronological ages of the subjects. He found a correlation of - .42. How should this result be interpreted?
Answer: There is an moderate relationship between the aptitude test scores with the chronological ages of the subjects.
Step-by-step explanation:
The correlation coefficient tells about the strength and direction of the relation ship between any 2 variables. When the value of correlation coefficient lies between -0.5 to -0.3 or 0.3 to 0.5, then it indicates that there is moderate association between variables.Here , variables → aptitude test scores and chronological ages of the subjects.
Since correlation coefficient (-0.42) lies between -0.5 and -0.3 .
[-0.5< -0.42< -0.3]
That means there is an moderate relationship between the aptitude test scores with the chronological ages of the subjects.
In Littletown, the probability that a baseball team goes to the city playoffs is 0.30. the probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.20.
THIS IS THE COMPLETE QUESTION BELOW;
In Littletown, the probability that a baseball team goes to the city playoffs is 0.30. the probability that the team goes to the state playoffs given that the team goes to the city playoffs is 0.20.
What is the probability that a randomly selected team from Littletown goes to the city and state playoffs?
A. 0.10
B.0.50
C. 0.66
D. 0.06
Answer:
OPTION D is correct
d)0.06
the probability that a randomly selected team from Littletown goes to the city and state playoffs is [tex]0.06[/tex]
Step-by-step explanation:
The probability that a baseball team goes to city playoffs is 0.30.
P(baseball team goes to city playoffs)=0.30
The probability that the team goes to state playoffs given that the team goes to the city playoffs is 0.20.
P(team goes to state playoffs given that the team goes to the city playoffs)=0.20
From our knowledge of set, we know that
P(A | B)= P(A ∩ C)/P(C)
where A= city playoffs
B= state playoffs
P(State play off | city play off)=0.20
P(State play off ∩ city play off)/P(city play off,)=0.20
P(State play off ∩ city play off)/0.30 =0.20
P(State play off ∩ city play off)= 0.30 × 0.20
= 0.06
Hence,the probability that a randomly selected team from Littletown goes to the city and state playoffs is 0.06
determine whether the series is absolutely convergent, conditionally convergent, or divergent sin(n)/3^n convergent
Answer:
absolutely convergent
Step-by-step explanation:
given data
sin(n)/3^n
solution
we have given term [tex]\frac{sin(n)}{3^n}[/tex]
when n = 1
and we know that
value of sin(n) ≤ 1
so that we can say that
[tex]\frac{sin(n)}{3^n}[/tex] ≤ [tex]\frac{1}{3^n}[/tex] or [tex](\frac{1}{3})^n[/tex]
here [tex]\frac{1}{3^n}[/tex] is converges this is because common ratio in geometric series
here r is [tex]\frac{1}{3}[/tex] and here it satisfy that -1 < r < 1
so it is converges
and
[tex]\frac{sin(n)}{3^n}[/tex] is also similar
so it is converges
and here no [tex](-1)^n[/tex] term is
so we can say series is absolutely convergent
A 160-lb man carries a 5-lb can of paint up a helical staircase that encircles a silo with radius 20 ft. If the silo is 90 ft high and the man makes exactly three complete revolutions, how much work is done by the man against gravity in climbing to the top
Weight of man and paint = 160 + 5 = 165 total pounds.
Gravitational force is independent of the path taken so we can ignore the radius of the silo.
Work done = total weight x height
The problem says he climbs to the top so overall height is 90 feet
Work = 165 lbs x 90 ft = 14,850 ft-lbs
Rewrite the expression as an equivalent ratio of logs using the indicated base.log17(52.875) to base 10.
Answer:
[tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]
Step-by-step explanation:
Given
[tex]log_{17}(52.875)[/tex]
Required
Convert to base 10
To do this, we make use of the following logarithm laws;
[tex]log_ba = \frac{log_{10}a}{log_{10}b}[/tex]
In the given parameters;
[tex]a = 52.875[/tex]
[tex]b = 17[/tex]
Substitute these values in [tex]log_ba = \frac{log_{10}a}{log_{10}b}[/tex]
[tex]log_{17}52.875 = \frac{log_{10}52.875}{log_{10}17}[/tex]
Represent as a ratio
[tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]
Hence;
[tex]log_{17}(52.875)[/tex] is represented as [tex]log_{17}52.875 = log_{10}52.875 : log_{10}17}[/tex]
Expression [tex]log_{17} 52.875[/tex] can be written as in form of ratio of log [tex]\frac{log_{10} 52.875}{log_{10} 17}[/tex] .
Any logarithmic expression [tex]log_{a} b[/tex] can we written as in form of ratio of log on base 10.
[tex]log_{a} b=\frac{log_{10} b}{log_{10} a}[/tex]
Here logarithmic expression is, [tex]log_{17} 52.875[/tex] comparing with above expression.
We get, [tex]b=52.875,a=17[/tex]
Substitute values of a and b in above expression.
We get, [tex]log_{17} 52.875=\frac{log_{10} 52.875}{log_{10} 17}[/tex]
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