Answer:
3*∑ (1/2)^n = 6
Step-by-step explanation:
We have the summation from n = 1 to n = ∞, for:
∑ 3/(2)^(n - 1)
We know that the summation between k = 0, and k = N - 1 for:
∑ r^k = (1 - r^N)/(1 - r)
if we have the summation between k = 0 and k = ∞ - 1 = ∞
(here we used that ∞ is really big, then ∞ - 1 = ∞)
In the numerator we will have the term r^∞, if 0 < r < 1, then r^∞ = 0.
Then if we assume that 0 < r < 1 we can write:
∑ r^k = 1/(1 - r)
In our case, we can rewrite our summation as:
3*∑ (1/2)^n
for n = 0 to n = ∞
You can see that i changed the limits for n, this does not really matter because we are summing between a number and infinity, the only thing you need to take care is that now the power is n, instead of (n - 1)
Then we have r = (1/2) which is clearly smaller than 1.
then (1/2)
Then this summation is equal to:
3*∑ (1/2)^n = 3*( 1/(1 - 1/2)) = 3*( 1/( 2/2 - 1/2)) = 3*( 1/(1/2)) = 3*2 = 6
3*∑ (1/2)^n = 6
Please Help WILL MARK BRAINLIEST
18 Points
Maryann is tracking the change in her vertical jump over 6 months. Use the table to write a linear function that models her jump distance.
Month Vertical Jump in inches
0 16
2 17
4 18
6 19
f of x equals one half times x plus 16
f of x equals one half times x plus 19
f(x) = 2x + 16
f(x) = 2x + 19
Answer:
Part 1) Option A. f of x equals one half times x plus 16
Part 2) Option A. x = 5
Part 3) Option C. x − 4y = −9
Part 4) Option A. The number of rides is the independent variable, and the total cost is the dependent variable.
Step-by-step explanation:
Part 1)
Let
x -----> the number of months
y ----> vertical jump in inches
step 1
Find the slope
we have the points
(0,16) and (2,17)
The equation of the line in slope intercept form is
we have
-----> the point (0,16) is the y-intercept
substitute
convert to function notation
f(x)=y
Part 2) What is the equation of a line that contains the points (5, 0) and (5, −2)?
step 1
Find the slope
we have the points
(5, 0) and (5, −2)
the slope is undefined
This is a vertical line (parallel to the y-axis)
therefore
The equation is
x=5
Part 3) Choose the equation that represents a line that passes through points (−1, 2) and (3, 1)
step 1
Find the slope
we have the points
(−1, 2) and (3, 1)
step 2
Find the equation of the line into point slope form
we have
substitute
Convert to standard form
Multiply by 4 both sides to remove the fraction
Part 4) Jewels has $6.75 to ride the ferry around Connecticut. It will cost her $0.45 every time she rides. Identify the dependent variable and independent variable in this scenario
we know that
The independent variable is the variable whose change isn’t affected by any other variable (An example the age and time)
The dependent variable it’s what changes as a result of the changes to the independent variable (An example of a dependent variable is how tall you are at different ages. The dependent variable (height) depends on the independent variable (age))
Let
x ----> the number of rides
y ----> the total cost in dollars
In this problem
The independent variable or input is the number of rides
The dependent variable or output is the total cost
-brainly user
Answer:
Your function would be y = 1/2x + 16.
Explanation:
Points: (0, 16); (2, 17)
Slope: m = (17 - 16) / (2 - 0) = 1/2
Slope intercept form: y = mx + b
So, if the slope equals 1/2 and the y-intercept is (0, 16), you would use substitution to get y = 1/2x + 16.
Therefore, your ending function is y = 1/2x + 16.
3/4+4/5-7/10 i dont know it
Answer:
17/20
Step-by-step explanation:
[tex]\frac{3}{4}[/tex] + [tex]\frac{4}{5}[/tex] - [tex]\frac{7}{10}[/tex]
common denominator is 20
15/20 + 16/20 - 14/20
17/20
could someone pls help me with this math problem?
help me pls theheheh
Answer:
108 schools
Step-by-step explanation:
Write and Solve an equation to find the value of x and a missing angle in the triangle below.
could someone maybe help me with this ?
Answer:
The scale factor is 3
Step-by-step explanation:
The answer is 3
What is the value of 6(2b-4) when b=5?
Answer:
36
Step-by-step explanation:
Substitute b=5 to the expression:
=6(2(5)−4)
Evaluate inside the parentheses. Multiply 2 and 5 first:
=6(10−4)
Then subtract:
=6(6)
Finally, multiply:
=36
Answer: The value of 6(2b-4) when b=5 is 36.
Step-by-step explanation: Given expression: 6(2b-4). To find the value of 6(2b-4) at b= 5, we need to substitute the b=5 in the expression, we get….Therefore, the value of 6(2b-4) is 36, when b=5.
Please help me on maths
Answer:
x = 25
Step-by-step explanation:
x + 25 + 2x - 10 + 90 = 180
3x + 105 = 180
3x = 75
x = 25
Please help I don’t understand what to do
x⁰ = 360 degree- ( 246⁰ + 66⁰)
= 360 degree- 312⁰
= 48 ⁰
Answer:
x = 114
Step-by-step explanation:
Remark
You are trying to figure out what the arc is in degrees. The arc formula is
Intersect angle = 1/2( the furthest arc - the smaller closer arc).
Givens
Intersect angle = 66 degrees
Closer arc = x
Further or largest Arc = 246
Solution
66 = 1/2 (246 - x) Multiply both sides by 2 and remove the brackets.
132 = 246 - x Subtract 246 from both sides.
132 - 246 = - x
- 114 = - x Multiply both sides by -1
-1 (-114) = -1 * (-x)
x = 114
Raymond is building a new dog run with a raised border in his backyard. The boards on the two shorter sides are 6 feet thick, and the boards on the two longer sides are 4 feet thick. Raymond wants the outer length of the dog run to be 4 times its height and the outer width to be 2 times its height. He also wants the boards to rise 4 feet above the level of the grass in the dog run. Use x as the variable throughout the entire problem. Write a simplified expression in standard form that represents the volume of the grass in the dog run.
Answer:
The answer is 30.
Step-by-step explanation:
Someone please help with this
Answer:
A
Step-by-step explanation:
I said so
Answer:
C. They are similar triangles.
Step-by-step explanation:
they have the same angle measures, but not the same side lengths. so they are similar but not congruent.
hi can someone answer this
Answer:
B
Step-by-step explanation:
When two angles are on the interior like that, they are adding up to 180 degrees in total.
So, x would be 20 because
2x+60=
2 times 20, plus 60 = 100
and 3x+20=
And 3 times 20, plus 20 = 80
Adding up 100 and 80, you get 180 degrees.
I hope this helps. I'm a student too but I hope I explained it relatively ok.
need help with simple question
Answer:
I think it is 10
Step-by-step explanation:
I said I think it might be 9
Use the table to identify the value of p and q that should be used to factor x^2-3x-10 as (x+p)(x+q) I’ve seen the answer with positive 3x but not a answer for negative
Answer:
1
Step-by-step explanation:
1 is the right answer for this question
Draymond has $10.00 for lunch. He and his friend order pizza for $6,90 and two drinks for $1.50 each. Does he have enough money? Explain how you know below for full credit.
Answer:
yes. the total when added together is $9.90, meaning that he has just enough for them to get a pizza and one drink each.
Step-by-step explanation:
6.90
1.50
1.50
9.90
Answer:
Yes, he has enough money.
Step-by-step explanation:
He will have .10 left over. The pizza is $6.90 and the drinks are $1.50 each.
1.50 + 1.50 = 3.00
6.90 + 3.00 = 9.90
He spends $9.90, so he will be 10 cents short of spending all of his lunch money. Therefore, he has enough money.
Find the unit rate
34 carbs for every 1/3 serving
Answer:
102.010201 carb per serving
Step-by-step explanation:
What is the slope of a line that passes through the points (-3,-6) and (8, 16) ?
Answer:
slope = 2
Step-by-step explanation:
Chandra had 9 jugs of juice at her party.Eacu jig had 1 gallon of juice in it at the start of the party.
Answer:
could you explain more clearly for me? if Chandra had 9 jugs, each was one gallon, what's the take away? I need to know for example: each member had 2 cups of juice which would sum up to (insert number) how much juice was left?
Help 10 pts!!!
A cedar chest is a shaped like a rectangular prism. The cedar chest is 2 feet tall, 4 feet wide, and 2 feet deep.
What is the surface area of the cedar chest?
Answer:
40 ft^2
Step-by-step explanation:
lateral surface area -Slat = 24 ft^2
top surface area-Stop = 8 ft^2
bottom surface area -Sbot = 8 ft^2
24+8+8= 40
total surface area -Stot = 40 ft^2
Answer:
40
Step-by-step explanation:
took the test
PLEASE HURRY THANK YOU!!!!
Answer:
-125
Step-by-step explanation:
[-5]^3 = -125
In exercises 8-10, write a system of linear equations that has the ordered pair as its solution. (-6, -2)
Answer:
(8) [tex]x + y = -8[/tex] and [tex]2x - y = -10[/tex]
(9) [tex]3x - y = -54[/tex] and [tex]4x + y = -30[/tex]
(10) [tex]x + y = 2[/tex] and [tex]x - y = 2[/tex]
Step-by-step explanation:
Given [Missing from the question]
[tex](8).\ (-6,-2)\ \\ (9).\ (-12,18)\ \\ (10).\ (2,0)[/tex]
Required
Write a system of linear equations
The solutions to this question is open and have different solutions
Solving (8) (-6,-2)
Let the equations be: x + y and 2x - y
[tex]x + y = -6 - 2[/tex]
[tex]x + y = -8[/tex] --- (1)
[tex]2x - y = 2 * (-6) - (-2)[/tex]
[tex]2x - y = -10[/tex] -- (2)
So, the equations are:
[tex]x + y = -8[/tex] and [tex]2x - y = -10[/tex]
Solving (9) (-12, 18)
Let the equations be: 3x - y and 4x + y
[tex]3x - y = 3 *(-12) - 18[/tex]
[tex]3x - y = -54[/tex]
[tex]4x + y = 4 * (-12) + 18[/tex]
[tex]4x + y = -30[/tex]
So, the equations are:
[tex]3x - y = -54[/tex] and [tex]4x + y = -30[/tex]
Solving (9): (2,0)
Let the equations be: x + y and x - y
[tex]x + y = 2 + 0[/tex]
[tex]x + y = 2[/tex]
[tex]x - y = 2 - 0[/tex]
[tex]x - y = 2[/tex]
So, the equations are:
[tex]x + y = 2[/tex] and [tex]x - y = 2[/tex]
Find the 11th term in the geometric sequence: 4, 6, 9,....
Answer:
69
Step-by-step explanation:
let the first term be n
second term = 2 + n
third term = 3 + second term so we can conclude that the other term will be:
forth term = 4 + third term
fifth term = 5 + forth term etc.
eleventh term will be 11 + 10 term
based on observations the tenth term is 58 so
eleventh term= 11 + 58
= 69
i need help with my math please
2(3×+4)=4×+12 i need help with this problem
Answer:
x = 2
Step-by-step explanation:
2(3x + 4) = 4x + 12
6x + 8 = 4x + 12
2x + 8 = 12
2x = 4
x = 2
The histogram gives information about the waiting time
Answer:
what historian
what was the information
Miguel compró 253 Kilos de pescado para venderlo en su negocio, si decide vender cada kilo de pescado en Bs 1.900.000. Entonces, ¿Cuánto dinero recaudó en total por la venta del pescado?
Answer:
Miguel recaudó Bs 480.700.000 por la venta del pescado.
Step-by-step explanation:
Con la información proporcionada puedes calcular el dinero que recaudó en total por la venta del pescado multiplicando el precio de venta de cada kilo de pescado por el número de kilos que Miguel compró:
Número de kilos comprados=253
Precio de venta por kilo=1.900.000
Total vendido=253*1.900.000
Total vendido=480.700.000
De acuerdo a esto, la respuesta es que Miguel recaudó Bs 480.700.000 por la venta del pescado.
A prism is filled with 70 cubes with a side length of 1 2 unit. What is the volume of the prism in cubic units? Enter answer as a mixed number in its simplest form.
Answer:
The volume of the cube is;
[tex]8\dfrac{3}{4} \ cube \, units[/tex]
Step-by-step explanation:
The parameters of the prism are;
The number of cubes used to fill the prism, n = 70 cubes
The side length of each cube, s = 1/2 unit
The volume of the cube, V = n × s³
∴ Therefore, the volume of the cube, V = 70 × (1/2)³ = [tex]8\dfrac{3}{4} \ cube \, units[/tex] = 8.75 cube unit
i need help with my last two questions:)
Answer:
5. (a)
6. (b)
I am hoping that this will help you
let fill this out it is timed so pls do it quickly
Answer:
They have no relation, except for the fact that they intersect. If the equations were instead y = +5/4x - 1/2 and y = -4/5x + 2, or y = +4/5 + 2 and y = -5/4x -1/2, then they would be perpendicular.
Option 3 is the right answer.
Step-by-step explanation:
For the given lines y = -4/5x+2 and y = -5/4x - 1/2
we have to identify whether lines are parallel or perpendicular.
As we know if two lines are perpendicular then gradients of two lines will in the form of
m1 m2=(-1)
and if the lines are parallel then the gradients of the lines will be same.
m1=m2
Here m1 = -4/5 and m2 = -5/4
Therefore
m1m2=(-4/5)(-5/4)=(+1)
and
m1≠m2
So both the lines are neither parallel nor perpendicular to each other.
Option 3 is the right answer.
HELPPPPPPP What is the volume? Use the pi button on your calculator. Round to nearest hundredth. (Don't include units, just the #.) *
Answer:
The volume is 2703.730036 (I didn't round it)
Step-by-step explanation: