Answer:
The nth bounce a sub n is 0.25 (a sub n-1)
0.625 cm
Recursive formula of the sequence → [tex]T_n=10240(\frac{1}{4})^{n-1}[/tex]
Explicit formula of the sequence → [tex]T_1=10240, \\T_{n+1}=T_n(0.25)[/tex]
Height of the ball after 8th bounce will be 0.625 cm.
Geometric sequence and its explicit and recursive formula,If a sequence is in the form of [tex]ar,ar,ar^2,ar^3.....[/tex] n terms,Sequence will be the geometric sequence and the explicit formula
of the sequence will be,
[tex]T_n=ar^{n-1}[/tex]
Here, [tex]a=[/tex] First term
[tex]r=[/tex] Common ratio
[tex]n=[/tex] Number of terms
Similarly, recursive formula will be,[tex]a=[/tex] First term
[tex]T_{n+1}=T_n(r)[/tex]
From the table attached,
There is common ratio between the successive term and previous term under the column (height after the bounce) is,
[tex]\frac{T_2}{T_1}=\frac{2560}{10240}=\frac{1}{4}[/tex]
[tex]\frac{T_3}{T_2}=\frac{640}{2560}=\frac{1}{4}[/tex]
Therefore, height of the ball after each bounce will represent a geometric sequence.
Explicit formula of a geometric sequence will be given by the expression,
[tex]T_n=10240(\frac{1}{4})^{n-1}[/tex]
Recursive formula for the sequence will be,
[tex]T_1=10240[/tex]
[tex]T_{n+1}=T_n(\frac{1}{4})[/tex]
By using recursive formula,
Height of the ball after 8th bounce,
[tex]T_8=10240(\frac{1}{4})^{8-1}[/tex]
[tex]=10240(0.25)7[/tex]
[tex]=0.625[/tex] cm
Therefore, explicit formula to represent the height of the ball will be [tex]T_n=10240(\frac{1}{4})^{n-1}[/tex]recursive formula will be, [tex]T_1=10240\\T_{n+1}=T_n(0.25)[/tex]
And height of the ball after 8th bounce will be 0.625 cm.
Learn more about the geometric sequence here,
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A gray crayon is made with 5mL of black wax for every 6 mL of white wax
Worth 17 points! Help me please!!! Look in the picture
Instructions: give me each answer with the question please
Math is due tomorrow NO links are allowed or DONT answer if your not going to help
Answer:
Part A
1. After 4 weeks of work, Jeremy has saved 300
2. Jeremy worked 8 weeks in order to save $600
3. For every one week of work, Jeremy saved 75 dollars
4. If Jeremy works 15 weeks, then he can expect to save 1,125 dollars
Part B
1. Saeed orders 15 meals and his total cost of delivery is $24
2. Saeed paid $32 to have 20 meals delivered
3. For every meal delivered, Saeed is charged $1.6
4. If Saeed pays $19.20 in delivery fees then he ordered 12 meals
Step-by-step explanation:
Part A
The given graph gives the proportional relationship between total amount saved and the number of weeks worked
1. Reading from the graph, at the point where the vertical line from point 4 touches the line of the graph, an horizontal line to the vertical y-axis touches the y-axis at 300
Therefore;
After 4 weeks of work, Jeremy has saved 300
2. The point where an horizontal line from point 600 on the vertical y-axis touches the line of the graph, a vertical line drawn to the horizontal, x-axis touches the x-axis at 8
Therefore;
Jeremy worked 8 weeks in order to save $600.
3. The rate of change of the amount saved to the number of weeks worked, 'm', for the given proportional relationship (straight line relationship, passing through the origin) is given as follows;
Rate of change, m = Constant = y/x
∴ Rate of change of the amount saved to the number of weeks worked = (300-0)/(4 weeks- 0 week) = 75/week
Therefore;
For every one week of work, Jeremy saved 75 dollars
4. The amount Jeremy would have saved in 15 weeks, 'A', is given as follows;
A = m × n
Where;
m = The rate of change of the amount saved to the number of weeks worked = 75/week
n = The number of weeks worked
∴ A = 75/week × 15 = $1,125
Therefore;
If Jeremy works 15 weeks, then he can expect to save 1,125 dollars
Part B
From the graph, we have;
1. From the graph there is a proportional relationship between the total cost of delivery and the number of meals
At the point a vertical line drawn to the line of the graph from 15 on the horizontal axis (number of meals), a horizontal line drawn to the vertical y-axis touches the y-axis at 24
Therefore;
1. Saeed orders 15 meals and his total cost of delivery is $24
2. From the point where the horizontal line from 32 on the vertical axis touches the linear graph of the relationship between the total cost of delivery and the number of meals, a vertical line drawn down to the horizonal axis touches the horizontal x-axis at 20
Therefore;
Saeed paid $32 to have 20 meals delivered
3. The rate of change of the total cost of delivery to the number of meals, 'm', is given as follows;
m = y/x (for proportional relationships)
Taking any corresponding 'x' and y-values
m = 16/10 = 32/20 = 24/15 = 1.6 Dollars/meal
Therefore;
For every meal delivered, Saeed is charged $1.6
4. From m = y/x = 1.6
When y = $19.20
x = y/m = $19.20/($1.6/meal) = 12 meals
Therefore;
If Saeed pays $19.20 in delivery fees then he ordered 12 meals.
When do you first start to see a moderate amount
of overlap in these two graphs?
when the difference in
means is around 40
when the difference in
means is around 20
when the difference in
means is around 5
Answer:
When the difference in the mean is about 20
Step-by-step explanation:
I did the test
Answer: around 20
Step-by-step explanation:
what is 10 x 40 to the 12 power divided by 3 x 4
Answer:
33.33333333
Step-by-step explanation:
The volume of a cylinder is 80 cubic centimeters. If the diameter and
height of the cylinder are multiplied by 4/5, what is the volume of the new
cylinder?
Answer:2 yds and h
Step-by-step explanation:
The volume of the new cylinder will be equal to 40.96 cubic centimeters.
What is the volume of a cylinder?The amount of space inside a cylinder is its volume. You can find it by dividing the base area by the height.
The formula to calculate the volume of the cylinder is given below:-
V = πr²h
Given that volume of a cylinder is 80 cubic centimeters. The diameter and height of the cylinder is multiplied by 4/5. The new volume will be:-
Vi= πr²h = 80 cubic centimeters.
The new volume will be calculated as:-
Vn= π (4/5r)²(4/5)h
Vn = (64 / 125 ) πr²h
Vn = (64 / 125 ) x Vi
Vn = (64 / 125 ) x 80
Vn = 40.96 cubic centimeters.
Therefore, the volume of the new cylinder will be equal to 40.96 cubic centimeters.
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Hey! Can someone help me with this! Please thank u!
Step-by-step explanation:
1. vertical opposite angles
2. corresponding angles
3. alternate interior angles
4. alternate exterior angles
5. corresponding angles
6. vertical opposite angles
7. alternate exterior angles
8. vertical opposite angles
9. corresponding angles
10. alternate exterior angles
Which linear equation represents the table shown below?
~ y=6x+2
~ y=x+4
~ y=4x+2
~y=4x-2
I need help I don’t understand
Answer:
x = 9
Step-by-step explanation:
By the property of intersecting secants:
[tex]4(x - 3 + 4) = 5(x - 6 + 5) \\ \\ 4(x + 1) = 5(x - 1) \\ \\ 4x + 4 = 5x - 5 \\ \\ 4x - 5x = - 5 - 4 \\ \\ - x = - 9 \\ \\ x = 9[/tex]
hi i need help with this question asap ty ty ty!!!
Work out the size of angle A.
A
11 cm
9 cm
38°
B
С
A bacteria culture is grown with a population of 15 million cells and kept under observation. The bell population is found to double every hour. How can we use geometric sequences and series to find the total population after six hours? Show all work.
Answer:
Population after 6 hours is 2.44 *10^12
Step-by-step explanation:
The geometric population growth formula is
[tex]P = P_0 * e^{kt}[/tex]
Substituting the given values in above equation we get
[tex]P = 15 *10^6 * e^{2 * 6}\\P = 15 *10^6 * 162754.791\\P = 2.44 *10^{12}[/tex]
Population after 6 hours is 2.44 *10^12
Tom has a cube, a rectangular prism,and a traiangular prism. Which of his shapes has MORE than 6 verticles
a diameter of 120 feet. To the nearest foot, what is the minimum length of fencing he needs to buy? If the fence costs $2.10 per foot, what will be the total cost?
Step-by-step explanation:
they have 122.1 of total of cost
Answer:
It is assumed the full circular fencing is needed.
Circumference of the circle = the length of fencing:
C = πd = 3.14*120 feet = 376.8 feet ≈ 377 feetTotal cost:
377*$2.10 = $791.70What is the distance between the following points
Answer:
5
Step-by-step explanation:
Use pythagorean theorem. The rise is 3 units and the run is 4 unites. Now the length of the line we are trying to find is a hypothenuse(the side opposite of the right angle
Complete the ratio table.
15
14
42
60
56
75
70
90
In ΔIJK, j = 540 inches, ∠I=54° and ∠J=69°. Find the area of ΔIJK, to the nearest square inch.
Answer:
105963
Step-by-step explanation: delta math
Please help due soon!!
Answer: [(3/4)π] in² or (0.75π) in²
Step-by-step explanation:
Here, we are asked to find the area of a sector. So we are going to use the formula: A=πr²(θ/360)
--------------------------------------------------------------
Given
r=3 in
θ=30°
Solve
A=πr²(θ/360)
A=π(3)²(30/360)
A=9π(1/12)
A=[(3/4)π] in²
A=(0.75π) in²
Hope this helps!! :)
Please let me know if you have any questions
Find the cube root of -8.
Answer:
The cube root of -8 is -2
Step-by-step explanation:
Factor the numbers 8=2^3
-∛2³
Apply radical rule;
∛2³=2
=-2
HOPE THIS HELPED!!!
sundae that contains over 2 kilograms of ice cream plus any number
Ping's Ice Cream Palace offers a special
of toppings.
Write an inequality that describes S, the weight of the special sundae in kilograms.
Answer:
S≥2+x
Step-by-step explanation:
I got stuck on a question on edge can anyone help?
Answer:
A and D
Step-by-step explanation:
find An Equation Of The Line Containg(3,-4) and Having slope -2.If This Line Contain The Points (a,8) and (5,b) find a and b
Answer:
equation: y=-2x+2
a=-3
b=-8
Step-by-step explanation:
we need to find the equation of the line containing the point (3,-4) and has the slope (m) of -2
slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
we can plug what we know into the equation:
y=-2x+b
we need to find b though
since the point will pass through the point (3,-4) we can subsitute it into the equation to find b
-4=-2(3)+b
-4=-6+b
2=b
the y intercept is 2
so the equation is y=-2x+2
the line also contains the points (a,8) and (5,b)
first, let's find a
a is the x value of the point
we know the value of y (8)
substitute y as 8 and solve for x
8=-2x+2
subtract
6=-2x
-3=x=a
so a is -3
now find b
b is the y value of the point
we know the x value (5)
substitute x as 5 and solve for y
y=-2(5)+2
y=-10+2
y=-8=b
so b is -8
hope this helps!
A.45
B.30
C.90
D.180
E.40
F.55
G.130
H.50
Max and Jay Are running a lemonade stand they spent $12 on all the material and charge $1.50 for each cup of lemonade write an equation that will allow you to calculate the profit (P) if you are told the number of cups (c) that are sold.
Answer:
P = $1.50c - $12
Step-by-step explanation:
profit = total revenue - total cost
total revenue = price per cup x total cup sold = $1.5 x c = 1.5c
Cost = $12
"sports discount" has uniforms for 68$. They are offering a 20% discount on each uniform, and a 7 percent sales tax will be applied to the discount price. What would be the final cost for eight uniforms after the discount and sales tax
Answer:
58.208 times 8 equals 465.664 rounded down to 465.66
Step-by-step explanation:
Answer:
$465.66
Step-by-step explanation:
First, we are buying 8 uniforms. Therefore, the total price on a normal day would be 8x68 = $544
However, on this day, there is a 20% discount. In other words, we are only paying 80% of the original price as percentages are always out of 100.
The price after the sports discount will be 544x0.8 = $435.2
On top of this, we have to pay a sales tax of 7 percent. The 7 percent is an additional cost to the discounted price of 435.2, hence we add 0.07 (7 percent in decimals) onto 1 (100% in decimals).
This gives us 435.2 x ( 1 + 0.07 ) = 465.664.
Because currency is to 2 decimal points (1 cent), the final answer will be 465.66, or 465 dollars and 66 cents.
Pls help me with dis question
Answer:
3 1/15
Step-by-step explanation:
Product means multiply
. 3m = 16.8. what does m equal to?
Answer:
m = 56
Step-by-step explanation:
.3m = 16.8
3m = 168
m = 168/3
m = 56
Find the measure of the angle to nearest degree.
Answer:
I think the answer is meant to be 32°
Step-by-step explanation:
I took 0.55 which is the angle in radians, multiplied it by the value of 180, and then divided by π
Select ALL of the real-life situations could be represented by finding surface area.
How much paint is needed to cover a box.
How much water is needed to fill a fish tank.
How many pairs of socks fits in a suitcase.
How much rice fits in a jar
How much cardboard is needed to make a box.
Answer:
How many pairs of socks fits in a suitcase.
How much rice fits in a jar
How much cardboard is needed to make a box.
Step-by-step explanation:
Two of the angles in a triangle measure 81° and 86°. What is the measure of the third angle?
Answer:
13°
Step-by-step explanation:
The reason is because the sum of all the angles in a triangle add up to 180°, so to find the last angle you add 81°+86°=167°
Subtract: 180°-167°=13°
Hope this helped!
Stay safe and have a wonderful day/night!
Your friend Bella was here :)
SOMEONE PLEASE HELP MEEE!!!
Answer: 1080
Step-by-step explanation:
Heres why:
SA is L*W*H as the same formula as volume.