Answer: a = 2.5 (an-1)
Step-by-step explanation: trust me;)
The function which is used to represent the geometric progression 8, 20, 50, 125, 312.5, ... is [tex]a_{n} = 8(2.5)^{n-1}[/tex].
What is geometric progression?sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is as a geometric sequence of numbers.
Formula for nth term of geometric progression[tex]a_{n} =ar^{n-1}[/tex]
Where,
[tex]a_{n}[/tex] is the nth term of the sequence or geometric progression
n is the total number of terms
r is the common ratio
and a is the first term
According to the given question
We have
A geometric progression
8, 20, 50, 125, 312.5
Now the common ratio for the above progression is given by
[tex]r = \frac{20}{8} = 2.5[/tex]
And the first term is
a = 8
Therefore, the function which is used to represent the above sequence is given by
[tex]a_{n} = 8(2.5)^{n-1}[/tex]
Hence, the function which is used to represent the geometric progression 8, 20, 50, 125, 312.5, ... is [tex]a_{n} = 8(2.5)^{n-1}[/tex].
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John earned $12 a day for babysitting his siblings after school each weekday (he did not babysit on weekends). He liked to have a small amount of money to spend on treats at the school canteen that his parents refuse to buy, but he also wanted to build up some savings. John decided to put a fraction of his earnings into a jar straight away. He spent all the rest on canteen treats.
How much money did John earn over a nine week term?
After 9 weeks, John had $378 in his jar. What percentage of his money did he save?
Answer:
He earns $540
70% of his money went to savings
Step-by-step explanation:
9 weeks x 5 days a week = 45 days
45 days x $12 a day = $540
378 * 100 / 540 = (378*100) / 540 = 37800/540 = %70
How would you find the intercept for the equation y^2=2-3x-2x^2? I need the steps to understand
9514 1404 393
Answer:
x-intercepts: -2, +1/2y-intercepts: ±√2Step-by-step explanation:
You always find the intercepts by setting the known coordinate to its known value and solving for the value of the unknown coordinate.
An x-intercept is always found on the line y=0. Setting y=0 and solving for x, we find ...
0 = 2 -3x -2x^2
x^2 +3/2x -1 = 0 . . . . . . . . . . . . . . . . divide by -2
(x2^2 +3/2x +(3/4)^2) -1 -(3/4)^2 = 0 . . . . . complete the square
(x +3/4)^2 = 25/16 . . . . . add 25/16 and write as a square
x +3/4 = ±5/4 . . . . . . . take the square root
x = -3/4 ±5/4 = -8/4, +2/4
The x-intercepts are -2 and +1/2.
__
A y-intercept is always found on the line x=0. Setting x=0 and solving for y, we find ...
y^2 = 2 -0 -0
y = ±√2
The y-intercepts are -√2 and +√2.
_____
A graphing calculator can give you a good idea of what the intercepts are.
Calculate the arithmetic mean of the numbers.
-16, -9, and 4
Answer:
-7
Step-by-step explanation:
The arithmetic mean of the numbers - 16, - 9 and 4 is,
⇒ - 7
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
Numbers are,
⇒ - 16, - 9 and 4
Now, We can formulate;
The arithmetic mean of the numbers - 16, - 9 and 4 is,
⇒ (- 16 + (- 9) + 4 ) / 3
⇒ (- 16 - 9 + 4) / 3
⇒ - 21 / 3
⇒ - 7
Thus, The arithmetic mean of the numbers - 16, - 9 and 4 is,
⇒ - 7
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If C = C(q) is a firm's total cost function, the quantity epsilon_{c} = q/C * (dC)/(dq) is called the elasticity of cost at the output q . Discuss the relationship between marginal cost and average cost for the intervals of being higher and lower than 1 (15 points). epsilon_{c}
Answer:
the answer is 5,746 = c
Step-by-step explanation:
What are the coordinates of point P?
O (-4, 3)
O (-3, 4)
0 (3,-4)
O (4, -3)
Answer:
(-4, 3)
Step-by-step explanation:
You have to go -4 on the x-axis, and +3 on the y-axis
Help please ASAP !
uppose a normal distribution has a mean of 16 and a standard deviation of 4. A value of 26 is how many standard deviations away from the mean
Answer:
2.5 s. d.
Step-by-step explanation:
Use the formula for calculating z scores:
26 - 16
z = ------------- = 10/4 = 2.5
4
Here the value 26 is 2.5 standard deviations above the mean (16).
10000+2000003
ghsrhrs
- BRAINLIEST answerer
Answer: 2010003
Step-by-step explanation: because 10000+2000003= 2010003
Math may be hard but you gotta learn to get smarter
y=1/2x-4 in Standard Form
[tex]y =\dfrac 12 \cdot x -4\\\\\implies y = \dfrac{x-8}2\\\\\implies 2y = x-8\\\\\implies x -2y=8[/tex]
I need help with this also I had was to repost it again because someone deleted it
Answer: 8:05
Step-by-step explanation:
Answer: 8:05
Step-by-step explanation:
41 divided by 533 estimate it and its long division and I have to find the R
Answer:
12 R20
Step-by-step explanation:
changed 41 to 40 and 533 to 500. work is in file above.
divide 24 apples between Roopa and Amita in ratio 5:7
Answer:
Roopa: 10
Amita: 14
Step-by-step explanation:
5x+7x=24
12x=24
x=2
5x=10
7x=14
Answer:
Step-by-step explanation:
5/7*24
=5/7*24
=17.14 apples
i need help fast please
Solve this and show steps
4.5×8-(0.4+9.6-(3.6-1.8))
Answer:
27.8
Step-by-step explanation:
You need to do brackets first
3.6-1.8 = 1.8
Then substitute
4.5 x 8- (0.4 + 9.6- 1.8)
0.4+9.6-1.8=8.2
4.5 x 8 - 8.2 =27.8
please this is half my grade!!!
Benjamin has a ladder that is 15 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 13.8 ft above the ground. What is the angle, rounded to the nearest tenth, that the ladder makes with the ground? Show your work
2. What is the length of side YZ to the nearest tenth? Show your work.
side XY is 11 feet, and angle Z is 35 degrees(this is a right triangle)
3. What are the exact measures of the other two sides of the triangle? Use special right triangles ratios and show your work.
Side AC is 14 feet, this is a right triangle, and angle A is 30 degrees
The special right triangle is the right triangle that have acute angle values
that simplify the process of finding its dimensions.
The correct values are;
1. The angle the ladder makes with the ground, is approximately 66.93°
2. The length of YZ is approximately 19.18 ft.
3. CB = 7 ft. and AB = 7·√3 ft.
Reasons:
1. The length of the ladder = 15 ft.
Height of the ladder above the ground, h = 13.8 ft.
Required:
The angle the ladder makes with the ground.
Solution:
The angle the ladder makes with the ground is given by the equation;
[tex]sin(\theta) = \dfrac{Length \ of \ the \ ladder}{Height\ of \ the \ ladder \ above the \ ground} = \dfrac{13.8}{15} = 0.92[/tex]
[tex]\theta = arcsin\left(0.92 \right) \approx 66.93^{\circ}[/tex]
2. The given parameters are;
XY = 11
∠Z = 35°
YZ = Required
In a right triangle, the side facing the acute angle is a leg of the triangle.
Therefore;
XY is the opposite side to ∠Z
[tex]sin(\angle Z) = \dfrac{XY}{YZ}[/tex]
Which gives;
[tex]sin(35^{\circ}) = \dfrac{11}{YZ}[/tex]
[tex]YZ= \dfrac{11}{sin(35^{\circ}) } \approx 19.18[/tex]
YZ ≈ 19.18 ft.
3. AC = 14 ft.
∠A = 30
Required:
The length of the other two sides
Solution:
Where by AC is the hypotenuse side, we have;
CB = AC × sin(∠A)
Therefore;
CB = 14 × sin(30°) = 7
CB = 7 ft.
AB = AC × cos(∠A) = 14 × cos(30°) = 7·√3
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1. The angle the ladder makes with the ground, is approximately 66.93°
2. The length of YZ is approximately 19.18 ft.
3. CB = 7 ft. and AB = 7·√3 ft.
Wanda is a nurse at a busy city hospital. What qualities might help Wanda in her career?
Answer:
b.
This may be the complete question:
Wanda is a nurse at a busy city hospital. What qualities might help Wanda in her career?
a. Wanda is task oriented and likes to be alone.
b. Wanda has a lot of energy and is a good multitasker.
c. Wanda has remarkable typing skills and does well with computers.
d. Wanda has very good concentration skills and likes to create things with her hands.
Answer: b.
A glue company needs to make some glue that it can sell for $120 per barrel. It wants to use 150 barrels of glue worth $100 per barrel, along with some glue worth $150 per barrel and glue worth $190 per barrel. It must use the same number of barrels of $150 and S190 glue. How much of the $150 and $190 glue will be needed? How many barrels of $120 glue will be produced
Jada, Elena, Lin walked a total of 37 miles last week. Jada walke 4 miles in Elena, and Lin walked 2 more miles than Jada.
Click on picture for more info :333
I AM BEING NICE TODAY. DONT I REPEAT DONT TAKE THE POINTS AND ANSWER A NONSENSICAL ANSWER. THIS WILL END UP IN AN REPORT LIKE BIG TIME >:<
I AM GIVING 100 POINTS AND BRAINLIEST. PRIZE GOES TO ONE WHO ANSWER FIRST AND CORRECTLY.
ATQ
[tex]\\ \sf\longmapsto m+m+4+m+6=37[/tex]
[tex]\\ \sf\longmapsto 3m+10=37[/tex]
[tex]\\ \sf\longmapsto 3m=27[/tex]
[tex]\\ \sf\longmapsto m=9[/tex]
Elena=9miJade=13miLin=15miTen less than the product of a number and 45.
Answer:
45*x-10
Step-by-step explanation:
10 less than a number would give you
x - 10
and the product of a number means your multiplying and your multiplying 45 so you would get
45*x
add them together and you get
45*x-10
A certain book has 200 pages, and 47 of these pages have an illustration. If one of the book's pages
is selected at random, what is the probability of selecting a page with an illustration? (Express your
answer as a decimal or fraction, not as a percent.)
Answer: fraction:47/200 desimal:0.235
Step-by-step explanation:
What series of transformation will not map figure H onto itself
Answer:
D
Step-by-step explanation:
Given a square with vertices at points (2,1), (1,2), (2,3) and (3,2)
Consider option D.
1st transformation will map vertices of the square into points
....2nd transformation = reflection over y = -x + 2 will map vertices into points ....These points are not the vertices of the initial square.
I hope it helps.
[tex]\sqrt{17} \times \sqrt{17}[/tex]
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The equivalent value is ~
[tex] \boxed{17}[/tex]
[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
[tex] \sqrt{17} \times \sqrt{17} [/tex][tex]( \sqrt{17}) {}^{2} [/tex][tex]{(17 {}^{ \frac{1}{2}}) }^{2} [/tex][tex]17[/tex]What is the surface area of the cylinder with height 8 km and radius 4 km? Round
your answer to the nearest thousandth.
The solution is: the surface area of the cylinder is 301.44 km².
Here, we have,
from the given diagram, we get,
For surface area of a cylinder:
A = 2(π) × (radius) × (height) + 2(π)×(radius squared)
For the first half of that equation:
2(π) × (radius) × (height)
2 × (3.14) × (4) × (8)
= 200.96 km²
Now the second half of that equation, the area of the circle ends:
2(π)×(radius squared)
= 2 × (3.14) × (4) × (4)
= 100.48 km²
Add them up:
200.96 km² + 100.48 km² = 301.44 km²
Hence, The solution is: the surface area of the cylinder is 301.44 km².
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A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). The one-time fixed costs will total $26,780 . The variable costs will be $9 per book. The publisher will sell the finished product to bookstores at a price of $22 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
Answer: 2,435
Step-by-step explanation:
trust
What is the other endpoint of the segment with midpoint (-3) and endpoint (-7)?
O 4
O 1
0-11
0-5
Answer:
1
Step-by-step explanation:
From -3 to -7 the distance is 4 (-3--7=4). Midpoint means that point -3 bisects the segment into two equal parts. So, the other endpoint is 4 units away from -3. Since -3+4=1, 1 is answer.
Elizabeth bought lemons (l) and apples (a). Each apple costs 35¢ and each lemon costs 15¢. All together, she bought 17 lemons and apples for $3.95. Which system can be used to determine how many of each she bought?
Step-by-step explanation:
Given:
Lemons - l and apples - aa = 35¢, l = 15¢Number of apples and lemons = 17Cost of lemons and apples = $3.95 = 395¢System as per question:
a + l = 1735a + 15l = 395Or
a + l = 170.35a + 0.15l = 3.95Step-by-step explanation:
Let the number of apples be a and lemons be l . Then ,
=> a + l = 17
Also ,
=> 35a + 15l = $ 3.95
What is the y intersect. Pls help
Answer:
total shipping cost
Step-by-step explanation:
PLEASE ASAP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!11
Answer:
3/2
Step-by-step explanation:
Finding the slope of a line on a graph is easier if you can identify places where the line crosses grid intersections. We see two of those to be ...
(4, 1) and (6, 4)
The second of these points is 4-1 = 3 grid squares higher than the first point. It is also 6 -4 = 2 grid squares to the right. The slope is the ratio of these values:
slope = "rise"/"run" = 3/2
The slope of the graphed line is 3/2.
The tape diagram represents an equation.
р
p
36
Find the value of p that makes the equation true.
Answer:
It's 6
p=6
Step-by-step explanation:
how many trees will be planted when 5 are cut down
