Answer:
B, C, E
Step-by-step explanation:
Got it right on edge
The series C: 625 – 125 + 25 – 5 + … converges. Explanation given.
What is common ratio?The distance between each number in a geometric series is known as the common ratio. The ratio between two consecutive numbers, or a number divided by the number before it in the sequence, is known as the common ratio since it is the same for all numbers or common.
Given series:
A: 9 + 81 + 729 + …
B: 1 + 0.25 + 0.0625 + 0.015625 + …
C: 625 – 125 + 25 – 5 + …
D: 8 – 16 + 32 – 64 + …
To prove convergence:
A: 9 + 81 + 729 + …
Simplifying,
9 + (9)² + (9)³+ ....
The first term = 9
The second term = (9)²
So, the ratio = 9
That means, the geometric series with common ratio
IrI = 9 > 1
So, if the common ratio of geometric series is greater than 1 then the series diverges.
B: 1 + 0.25 + 0.0625 + 0.015625 + …
Simplifying,
1 + (1/4) + 1/(4)²+ ....
The first term = 1
Second term = 0.25
Third term = 0.0625
The ratio r = 4
IrI = 4 > 1
So, if the common ratio of geometric series is greater than 1 then the series diverges.
C: 625 – 125 + 25 – 5 + …
Simplifying,
The first term = 625
Second term = 125
Third term = 25
The ratio r = -125/625 = -1/5
IrI = 1/5 < 1
So, if the common ratio of the series is lesser than 1 then the series converges.
D: 8 – 16 + 32 – 64 + …
The first term = 8
Second term = -16
The ratio = -16/8 = -2
IrI = 2> 1
So, if the common ratio of the series is greater than 1 then the series diverges.
Therefore, the series C converges.
To learn more about the common ratio;
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Homework (5)
18. GEOGRAPHY In the continental United States,
the ratio of states that border an ocean to states
that do not border an ocean is 7:9. How many
of the states border an ocean?
Answer:
28
Step-by-step explanation:
Let's set the ratio as
7x : 9x
If you add all the states that border an ocean and do not, you will get 48 states (because Alaska and Hawaii are not part of the continental US, as they do not touch the "main" part of the country)
So, we can write this equation.
7x + 9x = 48
Simplify.
16x = 48
Divide both sides by 16.
x = 4
Now, find how many states border an ocean. In our ratio, the number of states that border an ocean was 7x. Substitute x = 4 into 7x
7 * x = 7 * 4 = 28
The number of states that border an ocean is 28.
I hope this helps! Feel free to ask any questions!
Consider the expression 16a + 4c.
Part B
What is the value of the expression
when a = -2 and c = -1?
13 The Lozano's chartered a boat over the holiday
weekend. The cost for the day was $350 plus the
6.5% sales tax. They also decided to tip their
guide 25% of the original cost of the boat rental.
What is the total amount they paid?
Answer:
$460.25
Step-by-step explanation:
350 + .065(350) + .25(350)
= 350 + 22.75 + 87.5
$460.25
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer: 23
Step-by-step explanation:
x = 90 - 67
x = 23
what is the value of 4/15 divide 2/3
Answer:
0,4
Step-by-step explanation:
4/15 : 2/3 = 4/15 × 3/2 = 2/5 × 1 = 0,4
What if the bag did not tell us how many total servings and only told us how many total cups?
If the bag of dry fruit has 5 cups and each serving is ¼ of a cup, how many servings would the bag have?
Answer:
20 servings
Step-by-step explanation:
To find how many servings the bag would have, divide 5 by 0.25:
5/0.25
= 20
So, the bag would have 20 servings
Are the ratios 9:15 and 3:5 equivalent
Answer: true
Step-by-step explanation:
Please need help thank
Answer:
5/6 yard
Step-by-step explanation:
6/6 - 1/6= 5/6 yard
Can someone please help me..
What fraction of the shape is shaded?
Answer:
1.75/8 would be your answer if im right.
Answer:
dude I want the same ans can anyone help plzz
Page 153
30. A car's value is a function of many things,
including the total mileage on the car. The
following graph illustrates the depreciation of a
car as more miles are driven. Find the value of
f(50,000) and explain its meaning. What is the
range of this function?
Car's valde
$14,000
$12,000
$10,000
$8.000
$6,000
$4,000
$2,000
$0
20,000 40.000 60.000 80.000 100.000 120,000
Mileage
Can someone answer this please!!! I only have 5 mins and u will get Brainly too :)
Answer:
18 units square
Step-by-step explanation:
Given
The attached trapezium
Required
Determine the area
From the attachment, the height, h is:
[tex]h = 3\ units[/tex]
And parallel sides are:
[tex]s_1 = 3[/tex]
[tex]s_2 = 9[/tex]
So, the area is calculated as:
[tex]Area = \frac{1}{2}(s_1 + s_2) * h[/tex]
[tex]Area = \frac{1}{2}(3 + 9) * 3[/tex]
[tex]Area = \frac{1}{2} * 12 * 3[/tex]
[tex]Area = \frac{36}{2}[/tex]
[tex]Area = 18[/tex]
Pls answer this for mw
Answer:
True.
Step-by-step explanation:
< ABF and < FBE are supplementary angles because when we sum up both we get 180°
Hope it will help :)❤
A jar contains 666 red jelly beans, 666 green jelly beans, and 666 blue jelly beans.
If we choose a jelly bean, then another jelly bean without putting the first one back in the jar, what is the probability that the first jelly bean will be green and the second will be green as well?
Answer:
666/1998 x 665/1997 = 665/5991 or 0.110999833083
A school earns $70 from selling 50 tickets for the school play. Each ticket costs the same price.
How much does the school earn for one ticket ??
Write the pair of fractions as a pair of fractions with
common denominator
1/2 and 1/3
Answer:
3/6 & 2/6
1/2 x 3, 1x3=3, 2x3=6, so it's 3/6.
1/3 x 2, 1x2=2, 3x2=6, so it's 2/6.
FIRST TO ANSWER GETS BRAINLIEST!!!
Find the y-intercept of the following line:
y=−8x+7
Answer:
7
Step-by-step explanation:
y = mx + b
The y-intercept is b.
y = -8x + 7
The y-intercept is 7.
A cyclist starts from the point si = (7, 7, 4) at t = 0 and moves with a constant velocity of v → =(4, 5, 5) and cyclist motion can be depicted by the expression, s = si + vt which gives position vector of cyclist. Determine the distance travelled by the cyclist between t = 4 s and t = 23 s. (Distance is in meters)
A. 154.36 m
B. 157.36 m
C. 152.36 m
D. 155.36 m
Answer:
A. 154.36 m
Step-by-step explanation:
I got it "Correct"
Answer:
A. 154.36 m
Step-by-step explanation:
Have a great day
pls pls pls pls helpppp
Answer:
30
Step-by-step explanation:
21*10=210
210/7=30
x=30
Answer:
30..
Explanation
Please help.A teacher asked her pupils what their favourite school subject was.
PE
27
Maths
English
135
Science
3 pupils said PE was their favourite subject.
How many pupils said that Maths was their favourite subject?
Angie has 3 pink bows, 1 blue bow, and 6 purple bows in a box. She will randomly choose 1 bow from the box.
What is the probability Angie will choose a purple bow?
Who know this answer
Answer: BASE 10
Step-by-step explanation:
The following radical equation has a solution set {x = ?} and an extraneous root x = ?.
Answer:
x=2; the extraneous root x=42.
All the details are in the attached picture, the answer is marked with red colour.
The solution set is {2, 42} & the extraneous root is 42
What is extraneous root ?
If there are two roots in an equation, and one of them does not properly satisfy the equation, then the root is called extraneous root of that equation.
What are the roots ?Given equation is,
[tex]2+\sqrt{2x-3}=\sqrt{x+7}[/tex]
Squaring both sides we get,
[tex]2^{2} +2(2)(\sqrt{2x-3} )+(\sqrt{2x-3}) ^{2} = (\sqrt{x+7}) ^{2}[/tex]
⇒ [tex]4+4\sqrt{2x-3} +2x-3=x+7\\[/tex]
⇒ [tex]4\sqrt{2x-3} =6-x[/tex]
Again, squaring both sides we get,
⇒ [tex](4\sqrt{2x-3}) ^{2} =(6-x)^{2}[/tex]
⇒ [tex]16(2x-3)=6^{2} -12x+x^{2}[/tex]
⇒ [tex]32x-48=36-12x+x^{2}[/tex]
⇒ [tex]x^{2} -44x+84=0[/tex]
⇒ [tex]x^{2} -42x-2x+84=0[/tex]
⇒ [tex](x-42)(x-2)=0[/tex]
So, x = 2 & 42
Here extraneous root is 42.
Learn more about extraneous root here :
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Data represented by quantities is called data.
Shawna went shopping at the thrift store yesterday and came home with 12 items and she only spent $31.50. She only got shirts and pants. If each shirt cost $2 and each pair of pants cost $3.50, which system of equations would represent this situation?
Please help ASAP!!!!
Answer:
-4
Step-by-step explanation:
32÷-8=-4
Q1: A number minus 4 is greater than 2 times a number
Answer:
x - 4 > 2x
(see below to solve for x if needed)
Step-by-step explanation:
"Greater than" is key word for the greater than symbol: >.
"A number" can be represented by x.
So "a number minus four" would be x - 4 and "two times a number" would be 2x.
So "A number minus 4 is greater than 2 times a number" is:
x - 4 > 2x
If you were to solve for x, it would be:
x - 4 > 2x
-x -x
-------------
-4 > x
x < -4
6, 2, 7, 8, 8, 8, 5, 10, 10
What is the standard deviation of the data?
2.38 first cousins
2.52 first cousins
5.65 first cousins
6.36 first cousins
Answer:
2.52
Step-by-step explanation:
On edg
(-4)-(-2)-{(-5)-[(-7)+(-3)-(-8)]}
Answer:
1
Explanation:
I used the calculator.
Donna and Darcy collected newspapers for recycling. Donna collected 5 3/4 pounds of newspaper. Darcy collected 2 1/4 pounds of newspaper. How much newspaper did they collect between them?
Answer:
8 pounds
Step-by-step explanation:
5 3/4 + 2 1/4 = 7 4/4 = 8