Answer:
yes!
Step-by-step explanation:
Which geometric series converges?
Answer:
Option 2: 1 + 1/2 + 1/4 + 1/8+...
Step-by-step explanation:
When a geometric series converges, it has a common ratio that is in between -1 and 1. We can start by finding the common ratios of all the options and then see which one converges.
In the first option, each term is 3 times the term before it, meaning it has a ratio of 3. 3 does not fit in the range we defined, so this series does not converge.
In the second option, each term is half the term before it. This means the common ratio is 1/2. 1/2 is in the range, so this series converges.
In the third option, we can see that the common ratio is -4 since it is the number being brought to a power. -4 does not fit in the range we defined, so this series does not converge.
In the fourth option, we can see the common ratio is 2 since it is the number you multiply by tone more time to get the next term. 2 does not fit in the range we defined, so this series does not converge.
From this, we can see the second option(1 + 1/2 + 1/4 + 1/8+...) is the solution.
The geometric series [tex]1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}[/tex] converges by the rule of convergence. Thus, the option [tex]2[/tex] from the given options is correct.
When a geometric series converges, it has a common ratio that is in between [tex]-1[/tex] and [tex]1[/tex].
The convergence of the geometric series depends on the common ratio [tex]r[/tex]. When [tex]r[/tex]>1, then the series diverges.When [tex]r[/tex]<1, then the series converges, and when [tex]r[/tex] = 1, then the series oscillates.
The common ratio [tex]r[/tex] of the series [tex]\dfrac{1}{81} +\dfrac{1}{27} +\dfrac{1}{9} +\dfrac{1}{3}[/tex] is greater than [tex]1.[/tex] So, the series diverges.
For the series, [tex]1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}[/tex] , the common ratio [tex]r[/tex] is [tex]\dfrac{1}{2}[/tex], which is less than [tex]1[/tex] . So, the series converges.
For the series, [tex]\sum 7(-4)^n[/tex] , here the common ratio is [tex]-4[/tex] which does not lie in the range of convergence. Thus the given series is not convergent.
For the series,[tex]\sum \dfrac{1}{5}(2)^{n-1}[/tex] the common ratio is 2. So, the series is not convergent.
The geometric series is [tex]1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}[/tex].
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A teacher is four times as old as a student. In 28 years, the student's age will be half of the teacher's age. How old are they now?
The age of the teacher is
years.
The age of the student is
years
Please send me the graph of -x²-5x+6
Answer:
-\left(x-1\right)\left(x+6\right)
Step-by-step explanation:
-\left(x^2+5x-6\right)
The water level at a local pier rises and falls with the tide. Yesterday, the maximum depth of the water at the pier was 8 feet, and the minimum depth was 4 feet. High tide occurred at 12:00 am and low tide occurred at 12:20 pm. Which function models the depth, in feet, of the water at the pier yesterday, as a function of the time t in minutes past high tide?
Answer: C, Bottom Left
Step-by-step explanation:
The function that models the depth, in feet, of the water at the pier yesterday, as a function of the time t in minutes past high tide is: 2 cos(π/740t)+6.
What is function model?Amplitude
A = 8 - 6
A = 2 ft
Average depth
A = (4 + 8)/2
A = 6 ft
Hence:
A+B=8
-A+B=4
1/2t=12×60×20=740
w=2π/t=π740
When t=0
d=2sin4+6=8
4=π/2
Hence:
d(t)=2 sin(π/740t + 4)+6
2 cos(π/740t)+6
Therefore the function that models the depth, in feet, of the water at the pier yesterday, as a function of the time t in minutes past high tide is: 2 cos(π/740t)+6.
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Multiply. (2x-1)(3x+5)
ANSWER
6x² + 7x - 5
Step-by-step explanation:
(2x-1)(3x+5)
= 6x² + 10x - 3x - 5
= 6x² + 7x - 5
Answer:
6x² + 7x - 5
Step-by-step explanation:
FOIL method
Multiply the First terms
2x * 3x = 6x²
Then the Outer terms
2x * 5 = 10x
Inner terms
-1 * 3x = -3x
Last terms
-1 * 5 = -5
--------------------------
All together
6x² + 10x - 3x - 5
Combine like terms
6x² + 7x - 5
what is the angle of d
Answer:
115°
Step-by-step explanation:
65 +65 = 130
360-130= 230
230÷2= 115
PLEASE HELP ME WITH THIS
Gabriela is solving the following equation. Her steps are shown:
Gabriella is not sure she has solved the problem correctly. How can you convince Gabriella if she has solved the problem correctly / incorrectly? If she has solved the problem incorrectly, solve it and convince her of the solution
Answer:
Solution given:
5(9x-8)=4(x+2)
45x-40=4x+8
45x-4x=40+8
41x=48
x=[tex] \frac{48}{41} [/tex]
Gabriella is not correct:
she has done in distribution
5(9x-8)=4(x+2)
45x-40=4x+8 not 45x-8=4x+2.
No, Gabriela is not solving correctly because her second step is wrong.
What is a fraction?In a fraction the upper part is known as numerator and the lower part is known as denominator.
How to solve the problem?The problem is as under
(9x-8)/4=(x+2)/5
The above problem is solved as
5(9x-8)=4(x+2)
45x-40=4x+2
41x=42
x=42/41
Hence the value of x is 42/41 therefore the solution of Gabriella is wrong.
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In
any
School there are 7000
students 45%. are boys. How many
boys are there? How
many girls
are there
Answer: there are 3150 boys and 3850 girl
Step-by-step explanation:
45÷100×7000= 3150 and 7000- 3150 = 3850
Hope this helps!!
Plz help me well mark brainliest if you are correct!!.....
Step-by-step explanation:
the base is 5unit and the height is 9unit
Answer:
The base is 5 units the height is 9 units
Step-by-step explanation:
Just count the blocks in the diagram
base = 5
Height = 9
what is 1+1-(3x3)-(1x9)
pls, be honest. 20 points
Answer:
it is 5.7 so it should be in between the 5 and 6 but closer to the 6.
Step-by-step explanation:
Hope this helps have a great day! :)
Answer: 5.7
Step-by-step explanation:
Because it’s closer to six but still In the 5 range.
if there 10 students and 2/5 play soccer how many students play soccer?
Answer:
4
Step-by-step explanation:
2 out of 5 play so if there is 10 students 10*2/5 = 4 students
Answer:
4 students would play soccer
Step-by-step explanation:
To make the total students 10 instead of 5 we multiply the information by 2. 2/5 times 2 equals 4/10. So 4 out of 10 studento play soccer
Define Hypotenus
I have forgotten what it is
In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.
It is useful in different situations involving the need to find distance or the measure of an angle.
Use the Pythagorean theorem to calculate the hypotenuse from right triangle sides. Take a square root of sum of squares: c = √(a² + b²)
Expand and simplify (2x + 1)(x + 3)
2x2 + 7x + 3 -answer
(2x + 1) (x + 3)
(2x * x) + (2x * 3) + (1 * x) + (1 * 3)
2x2 + 6x + x+3
2x2 + 7x + 3
ILL GIVE BRAINLIEST PLSSSS HELP BASICALLY EVERYTHING IS IN THE PICTURE IF YOU ANSWER THIS WRONG OR PUT RANDOM WORDS OR A LINK I WILL REPORT YOU FASTER THAN THIS IS DUE
Each day 1/2 of the money that is in a bank is removed .no money is added to the vault .which of the following models the situation
Angle Relationships
For the triangle above, find sin B.
a. 25°
b. 0.385
c. 0.923
d. 18°
Please select the best answer from the choices provided
Answer:
c
Step-by-step explanation:
12/13=0.923 , and also sinb is ac/ab
Answer:
C. 0.923
Step-by-step explanation:
I calculated it logically
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. What value of x satisfies this equation? 1.5(4)^2x=12 Round your answer to the nearest hundredth. The value of x is .
Answer:
O.75
Step-by-step explanation:
The value of x in the equation 1.5(4)^2x is equal to 12 is 3/4 after equation the power of same base.
What is integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
We have an equation:
[tex]\rm 1.5(4)^2^x=12[/tex]
[tex]\rm (4)^2^x=8[/tex]
[tex]\rm (2^2)^{2x}= 2^3[/tex]
[tex]\rm 2^{4x}=2^3[/tex]
4x = 3 (equating powers of same base)
x = 3/4
Thus, the value of x in the equation 1.5(4)^2x is equal to 12 is 3/4 after equation the power of same base.
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The Clothes Barn is having a 65% off sale on all the dresses. Jennifer paid $43.75 for a dress that was on
sale. What was the original price of the dress?
1. $125.00
2. $28.44
3. $15.31
4. $105.00
Answer:A
Step-by-step explanation:
I used the process of elimination. I did, 125 x .65 to get 81.25. Then, I subtracted 81.25 to 125. To get 43.75.
The original price of the dress was $125.00.
What is the percentage?A percentage is a number or ratio that can be expressed as a fraction of 100 in mathematics. If we need to calculate the percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage denotes a part per hundred.
How to solve this problem?Given that the discount = 65%
Sale price = $43.75
Let the original price of the dress is $x.
Now, sale price = x - x * 65% = x - x * 65/100 = (100 - 65)x/100 = 35x/100
We can write
35x/100 = 43.75
i.e. x = (43.75 * 100)/35 = 4375/35 = 125
Therefore, the original price of the dress was $125.00. So, option 1 is correct.
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A rectangle is graphed on a coordinate plane. The rectangle’s two lines of symmetry are the x-axis and the y-axis. Evie says that means the vertices are reflections of each other over the x-axis and y-axis. Is she correct? Explain your reasoning NO LINKS worth 50 points
Answer:
Can you add a picture if there are any?
Step-by-step explanation:
Property of 10+5=5+10
Answer:
Commutative Property of Addition
Answer:
Commutative property
Step-by-step explanation:
The commutative property is when the order of the addends is changed, the sum stays the same.
Ex. 3+7 = 7+3
Both 3+7 and 7+3 = 10
Write 123,000,000 as a multiple of a power of 10.
Answer:
1.23 x 10^8
hope this helps
have a good day :)
Step-by-step explanation:
Find the measure of the angle(s)
Help
Answer:
759
Step-by-step explanation:
5.
Which value of x would satisfy this inequality?
V3
4
2
A А.
С
D
000
4
10
Answer:
C) 4/5
Step-by-step explanation:
pi/4 = 0.7853981634
[tex]\frac{\sqrt{3} }{2}[/tex] = 0.8660254038
3/4 = 0.75. It's less than pi/4, so not correct
9/10 = 0.9. It's more than 0.866, so not correct
4/5 = 0.8. It's right for both condition
8/9 = 0.888. It's more than 0.866, so not correct.
A lock has a 3-number code made up of 15 numbers. If none of the numbers are allowed to repeat, how many different ways can you choose three different numbers in order for a unique code?
Answer:2730
Step-by-step explanation:
The number of ways we can choose three different numbers in order for a unique code for this case is 2730
How many ways k things out of m different things (m ≥ k) can be chosen if order of the chosen things doesn't matter?We can use combinations for this case,
Total number of distinguishable things is m.
Out of those m things, k things are to be chosen such that their order doesn't matter.
This can be done in total of [tex]^mC_k = \dfrac{m!}{k! \times (m-k)!}[/tex] ways.
If the order matters, then each of those choice of k distinct items would be permuted k! times.
So, total number of choices in that case would be:
[tex]^mP_k = k! \times ^mC_k = k! \times \dfrac{m!}{k! \times (m-k)!} = \dfrac{m!}{ (m-k)!}\\\\^mP_k = \dfrac{m!}{ (m-k)!}[/tex]
This is called permutation of k items chosen out of m items (all distinct).
Given that:
The considered lock as a 3 number codeThere are 15 numbers available.None of the number can repeat.In a lock, the order of the way numbers are arranged matters.
Because of no repetition allowed, we can simulate this situation as:
The number of ways we can choose 3 numbers out of 15 numbers with order = The number of different ways we can choose three different numbers in order for a unique code.
And we have:
The number of ways we can choose 3 numbers out of 15 numbers with order = [tex]^{15}P_3 = \dfrac{15!}{(15-3)!} = \dfrac{15 \times 14 \times 13 \times 12!}{12!} = 2730[/tex]
Thus, the number of ways we can choose three different numbers in order for a unique code for this case is 2730
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Please, Please help! :(
Answer:
first blank is 3
second blank is 126
Step-by-step explanation:
the ratio is 2:3 so you must keep that the same in the table
The one for chocolates is 3 and the one for peppermints is 126
Please help me find 'x' your help would be much appreciated
-Thanks
Answer:
x=25.
Step-by-step explanation:
We know because of corresponding angles, the sum of the angle adjacent to (2x-5) and (2x-5) is 180 degrees
2x-5+5x+10=180
7x+5=180
7x=175
x=25
Triangle ABC is graphed in the coordinate plane with vertices A(1, 1); B(3, 4) and C(- 1, 8) as shown in the figure.
Answer:
(-4,-2)
Step-by-step explanation:
B(3,4)
x=3 , y=4
(3-7,4-6)
(-4,-2)
Transformation involves changing the position of a shape.
The coordinates of B after the translation is (-4,-2)
The vertices are given as:
[tex]\mathbf{A =(1,1)}[/tex]
[tex]\mathbf{B =(3,4)}[/tex]
[tex]\mathbf{C =(-1,8)}[/tex]
The translation rule is given as:
[tex]\mathbf{(x-7,y-6)}[/tex]
So, the coordinates of B' is calculated using:
[tex]\mathbf{(x,y) \to (x-7,y-6)}[/tex]
This gives
[tex]\mathbf{(3,4) \to (3-7,4-6)}[/tex]
[tex]\mathbf{(3,4) \to (-4,-2)}[/tex]
Rewrite as:
[tex]\mathbf{B' = (-4,-2)}[/tex]
Hence, the coordinates of B after the translation is (-4,-2)
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Given: cosθ= 4/5
Find: sin2θ
Answer:
cos theta=4/5
b/h=4/5
b=4 and h=5
p=?
H^2=P^2+B^2
5^2=P^2+4^2
25-16=P^2
9=P^2
[tex]\sqrt{9}[/tex]=P
3=P
Now,
sin2theta
=p/h2
=3/5*2
=9/5
Step-by-step explanation:
Answer:
About 36.87 degrees; sinθ=3/5
Step-by-step explanation:
Note: I made an assumption with the Find: sin2θ part of your question, as it turned up as invalid when working on it on my end. Therefore, I assumed that it was sinθ. If it was something else, tell me and I can correct the answer/content.
Since within a triangle there are three sides when solving an angle, being opposite, adjacent and hypotenuse.
By already having cosθ=4/5. the rest of the problem can be solved. Since cosine is adjacent over hypotenuse, we can use the Pythagorean Theorem, solving for one of the legs of the triangle with:
c^2-b^2=a^2
Now, just plug in c as the 5 (the hypotenuse) and b as 4 (one of the legs).
5^2-4^2=a^2
25-16=a^2
9=a^2
a=3
The other leg is 3. With this, 3 would be the opposite angle from sin 20. Therefore, it can be plugged in the sine equation to get the answer. Remember, sine is Opposite/Hypotenuse.
sinθ=3/5
Move over the sine to then opposite side, inverse it:
θ=sin-1 3/5
Use a calculator.
θ = about 36.87 degrees.
HELP! PLEASEEEEE
IMAGE BELOW!
Answer:
Quadrant I and Quadrant II
Step-by-step explanation:
Quadrant I has both positive x and y coordinates,Quadrant II has a negative x coordinate but the y coordinate is positive.