Answer: (a) {a, ar, ar², ar³, ar⁴, ar⁵...}, (b) arⁿ⁻¹
For part (a), the question gives us the first term a, and then asks us to apply the common ratio r six times.
In order for ar = a, the nth term of r will have to equal 0 (this implies that n is an exponent; thus giving us the first term a, as r = 1).
Since we use this method on the first term, we must use it for the next five, in which r gains an additional exponent for every consecutive value (nth term) thereafter.
Ultimately getting: {a, ar, ar², ar³, ar⁴, ar⁵...}
For part (b), we first have to understand that the sequence does not start at 0, but at 1 for n. In order for ar = a, with n = 1, there needs to be subtraction of -1 within the exponent. So that arⁿ⁻¹
If we check and apply this, we can see that:
{ar¹⁻¹, ar²⁻¹, ar³⁻¹, ar⁴⁻¹, ar⁵⁻¹, ar⁶⁻¹...} = {a, ar, ar², ar³, ar⁴, ar⁵...} = arⁿ⁻¹ = Tn
helpppppppppppppppppppppp plsssssssssssssssss
m∠b= 25°
Answer:
Step-by-step explanation:
The total of all angles in the triangle is 180
You already know 2 values for the triangle, Angle A 25 as well as Angle C 90
Your formula is
180 - 90 -25
1 red marble, 3 green, 4 blue. What is the probability of picking a yellow marble?
Answer:
zero probability, which means impossible
Step-by-step explanation:
there are no yellow marbles to select from
What is the probability that the arrow will land on 1 or 2?
A. 2/5
B. 2/3
C. 3/4
D. 1/5
The probability that the arrow will land on 1 or 2 is 2/5.
What is Probability ?Probability is the ratio of occurring a certain event out of the total possible events.
If the given statement contains OR we use addition and if the given statement contains AND we use multiplication.
From the given data
Total no. of regions in the circle is 5
The probability that the arrow will land on 1 or 2 is
P(1) = 1/5
P(2) = 1/5
∴ P(1) or P(2) is
= 1/5 + 1/5
= 2/5
Here we have used addition because of OR statement.
Learn more about Probability :
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The five new teachers at a school were surveyed. Is this sample of teachers at the school likely to be biased?
Answer:
yes because since they are new they are all going to have a different opinion on the school than other teachers thats been there for years
hope this helps
have a good day :)
Step-by-step explanation:
Yes, it would likely be biased because they might be like an advertisement since they weren't teaching for years at this school.
If this helps, please mark me brainliest!
Have an amazing day!
Find the value of x.
Answer:
X=23
Step-by-step explanation:
Help please !!!!!!!!!!!
CSC B = 25/7 and the sec B =25/24 find tan B??
Answer:
tan β = [tex]\frac{7}{24}[/tex]
Step-by-step explanation:
Using the identities
sin x = [tex]\frac{1}{cscx}[/tex] , cos x = [tex]\frac{1}{secx}[/tex] , tan x = [tex]\frac{sinx}{cosx}[/tex] , then
sinβ = [tex]\frac{1}{\frac{25}{7} }[/tex] = [tex]\frac{7}{25}[/tex]
cos β = [tex]\frac{1}{\frac{25}{24} }[/tex] = [tex]\frac{24}{25}[/tex]
Then
tan β = [tex]\frac{\frac{7}{25} }{\frac{24}{25} }[/tex] = [tex]\frac{7}{25}[/tex] × [tex]\frac{25}{24}[/tex] = [tex]\frac{7}{24}[/tex]
Answer:
tanβ = 7/24
Step-by-step explanation:
Given:
cscβ = 25/7
secβ = 25/24
tanβ = ?
Recall:
cscβ = 1/sinβ
secβ = 1/cosβ
tanβ = sinβ/cosβ
Rewrite and simplify:
tanβ = sinβ/cosβ
tanβ = (1/cscβ)/(1/secβ)
tanβ = (1/(25/7))/(1/(25/24))
tanβ = (7/25)/(24/25)
tanβ = (7/25)(25/24)
tanβ = (7*25)/(25*24)
tanβ = 175/600
tanβ = 35/120
tanβ = 7/24
If v² = u² + 2gs, find the value of s when v = 25, u = 12 and g = 10
Answer:
24.05
Step-by-step explanation:
v² = u² + 2gs
(25)² =(12)² +2(10)s
625=144+20s
625-144=20s
481=20s
481/20=s
24.05=s
s=24.05
what is the perimeter of a rectangle with sides of 4 inches by 8 inches?
hi ^^
---------------------------------------
here's your answer: P=24in
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bye <3
Divide £90 in the ratio of 3:7
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Answer:
The answer would be B because the y intercept is how much he changes per hour
Answer:
Your answer should be C
Step-by-step explanation:
Letter A was tempting, but 120 for 1 hour. Then 180 for 2.5 means that is had a y intercept. So it couldn't be A. The other ones were easy to rule out because they only told a fraction of what was shown.
Answers are 36,54,198,72
Answer:
72°
Step-by-step explanation:
∠ AOB = 20% of 360° = 0.2 × 360° = 72°
arc AB is equal to the angle subtended at the centre , that is
arc AB = 72°
If you deposit $2000 into an account paying 6% annual interest, how much money will be in the account, after 5 years if it is compounded daily
Answer:
$2,699.72
Step-by-step explanation:
Given that
The deposited amount is $2,000
The annual rate of interest is 6%
And, the time period is 5 years
We need to find out the amount that would be in the account in the case when it is compounded daily
So,
The following formula should be used
= Deposited amount × e^(rate, time period)
= $2,000 × e^(0.06,5)
= $2,000 × e^0.3
= $2,699.72
Make
x
the subject of the formula
5
x
=
t
Answer:
5x=t
x=t/5
This should be your answer
12. Karen borrowed a sum of money for some big screen TVs and a
waterfall for her restaurant. If she borrowed $10,200 and received a 3.85
% interest rate compounded continuously, how much did Karen pay in
interest over a 7 year period? Round your answer to the nearest whole
number.
Answer:
$3,155
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 3.85/100
r = 0.0385 rate per year,
Then solve the equation for A
The formula is given as:
A = Pe^rt
Where
P = Principal = $10,200
r = interest rate = 0.0385
t = Time in years = 7
A = Amount paid after t years
A = 10,200.00 × e^(0.0385×7)
A = $13,354.96
A = P + I where
P (principal) = $10,200.00
I = $13,354.96 - $10,200
I (interest) = $3,154.96
Therefore, the amount of money Karen paid after 7 years in interest to the nearest whole number is $3,155
Convert the rectangular equation to polar form. Assume a > 0.
x^2+y^2-7ay=0
Answer:
[tex]r=9a\cos(\theta)[/tex]
Step-by-step explanation:
the answer is on study.com :|
2x^2+7x-4=0 by factor ing
Answer:
[tex]x=0.5, \\\\x=-4[/tex]
Step-by-step explanation:
Factoring is the process by which one rewrites an equation or number out as the product of many numbers or expressions. In the given situation, one is asked to factor the following equation,
[tex]2x^2 +7x - 4=0[/tex]
In factored form,
[tex](2x-1)(x+4)=0[/tex]
Use the zero product property, this states that any number times zero equals zero. Therefore, set each factor equal to zero and solve for the parameter (x),
[tex]2x-1=0[/tex]
Inverse operations,
[tex]2x=1\\x=0.5[/tex]
[tex]x+4=0[/tex]
Inverse operations,
[tex]x=-4[/tex]
[tex]\huge\boxed{Answer\hookleftarrow}[/tex]
[tex]x =\frac{1}{2},-4[/tex]
[tex]\huge\boxed{Explanation\hookleftarrow}[/tex]
Mark as Brainliest
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Caroline earns $12.00
per hour at her job. Which answer choice is an equation that correctly represents
the total amount of money, m, that Caroline earns after working for a certain number of hours, h?
What is the quotient StartFraction 15 p Superscript negative 4 Baseline q Superscript negative 6 Baseline Over negative 20 p Superscript negative 12 Baseline q Superscript negative 3 Baseline EndFraction in simplified form? Assume p not-equals 0, q not-equals 0.
Answer:
[tex]-\frac{3p^8}{4q^3}[/tex]
Step-by-step explanation:
[tex]\frac{15p^{-4}q^{-6}}{-20p^{-12}q^{-3}}[/tex] can be broken down into three fractions, coefficients, powers of p, powers of q.
[tex]-\frac{15}{20}\cdot\frac{p^{-4}}{p^{-12}}\cdot\frac{q^{-6}}{q^{-3}}[/tex]
Simplify the first fraction, then simplify the others by subtracting numerator exponents minus denominator exponents.
[tex]-\frac{3}{4} p^{-4-(-12)} q^{-6-(-3)} =-\frac{3}{4} p^8 q^{-3} = \alpha -\frac{3p^8}{4q^3}[/tex]
Someone please help!
Answer:
f(3)= 12
Step-by-step explanation:
if f(1)= 4 then f(3)= 12
p less than 6 times b
Step-by-step explanation:
p< 6b is for p less than 6 times b.
Answer:
6b > p
Step-by-step explanation:
The question is not clear, just in case you are asking the equation.
PLEASE HELP !!!
Mai correctly used the Fermi process and the following estimates to determine how many packs of gum would fit inside the gymnasium she plays basketball in.
Mai correctly used the Fermi process and the following estimates to determine how many packs of gum would fit inside the gymnasium she plays basketball in.
a. [tex]\frac{4x10^5}{4x10^-^4}[/tex] = 1 x 10^9
b. [tex]\frac{4x10^5}{4x10^-^4}[/tex] = 1 x 10^1
c. [tex]\frac{4x10^6}{4x10^-^4}[/tex] = 1 x 10^10
d. [tex]\frac{4x10^6}{4x10^-^4}[/tex] = 1 x 10^2
Answer:
Hello! Hope you having a great morning! Your answer is, B)
Hope this helped! Brainiest plz! Hope you make a 100% and have a nice day!
Answer:
the answer is A
Step-by-step explanation:
i just took the quiz
Does anyone know how to solve this??
Answer:
a) (f + g)(x) = x² - 2x + 3x - 4 = x² + x - 4
domain: x E R
b) (f - h)(x) = x² - 2x - ( - 2x + 1) = x² - 1
domain: x E R
c) (f.g)(x) = (x² - 2x)(3x - 4) = 3x³ - 10x² + 8x
domain: x E R
d)
[tex]( \frac{h}{f} )(x) = \frac{ - 2x + 1}{x {}^{2} - 2x} [/tex]
domain: x E R\{0; 2}
……………..
please help.
Answer:
Hello! answer: x = 1
Step-by-step explanation:
This triangle will add up to 180 degrees 85 + 64 = 149 180 - 149 = 31 4 × 1 = 4 4 + 27 = 31 therefore x = 1 Hope that helps!
Warren has $10,000 to invest. He finds a bank that will give him a 9% interest rate. After investing, he leaves it untouched for 8 years.
How much is in the account if it is compounded monthly? $
How much is in the account if it is compounded continuously? $
*NOTE: Round to the nearest penny (hundredths place).
Answer:
The final balance is £20,489.21.
The total compound interest is £10,489.21
Step-by-step explanation:
pretty sure you know the answer after you round this
Khan uses 78 feet of fence to make a rectangular pen for his pet rabbit. The length of the pen is 25 feet what is the width of the rectangular pen
The width of the rectangular pen is equal to 14 feet.
Given the following data:
Perimeter of rectangle = 78 feet.Length = 25 feet.To calculate the width of the rectangular pen:
Formula for the perimeter of a rectangle.Mathematically, the perimeter of a rectangle is given by the formula;
[tex]P=2(L+W)[/tex]
Where:
P is the perimeter of a rectangle.L is the length of a rectangle.W is the width of a rectangle.Substituting the parameters into the formula, we have;
[tex]78=2(25+W)\\\\78=50+2W\\\\2W=78-50\\\\2W=28\\\\W=\frac{28}{2}[/tex]
Width, W = 14 feet.
Read more on the width of a rectangle here: https://brainly.com/question/17297081
Explanation: Zero Exponent
So far we have looked at powers of 10 with exponents greater than 0.
What would happen to our patterns if we included 0 as a possible exponent?
1. Write 10^12 × 10^0 with a power of 10 with a single exponent using the appropriate exponent rule. Explain or show your reasoning.
A. What number could you multiply 10^12 by to get this same answer?
Answer:
1) We can use the following property to simplify the product of powers as follows:
[tex]a^{m}\cdot a^{n} = a^{m + n}[/tex], [tex]a\in \mathbb{R}[/tex], [tex]m,n\in \mathbb{Z}[/tex] (1)
Therefore, we have the following result:
[tex]10^{12}\cdot 10^{0} = 10^{12+0} = 10^{12}[/tex]
A) [tex]10^{12}[/tex] must be multiplied either by [tex]10^{0}[/tex] or by [tex]1[/tex] to get the same answer.
Step-by-step explanation:
1) We can use the following property to simplify the product of powers as follows:
[tex]a^{m}\cdot a^{n} = a^{m + n}[/tex], [tex]a\in \mathbb{R}[/tex], [tex]m,n\in \mathbb{Z}[/tex] (1)
Therefore, we have the following result:
[tex]10^{12}\cdot 10^{0} = 10^{12+0} = 10^{12}[/tex]
A) In addition, we can use this property:
[tex]\frac{a^{m}}{a^{n}} = a^{m-n}[/tex], [tex]a\in \mathbb{R}[/tex], [tex]m,n\in \mathbb{Z}[/tex]
We can apply the property mentioned above:
[tex]10^{12}\cdot 10^{0} = 10^{12}\cdot (10^{n-n}) = 10^{12}\cdot \left(\frac{10^{n}}{10^{n}} \right) = 10^{12} \cdot 1 = 10^{12}[/tex]
In consequence, we conclude that [tex]10^{0} = 1[/tex]. [tex]10^{12}[/tex] must be multiplied either by [tex]10^{0}[/tex] or by [tex]1[/tex] to get the same answer.
Answer to this??????
Answer:
its 40 milmeters
Step-by-step explanation:
please answer accurately and not a short answer if you don't know then don't answer thank u, and if u want to spam my answer then I will report u thank u.
Answer:
420cm^3 (cubed) = volume when tripled
Step-by-step explanation:
1. when you multiply 7*4*5=140 (volume of the prism originally)
2. 140*3=420 (final answer)
Answer:
A. 140 cm
B. 3780 cm
Step-by-step explanation:
The volume formula for a rectangular prism is lwh, and 7 times 4 times 5 equals 140.
If you triple all those amounts, then you get 21 (7 times 3), 12 (4 times 3), and 15 (5 times 3), and when you multiply those you get 3780.
I hope this helps :)
The candy shop made 3/18 pounds of chocolate they sold 1 pounds how many pounds of chocolate do they have left
The question is incomplete. Please see the complete question below
The candy shop made 3 1/18 pounds of chocolate they sold 1 1/4pounds how many pounds of chocolate do they have left
Answer:
15/8
Step-by-step explanation:
The shop made 3 1/8 pound of chocolate
They sold 1 1/4 of chocolates
Hence the number of chocolates left can be calculated as follows
3 1/8-1 1/4
= 25/8-5/4
= 15/8
What is the expanded form of the number below?
700 +90 +0.1 +0.04
1)
700 + 9 + 0.1 + 0.04
709.104
70 + 9 + 0.1 +0.004
700 + 9 + 0.1 + 0.004