Answers
Given:
The sequence is 8, 10, 12.5, 15.625,...
To find:
The explicit formula for the given sequence.
Solution:
We have,
8, 10, 12.5, 15.625,...
Here, the first terms is 8.
[tex]\dfrac{10}{8}=1.25[/tex]
[tex]\dfrac{12.5}{10}=1.25[/tex]
[tex]\dfrac{15.625}{12.5}=1.25[/tex]
The common ratio is 1.25. So, the given sequence is a geometric sequence.
The explicit formula for a geometric sequence is:
[tex]a_n=ar^{n-1}[/tex]
Where, a is the first term and r is the common ratio.
The explicit formula for the given geometric sequence is:
[tex]a_n=8(1.25)^{n-1}[/tex]
Therefore, the correct option is A.
Related Questions
a television regularly cost $180 but is on sale for 40% off there is a 5% sales tax on the sales price how much does the television cost after the discount and sales tax
Answers
Answer:
$102.60
Step-by-step explanation:
i am pretty sure this is correct
Please help! I need this fast!
Answers
Answer:
E. (6,4
F. (4,6)
G. (3,0)
H. (0,3)
Step-by-step explanation:
What is the length of the missing leg?
Answers
Complete the pattern: 2×4=8 20×4=80 200×4=800 2000×4=
Answers
just add another 0
Tristan paid $17.50 to buy 2 pounds of peanuts and 3 pounds of cashews. Rivka paid $19.00 to buy 5 pounds of peanuts and 2 pounds of cashews. If both people paid the same price per pound, what was the price per pound for the cashews?
A. $2.00
B. $3.80
C. $4.50
D. $8.75
Answers
Answer:
C. $4.50
Step-by-step explanation:
hello, there.
1) 2p + 3c = 17.50
2) 5p + 2c = 19.00
:
Solve equation 1 for p
:
p = (17.50 - 3c) / 2
:
Substitute for p in second equation
:
(5(17.50 - 3c) / 2) + 2c = 19.00
:
Multiply both sides of = by 2
:
(5(17.50 - 3c)) + 4c = 38.00
:
87.50 - 15c + 4c = 38.00
:
-11c = -49.50
:
c = 4.50
:
---------
Cashews are $4.50 per pound
--------------
:have a great day.
Answer:
C
Step-by-step explanation:
Let p represent the cost for one pound of peanuts and let c represent the cost for one pound of cashews.
Two pounds of peanuts and three pounds of cashews cost $17.50. So:
[tex]2p+3c=17.5[/tex]
Five pounds of peanuts and two pounds of cashews cost $19.00. So:
[tex]5p+2c=19[/tex]
This yields a system of equations.
We can solve this using elimination. We can multiply the first equation by -5, and the second by 2. Therefore:
[tex]-5(2p+3c)=-5(17.5)[/tex]
Multiply:
[tex]-10p-15c=-87.5[/tex]
And:
[tex]2(5p+2c)=2(19)[/tex]
Multiply:
[tex]10p+4c=38[/tex]
Now, we can add the two equations together:
[tex](-10p-15c)+(10p+4c)=(-87.5+38)[/tex]
Combine like terms:
[tex]-11c=-49.5[/tex]
Therefore:
[tex]c=4.5[/tex]
So, a pound of cashews costs $4.50.
Our answer is C.
Notes:
To solve for the cost for peanuts, we can use the first (or second equation) again:
[tex]2p+3c=17.5[/tex]
Substitute:
[tex]2p+3(4.5)=17.5[/tex]
Solve for p:
[tex]2p+13.5=17.5\Rightarrow 2p=4\Rightarrow p=2[/tex]
So, a pound of peanutes cost $2.00.
Mario and his 2 brothers are selling lemonade. Mario brought one and a half liters, Javier brought 2 liters, and Ernesto brought 450 milliliters. How many total milliliters of lemonade did the boys have? (1 L = 1,000 mL) *
Answers
Answer:
3,950
Step-by-step explanation:
See image for question.
Please show workings and diagrams.
Answers
Answer:
a) 258 kmb) 267°c) 87°Step-by-step explanation:
Refer to attached diagram (not to scale).Given details are reflected.First find the measure of angle Q
m∠Q = 36° + (180° - 125°) = 91°a) Use law of cosines to find x:
x = √(160² + 200² - 2160*200*cos 91°) = 258 km (rounded)Use the law of sines to find the missing angles:
258 / sin 91 = 160 / sin R = 200 / sin Pm∠R = arcsin (160 sin 91° / 258) = 38°m∠P = 180° - (91° + 38°) = 51°b) Bearing P from R:
360° - (55° + 38°) = 267°c) Bearing R from P:
36° + 51° = 87°Answer:
a) Use law of consines to find x:
x=(160 2+200 2-2160×200× cos 91 grades) =258 km.
b) Bearning P from R:
360 grades - ( 55 degrees + 38 degrees)
Write the fifteenth term of the binomial expansion of (a^2+b)^20
Answers
Answer:
The fifteenth term of the binomial expansion of [tex](a+b)^{20}[/tex] is [tex]38760\cdot a^{6}\cdot b^{14}[/tex].
Step-by-step explanation:
Let be a binomial of the form [tex](a+b)^{n}[/tex], where [tex]a, b\in \mathbb{R}[/tex] and [tex]n\,\in\mathbb{N}^{+}[/tex]. The expansion of this polynomial is defined below:
[tex](a+b)^{n} = \Sigma\limits_{k=0}^{n}\,\frac{n!}{k!\cdot (n-k)!}\cdot (a^{n-k}\cdot b^{k})[/tex] (1)
Where:
[tex]n[/tex] - Number of terms of the expanded polynomial.
[tex]k[/tex] - Index associated to [tex]k[/tex]-th term of the expanded polynomial.
For all [tex]n[/tex]-th binomial, we a sum of [tex]n+1[/tex] terms. If the given binomial has a term of [tex]20[/tex], then we have 21 terms and the fifteenth term of the polynomial corresponds to the [tex]14[/tex]-th term. Then, the fifteenth term of the binomial is:
[tex]c_{14} = \frac{20!}{14!\cdot 6!}\cdot (a^{6}\cdot b^{14})[/tex]
[tex]c_{14} = 38760\cdot a^{6}\cdot b^{14}[/tex]
The fifteenth term of the binomial expansion of [tex](a+b)^{20}[/tex] is [tex]38760\cdot a^{6}\cdot b^{14}[/tex].
A house painter mixed 5 gal of blue paint with every 9 gal of yellow paint in order to make a green paint. Which ratio of gallons of blue paint to gallons of yellow paint will make the same shade of green paint?
A. 30:54
B. 6:10
C. 10:45
D. 27:15
Answers
7/12 minus 1/6 gggggggggggggggggggg
Answers
Answer:
[tex] \frac{5}{12} [/tex]
Step-by-step explanation:
[tex] \frac{7}{12} - \frac{1}{6} \\ \\ = \frac{7}{12} - \frac{2}{12} \\ \\ = \frac{7 - 2}{12} \\ \\ = \frac{5}{12} [/tex]
Answer:
0.41666666666
or
5/12
Step-by-step explanation:
Grace earns $7 for each car she washes. She always saves $20 of her weekly earnings. This week, she wants to have at least $69 in spending money. How many cars must she wash? Enter and solve an inequality to represent this situation. Enter your value as a simplified mixed number, if necessary.
Answers
Answer:
She need to wash 9 cars
Step-by-step explanation:
Maria has two options for buying a new computer. She can pay $750 right now, or she can pay $24.99 each month for 3 years. How much more will Maria pay if she makes payments for 3 years?
Answers
Answer:
$149.64
Step-by-step explanation:
Recall that there are 12 months in a year. Thus, 3 years would be 36 months.
$24.99 times 36 months comes to $899.64. To determine how much more Maria will pay by making monthly payments is $899.64 less $750, or $149.64.
57.4g of sugar is needed to make 7 cakes. How much sugar is needed for 9 cakes?
Answers
Answer:
73.8 g
Step-by-step explanation:
57.4/7 = 8.2 per cake
8.2 x 9 = 73.8 g
Answer:
I'm pretty sure the answer would be 73.8g
Step-by-step explanation:
Solve for x. -4x + 6(6– 2x) = -7x – 36 Select one:
a. -7
b.15
c.8
d.3
Answers
Answer:
8
-4x+6(6-2x) = -7x - 36
-4x+36-12x = -7x-36
-16x+36 = -7x-36
-16x +7x = -36-36
-9x = -72
x = 72/9
x = 8
The Pythagorean Theorem states that, in a right triangle, the square of the length of the hypotenuse equals the
sum of the squares of the lengths of the legs. Which of these models support the validation of this theorem?
Answers
Mrs. Washington earns a gross salary of
$64,000. She paid 7% in income taxes in 2014.
Which of the following best represents the
amount of money Mrs. Washington paid in
income tax in 2014?
Answers
Answer:
$4480
Step-by-step explanation:
64,000*.07= 4480
How much interest does a $407 investment earn at 6% over seven years?
Answers
Answer:
$204.98
Step-by-step explanation:
407(1+0.06)^7
611.98
611.98-407
204.98
So it made $204.98
Hope this helps
Alina drew a model of a square pyramid. The dimensions of the model are
shown in the diagram.
Answers
Answer:
400
Step-by-step explanation:
Volume=⅓*B*h
B=10×10=100
Bh=100×12=1200
then divide by
1200÷3=4
The volume of a pyramid with a square base is 400 cm³.
What is a pyramid?A pyramid is a structure where outer surfaces are triangular and converge to a point at the top.
The volume of a pyramid with a square base is given as:
Volume = 1/3 x base area x height
We have,
The volume of a pyramid with a square base is given as:
Volume = 1/3 x base area x height
Now,
Height = 12 cm
Base area = 10² = 100 cm²
Now,
Volume.
= 1/3 x 100 x 12
= 400 cm³
Thus,
The volume of a pyramid with a square base is 400 cm³.
Learn more about pyramid here:
https://brainly.com/question/17615619
#SPJ7
2) A circle has an area of 121 ñ cm. Find its circumference. (Round your answer to the
nearest tenth.).
Answers
Answer:
If the area is 121 cm the answer is 38.99 if its 12 cm then the answer is 12.28
Step-by-step explanation:
Im not sure if correct but i tried
This is the graph of f(x). What is the value of f(3)?
Answers
Answer:
Option C. 8 will be your answer
Step-by-step explanation:
hope it helps you...
have a great day!!!
3. Which among the statements is true?
a. Every parallelogram is a rhombus.
b. Every rectangle is a square.
c. Every rhombus is a rectangle.
d. Every square is a rectangle.
Answers
PLEASE I ACTUALLY NEED HELP ;(
Answers
Answer:
[tex]\sqrt{18x^4y}[/tex]Step-by-step explanation:
3x²[tex]\sqrt{2y}[/tex] = [tex]\sqrt{(3x^2)^22y}[/tex] =[tex]\sqrt{18x^4y}[/tex]Answer:
√{18x⁴y}=√?
?=18x⁴y is your answer
What is the slope of the line that passes through the points (-10, 9) and (9, 9)
Answers
Step-by-step explanation:
the answer is on foto
y = 9
Which statement about the two triangles is correct?
Answers
Answer:
The second choice
Step-by-step explanation:
i dunno how to explain it
I WILL GIVE BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
IF YOU SEND ONE MORE LINK AGAIN I WILL REPORT YOU!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
What is your question
Step-by-step explanation:
I do not see a question
Answer:
where is the question at?
Step-by-step explanation: I don'tsee it
Each side of a square is 3inches long.a student increases the length of each side by 3inches.the are of the new Square is how many times the area of original square?
A=2
B-3
C=4
D=a
Answers
Hey, this is an ape3x question id really appreciate it if someone could help me on this..
Answers
Answer:
<4 and <8 are corresponding angle
What is the rate of change in the equation?
Answers
Answer:
-5
Step-by-step explanation:
The rate of change is normally the number not attached to X so in this equation it is-5.
Oliver deposits $1,000 in his Interest-bearing bank account. The balance increases by %15 each month
Answers
Step-by-step explanation:
Oliver deposits P= $1,000
Then total amount A after n months given that the balance increases by %15 each month can be calculated as
[tex]A= 1000(1+15/100)^n[/tex]
Assuming the increase in amount is compounded monthly.
Oliver lives in a state with no state income tax. He pays $180 in payroll tax each week. If the federal income tax is 0.75 of the payroll tax, how much are the other taxes?
Answers
Answer:
The other taxes are $135.
Step-by-step explanation:
From the information provided, you know that Oliver pays $180 in payroll tax and that the federal income tax is 0.75 of the payroll tax, so in order to find how much are the other taxes you have to calculate the 0.75 of the payroll tax Oliver pays:
180*0.75=135
According to this, the answer is that the other taxes are $135.