Answer:
S₉ = 255.5
Step-by-step explanation:
the sum to n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 0.5 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{1}{0.5}[/tex] = 2 , then
S₉ = [tex]\frac{0.5(2^{9}-1) }{2-1}[/tex]
= [tex]\frac{0.5(512-1)}{1}[/tex]
= 0.5(511)
= 255.5
Brandon invested $41,000 in an account paying an interest rate of 3% compounded
continuously. Evan invested $41,000 in an account paying an interest rate of 37%
compounded quarterly. To the nearest dollar, how much money would Brandon have
in his account when Evan's money has doubled in value?
After 1.959 years Evan's money has doubled in value and at that time Brandon have $43,481.78 in his account.
What is compound interest?It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.
We can calculate the compound interest using the below formula:
[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]
Where A = Final amount
P = Principal amount
r = annual rate of interest
n = how many times interest is compounded per year
t = How long the money is deposited or borrowed (in years)
Let's suppose, after t time, Evan's money has doubled in value.
[tex]\rm 2P = P(1+\dfrac{0.37}{4})^{4t}[/tex]
After solving
x = 1.959 years
Use x = 1.959 years to get how much money would Brandon have.
[tex]\rm A = P e^{rt}[/tex]
[tex]\rm A = 41000\times e^{0.03\times 1.959}[/tex]
A = $43,481.78
Thus, after 1.959 years Evan's money has doubled in value and at that time Brandon have $43,481.78 in his account.
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Someone can you please help me thank you 12 points
Answer:
The image isn't quite clear
Find the quotient 3 6/7 divided by 5/21
Pls explain bc I’m having finals and I need a bit more help with this
Answer:
81/5 or 16 1/5.
Step-by-step explanation:
First convert the mixed number to an improper fraction:
3 6/7
= (3*7 + 6) / 7
= 27/7.
So we have
27/7 / 5/21
Invert the second fraction and multiply:
= 27/7 * 21/5
= (27*21) / (7*5)
= (27*3) / 5 ( as 21/7 = 3)
= 81/5
= 16 1/5.
Find the surface area of a cylinder the has a base radius of 2 feet and the height of 14 feet
Answer: If I am correct the answer is 201.06ft²
please do correct me if i am wrong.
Step-by-step explanation:
A=2πrh+2πr2=2·π·2·14+2·π·22≈201.06193ft²
A craft store sells 9 cm of ribbon for $0.72 . Write an equivalent rate that shows the cost of 27 cm of ribbon
Answer:
$2.16
Step-by-step explanation:
if the store sells 9 cm for $0.72
they are selling 27 cm now which is 3 times the amount of 9
so if 27 is 3 x the amount of cm than we need to triple to amount of the cost to.
and 0.72 x 3 is 2.16.
Please Vote Me Brainliest. Thank You.
what is the equation of the parabola?
a- y= -1/8(x+3)^2 +2
b- y=1/8(x-3)^2-2
c-y=1/8(x+2)^2+3
d-y=-1/8(x-2)^2-3
WILL GIVE BRAINLIEST
Answer:
D. y = -1/8(x-2)² - 3
Step-by-step explanation:
General eqaution of a parabola : y = a(x-h)² + k where (h,k) is the vertex and a determines whether the parabola goes up or down as well as the width of the parabola
step 1 identify vertex
the vertex is the point that starts the curve
the vertex appears to be at (2,-3)
step 2 plug in h and k using the x and y values of the vertex
again we have y = a(x-h)² + k where (h,k) is the vertex
here the vertex is (2,-3) so h = 2 and k = -3
we get y = a(x-2)² - 3
because the curve goes down a must be negative 1/8
so the final equation would be y = -1/8(x-2)² - 3 meaning D would be the answer
Which represents the area of the shaded region?
area of the circle – area of the square – area of the triangle
area of the triangle – area of the square + area of the circle
area of the triangle + area of the square + area of the circle
area of the circle – area of the triangle + area of the square
The area of the shaded region is Area of the Circle - Area of the Triangle + Area of the Square.
Hence, option D) is the correct answer.
What is the representation of the area of the shaded region?From the diagram below;
A triangle is inscribed in a circleA Square is inscribe in a triangle.Only the the circle and square are shaded.To get the shaded region, we say;
Area of the Circle - Area of the Triangle + Area of the Square.
The area of the shaded region is Area of the Circle - Area of the Triangle + Area of the Square.
Hence, option D) is the correct answer.
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What is the volume of the rectangular prism?
94.5 yd3
58.0 yd3
25.5 yd3
20.5 yd3
Answer:
94.5yd³
Step-by-step explanation:
volume = length × width × height
length = 7 yd , width = 4.5 yd and height = 3 yd
so volume = 7 × 4.5 × 3 = 94.5yd³
I need help with this asap (50 Points)
Answer:
Multiply this measurement by two to account for both sides. Add the three separate measurements together. Because surface area is the total area of all of the faces of an object, the final step is to add all of the individually calculated areas together.
Step-by-step explanation:
a kiddie pool is 10 feet long and 5 feet wide. surrounding each side of the kiddie pool is a cement walkway of uniform width. The combined area of the pool and the walkway is 104 ftsquared. Find the width of the walkway.
Answer:
1.59 ft.. sort of
Step-by-step explanation:
4th and final attempt:
10 * 5 + 2(10x + 2x) + 2(5x) = 104
50 + 2(12x) + 10x = 104
50 + 24x + 10x = 104
50 + 34x = 104
34x = 104 - 50
34x = 54
x = 54 / 34
x ~= 1.59
On a coordinate plane, a line is drawn from point a to point b. point a is at (9, negative 8) and point b is at (negative 6, 7). what are the x- and y- coordinates of point p on the directed line segment from a to b such that p is two-thirds the length of the line segment from a to b? x = (startfraction m over m n endfraction) (x 2 minus x 1) x 1 y = (startfraction m over m n endfraction) (y 2 minus y 1) y 1 (2, –1) (4, –3) (–1, 2) (3, –2)
Using proportions, it is found that the coordinates of p in the line segment are given as follows: (-1,2).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the points are:
Point a(9, -8).Point b(-6, 7).Point p(x, y).p is two-thirds the length of the line segment from a to b, hence:
[tex]p - a = \frac{2}{3}(b - a)[/tex]
For the x-coordinate, we have that:
[tex]x - 9 = \frac{2}{3}(-6 - 9)[/tex]
x - 9 = -10
x = -1
For the y-coordinate, we have that:
[tex]y + 8 = \frac{2}{3}(7 - (-8))[/tex]
y + 8 = 10
y = 2.
The coordinates of p are (-1,2).
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Answer: (-1,2)
Step-by-step explanation: took the test, got it right!
I would very much like to thank Aklee18oo for everything. this is my last question please see the attachment.
Answer:
8mm
Step-by-step explanation:
The volume of a cylinder is the base area times the height. The base is a circle, and we are not given the radius, so let the radius of the circle of the base of the circle be r. The area of a circle would be [tex]\pi r^{2}[/tex]. This multiplied by the height, which is 15, is [tex]15\pi r^{2}[/tex]. The volume is given to be 753.6, so we can make this an equation:
753.6 = [tex]15\pi r^{2}[/tex]
We are told to use 3.14 for pi, so:
[tex]753.6 = 15 * 3.14 * r^{2}[/tex]
[tex]r^{2} = 16[/tex]
[tex]r = 4[/tex]
The diameter is twice the radius, so the diameter is 8mm.
Answer:
8 mm
Step-by-step explanation:
Formula to find volume :
Volume (cylinder) = πr²h
⇒ 753.6 = 3.14 × r² × 15
⇒ 47.1 × r² = 753.6
⇒ r² = 753.6/47.1
⇒ r² = 16
⇒ r = 4 mm
Relating radius and diameter :
Diameter = 2 × Radius
⇒ Diameter = 2 × 4 mm
⇒ Diameter = 8 mm
Find the volume of the figure below. round if necessary.
Answer:
Step-by-step explanation:
Question 8 of 10
If you vertically compress the absolute value parent function, f(x) = 1x1, by a
factor of 3, what is the equation of the new function?
A. g(x) = |3|
B. g(x) = 3|4|
O C. g(x) = |x - 3|
D. g(x) = 1/3|x|
Answer:
your answer should be c
Step-by-step explanation:
5 star?
If you vertically compress the absolute value parent function, f(x) = 1x1, by a factor of 3 then the equation of the new function is g(x) = (1/3)|x|
What is a function?A relation is a function if it has only One y-value for each x-value.
The absolute value function, f(x) = |x|, has a "V" shape with the vertex at (0, 0).
f(x) can also be called as parent function.
A parent function is the simplest function that still satisfies the definition of a certain type of function
When we vertically compress the graph by a factor of 3, we are multiplying the y-value by 1/3.
So the new function g(x) can be expressed as:
g(x) = (1/3) f(x)
g(x) = (1/3)|x|
Hence, if you vertically compress the absolute value parent function, f(x) = 1x1, by a factor of 3 then the equation of the new function is g(x) = (1/3)|x|
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what is the domain of f(x)=2log _3(4x−8)
Answer:
{X€ IR : x>2}
Or
[tex]x \in \: )2 \: + \infty ([/tex]
Slove the inequality for u.
23> u-2
Answer:
u < 25.
Step-by-step explanation:
u - 2 < 23
Add 2 to both sides:-
u - 2 + 2 < 23 + 2
u < 23 + 2
u < 25.
Answer:
23+2>u
25>u
(25,-∞)
this is the answer
coles rectangular garden has an area of 54 square feet what could be the dementions of the garden
Answer:
The garden dimension are 9ft and 6ft
Step-by-step explanation:
As promised, Ive attached my work
There also could be the sizes of
3ft by 18ft
2ft by 27ft
1ft by 54ft
Explain how to use a protractor to find the measure of angle RTV.
Answer:
How to measure an angle with a protractor:
Place the midpoint of the protractor on the VERTEX of the angle.
Line up one side of the angle with the zero line of the protractor (where you see the number 0).
Read the degrees where the other side crosses the number scale.
Step-by-step explanation:
you can use a protractor to measure and draw angles. To measure angles with a protractor, first place the center point along the bottom edge of the protractor over the vertex of the angle you're measuring. Line up the bottom edge of the protractor with one leg of the angle.
If UV = 8x − 12, VW = x + 8, and UW = 2x + 10, what is UW?
Answer:
Find the value of x
In this problem i will assume that U,V and W are collinear and V is between U and W
so
----> by addition segment postulate
substitute the given values
solve for x
step 2
Find the value of VW
substitute the value of x
Step-by-step explanation:
helppppppppp asa-pppppppppppppppppp-
Answer:
I got the mean of A is 6 and the mean of b is 3.5
Step-by-step explanation:
If correct i dont mind brainlest
1. Juanita is thinking of two positive whole
numbers. The sum of the whole numbers
is 15. How many possible whole number
combinations are there?
Answer:
i believe its seven combinations
Step-by-step explanation:
=
Interim Checkpoint: Grade 7 Checkpoint 4 - Part 1
Write an equation that you can use to solve for X.
Enter your answer in the box.
100°
60
60 is the amazing cool answer XD
cane someone do this please
The product of the matrices is an identity matrix. Then Both the matrices are multiplicative inverse to each other.
What is the matrix?A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The a_{ij} element in a matrix, such as M, refers to the i-th row and j-th column element.
The matrices are given below.
[tex]\left[\begin{array}{ccc}-3&7\\-2&5\end{array}\right] \ and \ \left[\begin{array}{ccc}-5&7\\-2&3\end{array}\right][/tex]
Then show that both the matrices are multiplicative inverse to each other.
If the product of the matrices is an identity matrix then the matrices are multiplicative inverse to each other.
Then we have
[tex]\left[\begin{array}{ccc}-3&7\\-2&5\end{array}\right] \left[\begin{array}{ccc}-5&7\\-2&3\end{array}\right] = \left[\begin{array}{ccc}1&0\\0&1\end{array}\right][/tex]
Then both the matrices are multiplicative inverse to each other.
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The measures of the angles of a triangle are shown in the figure below. Solve for x.
(2x+17)°
(2x+5)°
Step-by-step explanation:
or, x°+(2x+17)°(2x+5)°=180°
or, x°+2x°+17°+2x°+5°=180°
or, 5x°+22°=180°
or, 5x°=180°-22°
or, 5x°=158°
or, x°=158/5
or, x°=31.6
now,
(2x+17)°=2*31.6+17=80.2°
(2x+5)°=2*31.6+5=68.2°
Two companies offer river tubing trips.
• The first company charges $7.50 rental fee for the tube and $3.00 an hour.
• The second company charges $10.50 rental fee for the tube and $2.00 an hour.
What is the minimum number of hours a person would need to rent a tube in order for
the second company to be a better deal?
Minimum number of hours which a person need to rent a tube in order for the second company to be a better deal is more than 2.5 hours.
What is a mathematical model?A mathematical model is the model which is used to explain any system, the effect of the components by study and estimate the functions of systems.
Two companies (first and second) offers river tubing trips and the rates of them are as follows: The first company charges $7.50 rental fee for one tube, with a charge of $3.00 an hour.
For the x hours, the charge of the company is,
7.50+3.00x
The second company charges $10.50 rental fee for one tube with a charge of $2.00 an hour. For the x hours, the charge of the company is,
10.50+2.00x
Let x is the hour at which the cost of both companies are equal. Thus,
7.50+3.00x=10.50+2.00x
3x-2x=10.5-7.5
x=2.5
Thus, the minimum number of hours which a person need to rent a tube in order for the second company to be a better deal is more than 2.5 hours.
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Match each mineral property to the correct description. HELP PLS
lmk if any of these are wrong :)
Answer:
Left Side A → Right Side A
Left Side B → Right Side B
Left Side C → Right Side E
Left Side D → Right Side D
Left Side E → Right Side C
Answer:
The person above me is probably correct on theirs, but failed to realize that its mixed up differently on everyone else’s. Here are the answers-
Need some help, please explain your Answer! Thanks!
Unit rate
Total built/Total days spent8-1/4÷5-1/233/4÷11/233/4×2/113/21.5miles per dayAnswer:
1½ miles/day .
Step-by-step explanation:
To find:-
The rate at which the construction crew built thr road.Answer:-
It is given that the crew made 8¼ miles of road in 5½ days . To find the rate of work done , simply divide the total length of road nade by total time taken . That would be , ( rate is represented by "r" . )
[tex]:\implies \sf r = 8\dfrac{1}{4}\div 5\dfrac{1}{2} \ miles/day\\[/tex]
Convert the mixed fraction into improper fraction.
[tex]:\implies \sf r = \dfrac{33}{4}\div \dfrac{11}{2} \ miles/day \\[/tex]
For dividing them , multiply the reciprocal of 11/2 by 33/4 as ,
[tex]:\implies \sf r = \dfrac{33}{4}\times \dfrac{2}{11} \ miles/day\\[/tex]
[tex]:\implies \sf r = \dfrac{3}{2} \ miles/day \\[/tex]
[tex]:\implies \sf \pink{ r = 1\dfrac{1}{2}\ miles/day } \\[/tex]
Hence the unit rate of constructing the road is 1½ miles/day .
The price went down by 15%, and went 340 money. What was the previous price? ASAPP PLSS
The previous price given the percentage decrease is 400.
How to find the previous price?It follows from the task content that the previous price of the commodity is required;
let, x = previous price
New price = 340
Percentage decrease = 15%
Hence, it follows from the given information that;
340 = x - (15% × x)
340 = x - (0.15x)
340 = 0.85x
x = 340/0.85
x = 400
Therefore, the previous price given the percentage decrease is 400.
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What is the shortest time it takes it to collect a container of water?
Answer:
45 minutes
Step-by-step explanation:
The minimum of a box-and-whisker plot is the leftmost endpoint, called the "whisker". This minimum is the smallest value collected in the data.
your parents are trying to decide what company to invest their money in for your college tuition expenses. They are given the annual profit for the last five years of two companies they are interested in
To make an informed decision about the best place to invest money, there would have to be an evaluation of the best company and their annual profits.
What is a Financial Investment?This refers to the placing of money or asset with the hope and plan that it would appreciate after a certain period of time.
Hence, we can see that because your question is incomplete, a general overview has to be used, and thus, by the use of financial analysis by checking the annual profit over the last five years, the best choice would emerge.
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