Answer:
42 + 2/3
Step-by-step explanation:
First, to calculate the sum of an infinite geometric series, our formula is
a₁/(1-r), with a₁ being the first term of the series and r being the common ratio. Therefore, we want to find both a₁ and r.
To find r, we can first determine that 2 * r = a₄ and a₄ * r = a₅, as the ratio separates one number from the next in a geometric series. Therefore, we have
2 * r * r = a₅
2 * r² = 1/8
divide both sides by 2 to isolate the r²
r² = 1/16
square root both sides to isolate r
r =± 1/4. Note the ± because r²=1/16 regardless of whether r = 1/4 or -1/4. However, because all terms are positive, r must be positive as well, or a₄, for example, would be 2 * (-1/4) = -0.5
Therefore, r = 1/4 .
To find the first term, we know that a₁ * r = a₂, and a₂ * r = a₃. Therefore, a₁ * r² = a₃ = 2
a₁ * 1/16 = 2
divide both sides by 1/16 to isolate a₁
a₁ = 2 * 1/ (1/16)
= 2 * 16
= 32
Plugging a₁ and r into our infinite geometric series formula, we have
a₁/(1-r)
= 32 / (1-1/4)
= 32/ (3/4)
= 32/ 0.75
= 42 + 2/3
A woman sold an article for 200 GH cedis and made a profit of 25%. Find the cost price of the article.
Answer:
160
Step-by-step explanation:
x = original price
x+ 25% x = 200
Change to decimal form
x + .25x = 200
1.25x = 200
Divide each side by 1.25
x = 200/1.25
x =160
The original price was 160
72°
Х
68
HSJDJFJDJFJRJDJFJDJFJFJJFHFJFJF
Answer:
140
Step-by-step explanation:
The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle
x = 72 + 68
x = 140
What is the sign of y + x?
y
0
Choose 1 answer:
Positive
B
Negative
Zero
Answer:
C
Step-by-step explanation:
As y is zero, y/x will be zero
1. The local ice cream shop has had a great month in sales. Based on the Information below, calculate the operating ratio.
cost of goods sold = $2,500.00
net sales = $18,200.00
operating expenses = $4,350.00
O 62 percent
O 38 percent
O 71 percent
O 32 percent
The operating ratio of the local ice cream shop is 38 percent
The cost of goods sold is $2,500
The net sales is $18,200
The operating expenses is $4,350
The operating ratio can be calculated as follows
= cost of goods sold+ operating expenses/total revenue
= 2500+4,350/18,200
= 6,850/18,200
= 0.376×100
= 37.6
= 38%
Hence the operating ratio is 38%
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What is the length of segment AB
A) 3
B) [tex]\sqrt{20}[/tex]
C) [tex]\sqrt{41}[/tex]
D) 9
Answer: [tex]\large \boldsymbol {C) \ AB=\sqrt{41} }[/tex]
Step-by-step explanation:
The formula for the distance between points:[tex]\bf AB= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] Coordinates of point A (0;5 ); coordinates of point B(4;0)[tex]\bf AB= \sqrt{(0-4)^2+(5-0)^2} =\sqrt{16+25} =\sqrt{41}[/tex]
collen family plans to paint the window of their house. her father will paint twice as many window as her mother, and collen and her 2 brothers will paint an equal number of the rest of the windows
Answer:
21 windows
Step-by-step explanation:
colleen's family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and Colleen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?
Answer: Let the number of window Colleen father would paint be x while that of her mother be y. Since her father will paint twice as many window as her mother, therefore the number of windows painted by the father x = 2y
Let the number of windows each painted by Colleen and her 2 brothers be z since they would paint the same number of windows. The total number of windows to be painted = 2y + y + z + z + z = 3y + 3z = 3(y + z).
Then number of windows needed to be painted by Colleen and her mother is given as z + y. Since Colleen painted 7 windows as her share and her mother share i.e. y + z = 7
Therefore the total number of windows = 3(y + z) = 3(7) = 21 windows
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Answer: The eldest child received $465,000, the middle child received $13,000, and the youngest received $93,000.
Step-by-step explanation: Subtracting $13,000 from $571,09 leaves the youngest and eldest’s money, $558,000. Dividing the amount left by 6 gives you the youngest siblings check and a total of $93,000. To find how much the eldest receives, you subtract $93,000 from $558,000 leaving the eldest $465,000.
268×7{34_56}÷890
Ayudaaa
268×7(34-56)÷890
= -5159
Must click thanks and mark brainliest
The width of a rectangle measures (2.3a + 9.9) centimeters, and its length
measures (6.3a - 2.6) centimeters. Which expression represents the perimeter, in
centimeters, of the rectangle?
12.2a +3.7
O 7.3 + 8.60
O 17.2a + 14.6
O 7.4 +24.4a
Answer:
17.2a+14.6
Step-by-step explanation:
What is the multiplicity of each of the roots of the graph of
f(x) = 2x4 + 12x} + 16x2 – 12x – 18?
A.-3, multiplicity 2; -1, multiplicity 1; 1, multiplicity 1
B.-3, multiplicity 2; 1, multiplicity 2
C.-3, multiplicity 1; -1, multiplicity 1; 1, multiplicity 1
D.-3, multiplicity 2; -1, multiplicity 3; 1, multiplicity 1
Answer:
The correct option is;
C. -3, multiplicity 2; -1, multiplicity 1; 1, multiplicity 1
Please find attached the required function graph
Step-by-step explanation:
To solve the equation f(x) = 2·x⁴ + 12·x³ + 16·x² -12·x - 18, by graphing the function, we have;
x [tex]{}[/tex] F(x)
-4[tex]{}[/tex] 30
-3[tex]{}[/tex] 0
-2[tex]{}[/tex] 6
-1[tex]{}[/tex] 0
0 [tex]{}[/tex] -18
1[tex]{}[/tex] 0
2[tex]{}[/tex] 150
The shape of a graph with multiplicity of 2
Given that the graph bounces of the horizontal axis at the y-intercept at point x = -3, the factor (x - 3) must be a quadratic of the form (x - 3)², thereby having a multiplicity of 2 in the solution which are;
x = 1, -1, and, giving
(x - 1)·(x + 1)·(x - 3)² = 0
Therefore, the correct option is -3, multiplicity 2; -1, multiplicity 1; 1 multiplicity 1.
Answer:
C
Step-by-step explanation:
Help anyone can help me do the question,I will mark brainlest.
area of shaded region is 537.5cm^2
11. House Prices In 1985, the median selling price of an
existing single-family home in Atlanta, Georgia, was
$66,200. Between 1985 and 1990, the average price in-
creased by 30%. Between 1990 and 2005, the average
price increased again, this time by 15%. What was the
median house price in Atlanta in 2005? -
Answer:
$98,969Step-by-step explanation:
$66,200 - the median selling price of a home in 1985
and the price increased by 30%:
66,200•30% = 66,200•0.3 = 19,860
66,200 + 19,860 = 86,060
$86,060 - the median selling price of a home in 1990
and the price increased by 15%
86,060•15% = 86,060•0.15 = 12,909
86,060 + 12,909 = 98,969
$98,969 - the median house price in Atlanta in 2005
If graphs have a linear equations in a system are concurrent having the same slope and the same y-intercept what does that mean about possible solutions
Answer:
Infinite Amount of Solutions
Step-by-step explanation:
Since we have concurrent systems (same slope + same y-int), we know that the systems of equations would be the exact same line. If that is the case, the we would know that ANY value input would work. You could even test it mathematically, and it would give you infinite amount of solutions.
y=1/3x+5 through (2,1)
Answer:
No solution
Step-by-step explanation:
1 = 1/3(2) + 5
1 = 17/3
1 is not equal to 17/3
so the answer has no solution meaning the point does not exist in the graph.
Helppp plssss help meeee
Answer:
C. $1,260
Step-by-step explanation:
80 × 14.5 = 1,160
2,500 × 0.04 = 100
Answer:
C. $1260
Step-by-step explanation:
2. A business man sold an article at a gain of 10%. Had he sold the article at a gain of 20% he would have gained Rs. 55 more. Find the cost price of the article.
Step-by-step explanation:
Let SP1 be x
P%=10%
CP=SP×100/100+%P
= x+100/100+10
= 100x/110
SP2= x+55
CP= SP×100/100+%P
or 100x/110= x+55×100/120
or x/110=x+55/120
or 24x-22x=22×55
or 2x=1210
or x=1210/2
or x=605
Now,
CP=100x/110
=100×605/110
=60500/110
=Rs 550
A wall in Marcus's bedroom is 8 2/5 feet high and 16 2/3 feet long. If he paints 1/2 the wall blue, how many square feet will be blue?
Answer:
70 ft^2
Step-by-step explanation:
Find the area of the wall
A = l*w where l is the length and w is the width
A = 8 2/5 * 16 2/3
Change to improper fractions
A = 42/5 *50/3
Rewriting
A = 42/3 * 50/5
= 14 * 10
A = 140 ft^2
He paints 1/2
1/2 (140) = 70 ft^2
Question 4 Choice Worth 4 point
On a coordinate grid both point (1, 2) and point (-3, -3) are reflected across the y-axis. What are the coordinates of the reflected points
What is the volume of this rectangular prism?
Answer:
1
Step-by-step explanation:
rectangular prism volume = Width * Height * Length
Width = 1.33
Height = .6
Length = 1.25
volume = 1
Will Mark Brainlest Help pls
Answer:
Hello,
[tex]\begin{bmatrix}-2&2\\3&5\\\end{bmatrix}\\\\[/tex]
Step-by-step explanation:
[tex]\begin{bmatrix}2&3\\5&7\end{bmatrix}-A=\begin{bmatrix}3&1\\-2&-3\end{bmatrix}+\begin{bmatrix}1&0\\0&1\end{bmatrix}\\\\\\\begin{bmatrix}2&3\\5&7\end{bmatrix}-A=\begin{bmatrix}2&3\\5&7\end{bmatrix}-\begin{bmatrix}4&1\\-2&-2\end{bmatrix}\\\\\\A=\begin{bmatrix}-2&2\\3&5\end{bmatrix}\\\\[/tex]
A room is twice as long as it is broad and its height is 8 m. if the cost of painting its walls at Rs. 20 per m² is Rs 9600 , find the cost of carpeting its floor at Rs. 400 per m²
Answer:
Step-by-step explanation:
no body is answering
based on the graph the coordinates for do1 of x
Answer:
(4,0)
Step-by-step explanation:
1. X= (4,0) the coordinates of x
can u help me on this... I will mark u as brilliant students.. plz
Answer:
For number 5 . a= 3 and b = -1
A machine fills 680 bottles in 5hours how many bottles will it fill in three hours?
Answer:
408 bottles
Step-by-step explanation:
the machine can fill 136 bottles in 1 hour, 136×3=408
Answer:
408
Step-by-step explanation:
680 bottles in 5 hours
in three hours:
1 hour =680/5=136
in three hours:it will be 136*3=408
how many terms are there in the expressions 1 + 2k - j
Answer:
3 terms
Step-by-step explanation:
A term in mathematics, especially in Algebra, could be a number, a variable, variable together with a number or variables multiplied together as a single whole. Terms are usually separated with either negative or positive sign in an expression.
In the expression, [tex] 1 + 2k - j [/tex] , there are 3 terms here spared by either the negative sign or the positive.
The 3 terms are: [tex] 1, 2k, j [/tex].
Where v is the final velocity (in m/s), u is the initial velocity (in m/s), a is the acceleration (in m/s²) and s is the distance (in meters). Find v when u is 8 m/s, a is 3 m/s², and s is 19 meters. A. 15 m B. 130−−−√ m C. 178−−−√ m D. 13 m
Answer:
C. 178−−−√ m
Step-by-step explanation:
Given the following :
v = final velocity (in m/s)
u = initial velocity (in m/s)
a = acceleration (in m/s²)
s = distance (in meters).
Find v when u is 8 m/s, a is 3 m/s², and s is 19 meters
Using the 3rd equation of motion :
v^2 = u^2 + 2as
v^2 = 8^2 + 2(3)(19)
v^2 = 64 + 114
v^2 = 178
Take the square root of both sides :
√v^2 = √178
v = √178
HELLLOPPPPPPP HELPPP ASAPPP PLEASE !!
Answer:
10 = c
Step-by-step explanation:
Distribute -4 to the parentheses:
8 = 8c - 4(c + 8)
8 = 8c - 4c - 32
Add like terms:
8 = 4c - 32
Add 32 to both sides:
40 = 4c
10 = c
Answer:
Question:
8=8c-4(c+8)
Step-by-step explanation:
8=8c-4c-32
8=4c-32
8+32=4c
40=4c
Or
4c=40
c=10
Who’s salary represents the median of the data in the table?
Answer:
Rajesh salary is the median
Step-by-step explanation:
Am not good in explanation
Answer:
1: Ram
Step-by-step explanation:
The median is the middle number in a sorted, ascending or descending, list of numbers and can be more descriptive of that data set than the average. The median is sometimes used as opposed to the mean when there are outliers in the sequence that might skew the average of the values
if we put these salaries in order we can find out what the median salary is.
32,701 , 45,600 , 52,000 , 67,250 , 71860.
The number in the centre or the middle is 52,000. That is Ram's salary.
The answer is 1. Ram
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Find the missing side of this right
triangle.
Х
7
12
X =
V[?
Answer:
[tex]\sqrt{193}[/tex]
Step-by-step explanation:
[tex]a^{2} +b^{2} =c^{2}[/tex]
a = 7
b = 12
[tex]7^{2} + 12^{2}[/tex] = 193
I hope this helped!! :)have a great day! :) Help me!!! Please to solve this problem of o. Math
a) Given a function f(x) = 2x + 3. Find (a) f(1), (b) f(-5), (c) f(a), (d) f(a + 2) (e) f(b)?
b) let f(x) = x + 4 define a function in the closed interval of -55x55, find f(-2), f(3) and f(7).
a:-
f(x)=2x+3
[tex]\\ \rm\Rrightarrow f(1)=2(1)+3=2+3=5[/tex]
[tex]\\ \rm\Rrightarrow f(-5)=2(-5)+3=-10+3=-7[/tex]
[tex]\\ \rm\Rrightarrow f(a)=2a+3[/tex]
[tex]\\ \rm\Rrightarrow f(a+2)=2(a+2)+3=2a+4+3=2a+7[/tex]
[tex]\\ \rm\Rrightarrow f(b)=2b+3[/tex]
b:-
f(x)=x+4
[tex]\\ \rm\Rrightarrow f(-2)=(-2)+4=2[/tex]
[tex]\\ \rm\Rrightarrow f(3)=3+4=7[/tex]
[tex]\\ \rm\Rrightarrow f(7)=7+4=11[/tex]
Step-by-step explanation:
[tex]thank \: you[/tex]