The sum of the first 14 terms of the finite geometric series 0.5+ (-1) +2+... is -2730.5
How to determine the sum of the series?The series is given as:
0.5+ (-1) +2+...
The above series is a geometric series, with the following parameters:
First term, a = 0.5Common ratio, r = -2Number of terms, n = 14The sum of the first 14 terms is calculated using:
[tex]S_n= a *(1 - r^n) \div (1 - r)[/tex]
So, we have:
[tex]S_{14}= 0.5 *(1 - (-2)^{14}) \div (1 + 2)[/tex]
Evaluate
[tex]S_{14}= -2730.5[/tex]
Hence, the sum of the series is -2730.5
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Steven is puiting a design that contains two repeating patterns that start in the same place. One pattern repeats every 12 inches and the other repeats every 18 inches. How many inches will it take for the patterns to begin together again?
Answer:
36
Step-by-step explanation:
So, taking 12 inches and 18 inches, we can figure out where they both meet. To do this, you want to change these number into a fraction (12/18). Simplifying this gives you 2/3. So if you flip this fraction (3/2) and then use these number and multiply them with the first numbers (so we do 3*12 and 2*18, they both equal 36, so they would both meet at 36, our final answer. they would also meet at 72, 108, 144, etc. if you were to keep going.
Simplify: [tex]\sqrt{\frac{144}{25} }[/tex].
Answer:
[tex]\frac{12}{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{\frac{144}{25}}=\frac{\sqrt{144}}{\sqrt{25}}=\frac{12}{5}[/tex]
Given term:
[tex]\sqrt{\dfrac{144}{25} }[/tex]
This term can also be written as;
[tex]\implies \sqrt{\huge\text{(}\dfrac{144}{25} \huge\text{)}}[/tex]
Clearly, we can see that 144 and 25 are perfect squares. Then,
[tex]\implies\sqrt{\huge\text{(}\dfrac{12^{2} }{5^{2} } \huge\text{)}}[/tex]
According to an exponent property, (a²/b²) = (a/b)². Then,
[tex]\implies\sqrt{\huge\text{(}\dfrac{12}{5} \huge\text{)}^{2} }[/tex]
Since 12/5 is being squared inside the root, we can remove the squared symbol and take out 12/5 from the root. Then we get;
[tex]\implies\sqrt{\huge\text{(}\dfrac{12}{5} \huge\text{)}^{2} } \ = \ \dfrac{12}{5} \ = \ \boxed{2.4}[/tex]
Therefore, the simplified term is 2.4.
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What is the slope of the line that
passes through these two points?
(2, 3)
(2,9)
Answer:
Slope = undefined.
Step-by-step explanation:
Given two points:
(2,3) & (2,9)To Find:
The slopeSolution:
Using slope's formulae,
[m denotes slope]
[tex] \boxed{ \rm{m = \cfrac{y_2 -y_1 }{x_2 - x_1} }}[/tex]
According to the question,here:
(y_2,y_1) = (9,3)(x_2,x_1) = (2,2)Substitute them onto the formulae:
[tex] \rm \: m = \cfrac{9 - 3}{2 - 2} [/tex]
Simplify.
[tex] \rm \: m = \cfrac{6}{2 - 2} [/tex]
[tex]\rm \: m = \cfrac{6}{0} = \boxed{ \rm \: undefined}[/tex]
if an expression contains division by 0 , then It's undefined.
So, slope(m) = undefined.
Round off 380•59 to the nearest whole number easy 5points
Answer:
381
Step-by-step explanation:
that's the nearest whole number
state the value of factorial 6 !
[tex] \\ [/tex]
ty! ._.
[tex]x^{2} +x = 12[/tex]
answer ?
Answer:
x = 4 and x = -3
Step-by-step explanation:
⇒ x² + x = 12
⇒ x² + x - 12 = 0
⇒ x² + 3x - 4x - 12 = 0
⇒ x(x + 3) - 4(x + 3) = 0
⇒ (x - 4)(x + 3) = 0
⇒ x = 4 and x = -3
Hey there!
x^2 + x = 12
SUBTRACT 12 to BOTH SIDES
x^2 + x - 12 = 12 - 12
SIMPLIFY IT!
x^2 + x - 12 = 0
SET the FACTORS to EQUAL to 0
x - 3 = 0 OR x + 4 = 0
SIMPLIFY IT!
x = 3 or x = -4
Therefore, the answer is:
x = 3 or x = -4
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Acidity is measured on the pH scale. The acidity of a substance is given by pH=−logH, where H is the concentration of Hydrogen ions. If a substance has a pH of 7, what is its H value?
Answer:
1 x 10^-7
Step-by-step explanation:
[H+] = 10^-pH
[H+] = 10^-7
Multiply 3hrs 40mins by 7
Answer:
25 hour 40 minutes
Step-by-step explanation:
3 hrs X 7 is = 21 hours
then you mutliply 40 mins times 7 which is equal to 280mins
the you divide 280mins by 60 mins because 60 minutes is equal to an hour and you come out with 4 hours and 40 minutes which you add to 21 which is equal to 25 hours!
Hope This Helps!
Which graph represents a circle whose equation is (x+3)² + (y-1)² = 4?
Answer:
A
Step-by-step explanation:
Equation describing a circle: (x - x0)^2 + (y - y0)^2 = r^2
(x0, y0) is the centrer is short for radiusThe given equation is: (x + 3)^2 + (y - 1)^2 = 4
=> (x - (-3))^2 + (y - 1)^2 = 2^2
Coordinates of the centre: (-3, 1)Radius: 2Therefore, the answer is A.
Add 3/4 + (−2 1/2) using the number line.
Select the location on the number line to plot the sum.
Answer:
Heyyy!!!!
Alrighty... here it goes....
Step-by-step explanation:
3/4 + (-2 1/2)
okay... the first thing you have to do is convert 1/2 into fourths. that'll make it way easier to solve..... like way easier.....
then rewrite the expression to get 3/4 + (-2 2/4)
now we know that + - = -
basically you subtract since adding a negative makes you subtract...
3/4 - 2 2/4 gives you - 1 3/4
all you have to do is plot that on the number line and you should be good to go
Assume you are going to buy a new Nissan Rouge priced at $38250.00 and after the deal you have found out that the sales tax is 9%. Estimate the answer
At a Forex Bureau, one US dollar costs Ug.sh.2800. How much Ugandan shillings will a tourist who has US dollars 600 get?
Answer:
1,680,000 shillings
Step-by-step explanation:
As one US dollar is 2800, and the dollar is repeated 600 times. You multiply Both
=2,800×600
=1,680,000 shillings
--~Hope you understood~--
Find the perimeter of the figure to the nearest hundredth. perimeter: about cm
The perimeter of the figure to the nearest hundredth is 50.26 cm.
Perimeter of a figure.The perimeter of a figure is the sum of the whole sides of the figure.
The perimeter of the figure can be found as follows:
perimeter of the figure = 12 + 5 + 5 + circumference of the semi circle
circumference of the semi circle = πr
where
r = radiusperimeter of the figure = 22 + πr
perimeter of the figure = 22 + 3.14(9)
perimeter of the figure = 22 + 28.26
perimeter of the figure = 50.26 cm
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Can someone help me with this please?
f hi I chhiring Tamang I read in hdidieje
A regular-size box of dog treats measures 314 inches by 712 inches by 12 inches. The manufacturer also sells a small-size box that has a volume that is 310 of the volume of the regular-size box.
What is the volume of the small-size box of dog treats?
Enter your answer as a mixed number in simplest form by filling in the boxes.
(its going to be a mixed number) in³
The volume of the small-size box of dog treats will be equal to V=8654.24 In³
What is volume?Volume is defined as the space occupied by any body in the three-Dimensions. All three parameters are required for the volume like length,width and height of the cube or Cuboid
The volume of the rectangular box will be:-
V=LxWxH
V=314x712x12
So the volume of small size box will be:-
V=2682816÷310=8654.24
Hence the volume of the small-size box of dog treats will be equal to
V=8654.24 In³
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Evaluate the difference quotient
f(x)-f(1)/X-1, where f(x)=X +5/x+1
Answer:
C) [tex]\displaystyle\frac{-2}{(x+1)}[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{f(x)-f(1)}{x-1}\\ \\\frac{\frac{x+5}{x+1}-\frac{1+5}{1+1}}{x-1}\\ \\\frac{\frac{x+5}{x+1}-\frac{6}{2}}{x-1}\\\\\frac{\frac{2(x+5)}{2(x+1)}-\frac{6(x+1)}{2(x+1)}}{x-1}\\\\\frac{\frac{2(x+5)-6(x+1)}{2(x+1)}}{x-1}\\\\\frac{\frac{2x+10-6x-6}{2(x+1)}}{x-1}\\\\\frac{\frac{-4x+4}{2(x+1)}}{x-1}\\\\\frac{\frac{-4(x-1)}{2(x+1)}}{x-1}\\\\\frac{-4}{2(x+1)}\\ \\\frac{-2}{(x+1)}[/tex]
Nannette buys a $5000 20-year bond that has a coupon rate of 2.5 %. If she keeps the bond to maturity, how much money plus principal interest will she have collected over the life of the bond?
The total amount collected over the life of the bond is $7,500.
What is the total amount collected?A bond is a debt instrument that entitles its holder to regular interest payments. At the end of the life of the bond, the bondholder receives the amount invested back.
Total earnings = interest + amount invested
(20 x 0.025 x 5000) = $2500
Amount invested = $5000
= 2500 + 5000 = $7,500
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What is the area of the triangle Base is 6 ft height is 5 ft.
Answer:
Area of a triangle = 0.5 * base * height = 0.5 * 6 * 5 = 15 sq. ft
Answer:
Area = 0.5 * base * height
0.5 * 6 * 5 = 15
Area = 15 sq ft
Evaluate 6ab + 2c if a = 3, b = 10, and c = 7
Answer:
6 (3 ×10 ) + 2 (7)
6(30) + 14
180 + 14
= 194
Answer: 194
Step-by-step explanation:
Given:
6ab + 2c
a = 3, b = 10, c = 7
Solve:
1. Plug in what you know and solve for your answer
⇒ 6(3)(10) + 2(7)
⇒ 6(30) + 14
⇒ 180 + 14
⇒ 194
33. Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number.
505 m² :519 m ²
505 m ²: 533 m ²
497 m ²: 519 m ²
497 m ²: 533 m ²
Answer: ⬇️⬇️⬇️⬇️
Lateral area = 505 m² ; Surface area = 519 m²
Hope I helped
Lateral area = Perimeter x height
Lateral area = (2 + 7 + 7.28) x 31 = 16.28 x 31 = 505 m²
Surface area = 2(1/2 x 2 x 7) + 505 = 519 m²
Answer: Lateral area = 505 m² ; Surface area = 519 m²
What is the median of this data set?
{16, 16, 16, 19, 20, 22, 23, 24, 24}
Answer:
The median is 20
Step-by-step explanation:
They are already in order so you would just have to find the middle.......
Hope this helps.......if not then sorry for wasting your time and may God bless you
Please help I put 50 points into this
Answer:
B,C,E
Step-by-step explanation:
Answer:
A, C, D
Step-by-step explanation:
A ray can have 2 endpoints
And because of that it can be named more than one way.
That means that B&E are wrong
21 slices from 3 cakes = 84 slices from cakes equivalent rates
Answer:
12 cakes.
Step-by-step explanation:
There are 21/3 = 7 slices from each cake.
84 / 7 = 12.
which ordered pair in the form (x,y) is a solution of this equation?
7x-5y=28
(-3,-2)
(-2,-3)
(0,4)
(4,0) will give brainly to who ever gets it right please and thank you
Answer:
I think is 4,0
Step-by-step explanation:
if u divide 28 by seven u would get 4 and u cant divide 28 by 5 sooo it would be a decimal but that isnt an option so imma say its the last one
6) What time will it be 17 hours and 53 minutes before 4:37 a.m.? Military time
Answer:
17:53=5:53pm
Step-by-step explanation:
An architect is designing a house. She wants the bedroom to have the dimensions of 10 ft by 4 ft by 7 ft. The architect doubles all three dimensions to create the den. Does that mean the den will have double the volume of the bedroom?
The volume of the den ( 2240ft³ ) is 1960ft³ more than the volume of the bedroom ( 280ft³ ).
Hence, the den will not have double the volume of the bedroom.
Does the den have double the volume of the bedroom?Given the dimensions in the question, the bedroom and the den takes the shape of rectangular prism.
Volume of rectangular prism is expressed as;
V = l × b × h
Given that;
Length of the bedroom l = 10ftBreadth of the bedroom B = 4ftHeight of the bedroom h = 7ftLength of the den = 2l = 2×10ft = 20ftBreadth of the den = 2B = 2×4ft = 8ftHeight of the den = 2h = 2×7ft = 14ftFirst we calculate the volume of the bedroom.
V = l × b × h
Vr = 10ft × 4ft × 7ft
Vr = 280ft³
Next, we determine the volume of the den
V = l × b × h
Vd = 20ft × 8ft × 14ft
Vd = 2240ft³
The volume of the den ( 2240ft³ ) is 1960ft³ more than the volume of the bedroom ( 280ft³ ).
Hence, the den will not have double the volume of the bedroom.
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Helppp I need this asap
Answer:
[tex]x = 35[/tex]
Step-by-step explanation:
We can use Similar Triangles Ratios to solve for the missing side length. First setup your ratios:
[tex]\frac{42}{6} = \frac{x}{5}\\x = \frac{42}{6} \times 5\\x = 35[/tex]
Answer:
35
Step-by-step explanation:
The sides are in proportion.
[tex]\frac{AB}{PQ} =\frac{AC}{PR}[/tex]? / 5 = 42 / 6? = 5 × 7? = 35On a map, 1 inch equals 25 miles. Two cities are 3 inches apart on the map. What is the actual distance between the cities?
Answer:
75 Miles apart
Step-by-step explanation:
I = inches on a map
I=25
3I=75
75 miles apart
Please helppppppppppp
Which graph shows the solution to the system of linear inequalities?
Answer:
this is answer
Step-by-step explanation:
To graph a linear inequality in two variables (say, x and y ), first get y alone on one side. Then consider the related equation obtained by changing the inequality sign to an equality sign. The graph of this equation is a line. If the inequality is strict ( < or > ), graph a dashed line.