The rule that the defines the sum Sn is [tex]S_n =\frac{9 * (1 - r^n )}{0.6}[/tex]
How to determine the expression for Sn?The formula of the sequence is given as:
an = 9(0.4)^n
The above means that:
The first term, a = 9Common ratio, r = 0.4The sum Sn is then represented as:
[tex]S_n =\frac{a(1 - r^n )}{1 - r}[/tex]
So, we have:
[tex]S_n =\frac{9 * (1 - r^n )}{1 - 0.4}[/tex]
Evaluate the difference and divide
[tex]S_n =\frac{9 * (1 - r^n )}{0.6}[/tex]
Hence, the rule that the defines the sum Sn is [tex]S_n =\frac{9 * (1 - r^n )}{0.6}[/tex]
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| x- ( - 18) | if x < - 18
Answer:
well x-(-18) x+18 but the if part is x<-18 will stay the same
Step-by-step explanation:
what’s the geometric mean between 40 and 30????
Hi Student!
In the question we are given two numbers and told to find the geometric mean of them. A normal mean would be just taking the average by multiplying them against each other and dividing by two. However, for geometric mean we multiply them against each other but put them inside of a square root.
[tex]mean = \sqrt{a*b}[/tex]
[tex]mean = \sqrt{40*30}[/tex]
[tex]mean = \sqrt{1200}[/tex]
[tex]mean = \sqrt{20^2*3}[/tex]
[tex]mean = 20\sqrt{3}[/tex]
Therefore, our geometric mean is [tex]34.64[/tex] or [tex]20\sqrt{3}[/tex].
PLEASE HELP!!!
Which of the following is the Best Buy?
1 L for $1.68
0.5 L for $1.29
2 L for $3.40
3 L for $5.07
Answer:
it's 1 L
Step-by-step explanation:
it's pretty easy just do some multiplication
what equations will give me this
Answer:
2[tex]n[/tex] = [tex]\alpha n[/tex] and [tex]n + n[/tex] = [tex]\alpha n[/tex]
Step-by-step explanation:
Find the gradient of the line segment between the points (-5,-2) and (4,3).
Give your answer in its simplest form.
Answer:
5/9
Step-by-step explanation:
Solution
The gradient of the line ment when two segment given (X1, Y1) and (X2, Y1) is points
m =
[tex] \frac{y2 - y1}{x2 - x1 } [/tex]
Here two points given, (-5,-2) and (4,3)
gradient (m):
[tex] \frac{3 - ( - 2)}{4 - ( - 5)} [/tex]
A marathon swim follows a triangular course marked with three buoys, A, B, and C. The distance from buoy A to B is 400 meters, B to C is 500 meters, and C to A is 600 meters. What is the smallest angle the swimmers must turn between the buoys
By applying the law of cosine, the smallest angle which the swimmers must turn between the buoys is 41.4°.
How to determine the smallest angle?In order to determine the smallest angle which the swimmers must turn between the buoys, we would apply the law of cosine.
Given the following data:
Side AB = c = 400 meters.Side BC = a = 500 meters.Side CA = b = 600 meters.
Form the law of cosine, we have:
[tex]CosC =\frac{a^2 + b^2 - c^2}{2ab} \\\\CosC =\frac{500^2 + 600^2 - 400^2}{2 \times 500 \times 600}\\\\CosC =\frac{450000}{600000}\\\\C = cos^{-1} 0.75\\\\[/tex]
C = 41.4°.
For angle B, we have:
[tex]CosB =\frac{a^2 + c^2 - b^2}{2ac} \\\\CosB =\frac{500^2 + 400^2 - 600^2}{2 \times 500 \times 400}\\\\CosB =\frac{1}{8}\\\\B = cos^{-1} 0.125\\\\[/tex]
B = 82.8°.
For angle A, we have:
[tex]CosA =\frac{b^2 + c^2 - a^2}{2bc} \\\\CosA =\frac{600^2 + 400^2 - 500^2}{2 \times 600 \times 400}\\\\CosA =\frac{9}{16}\\\\A = cos^{-1} 0.5625\\\\[/tex]
A = 55.8°.
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m = − 1 6 , (6, −3) y =
5
6
x + 3
Answer:
6
Step-by-step explanation:
that is because 6 is x and y is -3
Given the following absolute value equation, what would the coordinates of the vertex be?
y= -3 |x-5| +2
A (−5,2)(-5,2)(−5,2)
B (−3,−5)(-3,-5)(−3,−5)
C 5,2)(5,2)(5,2)
D (2,−5)(2,-5)(2,−5)
Answer:
C. (5,2)
Step-by-step explanation:
For parent function f(x) with vertex at (0, 0), translating it horizontally by "h" and vertically by "k" makes it look like
f(x -h) +k
and the vertex moves to (h, k).
__
Here, the parent function |x| has its vertex at (0, 0). Writing it as ...
-3|x -5| +2
moves its vertex to (h, k) = (5, 2).
_____
Additional comment
The factor -3 serves to reflect the graph over the x-axis and expand it vertically by a factor of 3. It has no effect on the translation of the vertex.
What theorem can be used to prove that the two triangles are similar? A) SSS Similarity Theorem B) SAS Similarity Theorem C) SSA Similarity Theorem
Answer:
C) SSA Similarity Theorem
Step-by-step explanation:
The SAS Similarity Theorem asserts that if two sides of one triangle are proportionate to two sides of another triangle, and both triangles' included angles are congruent, the two triangles are similar.
HELP ASAP PLEASE, this is the last question i promise T^T
WILL MARK BRAINLIEST AND GIVE POINTS
find the perimeter of a circular sector if the diameter of its circle equals 10cm and its arc length = 10cm. equals = ......... cm.
a) 10
b) 20
c) 30
d) 40
an explanation for future reference would be greatly appreciated, thank youuu <33
Answer:
A= 10
Step-by-step explanation:
[10 + 2/360˚(10)]
What is the area of the painting shown ?
Area = length x width
Length = x + 6 + x + 2 = 2x + 8
Width = x + 4 + x = 2x + 4
area = 2x + 8 * 2x + 4
multiply each term by each term
Area = 4x^2 + 24x + 32
Answer: I think this is correct but i'm not sure! the answer should be 48 im not sure though
Step-by-step explanation:
6 x 2 = 12 x 4 = 48
Find the values of the numbers m and n that will make (2x + m)2 = 4x2 + nx + 9 true, given
that both m and n are positive numbers.
The values of the numbers m and n that makes the given expression true are 3 and 12 respectively
Solving an equationFrom the question, we are to determine the values of the numbers m and n that will make the given expression true
The given expression is
(2x + m)² = 4x² + nx + 9
Opening the bracket on the left hand side,
(2x + m)²
(2x + m)(2x + m)
4x² + 2mx + 2mx + m²
4x² + 4mx + m²
∴ 4x² + 4mx + m² = 4x² + nx + 9
By comparing,
4mx = nx;
Then, 4m = n
and
m² = 9
∴ m = ±√9
m = ±3
Since we are given that both m and n are positive numbers,
∴ m = 3
Substitute the value of m into the equation, 4m = n
4×3 = n
∴ n = 12
Hence, the values of the numbers m and n that makes the given expression true are 3 and 12 respectively
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y=
\,\,x^2+4x-4
x
2
+4x−4
y=
y=
\,\,x-6
x−6
Can someone help
kaitlin buys candy that costs $8 per pound. she will spend less than $40 on candy. what are the possible numbers of pounds she will buy?
use p for the number ofpounds kaitlin will buy.
write your answer as an inequality solved for p.
Answer:
x≤5p
Step-by-step explanation:
40/8=5 Kaitlin can buy UP TO 5 pounds of candy at $8/pound. So she will buy less than or equal to 5 pounds
Please help!!! thank you!
Answer:
30 again if I’m wrong then it’s 40
Step-by-step explanation:
most of the pizzas that are sold are in the 30’s or below
in need of some help <3
If ∆ABC~∆XYZ, area (∆ABC) : the area (∆XYZ) = 4:9, then AB:XY is...
Answer:
AB : XY = 2 : 3
Step-by-step explanation:
We know that :
area ∝ length²So, if the areas ΔABC and ΔXYZ are in the ratio 4 : 9, then :
ΔABC : ΔXYZ ∝ AB² : XY²4 : 9 ∝ √4 : √94 : 9 ∝ 2 : 3Which set of real numbers contains 23 and .45?
rational numbers
integers
natural numbers
whole numbers
Answer:
Option A, rational numbers
Step-by-step explanation:
Step 1: Determine which option is correct
Option B and D are automatically ruled out because only one of them is a whole number and the other one is a decimal. Option C doesn't work also because natural numbers are all the whole numbers that are greater than 1. The only option that makes sense is option A which includes whole numbers and decimals.
Answer: Option A, rational numbers
In general, 60 beats per minute (bpm) is a heart rate that is considered too slow for an adult when at rest and 100 bpm is considered too high. As one way of measuring the stress of Canadian air traffic controllers, heart rates of 173 randomly selected air traffic controllers were measured across Canada. Of this sample of air traffic controllers, 47 had a resting heart rate over 100 bpm. What is the true proportion of air traffic controllers in Canada with resting heart rates over 100 bpm
The true proportion of air traffic controllers in Canada with resting heart rates over 100 bpm is; 0.2717 or 27.17%
How to calculate true proportion?We are given;
Sample size; n = 173
Number of people who had a resting heart rate over 100 bpm = 47
Now, formula for true proportion is;
p' = x/n
where;
x represents the number of successes
n represents the sample size.
p′ is the sample proportion which is the point estimate for the true population proportion.
Thus;
p' = 47/173
p' = 0.2717
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kyle is pulled back on a swing so that the rope forms an angle of 30 degress with the vertical the distance from the top of the swing set directly to the ground is 12 feet find kyles height off the ground
Answer:
12 ft - 2 ft = 10 ft
The rope is 10 feet long.
10 · cos 30° = 10 · √3 / 2 = 8.66 ft
x = 12 - 8.66 = 3.34 ft
Answer:
A ) 3.34 feet
Using the identity sin? O + cos? O = 1, find the value of tan O, to the nearest
hundredth, if sin 0 = 0.27 and 0 < 0 < 7
Answer:
3.7
Step-by-step explanation:
Given
sin²θ + cos²θ = 1sinθ = 0.27Solving for cosθ
cos²θ = 1 - sin²θcos²θ = 1 - (0.27)²cos²θ = 0.0729Finding tanθ
tanθ = sinθ / cosθtanθ = 0.27 / 0.0729tanθ = 3.7Verifying it lies in the range
θ = tan⁻¹ (3.7)θ = 74.88° Range is : 0 < θ < π/2 [or 0 < θ < 90°]It lies in the range [Verified]radical 54 simplified
The volume of a sphere with radius r
is given by the formula V=4/3 π r^3.
Find the volume of a sphere with radius 8 cm is
Answer:
2143.57 cm³[tex] \: [/tex]
Step-by-step explanation:
In the question, it is given that a sphere has a radius of cm and we have to find the volume of the sphere.
To Find the volume of the cone, we must know this formula :
[tex]\\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { Volume_{(sphere) }= \dfrac{4}{3} \: \pi {r}^{3}}}}}}}} \\ \\[/tex]
Now, we will substitute the values in the formula :
[tex]\\{\longrightarrow{ \qquad{ {\pmb{\sf { Volume_{(sphere) }= \dfrac{4}{3} \: \times 3.14 \times {(8)}^{3}}}}}}} \\ \\[/tex]
[tex]\\{\longrightarrow{ \qquad{ {\pmb{\sf { Volume_{(sphere) }= \dfrac{4}{3} \: \times 3.14 \times 512}}}}}} \\ \\[/tex]
[tex]\\{\longrightarrow{ \qquad{ {\pmb{\sf { Volume_{(sphere) }= \dfrac{4}{3} \: \times 1067.68}}}}}} \\ \\[/tex]
[tex]\\{\longrightarrow{ \qquad{ {\pmb{\sf { Volume_{(sphere) }= \dfrac{4 \times 1067.68 }{3} \: }}}}}} \\ \\[/tex]
[tex]\\{\longrightarrow{ \qquad{ {\pmb{\sf { Volume_{(sphere) }= \dfrac{6430.72 }{3} \: }}}}}} \\ \\[/tex]
[tex]\\{\longrightarrow{ \qquad{ {\pmb{\sf { Volume_{(sphere) }= 2143.57}}}}}} \\ \\[/tex]
Therefore,
The volume of the sphere is 2143.57 cm³write down all the prime numbers
Answer:
The prime numbers from 1 to 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
Step-by-step explanation:
also it goes on and on so i dont think you meant but i hope this helps if it dosnt m very sorry
Can someone help me with this please
Use the following data set to answer questions 9-16:
11, 18, 8, 15, 24, 14 9.
Identify the median. Round to the nearest tenth.
Answer:
The answer is 14
Step-by-step explanation:
Put the numbers in order from least to greatest
9,8,11,14,15,18,24
Then you find the number in the middle and in this case that number would be 14
Hope this helps:)....if not then sorry for wasting your time and may God bless you:)
Find the length of the segment that joins the points (-5,2) and (4,-3).
Answer:
10.2956
Step-by-step explanation:
formula:
d = √((x2-x1)2 + (y2-y1)2)
(x1, y2) and (x2, y2)
(-5,2) and (4,-3).
Find the difference between coordinates:
(x2-x1) = (4 - -5) = 9
(y2-y1) = (-3 - 2) = -5
Square the results and sum them up:
(9)2 + (-5)2 = 81 + 25 = 106
Now Find the square root and that's your result:
Exact solution: √106 = √106
Approximate solution: 10.2956
I am thinking of a number. I multiply it by 8 and subtract 56.
I get the same answer if I multiply by 5 and subtract 8
What is my number?
Answer:
16
Step-by-step explanation:
[tex]8x-56=5x-8\\\\3x-56=-8\\\\3x=48\\\\x=16[/tex]
So, the number is 16
If cost of 15 eggs is Rs. 75, then find out the cost of 4 dozens eggs.
a.₹ 185
b.₹ 150
c.₹ 300
d.₹ 240
Answer:
The answer is d 240. You will first find how much 1 egg costs then times 12 times 4 equal to 48 times how much 1 egg Costs equal to 240
3
Find the surface area of the figure shown below.
1 mm
1 mm
1 mm
Figure not drawn to scale
Surface area is?
Answer:
6
Step-by-step explanation:
Since this is a cube, and the lengths that are given are 1 mm, then you just add all the sides of a cube. There are 6 sides in a cube, 1+1+1+1+1+1=6
the original price for a set of golf clubs is $500 at the beginning of the seasons the price was marked up by 20% at the end of the seasons the price at the beginning of the season is marked down by 20% how does the final price compare with the original price of $500
Answer: The final price is less than the original
Step-by-step explanation:
Let us break this down a bit.
The original price is $500
-> At the beginning, the price was marked up by 20%
-> At the end, the price at the beginning of the season is marked down by 20%
We are solving for: "How does the final price compare with the original price of $500"
First, we will find the price at the beginning.
-> Please note a percent divided by 100 becomes a decimal
20% / 100 = 0.2
$500 * 0.2 = $100
$500 + $100 = $600
Now, we will find the price at the end.
$600 * 0.2 = $120
$600 - $120 = $480
The final price is less than the original price of $500.
Answer:
Step-by-step explanation:
price marked up by 20%= 500+ [tex]\frac{20}{100}[/tex]×500
=$600
price marked down by 20%= 600- [tex]\frac{20}{100}[/tex]×600
=$480
the final price is less than the original price
