The common ratio between the sum of a certain infinite geometric series is 2. the sum of the squares of all the terms is 3 is, - 1/9
Now, We can formulate;
⇒ { a/ 1-r} = 2
And, a²/ (1 - r²) = 5
⇒ 2a/ ( 1+r ) = 5
⇒ 2(2 - 2r)/ 1 + r = 5
⇒ 4 - 4r = 5 + 5r
⇒ 9r = - 1
⇒ r = - 1/9
Thus, The common ratio between the sum of a certain infinite geometric series is 2. the sum of the squares of all the terms is 3 is, - 1/9
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Help!!
how many combinations do I have it I select 4 things from a total of 9 without replacement? (9C4)
4 things can be selected from a total of 9 without replacement in 126 times without replacement.
What is Combination?Combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of selection does not matter.
How to determine this
To calculate the combination without replacement
nCr = n!/r!(n-r)!
9C4= 9!/4!(9-4)!
= 9!/4!(5!)
= 9*8*7*6*5*4*3*2*1/4*3*2*1*5*4*3*2*1
= 362880/24*120
= 362880/2880
= 126
Therefore, it can be combined in 126 times
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The polar coordinate (3, 45°) lies in the same location on the polar plane as (-3, Ø), where -360° < Ø < 0.
What is Ø?
The polar coordinate (3, 45°) lies in the same location on the polar plane as (-3, Ø), where -360° < Ø < 0. Then, the value of Ø is 45°.
The polar coordinates (r, θ) represent a point on the polar plane, where r is the radial distance from the origin (in this case, 3 units) and θ is the angle measured counterclockwise from the positive x-axis (in this case, 45°).
According to the given statement, the polar coordinate (-3, Ø) lies in the same location on the polar plane as (3, 45°). This means that these two points represent the same location, and their radial distances and angles must be equivalent.
Comparing the radial distances;
|r| = 3 (for (3, 45°))
|-r| = 3 (for (-3, Ø))
Since |-r| = |r|, we can conclude that r = -r, which implies r = 0, as r cannot be negative in polar coordinates.
Comparing the angles;
θ = 45° (for (3, 45°))
θ = Ø (for (-3, Ø))
Since the angles are equivalent, we can equate them:
45° = Ø
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please help for this question
Using the translation vector of 3 units up and 1 unit right resulted to image coordinate of
(3, 7)
(3, 5)
(2, 5)
The image is attached
How to find the translation vectorThe translation vector is of the rule 3 units up and 1 unit to the right
The coordinate of the preimage are
(2, 4)
(2, 2)
(1, 2)
The translation is done as below
(2 + 1, 4 + 3) = (3, 7)
(2 + 1, 2 + 3) = (3, 5)
(1 + 1, 2 + 3) = (2, 5)
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Help I am so confused. Thank you pic at bottom
1A) This sampling technique employed is known as a systematic random sample.
1B) The demographic examined in the study is the total production run of 15,600 LED monitors. The representativeness of the sample within such population is relied upon if every 120th monitor selected is an unbiased, irregular choice from the larger collective.
How to explain the samplingFor question 2, the sampling method utilized here is called a convenience sample. Kenya only enquires the middle school pupils in her 7th grade science course, which cannot be characterized as a representative or randomly chosen group of all middle school learners.
The sample may not accurately reflect the population because it merely involves students in her lesson, and not necessarily those enrolled at her school or district.
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IZ:
eighted Average
Calculator
There are 15 people in a book club. Ten people read for an average of 65 minutes each day. The remaining people read for an average
of 35 minutes each day.
What was the average reading time for the entire book club each day?
Enter your answer in the box.
min
1 2 3 4
5 Next >
Readin
The average reading time for the entire book club each day is 55 minutes
What was the average reading time for the entire book club each day?From the question, we have the following parameters that can be used in our computation:
10 with a weight of 65 minutes5 with a weight of 35 minutesThe weighted average of the numbers is calculated as
Average = Product of numbers and weights/Sum of weights
So, we have
Average = (10 * 65 + 5 * 35)/15
Evaluate
Average = 55
Hence, the weighted average is 55
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HELP ASAP
Find the diameter of the sphere.
Round to the nearest
hundredth.
Rounding to the nearest hundredth, the diameter of the sphere is approximately 4.26 cm.
What is the diameter of the sphere?A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.
The surface area of a sphere is expressed as:
S = 4πr²
Where S is the surface area and r is the radius of the sphere.
Given that surface area of 18.2π cm²
We can solve for the radius as follows:
S = 4πr²
r = √( S / 4π )
r = √( 18.2π / 4π )
r = 2.13 cm
The diameter of the sphere is twice the radius, so:
d = 2r
d = 2( 2.13cm )
d = 4.26 cm
Therefore, the diameter of the sphere is 4.26 cm.
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Heart attacks cause many deaths. Researchers in the Physicians Health Study (1989) gave a large sample of healthy male physicians either a low dose of aspirin or a placebo.
In this example of heart attack, it would be appropriate to calculate Conditional row percentages. Therefore, the correct option is option A.
When the blood supply for the heart is significantly impeded or blocked, a heart attack happens. The accumulation of fat, cholesterol, and other chemicals in the heart's (coronary) arteries is typically what causes the obstruction. Plaques are the name given to the fatty, cholesterol-containing deposits.
Atherosclerosis is the name for the phenomenon of plaque accumulation. A plaque may occasionally burst and generate a clot that restricts blood flow. A portion for the heart muscle can be harmed or destroyed by a shortage of blood flow. In this example, it would be appropriate to calculate Conditional row percentages.
Therefore, the correct option is option A.
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Your question is incomplete but most probably your full question was,
If r = 6 and the measure of the central angle 2pi/3, what is the length of the intercepted arc
The length of the intercepted arc is 4π unit.
We have,
Angle = 2π/3 = 2(180)/ 3 = 120 degree
r = 6 unit
So, length of Arc
= θ /360 x 2πr
= 120/360 2 π(6)
= 1/3 (12)π
= 4π unit
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Find the height of the rectangular prism (You should have at least 3 steps shown in your work)
Answer:
[tex]12 \times 10 \times h = 3600[/tex]
[tex]120h = 3600[/tex]
[tex]h = 30[/tex]
The height is 30 millimeters.
The amount of pollution entering the atmosphere varies directly as the number of people living in an area. If 35,000 people create 21,350 tons of pollutants, how many tons enter the atmosphere in a city with a population of 500,000?
Please Help
The city with a population of 500,000 would produce 305,000 tons of pollutants.
We have,
Let's call the unknown amount of pollutants in the second city "x".
According to the problem,
The amount of pollution is directly proportional to the number of people. This means that we can set up a proportion:
Pollution/number of people
= pollution/number of people
Using the values we know:
= 21350/35000
= x/500000
Simplifying:
0.61 = x/500000
To solve for x, we can cross-multiply:
0.61 x 500000 = x
x = 305000
Therefore,
The city with a population of 500,000 would produce 305,000 tons of pollutants.
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3. Olivia's mother surprised her with pasta packed in a rectangular prism shaped lunch box. How much quantity of pasta is served to Olivia given that the dimensions of the rectangular prism are as follows:
length= 5 in , width= 4 in, height= 3 in
The quantity of pasta is served to Olivia is 60 in³.
Olivia's mother packed her lunch in a lunch box which is in the shape of rectangular prism, with dimension = length= 5 in, width= 4 in, height= 3 in,
We need to find the quantity of the lunched packed in the box,
So, we will find the volume of the box = length × width × height
= 5 × 4 × 3
= 60 in³
Hence the quantity of pasta is served to Olivia is 60 in³.
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What is the value of S?
A circular table measures 2.5 feet across the diameter of its top. What is the approximate area of the table top. Use 3.14 for TT.
O 9.42 ft²
O 19.63 ft²
O 4.91 ft²
O 7.85 ft²
Use the numbers 3 and 4 to make a fraction that is greater than 1 and a fraction less than 1. Explain how you made your fractions without a number line so it says greater not lesser that is my question
The fraction 4/3 we get by using the numbers 3 and 4 to make a fraction that is greater than 1 and a fraction less than 1
To make a fraction greater than 1 using the numbers 3 and 4, we can divide 3 by 4 and add 1.
3/4 + 1 = 7/4
The resulting fraction, 7/4, is greater than 1 because the numerator (7) is greater than the denominator (4).
We can also see this by writing 7/4 as a mixed number:
7/4 =[tex]1\frac{3}{4}[/tex]
The whole number part of the mixed number is 1, which means the fraction is greater than 1.
To make a fraction less than 1 using the same numbers, we can divide 4 by 3. This gives us:
4/3
The resulting fraction, 4/3, is less than 1 because the numerator (4) is smaller than the denominator (3).
We can also see this by writing 4/3 as a mixed number:
4/3 =[tex]1\frac{1}{3}[/tex]
The whole number part of the mixed number is 1, which means the fraction is less than 1.
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Determine which function is represented by the graph. Do not use a calculator. (a) f ( x ) = 4 cos ( x + π ) (b) f ( x ) = 4 cos 4 x (c) f ( x ) = 4 sin ( x − π ) (d) f ( x ) = − 4 cos ( x + π ) (e) f ( x ) = 1 − sin x 2
Answer:
The graph of the function appears to be a cosine function that has been shifted to the left by π/2 units, and has an amplitude of 4.
Option (a) is a cosine function that has been shifted to the left by π units, but does not have the amplitude of 4.
Option (b) is a cosine function that has a period of π/2, which is much shorter than the period of the graph.
Option (c) is a sine function that has been shifted to the right by π units, but does not have the amplitude of 4.
Option (d) is a cosine function that has been shifted to the left by π units and has the correct amplitude of 4.
Option (e) is not a cosine or sine function, so it cannot be the correct answer.
Therefore, the function represented by the graph is:
f(x) = -4 cos(x + π)
which is Option (d).
Step-by-step explanation:
PLEASE HELP (WILL GIVE BRAINLIEST)
Answer:
V = π(19.1^2)(11.8) = 13,523.8 cubic mm
V = 3.14(1.91^2)(11.8) = 13,516.9 cubic mm
Solve for θ if −10sinθ−8=5√3−8 and 0≤θ<2π.
The value of variable θ would be,
⇒ θ = 5π/3 and θ = 4π/3
We have to given that;
Expression is,
⇒ - 10sin θ - 8 = 5√3 - 8
Now, We can simplify as;
⇒ - 10sin θ - 8 = 5√3 - 8
⇒ - 10sin θ = 5√3
⇒ sin θ = - 5√3/10
⇒ sin θ = - √3/2
We know that sinθ = -√3/2 when θ = 4π/3 and θ = 5π/3 (among other angles).
However, since 0 ≤ θ < 2π, only the angles in the second and third quadrants are valid solutions for sinθ = -√3/2.
Therefore, the solutions are θ = 5π/3 and θ = 4π/3, option D is correct.
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Find the value of each variable. Round your answers to the nearest tenth.
Answer:
k = 8.4; j = 13.1
Step-by-step explanation:
We can find the measures of j and k using trigonometric ratios, namely the tangent ratio and the cosine ratio
The tangent ratio is tan(reference angle) = opposite / adjacent, while the cosine ratio is cos(reference angle) = adjacent / hypotenuseIf we allow 40 to be our reference angle...
the measuring j units is the hypotenuse, the side measuring k is the opposite side, and the side measuring 10 is the adjacent side.Because we're not given the measure of either j or k, we have to use 10 each time
Steps to find j:
To find j, we can use the cosine ratio:[tex]cos(40)=\frac{10}{j}\\ \\j*cos(40)=10\\\\j=\frac{10}{cos(40)}\\ \\j=13.05407289\\\\j=13.1[/tex]
Steps to find k:
To find k, we can use the tangent ratio:[tex]tan(40)=\frac{k}{10}\\ \\10*tan(40)=k\\\\8.390996312=k\\\\8.4=k[/tex]
evaluate the function at the indicated value, using the technique indicated.
9. Find w(-3) using synthetic substitution:
w(x)=11x³ -6x² +2
Using synthetic division, the value at w(-3) of the expression w(x)=11x³ -6x² +2 is -349
What is synthetic substitution?Synthetic substitution is a mathematical method that is used for evaluating the algebra polynomial in the simpler process.
To determine the value of the polynomial at w = -3, we need to carry out the synthetic division.
Then, the value of the remainder is taken as the value of the expression at the particular value
We have the expression as;
w(x)=11x³ -6x² +2/x-3
Let's carry out the synthetic division
Then, this is represented as;
-3) 11 -6 0 2
-33 -117 -351
11 -39 -117 -349
The value is -349
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Add and simplify 12ft. 8in. + 16ft. 11in.
Answer:
Step-by-step explanation:
29 ft
7 in
Question 2 (1 point) A new car cost $30,000. Each year, it depreciates by an average of 14%. What rule is the explicit rule for the situation?
A. an = 30,000 . 0.14n-1
B. an = 30,000 . 0.86n-1
C. an = 30,000 . 1.14n-1
The explicit rule for the situation whereby a new car that costs $30,000 depreciates at an average rate of 14% per year, giving the depreciated value of the car after n years, is given by B. an = 30,000 × 0.86^n-1.
What is the depreciated value of an asset?The depreciated value of an asset in any year can be determined using the exponential decay function or equation.
An exponential decay equation shows the value of an asset given a constant rate of periodic decrease.
The cost of the new car = $30,000
The average depreciation rate per year = 14%
Depreciation factor = 86% or 0.86 (1 - 14%)
Let the number of years after the purchase = n
Let the depreciated value after n years = an
Decay Equation:an = 30,000 × 0.86^n-1.
Thus, the correct explicit rule is Option B.
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Help please!!!!!!!!!!!!!!!!!!!!
The relationships between the figures is a dilation of 3.5 from the small triangle to the big triangle
Analyzing the relationships between the figuresFrom the question, we have the following parameters that can be used in our computation:
The two triangles
From the figure, we can see that
The shapes have the same orientationOne of the triangles is bigger than the otherThe side lengths of the triangles are in proportionThese mean that the triangles are related by dilation
The constant of dilation is then calculated as
k = (7, 7)/(2, 2)
Evaluate
k = 3.5
Hence, the scale factor is 3.5
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If m varies directly with n and m=209 when n=22, find n when m=361
Answer:174
Step-by-step explanation:
209-22=187
361-22=174
The data set is: 6, 2, 6, 3, 5, 6, 7, 9, 1 For this question, find the IQR
The IQR of the data set is 4.
First, let's arrange the data set in order from smallest to largest:
1, 2, 3, 5, 6, 6, 6, 7, 9
Next, let's find the median (Q2) of the data set. Since there are an odd number of values in the data set, the median is the middle value:
Q2 = 6
Now, let's find the median (Q1) of the lower half of the data set. This includes the values from the minimum (1) up to (but not including) the median (6). There are four values in this lower half, so the median is the average of the two middle values:
Q1 = (2 + 3) / 2 = 2.5
Finally, let's find the median (Q3) of the upper half of the data set. This includes the values from the median (6) up to (and including) the maximum (9). There are also four values in this upper half, so the median is the average of the two middle values:
Q3 = (7 + 6) / 2 = 6.5
Now that we have Q1, Q2, and Q3, we can calculate the IQR as:
IQR = Q3 - Q1
IQR = 6.5 - 2.5
IQR = 4
Therefore, the IQR of the given data set is 5.5.
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Given this unit circle what is the value of x? HELP PLEASE
Answer:
x = - [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
consider the right triangle formed by the x- axis, the y- coordinate of the given point and the radius of the circle 1 , to the point from the centre.
using Pythagoras' identity
x² + ( [tex]\frac{4}{5}[/tex] )² = 1²
x² + [tex]\frac{16}{25}[/tex] = 1 ( subtract [tex]\frac{16}{25}[/tex] from both sides )
x² = 1 - [tex]\frac{16}{25}[/tex] = [tex]\frac{9}{25}[/tex] ( take square root of both sides )
x² = ± [tex]\sqrt{\frac{9}{25} }[/tex] = ± [tex]\frac{\sqrt{9} }{\sqrt{25} }[/tex] = ± [tex]\frac{3}{5}[/tex]
since the given point is in the second quadrant , then
x = - [tex]\frac{3}{5}[/tex]
math hw for tonight
help solve this problem! Thank you!
ap cal bc
The slope of the polar curve at θ = π/4 is 24. Therefore, option D is correct.
To find the slope of the polar curve r = 6cos(2θ) - 5 at θ = π/4, we need to find the derivative of r with respect to θ, and then substitute θ = π/4 into the resulting expression.
Using the chain rule of differentiation, we have:
dr/dθ = dr/d(cos(2θ)) * d(cos(2θ))/dθ
To find the first derivative, we can use the power rule of differentiation:
dr/d(cos(2θ)) = -12sin(2θ)
To find the second derivative, we can use the chain rule again:
d(cos(2θ))/dθ = -2sin(2θ)
Substituting these into the expression for dr/dθ, we get:
dr/dθ = -12sin(2θ) * (-2sin(2θ)) = 24sin^2(2θ)
Now, substituting θ = π/4, we get:
dr/dθ|θ=π/4 = 24sin^2(π/2) = 24
The slope of the polar curve at θ = π/4 is therefore 24.
None of the given options match this result.
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PLEASE HELP ( WILL GIVE BRAINLIEST)
Answer:
26,225.3 = 3.14(12^2)h + (2/3)(3.14)(12^3)
26,225.3 = 452.16h + 3,617.28
452.16h = 22608.02
h = 50 feet
26,225.3 = π(12^2)h + (2/3)π(12^3)
26,225.3 = 144πh + 1,152π
144πh = 26,225.3 - 1,152π
h = (26,225.3 - 1,152π)/(144π)
h = 49.97 feet = 50 feet
Find the prime fractorization of the number 130
The calculated value of the prime fractorization of the number 130 is 2 * 3 * 5
Finding the prime fractorization of the number 130From the question, we have the following parameters that can be used in our computation:
Number = 130
When the above number is expanded, we have
Number = 2 * 5 * 13
The above product of numbers cannot be further simplified
This means that 2 * 5 * 13 is the prime fractorization of the number 130
Hence, the prime fractorization of the number 130 is 2 * 3 * 5
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y=2x-6
x+y=3
graph it and get the solution
Signed numbers are also called directed numbers true or false
The given statement, "Signed numbers are also called directed numbers" is true.
Signed numbers are numbers that can be positive, negative, or zero, and they are sometimes referred to as directed numbers because they have a direction or orientation on the number line. Positive numbers are usually associated with movements to the right on the number line, while negative numbers are associated with movements to the left.
Therefore, the given statement, "Signed numbers are also called directed numbers" is true.
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