how many terms of the series do we need to add in order to find the sum to the indicated accuracy? (your answer must be the smallest possible integer.) term:
Answers
To find the smallest possible integer of the terms of the series that need to be added to find the sum to the indicated accuracy, we use the formula for the remainder of the geometric series.
The formula for the remainder of the geometric series is R = a (1 - rn) / (1 - r)Where R is the remaining term of the geometric series,a is the first term of the geometric series,r is the common ratio of the geometric series,n is the number of terms of the geometric series up to the given partial sum.
The formula for the sum of a finite geometric series is:S = a (1 - rn) / (1 - r)By using the formula for the remainder of the geometric series, the smallest possible integer of the terms of the series that need to be added to find the sum to the indicated accuracy is given by:S - Sn = RWhere, S is the sum of the geometric series,S_n is the sum of the first n terms of the geometric series.
From the given question, the number of terms of the geometric series required to find the sum to the indicated accuracy is not given.
Hence, we cannot find the smallest possible integer of the terms of the series that need to be added to find the sum to the indicated accuracy.
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Correct question:
How many terms of the series do we need to add in order to find the sum to the indicated accuracy?
Related Questions
in words explain how to determine the y intercepts of a rational function. be sure to include if theres a specific way to easily find the y intercept and the possible number of y intercepts
Answers
Answer:
evaluate f(0)there will be 0 y-intercepts if f(0) is undefined, 1 otherwise.Step-by-step explanation:
You want to know how to determine the y-intercepts of a rational function, and their possible number.
Rational functionA rational function f(x) is the ratio of two polynomial functions p(x) and q(x):
f(x) = p(x)/q(x)
As such, both numerator and denominator have single function values for any value of the independent variable. The y-intercept of f(x) is ...
f(0) = p(0)/q(0)
The values of p(0) and q(0) are simply the constant terms in those respective functions.
The simple way to find the y-intercept is to look at the ratio of the constant terms in the polynomial functions making up the rational function. If that is defined, there is one y-intercept. If it is undefined (q(0)=0), then there are no y-intercepts.
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worth 11 points and actually help me instead of taking the points plz
Answers
Answer:
C'(-1,1)
Step-by-step explanation:
The coordinates of C are (-2,4).
The translation is (x+1,y-3), so we take the x value -2 and the y value 4 and plug it in.
(-2+1,4-3)
=(-1,1)
C' has the coordinates (-1,1)
Answer:
Its ([-1],[1])Step-by-step explanation:
By (x+1, y-3), the trapezoid wll move 1 point to the right, and 3 points down.
Which is the balanced equation for S3 + O2 – SO2?
O O O O
S8 + 016 — 8S02
Se + O₂ → S₂ + O2
Se + O₂ → S₂0₂
Sg + 802 – 8802
Answers
S3 + 3O2 ——-> 3SO2
Which of the following represents the total area of the figure?
44 ft²
400 ft²
440 ft²
484 ft²
Answers
Answer:
484 ft²
Step-by-step explanation:
The area of the given figure= area of right angled triangle ABC + area of rectangle BCDE + area of triangle DEF
=1/2 * base*height+ length*height+ 1/2*base*height
here base of triangle is equal to height of triangle ABC
=1/2*8*22+22*16+1/2*22*4
=484 ft²
An architect is designing a new library. As shown, the library’s floor plan is a rectangle divided into a bookshelf space with bookshelves, and a reading space with a rug and chairs. Each bookshelf is x ft wide and x + 3 ft long. The bookshelves are 3 ft from each other. The walkway between the two rows of bookshelves is 2 ft wide.
Answers
1) We were told to look for the dimension of the bookshelf space which are the Length and Width.
\(\begin{gathered} \text{Length of the bookshelf space=5}\times3ft+6(xft) \\ \text{Length}=15ft+6\text{xft}=3(5+2x)ft \end{gathered}\)Since we have 5numbers of the 3ft and 6numbers of the bookshelf,
Therefore, the Length= 3(5+2x)ft.
\(\begin{gathered} \text{Width}=2(x+3)ft+2ft \\ =2xft+6ft+2ft=2\text{xft}+8ft=2(x+4)ft \\ \end{gathered}\)Since the width of the bookshelf space consists of 2numbers of the bookshelf,
Therefore, the Width= 2(x+4)ft.
Therefore, the dimensions of the bookshelf space are given below:
Length=3(5+2x)ft
Width=2(x+4)ft.
2) Area of the bookshelf space= Length×width
\(\begin{gathered} \text{Area}=3(5+2x)\times2(x+4) \\ =(15+10x)(2x+8) \\ =15(2x+8)+10x(2x+8) \\ =30x+120+20x^2+80x \end{gathered}\)\(\begin{gathered} \text{Area}=20x^2+30x+80x+120 \\ =20x^2+110x+120 \end{gathered}\)The area of the bookshelf space is 20x²+110x+120.
A bike has been marked up by 15%. If its original price was $300, what is the selling price?
Answers
Here’s the answer
It will be 15% of 300
Which is 45
Now we have to add older price in this
And the final answer will be $345
Hope it helps :)
Answer:
$345
Step-by-step explanation:
Cp= $300
MP= 115%×$300
=$345
In a study of cell phone usage and brain hemispheric dominance, an internet survey was e-mailed to subjects randomly selected from an online group involved with ears. There were surveys returned. Use a 0. 01 significance level to test the claim that the return rate is less than 20%. Use the p-value method and use the normal distribution as an approximation to the binomial distribution.
Answers
The statistics z is -1.878 and the p value is 0.0302
Given,
Number of random sample selected, n = 6967
Number of surveys returned, x = 1331
Estimated proportion of return rate;
p = 1331/6967 = 0.192
Significance level, ∝ = 0.01
z would represent the statistic
We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:
Null hypothesis, p₀ ≥ 0.2
Alternative hypothesis, p₀ < 0.2
The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)
That is,
z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878
Using the alternative hypothesis and the following probability, we can now get the p value:
p value = p(z < - 1.878) = 0.0302
We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.
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A 2.45-m wide rectangular channel with a discharge of 2.83 m3/sec. has a bed slope of
Answers
The required specific energy increases with increasing depth and the water surface profile will be rapidly varied.
To determine the type of water surface profile for different depths in the rectangular channel, we can use the concept of specific energy and Manning's equation.
The specific energy (E) is given by the equation:
E = y + (V² / (2g)) + (Sf * x)
Given values:
Width of the rectangular channel (b) = 2.45 m
Discharge (Q) = 2.83 m³/sec
Bed slope (Sf) = 0.003
Manning's roughness factor (n) = 0.015
For each depth, we can calculate the velocity (V) using Manning's equation and then determine the specific energy (E) using the equation mentioned above.
Depth 1 (y₁ = 1.52 m):
First, let's calculate the velocity (V₁) using Manning's equation:\(V_1 = (1/n) * (R_1^{2/3}) * (S_f^{(1/2)})\)
The hydraulic radius (R₁) can be calculated as:
R₁ = (b * y₁) / (b + 2y₁) = (2.45 * 1.52) / (2.45 + 2 * 1.52) ≈ 0.678 m
Substituting the values
\(V_1= (1/0.015) * (0.678 ^{2/3}) * (0.003^{1/2})\) ≈ 2.81 m/s
Now, let's calculate the specific energy (E₁) using the equation:
E₁ = y₁ + (V₁² / (2g)) + (Sf * x)
Substituting the values:
E₁ = 1.52 + (2.976² / (2 * 9.81)) + (0.003 * x)
The above expression shows, the specific energy increases with increasing depth, and the water surface profile will be rapidly varied.
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Given question is incomplete, the complete question is:
2.45-m wide rectangular channel with a discharge of 2.83 m³/sec. has a bed slope of 0.003 and Manning's roughness factor of 0.015. What is the type of water surface profile for depths of 1.52 m, whether it is rapidly varied or not?
Factor this & please show all work.. I will give brainliest:)
Answers
Answer:
\((7n - 4) (7n^{2} + 8)\)
Step-by-step explanation:
\(49n^{3} - 28n^{2} + 56n - 32\)
\(= (49n^{2} - 28n^{2}) + (56n - 32)\)
\(= 7n^{2} (7n - 4) + 8 (7n - 4)\)
\(= (7n - 4) (7n^{2} + 8)\)
What is the slope of this line
Answers
Answer:
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line
Step-by-step explanation:
Remeber what a slope is :-)
let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b) find sin (θ+y)
Answers
In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement
\(\sin (\theta)=\frac{3}{5}\)Describes the following triangle
To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation
\(x^2+3^2=5^2\)Solving for x, we have
\(\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}\)The missing length of the first triangle is equal to 4.
For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression
\(\tan (y)=\frac{12}{5}\)Describes the following triangle
Using the Pythagorean Theorem again, we have
\(5^2+12^2=h^2\)Solving for h, we have
\(\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}\)The missing side measure is equal to 13.
Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.
The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles
\(\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}\)To calculate the sine and cosine of the sum
\(\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}\)We can use the following identities
\(\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}\)Using those identities in our problem, we're going to have
\(\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}\)
Find the equation of a line that is perpendicular to 4x+6y=1 and that has a greater intercept to the line 2x+3y=18
Answers
Answer:
The equation of the the line that is perpendicular to 4·x + 6·y = 1 and that has a greater intercept to the line 2·x + 3·y = 18 can be 2·y - 3·x = 14
Step-by-step explanation:
The line which is perpendicular to the required line = 4·x + 6·y = 1
The line with which the required line has a greater intercept = 2·x + 3·y = 18
Solution;
The relationship between the slope, m₁, of a straight line, y = m₁·x + c₁ perpendicular to another straight line, y = m₂·x + c₂, with slope m₂ is given as follows;
m₁ = -1/m₂
Rewriting the equation of the given line in slope and intercept form gives;
4·x + 6·y = 1
6·y = 1 - 4·x
y = 1/6 - 4·x/6 = 1/6 - 2·x/3 = 1/6 - (2/3)·x
∴ y = 1/6 - (2/3)·x
Therefore, the slope, 'm₁', of the line y = 1/6 - (2/3)·x, is m₁ = -(2/3)
The slope of the perpendicular line, is therefore, m₁ = -1/m₂
∴ m₂ = -1/m₁
m₂ = -1/(-(2/3)) = 3/2
The intercept of a straight line of the form y = m·x + c is 'c'
The intercept of the line 2·x + 3·y = 18 is obtained by rewriting the equation of the line in slope and intercept form as follows;
2·x + 3·y = 18
y = 18/3 - (2/3)·x = 6 - (2/3)·x
y = 6 - (2/3)·x = -(2/3)·x + 6
y = -(2/3)·x + 6
By comparing the above equation to the equation, y = m·x + c, we have;
c = 6
The intercept of the line y = -(2/3)·x + 6, which is the same line as 2·x + 3·y = 18 is 6
∴ The intercept of the required line, c₂ > 6
The equation of the required line in slope and intercept form, y = m·x + c, can therefore be;
y = (3/2)·x + 7
By multiplying by 2, we get;
2·y = 3·x + 14
∴ The equation of the line can be 2·y - 3·x = 14.
Kyle has $25 and gets a job walking Chihuahuas for $2 per hour. Sophia has $4 and walks Rottweilers for $9 per hour. How many hours will they both have to work to have the same amount of money?
Answers
Answer:
3 hours
Step-by-step explanation:
Let k represent Kyle's balance after h hours. Let s represent Sophia's balance after h hours. Then we have ...
k = 25 +2h
s = 4 +9h
We want to find h so that k=s:
25 +2h = 4 +9h
21 = 7h . . . . . subtract 4+2h
3 = h . . . . . . . divide by 7
If both work 3 hours, they will have the same amount of money.
Point (−3, 1) is reflected across the y-axis. What are the coordinates of its image? Enter the correct coordinates in the boxes.
Answers
Answer:
(3,1)is the correct ans
Answer:
(3, 1 )
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , then
(- 3, 1 ) → (3, 1 )
anita has a success rate of 80% on free throws in basketball
Answers
Answer:
what is the question there is no context
a sphere is filled with air. if the volume of the sphere is increasing at a rate of 569 cubic inches per minute, what is the rate, in inches per minute, at which the radius of the sphere is changing when the radius is 4 inches? submit an exact answer. remember that the volume of a sphere is v
Answers
The rate, in inches per minute, at which the radius of the sphere is changing when the radius is 4 inches is 2.83
What is the Volume of a Sphere?
The capacity of a sphere is its volume. It is the area that the sphere occupies. Cubic measurements of a sphere's volume include m3, cm3, in3, etc. The sphere has a circular, three-dimensional form. Its form is determined by three axes: the x, y, and z axes. Sports like basketball and football are all instances of spheres with volume.
Since the cross-section of the sphere is a circle, the volume in this case is dependent on the diameter of the sphere's radius. The area or region of a sphere's outer surface is known as its surface area. We may use the following formula to get the volume of a sphere whose radius is "r":
Here, In the question, It is given that:
Radius = 4inch.
Rate of increase = 569 cubic inches;
So, using the Volume of Sphere, formula:
\(\begin{aligned}v=\frac{4}{3} \pi r^3 \\\frac{d v}{d t} &=\frac{d}{d t}\left[\frac{4}{3} \pi r^3\right] \\&=\frac{4 \pi}{3}\left(3 r^2\right) \frac{d r}{d t} \\\frac{d v}{d t} &=4 \pi r^2 \frac{d r}{d t}\end{aligned}\)
\(\begin{aligned}&\frac{d r}{d t}=\frac{\frac{d v}{d t}}{4 \pi r^2}\\&\left.\frac{d r}{d t}=\frac{569}{(4 \pi)(4)^2}=\frac{d}{d t}_{r=4}^{d r^2}=569\right]\\&\frac{d v}{d t}=\frac{569}{64 \pi} \sim 2.83\end{aligned}\)
Hence, the rate, in inches per minute, at which the radius of the sphere is changing when the radius is 4 inches is 2.83
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The number of cases of a disease
increases by the same factor each year, as
shown in the table below.
Write an expression for the number of
cases of the disease after n years.
Start
End of year 1
End of year 2
End of year 3
Number of cases
1400
2100
3150
4725
Answers
Answer:
N*r^n
Step-by-step explanation:
Let the initial number of cases at the start of year 1 be represented by N.
From the given information, we know that the number of cases increases by the same factor each year. Let this factor be represented by r.
Then, at the end of year 1, the number of cases would be N*r, since it has increased by a factor of r.
Similarly, at the end of year 2, the number of cases would be Nrr, or N*r^2.
At the end of year 3, the number of cases would be Nrrr, or Nr^3.
We can use this pattern to write a general expression for the number of cases after n years:
N * r^n
where N is the initial number of cases, r is the common factor by which the number of cases increases each year, and n is the number of years elapsed.
If an automobile slows from 26 m/s 18 m/s in the period of 4.0 s what was the average acceleration
Answers
Answer: -2
Step-by-step explanation:
What is the area of a 24-inch rug? Use area of a circle formula: A = πr²
Answers
Please help!! I am so confused on how to do this.
Answers
Answer:
its 62!
p-by-step explanation:
Answer:
62.
Step-by-step explanation:
A=2(wl+hl+hw)=2·(3·5+2·5+2·3)=62
Sabrina decided to try bungee jumping at a local business, which had her sign a waiver before participating in a jump. If Sabrina breaks her leg, why will she not be able to sue the business for negligence?
Select one: a. The company has a business license b. The company followed industry standard safety practices c. Common law fellow servant rule d. Assumption of risk
Answers
Sabrina will not be able to sue the business for negligence because of the concept of assumption of risk.
The correct answer is d. Assumption of risk. When participating in activities such as bungee jumping, individuals are often required to sign a waiver that acknowledges the inherent risks involved in the activity. By signing the waiver, Sabrina would have agreed to assume the risks associated with bungee jumping, including the possibility of injury. This concept of assumption of risk means that Sabrina voluntarily participated in the activity, understanding and accepting the potential dangers. Therefore, if she breaks her leg during the jump, she cannot sue the business for negligence because she willingly assumed the risks involved.
The waiver serves as a legal document that protects the business from liability claims in cases where participants suffer injuries or accidents while engaging in inherently risky activities. By signing the waiver, Sabrina acknowledged that she understood the potential risks and agreed to release the business from any liability resulting from her participation. This legal principle is based on the idea that individuals should take personal responsibility for their decisions to engage in risky activities and should not hold others liable for the inherent dangers that they voluntarily chose to expose themselves to. Consequently, Sabrina's signed waiver would likely prevent her from successfully suing the business for negligence if she were to break her leg during the bungee jump.
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Tiffany has a goal to complete a triathlon. The race consists of a 0.93-mile swim, a 24.8-mile bike ride, and a 6.2-mile run. In training, Tiffany can swim at an average pace of 2.2mph. She rides her bike at an average of 18.2mph and runs at 5.1mph. Estimate how long it will take her to complete the triathlon.
Answers
Answer:
3 hours
Step-by-step explanation:
Time = distance / rate
.93 miles / 2.2 mile/hr + 24.8 mile / 18.2 m/hr + 6.2 mile / 5.1 mile/hr = 3.00 hr
Finally, the total time in which Tiffany will complete the race will be 3 hours.
What is speed?speed is a quantity that expresses the relationship between the space traveled by an object. That is, the speed is associated with the change of position of an object in space within a certain amount of time.
Given that The race consists of a 0.93-mile swim, a 24.8-mile bike ride, and a 6.2-mile run.
In training, she can swim at an average pace of 2.2mph. She rides her bike at an average of 18.2mph and runs at 5.1mph.
We know that Time = distance / rate
So, total time= 0.93 miles / 2.2 mile/hr + 24.8 mile / 18.2 m/hr + 6.2 mile / 5.1 mile/hr
total time = 3.00 hr
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product of 2 2/3 and 4 4/5
Answers
Answer: In decimal form, it's 12.8, or improper fraction 64/5, or mixed number 12 4/5
Step-by-step explanation:
(2 2/3)*(4 4/5)
convert the improper fraction into a mixed number: 2*3+2/3* 4 4/5
calculate the product: 6+2/3*4 4/5
convert 4 4/5
64/5= 12 4/5
Hope this helps!
PLEASE I NEED HELPPPPP!!!!!!!!! Determine the measure.
Answers
Answer:
710°
Step-by-step explanation:
360° because you make a full rotation + 270° because you go 3/4 of the way around + 80° = 710° total.
Principal Phillipi used a random sample of 20 student records to determine how far, in miles, students live from the school. The results are shown below. 3, 4, 5, 3, 4, 5, 6, 5, 4, 3, 2, 3, 4, 5, 6, 4, 8, 4, 3, 2 What is the mean distance that his students live from the school, rounded to the nearest tenth? 4. 1 miles 4. 2 miles 8. 0 miles 8. 3 miles.
Answers
The mean distance that Principal Phillipi's students live from the school, rounded to the nearest tenth, is 4.2 miles.
To find the mean distance, we sum up all the distances and divide by the total number of observations.
In this case, the given distances are 3, 4, 5, 3, 4, 5, 6, 5, 4, 3, 2, 3, 4, 5, 6, 4, 8, 4, 3, and 2. Adding them together gives us a sum of 87.
Dividing this sum by the total number of observations (which is 20 in this case) gives us an average distance of 4.35 miles.
However, the question asks for the mean distance rounded to the nearest tenth. Rounding 4.35 to the nearest tenth gives us 4.4 miles. Therefore, the correct answer is 4.4 miles.
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PLEASE ANSWER ASAP PLS The equation of a parabola is y=1/8x^2−4x+41. What is the equation of the directrix?
Answers
Answer: 7
Step-by-step explanation:
researcher records the following scores for an Olympic gymnast following her routine: 9.9, 9.8, 9.6, 9.5, 9.7, 9.1, 8.9, and 9.8. What is the range for the scores?
1.0 (9.9 to 8.9)
0.3 (9.8 to 9.5)
0.5 (9.6 to 9.1)
It is not possible to compute a range with an even number of scores.
Answers
The range for the scores is 1.0 (from 9.9 to 8.9). The range is the difference between the highest and lowest numbers in a set of numbers. In this case, the highest score is 9.9 and the lowest score is 8.9, so the range is 1.0.
In mathematics, the range of a function can refer to one of two similar terms:
the common area of the function
The image of the function
Given two groups X and Y, the binary relation f between X and Y is a (exact) function (X to Y), if there is a y in Y for every x in X, so f is associated with y. The sets X and Y are called the area of f and the common domain, respectively.
The range is a measure of dispersion in a set of numbers. To find the range, you need to subtract the lowest score from the highest score. In this case, the scores for the Olympic gymnast are: 9.9, 9.8, 9.6, 9.5, 9.7, 9.1, 8.9, and 9.8.
First, identify the highest and lowest scores:
Highest score: 9.9
Lowest score: 8.9
Next, subtract the lowest score from the highest score:
Range = 9.9 - 8.9
The range for the scores is 1.0 (9.9 to 8.9).
Your answer: 1.0 (9.9 to 8.9)
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What multiplication equattion can be used to explain the solution to 15 / 1/3
Answers
Step-by-step explanation:
15 / (1/3) is equal to 15 x 3/1 = 15 x 3 = 45
Reciprocal of 1/3 = 3/1
So, the multiplication equation that explains the solution is:
15 * (3/1) = 45
Therefore, 15 divided by 1/3 is equal to 45.
HELP!! WILL MAKE BRAINLIEST!!
The equation(24x^2 + 25x - 47)/(ax--2) = -8x - 3 - 53/(ax--2) is true of all values of x≠2/a where a is a constant. What is the value of a?
Please help me there is no multiple choice :(
Answers
Answer:
-3
Step-by-step explanation:
The fastest way to solve this problem is to multiply each side of the given equation by in order to get rid of the fraction. After you do this you should have:
Then multiply \((-8x-3)\) and \((ax-2)\) using FOIL:
\(24^2+25x-47=-8ax^2-3ax+16x+6-53\)
Then reduce on the right side of the equation:
\(24x^2+25x-47=-8ax^2-3ax+16x-47\)
Because the coefficients of the \(x^2\) term have to be equal on both sides of the equation, reduce from \(-8a=24\) to \(a = -3\) by dividing both sides by \(-8\).
Which number has a 3 with a value that is 100 times greater than the value of the 3 in 20.345
Answers
Answer:
600
Step-by-step explanation:
you add