Answer:
Wedge Z requires the least amount of force to do a job.Step-by-step explanation:
In physics, Work is defined as the energy needed to move certaing object through a certain distance. Specifically, the work done is directly proportional to the force exerted and the distance.
It's important to know that a change of point is needed to have actually work done, physically speaking. This means if the object doesn't move, then there's no work done.
Mathematically, the work is defined
[tex]W= F \times d[/tex]
Isolating the force
[tex]F=\frac{W}{d}[/tex]
So, notice that the distance is inversely proportional to the force needed, which means the less distance, more force we need.
Now, the problem is giving wides and slopes, which we can use to find heights. And we know already that the less distance we have, the greater force we need, or the most distance, the least force.
Let's find which wedge has the greatest vertical distance.
[tex]m=\frac{y}{x}[/tex]
Wedge 1.[tex]5=\frac{y}{2} \implies y=10[/tex]
Wedge 2.[tex]8=\frac{y}{4} \implies y=32[/tex]
Wedge 3.[tex]9=\frac{y}{3} \implies y=27[/tex]
Wedge 4.[tex]10=\frac{y}{5}\\ y=50[/tex]
Notice that the last wedge has greater vertical distance, that means Wedge Z requires least amount of force to do a job.
Answer:
The correct answer is Y not Z.
Step-by-step explanation:
Olivia is carpeting her living room. It is 6-by-7.5 feet. If she wants to buy 10 percent extra for waste, how m any square feet of carpet should she buy? A. 45 square feet B. 49.5 square feet C. 55 square feet D. 59.5 square feet
Answer:
49.5 square feet.
Step-by-step explanation:
6 by 7.5 means 6 x 7.5.
6 x 7.5 = 45
She wants to by 10% extra.
45 is 100% so multiply 45 by 1.1.
45 x 1.1 = 49.5
Olivia's room area is 45 square feet. Considering a 10% extra for waste, she should buy 49.5 square feet of carpet.
Explanation:To calculate how much carpet Olivia should buy including waste, we first need to figure out the area of her room. The area of a rectangle is found by multiplying the length by the width, so in this case, we multiply 6 feet by 7.5 feet, which equals 45 square feet. Then we factor in the 10 percent extra for waste - which is 4.5 square feet (10% of 45). Adding these together, we get a total of 49.5 square feet. Therefore, Olivia should buy 49.5 square feet of carpet. The correct answer is B. 49.5 square feet.
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0.273 repeating decimal into a fraction
Decimal:0.273 or 0.273273273
Fraction:273/999=91/333
Answer:
0.273 as a fraction is 273/1000
0.273273273... as a repeating decimal, (273/999) as repeating decimal fraction.
[tex]\sqrt{91 - 40\sqrt{3} }[/tex]
Answer:
[tex]5\sqrt{3} - 4[/tex]
Step-by-step explanation:
[tex]\sqrt{(4-5\sqrt{3} )^{2} }[/tex]
[tex]5\sqrt{3} - 4[/tex]
The heights of a group of boys and girls at a local middle school are shown on the dot plots below
Boys' Heights
40 41 44 46 48 60 62 64
C
Inches
M
Girls' Heights
40 41 44 46 48 50 52 54 56 58
40 is the height of the boy and the inch is C
Circle O is shown. Secant K L intersects tangent K J at point K outside of the circle. Tangent K J intersects circle O at point M. Secant K L intersects the circle at point N. The measure of arc M N is 62 degrees. The measure of arc M L is 138 degrees.
Shondra wants to find the measure of angle JKL. Her work is started. What is the measure of angle JKL?
m∠JKL = One-half (138 – 62)
m∠JKL =
°
Answer: 38
138 - 62 = 76
1/2 > 0.5
so 76 x 0.5 = 38
Step-by-step explanation:
Answer:
38
Step-by-step explanation:
According to a survey, 2323% of residents of a country 25 years old or older had earned at least a bachelor's degree. You are performing a study and would like at least 1010 people in the study to have earned at least a bachelor's degree. (a) How many residents of the country 25 years old or older do you expect to randomly select? (b) How many residents of the country 25 years old or older do you have to randomly select to have a probability 0.9450.945 that the sample contains at least 1010 who have earned at least a bachelor's degree? (a) The number of randomly selected residents is 4444. (Round up to the nearest integer.) (b) The number of randomly selected residents, with a probability 0.9450.945 containing at least 1010 who have earned at least a bachelor's degree, is 2828. (Round up to the nearest integer.)
Answer:
a) 44
b) 64
Step-by-step explanation:
Applying the central limit theorem, the proportion of the random sample of 25 years old or older that have earned at least a bachelor's degree will be equal to the population proportion of 23%.
Mean = np
Mean = 10
p = 0.23
n = ?
10 = n×0.23
N
n = (10/0.23) = 43.5 = 44 to the nearest whole number.
b) This is a binomial distribution problem with the probability known and the number of trials unknown.
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = ?
x = Number of successes required = 10
p = probability of success = 0.23
q = probability of failure = 1 - 0.23 = 0.77
P(X ≥ 10) = 0.945
P(X ≥ 10) = 1 - P(X < 10) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9)]
0.945 = 1 - [Σ P(X=x)] (with the summation of x from 0 to 9)
Using the trial and error method on the binomial distribution formula calculator, n is obtained to be 64.
Hope this Helps!!!
Final answer:
To have a high likelihood of sampling at least 10 people with a bachelor's degree, using the survey information that 23% of the population holds such a degree, you would want to sample about 44 individuals. For a probability of 0.945 of having at least 10 degree-holders in your sample, you would need to sample approximately 28 individuals.
Explanation:
Considering the survey indicating that 23% of residents 25 years old or older have earned at least a bachelor's degree, to ensure at least 10 people in a study have a bachelor's degree, you would ideally use the proportion of the population with this degree to determine the size of the sample needed.
Expected Sample Size
If you are selecting individuals at random and want to calculate the expected number of people you need to sample to find 10 people with a bachelor's degree, you divide the number of people needed by the probability of an individual having a bachelor's degree. In mathematical terms, you are expected to sample 10 / 0.23 ≈ 43.48, which we round up to the next whole number, giving us 44 people.
Sample Size for Desired Probability
To achieve a probability of 0.945 that your sample contains at least 10 people with a bachelor's degree, you would utilize statistical methods or software that applies the binomial or hypergeometric distribution formulas. This question seems to indicate that the answer is 28 individuals, which suggests that a calculation has already been made to determine this number.
Over the past decade, the mean number of hacking attacks experienced by members of the Information Systems Security Association is 510 per year with a standard deviation of 14.28 attacks. The distribution of number of attacks per year is normally distributed. Suppose nothing in this environment changes.
1. What is the likelihood that this group will suffer an average of more than 600 attacks in the next 10 years?
Answer:
[tex]P(X>600)=P(\frac{X-\mu}{\sigma}>\frac{600-\mu}{\sigma})=P(Z>\frac{600-510}{14.28})=P(z>6.302)[/tex]
And we can find this probability using the complement rule and the normal standard distribution and we got:
[tex]P(z>6.302)=1-P(z<6.302)=1-0.99999 \approx 0[/tex]
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the number of attacks of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(510,14.28)[/tex]
Where [tex]\mu=510[/tex] and [tex]\sigma=14.28[/tex]
We are interested on this probability
[tex]P(X>600)[/tex]
And the best way to solve this problem is using the normal standard distribution and the z score given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
If we apply this formula to our probability we got this:
[tex]P(X>600)=P(\frac{X-\mu}{\sigma}>\frac{600-\mu}{\sigma})=P(Z>\frac{600-510}{14.28})=P(z>6.302)[/tex]
And we can find this probability using the complement rule and the normal standard distribution and we got:
[tex]P(z>6.302)=1-P(z<6.302)=1-0.99999 \approx 0[/tex]
Given the mean and standard deviation for the number of hacking attacks, the z-score for 600 attacks is about 6.30.
The question asks for the likelihood that the group will suffer an average of more than 600 hacking attacks per year over the next 10 years, given that over the past decade the mean number of hacking attacks experienced by members is 510 per year with a standard deviation of 14.28 attacks. Considering the normal distribution of these hacking attacks, we can calculate this probability by finding the z-score corresponding to 600 attacks and then using the standard normal distribution table to find the probability of exceeding this value.
To calculate the z-score for 600 attacks, we use the formula:
Z = (X - μ) / σ
Where X is the value in question (600 attacks), μ (mu) is the mean (510 attacks), and σ (sigma) is the standard deviation (14.28 attacks). Substituting the given values:
Z = (600 - 510) / 14.28 ≈ 6.30
Looking up a z-score of 6.30 in the standard normal distribution table, we find that the area to the left of this z-score is almost 1, meaning the probability of experiencing more than 600 attacks is extremely small, approaching 0. Thus, it is incredibly unlikely that this group will suffer an average of more than 600 attacks in the next 10 years if nothing changes in their environment.
Write an expression that gives the requested sum.
The sum of the first 16 terms of the geometric sequence with first term 9 and common ratio 2
Answer:
The sum of the first 16 terms of the geometric sequence
[tex]S_{16} = \frac{9(2^{16}-1) }{2-1}[/tex]
S₁₆ = 5,89,815
Step-by-step explanation:
Explanation:-
Geometric series:-
The geometric sequence has its sequence Formation
a , a r, ar² , ar³,...…..a rⁿ be the n t h sequence
Given first term a=9 and common ratio 'r' = 2
The sum of the first 16 terms of the geometric sequence
[tex]S_{n} = \frac{a(r^{n}-1) }{r-1} if r>1[/tex]
Given first term a=9 , 'r' = 2 and n=16
[tex]S_{16} = \frac{9(2^{16}-1) }{2-1}[/tex]
[tex]S_{16} = \frac{9(2^{16}-1) }{1}= 9(65,536-1)=5,89,815[/tex]
A sphere has a diameter of 8 cm. Which statements about the sphere are true?
Answer:
I believe the correct statements are 1), 2), and 3).
The statements provided in the question are all true. The sphere has a radius of 4 cm (A), the diameter's length is twice the length of the radius (B), and the volume of the sphere is 256/3 π cm³ (C).
A) The sphere has a diameter of 8 cm, which is the distance between two points on the surface of the sphere passing through its center. By definition, the diameter is twice the length of the radius. Thus, to find the radius of the sphere, we divide the diameter by 2:
Radius = Diameter / 2
Radius = 8 cm / 2
Radius = 4 cm
B) This statement is true. As mentioned earlier, the diameter of the sphere (8 cm) is indeed twice the length of its radius (4 cm).
C) The volume of a sphere can be calculated using the formula:
Volume = (4/3) * π * Radius³
Now, let's calculate the volume using the given radius:
Volume = (4/3) * π * (4 cm)³
Volume = (4/3) * π * 64 cm³
Volume = 256/3 * π cm³
Hence the correct option is (a), (b) and (c).
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Complete Question:
A sphere has a diameter of 8 cm.
A) The sphere has a radius of 4 cm.
B) The diameter’s length is twice the length of the radius.
C) The volume of the sphere is 256/3 π cm³
g Using calculus and the SDT (then FDT if necessary), find all global and local maximum and minimums given the function f(x) = x 3 + x 2 − x + 1 where x ∈ [−2, 1 2 ]. Clearly identify critical values and show the SDT then the FDT if the SDT didn’t provide an answer and then interpret the solution.
Answer:
[tex]S_{1 } (x,y) = (0.333, 0.815)[/tex] (Absolute minimum) and [tex]S_{2} (x,y) = (-1, 2)[/tex] (Absolute maximum)
Step-by-step explanation:
The critical points are determined with the help of the First Derivative Test:
[tex]f'(x) = 3\cdot x ^{2} +2\cdot x -1[/tex]
[tex]3\cdot x^{2} + 2\cdot x - 1 = 0[/tex]
The critical points are:
[tex]x_{1} \approx 0.333[/tex] and [tex]x_{2} \approx -1[/tex]
The Second Derivative Test offers a criterion to decide whether critical point is an absolute maximum and whether is an absolute minimum:
[tex]f''(x) = 6\cdot x +2[/tex]
[tex]f''(x_{1}) = 3.998[/tex] (Absolute minimum)
[tex]f''(x_{2}) = -4[/tex] (Absolute maximum)
The critical points are:
[tex]S_{1 } (x,y) = (0.333, 0.815)[/tex] (Absolute minimum) and [tex]S_{2} (x,y) = (-1, 2)[/tex] (Absolute maximum)
The global maximum is at x = -1 with f(-1) = 2, and the global minimum is at x = -2 with f(-2) = -1.
To find the global and local maxima and minima of the function f(x) = [tex]x^3 + x^2[/tex] − x + 1 over the interval [-2, 1/2], follow these steps:
Find critical points: First, we need to find the derivative of the function f(x):
f'(x) = [tex]3x^2[/tex]+ 2x - 1
Solve f'(x) = 0 to find critical points within the interval:
[tex]3x^2[/tex]+ 2x - 1 = 0
Using the quadratic formula x = (-b ± √(b²-4ac)) / 2a, where a = 3, b = 2, and c = -1:
x = [-2 ± √(4 + 12)] / 6
x = [-2 ± 4] / 6
This gives two solutions:
x = 1/3 and x = -1
Both are within the interval [-2, 1/2], so we consider these as critical points.
Second Derivative Test (SDT): Find the second derivative to apply the SDT:
f''(x) = 6x + 2
Evaluate f''(x) at the critical points:
f''(-1) = 6(-1) + 2 = -4 (which is negative, indicating a local maximum)
f''(1/3) = 6(1/3) + 2 = 4 (which is positive, indicating a local minimum)
Evaluate the function at the endpoints: Compute f(x) at the bounds of the interval:
f(-2) = (-2)³ + (-2)² - (-2) + 1 = -8 + 4 + 2 + 1 = -1
f(1/2) = (1/2)³ + (1/2)² - (1/2) + 1 = 1/8 + 1/4 - 1/2 + 1 = 7/8
Additionally, compute the function at the critical points:
f(-1) = (-1)³ + (-1)² - (-1) + 1 = -1 + 1 + 1 + 1 = 2
f(1/3) = (1/3)³ + (1/3)² - (1/3) + 1 = 1/27 + 1/9 - 1/3 + 1 ≈ 0.963
Interpret the results:
The maximum and minimum values for f(x) over [-2, 1/2] are:
Local maximum at x = -1 with f(-1) = 2
Local minimum at x = 1/3 with f(1/3) ≈ 0.963
Global maximum at x = -1 with f(-1) = 2
Global minimum at x = -2 with f(-2) = -1
you have $15,000 to invest for 5 years at 5.5% annual interest rate that is compounded continuously. how much money will you have at the end of 5 years?
Answer:
$19,747.96
Step-by-step explanation:
You are going to want to use the continuous compound interest formula, which is shown below:
[tex]A = Pe^{rt}[/tex]
A = total
P = principal amount
r = interest rate (decimal)
t = time (years)
First, lets change 5.5% into a decimal:
5.5% -> [tex]\frac{5.5}{100}[/tex] -> 0.055
Next, plug in the values into the equation:
[tex]A=15,000e^{0.055(5)}[/tex]
[tex]A=19,747.96[/tex]
After 5 years, you will have $19,747.96
Which decimal goes where the H is?
Answer:
sorry bro i sant yo eran poinst
Step-by-step explanation:
jajajajajjaja
Find the value of x in the triangle shown below.
Answer:
x=8
Step-by-step explanation:
We can use the Pythagorean theorem to solve
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
6^2 + x^2 = 10^2
36 + x^2 = 100
Subtract 36 from each side
36-36 +x^2 = 100-36
x^2 = 64
Take the square root of each side
sqrt(x^2) = sqrt(64)
x = 8
Answer:
x = 8
Step-by-step explanation:
According to Pythagorean Theorem
[tex]AB {}^{2} + BC {}^{2} = AC {}^{2} [/tex]
here
[tex]AB = x \\ BC = 6 \\ AC = 10[/tex]
Now,
[tex] {x}^{2} + {6}^{2} = 10 {}^{2} \\ {x}^{2} = {10}^{2} - {6}^{2} \\ x {}^{2} = 100 - 36 \\ {x}^{2} = 64 \\ x = \sqrt{64} \\ x = 8[/tex]
AB = x = 8
8x9-2-3 = 32
Where do the parentheses go
Answer:
8 * (9 - 2 -3) = 32
Step-by-step explanation:
8 * (9 - 2 - 3)
8 * (4)
32
Answer:
8x(9-2-3) = 32
Step-by-step explanation:
8x9-2-3 = 32
We need 8*4 to get to 32
so 9 -2-3 need to equal 4
That means we need the parentheses around this term because
9-2 = 7
7-3 =4
8x(9-2-3) = 32
suppose that no one demanded a hotel room at $150. At this price how much profit would a hotel owner earn
Answer:
Depending on how many people buy hotel rooms, then there is no answer
Step-by-step explanation:
(The question is not specific enough)
how do the identity and associative property work?
Answer:
Step-by-step explanation:
The associative property is helpful while adding or multiplying multiple numbers. By grouping, we can create smaller components to solve. It makes the calculations of addition or multiplication of multiple numbers easier and faster. Here, adding 17 and 3 gives 20.
the identity property of 1 says that any number multiplied by 1 keeps its identity. In other words, any number multiplied by 1 stays the same. The reason the number stays the same is because multiplying by 1 means we have 1 copy of the number.
What is 2.888888 as a fraction?
Answer:
26/9
Step-by-step explanation:
8/9=.88888888888889 (on calc)
2+8/9
18/9+8/9
=26/9
A school has one computer for every 17 students. If the school has 714 students, how many computers does it have?
Answer:
42 computers
Step-by-step explanation:
If there is 1 computer per 17 students, then we simply divide the amount of students by 17 to get the amount of computers.
Answer:
42
Step-by-step explanation:
714/17= 42
John has 1/3 as much money as grant. Grant gives John 9$. Now grant has 6$ more than John. How much money do grant and John have in all
Answer:
48 dollars
Step-by-step explanation:
grant originally had 36 and john had 12
decrease grant by 9 and increase john by 9
grant has 27, and john has 21
difference is 6 so the sum is 48.
Answer:
48 dollars
Step-by-step explanation:
Total money of Grant : 36
Total money of John : 12
Grant gave 9 dollars to John : 36 - 9 = 27
Now John has 21 dollars ( 12 + 9 = 21 )
So , 21 + 27 = 48
Thus , John and Grant have 48 dollars in total
Sheryl takes a summer job selling hats for a local soccer team. She realizes that there is a relationship between the number of games the team wins each season and the number of hats vendors like her tend to sell. She collects data from the past several seasons. The scatter plot shows her data and the line of best fit.
Using technology, she finds that the equation of the line of best fit is y = 3.75x + 13.75.
Based on the equation for the line of best fit, about how many hats can Sheryl predict she will sell if the team wins 9 games this season?
A.
48 hats
B.
42 hats
C.
9 hats
D.
10 hats
Answer:
47
Step-by-step explanation:
x is games won
y is hats sold
[tex]y=3.75x+13.75\\y=3.75(9) + 13.75\\y=47.5[/tex]
Since you can't sell .5 of a hat- you need to round this answer.
Answer:
48
Step-by-step explanation:
Help me please I’m trying to figure out the answer and I can’t
Answer:
One thing that is alike is that both expressions start off as a division statement/fraction
Step-by-step explanation:
One things that is not alike is that Expression A has 3 variables while Expression B doesn't.
A gourmet pizza café sells three sizes of pizzas. If you buy all three sizes, it costs $46.24. A medium pizza costs $15.75 and a large pizza costs $17.50. How much does the small pizza cost? What did you need to do to solve this problem?
Answer:
Step-by-step explanation:
You need to subtract the prices of the medium and large from the total
Small = 46.24 - medium - large
17.50 + 15.75 = 33.75
S = 46.24 - 33.75
S = 12.99
A scientist claims that a smaller proportion of members of the National Academy of Sciences are women when compared to the proportion of women nationwide. Let p1 represent the proportion of women in the National Academy of Sciences and p2 represent the proportion of women nationwide. Which is the correct alternative hypotheses that corresponds to this claim?
A.Ha: p1 - p2 < 0
B.Ha: p1 - p2 > 0
C.Ha: p1 - p2 ? 0
Answer:
Correct option: (A) p₁ - p₂ < 0.
Step-by-step explanation:
The claim made by the scientist is that the proportion of female members of the National Academy of Sciences is less than the proportion of female members nationwide.
To test this claim we can difference between two proportions z-test.
It is assumed that p₁ is the proportion of women in the National Academy of Sciences and p₂ is the proportion of women nationwide.
Then we nee to test whether p₁ - p₂ < 0 or not.
The hypothesis can be defined as:
H₀: The proportion of women in the National Academy of Sciences is not less than the proportion nationwide, i.e. p₁ - p₂ ≥ 0.
H₀: The proportion of women in the National Academy of Sciences is less than the proportion nationwide, i.e. p₁ - p₂ < 0.
Thus, the correct option is (A).
As the saying goes, “You can't please everyone.” Studies have shown that in a large
population approximately 4.5% of the population will be displeased, regardless of the
situation. If a random sample of 25 people are selected from such a population, what is the
probability that at least two will be displeased?
A) 0.045
B) 0.311
C) 0.373
D) 0.627
E) 0.689
Answer:
Step-by-step explanation:
The correct answer is (B).
Let X = the number of people that are displeased in a random sample of 25 people selected from a population of which 4.5% will be displeased regardless of the situation. Then X is a binomial random variable with n = 25 and p = 0.045.
P(X ≥ 2) = 1 – P(X ≤ 1) = 1 – binomcdf(n: 25, p: 0.045, x-value: 1) = 0.311.
P(X ≥ 2) = 1 – [P(X = 0) + P(X = 1)] = 1 – 0C25(0.045)0(1 – 0.045)25 – 25C1(0.045)1(1 – 0.045)24 = 0.311.
The probability that at least two people will be displeased in a random sample of 25 people is approximately 0.202.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
This problem can be solved using the binomial distribution since we have a fixed number of trials (selecting 25 people) and each trial has two possible outcomes (displeased or not displeased).
Let p be the probability of an individual being displeased, which is given as 0.045 (or 4.5% as a decimal).
Then, the probability of an individual not being displeased is:
1 - p = 0.955.
Let X be the number of displeased people in a random sample of 25.
We want to find the probability that at least two people are displeased, which can be expressed as:
P(X ≥ 2) = 1 - P(X < 2)
To calculate P(X < 2), we can use the binomial distribution formula:
[tex]P(X = k) = (^n C_k) \times p^k \times (1 - p)^{n-k}[/tex]
where n is the sample size (25), k is the number of displeased people, and (n choose k) is the binomial coefficient which represents the number of ways to choose k items from a set of n items.
For k = 0, we have:
[tex]P(X = 0) = (^{25}C_ 0) \times 0.045^0 \times 0.955^{25}[/tex]
≈ 0.378
For k = 1, we have:
[tex]P(X = 1) = (^{25}C_1) \times 0.045^1 \times 0.955^{24}[/tex]
≈ 0.42
Therefore,
P(X < 2) = P(X = 0) + P(X = 1) ≈ 0.798.
Finally, we can calculate,
P(X ≥ 2) = 1 - P(X < 2)
= 1 - 0.798
= 0.202.
Thus,
The probability that at least two people will be displeased in a random sample of 25 people is approximately 0.202.
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can you guys pls help ( MARKING BRAINLIST ) :)!!
Answer:
(36/4)-(36/9)=5
(8x3)-12=12
Step-by-step explanation:
36/4=9, 36/9=4, and 9-4=5
8x3=24 and 24-12=12
g 6. Provide an example of (a) a geometric series that diverges. (b) a geometric series PN n=0 an, that starts at n = 0 and converges. Find its sum. (c) a geometric series PN n=1 an, that starts at n = 1 and converges. Find its sum. (d) Explain how the sums for a geometric series that starts at n = 0 differs from the same series that starts at n = 1.
Answer:
Check step-by-step-explanation.
Step-by-step explanation:
A given criteria for geometric series of the form [tex]\sum_{n=0}^{\infty} r^n[/tex] is that [tex]|r|<1[/tex]. Other wise, the series diverges. When it converges, we know that
[tex] \sum_{n=0}^\infty r^n = \frac{1}{1-r}[/tex].
So,
a)[tex]\sum_{n=0}^\infty (\frac{3}{2})^n[/tex] diverges since [tex]\frac{3}{2}>1[/tex]
b)[tex]\sum_{n=0}^\infty (\frac{1}{2})^n [/tex]converges since [tex]\frac{1}{2}<1[/tex], and
[tex]\sum_{n=0}^\infty (\frac{1}{2})^n= \frac{1}{1-\frac{1}{2}} = \frac{2}{2-1} = 2[/tex]
c)We can use the series in b) but starting at n=1 instead of n=0. Since they differ only on one term, we know it also converges and
[tex]\sum_{n=1}^{\infty}(\frac{1}{2})^n = \sum_{n=0}^{\infty}(\frac{1}{2})^n-(\frac{1}{2})^0 = 2-1 = 1[/tex].
d)Based on point c, we can easily generalize that if we consider the following difference
[tex]\sum_{n=1}^\infty r^n-\sum_{n=0}^\infty r^n = r^0 = 1[/tex]
So, they differ only by 1 if the series converges.
Final answer:
A divergent geometric series has a common ratio (r) greater than 1. A convergent geometric series has a common ratio (r) between -1 and 1. The sums of geometric series that start at n = 0 and n = 1 are different because the first term is included or omitted.
Explanation:
The questions can be answered as -
(a) A geometric series that diverges is an example where the common ratio (r) is greater than 1. An example of a divergent geometric series is: 2 + 4 + 8 + 16 + ...
(b) A geometric series that converges is an example where the common ratio (r) is between -1 and 1. An example of a convergent geometric series starting at n = 0 is: 1 - 1/2 + 1/4 - 1/8 + ... To find its sum, we can use the formula for the sum of a geometric series: S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio. Plugging in the values, the sum of this series is 2/3.
(c) A geometric series that starts at n = 1 and converges can have a different sum since the first term is omitted from the calculation. An example of such a series is: 1/2 + 1/4 + 1/8 + 1/16 + ... To find its sum, we use the same formula as in part (b) but with a different first term. In this case, the sum of the series is 1/2.
(d) The sums for a geometric series that starts at n = 0 and n = 1 are different because the first term is included in the sum for n = 0 but omitted in the sum for n = 1.
HELP! Given the inequality select ALL possible solutions
A national consumer magazine reported the following correlations.
The correlation between car weight and car reliability is -0.30.
The correlation between car weight and annual maintenance cost is 0.20.
Which of the following statements are true?
I. Heavier cars tend to be less reliable.
II. Heavier cars tend to cost more to maintain.
III. Car weight is related more strongly to reliability than to maintenance cost.
a. III only
b. I, II, and III
c. I and II
d. I only
Answer:
Correct option: (b).
Step-by-step explanation:
The correlation coefficient is a statistical degree that computes the strength of the linear relationship between the relative movements of the two variables (i.e. dependent and independent). It ranges from -1 to +1.
Negative correlation is a relationship amid two variables in which one variable rises as the other falls, and vice versa. A positive correlation occurs when one variable declines as the other variable declines, or one variable escalates while the other escalates.
In statistics, a perfect positive correlation is represented by +1 and -1 indicates a perfect negative correlation.
The closer the correlation value is to 1 the stronger the relationship between the two variables.
Let,
X = car weight
Y = car reliability
Z = annual maintenance cost
It is provided that:
Corr. (X, Y) = -0.30
Corr. (X, Z) = 0.20
The correlation coefficient of car weight and car reliability is negative. This implies that there is a negative relation between the two variables, i.e. as the weight of the car increases the reliability decreases and vice-versa.
And the correlation coefficient of car weight and annual maintenance cost is positive. That is, the two variables move in the same direction, i.e. as the weight of the car increases the annual maintenance cost also increases.
The correlation coefficient value of (X, Y) is closer to 1 than that of (X, Z).
This implies that the relationship between car weight and car reliability is much more stronger that the relationship between car weight and annual maintenance cost.
Thus, all the provided statement are correct.
Hence, the correct option is (b).
Final answer:
The correlations indicate that heavier cars tend to be less reliable and cost more to maintain. (option b) I, II, and III.
Explanation:
The given correlations between car weight and car reliability (-0.30) and car weight and annual maintenance cost (0.20) can be used to determine the relationship between these variables.
I. Heavier cars tend to be less reliable.
II. Heavier cars tend to cost more to maintain.III. Car weight is related more strongly to reliability than to maintenance cost.Based on the given correlations, the following statements are true:
I. Heavier cars tend to be less reliable.II. Heavier cars tend to cost more to maintain.III. Car weight is related more strongly to reliability than to maintenance cost.Therefore, the correct answer is (option b) I, II, and III.
10. Use the trigonometric ratio tan 0 = 3/4 to write the other five trigonometric ratios for 0
I hope this helps you
Jaylon spent $21.60 of the $80 he got for his birthday. What percent of his money did he spend? Oh
Answer:
27%
Step-by-step explanation:
Jaylon spent 27% of his birthday money.
Answer:
27%
Step-by-step explanation:
To find the percent spent, take the amount spent and put it over the total
21.60 /80
.27
Multiply by 100% to put in percent form
27%