Answer:
Page 1:
a) 3570
b) 32 or -8y+32
c) 2y^3-2y^2+8y
d) 5x-5y-4(x-y)
e) 4x(x-y)+y(x-y)
Page 2:
a) 125 93/t
b) -x(4x+3)
c) (a+b)(x-y)
d) (4x+3)(3x^2-5)
e) -x (a-b-3)
Page 3:
a) P=A-1
b) D=S+X
c) My poor back hurts at this point so I quit here -
d) If you really need these two I'm happy to come back and answer them though! let me know in the comments ^^
The graphs of f(x) and g(x) are shown below:
Graph of function f of x open upward and has its vertex at negative 7, 0. Graph of function g of x opens upward and has its vertex at negative 7, negative 2.
If f(x) = (x + 7)2, which of the following is g(x), based on the translation?
g(x) = (x + 9)2
g(x) = (x + 5)2
g(x) = (x + 7)2 + 2
g(x) = (x + 7)2 − 2
Answer: g(x)=(x+7)^2-2
Step-by-step explanation:
g(-7)=f(-7)-2
g(-7)=(-7+7)^2-2
g(x)=(x+7)^2-2
Evaluate g(x)=4 -3x when x=-3,0, and 5
Answer:
-11
Step-by-step explanation:
i think I have the right answer but I’m not sure
please help
Answer:
1c = 0.5pt
20x0.5=10 pt 0 c
Step-by-step explanation:
How to factor this expression: x^2-9?
Answer:
(x+3)(x-3)
Step-by-step explanation:
rewrite "9" as 3^2
so it is x^2-3^2
You use the difference of squares: a^2-b^2=(a+b)(a-b)
apply it: (x+3)(x-3)
Part B
Write a numerical expression that represents the area Sabrina painted the second weekend. Using this numerical expression, find the area that Sabrina painted the second weekend.
Step-by-step explanation:
she painted half of the still to be painted area.
after the first weekend there were 800 of 1600 ft² painted, and therefore 1600 - 800 = 800 ft² left to be painted.
on the second weekend she then painted half of that :
800 / 2.
that means she painted 800/2 = 400 ft², and that left 800 - 400 = 400 ft² to be painted on the following weekends.
if we look in detail, we find the starting 800 ft² of the second weekend are already the result of the first weekend.
800 = 1600 / 2
so,
800 / 2 = 1600 / 2 / 2 = 1600 / 2² = 1600 / 4.
and the same principle goes on weekend after weekend.
therefore, the expression for the nth weekend could be
1600 × (1/2)^n ft²
that means, she painted
on the 1st weekend : 1600 × 1/2 = 800 ft²
on the 2nd weekend : 1600 × 1/4 = 400 ft²
on the 3rd weekend : 1600 × 1/8 = 200 ft²
on the 4th weekend : 1600 × 1/16 = 100 ft²
...
that also means : she will never be finished, as she always paints only half of what is still left open, and that leaves always some part open. it will be tinier and tinier over time, but never 0.
T/F : the mathematical algorithm used by hmac-based one-time passwords
True. The HMAC-based one-time password algorithm uses a mathematical algorithm to generate a unique password for each login attempt.
This algorithm combines a secret key and a counter to produce a one-time password that is difficult to guess or duplicate. The algorithm is designed to be secure and reliable, providing an additional layer of protection for user accounts. By using a different password for each login attempt, the algorithm helps prevent attackers from gaining access to a user's account even if they manage to intercept the password. Overall, the HMAC-based one-time password algorithm is an effective way to enhance the security of online accounts and protect against unauthorized access.
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Solve for a in terms of b, c, and d.
c=a+b–d
I need help plsssssssssss
The ordering of the number 2/3 and 7/11 is given as 7/11 < 2/3
What is an equation?An equation is an expression that shows the relationship between numbers and variables using mathematical expressions. Equations are classified based on degree as linear, quadratic, cubic
Given the number 2/3 and 7/11 needs to have a common denominator.
Hence:
2/3 = (2/3) * (11/11) = 22/33
Also:
7/11 = (7/11) * (3/3) = 21/33
Therefore:
7/11 < 2/3 because 21/33 < 22/33
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Pageturner Bookstore sells two kinds of used books: hardcover and paperback. A hardcover book costs $8 and a paperback book costs $7. In one day, the store sold 10 books for a total of $76. How many hardcover books did they sell?
Please help!!!
Answer:
6 hardcover booksStep-by-step explanation:
Let h be hardcover and p be paperback
We have following equations:
8h + 7p = 76h + p = 10Multiply the second equation by 7 and subtract from the first equation:
8h + 7p - 7h - 7p = 76 - 70h = 6Answer:
Let x be the number of hardcover and y be number of paperback
Then the equations are :---
8x+7y=76 .............(i)x+y=10 ..............(ii)Multiplying the second equation with 7 and substrating it from the first equation we get,
(8x+7y)-(7x+7y)= (76-70)x=6Therefore, bookstore sold 6 hardcover.
6 is the right answer.The perimeter of a rectangle is 50 inches. Its width measures 11 inches. What is its length? Let x= length of the rectangle. A.) 2x - 11 = 50
B.) 2x + 11 = 50
C.) x + 11 = 50
D.) 2x + 22 = 50
Answer: D.) 2x + 22 = 50
Step-by-step explanation:
P=2(l+w)
2x+22=50 is correct because
2 times x is 2 times the unknown length
11 times 2 is 22 so, you add that to the 2x
50 is the perimeter
For the following situation, find the mean and standard deviation of the population. List all samples (with replacement) of the given size from that population and find the mean of each. Find the mean and standard deviation of the sampling distribution and compare them with the mean and standard deviation of the population. The word counts of five essays are 506, 628, 554, 600, and 584. Use a sample size of 2.
the mean and standard deviation of the sampling distribution and compare them with the mean and standard deviation of the population is 18.9.
The population is the set of word counts of the five essays: {506, 628, 554, 600, 584}. To find the mean and standard deviation of the population, we use the formulas:
Mean = (sum of values) / (number of values)
Standard deviation = sqrt[(sum of squared deviations) / (number of values)]
Using these formulas, we get:
Mean = (506 + 628 + 554 + 600 + 584) / 5 = 574.4
Standard deviation = sqrt[((506-574.4)^2 + (628-574.4)^2 + (554-574.4)^2 + (600-574.4)^2 + (584-574.4)^2) / 5] ≈ 36.5
To list all samples of size 2 with replacement from the population, we can simply list all pairs of elements from the population, allowing for repetition. We get:
{506, 506}, {506, 628}, {506, 554}, {506, 600}, {506, 584}
{628, 506}, {628, 628}, {628, 554}, {628, 600}, {628, 584}
{554, 506}, {554, 628}, {554, 554}, {554, 600}, {554, 584}
{600, 506}, {600, 628}, {600, 554}, {600, 600}, {600, 584}
{584, 506}, {584, 628}, {584, 554}, {584, 600}, {584, 584}
To find the mean of each sample, we simply take the average of the two elements in each sample. For example, for the sample {506, 628}, the mean is (506 + 628) / 2 = 567.
We can list all 25 sample means and calculate their mean and standard deviation. We get:
Sample means: 506, 567, 555, 553, 545, 567, 628, 591, 553, 570, 555, 591, 554, 553, 554, 600, 575, 567, 570, 554, 584, 570, 591, 575, 584
Mean of sample means = (sum of sample means) / (number of samples) ≈ 565.4
Standard deviation of sample means = sqrt[((506-565.4)^2 + (567-565.4)^2 + ... + (575-565.4)^2) / 25] ≈ 18.9
The mean of the sampling distribution is close to the mean of the population, which is expected since the sample means are unbiased estimators of the population mean. The standard deviation of the sampling distribution is smaller than the standard deviation of the population, which is expected since the standard deviation of the sampling distribution decreases as the sample size increases.
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why do you square the deviations from the mean in one step of computing the standard deviation and then reverse it later by taking the square root?
The process of computing the standard deviation involves squaring the deviations from the mean, and then taking the square root of the sum of squares of the deviations from the mean, which is divided by one less than the number of observations.
This is done in order to counteract the effects of negative and positive deviations that may offset each other, thereby giving a biased result. This is why the deviations from the mean are squared to eliminate the effects of positive and negative deviations that cancel out each other.
By squaring the deviations, the sum of squares is always positive and retains the relative magnitude of the deviations. The reason for taking the square root of the sum of squares is to bring back the unit of measure of the original data that was squared, such as feet, meters, dollars, etc.
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help asap if you can pls an thank u!!!!!!!
The value of angle S is 53°
What is exterior angle theorem?Exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles.
With this theorem we can say that
7x+2 = 4x+13+19
collecting like terms
7x -4x = 13+19-2
3x = 30
divide both sides by 3
x = 30/3
x = 10
Since x = 10
angle S = 4x+13
angle S = 4(10) +13
= 40+13
= 53°
Therefore the measure of angle S is 53°
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10. Set up and evaluate the definite integral for the area of the surface generated by revolving the curve a) (3 pts.)y= 6x 3+ 2x1 ,1≤x≤2, about the x-axis; b) (3 pts.) x= 4y−1,1≤y≤4, about the y-axis.
The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:
∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx
To calculate dy/dx, we differentiate the given equation:
dy/dx = 18x^2 + 2
Substituting this back into the integral, we have:
∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx
Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.
b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:
∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy
To calculate dx/dy, we differentiate the given equation:
dx/dy = 4
Substituting this back into the integral, we have:
∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy
Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.
By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.
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PLEASE HELP ME! !!!!!!
at a particular time of a day a 7m high flash cast a shadow which is 8.2 metre long what is the height of the building which cast a shadow 20.5 is in length at the same moment
IT IS IM UNITARY MEATHOD
DIRECT VARIATION
I WILL MARK U BRAINLIEST
Answer:The height of the building which caste a shadow 20.5 m in length is 17.5 m.
Step-by-step explanation:
Given : At a particular time of a day, a 7 high flagstaff castes a shadow which is 8.2 m long.
To find : What is the height of the building which castes a shadow 20.5 meters in length at the same moment?
Solution :
A 7 high flagstaff castes a shadow which is 8.2 m long.
i.e. Shadow of length 8.2 m = 7 m
The shadow of length 1 m = m
The shadow of length 20.5 m = m
The shadow of length 20.5 m = 17.5 m
Therefore, The height of the building which caste a shadow 20.5 m in length is 17.5 m.
Justin is taking an anti-inflammatory drug and the instructions say that the patient must receive 8 mg for each 16 kg of body weight. If Justin weighs 259 lb, what dosage should he receive?
Answer:
58.86 mg
Step-by-step explanation:
8 mg = 16 kg
1 kg = 2.2 lb
use substitution
8 mg = 16 (2.2 lb)
8 mg = 35.2 lb
8 mg / 35.2 lb = x mg / 259 lb
2072 = 35.2 x
x = 58.86 mg
At M3 Consulting, the probability the computer network crashes on any workday equals 0.16.Calculate the probability that during a regular work week (Monday through Friday), the computernetwork crashesa. on both Monday and Tuesday.b. for the first time Thursday.c. every day.d. on at least one day.
a. The probability that the network crashes on both Monday and Tuesday is 0.1024; b. The probability that the network crashes for the first time on Thursday is 0.1389 ; c. The probability that the network crashes every day is 0.0001; d. The probability that the network crashes on at least one day is 0.3222.
We can approach this problem using the binomial distribution. Let X be the number of days in a week that the network crashes. Then X follows a binomial distribution with parameters n = 5 (number of days in a workweek) and p = 0.16 (probability of a crash on any given day).
a. The probability that the network crashes on both Monday and Tuesday is:
P(X = 2) = (5 choose 2) * (0.16)² * (1-0.16)³
= 0.1024
b. The probability that the network crashes for the first time on Thursday is the probability that it does not crash on Monday, Tuesday, or Wednesday, but does crash on Thursday and/or Friday. So:
P(X = 1) * P(no crashes on Monday, Tuesday, Wednesday) = (5 choose 1) * (0.16) * (1-0.16)⁴ * (0.84)³
= 0.3808 * 0.3652
= 0.1389
c. The probability that the network crashes every day is:
P(X = 5) = (5 choose 5) * (0.16)⁵ * (1-0.16)⁰
= 0.0001
d. The probability that the network crashes on at least one day is the complement of the probability that it does not crash at all during the week:
P(X >= 1) = 1 - P(X = 0)
= 1 - (5 choose 0) * (0.16)⁰ * (1-0.16)⁵
= 1 - 0.6778
= 0.3222
Therefore, a. The probability that the network crashes on both Monday and Tuesday is 0.1024; b. The probability that the network crashes for the first time on Thursday is 0.1389 ; c. The probability that the network crashes every day is 0.0001; d. The probability that the network crashes on at least one day is 0.3222.
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T/F?The probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring.
This statement is False as the probability of intersection of two events is always less than the probability of union.
This assertion is untrue. Contrary to popular belief, the likelihood of two occurrences coming together is always higher than or on pair with the likelihood of them colliding.
The chance of two events A and B occurring together can be calculated using the following formula to see why:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)According to this equation, the probability of A and B joining together is equal to the total of their individual probabilities less the likelihood of their colliding.
When we rewrite this calculation and focus only on the likelihood of the intersection, we obtain:
P(A ∩ B) = P(A) + P(B) - P(A ∪ B)Now it is clear that the probability of the intersection is determined by subtracting the probability of their union from the sum of the probabilities of A and B.
P(A) and P(B) are both less than or equal to P(A B), since probabilities can never be negative. P(A + B) is therefore less than or equal to twice P(A + B) when they are added together. Thus, it follows:
P(A) + P(B) - P(A ∪ B) ≤ P(A ∪ B)This indicates that, contrary to what the original statement implied, the probability of the intersection is not greater than or equal to the probability of the union.
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HELPPPPPOO MEEEEE 2.0
Answer:
I think the answer would be 60
Hope it was helpful .
Step-by-step explanation:
400 × 0.15 = 60
Last week, Latoya drove 259 miles. This week, she drove k miles. Using k, write an expression for the total number of miles she drove in the two weeks.
Answer:
259+k=x
Step-by-step explanation:
x= total number of miles
Which set of number could represent the length of the sides of a right triangle
A. 3, 4, 6
B. 4, 5, 7
C. 5, 12, 13
D. 7, 20, 21
E. 8, 15, 16
Answer:A I Believe
Step-by-step explanation:
Apply Newton's Method to approximate the x-value(s) of the indicated point(s) of intersection of the two graphs. Continue the iterations until two successive approximations differ by less than 0.001. [Hint: Let h(x) = f(x) − g(x).] (Round your answer to four decimal places.)
f(x) = x^6
g(x) = cos(x)
Answer:
Using Newton's Method, the points of intersection between f(x) = x^6 and g(x) = cos(x) are approximately (0.8241, f(0.8241)) and (2.3111, f(2.3111)), where f(x) = x^6.
To find the points of intersection of the graphs of f(x) = x^6 and g(x) = cos(x), we can solve the equation h(x) = f(x) - g(x) = x^6 - cos(x) = 0.
Explanation:
We will use Newton's Method to approximate the x-value(s) of intersection. The formula for Newton's Method is:
x_n+1 = x_n - f(x_n)/f'(x_n)
where x_n is the nth approximation of the root, f(x_n) is the function evaluated at x_n, and f'(x_n) is the derivative of the function evaluated at x_n.
Let h(x) = x^6 - cos(x), then
h'(x) = 6x^5 + sin(x)
Now we need to choose a starting value for x. By graphing the two functions, we can see that there are two points of intersection in the interval [0,1]. Let's choose x = 0.5 as our starting value.
x_0 = 0.5
x_1 = x_0 - h(x_0)/h'(x_0) = 0.5352
x_2 = x_1 - h(x_1)/h'(x_1) = 0.8656
x_3 = x_2 - h(x_2)/h'(x_2) = 0.8249
x_4 = x_3 - h(x_3)/h'(x_3) = 0.8241
Thus, the approximate value of the first intersection point is x = 0.8241.
Now we need to find the second intersection point. By graphing the two functions, we can see that there is another intersection point in the interval [2,3]. Let's choose x = 2.5 as our starting value.
x_0 = 2.5
x_1 = x_0 - h(x_0)/h'(x_0) = 2.3214
x_2 = x_1 - h(x_1)/h'(x_1) = 2.3111
x_3 = x_2 - h(x_2)/h'(x_2) = 2.3111
Thus, the approximate value of the second intersection point is x = 2.3111.
Therefore, the points of intersection of the two graphs are approximately (0.8241, f(0.8241)) and (2.3111, f(2.3111)), where f(x) = x^6.
Hope this helps you in some way! I'm sorry if it doesn't. If you need more help, ask me! :]
sam's probability of getting an a on an individual test is 75%. if he takes 12 tests, whatis the probability he gets as on exactly 10 of those tests?
The probability that Sam gets exactly 10 A's out of 12 tests is 0.234 or about 23.4%.
To solve this problem, we can use the binomial probability formula. The formula is:
\(P(X=k) = (n choose k) * p^k * (1-p)^(n-k)\)
Where:
- P(X=k) is the probability of getting exactly k successes
- n is the number of trials (tests)
- k is the number of successes (getting an A)
- p is the probability of success on each trial (getting an A)
- (n choose k) is the binomial coefficient, which can be calculated as \(n! /\)\((k! * (n-k)!)\)
Using this formula, we can plug in the values given in the problem:
n = 12 (number of tests)
k = 10 (number of A's)
p = 0.75 (probability of getting an A)
P(X=10) = (12 choose 10) * 0.75^10 * (1-0.75)^(12-10)
P(X=10) = (12! / (10! * 2!)) * 0.75^10 * 0.25^2
P(X=10) = 66 * 0.0563 * 0.0625
P(X=10) = 0.234
Therefore, the probability that Sam gets exactly 10 A's out of 12 tests is 0.234 or about 23.4%.
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Solve for P
6p - 2 - 3p = 4
Solve for W
7w - 5 = -2w + 22
Answer:
p=2 w=3
Step-by-step explanation:
6p-2-3p=4 combine like terms. 3p-2=4. add 2 to both sides. 3p=6. divide 6 both sides by 3. p=2
7w-5=-2w+22. Combine like terms on same sides. 7w+2w=5+22. 9w=27. Divide both sides by 9. w=3.
Answer:
p = 2w = 3Step-by-step explanation:
Solve for P
6p - 2 - 3p = 4
6p - 3p = 4 + 2
3p = 6
p = 6/3
p = 2
Solve for W
7w - 5 = -2w + 22
7w + 2w = 22 + 5
9w = 27
w = 27/9
w = 3
please Evaluate 27 times ( 1/3) to the 3 power. A). 1 B). 3 C). 9 D). 27
Answer:
you want to follow PEMDAS so you would multiply 27 by 1/3 to get 81.003, which you would round to 81, then you would multiply 8 to the third power and you would get 512.
Step-by-step explanation:
27(1/3)^3
81^3
512
50 points!!!
ok, so i was just browsing for questions to answer...and im just wondering..why are all these creeps and 12 yr olds looking for love on brainly?? like im honestly wondering
To implement effective moderation policies, provide clear guidelines, and educate users about appropriate online behavior. Individuals should exercise caution when interacting online and report any concerning behavior to the platform administrators.
It's understandable to feel surprised or concerned when encountering inappropriate or unexpected behavior on online platforms. While I cannot directly address the specific behavior you mentioned on Brainly or other platforms, I can offer some insights into why such situations might occur.
1. Anonymity: The anonymity provided by online platforms can embolden individuals to engage in inappropriate or immature behavior that they might not exhibit in face-to-face interactions. This anonymity can attract people who seek attention or want to explore subjects they may not feel comfortable discussing openly.
2. Lack of monitoring: Online platforms vary in terms of their moderation and monitoring practices. Some platforms may have limited measures in place to prevent or address inappropriate behavior. This can create an environment where certain individuals feel more inclined to engage in inappropriate activities or seek attention in ways that are not conducive to the platform's intended purpose.
3. Misinterpretation: In some cases, individuals may not fully understand the intended purpose of the platform they are using. They might mistakenly perceive it as a place to seek romantic relationships or engage in inappropriate conversations, especially if they are not properly guided or supervised by responsible adults.
4. Age verification challenges: Online platforms face challenges in verifying the ages of their users, particularly in cases where individuals misrepresent their age. This can lead to situations where younger individuals may encounter content or interactions that are not suitable for their age group.
It is important for online platforms to implement effective moderation policies, provide clear guidelines, and educate users about appropriate online behavior. Additionally, individuals should exercise caution when interacting online and report any concerning behavior to the platform administrators.
Remember, it is crucial to prioritize online safety and maintain a respectful and responsible digital presence.
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Pls need help ASAP been stressing need in 10 mins
Answer:
It's choice 2.
Step-by-step explanation:
The nth value is 1 more than twice the previous value
- for example, 15 = 2*7 + 1.
Finally get to swoop in and answer!
Each new value is 1 plus twice the previous value.
First value is 1. Then,
1 plus twice 1 = 3, the second value.
Second value is 3
1 plus twice 3 = 7, so
Third value is 7
and so on (this is merely a check)
how many 8-letter arrangements can be formed from the 26 letters of the alphabet (without repetition) that include at most three of the five vowels and in which the vowels appear in alphabetical order? (hint: break into cases.)
The total number of arrangements, we can simply add up the results from each case:
C(21,8) + C(5,1) C(21,7) 8 + C(5,2) C(21,6) 2
Now, We can solve this problem, we can break it down into three cases, based on the number of vowels included in the arrangement.
Hence, Here are the three cases:
Case 1: No vowels included: In this case, we need to select 8 letters from the 21 consonants in the alphabet.
This can be done with C(21,8) ways.
Case 2: One vowel included:
Here, we need to select one of the five vowels and then select 7 letters from the 21 consonants.
The vowel can be placed in any of the 8 positions, but once it is placed, the other vowels must be placed in alphabetical order.
Therefore, the number of arrangements in this case is, C(5,1) C(21,7) 8.
Case 3: Two vowels included: In this case, we need to select two of the five vowels, and then select 6 letters from the 21 consonants.
Again, the vowels must be placed in alphabetical order once they are selected.
However, we have two possible orders to place the vowels - either at the start or in the middle of the 8-letter arrangement.
Therefore, the number of arrangements in this case is C(5,2) C(21,6) 2.
So, The total number of arrangements, we can simply add up the results from each case:
C(21,8) + C(5,1) C(21,7) 8 + C(5,2) C(21,6) 2
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Find the common ratio and the number of terms in the given finite geometric sequence.a_n={2,1, \frac{1}{2} ,..., \frac{1}{1024} }The common ratio is AnswerThere are Answer terms.
Notice that:
\(\begin{gathered} 1=2*\frac{1}{2}, \\ \frac{1}{2}=1*\frac{1}{2}. \end{gathered}\)Therefore, the common ratio is:
\(\frac{1}{2}.\)The mth term of the sequence has the general form:
\(a_m=2(\frac{1}{2})^{m-1}.^\)Setting
\(a_m=\frac{1}{1024},\)we get:
\(\frac{1}{1024}=2(\frac{1}{2})^{m-1}.\)Solving the above equation for m, we get:
\(\begin{gathered} \frac{1}{2*1024}=\frac{1}{2^{m-1}}, \\ 2048=2^{m-1}, \\ log_2(2048)=m-1(log_22), \\ 11=m-1, \\ m=11+1, \\ m=12. \end{gathered}\)Finally, we get that there are
\(12\)terms in the finite geometric sequence.
Answer:
First blank:
\(\frac{1}{2},\)Second blank:
\(12.\)A company make color televiion et. It produce a bargain et that ell for $ profit and a deluxe et that ell for $ profit. On the aembly line, the bargain et require hour, while the deluxe et take hour. The cabinet hop pend hour on the cabinet for the bargain et and hour on the cabinet for the deluxe et. Both et require hour for teting and packing. On a particular production run, the company ha available work-hour on the aembly line, work-hour in the cabinet hop, and work-hour in the teting and packing department
The maximum number of bargain sets the company can produce in the given production run is 200 sets. The maximum number of deluxe sets the company can produce in the given production run is 150 sets.
1. Calculate the total number of work hours available on the assembly line, in the cabinet shop, and in the testing and packing department:
-Assembly line: 10 x 8 = 80 hours
-Cabinet shop: 6 x 8 = 48 hours
-Testing and packing: 7 x 8 = 56 hours
2. Calculate the number of work hours needed to assemble one bargain set:
-Bargain set: 10 hours
3. Calculate the number of work hours needed to assemble one deluxe set:
-Deluxe set: 12 hours
4. Calculate the number of work hours needed to assemble the cabinets for one bargain set:
-Bargain set: 6 hours
5. Calculate the number of work hours needed to assemble the cabinets for one deluxe set:
-Deluxe set: 8 hours
6. Calculate the number of work hours needed for testing and packing both types of sets:
-Testing and packing: 8 hours
7. Calculate the maximum number of bargain sets that can be produced in the given production run:
-Maximum bargain sets: 80 (assembly line) + 48 (cabinet shop) = 128 (total)
-128 (total) / 10 (assembly time per set) = 12.8
-Therefore, the maximum number of bargain sets that can be produced in the given production run is 12 sets.
8. Calculate the maximum number of deluxe sets that can be produced in the given production run:
-Maximum deluxe sets: 80 (assembly line) + 48 (cabinet shop) = 128 (total)
-128 (total) / 12 (assembly time per set) = 10.6
-Therefore, the maximum number of deluxe sets that can be produced in the given production run is 10 sets.
9. Add the two totals together to get the total number of sets:
-Total sets: 12 (bargain sets) + 10 (deluxe sets) = 22 sets
10. Subtract the total number of sets from the total number of work hours available to get the maximum number of sets that can be produced:
-Maximum sets: 128 (total available work hours) - 22 (total sets) = 106 sets
11. Divide the maximum number of sets by the number of hours needed to assemble each type of set to get the maximum number of bargain and deluxe sets that can be produced:
-Max bargain sets: 106 (max sets) / 10 (hours per set) = 10.6
-Therefore, the maximum number of bargain sets the company can produce in the given production run is 10 sets.
-Max deluxe sets: 106 (max sets) / 12 (hours per set) = 8.8
-Therefore, the maximum number of deluxe sets the company can produce in the given production run is 8 sets.
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