the dimensions of the window that will allow in as much light as possible, given 12 feet of frame material, are approximately 3.22 feet by 2.15 feet.
what is dimensions ?
Dimensions refer to the measurements or extent of something in terms of length, width, and height. In mathematics, dimensions can also refer to the number of coordinates needed to specify the position of a point in a given space. For example, a point in two-dimensional space
In the given question,
Let's assume that the rectangular window has width "w" and height "h". The semi-circle on top of the rectangular window will have a diameter equal to "w" (since it covers the entire width of the rectangular window).
The perimeter of the window frame is given by:
P = 2w + h + πw/2
We know that there are 12 feet of frame material available, so we can write:
2w + h + πw/2 = 12
To maximize the amount of light coming in through the window, we want to maximize the area of the window. The area of the window is given by:
A = wh + πw²/4
Using the equation for P above, we can solve for h:
h = 12 - 2w - πw/2
Substituting this into the equation for A, we get:
A = w(12 - 2w - πw/2) + πw²/4
Simplifying this expression, we get:
A = (3π/4)w² - 2w² + 12w
To maximize the area, we need to take the derivative of this expression with respect to "w" and set it equal to zero:
dA/dw = (3π/2)w - 4w + 12 = 0
Solving for "w", we get:
w = 12/(3π/2 - 4) ≈ 3.22 feet
Substituting this value of "w" back into the equation for h, we get:
h = 12 - 2(3.22) - π(3.22)/2 ≈ 2.15 feet
Therefore, the dimensions of the window that will allow in as much light as possible, given 12 feet of frame material, are approximately 3.22 feet by 2.15 feet.
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An ndhs asked subjects whether family planning has any benefits. of 1245 sampled subjects, 651 responded definitely or probably beneficial, and 594 responded definitely or probably not beneficial. the proportion responding definitely or probably beneficial was 651/1245 = 0.523.
This indicates that approximately 47.7% of the sampled subjects responded definitely or probably not beneficial to family planning.
From the given data, we can analyze the proportions of respondents who considered family planning beneficial and those who did not.
The proportion of respondents who responded definitely or probably beneficial is 651 out of 1245 sampled subjects. Therefore, the proportion can be calculated as:
Proportion = 651/1245 ≈ 0.523
This indicates that approximately 52.3% of the sampled subjects responded definitely or probably beneficial to family planning.
On the other hand, the proportion of respondents who responded definitely or probably not beneficial is 594 out of 1245 sampled subjects. The proportion can be calculated as:
Proportion = 594/1245 ≈ 0.477
This means that roughly 47.7% of the sampled participants indicated that family planning was either definitely advantageous or probably not beneficial.
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hockey is not popular as cricket in india why
Answer:
because it is tough to play Hockey being a national game.
Scott is conducting a science experiment. He has 3. 74 liters of liquid A and 3. 65 of liquid B. He pours both liquids into a container. How much liquid is in the container? Estimate and solve. Is your answer reasonable?
He has 3. 74 liters of liquid A and 3. 65 of liquid B: 7.39 liters of liquid is in the container.
= 7.39 liters
I would round 3.74 down to 4.00,
and round 3.65 down to again 4.00
4.00 + 4.00 = 8.00
since 7.39 is close to 8.00, thus the answer is reasonable
Estimation implies approximating an amount to the exactness required. This is finished by adjusting the numbers in question and finding a fast and harsh solution. Adjusting a number to the nearest tenth.
Rounding to the nearest tenth means changing the given number to a rough worth without changing the entire piece of the number. For rounding numbers to the nearest tenth, we want to notice the spot values after the decimal point. For instance, to adjust 3.864 to the nearest tenth, we get 3.9
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What is the slope and y intercept of the following linear equation:y=1/3×-2
Answer:
Step-by-step explanation:
The general formula for slope-intercept form is y = mx + b
We can see that m (slope) equals 1/3 here. We can also see that the y-intercept (b) is -2. Another way to find the y intercept is to make x equal to 0. You get 0 - 2 which equals -2
Note:
If youre ever asked for the x-intercept, make y equal to zero and solve for x.
2. Write the answer to the following questions in a single sentence. a) What is the problem of using an even value of k in the k-NN classifier? 1 b) What is the reason that has led the Bayesian Belief Network to emerge? 1 c) What is the necessity of using scaling in k-NN? 1 d) Write a mathematical relation between Manhattan distance and Euclidean distance. 1 e) Why is a dendrogram not applicable on K-means clustering algorithm? 1 1 f) What is the appropriacy of using minimum spanning tree (MST) other than all other types of trees to divisive hierarchical clustering? 1 g) What are the observations, for which the size of proximity matrix can be reduced from m2 to about m2/2? 1 h) Why is the matching each transaction against every candidate computationally expensive in brute-force approach? 1 i) Write a mathematical relation between k (from k-itemset) and w (maximum transaction width)? j) Given a transaction t of n items, what are the possible subsets of size 3? 1 3 k) If number of items, d = 3 is given, calculate the total number of possible association rules in brute-force approach using two different ways.
a) Using an even value of k in the k-NN classifier can lead to ties in the decision-making process.
b) The emergence of Bayesian Belief Network is driven by the need for probabilistic models to represent uncertain knowledge and make inferences.
c) Scaling is necessary in k-NN to ensure that features with larger ranges do not dominate the distance calculation.
d) The mathematical relation between Manhattan distance and Euclidean distance is given by Manhattan distance = √(Euclidean distance).
e) A dendrogram is not applicable in K-means clustering algorithm because it does not provide a hierarchical representation of the clusters.
f) Minimum spanning tree (MST) is appropriate for divisive hierarchical clustering as it allows for a step-by-step division of clusters based on the minimum dissimilarity.
g) The size of the proximity matrix can be reduced from m^2 to about m^2/2 for symmetric distance measures.
h) Matching each transaction against every candidate is computationally expensive in brute-force approach due to the high number of comparisons required.
i) The mathematical relation between k (from k-itemset) and w (maximum transaction width) depends on the specific problem or algorithm being used.
j) The possible subsets of size 3 in a transaction t of n items can be calculated using the combination formula: C(n, 3) = n! / (3! * (n-3)!).
k) The total number of possible association rules in brute-force approach with d = 3 items can be calculated as 3^2 - 3 = 6 using the formula 2^(d^2) - d.
Using an even value of k in the k-NN classifier can lead to ties in the decision-making process. When k is even, there is a possibility of having an equal number of neighbors from different classes, resulting in ambiguity in assigning the class label.
The Bayesian Belief Network has emerged as a solution to represent uncertain knowledge and make inferences. It utilizes probabilistic models and graphical structures to capture the dependencies and conditional relationships between variables, allowing for reasoning under uncertainty.
Scaling is necessary in k-NN to ensure fair comparison between features with different ranges. Without scaling, features with larger numerical values would dominate the distance calculation and potentially bias the classification process.
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Waldo Books needs to decide how many copies of a new hardcover release to purchase for its shelves. The store has assumed that demand will be 50, 100, 150, or 200 copies next month, and it needs to decide whether to order 50, 100, 150, or 200 books for this period. Each book costs Waldo $20 and can be sold for $30. Waldo can sell any unsold books back to the supplier for $4.
(a) Which option should Waldo choose if it uses the maximax criterion?
(b) Which option should Waldo choose if it uses the maximin criterion?
(c) Which option should Waldo choose if it uses the equally likely criterion?
(d) Which option should Waldo choose if it uses the criterion of realism with a = 0.7?
(e) Which option should Waldo choose if it uses the minimax regret criterion?
Answer:
(a) Maximax criterion: Order 200 books.
(b) Maximin criterion: Order 200 books.
(c) Equally likely criterion: Order 200 books.
(d) Criterion of realism with a = 0.7: Calculate the expected payoff based on the chosen value of a and select the corresponding option.
(e) Minimax regret criterion: Order 200 books.
Step-by-step explanation:
The maximax criterion involves selecting the option with the highest possible payoff. We will calculate the maximum payoff for each option and choose the one with the highest value.Payoff for ordering 50 books:
Revenue = 30 * 50 = $1500
Maximum payoff = $1500Payoff for ordering 100 books:
Revenue = 30 * 100 = $3000
Maximum payoff = $3000Payoff for ordering 150 books:
Revenue = 30 * 150 = $4500
Maximum payoff = $4500Payoff for ordering 200 books:
Revenue = 30 * 200 = $6000
Maximum payoff = $6000Based on the maximax criterion, Waldo should choose the option of ordering 200 books since it has the highest maximum payoff.(b) Maximin Criterion:
The maximin criterion involves selecting the option with the highest minimum payoff. We will calculate the minimum payoff for each option and choose the one with the highest value.Payoff for ordering 50 books:
Revenue = 30 * 50 - (20 * 50 - 4 * 50) = $900
Minimum payoff = $900Payoff for ordering 100 books:
Revenue = 30 * 100 - (20 * 100 - 4 * 100) = $1800
Minimum payoff = $1800Payoff for ordering 150 books:
Revenue = 30 * 150 - (20 * 150 - 4 * 150) = $2700
Minimum payoff = $2700Payoff for ordering 200 books:
Revenue = 30 * 200 - (20 * 200 - 4 * 200) = $3600
Minimum payoff = $3600Based on the maximin criterion, Waldo should choose the option of ordering 200 books since it has the highest minimum payoff.(c) Equally Likely Criterion:
The equally likely criterion assumes that each demand level is equally likely to occur. We will calculate the expected payoff for each option and choose the one with the highest value.Expected payoff for ordering 50 books:
Expected revenue = (30 * 50 + 4 * (50 - 50)) / 4 = $375
Expected payoff = $375Expected payoff for ordering 100 books:
Expected revenue = (30 * 100 + 4 * (50 - 100)) / 4 = $750
Expected payoff = $750Expected payoff for ordering 150 books:
Expected revenue = (30 * 150 + 4 * (50 - 150)) / 4 = $1125
Expected payoff = $1125Expected payoff for ordering 200 books:
Expected revenue = (30 * 200 + 4 * (50 - 200)) / 4 = $1500
Expected payoff = $1500Based on the equally likely criterion, Waldo should choose the option of ordering 200 books since it has the highest expected payoff.(d) Criterion of Realism with a = 0.7:
The criterion of realism involves assigning a weight (0 ≤ a ≤ 1) to the optimistic payoff and the remaining weight (1 - a) to the pessimistic payoff. We will calculate the expected payoff for each option using the given value of a and choose the one with the highest value.Expected payoff for ordering 50 books:
Expected revenue = a * (30 * 50) + (1 - a) * (30 * 50 - 20 * 50 + 4 * 50) = $450a
Expected payoff = $450aExpected payoff for ordering 100 books:
Expected revenue = a * (30 * 100) + (1 - a) * (30 * 100 - 20 * 100 + 4 * 100) = $900a
Expected payoff = $900aExpected payoff for ordering 150 books:
Expected revenue = a * (30 * 150) + (1 - a) * (30 * 150 - 20 * 150 + 4 * 150) = $1350a
Expected payoff = $1350aExpected payoff for ordering 200 books:
Expected revenue = a * (30 * 200) + (1 - a) * (30 * 200 - 20 * 200 + 4 * 200) = $1800a
Expected payoff = $1800aTo find the maximum expected payoff, we can compare the values of a * 450, a * 900, a * 1350, and a * 1800 for different values of a. The optimal value of a will determine the corresponding option.(e) Minimax Regret Criterion:
The minimax regret criterion involves calculating the regret for each option and selecting the one with the minimum regret. Regret represents the difference between the maximum possible payoff and the actual payoff.Regret for ordering 50 books:
Regret = 6000 - (30 * 50 - (20 * 50 - 4 * 50)) = $5250
Minimum regret = $5250Regret for ordering 100 books:
Regret = 6000 - (30 * 100 - (20 * 100 - 4 * 100)) = $4200
Minimum regret = $4200Regret for ordering 150 books:
Regret = 6000 - (30 * 150 - (20 * 150 - 4 * 150)) = $3150
Minimum regret = $3150Regret for ordering 200 books:
Regret = 6000 - (30 * 200 - (20 * 200 - 4 * 200)) = $2100
Minimum regret = $2100Based on the minimax regret criterion, Waldo should choose the option of ordering 200 books since it has the minimum regret.
Waldo Books is facing a decision theory problem. By different criteria, the decision to order books can change. By maximax, Waldo should order 200 books, by maximin, 50 books. By equally likely, realism, and minimax regret criteria, computations considering payoffs, optimism levels, and potential regrets are needed.
Explanation:This is a "decision theory problem" in the field of business and economics. Let's calculate the profit from each option. Profit will be $10 for each book sold (revenue of $30 minus cost of $20) and a loss of $16 for each book not sold (cost of $20 minus resell value of $4).
Maximax criterion is when Waldo selects the alternative with the highest possible outcome. In this case, Waldo should order 200 books as he could make the most profit if demand is also at 200. Maximin criterion is when Waldo chooses the option with the best worst-case scenario. Here, Waldo should order 50 books as this would minimize the potential for unsold books. For the equally likely criterion, each level of demand is assumed to be equally probable, so the average profit for each order size should be calculated. The number with the highest average profit should be chosen. In the criterion of realism (also considered a 'compromise' criterion), there's a coefficient of optimism (a value between 0 and 1) that measures the decision-maker's optimism. Here, 'a' is 0.7. The larger the 'a', the more optimistic the decision-maker is. We calculate [a*(max payoff)+(1-a)*(min payoff)] for each alternative and pick the largest. The minimax regret criterion is about minimizing the maximum regret. Regret is the difference between the payoff from the best decision and all other decision payoffs. The decision with the smallest maximum 'regret' is chosen. Learn more about Decision Theory here:
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Trevor paid a total of $1.08 in fines for an overdue library book. If the penalty for overdue books is $0.09 per day, how many days late was the book?
2 days
8 days
12 days
20 days
im new
srry
Please help me I will mark you with a crown!! :))))
Using the net below, find the surface area
of the triangular prism.
3 in.
6 in.
6 in.
16 in
3 in
7 in.
Surface Area =
[?] in.2
Answer:
114 in²
Step-by-step explanation:
Area Triangles:
2 · 1/2(3 · 6)3 · 618Area left rectangle:
6 · 3 = 18Area square:
6 · 6 = 36Area right rectangle:
6 · 7 = 42Area Total :
18 + 18 + 36 + 4236 + 36 + 4272 + 42114The area is \(\boxed{\text{114 square inches}}\)
-Chetan K
if f(x)=2x^2-3 find f(-3)
Answer:
15
Step-by-step explanation:
2(-3)^2-3
2(9)-3
18-3
15
Learn with an example
53 ft.
45 ft.
b
What is the length of the missing leg? If necessary, round to the nearest tenth.
What is 166.6789 to the nearest hundredth
Answer:
166.68
Step by Step:
166.678
The bolded number is greater than 5 meaning you have to round up.
so 166.678 is rounded to 166.68.
Hope this helped.
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate. ages of children: 5, 6, 7, 8, and 9
There are four levels of measurements in statistics, namely nominal, ordinal, interval, ratio. These levels are important when it comes to analyzing data, since it helps us determine the technique that we can use to support or refute our study.
In the nominal level, we can categorize data but they cannot be ranked. An example would be hair color. In an ordinal data, the data can be both categorize and ranked, but doing mathematical calculation may not make sense. Also, the intervals between rankings doesn't necessarily dictate how close or far apart the data are.
A good example is level of education. In an interval level, the data can be categorized, ranked, and measured but they do not have a true zero. An example could be a range of values that does not include zero. Lastly, in the Ratio level the data can be categorized, rank, and measured, and it has a true zero.
So ratio level is most appropriate for ages of children. Note that ages can be categorized, rank, and measured .Moreover, an age equal to zero means that there is no age or the absence of age.
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Prove, using the definition of the derivative, that if f(x) = cos (x), then f'(x) = -sinx.
The derivative of a function represents the rate of change of the function with respect to its variable. This rate of change is described as the slope of the tangent line to the curve of the function at a specific point. The derivative of the cosine function can be found by applying the limit definition of the derivative to the cosine function.
\(f(x) = cos(x) then f'(x) = -sin(x)\).
Let's proceed with the proof. Definition of the Derivative: The derivative of a function f(x) at x is defined as the limit as h approaches zero of the difference quotient \(f(x + h) - f(x) / h\) if this limit exists. Using this definition, we can find the derivative of the cosine function as follows:
\(f(x) = cos(x) f(x + h) = cos(x + h)\)
Now, we can substitute these expressions into the difference quotient: \(f'(x) = lim h→0 [cos(x + h) - cos(x)] / h\)
We can then simplify the expression by using the trigonometric identity for the difference of two angles:
\(cos(a - b) = cos(a)cos(b) + sin(a)sin(b)\)
Applying this identity to the numerator of the difference quotient, we obtain:
\(f'(x) = lim h→0 [cos(x)cos(h) - sin(x)sin(h) - cos(x)] / h\)
We can then factor out a cos(x) term from the numerator:
\(f'(x) = lim h→0 [cos(x)(cos(h) - 1) - sin(x)sin(h)] / h\)
We can then apply the limit laws to separate the limit into two limits:
\(f'(x) = lim h→0 cos(x) [lim h→0 (cos(h) - 1) / h] - lim h→0 sin(x) [lim h→0 sin(h) / h]\)
The first limit can be evaluated using L'Hopital's rule:
\(lim h→0 (cos(h) - 1) / h = lim h→0 -sin(h) / 1 = 0\)
Therefore, the first limit becomes zero:
\(f'(x) = lim h→0 - sin(x) [lim h→0 sin(h) / h]\)
Applying L'Hopital's rule to the second limit, we obtain:
\(lim h→0 sin(h) / h = lim h→0 cos(h) / 1 = 1\)
Therefore, the second limit becomes 1:
\(f'(x) = -sin(x)\)
Thus, we have proved that if \(f(x) = cos(x), then f'(x) = -sin(x)\).
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You are driving on the freeway and notice your speedometer says v
0
. The car in front of you appears to be coming towards you at speed
4
1
v
0
, and the car behind you appears to be gaining on you at the same speed
4
1
v
0
. What speed would someone standing on the ground say each car is moving? (b) Suppose a certain type of fish always swim the same speed. You watch the fish swim a certain part of a river with length L. You notice that it takes a time
6
1
t
0
for the fish to swim downstream but only
3
1
t
0
to swim upstream. How fast is current of the river moving? (c) You now want to swim straight across the same river. If you swim (in still water) with a speed of
t
0
3L
+ what direction should you swim in? (d) How long does it take to get across if the river has a width of
3
1
L.
When you observe the movement of the car in front of you on the freeway, you notice that the speedometer says v₀ and the car appears to be coming towards you at a speed of 41v₀.
Similarly, the car behind you is gaining on you at a speed of 41v₀. The speed that someone standing on the ground would say each car is moving would be v₀, as the cars seem to be at rest in relation to the ground.
When you want to swim straight across the river with a speed of t₀3L, you should swim perpendicular to the direction of the current.
The angle between the direction of your motion and the current direction will be 90 degrees
The width of the river is 31L, and you want to swim straight across it with a speed of t₀3L.
If we consider the time it takes to cross the river is t and the velocity of the current is vc, then:
31L = (t₀ − t)c31L = t₀(1 − t)t = 3t₀/2 - L/vc
We observe that it takes the fish 61t₀ to swim downstream and 31t0 to swim upstream.
Now we want to calculate the speed of the current of the river. If we let the speed of the fish be vf and the velocity of the current be vc, then
vf + vc = L/61t₀ and vf - vc = L/31t₀.
By adding these two equations, we get
vf = L(2/61t₀), and by subtracting the second equation from the first, we get
vc = L/61t₀ - L/31t₀ = L/183t₀
Therefore, we get that the speed of the current of the river is L/183t₀ for part (b). In part (c), we can determine that to swim straight across the river with a speed of t₀3L, we should swim perpendicular to the direction of the current, and in part (d), we can calculate the time it would take to cross the river with the given information.
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One batch makes 15 lemon bars and Josh ate 2. If Claire ate twice as many as him, how many lemon bars would be left from the batch? *
Answer:
There are 9 lemon bars left from the batch.
Step-by-step explanation:
One batch = 15 lemon bars
Josh: ate 2 lemon bars
\(15 - 2 = 13\)
13 lemon bars remaining.
Claire: ate twice as many as Josh
Meaning: 2 × 2 = 4
\(13 - 4 = 9\)
9 lemon bars remaining.
There are 9 lemon bars left from the batch.
Elmer spent the day at the mall. First, he bought five rabbits for $10 each. Later, he bought four cupboards for $70 each. After that, he found a twenty dollar bill. Also, he returned one rabbit. Write the total change to Elmer's funds as an integer.
Answer:
-300
Step-by-step explanation:
Step 1: Find the amount Elmer's funds decreased after purchasing the rabbits:
Let x represent Elmer's funds.
Since Elmer bought five rabbits for $10 each, he lost $10 5 times.
x - (10 * 5)
x - 50
Thus, Elmer lost (spent) $50 for the 5 rabbits.
Step 2: Find the amount Elmer's funds decreased after purchasing the cupboards:
Since Elmer bought four cupboards for $70 each, he lost $70 4 times:
x - (50 + (70 * 4))
x - (50 + 280)
x - 330
Thus, after purchasing the rabbits and cupboards, Elmer lost $330.
Step 3: Find the amount Elmer's funds increased after finding the twenty-dollar bill:
Since Elmer found a twenty-dollar bill, he gained $20
x - (330 + 20)
x - 310
Step 4: Find the amount Elmer's funds increased after returning one rabbit:
Since Elmer returned one rabbit, he gained $10:
x - (310 + 10)
x - 300
Thus, Elmer's funds changed totally by -$300.
Putting all the information together, we have:
x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10
x - 50 - 280 + 30
x - 330 + 30
x - $300
6th grade Compare the results of your friend's research and the DNA test. Which method do you think is more accurate? Explain.
For DNA testing the most popular and reliable way to collect samples is the oral buccal swab method.
What is DNA testing?
The Polymerase Chain Reaction (PCR) is the most used type of DNA analysis (PCR). Because PCR testing has improved the success rate of the analysis of old, deteriorated, or extremely tiny biological evidential materials, it has significantly advanced the area of forensic DNA testing.
Businesses compare their data from a database that might not yield conclusive findings. The majority of DNA testing businesses base their DNA accuracy checks on common genetic variants that can be identified in their database. As a result, if you employ various businesses, you can obtain different outcomes.
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since x to the power of bevelled 1 half end exponent is being divided by x to the power of bevelled 1 fifth end exponent, the quotient property is used, which states that the exponents bevelled 1 half and bevelled 1 fifth can be subtracted. however, when adding and subtracting fractions, the denominators need to be the same. the fractions bevelled 1 half and bevelled 1 fifth can be changed to bevelled 5 over 10 and bevelled 2 over 10, respectively. finally, the power of a power product is applied, which means that the exponents bevelled 3 over 10 and bevelled 1 fourth can be multiplied together.
X to the power of 3/10 multiplied by x to the power of 1/4.
When dividing x to the power of 1/2 by x to the power of 1/5, the quotient property states that the exponents 1/2 and 1/5 can be subtracted.
However, to add or subtract fractions, the denominators need to be the same. So, we can change 1/2 to 5/10 and 1/5 to 2/10. Now, we can subtract the exponents to get (5/10) - (2/10) = 3/10.
Finally, we can apply the power of a power property, which states that when multiplying two exponents, the exponents can be multiplied together.
Therefore, the final answer is x to the power of 3/10 multiplied by x to the power of 1/4.
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solving systems of equations by elimination
Answer:
\(\boxed{x = -1~~and~~ y =-2}\)
Step-by-step explanation:
-6x + y = 4
6x - 2y = -2 +
-y = 2
y = -2
.
Substitute the value of y to the one of equations
6x - 2y = -2
6x -2(-2) = -2
6x + 4 = -2
6x = -2 - 4
6x = -6
\(x = \frac{-6}{6}\)
x = -1
x = -1 and y = -2
Step-by-step explanation:
use elimination or subatitution method
hi! please help in math!
i need the solution/explanation on how you got the answer
(y + 3) = -8(x - 4)
what is the slope?
Answer:
slope m = - 8
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
y + 3 = - 8(x - 4) ← is in point- slope form
with slope m = - 8
The slope is :
↬ -8Solution:
Given: \(\bf{y+3=-8(x-4)}\)
To determine the slope, it's important to know the form of the equation first.
There are 3 forms that you should be familiar with.
The three forms of equations of a straight line are:
Slope Intercept (y = mx + b)Point slope (y-y₁) = m(x - x₁)Standard form (ax + by = c)This equation matches point slope perfectly.
The question becomes, how do you work with point slope to find slope?
Point slopeIn point slope, m is the slope and (x₁, y₁) is a point on the line.
Similarly, the slope of \(\bf{y+3=-8(x-4)}\) is -8.
Hence, the slope is -8.9. For f(x) = -x + 8, which statement is true? A f(x + k) = f(x) + k B f(x- k) = f(x) - k Cf(x + k) = f(x) + f(k) D f(x - k) = f(x) + k
Answer:
D. f(x - k) = f(x) + k
Step-by-step explanation:
You want to know the effect on f(x) = -x +8 when x is replaced by x±k.
Function evaluationA function is evaluated by replacing the independent variable in its definition by the function argument.
f(x) = -x +8
f(x +k) = -(x +k) +8 = (-x +8) -k = f(x) -k
When the sign of k changes, we have ...
f(x -k) = f(x) +k
The correct statement for the function is: f(x -k) = f(x) +k. And option(D) is write answer.
How to perform function evaluation?
In mathematics, function expression is mainly consist of dependent variable and the independent variable. And the function is evaluated by replacing the independent variable in its definition by the function argument.
According to the question, the given function expression is: f(x) = -x +8
Now, to know the effect on f(x) = -x +8 when x is replaced by x ± k. This transformation is known as scaling translation.
Therefore, the function expression can be written as:
f(x) = -x +8
⇒ f(x +k) = -(x +k) +8 = (-x +8) -k = f(x) -k
When the sign of k changes, we get: f(x -k) = f(x) +k
Hence, the correct statement for the function is: f(x -k) = f(x) +k
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Please help me I'm stuck. I will give 30 points for this one. Given triangle ABC tilde triangle PQR and your scale factor Complete the hotspots for these similar triangles and show work
The value for the hotspots of the similar triangles ∆ABC and ∆PWR are:
(1). angle B = 68°
(2). PQ = 5cm
(3). BC = 19.5cm
(4). area of ∆PQR = 30cm²
What are similar trianglesSimilar triangles are two triangles that have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion.
(1). angle B = 180 - (22 + 90) {sum of interior angles of a triangle}
angle B = 68°
Given that the triangle ∆ABC is similar to the triangle ∆PQR.
(2). PQ/7.5cm = 12cm/18cm
PQ = (12cm × 7.5cm)/18cm {cross multiplication}
PQ = 5cm
(3). 13cm/BC = 12cm/18cm
BC = (13cm × 18cm)/12cm {cross multiplication}
BC = 19.5cm
(4). area of ∆PQR = 1/2 × 12cm × 5cm
area of ∆PQR = 6cm × 5cm
area of ∆PQR = 30cm²
Therefore, the value for the hotspots of the similar triangles ∆ABC and ∆PWR are:
(1). angle B = 68°
(2). PQ = 5cm
(3). BC = 19.5cm
(4). area of ∆PQR = 30cm²
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The continuous random variable V has a probability density function given by: 6 f(v) = for 3 ≤ ≤7,0 otherwise. 24 What is the expected value of V? Number
The expected value of the continuous random variable V is 5. The expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.
To calculate the expected value of a continuous random variable V with a given probability density function (PDF), we integrate the product of V and the PDF over its entire range.
The PDF of V is defined as:
f(v) = 6/24 = 0.25 for 3 ≤ v ≤ 7, and 0 otherwise.
The expected value of V, denoted as E(V), can be calculated as:
E(V) = ∫v * f(v) dv
To find the expected value, we integrate v * f(v) over the range where the PDF is non-zero, which is 3 to 7.
E(V) = ∫v * (0.25) dv, with the limits of integration from 3 to 7.
E(V) = (0.25) * ∫v dv, with the limits of integration from 3 to 7.
E(V) = (0.25) * [(v^2) / 2] evaluated from 3 to 7.
E(V) = (0.25) * [(7^2 / 2) - (3^2 / 2)].
E(V) = (0.25) * [(49 / 2) - (9 / 2)].
E(V) = (0.25) * (40 / 2).
E(V) = (0.25) * 20.
E(V) = 5.
Therefore, the expected value of the continuous random variable V is 5.
The expected value represents the average value or mean of the random variable V. It is the weighted average of all possible values of V, with each value weighted by its corresponding probability. In this case, the expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.
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What is the value of 0 to the nearest tenth?
Answer:
0.0
Step-by-step explanation:
How many numbers between 1 and 200 are divisible by 4 or 6?
Between 1 and 200, there are 66 numbers that are divisible by either 4 or 6.
To find the numbers between 1 and 200 that are divisible by 4 or 6, we need to determine the count of numbers divisible by 4 and the count of numbers divisible by 6, and then subtract the count of numbers divisible by both 4 and 6 (since they would be counted twice).
Divisibility by 4:
To find the count of numbers divisible by 4, we divide 200 by 4 and round down to the nearest whole number. So, 200 divided by 4 equals 50, meaning there are 50 numbers divisible by 4 between 1 and 200.
Divisibility by 6:
Similarly, to find the count of numbers divisible by 6, we divide 200 by 6 and round down. 200 divided by 6 equals approximately 33.33, so there are 33 numbers divisible by 6 between 1 and 200.
Numbers divisible by both 4 and 6:
To find the count of numbers divisible by both 4 and 6, we need to find the count of numbers divisible by their least common multiple, which is 12. We divide 200 by 12 and round down, resulting in approximately 16.67. Thus, there are 16 numbers divisible by both 4 and 6 between 1 and 200.
Finally, we add the count of numbers divisible by 4 and the count of numbers divisible by 6 and subtract the count of numbers divisible by both 4 and 6 to get the total count of numbers divisible by either 4 or 6. Therefore, there are 50 + 33 - 16 = 67 numbers between 1 and 200 that are divisible by either 4 or 6.
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Given that \(c=\frac{2d+1}{3d-1}\),
1. calculate the value of c when d = \(\frac{1}{4}\)
2. express d in terms of c
Answer:
C = -6
Step-by-step explanation:
C = [2×1/4 + 1] ÷ [3×1/4 -1 ]
C = 3/2 ÷ -1/4
C = 3/2 × -4 = -6
C = 2d + 1 / 3d - 1
So, d = ( C + 1 ) / ( 3C - 2 )
1.
\(c = \frac{2d + 1}{3d - 1} \)
\(c = \frac{(2 (\frac{1}{4})) + 1}{(3 ( \frac{1}{4})) - 1 } \)
\(c = \frac{ \frac{1}{2} + 1}{ \frac{3}{4} - 1} \)
\(c = \frac{ \frac{1}{2} + \frac{2}{2} }{ \frac{3}{4} - \frac{4}{4} } \)
\(c = \frac{ \frac{1 + 2}{2} }{ \frac{3 - 4}{4} } \)
\(c = \frac{ \frac{3}{2} }{ \frac{ - 1}{4} } \)
\(c = \frac{3}{2} \times \frac{4}{ - 1} \)
\(c = \frac{3}{1} \times \frac{2}{ - 1} \)
\( c = \frac{6}{ - 1} \)
\(c = - 6\)
Given k(x) =x^3-2x, find k (3)
Answer: 21
Step-by-step explanation:
k(x) =x^3-2x
k(3) =3^3-2*(3)
k(3) =27-6
k(3) = 21
Write the linear equation that gives the rule for this table.
x y
1 10
2 5
3 0
4 –5
Write your answer as an equation with y first, followed by an equal's sign.
The linear equation that gives the rule for this table is y = -5x + 15
How to determine the linear equation?The table of values is given as:
x y
1 10
2 5
3 0
4 –5
On the above table, we can see that:
As x increases by 1, the value of y decreases by 5
This means that the slope is
Slope = -5
Also, the above table can be modified as follows (using the slope of -5)
x y
0 15
1 10
2 5
3 0
4 –5
This means that the y-intercept is
y-intercept = 15
A linear equation is represented as
y = slope * x + y-intercept
So, we have
y = -5x + 15
So, the equarion is y = -5x + 15
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Do the sides 11 cm, 20 cm, and 4 cm make a triangle? *
Answer:
No, the two sum of the two shorter sides of a triangle must be greater that the longer side.
Answer: yes it does and It will look something like this
Step-by-step explanation:
help!!!!!!!
Replace each * with a digit that makes the solution of the equation a whole number.
Find all possibilities.
5x – 516=49*
The * values that make the solution a whole number are given as follows:
* = 4 or * = 9.
What is the rule for divisibility by 5?The divisibility rule for 5 states that a number is divisible by 5 if its ones digit (i.e., the digit in the units place) is either 0 or 5. In other words, if the number ends in 0 or 5, then it is divisible by 5.
The solution to the equation is obtained as follows:
5x = (516 + 49*)
x = (516 + 49*)/5
Hence it is needed one of these two following cases:
6 + * = 0 -> * = 4.6 + * = 5 -> * = 9.More can be learned about divisibility by 5 at https://brainly.com/question/9462805
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