Which fraction is equivalent to StartFraction 2 Over 6 EndFraction? StartFraction 3 Over 7 EndFraction, because StartFraction 2 Over 6 EndFraction = StartFraction 2 + 1 Over 6 + 1 EndFraction = StartFraction 3 Over 7 EndFraction StartFraction 3 Over 9 EndFraction, because StartFraction 2 Over 6 EndFraction = one-third and One-third = StartFraction 3 Over 9 EndFraction StartFraction 3 Over 12 EndFraction, because StartFraction 2 Over 6 EndFraction = one-third and One-third = StartFraction 3 Over 12 EndFraction StartFraction 3 Over 8 EndFraction, because StartFraction 2 Over 6 EndFraction = one-half = StartFraction 2 + 1 Over 6 + 2 EndFraction = StartFraction 3 Over 8 EndFraction

The dimensions of the garden that minimize the cost are approximately 2.5 feet by 64.8 feet.

To find the dimensions of the garden that minimize the cost, we can use optimization techniques. Let's denote the length of the garden as L and the width as W.

The cost of the brick wall is $60 per foot, and since only one side is enclosed by the brick wall, the cost for that side is 60L. The cost of the metal fence is $40 per foot, and since three sides are enclosed by the metal fence, the cost for those sides is 40(2L + W).

The total cost C is the sum of the costs for the brick wall and the metal fence:

C = 60L + 40(2L + W)

Given that the area of the garden is 162 square feet, we have L * W = 162.

To minimize the cost, we can take the derivative of the cost function with respect to L and set it equal to zero:

dC/dL = 60 + 80 = 0

Solving for L, we find L = 2.5 feet.

Substituting L = 2.5 into the area equation, we get W = 162 / 2.5 = 64.8 feet.

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The angle of elevation of 61° and 72° with the height of the tower being 553.3 m. gives Vic's distance from Dan as approximately 356 meters.

Location of Vic relative to the tower = South

Vic's sight angle of elevation to the top of the tower = 61°

Dan's location with respect to the tower = West

Dan's angle of elevation in order to see the top of the tower = 72°

Height of the tower = 553.3m

\(tan( \theta) = \frac{opposite}{adjacent} \)

\(tan( 61 ^{ \circ}) = \frac{553.3}{ Vic' s\: distance \: to \: tower} \)

\(distance = \frac{553.3}{tan ( {61}^{ \circ} )} = 306.7\)

Similarly, we have;

\( Dan's distance = \frac{553.3}{tan ( {72}^{ \circ} )} = 179.8\)

Given that Vic and Dan are at right angles relative to the tower (Vic is on the south of the tower while Dan is at the west), by Pythagorean theorem, the distance between Vic and Dan d is found as follows;

Therefore;

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The given equation is dR/R = k dt, where dR represents the change in R and dt represents the change in time t. To solve this differential equation, we can separate the variables and integrate both sides.

Starting with the equation dR/R = k dt, we can rewrite it as dR = kR dt. Then, dividing both sides by R gives dR/R = k dt.

Next, we integrate both sides. On the left side, we have ∫dR/R, which evaluates to ln|R|. On the right side, we have ∫k dt, which evaluates to kt.

Therefore, the equation becomes ln|R| = kt + C, where C is the constant of integration.

To find the general solution, we can exponentiate both sides to eliminate the natural logarithm: |R| = e^(kt + C). Since e^C is a positive constant, we can rewrite this as |R| = Ce^kt. Finally, we can consider two cases: when R is positive, we have R = Ce^kt, and when R is negative, we have R = -Ce^kt. So, the general solution is R = Ce^kt or R = -Ce^kt, where C is an arbitrary constant.

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Answer:

65 hot dogs, 96 sodas

Step-by-step explanation:

x + (x + 31) = 161

2x + 31 = 161

2x = 130

x = 65

65 hotdogs

65 + 31 = 96

96 sodas

Answer:

Biased

Step-by-step explanation:

Asking people about their opinions on the park while in the park would give biased results. To get unbiased results, Kyle would have to ask people outside the park their opinions.

Mean, because there are no outliers that affect the center

third period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2

Sorted values : 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4

The mean = ΣX / n

n = sample size, n = 15

Mean = 34 / 15 = 2.666

The median = 1/2(n+1)th term.

1/2(16)th term = 8th term.

The 8th term = 2

The best measure of centre is the mean because the values for the second period has no outliers that might have affected the centre of the distribution.

Both interquartile range and standard deviation are measures of spread and not measures of centre.

complete question

A survey was taken of students in math classes to find out how many hours per day students spend

on social media. The survey results for the first., second-, and third-period classes are as follows:

First period: 2,4,3,1,0, 2, 1, 3, 1,4,9,2,4,3,0

Second period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2

Third period: 4,5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1,3

Which is the best measure of center for second period and why? (5 points)

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True. A pie chart is a graphical representation of data that shows how different categories or groups of data contribute to the whole.

The "slices" of the pie represent the relative sizes of each category or group, and these sizes are determined by the class frequencies. Class frequencies are the number of data points that fall within a certain range or class, divided by the total number of data points. Using relative class frequencies in constructing a pie chart ensures that the sizes of the slices accurately reflect the distribution of the data, making it easier to understand and interpret the information presented.

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Answer:

S18 = 288

Step-by-step explanation:

find the first and last term.

n = 1

a1 = 2 x 1 - 3

a18 = 2 x 18 - 3

(simplify the expression)

a1 = -1

a18 = 33

(use the formula for the sum of a finite arithmetic series)

                     a1 + a18

S18 = 18 x ---------------------

                           2

(use the substitute) substitute -1 for a1 and 33 for a18

                       -1 + 33

S18 = 18 x ---------------------

                             2

simplify the expression and ur done hope this helped x

ps. wheres my head :)

Answer:

81

Step-by-step explanation:

Standard form is a way of writing down very large or very small numbers easily. 103 = 1000, so 4 × 103 = 4000 . So 4000 can be written as 4 × 10³ . This idea can be used to write even larger numbers down easily in standard form. Small numbers can also be written in standard form.

Answer: 81

Step-by-step explanation:

The value of the expression is 0.5 × 10⁴.

Given is an expression 1.6 × 10⁻⁷ / 3.2 × 10⁻¹¹, we need to simplify it,

= 1.6 × 10⁻⁷ / 3.2 × 10⁻¹¹

= 1.6 × 10⁻⁷ × 10¹¹ / 3.2

= 0.5 × 10⁴

Hence the value of the expression is 0.5 × 10⁴.

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We have the next given expression:

(3y+5)(3y+4)

Simplify the expression:

(3y+5)(3y+4) = 3y*3y+*3y*4+*5*3y+5*4

= 9y²+12y+15y+20

=9y²+27y+20

Hence, the expression is a trinomial.

It is degree is given by the largest exponent number.

Then, the degree of the polynomial is 2.

Answer:

94%

Step-by-step explanation:

no of qn = 47(correctly answer)+3 (wrong answered)

                =50

percentage =47/50*100

                    =94

The maximum rectangular area that can be fenced can be

2499 sq meters.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

We know for a quadrilateral, A square has the maximum area.

We also know That the product of two numbers is maximum when the difference between them is minimum.

Given, A farmer has 2,000 meters of fencing and wants to use it to create a rectangular area for grazing.

So, 2(l + b) = 2000.

l + b = 1000.

For a square, it would be 500 and 500, But to be a rectangle it can be 49 and 51.

Therefore, The maximum area would be,

= (51×49) sq meters.

= 2499 sq meters.

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The absolute maximum of f(x) is 1 3/8 and it occurs at x = 1/8, while the absolute minimum is 0 and it occurs at x = 27.

To find the absolute extreme values of \(f(x) = 3x^{(2/3)} - x\)on the interval (0, 27), we need to find the critical points and the endpoints of the interval.

First, we find the critical points by setting the derivative equal to zero:

\(f'(x) = 2x^{(-1/3)} - 1 = 0\)

Solving for x, we get:

\(x^{(1/3)} = 1/2\)

\(x = (1/2)^3 = 1/8\)

Next, we check the endpoints of the interval:

\(f(0) = 0^{(2/3)} - 0 = 0\)

\(f(27) = 3(27)^{(2/3)} - 27 = 3{(3^2)} - 27 = 0\)

Now, we need to determine whether the critical point and the endpoints are maxima or minima. To do this, we use the second derivative test:

\(f''(x) = -2x^{(-4/3)}\)

At x = 1/8, f''(1/8) < 0, so it is a local maximum.

At x = 0 and x = 27, f''(0) = f''(27) = 0, so we can't use the second derivative test.

Since f(1/8) > f(0) and f(1/8) > f(27), the absolute maximum occurs at x = 1/8, where the value is:

\(f(1/8) = 3(1/8)^{(2/3)} - 1/8 = 3(1/2) - 1/8 = 1 3/8\)

The absolute minimum occurs at x = 27, where the value is:

\(f(27) = 3(27)^{(2/3)} - 27 = 0\)

Therefore, the absolute maximum of f(x) is 1 3/8 and it occurs at x = 1/8, while the absolute minimum is 0 and it occurs at x = 27.

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Answer:

m = 0.2 kg.

Step-by-step explanation:

Joint variation:

Q = kmT where k is a constant.

Subsituting the given values:

20930 = k*1*5

k = 20930 / 5 = 4186.

So the relation is:

Q = 4186mT

When Q = 8372 and T = 10:

8372 = 4186 * m * 10

m = 8372 / (4186*10)

m = 0.2 kg.

To find the total daily production at each plant, multiply the number of shifts by the production per shift for each type of beach ball, and then sum up the results for each type of ball.

To find the total daily production totals at each plant, we can use the number of shifts at each plant.
First, we need to calculate the total number of beach balls produced per shift at each plant.

For Plant 1, which has two shifts per day:
- The total number of beach balls produced in the first shift is 500 + 700 = 1200.
- The total number of beach balls produced in the second shift is 1300 + 1900 = 3200.

For Plant 2, which has three shifts per day:
- The total number of beach balls produced in the first shift is 400 + 1200 = 1600.
- The total number of beach balls produced in the second shift is 600 + 1600 = 2200.
- The total number of beach balls produced in the third shift is not provided.

Now, let's write the matrices to represent one day's total output at the two plants:

Plant 1:
[1200, 3200]

Plant 2:
[1600, 2200, ?]

Since the total number of beach balls produced in the third shift at Plant 2 is not provided, we will leave it as a question mark.

To find the difference between the daily production totals at the two plants, we need to calculate the sum of each plant's daily production totals.

For Plant 1: 1200 + 3200 = 4400.
For Plant 2: 1600 + 2200 + ? = ?

We cannot find the exact difference without knowing the total number of beach balls produced in the third shift at Plant 2.

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The two triangles below are similar and the value of x is 2.5mm

To determine the value of x, we can use the concept of similar triangles, which states that corresponding angles of similar triangles are equal, and corresponding sides are proportional.

In the given diagram, we have two triangles, one with sides measuring 12 mm, x mm, and 10 mm, and the other with sides measuring 3 mm, x mm, and an unknown side (which we'll label as y mm).

Since the triangles are similar, we can set up the following proportion based on their corresponding sides:

12 mm / 3 mm = 10 mm / y mm

To solve for y, we can cross-multiply:

12 mm * y mm = 3 mm * 10 mm

12y = 30

Dividing both sides of the equation by 12, we find:

y = 30 / 12

Simplifying the fraction, we get:

y = 5 / 2

Therefore, the value of x is equal to y, which means x = 5/2 or 2.5 mm.

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Answer:

The constant of variation is ¹/₄.

Step-by-step explanation:

When n varies jointly with f and g, we can write the following equation:

\(\boxed{n \propto fg \implies n = kfg}\)

where k is the constant of variation.

We are given that f = 2, g = 8, and n = 4.  

Substitute these values into the equation:

\(\implies 4 = k \cdot 2 \cdot 8\)

Solve for k:

\(\implies 4 = 16k\)

\(\implies \dfrac{4}{16} = \dfrac{16k}{16}\)

\(\implies \dfrac{1}{4}=k\)

Therefore, the constant of variation is ¹/₄.

\(\blue{\huge {\mathrm{CONSTANT \; VARIATION}}}\)

\(\\\)

\({===========================================}\)

\({\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}\)

\({===========================================}\)

\( {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} \)

\({===========================================}\)

\({\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}\)

If n varies jointly with f and g, the relationship between them can be written as:

where:

Using the given information, we can solve for k as follows:

Therefore, the constant of variation is 1/4.

\({===========================================}\)

Answer

\(168in^{2}\)

Step-by-step explanation:

SA=2(wl+hl+hw)

2·(6·2+9·2+9·6)

=168

Answer:

7172.6

Step-by-step explanation:

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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Answer:

Explanation:

To simplify a polynomial, we have to do two things: 1) combine like terms, and 2) rearrange the terms so that they're written in descending order of exponent.

First, we combine like terms, which requires us to identify the terms that can be added or subtracted from each other. Like terms always have the same variable (with the same exponent) attached to them. For example, you can add 1 "x-squared" to 2 "x-squareds" and get 3 "x-squareds", but 1 "x-squared" plus an "x" can't be combined because they're not like terms.

Let's identify some like terms below.

f(x)=−4x+3x2−7+9x−12x2−5x4

Here you can see that -4x and 9x are like terms. When we combine (add) -4x and 9x, we get 5x. So let's write 5x instead:

f(x)=5x+3x2−7−12x2−5x4

Let's do the same thing with the x-squared terms:

f(x)=5x+3x2−7−12x2−5x4

f(x)=5x−9x2−7−5x4

Now there are no like terms left. Our last step is to organize the terms so that x is written in descending power:

f(x)=−5x4−9x2+5x−7

Step-by-step explanation:

All formulas that model the sequence​ include the following:

E. aₙ =  aₙ₋₁ - 13.8, where a₁ = -7.4

F. aₙ =  6.4 - 13.8n

In Mathematics and Geometry, the nth term of an arithmetic sequence can be calculated by using this equation:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference of the given sequence by using the following formula;

Common difference, d = a₂ - a₁

Common difference, d = -21.2 - (-7.4)

Common difference, d = -13.8.

For the nth term of this arithmetic sequence, we have:

aₙ =  a₁ + (n - 1)d

aₙ =  -7.4 + (n - 1)-13.8

aₙ =  -7.4 - 13.8(n - 1)

aₙ =  -7.4 - 13.8n + 13.8

aₙ =  6.4 - 13.8n

aₙ =  aₙ₋₁ - 13.8, where a₁ = -7.4

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1. The alternative hypothesis (\(H_a\)) is that the percentage is actually more than the reported percentage \(H_a\): p > 0.41. 2. The test statistic is 2.89. 3. Since the alternative hypothesis states that the percentage is "more than" the reported percentage, the test is one-tailed. 4. The critical value for a one-tailed z-test with a significance level of 0.01. 5. The test statistic (2.89) is greater than the critical value (2.33). 6. A laptop is more than the reported percentage of 41%.

Step 1 of 6: State the null and alternative hypotheses.

The null hypothesis (H₀) is that the percentage of readers who own a laptop is 41% (reported percentage):

H₀: p = 0.41

The alternative hypothesis (Ha) is that the percentage is actually more than the reported percentage:

\(H_a\): p > 0.41

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

To find the test statistic, we can use the formula for the z-test for proportions:

z = (\(\hat p\) - p) / √(p * (1 - p) / n)

Where:

\(\hat p\) is the sample proportion (50% = 0.50)

p is the hypothesized proportion (41% = 0.41)

n is the sample size (260)

Calculating the test statistic:

z = (0.50 - 0.41) / √(0.41 * (1 - 0.41) / 260)

z ≈ 2.89

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Since the alternative hypothesis states that the percentage is "more than" the reported percentage, the test is one-tailed.

Step 4 of 6: Determine the decision rule for rejecting the null hypothesis, H0.

To determine the decision rule, we compare the test statistic to the critical value at a given significance level (α). In this case, the significance level is 0.01.

Looking up the critical value for a one-tailed z-test with a significance level of 0.01, we find it to be approximately 2.33.

Step 5 of 6: Make the decision to reject or fail to reject the null hypothesis.

Since the test statistic (2.89) is greater than the critical value (2.33), we can reject the null hypothesis.

Step 6 of 6: State the conclusion of the hypothesis test.

Based on the sample data, there is sufficient evidence at the 0.01 level to support the marketing executive's claim that the percentage of readers who own a laptop is more than the reported percentage of 41%.

The complete question is:

A publisher reports that 41% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually more than the reported percentage. A random sample of 260 found that 50% of the readers owned a laptop. Is there sufficient evidence at the 0.01 level to support the executive's claim?

Step 1 of 6: State the null and alternative hypotheses.

Step 2 of 6: Find the value of the test statistic. Round your answer to two decimal places.

Step 3 of 6: Specify if the test is one-tailed or two-tailed.

Step 4 of 6: Determine the decision rule for rejecting the null hypothesis, H₀.

Step 5 of 6: Make the decision to reject or fail to reject the null hypothesis.

Step 6 of 6: State the conclusion of the hypothesis test.

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When adding several numbers, the number of significant figures in the sum depends on the least precise measurement among the addends.

The sum can have as many significant figures as the addend with the fewest significant figures. The significant figures in a number represent the meaningful and known digits along with the estimated or uncertain digit. When adding numbers, it is important to consider the precision or the number of significant figures in each addend.

The sum of several numbers can have no more significant figures than the addend with the fewest significant figures. This is because the least precise measurement determines the overall precision of the result. Adding numbers with more significant figures than the least precise measurement would introduce additional uncertainty or digits that are not known with certainty.

For example, if you add 2.13 + 4.2 + 0.006, the least precise measurement is 0.006, which has three significant figures. Therefore, the sum should be reported with three significant figures as well, resulting in 6.33. Adding any additional digits beyond the least precise measurement would imply a higher level of precision than what is warranted by the original data.

In conclusion, the sum of several numbers should be reported with the same number of significant figures as the addend with the fewest significant figures to maintain accuracy and avoid introducing false precision.

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The amount of the annual depreciation has been $90.

The statement provides us with the following data:

The yearly depreciation of the table saw can be calculated by subtracting the depreciated value from the original cost and dividing by the number of years.

Yearly depreciation = (Original cost - Depreciated value) / Number of years

Yearly depreciation = ($810 - $450) / 4

Yearly depreciation = $360 / 4

Yearly depreciation = $90

Therefore, the amount of yearly depreciation for the table saw is $90.

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Answer:

D

Step-by-step explanation:

c=5/2-d/2

The / is the show fraction.

I am not 100% sure but it is what I am 99% sure about.