Determine the coordinates of W(-7 , 4) after a reflection in the line y = 9

Answer:

1.6 unit^2 (dec. form) or 1 3/5 unit^2 (frac. form)

Step-by-step explanation:

(1 1/5)(1 1/3)

(6/5)(4/3)

1.6 unit^2 (dec. form) or 1 3/5 unit^2 (frac. form)

The covariance Cov(X, Y) can be calculated for the given joint probability density function (pdf) f(x, y) = kr² over the region 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1.

To calculate the covariance Cov(X, Y), we need to determine the joint probability density function (pdf) of X and Y and apply the formula for covariance.

First, we need to find the constant k by integrating the joint pdf over its entire range to ensure it integrates to 1 (since it represents a probability density function).

The integral of f(x, y) over the region 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 is given by:

∫∫ f(x, y) dy dx = ∫∫ kr² dy dx.

Integrating with respect to y first, we get:

∫[0,1] ∫[0,1] kr² dy dx = k∫[0,1] r² [y=0 to y=1] dx

= k∫[0,1] r² dx

= k[r²x] [x=0 to x=1]

= k(r² - 0)

= kr².

Since the integral of the joint pdf over its entire range equals 1, we have kr² = 1, which implies k = 1/r².

Now, we can calculate the covariance Cov(X, Y) using the formula:

Cov(X, Y) = E[XY] - E[X]E[Y],

where E denotes the expected value.

Since X and Y are continuous random variables with a uniform distribution over the range [0,1], we have E[X] = E[Y] = 1/2.

To calculate E[XY], we integrate the product XY over the range [0,1] for both x and y:

E[XY] = ∫∫ xy f(x, y) dy dx

= ∫∫ xy kr² dy dx

= k∫∫ xyr² dy dx

= k∫[0,1] ∫[0,1] xyr² dy dx.

Integrating with respect to y first, we get:

E[XY] = k∫[0,1] ∫[0,1] xyr² dy dx

= k∫[0,1] [(1/2)xr² [y=0 to y=1]] dx

= k∫[0,1] (1/2)xr² dx

= (k/2)∫[0,1] xr² dx

= (k/2)[(1/3)x³r² [x=0 to x=1]]

= (k/2)(1/3)r²

= (1/2)(1/3)r²

= 1/6r².

Finally, we can calculate the covariance:

Cov(X,Y) = E[XY] - E[X]E[Y]

= 1/6r² - (1/2)(1/2)

= 1/6r² - 1/4.

Therefore, the covariance Cov(X, Y) for the given joint pdf f(x, y) = kr² over the region 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 is 1/6r² - 1/4.

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1. Proof that F is injective. Suppose that two different elements in the domain of F have the same image; that is, if x and y are elements of the domain of F and F(x)= F(y). We need to show that x=y. Let F(x) = F(y). This means that y1= x1/ (x1 + x2 + x3) = y1, y2= x2/ (x1 + x2 + x3) = y2 and y3= x3/ (x1 + x2 + x3) = y3.Now adding (1), (2), and (3), we have:y1+y2+y3= x1/ (x1 + x2 + x3) + x2/ (x1 + x2 + x3) + x3/ (x1 + x2 + x3)But this is equal to 1, therefore,x1 + x2 + x3= y1 + y2 + y3 = 1, or, equivalently, y1= 1- y2 - y3x1= (1- y2 - y3)(x1 + x2 + x3) = (1-y2 - y3), x2= y2(x1 + x2 + x3) = y2, and x3= y3(x1 + x2 + x3) = y3Thus, we have constructed an element of the domain of F, with different elements of the domain, that have the same image. Therefore, F is injective.

2. Find the investment directly without appealing to the Inverse Function Theorem. F(x1,x2,x3) = (y1,y2,y3)So, x1= (1- y2 - y3), x2= y2, and x3= y3Thus, the inverse of F is F-1(y1,y2,y3)= ((1-y2-y3),y2,y3)3. The domain of F. The domain of F is the set of all three-tuples, F(x1,x2,x3) where 0 ≤ xi ≤ ∞, and where at least one xi is positive. That is, Dom (F)={(x1,x2,x3)|x1≥0, x2≥0, x3≥0 and (x1,x2,x3)≠(0,0,0)}4. The range of F, which is the domain of F-1. The range of F is the set of all three-tuples, F(y1,y2,y3) where 0 ≤ yi ≤ 1, and where at least one yi is positive.

That is, Rng(F)={(y1,y2,y3)|y1≥0, y2≥0, y3≥0 and y1+y2+y3=1}5.  We have J_f(x) = ∣∣ ∂(y1,y2,y3) /∂(x1,x2,x3) ∣∣= ∣∣ ∂y1/∂x1 ∂y1/∂x2 ∂y1/∂x3 ∂y2/∂x1 ∂y2/∂x2 ∂y2/∂x3 ∂y3/∂x1 ∂y3/∂x2 ∂y3/∂x3 ∣∣= ∣∣ (1 / (x1 + x2 + x3) ) - (x1/ (x1 + x2 + x3)2) - (x1/ (x1 + x2 + x3)2) 0 1 / (x1 + x2 + x3) - (x2/ (x1 + x2 + x3)2) 0 0 1 / (x1 + x2 + x3) - (x3/ (x1 + x2 + x3)2) ∣∣= (1 / (x1 + x2 + x3) )((1 - y2 - y3) (1 - y2 - y3 - y3) - y2 (1 - y2 - y3) - y3(1 - y2 - y3)) = (1 / (x1 + x2 + x3) )((1 - y2 - y3 - y2 + 2y2y3 + y2 - y3 - 2y2y3 + y3 - y2y3 - y3 + y2y3)) = 1 / (x1 + x2 + x3) which is non-zero in the domain of F. Therefore, J_f(x) ≠ 0 when x ∈ Dom (F).

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Answer:

Tony should add $7.70

Step-by-step explanation:

22% = 0.22

0.22 x $35 = $7.70

Answer:

5 + 4 snice it's inside the circle and when you get your answer you times it with 3

Step-by-step explanation:

( 5 + 4 ) x 3

  9 x 3

27

(5+4) x 3 = 27

Answer:

B

Step-by-step explanation:

the notation answer would also be 3.246 × 10-4 i believe :)

Answer:

a) $93, $117.80, $86.80, $68.20

b) $365.80

Step-by-step explanation:

a)

Add 12 hours to each p.m. time to make the subtraction of hours easier.

Also, use decimal numbers to do the subtraction. Remember that 0:30 means 30 minutes which is 0.5 hour, so 7:30 is the same as 7.5 as a decimal.

Monday: 8:00 to 15:30

15:30 - 8:00 = 1.5 - 8 = 7.5 hours

7.5 hours * $12.40/h = $93

Wednesday: 7:30 to 17:00

17:00 - 7:30 = 17 - 7.5 = 9.5 hours

9.5 hours * $12.40/h = $117.80

Friday: 9:00 to 16:00

16:00 - 9:00 = 16 - 9 = 7 hours

7 hours * $12.40/h = $86.80

Saturday: 10:30 to 16:00

16:00 - 10:30 = 16 - 10.5 = 5.5 hours

5.5 hours * $12.40/h = $68.20

b) Add all the daily amounts above.

$93 + $117.80 + $86.80 + $68.20 = $365.80

Answer: 3. Tan; 4. 4.76; 5. 12

Step-by-step explanation: First question: SOH CAH TOA; if you draw a picture with the given information you know the Opposite and Adjacent sides to the upper left angle, or OA which is also Tan according to Soh Cah Toa. Second question: Use inverse tan(1/12) to solve. Third question: Same idea as the last question but use inverse sin(1/5)

Answer:

5π

Step-by-step explanation:

just need to find half of the circumference

Answer:

10

Step-by-step explanation:

use pythagorean theorm

√(8^2+6^2) = 10

Answer:

Distance between the points is 8 miles.

Step-by-step explanation:

Distance between tow points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is defined by,

Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Distance between the given points (2, -3) and (2, 5) will be,

Distance = [tex]\sqrt{(2-2)^2+(-3-5)^2}[/tex]

               = 8 units

Since, 1 unit = 1 mile

Therefore, distance between these points will be 8 miles.

Answer:

28.27 rounded orrrr 28.27433388 not rounded.

Step-by-step explanation:

area of circle=πr^2

radius=3 km

3^2=9

9*π

Step-by-step explanation:

Area of a circle = πr²

Radius (r) =1/2 Diameter

=60/2

=30km

Area = π x (30)²

= π x 900

= 2027km²

Answer:

200

Step-by-step explanation:

happy to help

The lateral area of  square based pyramid is 200 square feet

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

The given square base pyramid has four faces of triangles and one square shape base

The lateral surface area of pyramid formula 4 × (1/2)bl,

b = side length of the base, and

l = slant height

Lateral surface area =2 bl

=2×10×10

=200 square feet

Hence,  the lateral area of  square based pyramid is 200 square feet

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Answer: C is false

Step-by-step explanation: If B is correct and C is saying otherwise that must mean it's the only false choice :) brainliest would be appreciated :)

The probability of rolling a number less than 3 or an odd number is 3/5 in fraction form.

To compute the probability of rolling a number less than 3 or an odd number, we need to calculate the probability of each event separately and then subtract the probability of their intersection.

The probability of rolling a number less than 3 is 2/10, as there are two numbers (1 and 2) that satisfy this condition out of the ten possible outcomes.

The probability of rolling an odd number is 5/10, as there are five odd numbers (1, 3, 5, 7, and 9) out of the ten possible outcomes.

To compute the probability of their intersection (rolling a number less than 3 and an odd number), we observe that there is only one number (1) that satisfies both conditions.

Therefore, the probability of their intersection is 1/10.

To compute the probability of rolling a number less than 3 or an odd number, we sum the probabilities of each event and subtract the probability of their intersection:

Probability of rolling a number less than 3 or an odd number = (2/10) + (5/10) - (1/10) = 6/10 = 3/5.

Therefore, the probability of rolling a number less than 3 or an odd number is 3/5.

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For a real number x, by using mathematical induction it is shown that a[tex](1 + x)^{2n}[/tex] > 1 + 2nx for every positive integer n.

To prove the inequality a[tex](1 + x)^{2n}[/tex] > 1 + 2nx  for every positive integer n, we will use mathematical induction.

The inequality holds true for n = 1, and we will assume it is true for some positive integer k.

We will then show that it holds for k + 1, which will complete the proof.

For n = 1, the inequality becomes a[tex](1 + x)^2[/tex] > 1 + 2x.

This can be expanded as a(1 + 2x + [tex]x^2[/tex]) > 1 + 2x, which simplifies to a + 2ax + a[tex]x^2[/tex] > 1 + 2x.

Now, let's assume the inequality holds true for some positive integer k, i.e., a[tex](1 + x)^{2k}[/tex] > 1 + 2kx.

We need to prove that it holds for k + 1, i.e., a[tex](1 + x)^{2(k+1)}[/tex] > 1 + 2(k+1)x.

Using the assumption, we have a[tex](1 + x)^{2k}[/tex] > 1 + 2kx.

Multiplying both sides by [tex](1 + x)^2[/tex], we get a[tex](1 + x)^{2k+2}[/tex] > (1 + 2kx)[tex](1 + x)^2[/tex].

Expanding the right side, we have a[tex](1 + x)^{2k+2}[/tex] > 1 + 2kx + 2x + 2k[tex]x^2[/tex] + 2[tex]x^2[/tex].

Simplifying further, we get a[tex](1 + x)^{2k+2}[/tex] > 1 + 2(k+1)x + 2k[tex]x^2[/tex] + 2[tex]x^2[/tex].

Since k and x are positive, 2k[tex]x^2[/tex] and 2[tex]x^2[/tex] are positive as well.

Therefore, we can write a[tex](1 + x)^{2k+2}[/tex] > 1 + 2(k+1)x + 2k[tex]x^2[/tex] + 2[tex]x^2[/tex] > 1 + 2(k+1)x.

This proves that if the inequality holds for some positive integer k, it also holds for k + 1.

Since it holds for n = 1, it holds for all positive integers n by mathematical induction.

Therefore, we have shown that a[tex](1 + x)^{2n}[/tex] > 1 + 2nx  for every positive integer n.

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a) The Z-value corresponding to a confidence level of 95% can be determined as 1.96.

b) To determine the required sample size, we need additional information such as the population size or an estimated proportion. Without this information, we cannot calculate the sample size.

a) The Z-value represents the number of standard deviations a data point is from the mean in a standard normal distribution. For a confidence level of 95%, which corresponds to a 5% significance level, the critical Z-value is approximately 1.96. This value can be obtained from a Z-table or using statistical software.

b) To calculate the required sample size, additional information is needed, such as the population size or an estimated proportion. The sample size formula takes into account factors such as the desired margin of error, confidence level, and variability. Without these details, it is not possible to determine the sample size accurately.

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The important difference to note for the scales of measurement and how they are analyzed is whether they involve ratios, intervals, categories or numbers. The scales of measurement can be divided into four types: nominal, ordinal, interval, and ratio.

Nominal scales use categories or numbers to group data, but these categories or numbers have no inherent order or value. Examples of nominal scales include gender, race, or eye color. Ordinal scales use categories or numbers to group data, but these categories or numbers have a specific order or rank. Examples of ordinal scales include educational attainment, income, or level of agreement on a survey question.

Interval scales use numbers as responses on the scale, but the distance between the numbers is not meaningful. Examples of interval scales include temperature measured in Celsius or Fahrenheit, or IQ scores. Ratio scales use numbers as responses on the scale, but the distance between the numbers is meaningful and there is a true zero point. Examples of ratio scales include height, weight, or income.

In summary, the important difference to note for the scales of measurement and how they are analyzed is whether they involve categories or numbers, and whether the numbers have a specific order or rank, a meaningful distance between them, or a true zero point.

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Answer:

Let the total charge is y, the number of small arrangements is x.

Total charge will be:

Total charge will be:

Since the total charge is same in both shops, we have:

Solve for x:

Total cost is:

Small arrangements = 3, cost = $86

Answer: Big rectangle shades 1/4+1/2

Step-by-step explanation:

So have a Big

Answer:

Hello!

The answer is 8^18.

Step-by-step explanation:

Answer:

8^12

Step-by-step explanation:

Exponents are confusing at first. You subtract them when dividing, and add them when multiplying, if the base number is the same.

Picture 8 to the 15th as a numerator of:

8x8x8x8x8x8x8x8x8x8x8x8x8x8x8 over a denominator of

8x8x8

To solve that, you'd cancel out 3 of the top 8s and the three bottom 8s, marked in bold to be easier to see. This leaves you with

8^12

Does that help?

Happy to answer questions.

Answer:

x-intercept

y-intercept

Step-by-step explanation:

Answer:

x-intercept y-intercept

Answer:

54 cm²

Step-by-step explanation:

1 cm= 3 m

2 cm= 6 m

3 cm= 9 m

9×6=54

Area of bedroom= 54 cm²

Answer:

The temperature with the highest frequency is 54

Step-by-step explanation:

Given

The above data

Required

The temperature with the highest frequency

The first step, is to plot the stem and leaf plot.

[tex]\begin{array}{cc}{4} & {9\ \ } & {5} & {2\ 4\ 4\ 6\ 8} & {6} & {0\ 1\ } & {7} & {2\ 3\ } \ \end{array}[/tex]

Next, is to identify the leaf with the highest frequency.

The leaf is 4 (with frequency 2)

Next, is to identify the accompanying stem of the leaf

The stem is 5

Hence, the temperature with the highest frequency is 54

Answer:

B

Step-by-step explanation:

edg 2021

Answer:

222222222/1000000000

Step-by-step explanation:

Answer:

B. 1296 m^3

Step-by-step explanation:

To find the volume of a square pyramid, multiply the base by itself twice, then divide the height by 3. After getting both answers, multiply the answers.

In this case, the base is 18.

The height is 12.

First, we must multiply the base by itself twice.

18⋅18 = 324.

Next, divide the height by 3.

12/3 = 4.

Now that we have both answers, we multiply them.

324 ⋅ 4 = 1,296.

Therefore, 1,296 cm^3 is the volume of the square pyramid.

(a) The complete graph K41 has 820 edges. This can be calculated using the formula for the number of edges in a complete graph, which is given by the expression (n(n-1))/2, where n is the number of vertices. Substituting n = 41, we get (41(41-1))/2 = 820.

(b) The number of isomorphisms from K41 to itself is equal to the number of permutations of the vertices. This can be calculated as 41!, which represents the number of ways to arrange the vertices of K41.

(c) The graph C41 is not isomorphic to itself because it has a specific edge pattern. Thus, there are no isomorphisms from C41 to itself.

(d) The chromatic number of K41 is equal to its number of vertices, which is 41. This is because each vertex can be assigned a unique color, and no two adjacent vertices share the same color in a complete graph.

(e) The chromatic number of C41 is 2. This is because C41 contains a Hamiltonian cycle, which is a cycle that visits each vertex exactly once. A Hamiltonian cycle can be colored with only two colors, where adjacent vertices are assigned different colors.

(f) A spanning tree of K41 is a connected acyclic subgraph that includes all the vertices of K41. The number of edges in a spanning tree of K41 is equal to the number of vertices minus 1, which is 41 - 1 = 40.

(g) If a single edge is added between nonadjacent vertices of a tree with 41 vertices, the largest number of cycles the graph might have is 41. This can occur when the new edge connects two vertices that are at maximum distance from each other in the original tree, resulting in a new cycle.

(h) The smallest number of leaves possible in a spanning tree of K41 is 1. This can be achieved by removing all but one edge from K41, resulting in a single leaf node.

(i) The largest number of leaves possible in a spanning tree of K41 is 40. This can be achieved by removing all but one vertex from K41, resulting in a single vertex connected to 40 leaf nodes.

(g) The number of spanning trees that C41 has can be calculated using Cayley's formula, which states that a complete graph with n vertices has nn-2 spanning trees. Substituting n = 41, we get 4141-2 = 240 spanning trees for C41.

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Answer:

Sorry sis don't know the meaning