Find the area of the equilateral triangle to the nearest hundredth, given the radius.

The joint density for (U, V) is given by:

                = λ^2 * v * e^(-λv/u) * |(v/u)|

The marginal density for U is given by:

fU(u) = ∫f(u,v)dv

        = ∫λ^2 * v * e^(-λv/u) * |(v/u)|dv

        = λ^2 * u * ∫ve^(-λv/u)dv

        = λ^2 * u * (-(u/λ)^2 * e^(-λv/u))|v=0 to v=∞

        = λ^2 * u * (-(u/λ)^2)

        = λ^3 * u^2

The marginal density for V is given by:

fV(v) = ∫f(u,v)du

       = ∫λ^2 * v * e^(-λv/u) * |(v/u)|du

       = λ * v * ∫e^(-λv/u) * |(v/u)|du

       = λ * v * (∫e^(-λv/u)du)|v=0 to v=∞

       = λ * v * (-(u/λ) * e^(-λv/u))|u=0 to u=∞

       = λ * v * (-1)

       = λ * v

Therefore, the joint density for (U, V) is

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Answer:

y(x) = integral(6 c^2 - 20 x^3)/(5 x^2 + 3) dx = -2 x^2 + 1/5 log(5 i x + sqrt(15)) (-i sqrt(15) c^2 + 6) + 1/5 log(-5 i x + sqrt(15)) (i sqrt(15) c^2 + 6) + k_1, where k_1 is an arbitrary constant.

Step-by-step explanation:

Rewrite the equation to -((6 c^2 - 20 x^3) dx)/(3 + 5 x^2) + dy = 0 and solve

Solve (dy(x))/(dx) = (6 c^2 - 20 x^3)/(5 x^2 + 3):

Integrate both sides with respect to x:

Answer: y(x) = integral(6 c^2 - 20 x^3)/(5 x^2 + 3) dx = -2 x^2 + 1/5 log(5 i x + sqrt(15)) (-i sqrt(15) c^2 + 6) + 1/5 log(-5 i x + sqrt(15)) (i sqrt(15) c^2 + 6) + k_1, where k_1 is an arbitrary constant.

On solving the provided question, we can say that -  correlation coefficient , r= .95

The Pearson's correlation coefficient, also known as the Pearson's r, Pearson's product-moment correlation coefficient, bivariate correlation, or simply correlation coefficient, is a statistical indicator of the linear relationship between two sets of data.

[tex]S_{xx}[/tex] = ∑[tex]x^2[/tex] + [tex]nx^2[/tex] = 60

[tex]S_{yy} = 60[/tex]

r  = .95

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Answer:190 small packs and 4 cookies left over

Step-by-step explanation:

Add the boxes of cookies together 105+22=127

Multiply each box by 12

127 x 12=1524

Because we need to put them into smaller packs of 8 cookies

we need to divide by 8

1524÷8=190 small boxes

This is a total of 190 x 8=1520 cookies there are 4 cookies left over

Answer:

x is -7.5 or -14/2 or -7½

Step-by-step explanation:

- Supposing y varies directly with x

[tex] { \tt{y \: \alpha \: x}} \\ \: \: \: \: { \tt{y = kx}} [/tex]

[k is a constant of proportionality (k ≠ 0)]

- When y is 6, x is -2

[tex] \: \: \: \: \: \: \: \: \: { \tt{6 = (k \times ^{ - }2) }} \\ { \tt{6 = - 2k}} \\ { \tt{k = - 3 \: \: }}[/tex]

- Therefore, the equation is;

[tex]{ \boxed{ \tt{y = - 2x}}}[/tex]

- What is x when y is 15

[tex]{ \tt{15 = - 2x}} \\ { \tt{x = - 7.5}}[/tex]

The value of x is -5

The equation for a direct variation is y = kx, where k is the constant of variation. Since we know that y = 6 when x = -2, we can solve for k:

                                        k = y/x

                                        k = 6/-2

                                        k = -3

Therefore, the equation for this direct variation is y = -3x. To find x when y = 15, Substitute k = -3 and y = 15 into the equation

                                15 = -3x

Then solve x,

                       x = [tex]\frac{-15}{3}[/tex]

                        x = -5

Therefore, when y = 15, x = -5.

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True statement is number of observations that are within or below each of the classes.

A relative frequency describes how frequently a particular kind of event happens among all observations. It is a kind of frequency that employs fractions, percentages, and proportions. The ratio of the total number of events occurring in a scenario to the number of times an event occurs is known as relative frequency. Relative Frequency = Subgroup Frequency/Total Frequency is the formula for relative frequency. A relative frequency count is a way to count how many times an event happens compared to all the other events. It can be described as a percentage. It is frequently represented as a percentage as well.

Given

The relative frequency distribution describes the number of observations that fall within each class.

Statement which is true is,

Number of observations that are within or below each of the classes.

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Answer:

∠ b = 108° , ∠ d = 72°

Step-by-step explanation:

(a)

the sum of the 3 angles in a triangle = 180° , that is

∠ a + ∠ b + ∠ c = 180°

25° + ∠ b + 47° = 180°

∠ b + 72° = 180° ( subtract 72° from both sides )

∠ b = 108°

(b)

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles , then

∠ d = ∠ a + ∠ c = 25° + 47° = 72°

The length of XY in the given figure is 3 units.

same in size and form

Congruent refers to things that are exactly the same size and form. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Congruent refers to something that is "absolutely equal" in terms of size and form. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, then stack them on top of one another.

In the above question,

According to the congruency criteria

HI=XY

Hence, Value of XY is 3 units.

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Answer:

x ≥ 2.3

Step-by-step explanation:

Product means multiplication

10x ≥ 23  Divide both sides by 10

x ≥ 2.3

The proportion to calculate triangle side LM in the given triangle is 3/2

The side LM is calculated using the idea of similar triangle, in this case the triangles are equal in proportion to each other

To find the proportion we take the ratio of the sides this is done as follows

LM / HJ = MN / JK = LN / HK

substituting the values

MN / JK = 9 / 6 = 3 / 2

the proportion is = 3/2

to find LM

4.5 * 3/2

= 6.75 cm

Using proportion of 3/2 the length of side LM is solved to be 6.75 cm

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Answer:

  a) v(t) = 30600 -1440t

  b) 8 years

Step-by-step explanation:

You want an equation that models the value of a car that is initially $30,600 and falls at the rate of $1440 per year. Then you want the number of years it takes for the value to fall to $19,080.

Since the rate at which the value falls is a constant, we can use a linear equation for the model. Its form will be ...

  value = initial value - (depreciation per year) × years

  v(t) = 30,600 -1440t

The time it takes for the value to fall to 19080 can be found by solving for t:

  19080 = 30600 -1440t

  1440t = 30600 -19080 = 11520

  t = 11520/1440 = 8

After 8 years the car's value will be $19,080.

Answer: 55.6 or 55.60

Step-by-step explanation: Okay, so we have to add up all the numbers and divide by how many numbers there are, so we would add 50 + 52 + 71 (Including this outlier) + 54 + 51, to get 278. Now, since there are 5 numbers in the data set, we would divide 278 by 6, and you should get 55.6 or 55.60 (They are the same thing)

The recursion tree is log2m and has log2m nodes .

A recursive algorithm calls itself with smaller input values and returns the result for the current input by carrying out basic operations on the returned value for the smaller input.

A iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.

In the analysis of algorithms, the master theorem for divide-and-conquer recurrences provides an asymptotic analysis for recurrence relations of types that occur in the analysis of many divide and conquer algorithms.

Two integers x and y are given. x and y require n bit and m bit respectively. Two algorithms to compute x y need to be analyzed.

Iterative: The pseudocode for this algorithm is as follows.

product = x;

for i = 2 to y do

product = product * x

The result after the multiplication of two integers, one p bits long and another one q bits long requires p q bits to to store. Therefore, for a given i , we are multiplying one ( i − 1)n bits long integer with an n bit long integer. This multiplication cost is ( i − 1)n2 .

The resulting number after the multiplication is i.n bits long. Thus

adding up all the multiplication cost we get

n2 + 2n2 + 3n2 + . . . + (y − 1)n2. Thus the complexity of the iterative algorithm is O(n2y2) which exponential in

the input length of y which is m = log2 y.

Recursive: The pseudocode for this algorithm is as follows:

function recursive (x ,y)

if y is even then return (x(by2c))2

if y is odd then return x ∗ (x(by2)c)2.

Computing (x(by2c))2

requires a multiplication involving two y2

n bits integers. The cost of this operation is y24.n2 which is O(y2n2). The recurrence relation for this

recursive routine is

T(y) = O(n) when y is 1-bit long.

T(y) = T(y2) + O(y2n2) otherwise.

Applying the Master Theorem we can conclude that T(y) ∈ O(y2n2). The height

of the recursion tree is log2m and has log2m nodes.

Thus both the algorithms have the same worst case complexity.

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Two integers x and y are given. x and y require n bit and m bit respectively. Two algorithms to compute x y need to be analyzed.

product = x;

for i = 2 to y do

product = product * x

The result after the multiplication of two integers, one p bits long and another one q bits long requires p q bits to to store. Therefore, for a given i , we are multiplying one ( i − 1)n bits long integer with an n bit long integer. This multiplication cost is ( i − 1)n2 .

n2 + 2n2 + 3n2 + . . . + (y − 1)n2. Thus the complexity of the iterative algorithm is O(n2y2) which exponential in

the input length of y which is m = log2 y.

function recursive (x ,y)

if y is even then return (x(by2c))2

if y is odd then return x ∗ (x(by2)c)2.

Computing (x(by2c))2

requires a multiplication involving two y2

n bits integers. The cost of this operation is y24.n2 which is O(y2n2). The recurrence relation for this

recursive routine is

T(y) = O(n) when y is 1-bit long.

T(y) = T(y2) + O(y2n2) otherwise.

Thus both the algorithms have the same worst case complexity.

The value of  m/JHI and m/GHI is  angle 19 and 46.

What is  angle ?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.

[tex]\begin{aligned}2 x+7+8 x-2 & =65 \\10 x+5 & =65 \\10 x & =60 \\x & =6\end{aligned}[/tex]

m/JHI =(2x+7) = (2* 6+7)=12+7=19.

m/GHI = (8x - 2)° = (8*6-2)=48-2=46

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Step-by-step explanation:

the expected value is the sum of all values multiplied by their corresponding probabilities.

and a probability is always

desired cases / totally possible cases.

in the bag are

28 + 6 + 1 = 35 marbles

the probability to pull the gold is

1/35

the probability to pull a silver is

6/35

the probability to pull a black is

28/35 = 4/5

the expected value = $3×1/35 + $2×6/35 - $1×28/35 =

= 3/35 + 12/35 - 28/35 =

= -13/35 = -0.371428571... ≈

≈ -$0.37

that means (like with all games of that kind like all casino games) the bank will win in the long run.

your only chance to win is to play very few times and get a winner by pure chance. the longer you play you might actually hit a winner somewhere in between, but the surer you still lose in total.

Answer:

$20.5

Step-by-step explanation:

Answer:

D) Obtuse triangle

Step-by-step explanation:

Obtuse triangles have an angle greater than 90 degrees, and this triangle has an angle of 105.

Answer:

formula

= Pmt [(1 + i/n)^nt - 1] / (i/n)

answer in picture hihi ^_^

Step-by-step explanation:

The value of the function h(x) = f(x) – g(x) will be h(x) = log5(x) – x³ – 11. The correct option is D.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a cryptographer uses a combination of two functions to develop the initial "key” in a sequence of coded numbers. The functions are:

f(x) = log5(x) – 8

g(x) = x³ + 3

The value of the function h(x) = f(x) - g(x) is,

h(x) = f(x) - g(x)

h(x) = log5(x) – 8 - x³ - 3

h(x) = log5(x) – 8 - x³ - 11

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Answer:

D. h(x) = log5(x) – x3 – 11

Step-by-step explanation:

Answer:

input: n

output: 15

Step-by-step explanation:

⭐What is a linear function?

⭐To find the output that corresponds to n, we can:

⭐Remember:

Answer:

0, zero product property

Step-by-step explanation:

The Answers for the four parts are

a)  5-9+7-6=-3

b) -8 + 12-9-2=-7

c) 10-3-5 + 11 =13

d)  −2+2+7+8= 15

Integers come in three types:

Given:

a)  5-9+7-6

= -4 +7-6

= 3-6

=-3

So, the value of 5-9+7-6 is (-3).

b) -8 + 12-9-2

= 4-9-2

= -5-2

=-7

So, the value of -8 + 12-9-2 is (-7).

c) 10-3-5 + 11

= 7-5+11

= 2+11

=13

So, the value of  10-3-5 + 11 is (13).

d)  −2+2+7+8

= 0+7+8

= 7+8

= 15

So, the value of −2+2+7+8 is (15).

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The Translation of the Attached Question:

Solve as in the example

Answer:

The tightened spot is 10 feet away from the foot of the pole.

Step-by-step explanation:

1. Draw the diagram. Notice that the shape of the electric pole and its supporting wire creates a right triangle.

2. We know 2 side lengths already (26ft, 24ft), and we need to find 1 more side length. Therefore, to find the 3rd side length of a right-triangle, utilize Pythagoras' Theorem.

⭐What is the Pythagoras' Theorem?

3. Substitute the values of the side lengths into the equation, and solve for the unknown side length.

Let B= the distance from the tightened spot to the foot of the pole.

[tex](C)^2 = (A)^2 + (B)^2[/tex]

[tex]26^2 = 24^2 + B^2[/tex]

[tex]676 = 576 + B^2[/tex]

[tex]100 = B^2[/tex]

[tex]\sqrt{100} = \sqrt{(B)^2}[/tex]

[tex]10 = B[/tex]

∴ The tightened spot is 10 feet away from the foot of the pole.

Diagram:

Answer:

Tan(f) = 24/7

Step-by-step explanation:

Tan is opposite over adjacent.

The opposite of angle F is 24 and the adjacent is 7.

The number of visits Jim must make to make Plan A the cheaper option is 6 and 5 visits will cost the same.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Suppose n number of visits will make plan A cheaper than B.

The total cost of A <  total cost of B

50 + 10n < 25 + 15n

15n - 10n > 50 - 25

5n > 25

n > 5

n = 6

At n = 5

Total cost of A = 50 + 10 x 5 = $100

Total cost of B = 25 + 15 x 5 = $100

Hence "Jim needs to visit 6 times, and 5 visits will cost the same, for Plan A to be more affordable".

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