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Given that each term has a common difference, this is an arithmetic sequence as per the explicit formula that generates this sequence.

In this instance, the next word in the sequence is obtained by adding 2 to the previous term. To put it another way, a n = a 1 + d (n – 1) This is the arithmetic sequence’s formula.

Firstly, we have to find the initial phrase in a given series. Thereafter we have to find the shared difference between the following phrases in the sequence. For an explicit rule, replace the general form with the first term and common difference.

The distance between succeeding terms in an arithmetic series is always the same.

The difference between consecutive terms in the sequence 3, 5, 7, 9…, for instance, is an example of an arithmetic sequence.

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A probability distribution is a function that describes the likelihood of different outcomes in a random event or experiment.

(a) To find the distribution of R-n, we first need to find the joint distribution of the sample. Let Y = log(X), then the density function of Y is given by:

g(y) = f(e^y) * |(dx/dy)| = (1/2) * e^(-e^y) * e^y = (1/2) * e^(-e^y)

for y > 0.

Then the joint density function of Y1, Y2, ..., Yn is given by:

g(y1, y2, ..., yn) = ∏ g(yi) = (1/2^n) * exp(-∑ e^yi), y1 > 0, y2 > 0, ..., yn > 0.

Let Z = min(Y1, Y2, ..., Yn) and W = Y1 + Y2 + ... + Yn. Then we have:

Z = min(Y1, Y2, ..., Yn) = Y(n+1) (since Y is a decreasing function of X)

W = Y1 + Y2 + ... + Yn

Note that W follows the gamma distribution with shape parameter n and scale parameter 1, since the density function of Y is the same as the exponential distribution with mean 1. Thus,

fW(w) = (1/Γ(n)) * w^(n-1) * e^(-w)

for w > 0.

Now we can use the probability distribution transformation method to find the distribution of R-n = (n-1)W/Z:

First, we need to find the joint density function of W and Z:

g(w, z) = g(y1, y2, ..., yn) * |(dy1dy2...dyn/dwdz)|

= (1/2^n) * exp(-w) * n * e^(-z) * (e^z)^(n-1) * [(n-1)e^z]^(n-2) * e^z * [(n-1)e^z - w]^(1-n)

= n(n-1) * e^(-w-z) * w^(n-2) * z^(-n+1) * [(n-1)e^z - w]^(1-n), w < z/(n-1)

Then, we can find the distribution of R-n as follows:

P(R-n < r) = P((n-1)W/Z < r)

= P(W < rZ/(n-1))

= ∫∫g(w, z)dw dz, 0 < w < rZ/(n-1), w < z/(n-1)

After integrating out w, we get:

P(R-n < r) = ∫r/(n-1)^2 z^n e^-z/n dz, 0 < z < ∞

= 1 - Γ(n, r/(n-1)),

where Γ(a, x) is the upper incomplete gamma function.

Therefore, the distribution of R-n is a beta distribution with parameters (n-1, 1):

fR-n(r) = (n-1) * (1-r)^(n-2), 0 < r < 1.

(b) The order statistics of a sample of size n from an exponential distribution with mean β have the following joint density function:

g(x1, x2, ..., xn) = n!/β^n * exp(-∑ xi/β) * I(xi < x(i+1)), for x1 > 0, x2 > x1, ..., xn > xn-1.

where I(.)

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Answer:

29° C

Step-by-step explanation:

-17(-12)

=29

Hope this helps

Answer:

29C

Step-by-step explanation:

Above zero temperature = +17C

Below zero temperature = -12C

Difference= 17 - (-12C)

                 = 17 + 12 C

                 =29C

Answer:

-6

Step-by-step explanation:

Answer:

-12x^2+15x

Step-by-step explanation:

-3x(4x-5)

Distributive property:

-3x*4x-(-3x)*5

-3*4x^2+3*5x

Simplify:

-12x^2+15x

Answer:

Step-by-step explanation:

A is not graphed correctly. The graph is turned upside down from what it should be.

Answer:

2(y+10)

Step-by-step explanation:

factor out the common term 2

Answer:

2(y + 10)

Step-by-step explanation:

cannot find y unless this is supposed to equal something, but this is how you factor out the answer. let me know if you have any other questions!

Answer:$80

Step-by-step explanation:

The quotient of the polynomial 10x⁶ + 20x⁴ - 15x² by 5x² will be (2x⁴ + 4x² - 3).

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

The polynomials are given below.

10x⁶ + 20x⁴ - 15x² and 5x²

The factor of the polynomial 10x⁶ + 20x⁴ - 15x² will be given as,

10x⁶ + 20x⁴ - 15x² = (5x²) · (2x⁴ + 4x² - 3)

The quotient of the polynomial 10x⁶ + 20x⁴ - 15x² by 5x² will be given as,

⇒ (10x⁶ + 20x⁴ - 15x²) ÷ (5x²)

⇒ [(5x²) · (2x⁴ + 4x² - 3)] ÷ (5x²)

⇒ (2x⁴ + 4x² - 3)

The quotient of the polynomial 10x⁶ + 20x⁴ - 15x² by 5x² will be (2x⁴ + 4x² - 3).

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Answer: The answer is given below

Step-by-step explanation:

From store 1:

Latoya paid $17.64 for a 7.94-kg bag of dog food. The unit price will be the price paid divided by the quantity. This will be:

= $17.64/7.94

= $2.22 per kg

For store 2:

A few weeks later she paid $18.88 for an $8.39-kg bag at a difference store. The unit price in the second store will be: $18.88/8.39 = $2.25 per kg.

The unit price of the first store is a better buy because the price is cheaper.

Answer:

the price of the first store is cheaper by 0.03 dollars (2.25 - 2.22), that is to say 3 cents

Step-by-step explanation:

To calculate the unit price we must divide by the price by the weight, thus we will obtain the value for each kilogram of dog food:

First price:

17.64 / 7.94 = 2.22

In other words, the price is 2.22 dollars per kilogram.

Second price:

18.88 / 8.39 = 2.25

In other words, the price is 2.25 dollars per kilogram.

Which means, that the price of the first store is cheaper by 0.03 dollars (2.25 - 2.22), that is to say 3 cents.

The circumference of the cone is 9π units

The formula for calculating the circumference of a cone is expressed as;

C = 2πr

Such that the parameters are expressed as'

But we have that;

Volume = 448 pi units

Height = 21 units

Substitute the values, we have that;

448 = πr² × 21/3

Divide the values, we have;

448/7 = πr²

r² = 20. 38

r = 4. 5 units

Then,

circumference = 2×3. 14 × 4. 5

Multiply the values

Circumference = 28. 35 units or 9π units

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The z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

The z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

How to find the Z score

P(Z ≤ z) = 0.60

We can use a standard normal distribution table or a calculator to find that the z-score corresponding to a cumulative probability of 0.60 is approximately 0.25.

Therefore, the z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

For the second question:

We want to find the z-score such that the area under the standard normal distribution curve to the right of z is 0.30. In other words:

P(Z ≥ z) = 0.30

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.30 is approximately -0.52 (since we want the area to the right of z, we take the negative of the z-score).

Therefore, the z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

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In the formula p2 = mb/t, if m remains constant, b is doubled, and t is halved, then the value of p will increase.

This is because doubling b will increase the numerator of the fraction, while halving t will decrease the denominator of the fraction. This will result in a larger value for p2, and therefore a larger value for p.
To see this more clearly, let's plug in some numbers. Let's say that m = 2, b = 4, and t = 8. Plugging these values into the formula gives us:
p2 = (2)(4)/8 = 1
Now, let's double b and halve t. This gives us b = 8 and t = 4. Plugging these values into the formula gives us:
p2 = (2)(8)/4 = 4
As you can see, the value of p2 has increased from 1 to 4, which means that the value of p has also increased. Therefore, when m remains constant, b is doubled, and t is halved, the value of p will increase.

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The chart element that gives a realistic, three-dimensional look is D. plot area.

In a chart, the plot area is the area where the actual chart data is plotted. It is the main part of the chart where the lines, bars, or other data markers are displayed. To give a chart a realistic, three-dimensional look, shading and depth are applied to the plot area. This creates the illusion of depth and makes the chart appear more visually appealing and easier to read. The axis, chart area, and legend do not typically have a three-dimensional appearance, as they are typically two-dimensional elements that provide information about the chart data rather than displaying the data itself.

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The given lines of equations are not perpendicular to each other. Therefore, `θ = cos⁻¹(8/(4√10))` which is approximately `28.07°`.Since `θ ≠ 90°`, the given lines of equations are not perpendicular to each other.

Given lines of equations:

x = −2 + 2t, y = −6, z = 2 + 6tx=−1+t,y=1+t,z=t, t∈ R.

Firstly, we need to find the direction vectors of the two given lines.For the first equation,Let `t=1`, then the point on the line is `(-2+2(1), -6, 2+6(1))`=`(0, -6, 8)`.

Let `t=2`, then the point on the line is

\(`(-2+2(2), -6, 2+6(2))`=`(2, -6,\)14)`.T

herefore, direction vector `

\(v1 = (2, -6, 14)-(0, -6, 8)`=`(2, 0, 6)`\)

For the second equation, direction vector \(`v2 = (1, 1, 1)`.\\\)

Let the angle between the direction vectors `v1` and `v2` be `θ`.

Then, we know that `v1 • v2 = |v1||v2| cosθ`, where `•` represents the dot product of the vectors, and `|.|` represents the magnitude of the vector.

Thus, we have:

(2, 0, 6) • (1, 1, 1) = √(2²+0²+6²)√(1²+1²+1²) cosθ

=> 8 = √40√3 cosθ=> cosθ = 8/(4√10)

Therefore,

`θ = cos⁻¹(8/(4√10))`

which is approximately `28.07°`.

Since `θ ≠ 90°`, the given lines of equations are not perpendicular to each other.

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Answer:

It seems as though your old question was deleted. XD

Step-by-step explanation:

Remember that when you multiply a number by 10, the decimal point is moved one place to the right. Then:

Therefore, the answer is 275.4

Step-by-step explanation:

Slope intercept form of a line

y = mx + b     m = slope (rate of change)    b = yaxis intercept

    y=( ) x+4       m = slope = - 1   (rate of change)   and the starting point is b

     which is  0,4   (assuming it starts at the origin, x=0 start)

Answer:

48 ft 2

Step-by-step explanation:

The radius is 4 ft because it is half of the diameter.

3 * 4^2 = 3 * 16 = 48

Answer:

801.66

Step-by-step explanation:

calculator

Answer:

801.6632653061

Step-by-step explanation:

.......

I'm pretty sure it's census

Answer:

x = 25

y = 6

Step-by-step explanation:

In a parallelogram, opposite angles are equal.

2x and 50 are opposite angles,

2x = 50

Divide 2 on both sides,

x = 50 / 2

x = 25

In a parallelogram opposite sides are equal.

y + 5 and 11 are opposite sides,

y + 5 = 11

y = 11 - 5

y = 6

Answer:

x=25

y=6

Step-by-step explanation:

from the diagram,

2x= 50(opposite angles of a parallelogram)

2x= 50

dividing bothsides by 2

2x/2=50/2

x= 25

then,

y+5=11(opposite sides of a parallelogram)

y= 11-5

y= 6

The ratio of vowels to all letters in the word is 3 to 8

Given,

The word BALLOONS

We have to find the ratio of vowels to all letters in this word.

Ratio;

Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.

So,

The number of letters in BALLOONS = 8

The number of vowels = 3

The ratio of vowels to all letters in the word = 3 to 8

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Only D is true. The rest are not true

Answer:

4 party favors per guest

Step-by-step explanation:

3 bags multiplied by 8 party favors is equal to 24 party favors

then divide 24 party favors by 6 people to get 4 party favors per guest

The equation of the graphed parabola is y=a\((x+3)^{2}\)-4.

Given that parabola is plotted, concave up , with vertex located at coordinates (-3,-4).

We are required to find the equation of the graphed parabola.

The equation of a quadratic function of vertex (h,k) is given by:

y=a\((x-h)^{2}\)+k

In the above equation a is the leading coefficient.

We have been given point (-3,-4).

We have to just put the value of h=-3 and k=-4 and the required equation will be as under:

y=a\((x+3)^{2}\)-4

Hence the equation of the parabola which is plotted, concave up, with vertex located at coordinates (-3,-4) is y=a\((x+3)^{2}\)-4.

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The time it takes for a P100,000 deposit to triple itself at a compound interest rate of 6.1% compounded weekly is approximately 6.12 years.

To find the time it takes for a P100,000 deposit to triple itself at a compound interest rate of 6.1% compounded weekly, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (triple the initial deposit)

P = Principal amount (initial deposit)

r = Annual interest rate (6.1% or 0.061 as a decimal)

n = Number of times interest is compounded per year (weekly compounding means n = 52)

t = Time in years

In this case, we have:

A = 3P (triple the initial deposit)

P = P100,000

r = 0.061

n = 52

t = Time (unknown)

Substituting these values into the formula, we have:

3P = P(1 + r/n)^(nt)

Simplifying further, we get:

3 = (1 + 0.061/52)^(52t)

To isolate t, we can take the natural logarithm (ln) of both sides of the equation:

ln(3) = ln((1 + 0.061/52)^(52t))

Using the logarithmic property, we can bring down the exponent:

ln(3) = 52t * ln(1 + 0.061/52)

Now we can solve for t:

t = ln(3) / (52 * ln(1 + 0.061/52))

Using a calculator, the value of t comes out to approximately 6.12 years (rounded to two decimal places).

Therefore, the time it takes for a P100,000 deposit to triple itself at a compound interest rate of 6.1% compounded weekly is approximately 6.12 years.

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