A. What’s 0.9333.... as a fraction?

The PDF of W = X², if X has an exponential distribution with parameter λ, is equal to fW(w) = (1/2)λ√w × \(e^{(-\lambda \sqrt{w} )}\) for w ≥ 0 and fW(w) = 0 for w < 0.

To find the probability density function (PDF) of the random variable W = X² when X has an exponential distribution with parameter λ,

Apply a transformation to the original PDF.

Let us denote the PDF of X as fX(x) and the PDF of W as fW(w). We want to find fW(w).

To begin, let us express W in terms of X,

W = X²

Now, find the PDF of W, which is the derivative of the cumulative distribution function (CDF) of W.

So, find the CDF of W first.

The CDF of W is ,

FW(w) = P(W ≤ w)

Substituting W = X², we have,

FW(w) = P(X² ≤ w)

To determine the probability of X² being less than or equal to w,

consider that X can take on both positive and negative values.

So,  split the calculation into two cases,

First case,

X ≥ 0

In this case, X² ≤ w implies X ≤ √w, since X is non-negative.

Thus, we have,

FW(w) = P(X² ≤ w) = P(X ≤ √w)

Since X has an exponential distribution, its CDF is given by,

FX(x) = 1 -\(e^{(-\lambda x)}\)  for x ≥ 0

for the case X ≥ 0, we have,

FW(w) = P(X ≤ √w) = FX(√w) = 1 -\(e^{(-\lambda \sqrt{w} )}\)

Second case,

X < 0

X² ≤ w implies X ≤ -√w, since X is negative.

However, for X < 0, X² is always non-negative.

The probability is always 0 in this case.

Combining both cases, we can write the CDF of W as,

FW(w) = 1 - \(e^{(-\lambda \sqrt{w} )}\) for w ≥ 0

FW(w) = 0 for w < 0

Finally, to find the PDF fW(w), we take the derivative of the CDF with respect to w,

fW(w) = d/dw [FW(w)]

Differentiating, we have,

fW(w) = (1/2)λ√w × \(e^{(-\lambda \sqrt{w} )}\) for w ≥ 0

fW(w) = 0 for w < 0

Therefore, the PDF of W = X², when X has an exponential distribution with parameter λ, is given by,

fW(w) = (1/2)λ√w × \(e^{(-\lambda \sqrt{w} )}\) for w ≥ 0

fW(w) = 0 for w < 0

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The above question is incomplete, the complete question is:

If X has an exponential (λ) PDF, what is the PDF of W = X² ?

Answer:

B

Step-by-step explanation:

Subtraction mean how much less than a number

An exponential function to model the quail population is y = 765(1+0.16)ⁿ and the approximate population be after 4 years is 1384.65 quails.

Population growth is seen to increase at an exponential rate. We use the following to model this growth.

y = A₀(1 + r)ⁿ

where

y = value at time

A₀ = original value

r = rate of growth

n = time elapsed

An exponential function that models the quail population is set up like:

y = 765(1+0.16)ⁿ

so that, for example, if we wanted to figure out the population at time (4 years), then we would set up the function as follows,

y = 765(1+0.16)⁴

y = 765(1.16)⁴

y = 765* 1.81

to get

y = 1384.65 quails after 4 year has elapsed.

Hence, an exponential function to model the quail population is y = 765(1+0.16)ⁿ and the approximate population be after 4 years is 1384.65 quails.

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The expression 16x² + 40x + 25 is equivalent to (4x + 5)²

An equation is an expression that shows the relationship between numbers and variables using mathematical operators like addition, subtraction, multiplication and division. Equations can be linear, quadratic.

Given the quadratic equation:

16x² + 40x + 25

Solving the quadratic equation by factorization:

16x² + 40x + 25

16x² + 20x + 20x + 25

= 4x(4x + 5) + 5(4x + 5)

= (4x + 5)(4x + 5)

= (4x + 5)²

The expression is equivalent to (4x + 5)²

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James's current balance on his credit card is $900.

This amount represents the card's balance before the current charge of $1,500 and the finance charge of $60.

A credit card balance is the amount of the charges made on a credit card, including the finance charges, and therefore, owed to a credit card company.

Current current balance = $x

APR (Annual Percentage Rate) of interest = 30%

Monthly APR = 2.5% (30%/12)

Current purchase for the month = $1,500

Finance charge for the month = $60

Finance charge for the current purchase = $37.50 ($1,500 x 2.5%)

Finance charge for the current balance = $22.50 ($60 - $37.50)

The current balance that attracts the finance charge of $22.50 will be $900 ($22.50/2.5%).

Alternatively:

Since the monthly APR is 2.5% and the finance charge is $60 for the month, the balance at the end of the month is $2,400 ($60/2.5%).

Thus, the current balance on James' credit card is $900 ($2,400 - $1,500) while the end-of-the-month balance is $2,460 ($900 + $1,500 + $60).

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Step-by-step explanation:

answers I the above photo

some of the questions are not clear

Answer:

1. C(13inches)

2. A(40°)

3. B(126°)

4. C(50°)

5. 7cm

Step-by-step explanation:

According To the Question,

1. Given, The sum of all the sides of a STOP sign is 104 inches. A STOP sign is Octagon  with all sides equal.

Thus, Octagon has 8 equal side

So, Each Side Measure = 104/8 ⇔ 13inches

2. Given, In Triangle ABC, ∠A & ∠B each measure 70°

And, We Know Sum of all angles of a triangle is 180°.

Thus, ∠C = 180° - (∠A + ∠B)  ⇔  180°-140° ⇒ 40°

3. Given, The measures of the three angles of a quadrilateral are ∠A=49° ,∠B=58° & ∠C=127° .

And, We know sum of all angles of quadrilateral is 360°.

Thus, ∠D=360° - (∠A+∠B+∠C)  ⇔ 360°-234° ⇒ 126°

4. Given, The measure of all the Four angles of a quadrilateral are ∠A=(x+40)°, ∠B=130°, ∠C=x° & ∠D=(2x-10)° .

And, We know sum of all the angles of quadrilateral is 360°.

Thus, ∠A+∠B+∠C+∠D = 360°

Put all the Values, we get

x+40+130+x+2x-10 = 360

4x+160 = 360

4x = 200 ⇔ 200/4 ⇒ 50°

5. Given, the length of the two sides of an isosceles triangle are 3cm and 7cm .

Now, in order to form a triangle the sum of any two side of a triangle is always greater than the third side of a triangle.

So, We have an isosceles triangle in which two sides is always equal & we have given two sides of 3cm & 7cm .

Assume, if third side be 3cm (First Side+Third side > Second side)

3+3 ⇒6cm which is not greater than 7cm(thus, the Triangle not possible if we assume 3cm as triangle's third side)

Hence, The other Side of Triangle Surely be 7 cm.  

Step-by-step explanation:

about 7% (not exactly 7%, just about)

Answer:

About 7% sodium.

The rest is information you may find important later.

For homemade chocolate chip cookies.

__________________________________________________________

Questions about percentage? Feel free to ask me in the comments box.

The distribution for X is a negative binomial distribution, denoted as nb(x;6, 188​), with parameters r = 6 (number of successes), p = 8/18 (probability of success in each trial).

To compute the probabilities:

P(X = 2): nb(2;6, 8/18)

P(X ≤ 2): nb(0;6, 8/18) + nb(1;6, 8/18) + nb(2;6, 8/18)

P(X ≥ 2): 1 - P(X < 2) = 1 - P(X ≤ 1)

To calculate the mean value and standard deviation of X:

Mean (μ) = r * (1 - p) / p

Standard Deviation (σ) = sqrt(r * (1 - p) / (p^2))

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Answer:

Division property of equality

Step-by-step explanation:

-2x = 12  {Divide both sides by -2}

-2x/-2 = 12/-2

x = - 6

Division property of equality

Answer:

i think its -15x + 10y

Step-by-step explanation:

10x - 5y + 5 (5x + y)

10x- 5y + 25x+ 5y

combine

-15x + 10y

Answer:

$5.25

Step-by-step explanation:

8.75/5=1.75

1.75 x 3=5.25

Answer:

$5.25

Step-by-step explanation:

8.75 devided by 5 is 1.75 so for 1 cupcake it is $1.75. $1.75 X 3= $5.25

Answer:

3 lb and 5oz

Step-by-step explanation:

Conversions: 1 lb is equal to 16 oz, so divide 53 by 16, which gives you 3 with a remainder of 5.

The percentage of students who failed the second test given that they passed the first test is 55%.

Let's assume that there are 100 students in the class for simplicity.

Given that 45% of the students passed the first test, we have 45 students who passed the first test.

Out of the 45 students who passed the first test, 25% also passed the second test. This means that 25% of 45, which is (25/100) * 45 = 11.25 students, passed both tests.

Therefore, out of the 45 students who passed the first test, 11.25 students passed both tests. To find the percentage of students who failed the second test given that they passed the first test, we subtract the students who passed both tests from the total number of students who passed the first test.

45 - 11.25 = 33.75 students

Now, we need to find the percentage of 33.75 students out of the total number of students who passed the first test.

Percentage = (33.75 / 45) * 100 = 75%

So, the percentage of students who failed the second test given that they passed the first test is 75%.

Note: The assumption made here is for simplicity and the actual number of students may differ, but the percentage calculation remains the same.

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Answer: 1/3

Step-by-step explanation: 2/6 = 1/3

Answer:

Step-by-step explanation:

Given,

Total outcome = 6

No. of same colored shirts and shorts = 2

Therefore,

Probability of getting same colored shirts and shorts

\( = \frac{no. \: of \: outcome}{total \: outcome} \)

\( = \frac{2}{6} \)

\( = \frac{1}{3} (ans)\)

One year of education adds $1200 to a person's yearly income.

In the given model, the equation y = 1200x + 7000 represents the relationship between the years of education (x) and the yearly income (y) in a person's first job after completing schooling. According to the model, for every additional year of education, the yearly income increases by $1200. This implies that each year of education contributes an extra $1200 to a person's annual income. For example, if a person has completed 5 years of education, their yearly income can be estimated as y = 1200(5) + 7000 = $13,000.

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The  the dimension of the smallest area of the poster is 40 cm by 60 cm

Let the dimensions of the poster be x and y.

So, the area is:

area = xy

The area is given as 2400 cm^2.

So, we have:

xy = 2400

The printed area is represented as:

area = (x - 2(15))(y - 2(10))

area = (x - 30)(y - 20)

Make x the subject in

xy = 2400

x = 2400/y

Substitute 2400/y for x in

area = (2400/y - 30)(y - 20)

Express as:

area = (2400/y - 30)(y - 20)

Expand

area = 2400 - 48000/y - 30y + 600

Differentiate

A' = 48000y⁻² - 30

Set to 0

48000y⁻² - 30 = 0

48000y⁻² = 30

Multiply both sides by y^2

48000 = 30y²

Divide both sides by 30

y² = 1600

Take square roots

y = 40

x = 2400/40

x = 60

Hence, the dimension of the smallest area of the poster is 40 cm by 60 cm

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The possible solution set for the system is (- 1, 4) and (4, - 1).

Given are the equations as -

x + y = 3

x² + y² = 17

Refer to the graph of the function attached. The points of intersection represents the possible solution set.

Therefore, the possible solution set for the system is (- 1, 4) and (4, - 1).

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Answer:

i think it will be #3

Step-by-step explanation:

An increase in the rate of inflation will increase the nominal interest rate while lowering the real interest rate.

When the rate of inflation rises, it affects both the nominal and real interest rates. The nominal interest rate is the stated or observed interest rate, while the real interest rate is adjusted for inflation and represents the purchasing power of the interest earned or paid. Inflation erodes the purchasing power of money over time.

As inflation increases, lenders and investors demand higher nominal interest rates to compensate for the expected loss in purchasing power. However, while the nominal interest rate rises, the real interest rate, which takes inflation into account, decreases because the purchasing power of the interest earned or paid is reduced.

In summary, an increase in the rate of inflation will result in an increase in the nominal interest rate but a decrease in the real interest rate due to the erosion of purchasing power caused by inflation.

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The point (4,7) in the original function translates to the point (4,1) in the translated function f(x) = (x-6) + 3.

To find the point that the function f(x)=(x-6)+3 translates to, we need to substitute the x-coordinate of the given point (4,7) into the translated function and evaluate the corresponding y-coordinate.

Let's substitute x = 4 into the translated function:

f(x) = (x - 6) + 3

f(4) = (4 - 6) + 3

f(4) = -2 + 3

f(4) = 1

The translated point is (4, 1). This means that the original point (4,7) translates horizontally by shifting 6 units to the right and vertically by shifting 3 units upwards. The x-coordinate remains the same, while the y-coordinate changes.

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The interval μ - σ to Q3 corresponds to the smallest area under a normal curve because it includes only a small portion of the data set.

The answer to this question is option D, which is μ - σ to Q3. To understand why this is the correct answer, we need to first understand what each of the intervals represents. Q1 and Q3 are the first and third quartiles of the data set, respectively. μ is the mean of the data set, and σ is the standard deviation.

When we look at the interval μ - σ to Q3, we can see that it includes the upper quartile and some of the data points to the left of it. This means that the area under the normal curve within this interval will be relatively small compared to the other options.

On the other hand, option B includes the mean and a larger range of data points, which would result in a larger area under the curve. Option C includes Q1 and a larger range of data points, which would also result in a larger area. Option A includes both Q1 and Q3, which cover the majority of the data set and would therefore have the largest area under the curve.

In summary, the interval μ - σ to Q3 corresponds to the smallest area under a normal curve because it includes only a small portion of the data set.
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Dim Row A = 6 and Dim Col A = 6.

If the null space of a 7x9 matrix is 3-dimensional, then by the rank-nullity theorem, the rank of the matrix is:

Rank A = number of columns - dimension of null space

      = 9 - 3

      = 6

Therefore, Rank A = 6.

Since the rank of A is 6, the dimension of the row space of A is also 6 (because the row space is the orthogonal complement of the null space, and the sum of their dimensions equals the number of columns).

However, the number of rows of A is 7, so the row space cannot span all of R^7. Therefore, the row space of A has dimension less than or equal to 6.

Since the dimension of the row space of A is less than or equal to 6, and the rank of A is 6, it follows that the dimension of the column space of A (which is equal to the rank of A) is also 6.

Therefore, Dim Row A = 6 and Dim Col A = 6.

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The equation of the function is y = 12(3.7)^n

We have to note that if we have an exponential function, it then follows that we have to look at the arrangement of the graph so that we can be able to use the points that are on the graph to be able to read off the function that we want to work on.

In this case, the function that we want to work on is the function that has been graphed here and we can be able to read off the initial value and the rate of growth from the values of the graph that have been shown in the image.

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Answer:

12.50

Step-by-step explanation:

Answer:

(5d⁴ − 8)²

Step-by-step explanation:

I hope this is helpful!

Answer:

B

Step-by-step explanation:

The probability of winning $1000 a day for life is approximately 5.245 x 10^-11 and the probability of winning $1000 a week for life is approximately 1.07 x 10^-8. The probability of winning the jackpot ($1000 a day for life) is 1/(60^5 * 4), while the probability of winning $1000 a week for life is 1/(60^5).

In the Florida Lottery Cash4Life game, a player must select five numbers from 1 to 60 and then one Cash Ball number from 1 to 4. The jackpot prize is $1000 a day for life if all five numbers and the Cash Ball match the winning numbers drawn on Monday nights. If just all five numbers match the winning numbers, the player will win $1000 a week for life.
To determine the probability of winning $1000 a day for life, we can use the formula for the probability of independent events: P(A and B) = P(A) x P(B)

(a) To win the jackpot of $1000 a day for life, the player needs to match all five numbers and the Cash Ball. There are 60 options for each of the five numbers and 4 options for the Cash Ball. The total number of possible outcomes is 60^5 (60 choices for each of the five numbers) times 4 (for the Cash Ball). So the probability of winning the jackpot is 1/(60^5 * 4). (b) To win $1000 a week for life, the player needs to match only the five numbers, without considering the Cash Ball. The total number of possible outcomes for this scenario is 60^5. Therefore, the probability of winning $1000 a week for life is 1/(60^5).

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Answer:

-8

Step-by-step explanation:

f(x)=3x-5

f(-1)=3(-1)-5=-3-5=-8

Answer:

$37.60

Step-by-step explanation:

If 7 shirts = 32.90 then (32.90/7) x 8 = 37.60