Lily collected 37. 7 pounds of cans to recycle and plans to collect 4. 2 more pounds each week. In this situation, what is the value of the slope?

Answer:

6:

\( {x}^{2} - 2x - 3 \\ = (x - 3)(x + 1) \\ when \: y = 2 \\ x = 1 \\ vertex \: is \: (1, \: 2)\)

7:

\( {x}^{2} = - 625 \\ x = \sqrt{ - 625} \\ x = \sqrt{625} \times \sqrt{ - 1} \\ x = 25 \times \sqrt{ {i}^{2} } \\ x = 25 \times i \\ x = 25i\)

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:

A

Step-by-step explanation:

5/18 = 0.2777 = 0.27° so when you divided thd no. it is 0.277777 and 7 is repeat .

The percent error for the batteries is 20%

Estimated defective batteries as per Saif = 12 batteries

Actual defective batteries = 10

Percent error is given by the formula:

Percent error = (E-T/E)*100

where E is the experimental value and T is the theoretical value

Substituting the values in the formula we get:

= (12-10/12)*100

= 20%

The difference between an approximate or measured value and an exact or known value is expressed as a percentage error, also known as a % error. In science, it is used to document the discrepancy between a real or accurate value and a measured or experimental value.

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The linear function, f(x), passing through the points (-9,7) and (7,7) is given by f(x) = 7.

We have to find the linear function, f(x), passing through the points (-9,7) and (7,7).

Linear function has the standard form:

f(x) = mx + b,

where m is the slope of the line and

b is the y-intercept of the line.

We have to find the slope, m, first:

m = (y₂ - y₁) / (x₂ - x₁) = (7 - 7) / (7 - (-9)) = 0 / 16 = 0

Therefore, the slope of the line is 0.

Now, we have to find the y-intercept, b.

We can use the point (-9, 7) to find b.

7 = m(-9) + b => 7 = 0 + b => b = 7

Therefore, the y-intercept of the line is 7.

Now, we can write the linear function, f(x), as:

f(x) = mx + b => f(x) = 0x + 7 => f(x) = 7

Therefore, the linear function, f(x), passing through the points (-9,7) and (7,7) is given by:

f(x) = 7.

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Answer:

The answer is would be 1.2 or 1.22

The correct statement is: "A sample of size 30 is the smallest sample size that will have a sampling distribution that is approximately normal."

According to the central limit theorem, when the sample size is sufficiently large (typically around 30 or greater), the sampling distribution of the sample mean will approach a normal distribution regardless of the shape of the population distribution. This holds even if the population distribution is strongly skewed.

Therefore, in this case, a sample size of 30 is the smallest size that would ensure the sampling distribution of the sample mean is approximately normal, regardless of the right-skewness of the population distribution. Smaller sample sizes, such as a sample size of 10, may still provide useful information, but the sampling distribution may deviate more from a perfect normal distribution.

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Answer:

she got back 63 times

Step-by-step explanation:

Here, we want to know the number of times she is at bat

from the question, we are made to know that she strikes out twice after 9 times

So striking out 14 times, the number of times she has got back will be ;

14/2 * 9 = 63 times

A.) let's solve for T :

plugging in the values of x and y,

value of T = 3

B.) Expansion of 3g(8 + 3)

that's all...

The expected value in a binomial situation with n = 18 and π = 0.60 is E(X) = np = 18 * 0.60 = 10.8.

In a binomial situation, the expected value, denoted as E(X), represents the average or mean outcome of a random variable X. It is calculated by multiplying the number of trials, denoted as n, by the probability of success for each trial, denoted as π.

In this case, we are given n = 18 and π = 0.60. To find the expected value, we multiply the number of trials, 18, by the probability of success, 0.60.

n = 18 (number of trials)

π = 0.60 (probability of success for each trial)

To find the expected value:

E(X) = np

Substitute the given values:

E(X) = 18 * 0.60

Calculate the expected value:

E(X) = 10.8

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The greatest distance from the origin is 10, which corresponds to vertex L'' (6, 8) of the image triangle.

To determine the vertex of the image triangle that is the greatest distance from the origin, we need to follow the given transformations step by step and find the coordinates of the image vertices.

1. Translation: The given triangle is translated 4 units left and 3 units up.

  - Vertex L' is located at (-2 - 4, 5 + 3) = (-6, 8).

  - Vertex E' is located at (1 - 4, 4 + 3) = (-3, 7).

  - Vertex D' is located at (2 - 4, -2 + 3) = (-2, 1).

2. Reflection: The translated triangle is reflected over the line y = 4.

  - The line y = 4 acts as a mirror. The y-coordinate of each vertex remains the same, but the x-coordinate is reflected.

  - Vertex L'' is located at (-(-6), 8) = (6, 8).

  - Vertex E'' is located at (-(-3), 7) = (3, 7).

  - Vertex D'' is located at (-(-2), 1) = (2, 1).

Now, we have the coordinates of the image triangle vertices: L'' (6, 8), E'' (3, 7), and D'' (2, 1).

To determine which vertex is the greatest distance from the origin (0, 0), we can calculate the distances using the distance formula:

- Distance from the origin to L'': √[(6 - 0)² + (8 - 0)²] = √(36 + 64) = √100 = 10.

- Distance from the origin to E'': √[(3 - 0)² + (7 - 0)²] = √(9 + 49) = √58.

- Distance from the origin to D'': √[(2 - 0)² + (1 - 0)²] = √(4 + 1) = √5.

Therefore, the greatest distance from the origin is 10, which corresponds to vertex L'' (6, 8) of the image triangle.

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Answer:

Answer:

(a) 64°

(b) Yes, it is safe

Step-by-step explanation:

A fireman needs to get water to a second-floor fire. His ladder is 30 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.

(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest whole number and show all your work.

We solve the above question using the trigonometric function of Sine

sin θ = Opposite side/Hypotenuse sides

θ = Angle formed with the ground = ?

Opposite side = 27 ft

Hypotenuse side = 30 ft

Hence,

sin θ = 27 ft/30 ftsin θ = 9/10 = 0.9

θ = arc sin (0.9)

θ = 64.158067237°

Approximately to the nearest whole number = 64°

(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 70°.Will the ladder be safe the way it is positioned?

From the above calculation, the angle the ladder makes with the ground is 64° and now we want that angle to be 70°

Hence:

64° < 70°

Therefore, the ladder will be safe the way it is positioned.

Answer:

(a) 64°

(b) Yes, it is safe

Step-by-step explanation:

A fireman needs to get water to a second-floor fire. His ladder is 30 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.

(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest whole number and show all your work.

We solve the above question using the trigonometric function of Sine

sin θ = Opposite side/Hypotenuse sides

θ = Angle formed with the ground = ?

Opposite side = 27 ft

Hypotenuse side = 30 ft

Hence,

sin θ = 27 ft/30 ftsin θ = 9/10 = 0.9

θ = arc sin (0.9)

θ = 64.158067237°

Approximately to the nearest whole number = 64°

(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 70°.Will the ladder be safe the way it is positioned?

From the above calculation, the angle the ladder makes with the ground is 64° and now we want that angle to be 70°

Hence:

64° < 70°

Therefore, the ladder will be safe the way it is positioned

The DTKF equations for the given linear dynamic system are not the same as in the Gallager problem.

The DTKF (Discrete-Time Kalman Filter) equations are used for estimating the state of a dynamic system based on observed measurements. In the given system, the state equation is In = Xn-1, and the observation equation is Yn = X + 20n.

The DTKF equations consist of two main steps: the prediction step and the update step. In the prediction step, the estimated state and its covariance are predicted based on the previous state estimate and the system dynamics. In the update step, the predicted state estimate is adjusted based on the new measurement and its covariance.

For the given system, the DTKF equations can be derived as follows:

Prediction Step:

Update Step:

These DTKF equations are specific to the given linear dynamic system and differ from those in the Gallager problem, as they depend on the system dynamics, observation model, and noise characteristics.

The DTKF equations for the given linear dynamic system are not the same as in the Gallager problem. Each dynamic system has its own unique set of equations based on its specific characteristics, and the DTKF equations are tailored to estimate the state of the system accurately.

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Yes, the data collected from interviewing customers at one ShopRite store in Jersey City from Monday to Friday, 9 am-3 pm, could have some issues and biases.

Potential issues include:

1. Limited sample: By conducting interviews only at one store, the percentage of  responses will not provide a comprehesive view of the customer base in Jersey City.

2. Time bias: Surveying customers only between 9 am and 3 pm may exclude individuals who shop outside these hours, leading to an incomplete picture of shopping habits.

3. Location bias: ShopRite customers may not accurately represent the diverse needs and preferences of all Jersey City residents.

4. Self-reported data: Customers may not accurately recall their shopping habits, leading to biased responses.

While the data collected can provide some insights, it may not be sufficient to open a grocery store. You should consider expanding your survey to multiple locations and times, including weekends, and collecting demographic information to better understand the diverse needs of Jersey City residents. Additionally, researching market trends, competitors, and successful grocery store models in similar areas can help inform your business plan.

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(a) The values of \(a\) and \(b\) are \(0\) and \(k\), respectively.

(b) The values of \(c\) and \(d\) are \(0\) and \(\(2\pi\)\), respectively.

(c) Using \(t\) in place of \(\(\theta\)\), the function \(g(r,t)\) is \(\(e^{-r^2}\)\).

To rewrite the integral \(\( I = \int_{-k}^{k} \int_{0}^{k^2 - y^2} e^{-(x^2 + y^2)} \, dx \, dy \)\) in terms of polar coordinates, we need to determine the limits of integration and express the integrand in terms of polar variables.

(a) Limits of integration for \( r \):

In polar coordinates, the region of integration corresponds to the disk with radius \( k \). Since the variable \( r \) represents the radial distance from the origin, the limits of integration for \( r \) are \( 0 \) (inner boundary) and \( k \) (outer boundary).

Therefore, \( a = 0 \) and \( b = k \).

(b) Limits of integration for \( \theta \):

The angle \(\( \theta \)\) represents the azimuthal angle in polar coordinates. In this case, the region of integration covers the entire disk, so \(\( \theta \)\) ranges from \( 0 \) to 2π.

Therefore, \( c = 0 \) and \( d = 2\pi \).

(c) The integrand \(\( e^{-(x^2 + y^2)} \)\)) in terms of polar coordinates:

In polar coordinates, \( x = r\cos(\theta) \) and \( y = r\sin(\theta) \). Substituting these expressions into the integrand, we have:

\(\[ e^{-(x^2 + y^2)} = e^{-(r^2\cos^2(\theta) + r^2\sin^2(\theta))} = e^{-r^2} \]\)

Therefore, \(\( g(r, \theta) = e^{-r^2} \).\)

To summarize:

(a) \( a = 0 \) and \( b = k \)

(b) \( c = 0 \) and \( d = 2\pi \)

(c) \( g(r, t) = e^{-r^2} \)

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Step-by-step explanation:

In order to meet at point F, line DF must travel from the top line to the bottom line. If it crosses through E, the midway, that means that it is halfway to the bottom line. This means the distance D E is equal to E F, because both are the distance from midpoint E to one of the sides (top or bottom).

If D E and E F are equal length, then AB and BF must be the length as well, as it is the length DF line takes to get halfway down from the top. Since they are the same length, A F must be twice the length of AB.

Hope this helped!

Answer:

input = 6 leads to output = 15

input = 9 leads to output = 21

==================================================

Explanation:

If the input is x = 6, then,

y = 2x+3

y = 2(6)+3

y = 12+3

y = 15 is the output

Repeat those steps for x = 9

y = 2x+3

y = 2(9)+3

y = 18+3

y = 21 is the output

Answer:

68

Step-by-step explanation:

1 and 2 are supplementary, making the sum of the measures = 180. 180-146 = 34. 2 is a vertical angle to 4. 4=34. 34+34=68

Answer:

68

Step-by-step explanation:

Angle 1 is 146

Angle 2 is 180-146  (lines are 180 degrees)

180-146 = 34

Angle 2 and Angle 4 are congruent (equal) because they are  vertical  angles.

34 + 34 = 68

Answer:

ueidicjfkfktitorr*rtt

28

Answer:

A

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse h is equal to the sum of the squares on the other 2 sides, that is

h² = 20² + 20² = 400 + 400 = 800 ( take the square root of both sides )

h = \(\sqrt{800}\) ≈ 28 in ( to the nearest whole number )

Answer:

34y

Step-by-step explanation:

Answer:

11%

Step-by-step explanation:

1. Fill out the table with the correct numbers.

2. After you fillout the numbers, you should notice that under the column car and in the first row, there should be the number 18.

3. We know the total number of students under the age of 15 is 165.

4. To find the percent:

       18/165 * 100

               = 11%

Answer:

41%

Step-by-step explanation:

Look at the column "Age 15 and above".

Notice how the row total for that column is 195.

Also, look at "Bus".

Notice how there is a gap between 60 and 110.

To calculate the answer, you need to fill in the blanks using the surrounding numbers.

60 + 50 = 110, so to the right of "65" on "Age 15 and above", there should be a 50.

The "195" at the end of the row is now on the same row as the numbers: 65, 50, and a blank spot.

Now, all we have to do is simply ask ourselves what 65 + 50 gets us, and what we need to add to that to get 195.

65 + 50 = 115, 115 + 80 = 195.

Although, notice that this does not mean the answer is not 80%.

We need to find what percentage is 80 out of 195.

80 out of 195 = 41.03%.

By rounding, we will get an answer of 41%.

Answer:

3rd choice down

(x + 9) / (x + 1)

Step-by-step explanation:

(2x + 4 - x + 5) / (x + 1) = (2x - x + 4 + 5) / (x+ 1) = (x + 9) / (x + 1)

Answer:

x=18

Step-by-step explanation:

10x-4+x-14=180

11x-18=180

11x=180+18

11x=198

x=\(\frac{198}{11}\)

x=18

Answer:

x = 18

Step-by-step explanation:

(10x -4) + (x-14) = 180 (for linear pair)

<=> 10x + x - 4 - 14 = 180

<=> 11x - 18 = 180

<=> 11x = 180+18 = 18 . 10 + 18 = 18 . 11

<=> x = 18

Answer:

Step-by-step explanation:

You can write and equation for this problem.

as 20.27-2.01x= The left money for food.

x: is two.

SO applying the number to the equation:

20.27-4.02= Food money

$16.25 is the answer

Answer:

b. False

Step-by-step explanation:

The number of costumers that visit your store is a DISCRETE variable because is the set of countable costumers. We count a whole person not parts of a person.

For a continuous variable we are allowed to take any value in an interval. In our case we can not say we had 3.4 costumers. We can say the costumer bought 3.4 gallons of gas for their car.

number or costumers →discrete variable

number of gallons of gas →continuous variable

b. False

The values of the expressions are P 9, 3 = 504, C 9, 3 = 84, P 8, 8 = 40320 and C 9, 9 = 1

From the question, we have the following parameters that can be used in our computation:

(A) P9, 3. (B) C9, 3. (C) P8, 8. (D) C9, 9.

The above expressions are permutation and combination expressions

Using the above as a guide, we have

Expression (A) P9, 3

Apply the permutation formula

P n, r = n!/(n - r)!r!

So, we have

P 9, 3 = 9!/6!

Evaluate

P 9, 3 = 504

Expression (B) C 9, 3

Apply the combination formula

C n, r = n!/(n - r)!r!

So, we have

C 9, 3 = 9!/(6! * 3!)

Evaluate

C 9, 3 = 84

Expression (C) P8, 8

Apply the permutation formula

P n, r = n!/(n - r)!r!

So, we have

P 8, 8 = 8!/0!

Evaluate

P 8, 8 = 40320

Expression (D) C 9, 9

Apply the combination formula

C n, r = n!/(n - r)!r!

So, we have

C 9, 9 = 9!/(9! * 0!)

Evaluate

C 9, 9 = 1

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25000 in mutual funds

50000 in CD

Pool of money managed by a professional Fund Manager is termed mutual fund. It is a trust that collects money from other investors who have a common investment objective and invests the same in equities and bonds.

Let X be the amount in Mutual Funds

Y be the amount in CDs

the constraints:

Y = 2x

x>9000

Y = 75000 - x

There has to be at least 2x + x = 75000

                                       3x = 75000

                                        x = 25000

Objective function for the return of investment is R(x,y) = 0.06X + 0.07Y

After graphing linear equations and inequalities, the vertices of the critical region are as:

(9000,18000) --> 1710

(25000,50000)  ---> 4750

(75000,0) --> 3750

25000 in mutual funds

50000 in CD

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The probability of rolling a number greater than 6 is 1/4, or 0.25 as a decimal, or 25% as a percentage.

The die has 8 equally likely possible outcomes, which are the numbers 1 through 8. The probability of rolling a number greater than 6 is the same as the probability of rolling a 7 or 8.

Since each of these two outcomes is equally likely, the probability of rolling a number greater than 6 is:

P(rolling a number greater than 6) = P(rolling a 7) + P(rolling an 8)

The probability of rolling a 7 is 1/8, and the probability of rolling an 8 is also 1/8. Therefore:

P(rolling a number greater than 6) = 1/8 + 1/8 = 2/8 = 1/4

So the probability of rolling a number greater than 6 is 1/4, or 0.25 as a decimal, or 25% as a percentage.

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Answer:

I don't know but I think the answer is 3

The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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