the amount of time shoppers wait in line can be described by a continuous random variable, x, that is uniformly distributed from 4 to 15 minutes. calculate f(x).

The probability that it is in a winning position will be 0.8036.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

A coin that is 2 cm in diameter is tossed onto a grid of squares each having a side length of 4 cm. A coin is in a winning position if no part of it touches or crosses a grid line, otherwise it is in a losing position.

Then the probability of winning is calculated as,

P = [a² - πd² / 4] / (a²)

P = [4² - 3.14 x 2² / 4] / (4²)

P = (16 - 3.14) / 16

P = 0.8036

The probability that it is in a winning position will be 0.8036.

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The task is to factorize the given number N = 13589. By finding the prime factors of N, we can break the RSA encryption.

To factorize N = 13589, we can try to divide it by prime numbers starting from 2 and check if any division results in a whole number. By using a prime factorization algorithm or a computer program, we can determine the prime factors of N. Dividing 13589 by 2, we get 13589 ÷ 2 = 6794.5, which is not a whole number. Continuing with the division, we can try the next prime number, 3. However, 13589 ÷ 3 is also not a whole number. We need to continue dividing by prime numbers until we find a factor or reach the square root of N. In this case, we find that N is not divisible by any prime number smaller than its square root, which is approximately 116.6. Since we cannot find a factor of N by division, it suggests that N is a prime number itself. Therefore, we cannot factorize N = 13589 using simple division. It means that the RSA encryption with this particular N value is secure against factorization using basic methods. Please note that factorizing large prime numbers is computationally intensive and requires advanced algorithms and significant computational resources.

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Answer:

No, because 6² + 8² ≠ 12²

Step-by-step explanation:

In a right angled triangle,

Perpendicular² + Base² = Hypotenuse² (pythagoras theorem)

But in the given triangle; 6² + 8² ≠ 12²

36 + 64 ≠ 144

100 ≠ 144

Perpendicular² + base² ≠ hypotenuse²

Thus the given triangle is not right angled.

Answer:

20, 60

Step-by-step explanation:

3x=60

x=60/3

x=20

y=60

Answer:X=20 and Y=60

Step-by-step explanation: 3 x 20=60=60

The all values have been obtained.

As per data function is:

f(x, y, z) = xe + 4z cos'(Inx)

To find: Directions in which f(x, y, z) increases and decreases most rapidly at P(1, In2, 1/2) and Rates of change in these directions.

Let's first calculate the gradient vector,

∇f(x, y, z) = ∂f/∂x i + ∂f/∂y j + ∂f/∂z k,

∂f/∂x = eˣ + 4z cos'(lnx) * 1/x

∂f/∂y = 0

∂f/∂z = 4cos'(lnx)

Rate of change of f(x, y, z) at P(1, In2, 1/2) in the direction of vector,

v = ai + bj + ck is given by

D_vf(P) = ∇f(P).v

Now we need to find a unit vector in the direction of increasing f(x, y, z) and another unit vector in the direction of decreasing f(x, y, z) most rapidly.

Let's find the unit vector in the direction of increasing f(x, y, z) by taking

v = ∇f/|∇f| and the unit vector in the direction of decreasing f(x, y, z) most rapidly by taking

v = -∇f/|∇f|.

For increasing:

|∇f| = √(eˣ + 4z cos'(lnx) * 1/x)² + 0² + 4²

     = √(e¹ + 4 * 1/2 * 1/1)² + 16

     = √45v1

     = (1/sqrt(45))(∂f/∂x i + ∂f/∂y j + ∂f/∂z k)

At P(1, In2, 1/2) is

v1 = (1/sqrt(45))(e¹ + 4 * 1/2 * 1/1 i + 0 j + 4 k)

   = (1/sqrt(45))(e + 4k)

For decreasing:

|∇f| = √(eˣ + 4z cos'(lnx) * 1/x)² + 0² + (-4)²

     = √(e¹ + 4 * 1/2 * 1/1)² + 16

     = √45v2

     = (-1/sqrt(45))(∂f/∂x i + ∂f/∂y j + ∂f/∂z k)

At P(1, In2, 1/2) is

v2 = (-1/sqrt(45))(e¹ + 4 * 1/2 * 1/1 i + 0 j + 4 k)

    = (-1/sqrt(45))(e + 4k)

Now, we need to find the rates of change in the directions v1 and v2. Rate of change of f(x, y, z) at P(1, In2, 1/2) in the direction of v1 is,

D_v1f(P) = ∇f(P).v1

             = (1/sqrt(45))(e + 4k).(e + 4k)

            = (1/sqrt(45))(e² + 16)

            = (1/sqrt(45))(e² + 16)

For the direction of v2,Rates of change of f(x, y, z) at P(1, In2, 1/2) in the direction of v2 is,

D_v2f(P) = ∇f(P).v2

              = (-1/sqrt(45))(e + 4k).(e + 4k)

              = (-1/sqrt(45))(e² + 16)

              = -(1/sqrt(45))(e² + 16)

Therefore, Direction of increasing is (1/sqrt(45))(e + 4k), direction of decreasing is (-1/sqrt(45))(e + 4k), rates of change in the direction of increasing is (1/sqrt(45))(e² + 16) and rates of change in the direction of decreasing is -(1/sqrt(45))(e² + 16).

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When a 10% increase in income causes a 4% increase in quantity demanded of a good is income inelastic.

More specifically, the income elasticity of demand is calculated as the percentage change in quantity demanded divided by the percentage change in income. In this case, we have:

Income elasticity of demand = (% change in quantity demanded) / (% change in income)

= 4% / 10%

= 0.4

Since the income elasticity of demand is less than one, we say that the good is income inelastic. we can say that the income elasticity of demand for the good is positive and less than one. This means that the quantity demanded of the good does not increase proportionally as income increases. Instead, the increase in quantity demanded is less than the increase in income.

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As per similar rule:

So:

The 95th percentile of the wave-height distribution would be -0.052 meters.

The median of a distribution is the value that divides the data into two equal halves. To find the median of the wave-height distribution, we need to arrange the wave heights in order from lowest to highest and find the middle value. If there is an odd number of values, then the median is the middle value.

If there is an even number of values, then the median is the average of the two middle values. Since we do not have any data or values given for the wave-height distribution, we cannot determine the median.

The 100pth percentile of the wave-height distribution is the value below which 100p% of the data falls. In other words, if we rank all the wave heights from lowest to highest, the 100pth percentile is the height at which 100p% of the data lies below. A general expression for the 100pth percentile of the wave-height distribution (p) can be given as:

(p) = (1 - p) x + p y

Where x is the wave height corresponding to the (n-1)p-th rank, and y is the wave height corresponding to the np-th rank, where n is the number of observations in the distribution.

Using the model (p) = m as a 1-hour significant wave height (m) at a certain site, we can calculate the 100pth percentile for any given value of p. For example, if p = 0.95, then the 95th percentile of the wave-height distribution would be:

(0.95) = (1 - 0.95) x + 0.95 y

Simplifying this expression, we get:

y = (0.95 - 0.05x)/0.95

Substituting the value of (p) = m, we get:

m = (0.95 - 0.05x)/0.95

Solving for x, we get:

x = (0.95 - 0.95m)/0.05

Therefore, the value of the wave height corresponding to the 5th percentile of the distribution would be:

(0.05) = (1 - 0.05) x + 0.05 y

Simplifying this expression, we get:

x = (0.05y - 0.05)/(0.95)

Substituting the value of (p) = m, we get:

m = (0.05y - 0.05)/(0.95)

Solving for y, we get:

y = (0.95m + 0.05)/(0.05)

Therefore, the value of the wave height corresponding to the 95th percentile of the distribution would be:

(0.95) = (1 - 0.95) x + 0.95 y

Substituting the values of x and y, we get:

(0.95) = (1 - 0.95) [(0.95 - 0.95m)/0.05] + 0.95 [(0.95m + 0.05)/(0.05)]

Simplifying this expression, we get:

m = 0.95y - 0.05x

Substituting the values of x and y, we get:

m = 0.95 [(0.95m + 0.05)/(0.05)] - 0.05 [(0.95 - 0.95m)/0.05]

Simplifying this expression, we get:

m = 19m + 1 - 19

Solving for m, we get:

m = -0.052

Therefore, the 95th percentile of the wave-height distribution would be -0.052 meters.

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Linear equation is the equation in which the highest power of the unknown variable is one. The equation to find m, the number of months it will take for both accounts to have the same amount of money, can be given as,

\(112+25m+45=50+60m\)

Thus the option 4 is the correct option.

Given information;

The saving of the first runner is $112.

The amount of gift card the first runner received is $45 and the saving of each month is $25.

The saving of the second runner is $50.

The amount of second runner save each month is $60.

The number of months it will take for both accounts to have the same amount of money is m.

Linear equation is the equation in which the highest power of the unknown variable is one.

As the saving of the first runner is $112. and the amount of gift card the he received is $45. Also his saving of each month is $25. Thus the money saved by him in m months,

\(=112+45+25m\)

As the saving of the second runner is $50 and the amount he save each month is $60. Thus the money saved by him in m months,

\(=50+60m\)

For the same amount of saving in m months the above two equation must be equal. Therefore,

\(112+45+25m=50+60m\)

Rewrite the equation as,

\(112+25m+45=50+60m\)

Hence the equation to find m, the number of months it will take for both accounts to have the same amount of money, can be given as,

\(112+25m+45=50+60m\)

Thus the option 4 is the correct option.

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Answer:

Linear equation is the equation in which the highest power of the unknown variable is one. The equation to find m, the number of months it will take for both accounts to have the same amount of money, can be given as,

Thus the option 4 is the correct option.

Step-by-step explanation:

The probability that someone consumed > 36 gallons of bottled water is 27.09%. The probability that someone consumed between 30 and 40 gallons of bottled water is 63.72%.

The per capita consumption of bottled water is normally distributed with a mean of 30.9 gallons and a standard deviation of 10 gallons.

The formula to find the probability that someone consumed more than 36 gallons of bottled water is:

P(X > 36) = 1 - P(X ≤ 36)

By plugging in the values, we have:

P(X > 36) = 1 - P(Z ≤ (36 - 30.9) / 10) = 1 - P(Z ≤ 0.61)

From the z-table, we find that the probability of Z ≤ 0.61 is 0.7291.

Therefore, P(X > 36) = 1 - 0.7291 = 0.2709 or 27.09%.

The formula to find the probability that someone consumed between 30 and 40 gallons of bottled water is:

P(30 ≤ X ≤ 40) = P(Z ≤ (40 - 30.9) / 10) - P(Z ≤ (30 - 30.9) / 10)

By plugging in the values, we have:

P(30 ≤ X ≤ 40) = P(Z ≤ 0.91) - P(Z ≤ -0.91)

From the z-table, we find that the probability of Z ≤ 0.91 is 0.8186 and the probability of Z ≤ -0.91 is 0.1814.

Therefore, P(30 ≤ X ≤ 40) = 0.8186 - 0.1814 = 0.6372 or 63.72%.

The formula to find the probability that someone consumed less than 30 gallons of bottled water is:

P(X < 30) = P(Z ≤ (30 - 30.9) / 10)

By plugging in the values, we have:

P(X < 30) = P(Z ≤ -0.09)

From the z-table, we find that the probability of Z ≤ -0.09 is 0.4641.

Therefore, P(X < 30) = 0.4641 or 46.41%.

We need to find the z-score for the 90th percentile. From the z-table, we find that the z-score for the 90th percentile is 1.28. Therefore, we can find the corresponding value of X by using the formula:

X = μ + zσ

By plugging in the values, we have:

X = 30.9 + 1.28(10) = 44.88

Therefore, 90% of people consumed less than 44.88 gallons of bottled water.

In conclusion, the probability that someone consumed more than 36 gallons of bottled water is 27.09%. The probability that someone consumed between 30 and 40 gallons of bottled water is 63.72%. The probability that someone consumed less than 30 gallons of bottled water is 46.41%. Finally, 90% of people consumed less than 44.88 gallons of bottled water.

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Answer:

the second option

Step-by-step explanation:

in ax²+bx+c = 0:

\(x = \frac{-b+-\sqrt{b^2-4ac} }{2a}\)

subtract both sides by 6 to get to this form, as the right side will be left with 0

6x² + 8x - 6 = 0

here, the coefficient for x² (a) is 6, the coefficient for x (b) is 8, and the remaining number added on (c) is -6

plugging our numbers into the formula, we get

\(x = \frac{-8+-\sqrt{(-8)^2-4(6)(-6)} }{2(6)}\\= \frac{-8+-\sqrt{64-(-144)} }{12} \\= \frac{-8+-\sqrt{208} }{12} \\ = \frac{-8+\sqrt{208} }{12} or \frac{-8-\sqrt{208} }{12}\\= 0.53518375848 or -1.86851709182\\= approximately -1.87, 0.54\)

Answer:

u = 6/35

Step-by-step explanation:

w = k * u

w = ku

Where

k = constant of proportionality

if w=5 when u= 3

w = ku

5 = k * 3

5 = 3k

k = 5/3

find u when w is =2/7​

w = ku

2/7 = 5/3 * U

2/7 = 5/3u

u = 2/7 ÷ 5/3

= 2/7 × 3/5

= (2*3)/(7*5)

= 6/35

u = 6/35

In this question, we have only one observed data x1 and X1 follows Weibull (λ).

So, the likelihood given λ and k will be calculated as follows:

P(X1=x1;λ,k)=λk(x1λ)k−1e−(x1λ)k

Now, to calculate the likelihood of x1,

we need to integrate the above expression over k. After integrating,

we get the following expression:

L(λ;x1)=−ln(λ)−kln(x1)+ln(k−1)−(x1/λ)k

The likelihood given λ and k for x1 will be

L(λ;x1)=−ln(λ)−kln(x1)+ln(k−1)−(x1/λ)kb)

If we have n values of (

x1,...,xn) and (X1,...,Xn)

follows Weibull (λ), then the likelihood of this data given λ and k will be:

L(λ;x1,...,xn)= ∏i=1nλk(xiλ)k−1e−(xiλ)k

Now, if we take the log-likelihood of the above expression, then we get the following expression:

l(λ;x1,...,xn)=∑i=1n ln(λ) + (k-1)

ln(xi) - (xi/λ)^k

Using the partial derivative of the above expression and equating it to zero, we can get the maximum likelihood estimator of λ.c) .

To find the maximum likelihood estimator of λ, we will differentiate the log-likelihood function with respect to λ. We will then equate it to zero to find the value of λ that maximizes the likelihood.

∂ln(L)/∂λ= ∑i=1n (k/xi) − n/kλ

k=0n/kλk= ∑i=1n (k/xi)

λ=(∑i=1n (k/xi))^(-1/k)

The maximum likelihood estimator of

λ is (∑i=1n (k/xi))^(-1/k).

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Answer:

False

Step-by-step explanation:

The following statement is false so in conclusion it will not be enough for both bird houses

Cleopatra= 12 1/2

Jesse=6-10

20ft will not be enough for both jesse and cleopatra !

Hope this helps

                                                                                            -Tobie The dog <3

Answer: true

Step-by-step explanation:

Answer: True

Step-by-step explanation: Has to be true if a b and c are all numbers

The area of the polygon with the given vertices is

Area=9

This is further explained below.

Generally, A regular polygon is a polygon that is straight equiangular, and equilateral, according to the Euclidean geometry definition. Convex, star, or skew profiles may be assigned to regular polygons.

In conclusion, The specified vertices are used to calculate the area of the polygon.

A=9

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The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

Given function is,f(t) ={ t, 0 < t < π π < t < 2π}

where f(t + 2 π) = f(t)

Let's take Laplace Transform of f(t)

                     L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...f(t + 2π) = f(t)

∴ L{f(t + 2 π)} = L{f(t)}⇒ e^{2πs}L{f(t)} = L{f(t)}

     ⇒ [e^{2πs} − 1]L{f(t)} = 0L{f(t)} = 0

when e^{2πs} ≠ 1 ⇒ s ≠ 0

∴ The Laplace Transform of f(t) is

                       L{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                               = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...

                              = (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

The Laplace Transform of f(t) isL{f(t)} = L{t} + L{t + π}u(t − π) − L{t − 2π}u(t − 2π) + ...

                            = (1/s^2) + e^{−πs}(1/s^2) − e^{-2πs}(1/s^2) + ...= (1/s^2)[1 + e^{−πs} − e^{−2πs} + ...]

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Answer:

the third one answer choice

Step-by-step explanation:

⊕ Place the triangle on a coordinate grid such that vertex A is at the origin, and segment AC lies on the x-axis.

You will be able to see the length of segment AC and length of segment DE, and also will be able to see if AC║DE.

The range of the test scores in Mr. Miller's math class is 42.

Mathematically, the range refers to the difference between the highest value and the lowest value in a data set.

The range is computed by subtraction of the lowest value from the highest value.

Mr. Miller can use the range to measure the spread or dispersion of the test scores.

Test Scores:

52, 61, 69, 76, 82, 84, 85, 90, 94

Highest score = 94

Lowest score = 52

Range = 42 (94 - 52)

Thus, we can conclude that for the math students in Mr. Miller's class, the range of their test scores is 42.

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Answer:

Y = $2x + 8

Step-by-step explanation:

Variable cost per line = $2.00

For 3 lines, the Variable cost = $2 x 3 = $6

Total cost for 3 lines = $14.00

Fixed Charges = $14 - $6 = $8

Using the formula, total cost, Y = $2x + $8 = $14

Where x = number of lines needed.

Therefore, total cost, Y = ($2 x 3) + $8 = $14

Answer:

42

Step-by-step explanation:

3x + 12 + x = 180

4x  + 12 = 180

4x = 168

x = 42

Answer:

460

Step-by-step explanation:

each classroom has ab 20 students so 23x20=460

Answer:

460

Step-by-step explanation:

Say each class has about 20 student you would need to multiply 20 by 23 to get you answer.

Which is 460.

--------------------------------

Hopefully that helped.

Thus, the value of z = 72, when x = 6 for the given condition that z varies directly with the square of x.

The connection among two variables is known as a direct proportion when their ratios are comparable to a fixed value.

Given data:

z varies directly as x².

z= 8 when x= 2​.

So,

z ∝ x²

z = k x²

k = z/ x² (k is the constant of proportionality)

z= 8 when x= 2​.

k = 8/(2)²

k = 2

Now, when x = 6

z = k x²

z = 2 * (6)²

z = 72

Thus, the value of z = 72, when x = 6 for the given condition that z varies directly with the square of x.

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Answer:

The coordinate pair of the point D that will make AB perpendicular to CD is the D(6, 3)

Step-by-step explanation:

The slope of the given line AB can be presented as follows;

\(Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

\(m =\dfrac{-5-4}{2-(-1)} = \dfrac{-9}{3} =-3\)

The slope of a perpendicular line  to a given line is equal to the negative reciprocal of the slope of the given line

Therefore, the slope of the perpendicular to a line that has a slope of m is -1/m

The slope of the perpendicular to the line AB is therefore \(-\dfrac{1}{3}\)

From which we get the equation of the perpendicular to the line AB given as follows;

y - 4 = -1/3 × (x - 3)

y - 4 = -x/3 + 1

y = -x/3 + 1 + 4

y = -x/3 + 5

When x = 6, y = -6/3 + 5 = 3

Therefore, the coordinate pair of the point D that will make AB perpendicular to CD is the D(6, 3).

Using the slope concept, it is found that the coordinate pair is:

\(D\left(x, \frac{x}{3}+9\right)\)

The slope of a coordinate pair \((x_1,y_1)\) and \((x_2,y_2)\) is given by the change in y divided by the change in x, that is:

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

If two segments are perpendicular, the multiplication of their slopes is -1.

For segment AB, the slope is:

\(m = \frac{-5 - 4}{2 - (-1)} = -\frac{9}{3} = -3\)

At segment CD, we want that:

\(-3m = -1\)

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

Considering D(x,y), we have that:

\(\frac{y - 4}{x - 3} = \frac{1}{3}\)

Writing y as a function of x:

\(x - 3 = 3(y - 4)\)

\(3y - 12 = x - 3\)

\(3y = x + 9\)

\(y = \frac{x}{3} + 9\)

Thus, the coordinate pair is:

\(D\left(x, \frac{x}{3}+9\right)\)

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Answer:

k

Step-by-step explanation:

dw

Answer:

K

Step-by-step explanation:

Dw. Please give me like

Answer:

0.29

Step-by-step explanation:

12 divide by $3.48 is 0.29

The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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