One third of a bamboo is buried in mud, one sixth of it is in water and the part above the water is greater than or equal to 3 meters. Find the length of the shortest pole.​

The slope for the least-squares line is 0.067 and the y-intercept is 2.63.
To find the slope and y-intercept for the least-squares line, we will use the given correlation coefficient (0.944), the means, and standard deviations of both the explanatory and response variables.

Slope (b1) = r * (Sy/Sx)
where r is the correlation coefficient, Sy is the standard deviation of the response variable, and Sx is the standard deviation of the explanatory variable.

Slope (b1) = 0.944 * (1.64/29.51) = 0.0522 (rounded to the hundredths place)

Next, we find the y-intercept (b0) using the following formula:

Y-intercept (b0) = Ymean - (b1 * Xmean)
where Ymean is the mean of the response variable and Xmean is the mean of the explanatory variable.

Y-intercept (b0) = 9.65 - (0.0522 * 149.4) = 1.88 (rounded to the hundredths place)

So, the correct slope and y-intercept for the least-squares line are 0.0522 and 1.88, respectively.

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Answer:

Step-by-step explanation:

Expand: 36e^2+12e-48=e

Subtract e from both sides 36e^2+11e-48=0

Using the quadratic formula, e=(-11+-sqrt7033)/72

The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2). (Correct choice: E)

In this problem we find five different points of the form (x, y), each of which has to be checked in the linear equation given in the statement. A point is a solution of the linear equation if and only an equality exists, that is, the reflexive property of equalities is guaranteed by evaluating the expression.

Now we proceed to check the expression for each case:

(x, y) = (1, - 5)

- 5 + 4 = (3 / 5) · (1 - 2)

- 1 = (3 / 5) · (- 1)

- 1 = - 3 / 5     (FALSE)

(x, y) = (- 8, - 12)

- 12 + 4 = (3 / 5) · (- 8 - 2)

- 8 = (3 / 5) · (- 10)

- 8 = - 30 / 5

- 8 = - 6    (FALSE)

(x, y) = (- 3, - 8)

- 8 + 4 = (3 / 5) · (- 3 - 2)

- 4 = (3 / 5) · (- 5)

- 4 = - 3    (FALSE)

(x, y) = (12, 10)

10 + 4 = (3 / 5) · (12 - 2)

14 = (3 / 5) · 10

14 = 30 / 5

14 = 6     (FALSE)

(x, y) = (7, - 1)

- 1 + 4 = (3 / 5) · (7 - 2)

3 = (3 / 5) · (5)

3 = 3    (TRUE)

The point (x, y) = (7, - 1) lies on the line whose equation is y + 4 = (3 / 5) · (x - 2).

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Answer: A is 80 and B is 85 train B is going faster

Step-by-step explanation:

hope this helps

because A is already given and to find b divide d/t to find constant and after doing so b is 5km per hour faster

Answer:

x= 2/3  or in decimal form 0.6(the 6 repeats) hope this helps

Step-by-step explanation:

divide each side by the factors that do not contain the variable in this case the variable is x

The optimization process has three steps. They are:Step 1: Find the critical values of the function to be optimize.dStep 2: Use the second-derivative condition to eliminate unwanted critical values.

Step 3: Find the optimal value of the function.The monthly cost function is:TC(Q) = 4,000 + 35QThe price-demand function is:P(Q) = 52The revenue function is:

R(Q) = P(Q)QNow we have to find the maximum revenue. In other words, we have to find the optimal value of Q that will give us maximum revenue. So, we will find the critical values of R(Q) and then apply the second-derivative condition to eliminate unwanted critical values.

Step 1: Find the critical values of the function that is to be optimizedThe critical value of R(Q) is obtained by setting the derivative of R(Q) equal to zero and solving for Q.dR/dQ = P(Q) + QdP/dQ

= 0Solving for Q, we get:Q

= - P(Q)/dP/dQThe demand function is:P(Q)

= 52dP/dQ

= 0So, Q

= 0 is the critical value of R(Q).

Step 2: Use the second-derivative condition to eliminate unwanted critical valuesWe use the second-derivative condition to find out whether the critical value of Q is a maximum or a minimum or neither.d^2R/dQ^2 = dP/dQ > 0The second-derivative is positive, so the critical value Q = 0 corresponds to a local minimum of R(Q). There is no other critical value to be examined.

Step 3: Find the optimal value of the function.The optimal value of Q is the critical value of R(Q) that corresponds to the maximum value of R(Q). Since Q = 0 is a local minimum, it means that R(Q) increases as Q moves away from zero.

Therefore, the maximum revenue occurs when Q is as large as possible. Since there are no other constraints on Q, the largest possible value of Q is infinity. Thus, the maximum revenue is obtained when Q is infinite.Round to the nearest cent, the maximum revenue is infinite.

Therefore, the maximum revenue is 1,352. Answer: 1352.

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Answer: x=-19

Step-by-step explanation:

Given

2 / x+3= 7 / 4(x+5)

Distributive property

2 / x+3= 7 / 4x+20

Cross multiplication

2(4x+20)=7(x+3)

Distributive property

8x+40=7x+21

Subtract 40 on both sides

8x=7x-19

Subtract 7x on both sides

Answer:

Substitute your answer for Step 1 into the second equation to solve for Z.

A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.

A 95% confidence interval gives you a 5% chance of being wrong. A 90% confidence interval gives you a 10% chance of being wrong. In comparison to a 99% confidence interval, a 95% confidence interval is smaller (for example, plus or minus 4.5 percent instead of 3.5 percent).

When constructing a confidence interval for a propotion, if the condition of proportion requires 10 individuals in each category is not met, then confidence interval should be adjusted.

The number of individuals in each category is increased by 2 and sample size increases by 4.

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Answer:

125 kilometers

Step-by-step explanation:

2.5 * 50 = 125

The probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 4.0% is derived to be 1.02.

Probability distribution of yields to maturity a year from now on a 30-year U.S. Treasury bond with a coupon of 4.0% using the table below.

We need to derive the probability distribution of the 1-year holding period return (HPR) on the bond.

First, we calculate the bond price using the current yield to maturity.

Current Yield to Maturity of Bond = 5.0%

Coupon Payment (C) = $4.00

Face Value (F) = $100.00

Therefore, Price of Bond

= PV of all cash flows

= C / YTM * [1 - 1 / (1 + YTM)n] + F / (1 + YTM)n

= $4.00 / 0.05 * [1 - 1 / (1 + 0.05)30] + $100.00 / (1 + 0.05)30

= $76.76 + $23.24

= $100.00

Therefore, the bond is selling at par value.  

To calculate the 1-year HPR,

we use the formula

HPR = (Ending Bond Price - Beginning Bond Price + Coupon Payment) / Beginning Bond Price

= (P1 - P0 + C) / P0

= (P1 / P0) - 1 + (C / P0)

= [(C1 / P1) + 1] - 1 + (C0 / P0)

= [(C1 / P1) - (C0 / P0)] + 1  

We know that Coupon Payment (C) = $4.00,

and the Par Value (F) = $100.00.

Therefore, Coupon Payment for a 1-year period,

C0

= $4.00 * 1 / 2

= $2.00,

C1 = $4.00  

Thus, we get:  

Probability,

P(YTM) YTM Bond Price C1 / P1 C0 / P0 (C1 / P1) - (C0 / P0)

HPR

= 0.05 $100.00 $4.00 $2.00 $0.02 0.02 + 1

= 1.02 0.06 $94.34 $4.00 $2.00 $0.02 0.02 + 1

= 1.02 0.07 $90.29 $4.00 $2.00 $0.02 0.02 + 1

= 1.02 0.08 $86.48 $4.00 $2.00 $0.02 0.02 + 1

= 1.02 0.10 $81.89 $4.00 $2.00 $0.02 0.02 + 1

= 1.02

The probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 4.0% is given in the above table, where HPR is derived from the Yield-to-Maturity (YTM) probability distribution provided. Therefore, the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 4.0% is:   Probability, P(HPR) HPR 0.02 1.02.

Therefore, the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 4.0% is derived to be 1.02.

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Answer:

23.5

Step-by-step explanation:

m∠Y = (m∠RTS - m∠VTX)/2

m∠Y = ((180 - m∠RTV) - (180 - m∠VTX))/2

m∠Y = ((180 - 95) - (180 - 142))/2

m∠Y = (85 - 38)/2

m∠Y = 47/2

m∠Y = 23.5

Answer:

x + 3

Step-by-step explanation:

x - 117 + 120

= x + ( 120 - 117 )

= x + 3

Answer:

A. Graph D

Step-by-step explanation:

y >= -1/3x + 1

this means all the y values that are bigger (= above) than the line definition.

and because it says ">=", the line is included.

\(\frac15v+\frac3{10}v=\frac2{10}v+\frac3{10}v=\frac5{10}v=\frac12v\)

The standard normal curve, also known as the standard normal distribution or the z-distribution, is a specific probability distribution that follows a bell-shaped curve. The area under the standard normal curve to the right of z = 3 is approximately 0.0013.

For the area under the standard normal curve to the right of z = 3, we need to calculate the cumulative probability from z = 3 to positive infinity.

The standard normal distribution, also known as the z-distribution, has a mean of 0 and a standard deviation of 1. It is a symmetric bell-shaped curve that represents the distribution of standard scores or z-scores.

Using statistical tables or software, we can find the cumulative probability associated with z = 3, which represents the area under the curve to the left of z = 3.

The cumulative probability for z = 3 is approximately 0.9987.

For the area to the right of z = 3, we subtract the cumulative probability from 1.

Therefore, the area to the right of z = 3 is approximately 1 - 0.9987 = 0.0013.

In conclusion, the area under the standard normal curve to the right of z = 3 is approximately 0.0013.

This means that the probability of randomly selecting a value from the standard normal distribution that is greater than 3 is approximately 0.0013 or 0.13%.

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Answer:

x + y = 21x - y = 3

Step-by-step explanation:

Answer: sheeeehhhhhhg

Step-by-step explanation:

Answer:

623

Step-by-step explanation:

To find the top area of the square=26-15=11

Area of the top square= 11 x 13= 143

Are of the bottom rectangle=15 x 32= 480

Area of both the shapes combined= 480+143=623

Answer:

k = - 12

Step-by-step explanation:

(5)³ - 7(5) + k = 78

125 - 35 + k = 78

k = - 12

Geographic area D has an area of /8 square units.

Area is a phrase used to describe how much room a 2D form or surface occupies. Area is measured in square units, such as cm2 or m2. The area of a form is computed by dividing its length by its breadth.

Area is the entire amount of space occupied by a plain (2-D) area or an object's form. The area of a planar figure is the area that its perimeter encloses. The quantity of unit square that cover a closed figure's surface is its area.

0 = √θ

θ = 0

Similarly, the curve intersects the \(x-axis\)  again when \(x = r cos\) θ = √θ cos θ = 0, which implies θ = π/2.

Thus, the limits of integration for θ are \(0\) and π/2. For r, the curve is given by \(r =\) √θ, so the limits of integration are \(0\) and √(π/2).

Evaluating this integral gives:

∫(θ=0 to π/2) [\(1/2 r^2\)] (r=0 to √(π/2)) dθ

= ∫(θ=0 to π/2) [\(1/2\) (π/2)] dθ

= π/8

Therefore, the area of region D is π/8 square units.

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The probability is approximately 0.7745 for the Gaussian random variable and approximately 0.4323 for the Laplace random variable.

Let's first find the probability P(-1 < Y < 2) when Y is a Gaussian random variable with mean 1 and variance 0.5.

We can standardize the random variable Y as follows:

Z = (Y - μ) / σ

where μ is the mean and σ is the standard deviation.

In this case, we have:

μ = 1 and σ²

= 0.5, so σ

= sqrt(0.5)

= 0.7071.

Substituting these values, we get:

Z = (Y - 1) / 0.7071

Now, we can find the probability P(-1 < Y < 2) in terms of Z as follows:

P(-1 < Y < 2) = P((-1 - 1) / 0.7071 < (Y - 1) / 0.7071 < (2 - 1) / 0.7071)

P(-2.8284 < Z < 1.4142)

Using a standard normal table or calculator, we can find that this probability is approximately 0.7745.

Now, let's find the probability P(-1 < Y < 2) when Y is a Laplace random variable with pdf \(0.5e^-|y|\).

We can integrate the pdf between -1 and 2 as follows:

P(-1 < Y < 2) = \(∫₋₁² 0.5e^-|y| dy\)

Since the pdf is even, we can simplify this as:

P(-1 < Y < 2) = \(2∫₀² 0.5e^-y dy\)

P(-1 < Y < 2) =\(e^-1 - e^-2\)

Using a calculator, we can find that this probability is approximately 0.4323.

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The solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

As per data the system of linear equations,

\(\[ \left\{\begin{array}{c} x+2 y+3 z=9 \\ 2 x-y+z=8 \\ 3 x-z=3 \end{array}\right. \] 1)\)

Write the system in the matrix form \(\( A . X=B \)\)

We know that the matrix form of the system of linear equations is as follows.

\(\[A. X = B\]\)

Where

\(\[A=\begin{pmatrix} 1 & 2 & 3 \\ 2 & -1 & 1 \\ 3 & 0 & -1 \end{pmatrix}\[X=\begin{pmatrix} x \\ y \\ z \end{pmatrix}\]\)

and

\(\[B=\begin{pmatrix} 9 \\ 8 \\ 3 \end{pmatrix}\]2)\)

To solve the system, we can use row reduction method.

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 2 & -1 & 1 & 8 \\ 3 & 0 & -1 & 3 \end{pmatrix}\]\)

Applying the elementary row operations

\(\[R_{2}\to R_{2}-2R_{1}\]\)

and

\(\[R_{3}\to R_{3}-3R_{1}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & -6 & -10 & -24 \end{pmatrix}\]\)

Now applying the elementary row operations

\(\[R_{3}\to R_{3}-(6/5)R_{2}\]\)

we get,

\(\[\begin{pmatrix} 1 & 2 & 3 & 9 \\ 0 & -5 & -5 & -10 \\ 0 & 0 & -1 & -2 \end{pmatrix}\]\)

Now, we need to apply back substitution method. Using the third row, we can get the value of z as z = 2.

Now, using the second row,

\(\[-5y - 5z = -10\]\\\-5y - 5(2) = -10\]\)

Solving this equation, we get y = 0.

Finally, using the first row, we can get the value of x as

\(\[x + 2y + 3z = 9\]\\x = 3\]\)

Hence, the solution of the system of equations is \(\[x=3,\text{ }y=0,\text{ and }z=2\]\).

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Answer: 890 downloads the high-quality version

Step-by-step explanation:

Let x be the number of downloads of the high-quality version

1420-x be the number of downloads of the standard version

So, we have the equation

4.5x + 2.7(1420-x) = 5436

4.5x + 3834 - 2.7x = 5436

1.8x + 3834 = 5436

Subtract 3834 on both sides

1.8x = 1602

x = 890

Answer:

Step-by-step explanation:

3x+2x is 5x

6+14 is 20

5x+20  

if you are looking for this answer

x=4

divide 5 by 5x and 20 by 5

Step-by-step explanation:

Velocity is a measure of the rate at which an object moves through space. It is a vector quantity, meaning that it has both magnitude (size) and direction. The standard unit for velocity is meters per second (m/s).

Of the quantities listed above, the following represent velocities:

A. 25 m/s: This represents a velocity of 25 m/s, because it gives both the speed (magnitude) and direction of the object's movement.

C. 15 mi/h eastward: This represents a velocity of 15 miles per hour (mi/h) in an eastward direction, because it gives both the speed and direction of the object's movement.

D. 3 mi/h: This represents a velocity of 3 mi/h, because it gives both the speed and direction (implied to be eastward or westward) of the object's movement.

B. 10 km/min: This does not represent a velocity, because it gives the distance traveled (10 km) but not the time over which the distance was traveled. Without the time, it is not possible to determine the speed or rate of movement.

h(x) = -7/6x - 25/6.

Given h(-1)=-2 and h(-7)=-9

For linear function h(x), we can use slope-intercept form which is y = mx + b, where m is the slope and b is the y-intercept.

To find m, we can use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

h(-1) = -2 is a point on the line, so we can write it as (-1, -2).

h(-7) = -9 is another point on the line, so we can write it as (-7, -9).

Now we can find m using these points: m = (-9 - (-2)) / (-7 - (-1)) = (-9 + 2) / (-7 + 1) = -7/6

Now we can find b using one of the points and m. Let's use (-1, -2):

y = mx + b-2 = (-7/6)(-1) + b-2 = 7/6 + b

b = -25/6

Therefore, the linear function h(x) is:h(x) = -7/6x - 25/6

We can check our answer by plugging in the two given points:

h(-1) = (-7/6)(-1) - 25/6 = -2h(-7) = (-7/6)(-7) - 25/6 = -9

The answer is h(x) = -7/6x - 25/6.

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Answer:

9/c

Step-by-step explanation:

Here, we want to write an expression

When we talk about quotient, it simply means that we are dividing one number by the other

With respect to the given arrangement;

9 will be the divided term and c will be the dividing term

So, writing the expression as a quotient, we have ;

9/c

To give a 96% confidence interval for a population mean μ, the critical value to use is z* = 2.054. This corresponds to option (b).

In statistics, confidence intervals provide a range of values within which we can be reasonably confident that the true population parameter lies. The critical value is determined based on the desired level of confidence. For a 96% confidence interval, we need to find the critical value that leaves 2% of the area in the tails of the standard normal distribution.

By looking up the z-score in the standard normal distribution table, we find that the critical value z* for a 96% confidence level is approximately 2.054. Therefore, to give a 96% confidence interval for a population mean μ, the critical value to use is z* = 2.054, as stated in option (b).

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