Distance between skew lines Find the distance between the line L1 through the points A(1, 0, -1) and B(-1, 1, 0) and the line L2 through the points C(3, 1, -1) and D(4, 5, -2). The distance is to be measured along the line Perpendicular to the two lines. First find a vector n perpendicular to both lines. Then project rAC onton.

Answer:

A - \(\sqrt{5}\)

Step-by-step explanation:

\(\sqrt{15} = \sqrt{5} *\sqrt{3} \\\frac{\sqrt{5} *\sqrt{3}}{3*\sqrt{3}} = \frac{\sqrt{5}}{3}\)

Answer: √5/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

0.0154, I think, I apologize if this is wrong.

Linear regression adapts to sudden shifts to data patterns. [False]

Linear regression is a type of predictive analysis technique used to form a linear relationship between a dependent and an independent variable. However, linear regression does not adapt well to sudden changes in data patterns or outliers that could impact the model's accuracy. Therefore, it is not suitable for modeling data with sudden shifts. In such cases, non-linear regression methods or more complex models may be more appropriate.

Linear regression is a basic yet powerful technique for modeling relationships between variables. It is used for a wide range of applications, from predicting sales to estimating the impact of a variable on the outcome of interest. However, the accuracy of linear regression models can be impacted by outliers or sudden changes in data patterns. Therefore, it is important to carefully evaluate the data and select appropriate modeling techniques based on the specific characteristics of the dataset. Non-linear regression techniques or more advanced models may be better suited for modeling data with sudden shifts or extreme values.

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Answer:

range: (-1,-9,-4)

domain: (-7,-2,0,5)

Answer:

What is the range of the function?

(-7,-1) (-2,-4) (0,-1) (5,-9)

192

Answer:

A + B would be less than A - B

Step-by-step explanation:

Therefore, the covariance of 1.07x and 2y is approximately 11.984.

To find the covariance of 1.07x and 2y, we can use the property that the covariance is linear with respect to scalars. In other words, cov(aX, bY) = ab * cov(X, Y) for any constants a and b.

Given:

cov(x, y) = 5.6

Let's calculate the covariance of 1.07x and 2y:

cov(1.07x, 2y) = (1.07 * 2) * cov(x, y)

= 2.14 * 5.6

≈ 11.984

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Answer:

I litteraly have the same problem and no clue how to do I

Step-by-step explanation:

Answer:

804.672 km

Step-by-step explanation:

Answer:

It's 804.672 long in kilometers. If needed to be round then about 805 kilometers.

Step-by-step explanation:

You know that:

1 mile = 1.609344 km

So you'll do

500 * 1.609344 = 804.672 km

Answer:

The stunt plane finally finished his stunt at a height of 300m above the skyscraper which means he is at a height of h0 + 300 above sea level

Therefore , the total elevation (e)  would be :

e = 300 + 100

= 400m

The probability that the second card is a jack given that the first card was a 2 is 52/51.

To calculate the probability that the second card is a jack given that the first card was a 2, we need to consider the remaining cards in the deck after the first card is drawn.

When the first card is drawn and it is a 2, there are 51 cards remaining in the deck, out of which there are 4 jacks.

The probability of drawing a jack as the second card, given that the first card was a 2, can be calculated using conditional probability:

P(Second card is a jack | First card is a 2) = P(Second card is a jack and First card is a 2) / P(First card is a 2)

Since the first card is already known to be a 2, the probability of the second card being a jack and the first card being a 2 is simply the probability of drawing a jack from the remaining 51 cards, which is 4/51.

The probability of the first card being a 2 is simply the probability of drawing a 2 from the initial deck, which is 4/52.

P(Second card is a jack | First card is a 2) = (4/51) / (4/52)

Simplifying the expression:

P(Second card is a jack | First card is a 2) = (4/51) * (52/4)

P(Second card is a jack | First card is a 2) = 52/51

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Answer:

The easiest way to do this is to calculate the Area of the whole circle and then subtract the 1/4 of the missing piece.

So:

Answer:

\(\boxed {\boxed {\sf a \approx 190.9 \ yd^2}}\)

Step-by-step explanation:

There are 2 formulas for the area of a sector, but since we are given the central angle in degrees (not radians), we will use this formula:

\(a= \frac {\theta}{360} \times \pi r^2\)

Where θ is the central angle and r is the radius.

For this circle, the radius is 9 yards and the central angle is 270 degrees. We can substitute these values into the formula.

\(a= \frac {270}{360} \times \pi \times (9 \ yd )^2\)

Solve the fraction.

\(a=0.75 \times \pi \times (9 \ yd)^2\)

Solve the exponent.

\(a= 0.75 \times \pi \times 81 \ yd^2\)

Multiply all three numbers together.

\(a= 190.851753706 \ yd^2\)

The question asks us to round to the nearest tenth.

The 5 in the hundredth place tells us to round the 8 up to a 9.

\(a \approx 190.9 \ yd^2\)

The area of the sector is approximately 190.9 square yards.

answer

the number of buses is 3

the number of cars is 6

Step-by-step explanation:

total number of the students=165

total number of the vehicles=9

let x represent the number of cars

let y represent the number of buses

x+y=9...........equation 1

(the number of the cars plus the number of the buses= to the number of vehicles )

5x + 45y=165.......equation 2

(the number of student the car can hold plus the number of student the bus can hold= to the total number of the student in a class)

x+y=9.......eqn 1

5x +45y=165....eqn 2

make x the subject of the formula in eqn 1

x+y=9

x= 9-y

substitute for x= 9-y in eqn 2

5(9-y)+45y=165

45-5y+45y=165

-5y+45y=165-45

40y=120

divide both sides by 40

40y÷40=120÷40

y=3

since y represent number of buses,the numbet of bus is 3

Also,substitute for y=3 in eqn 1

eqn 1 is x+y=9

x+3=9

x=9-3

x=6

therefore,the number of cars is 6.

Answer:

34

Step-by-step explanation:

hope this helps :)

Answer:

34

Step-by-step explanation:

First, plug in numbers and then solve...

Step-by-step explanation:

When 508,000,000 is written in scientific notation, it will be represented as:

5.08 x 10^8

Therefore, the value of the exponent is 8.

Answer: -40 °C and -40 °F.

Step-by-step explanation:

Answer:

-40

Step-by-step explanation:

Let the temperature be x which is the same in Fahrenheit and Celsius. Then it must satisfy the Fahrenheit and Celsius conversion formula which is (Fahrenheit-32)*(5/9)=Celsius

x=(x-32)*(5/9)

9x=5x-160, x=-40

After answering the presented question, we can conclude that As a result, the line connecting the points A(-7, -1) and B(8, 2) is divided by the line x + y = 2 in the ratio about 65.63:56.63.

In mathematics, ratios demonstrate how frequently one number is contained in another. For example, if there are 8 oranges and 6 lemons in a fruit dish, the ratio of oranges to lemons is 8 to 6. In a similar vein, the orange-to-whole-fruit ratio is 8, whereas the lemon-to-orange ratio is 6:8. A ratio is an ordered pair of numbers a and b represented as a / b, where b is not zero. A ratio is an equation that equates two ratios. For example, if there is one male and three girls (for every boy she has three daughters), 3/4 are girls and 1/4 are boys.

\(m = (y2 - y1)/(x2 - x1) = (2 - (-1))/(8 - (-7)) = 3/15 = 1/5\\y - y1 = m(x - x1)\\y - (-1) = (1/5)(x - (-7))\\y + 1 = (1/5)(x + 7)\\y = (1/5)x + 6/5 - 1\\y = (1/5)x + 1/5\\x + (1/5)x + 1/5 = 2\\(6/5)x = 9/5\\x = 3\\\)

\(y = (1/5)(3) + 1/5\\y = 4/5\\AP = \sqrt[(3 - (-7))^2 + (4/5 - (-1))^2] = \sqrt[10^2 + 9/5^2] = \sqrt[100 + 81/25] = \Sqrt[4301]/5\\PB = \Sqrt[(8 - 3)^2 + (2 - 4/5)^2] = \sqrt[25 + 81/25] = \sqrt[3206]/5\\\)

The ratio in which AB is divided by x + y = 2 is:

\(AP:PB = \sqrt[4301]:\sqrt[3206] = 65.63:56.63 \\\)

As a result, the line connecting the points A(-7, -1) and B(8, 2) is divided by the line x + y = 2 in the ratio about 65.63:56.63.

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Answer:

If a vertical line crosses the relation on the graph only once in all locations, the relation is a function. However, if a vertical line crosses the relation more than once, the relation is not a function. Using the vertical line test, all lines except for vertical lines are functions.

Step-by-step explanation:

Answer:

If a vertical line crosses the relation on the graph only once in all locations, the relation is a function.

However, if a vertical line crosses the relation more than once, the relation is not a function.

Step-by-step explanation:

Using the vertical line test, all lines except for vertical lines are functions.

The number of cases per batch that should be produced to minimize cost is: 300 units

The number of cases per batch that should be produced to minimize cost can be found by using the Economic Order Quantity.

The Economic Order Quantity (EOQ) is a calculation performed by a business that represents the ideal order size that allows the business to meet demand without overspending. The inventory manager calculates her EOQ to minimize storage costs and excess inventory.  

Thus:

Number of cases per batch = √((2 * Setup costs * annual demand)/ holding costs for the year)

Solving gives:

√((2 * 30 * 15000)/10)

= √90000

= 300 units

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The probability that at least one call arrives within a 10-minute interval is:P(X≤10)=1−P(X>10)=1−e−λt=1−e−(1/x)×10. (long answer)

Given: The time between calls to a plumbing supply business is exponentially distributed with a mean time between calls of x. It follows that the distribution can be described by the equation `P(X≤x)=1−e−λx`.Here,λ is the rate parameter which is the inverse of the mean time between calls. It is given that the mean time between calls is x, so we have:λ=1/x.(a) The probability that there are no calls within a 30-minute interval is calculated using the exponential distribution formula `P(X>t)=e−λt` where t is the length of the time interval.

In this case, t=30 minutes.So the probability that there are no calls within a 30-minute interval is:P(X>30)=e−λt=e−(1/x)×30= e−30/x. (long answer) (b) The probability that at least one call arrives within a 10-minute interval is:P(X≤10)=1−P(X>10)=1−e−λt=1−e−(1/x)×10. (long answer)

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The solution to the equation "5*2-3^2 / (3^2-(-2))^2" after solving it is 1/121

To solve the equation 5*2-3^2 / (3^2-(-2))^2, we need to simplify the numerator and the denominator. This will give us this:

5*2-3^2 / (3^2-(-2))^2 =

= 10 - 9 / (9 - (-2))^2

Simplify further to make the number reduced

10 - 9 / (9 - (-2))^2

After the subtraction at the numerator level, the denominator figures have two minus signs which becomes a plus. As a result, we realize the value below

= 1 / (11)^2

In order to remove the bracket in the denominator, it implies that the number in bracket will be multiplied by itself since it is in the superscript of 2 which means 11 multiply by 11 or (11 x 11)

= 1/121

Therefore, to solve the equation 5*2-3^2 / (3^2-(-2))^2, one needs to simplify the equation and do the subtraction and addition from the numerator and the denominator respectively to realize the answer which is 1/121

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Answer: 1/121

Step-by-step explanation:

( 5 * 2 - 3^2 )/[ 3^2 - (-2)] ^ 2

= (10 - 9)/(9+2)^2

= 1 / 11^2

= 1/121

Answer:

838.08 in³

Step-by-step explanation:

volume of tank = (36×24×24)+(½×3.14×12²×24)

= 20,736 + 5,425.92

= 26,161.92 in³

the remaining water = 27,000 - 26,161.92

= 838.08 in³

Answer:

$1605

Step-by-step explanation:

1500 ⋅ 0.07 = 105

Add 105 to 1500

$1605

Hope I helped :)

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Answer:

Step-by-step explanation:

Find the Parabola with Focus (7,0) and Directrix x=-7 (7,0) x=-7. (7,0) ( 7 , 0 ) x=−7 x = - 7. Since the directrix is horizontal, use the equation of a parabola that opens left or right. ... Find the distance from the focus to the vertex. ... Substitute in the known values for the variables into the equation (y−k)2=4p(x−h) ( y - k ) 2 = 4 p ...

Using the distance formula, the equation of a parabola with directrix y=7 and focus (0,−7) is   \(x^2 = -28y\)

The focus = (0, -7)

The directrix:  y  =  7

The distance formula is given as:

\((x - a)^2+(y-b)^2= r^2\)

From the focus (0, -7)

a = 0,  b = -7

r  =  y - 7

Substitute a = 0, b = -7 and r = y - 7 into the equation above:

\((x - 0)^2 + (y +7)^2 = (y - 7)^2\\\\x^2 + y^2+14y + 49= y^2-14y+49\\\\x^2 = y^2-y^2-14y-14y+49-49\\\\x^2 = -28y\)

Using the distance formula, the equation of a parabola with directrix y=7 and focus (0,−7) is \(x^2 = -28y\)

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Answer:

30cm

Step-by-step explanation:

0.25 times 120 miles equals 30 cm

Answer:

Step-by-step explanation: