(Chapter 12) For any vectors u and v in V3, (u + v) X v= (u X v)

The equation of the plane through the point (9, 0, 3) and perpendicular to the line x = 3t, y = 6-t, z = 1 + 4t is  4y + z = 3

To find an equation of the plane, we need to find the normal vector of the plane. The normal vector is perpendicular to the plane and is also perpendicular to the line given in the question. We can find the direction vector of the line by taking the coefficients of t in the equations for x, y, and z.

The direction vector of the line is <3, -1, 4>. Since the normal vector is perpendicular to the direction vector, we can take the cross product of the direction vector with any other vector to find the normal vector. Let's take the cross product with the vector <1, 0, 0>:

Normal vector = <3, -1, 4> x <1, 0, 0> = <0, 4, 1>

Now we can use the normal vector and the point (9, 0, 3) to find the equation of the plane. The equation of a plane is given by:

ax + by + cz = d

Where  is the normal vector and d is a constant. Plugging in the normal vector and the point, we get:

0(9) + 4(0) + 1(3) = d

d = 3

So the equation of the plane is:

0x + 4y + z = 3

Or simply:

4y + z = 3

This is the equation of the plane through the point (9, 0, 3) and perpendicular to the line x = 3t, y = 6-t, z = 1 + 4t.

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The time it take riders to pass over the hill and reach ground level is 111.19 seconds .

Given :

the roller coaster's height expressed by the equation below;

h = -0.067t^2 + 7t + 50

where

t is the time in seconds

The driver will hit the ground at the point where h = 0

Substitute

-0.067t^2 + 7t + 50 = 0

Multiply through  by -1

0.067t^2 - 7t +-50 = 0

Factorize :

On factorizing, the positive value of "t" is 111.19 seconds

Hence the time it take riders to pass over the hill and reach ground level is 111.19 seconds

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Hey There!!

Your answer will be 3.

Step-by-step explanation:

Because, 2 + 1 = 3

Answer:

Hey!

Your answer is 3!

Step-by-step explanation:

2 + 1 = 3!

Hope this helps!

:>

Answer:

pls mark me brainlist .......my question was the same but no one ans I don't know

Answer:

Dont know if this is right but doubble check

Step-by-step explanation:

since the coyote is 32 and the total weight is 120 you would be 88 pounds for the fox and this is a a 3 to 8 ratio

Answer:

A,B,D,E

Step-by-step explanation:

The statements which are true shown below,

From graph attached below, It is observed that

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Answer:

it’s C. 0.02,0.2.1/2, 2 1/2

The probability that fewer than 3 of the 8 sampled people are unemployed is approximately 0.91, indicating that there is a high chance of having at least 3 employed people in the sample.

It can be solved using the binomial distribution formula.

Let X be the number of unemployed people in a sample of 8 from the city.

Then X follows a binomial distribution with parameters n = 8 and p = 0.16, since the probability of an individual being unemployed is 0.16.

The probability of fewer than 3 people being unemployed is the probability of X = 0, 1, or 2.

We can compute this probability as:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Using the binomial distribution formula:

P(X = k) = (n choose k) * p^k * (1 - p)^{(n - k)}

We can compute each term separately:

P(X = 0) = (8 choose 0) * 0.16⁰ * 0.84⁸ ≈ 0.3252

P(X = 1) = (8 choose 1) * 0.16¹* 0.84⁷ ≈ 0.3772

P(X = 2) = (8 choose 2) * 0.16² * 0.84⁶ ≈ 0.2035

Therefore,

P(X < 3) ≈ 0.3252 + 0.3772 + 0.2035 ≈ 0.906

Rounding to two decimal places, the probability that fewer than 3 of the 8 sampled people are unemployed is approximately 0.91.

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Answer:

the answer is x= -33

Step-by-step explanation:

The number of students in the telescope club by $x$ and the number of students in the math club by $y$.

$y=2x$Now, suppose there are $z$ students who are members of both clubs. Then the total number of students who are in the math club or the telescope club (or both) is given by:$x + y - z$ Substituting $y=2x$ in the above expression, we get:$x + 2x - z=3x - z$ Hence, the expression for the total number of students who are in the math club or the telescope club (or both) is $3x - z$.b)The number of students who are in the math club but not in the telescope club is given by:$y-z$ And the number of students who are in the telescope club but not in the math club is given by:$x-z$ Adding these two expressions, we get the total number of students who are in the math club or the telescope club but not both:$ y-z+x-z $.

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Answer:

g(x) = $16.49x + $10.50

$208.38

Step-by-step explanation:

Given the following:

Cost per bag = $16.49

Shipping and handling fee = $10.50

Number of bags ordered = x

If g(x) = total cost of bags

Bag cost = cost per bag × number of bags ordered

Bag Cost = $16.49 * x = $16.49x

Shipping and handling fee = $10.50

Total cost of bags = Bag cost + shipping and handling fee

g(x) = $16.49x + $10.50

Where x is the number of bags ordered.

Therefore, total cost of 12 bags equals ;

g(12) = $16.49(12) + $10.50

g(12) = $197.88 + $10.50

g(12) = $208.38

Answer:

g(x)=16.49x+10.50

$208.38

Step-by-step explanation:

let the cost of x bags = g(x)

cost of one bag = $16.49

cost of x bags = $16.49x

shipping and handling charges = $10.50

total cost of x bags = 16.49x + 10.50

g(x) = 16.49x + 10.50

To determine the cost of 12 bags, substitute x with 12 and simplify:

g(12) = 16.49(12) + 10.50

= 208.38

1 you are offered a gamble on the toss of a coin. if the coin shows tails, you lose $100. if the coin shows heads, you win $150. Yes one can  accept it.

As per the given data:

If you toss the coin.

Coin shows tails \($\rightarrow$\) lose $ 100

Coin shows heads \($\rightarrow$\) win $ 150

We would consider expected gain for us in each scenario.

Since, the probability of head is,

\(P(H) = \frac{1}{2}\)

The probability of Tail is,

\(P(T)=\frac{1}{2}\)

Therefore, expected gain \($=150 \times \frac{1}{2}+(-100) \times \frac{1}{2}$$$\)

= 75 - 50

= $ 25

Since, gain is positive number of 25 .

We can say on an average we can gain some Profit.

Hence one would accept the offer.

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Answer:the best predicted value of ý when the twin born first has an IQ of 109 is 107.50

Step-by-step explanation:

Given the regression equation:

ŷ = -2.59 + 1.01x

We need to predict the value of ý when x (IQ score of the twin born first) is 109.

So we substitute x = 109 into the regression equation:

ŷ = -2.59 + 1.01(109)

ŷ = -2.59 + 110.09

ŷ = 107.50

Therefore, the best predicted value of ý when the twin born first has an IQ of 109 is 107.50.

The solution to the given differential equation as required is; y = √(x² + 4).

As evident in the task content;

dy / dx = x / y, y(0) = -2

Therefore, we have that;

dy (y) = dx (x)

By integration of both sides indefinitely;

y² / 2 = x²/2 + C

y² = x² + 2c

y = √(x² + 2c)

Hence, using the initial conditions;

-2 = √(0² + 2c)

-2 = √2c

2c = 4

c = 2.

Hence, the required solution of the differential equation as given is; y = √(x² + 4) since c = 2.

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Step-by-step explanation:

a. 11 + x + y = 11 + x + y. True

b. 7 - 2x + 3y = 7 - 2x + 3y. True

c. 2x + 8 = 2x + 4. False

d. -5x - 45 = -5x - 45. True

To find the orthogonal projection of a vector onto a subspace, we can use the formula:

Projection of vector v onto subspace W = ((v ⋅ u1) / ||u1||^2) * u1 + ((v ⋅ u2) / ||u2||^2) * u2 + ...

where v is the vector we want to project, u1, u2, ... are the basis vectors spanning the subspace W, ⋅ denotes the dot product, and ||u|| represents the magnitude of vector u.

In this case, the vector to be projected is v = [49, 49, 49], and the subspace is spanned by u1 = [2, 3, 6] and u2 = [3, -6, 2].

First, we normalize the basis vectors:

||u1|| = √(2^2 + 3^2 + 6^2) = √49 = 7

u1_normalized = (1/7) * u1 = [2/7, 3/7, 6/7]

||u2|| = √(3^2 + (-6)^2 + 2^2) = √49 = 7

u2_normalized = (1/7) * u2 = [3/7, -6/7, 2/7]

Next, we calculate the dot products:

v ⋅ u1_normalized = [49, 49, 49] ⋅ [2/7, 3/7, 6/7] = (98/7) + (147/7) + (294/7) = 539/7 = 77

v ⋅ u2_normalized = [49, 49, 49] ⋅ [3/7, -6/7, 2/7] = (147/7) - (294/7) + (98/7) = -49/7 = -7

Now, we can calculate the projection:

Projection of v onto subspace W = (77 / ||u1||^2) * u1_normalized + (-7 / ||u2||^2) * u2_normalized

Plugging in the values:

Projection of v onto subspace W = (77 / 7^2) * [2/7, 3/7, 6/7] + (-7 / 7^2) * [3/7, -6/7, 2/7]

                                = (11/49) * [2, 3, 6] + (-1/49) * [3, -6, 2]

                                = [22/49, 33/49, 66/49] + [-3/49, 6/49, -2/49]

                                = [19/49, 39/49, 64/49]

Therefore, the orthogonal projection of the vector [49, 49, 49] onto the subspace spanned by [2, 3, 6] and [3, -6, 2] is [19/49, 39/49, 64/49].

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Answer:

initial amount is 130

decaying at 55%

Step-by-step explanation:

The margin of error for a 95% confidence interval with a population standard deviation of 0.5 hours and a sample size of n = 25 is approximately 0.196 hours.

To calculate the margin of error for a 95% confidence interval with a population standard deviation of 0.5 hours and a sample size of n = 25, we can use the formula:

Margin of Error = Critical Value * (Standard Deviation / √(Sample Size))

For a 95% confidence interval, the critical value corresponds to a z-score that leaves 2.5% of the area in each tail. Since we have a large enough sample size (n ≥ 30), we can use the z-score.

The z-score for a 95% confidence level is approximately 1.96.

Plugging in the values:

Margin of Error = 1.96 * (0.5 / √(25))

Calculating the expression:

Margin of Error = 1.96 * (0.5 / 5)

Margin of Error = 0.196

Therefore, the margin of error for a 95% confidence interval with a population standard deviation of 0.5 hours and a sample size of n = 25 is approximately 0.196 hours.

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Answer:

white sold = 16

yellow sold = 12

Step-by-step explanation:

w = # of white sold

y = # of yellow sold

w + y = 28   solve this for w

w = 28 - y

9.95w + 13.5y = 321.20     substitute w = 28-y into this expression and solve for y

9.95(28-y) + 13.5y = 321.20

278.60 - 9.95y + 13.50y = 321.20

278.60 + 3.55y = 321.20

3.55y = 321.20 - 278.60 = 42.60

y = 42.60/3.55 = 12   substitute this into w = 28 - y and solve for w

w = 28 - 12 = 16

The cubic equation is used to describe the glide path of a plane. The given information states that the plane is in level flight at an altitude of 1 mile and starts its descent 6 miles east of the airport.

The question provides information about the altitude of the plane is in and starts its descent 6 miles east of the airport. However, since the equation itself is not provided, we cannot determine the exact shape or characteristics of the glide path.
To better understand the glide path described by the cubic equation, we need to know the equation itself. Unfortunately, the equation is not provided in the question. Without the equation, we cannot determine the exact shape or characteristics of the glide path.
However, a cubic equation typically has the form:
y = ax^3 + bx^2 + cx + d
Where x represents the horizontal distance and y represents the vertical distance (altitude) from the ground. The coefficients a, b, c, and d determine the specific shape of the curve.
Without the specific equation, we cannot provide explanation or examples based on the given information. We would need the equation to calculate and visualize the glide path accurately.
In summary, the question provides information that the plane is in level flight at an altitude of 1 mile and starts its descent 6 miles east of the airport, about a plane's glide path being described by a cubic equation. However, since the equation itself is not provided, we cannot determine the exact shape or characteristics of the glide path.

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Answer:

-24

Hope that this helps!

Answer:

6558.75

Step-by-step explanation:

total value of 100 logs = total value of an average log x 100 total value of an average log = length of an average log x price per board foot

8.25 x 7.95 = 65.5875

65.5875 x 100 = 6558.75

Using an exponential function, it would take 824 minutes before the amount of medication in Aldi's bloodstream is effectively 0.

A decaying exponential function is given as;

\(A(t) = A(0)e^-kt\)

Where A = initial value

k = decay constant

We have the half-life of amoxicillin as 62minutes, to determine k, we get

\(A(62) = 0. 5(0)\)

\(A(62) = 0.5A(0)\)

\(0. 5A(0) = A(0) e^{-62k}\)

Solve the exponential function thus

\(e^{-62k} = 0. 5\)

㏑ \(e^{-62k}\) = ㏑ 0. 5

- 62k = ㏑ 0.5

Make k subject of formula

k = -㏑\(\frac{0. 5}{62}\)

k = 0. 011179

The equation is given by

\(A(t) = A(0)e^-0.011179\)

We have

\(0. 0001A(0) = A(0)e^-0.01179\)

\(e^-0.011179t = 0. 0001\)

㏑ \(e^-0.011179\) = ㏑ 0.0001

\(-0.011179t = In 0.0001\)

t = \(-\frac{In 0. 0001}{0. 011179}\)

t = \(824\)

Therefore, it would take 824 minutes before the amount of medication in Aldi's bloodstream is effectively 0.

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Answer:

B

Step-by-step explanation:

Area = length x width

Total surface area

=2(8*3) + 2(10*3) + 2(10*8)

=48+60+160

=268

Answer:

[6.26,6.29]U[6.31,6.34

Step-by-step explanation:

6.26

6.27

6.28

6.29

6.31

6.32

6.33

6.34

So in interval form [6.26,6.29]U[6.31,6.34]

The number of ways in which 6 policemen can be assigned to 12 coaches of a passenger train if he must ride in a different coach is 665,280.

The number of ways in which 6 policemen can be assigned to 12 coaches of a passenger train if they must ride in a different coach is given by :

12 × 11 × 10 × 9 × 8 × 7

This is because the first policeman can be assigned to any of the 12 coaches. Once he has been assigned to a coach, the second policeman can be assigned to any of the remaining 11 coaches.

Continuing in this way, the number of ways in which the policemen can be assigned to the coaches is:

12 × 11 × 10 × 9 × 8 × 7

Therefore, the number of ways in which 6 policemen can be assigned to 12 coaches of a passenger train if he must ride in a different coach is 665,280.

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The percentage of squirrels that have a weight between 3 and 5 pounds is; 95.017%

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