1ll mark brainlist pleassee help

The parametric equations are line through (0,0,0) in the direction of the vector v=uxw=(1,2,1).

The line through (0,0,0) and perpendicular to both U=(-2,1,0) and

w=(-1,0,1)

Therefore the line through (0,0,0) and parallel to (-2,1,0)

\(*10919-1-2, î+1=3618 = (1) ņ - (-2)5+ (1)a • Î +21 + û\)

=(1,2,1)

Therefore direction ratio of the line through (0,0,0) is (1,2,1) Therefore for equation of the line through (0,0,0) and perpendicular to both (-2,1,0) and \(w=(-1,0,17 is (0,, z) = (0,0,0) + x (1,2,1),\) & is constant.

\(.: X (1,4,2)= (0, 1, 0)+ [1,2,1]\)

Therefore parametric of the line through (0,0,0) in the direction of the vector v=uxw=(1,2,1)

Equivalent Equation of a Plane in Vector Form

The equation for a plane in the real number system R, where r is the position vector of any point on the plane and n is either a normal vector perpendicular to the plane or a parallel vector.

The normal vector must be perpendicular to both as the vectors are both parallel to the plane. Recall that a vector that is perpendicular to both vectors is created by taking the cross product of two vectors. This cross product's characteristic can be used to compute a normal vector to the plane, which results in the normal vector.

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In this case, we are given only a partial list of observations. To determine if the process is in control, we would need the complete set of observations to evaluate their values in relation to the control limits.

To construct a control chart and determine if the process is in control, we need to calculate the control limits using the given observations.

Let's start by calculating the average (x(bar)) and standard deviation (σ) of the observations:

Observations: 10, 3, 9, 9, 8, 4

Step 1: Calculate the average (x(bar)):

x(bar) = (10 + 3 + 9 + 9 + 8 + 4) / 6 = 43 / 6 ≈ 7.17

Step 2: Calculate the standard deviation (σ):

1. Calculate the squared deviation for each observation:

\((10 - 7.17)^2, (3 - 7.17)^2, (9 - 7.17)^2, (9 - 7.17)^2, (8 - 7.17)^2, (4 - 7.17)^2\)

= 6.9129, 18.9129, 2.5929, 2.5929, 0.6889, 10.5889

2. Calculate the average of the squared deviations:

(6.9129 + 18.9129 + 2.5929 + 2.5929 + 0.6889 + 10.5889) / 6 ≈ 7.9198

3. Calculate the square root of the average squared deviation:

σ = √(7.9198)

≈ 2.81

Now that we have the average (x(bar)) and standard deviation (σ), we can construct the control chart using two sigma limits. The control limits are calculated as follows:

Upper Control Limit (UCL) = x(bar) + (2 * σ)

Lower Control Limit (LCL) = x(bar) - (2 * σ)

UCL = 7.17 + (2 * 2.81)

≈ 12.79

LCL = 7.17 - (2 * 2.81)

≈ 1.55

Based on the control chart, if any of the observations fall above the UCL or below the LCL, it would indicate an out-of-control process.

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96 square ft

Step-by-step explanation:

The time taken by both to mow the lawn is 36 minutes.

This is a question of time and work.

It is given that:-

Time taken by boy to mow the loan = 90 minutes.

Time taken by girl to mow the loan = 60 minutes.

We have to find the time taken by both of them together to mow the lawn.

LCM(60,90) = 180

Let the total work to be done to mow the lawn be 180 units.

Hence,

Efficiency of boy = 180/90 = 2 units

Efficiency of girl = 180/60 = 3 units

Total efficiency = 2 + 3 = 5 units.

Hence, time taken by both of them to mow the lawn = 180/5 = 36 minutes.

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We will first convert the numbers to be operated on to fractions.

Performing subtraction operation gives:

Step-by-step explanation: Each game is $25.50 which in math means it has an "x"

So if x=1 then 25.50x says that 1 video game is $25.50

Set up the equation:

200 = 25.50x (divide both sides by 25.50 to isolate the x)

200/25.50 = 7.84

x = 7.84

You can't have 0.84 of a video game, so Roberto can only buy 7 of them.   The answer is correct good job!

The number of games that Roberto can buy \(\boldsymbol{8}\) video games.

"To understand the calculation, check below."

When two values are compared, an inequality shows whether one is less than, greater than, or simply not equal to the other.

It's a relation that compares two integers or other mathematical expressions in a non-equal way.

Total amount with Roberto \(=\$ 200\)

Let \(x\) denotes number of games that Roberto can buy.

Cost of each video game \(=\$25.50\)

So,\(25.50x\leq 200\\x\leq 7.8\)

Therefore, Roberto can buy \(\boldsymbol{8}\) video games.

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Answer:

Tu salario es $3600

Step-by-step explanation:

Porque hoy tienes 1/4 del salario total. Al principio tienes 4 times esa cantidad. Entonces debes multiplicar $900 x 4 = 3600

A rectangle with its base on the x-axis and its vertices on the curve

y =4 - x² can have a maximum area of 32/3√3.

The formula for calculating a rectangle's area is  A=length*breadth

The base's length is x.

y represents the curve's vertices (width).

Given that a rectangle's area increases as its base moves along the x-axis, our base will be 2x.

The rectangle's surface area will change to:

A = 2x ( 4 - x²)

When the area is at its largest, da / dx should be maximum.

A = 8x - 2x³

da/dx = 8 - 6x²

8 - 6x² = 0

6x² =  8

x² = 8/6

x  = √4/3

   =2/√3

We shall substitute 2/√3 into the region in order to obtain the maximum area.

A=  8x - 2x³

  = 8*2/√3 - 2*(2/√3)³

  =32/3√3

Therefore, the largest area a rectangle with a base on the x-axis and vertices on the curve y = 4 - x² can have is 32/3√3.

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The asymptotes of the original function f(x)=10x and the transformed function g(x) remain the same.

The transformation of reflecting the graph of f(x)=10x about the x-axis followed by shifting it left 12 units creates the new function g(x). The reflection about the x-axis results in the graph of g(x) being upside down compared to the graph of f(x). The shift left 12 units means that the entire graph of g(x) is shifted to the left on the x-axis by 12 units.

However, the transformation does not have any effect on the asymptotes of the function. Asymptotes are vertical or horizontal lines that a function approaches but never touches. They are determined by the behavior of the function as it approaches infinity or negative infinity. Reflecting the graph about the x-axis or shifting it left or right does not change the behavior of the function as it approaches infinity or negative infinity.

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Answer:

by adding 14581+418541=433,122

by adding 23427+23243=46,670

by substraction of both Numbers=

difference between both number is 386,452

Answer:

30'000 gallons approx

Step-by-step explanation:

day 2 - 500,000 gallons

day 4 - 250,000 gallons

day 6 - 125,000 gallons

day 8 - 62,500 gallons

day 10 - 31,250 gallons

The angle of refraction for the ray of light entering the bucket of water ≈ 48.8 degrees.

To determine the angle of refraction for a ray of light that enters a bucket of water from air, we can use Snell's law, which relates the indices of refraction and the angles of incidence and refraction.

Snell's law states:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

Where:

n₁ = index of refraction of the medium the light is coming from (air)

n₂ = index of refraction of the medium the light is entering (water)

θ₁ = angle of incidence

θ₂ = angle of refraction

n₁ (air) = 1.000293

n₂ (water) = 1.333

θ₁ (angle of incidence) = 25.0 degrees

To find the angle of refraction (θ₂), we need to rearrange Snell's law:

sin(θ₂) = (n₁ / n₂) * sin(θ₁)

Now we can substitute the given values into the equation and calculate the angle of refraction:

sin(θ₂) = (1.000293 / 1.333) * sin(25.0 degrees)

Using a calculator:

sin(θ₂) ≈ 0.7505

To find θ₂, we take the inverse sine (arcsine) of 0.7505:

θ₂ ≈ arcsin(0.7505) ≈ 48.8 degrees

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Answer:

-2

Step-by-step explanation:

-10 x 12 x -4 + 40 x -2 x 6 - 2

-120 x -4 - 80 x 6 - 2

480 - 480 - 2

0 - 2

-2

Answer:

42

Step-by-step explanation:

3 is equal to 42 degrees because when you have two parallel lines that have another line pass through both parallel lines the values of degrees are the same as the opposite side so:

42 = 3

2 = 4

and another way you could find the value of 3 is since there is a perpendicular line going through line p we know that since it is perpendicular that the angle between them is 90 so angle 3 is:

90 - (angle 4) = angle 3

You may use this method if you first solved for angle 4 or angle 2 and we can get angle 2 from:

180 - 42 = 138

we can do this because 42 + angle two should be 180 degrees since they are along line n.

Answer:

x + 3y - 9 = 0 or y = -1/3x + 3

Step-by-step explanation:

y - 2 = -1/3 (x - 3)

3y - 6 = -x + 3

x + 3y - 9 = 0

Answer:

y=−1/3x+3

Step-by-step explanation:

easy

(3,2)

slope: -1/3

make a graph

slope is rise over run

y - 2 = -1/3 (x - 3)

3y - 6 = -x + 3

x + 3y - 9 = 0

y=−1/3x+3

y-intercept is point where x is 0

y=mx+b

y=−1/3x+3

Answe

7

Step-by-step explanation:

204 dived by 3.5

i did 204 dived by 60 then

420 dived by 60

The time taken by the family to reach is T = 7 hours

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the speed be represented as S

Now , the value of S is

S = D / T

speed = distance / time = 204 miles / 3.4 hours = 60 miles per hour

where , the distance D = 420 miles

And , T = 420 / 60

T = 7 hours

Hence , the time taken for 420 miles is 7 hours

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Answer:

-2

Step-by-step explanation:

Note that slope-intercept form looks like: y = mx + b

In this case, isolate the y. Note the equal sign, what you do to one side, you do to the other. Subtract 2x from both sides:

2x (-2x) + y = 6 (-2x)

y = -2x + 6

Note in the slope-intercept form: y = mx + b

y = y

m = slope

x = x

b = y-intercept

In this case, your slope is -2. All lines parallel to the given equation will also have a slope of-2.

~

Answer:

Fraction: 13/30

Decimal: 0.43

Percentage: 43%

Answer:

$0.27

Step-by-step explanation:

1/4 The ratio of meters of streamers to cost of streamers is 1 : 0.09

     We want to know the ratio of centimeters of streamers to cost of  
     streamers.

2/4 We need to convert meters to centimeters.

      There are 100 centimeters in 1 meter.

      So, if 1 meter of streamers costs $0.09, then 100 centimeters of
      streamers also cost $0.09.

3/4 The ratio centimeters of streamers to cost for 300 centimeters of
      streamers.

      Now, we can find an equivalent ratio to find the cost for 300
      centimeters of streamers.

4/4 The streamers cost $0.27 per 300 centimeters.

Answer:

The coordinates of the vertex are

(-5;-9)

Answer:

(-5, -9)

Step-by-step explanation:

Use of the coordinate plane, center of the parabola 5 to the left and down 9.

Hope this helped!

The coordinates weighted average is 6.

The whole query is as follows:

The weights of the coordinates 3 and 8 are 2 and 3, respectively. Additionally, we must determine the weighted average.

The parameters are as follows:

Three has a weight of two.

The weight of coordinate 8 is 3.

Next, the weight average is determined as follows:

Weight average is equal to the product of the weight and the coordinates.

We thus have:

Average weight: (3 * 2 + 8 * 3)/(2 + 3)

Assess the quotient.

Average weight = 6

Consequently, the coordinates' weighted average is 6

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Answer:

\((244 - n)n \\ n = 3 \\ (244 - 3) \times 3 \\ = (241) \times 3 \\ = 723\)

the merchant uses 48 pounds of the $3 tea and 32 pounds of the $2.75 tea in the blend.

To determine the amount of each type of tea used in the blend, we can set up a system of equations based on the given information. Let's assume x pounds of the $3 tea are used and y pounds of the $2.75 tea are used.

The first equation represents the total weight of the mixture: x + y = 80 (equation 1).

The second equation represents the average price per pound of the mixture: (3x + 2.75y) / 80 = 2.90 (equation 2).

To solve this system of equations, we can use the method of substitution or elimination.

Using substitution, we can solve equation 1 for x: x = 80 - y. Substituting this into equation 2, we have (3(80 - y) + 2.75y) / 80 = 2.90.

Simplifying the equation, we get (240 - 3y + 2.75y) / 80 = 2.90.

Combining like terms, we have (240 - 0.25y) / 80 = 2.90.

Cross-multiplying, we get 240 - 0.25y = 2.90 * 80.

Simplifying further, we have 240 - 0.25y = 232.

Subtracting 240 from both sides, we get -0.25y = -8.

Dividing both sides by -0.25, we find y = 32.

Substituting this value of y into equation 1, we have x + 32 = 80.

Solving for x, we get x = 80 - 32 = 48.

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9514 1404 393

Answer:

  a) -3/5x² -2/5x +1/15 = 0

  b) √3/3x² +2√3/9x -√3/27 = 0

Step-by-step explanation:

The quadratic equation of interest is of the form ...

  (leading coefficient)(x^2 -(sum of roots)x +(product of roots)) = 0

The sum of the given roots is ...

  (-1 +√2)/3 +(-1 -√2)/3 = -2/3

The product of the given roots is ...

  (-1 +√2)/3×(-1 -√2)/3 = ((-1)² -(√2)²)/3² = -1/9

__

a) The quadratic is ...

  (-3/5)(x² +2/3x -1/9) = -3/5x² -2/5x +1/15 = 0

__

b) The quadratic is ...

  (√3/3)(x² +2/3x -1/9) = √3/3x² +2√3/9x -√3/27 = 0

The pattern will be attached in the figure attached, in the matrix form.

What is the matrix?

The arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns are known as matrices, which is the plural version of the word matrix. They are rectangular arrays with defined operations for addition, multiplication, and transposition. The constituents of the matrix are its numbers or entries. Vertical entries in matrices are referred to as columns, whereas horizontal entries are known as rows. A matrix is a rectangular array of numbers, variables, symbols, or expressions that are defined for operations like subtraction, addition, and multiplication. The number of rows and columns in a matrix determines its size, sometimes referred to as its order.

We can arrange it as A = (0 0 0 0 1 1 0 0 1)

We know A*TA = 0

If A has an entry 9 then, the sum of all the diagonal elements.

So the T will be the form of the matrix attached below.

Hence the Pattern will be attached in the figure attached.

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Answer:

21

and 24

Step-by-step explanation:

let the ratio be 7x and 8x

then,

7x + 8x = 45

15x = 45

X = 45/15

X =3

so

7x =7*3=21

8*=8*3=24

According to the given information, the noise level in a restaurant is normally distributed with an average of 30 decibels. To find the value below which 99% of the time the noise level is, we need to use the Z-table.

We know that 99% of the area under the normal curve is below a Z-score of 2.33 (found from the Z-table).

To find the corresponding noise level value, we use the formula:

Z-score = (X - μ) / σ

where X is the noise level value we want to find, μ is the average (30 decibels), and σ is the standard deviation (which is not given in this question).

However, we can use the empirical rule (68-95-99.7 rule) to estimate the standard deviation. According to the rule, 99.7% of the data falls within 3 standard deviations of the mean. So, if 99% of the time the noise level is below a Z-score of 2.33, then we can estimate that the standard deviation is approximately:

(2.33 x σ) = 3

Solving for σ, we get:

σ = 3 / 2.33 = 1.29 (approx.)

Now we can use the formula above to find the noise level value below which 99% of the time the noise level is:

2.33 = (X - 30) / 1.29

X - 30 = 2.33 x 1.29

X = 33.01

So, 99% of the time, the noise level in the restaurant is below 33.01 decibels (rounded to two decimal places).

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