calculate the distance a car will travel 3.5h if its speed averages 92.5km/h.

The vector parametric form of the line L, which is the intersection of the given planes P and Q is given by L: x = 2/5 + (-7/5)t y = 6/5 - (3/5)t z = t

Given the equation of two planes as follows: P: x - 2y - z = 4Q: 2x + y + z = 2

To find a parameterization of the line that is the intersection of the planes P and Q, we follow the following steps:

Step 1: Let us write the augmented matrix of the system of linear equations for the given two planes. P: x - 2y - z = 4Q: 2x + y + z = 2⇒The augmented matrix is [A | B] =⇒A

= [1 -2 -1 | 4; 2 1 1 | 2]

Step 2: We apply elementary row operations to transform the matrix A to reduced row echelon form (rref(A)).

[1 -2 -1 | 4; 2 1 1 | 2]R2-2R1

→ R2[1 -2 -1 | 4; 0 5 3 | -6]R2/5

→ R2[1 -2 -1 | 4; 0 1 3/5 | -6/5]R1+2R2

→ R1[1 0 7/5 | 2/5; 0 1 3/5 | -6/5]

Step 3: From the rref(A) matrix, we can say that the system of linear equations is consistent with unique solution. Therefore, the line that is the intersection of the given two planes P and Q is unique. Now, we can write the equation of the line in vector parametric form as follows.

x = a + t b, where 'a' is any point on the line, 'b' is the direction vector of the line, and 't' is a parameter.

Here, the values of 'a' and 'b' can be determined by solving the following systems of equations.1x + 0y + 7/5z = 2/5   (Obtained from the row echelon form)   ⇒ x = 2/5 - 7/5z y

= 6/5 - 3/5z z = z

The above equations can be written as follows: x = 2/5 + (-7/5)tz = zy

= 6/5 - (3/5)tz = z

The vector parametric form of the line L, which is the intersection of the given planes P and Q is given by L: x = 2/5 + (-7/5)t y

= 6/5 - (3/5)t z

= t

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Answer:

-1

Step-by-step explanation:

When the line is slanting down it means its negative.

Answer:

Step-by-step explanation:

The result is TR (20).

To determine the result of TR (915) - TR (895), the following logical-mathematical reasoning must be made:

We find a constant that is repeated in both values, which is TR.

In turn, both values have a different quantity, which multiplies that constant.

Therefore, you must perform this multiplication and then subtract the results, to obtain the final result.

Therefore, the result is TR (20).

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The probability that a randomly selected cup of hot chocolate would have a temperature of less than 166 degrees is approximately 0.0726, or 7.26%. This would not warrant a replacement cup as it is not considered unusual or significantly deviant from the mean.

- To obtain the probability that a randomly selected cup of hot chocolate would have a temperature of less than 166 degrees, we can use the Z-score and the standard normal distribution.

First, let's calculate the Z-score for the temperature of 166 degrees using the formula:

Z = (X - μ) / σ

where X is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

Z = (166 - 175) / 6.2

Z = -1.4516

Next, we can use a Z-table or a statistical software to find the probability associated with the Z-score of -1.4516.

Looking up the Z-score in the table, we find that the probability is approximately 0.0726.

- To determine whether this outcome is unusual or warrants a replacement cup, we can consider the significance level or the threshold for unusualness.

Commonly, a significance level of 5% (0.05) is used. If the probability of an outcome falls below this threshold, it can be considered unusual.

In this case, the probability of less than 166 degrees is 0.0726, which is greater than 0.05. Therefore, this outcome would not be considered unusual at a significance level of 5%.

It means that a cup of hot chocolate with a temperature below 166 degrees is within the expected range of temperatures based on the given mean and standard deviation and hence, it would not warrant a replacement cup.

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Answer:

The previous number keeps getting multiplied by - 5

Step-by-step explanation:

5 × -5 = -25

-25 × -5 = 125

125× -5 = -625

-625 × -5 = 3,125

3125 × -5 = -15,625

-15,625 × -5 = 78,125

78,125 × -5 = -390, 625

-390,625 × -5 = 1,953,125

1,953,125 × -5 = 9,765,625

:)

The 9th term of the geometric sequence is 5⁹.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

The formula to find nth term of the geometric sequence is \(a_n=ar^{r-1}\). Where, a = first term of the sequence, r= common ratio and n = number of terms.

The given geometric sequence is 5, 25, 125,..

To find the common ratio, divide the second term by the first term:

r = 25/5

r = 5

The formula for the nth term of a geometric sequence is:

aₙ = a₁ rⁿ⁻¹

Substitute n = 9, r = 5, and a₁ = 5:

a₉ = 5 (5)⁹⁻¹

a₉ = 5 (5)⁸

a₉ = 5⁹

Hence, the 9th term of the geometric sequence is 5⁹.

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Answer:

Whats the question?

Step-by-step explanation:

An equation that represents a given situation is 39+x=64.

The given statement is last week Sally had thirty-nine dollars. She washed cars over the weekend and now has sixty-four dollars.

We need to write an equation that represents a given situation.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the money earned by Sally over the weekend be x.

Now, 39+x=64

Therefore, an equation that represents a given situation is 39+x=64.

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Answer:

what is your question? it seems the answer would be 12 just by looking at this, but still what is the question exactly?

Step-by-step explanation:

Answer: if you are dividing the answer will be 12

(i wrote two since it dosent say what we need to do

if you are multiplying you answer will be 192

hope it helped!

Step-by-step explanation:

Answer:

They rode 14 miles before replacing each horse

Step-by-step explanation:

We will be working under the assumption that all three riders sat on one horse at a time and rode it while the other horses rested.

From the problem, we can understand that the horses were each ridden for the same distance. This means that to get the total distance a horse rode before it was changed, we can divide the total distance by the number of horses that were used for the journey.

Distance each horse rode = 182/ 13 = 14 miles.

Therefore, each horse was ridden for 14 miles before it was changed.

(i) The dynamic programming matrix with the min cost entries for the given strings is as follows: ''1 2 1 2 3; 2 1 2 1 2; 3 2 1 2 3; 4 3 2 1 2''.  (ii) The min cost solutions by tracing back the matrix entries from bottom right are: Substitute 'a' at position 2 with 'b', Substitute 'a' at position 1 with 'a'.

(i) To create the dynamic programming matrix for string edit, we can use the Levenshtein distance algorithm. The matrix will have the alphabets of string X along the rows and the alphabets of string Y along the column entries.

First, let's create the initial matrix:

```

     ''  b   a   b   b

  ---------------------

'' |  0   1   2   3   4

a  |  1

b  |  2

a  |  3

b  |  4

```

In this matrix, the blank '' represents the empty string.

To calculate the min cost entries, we will use the following rules:

1. If the characters in the current cell match, copy the cost from the diagonal cell (top-left).

2. If the characters don't match, find the minimum cost among three neighboring cells: the left cell (insertion), the top cell (deletion), and the top-left cell (substitution). Add 1 to the minimum cost and place it in the current cell.

Let's calculate the min cost for two entries in the matrix:

1. For the cell at row 'a' and column 'b':

 The characters 'a' and 'b' don't match, so we need to find the minimum cost among the neighboring cells.

     - Left cell: The cost is 2 (from the previous row).

  - Top cell: The cost is 1 (from the previous column).

  - Top-left cell: The cost is 0 (from the previous row and column).

  The minimum cost is 0. Since the characters don't match, we add 1 to the minimum cost. Thus, the min cost for this cell is 1.

2. For the cell at row 'b' and column 'b':

  The characters 'b' match, so we copy the cost from the top-left diagonal cell.

  The min cost for this cell is 0.

We can continue calculating the min cost entries for the rest of the cells in a similar manner.

(ii) To trace back the matrix entries from the bottom right and calculate the min cost solutions, we start from the bottom-right cell and move towards the top-left cell.

Using the matrix from part (i), let's trace back the entries:

Starting from the cell at row 'a' and column 'b' (cost 1), we compare the neighboring cells:

- Left cell: Cost 2

- Top cell: Cost 3

- Top-left cell: Cost 0

The minimum cost is in the top-left cell, so we choose that path. We have performed a substitution operation, changing 'a' to 'b'. We move to the top-left cell.

Continuing the process, we compare the neighboring cells of the current cell:

- Left cell: Cost 1

- Top cell: Cost 2

- Top-left cell: Cost 0

Again, the minimum cost is in the top-left cell. We have performed a substitution operation, changing 'b' to 'a'. We move to the top-left cell.

We repeat this process until we reach the top-left cell of the matrix.

The complete sequence of operations to transform string X into string Y is as follows:

1. Substitute 'a' at position 2 with 'b': "a b a b" → "a b b b"

2. Substitute 'a' at position 1 with 'a': "a b b b" → "b a b b"

By following this sequence, we achieve the transformation from string X to string Y with the minimum cost.

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Answer:

-5,-17 in 3rd quadrant

5,-17 in 4th quadrant

5,17 in 1st quadrant

-5,17 in 2nd quadrant

Answer:

(-5, -17) in 3rd Quadrant

(5, -17) in 4th Quadrant

(5, 17) in 1st Quadrant

(-5, 17) in 2nd Quadrant

-TheUnknownScientist

The perimeter of a square is given by the formula:

Where l is the side length of the square. This is because the square has 4 sides of the same length. Substitute l=10in to find the perimeter:

Therefore, the perimeter of the square is:

The percent of the second fruit salad is strawberries should be 10%.

= 25% - 15%

= 10%

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Answer:

\(\cos \left(90 ^\circ - x\right) \approx 0.1688\)

Step-by-step explanation:

We are given that:

\(\displaystyle \tan x = \frac{3}{7}\)

And we want to find the value of:

\(\displaystyle \cos \left(90^\circ - x\right)\)

Recall that by definition, tan(θ) = sin(θ) / cos(θ). Hence:

\(\displaystyle \frac{\sin x }{\cos x} = \frac{3}{7}\)

And by definition, sin(θ) = cos(90° - θ). Hence:

\(\displaystyle \frac{\cos \left(90^\circ - x\right)}{\cos x} = \frac{3}{7}\)

Multiply:

\(\displaystyle \cos \left(90 ^\circ - x\right) = \frac{3}{7} \cos x\)

Find cosine. Recall that tangent is the ratio of the opposite side to the adjacent side. Therefore, the opposite side is 3 and the adjacent side is 7.

Thus, by the Pythagorean Theorem, the hypotenuse will be:

\(\displaystyle h = \sqrt{3^2 + 7^2} = \sqrt{58}\)

Cosine is the ratio of the adjacent side to the hypotenuse. Therefore:

\(\displaystyle \cos x = \frac{7}{\sqrt{58}}\)

Thus:

\(\displaystyle \cos \left(90 ^\circ - x\right) = \frac{3}{7} \left(\frac{3}{\sqrt{58}}\right)\)

Use a calculator. Hence:

\(\cos \left(90 ^\circ - x\right) \approx 0.1688\)

The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

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Answer:

x = 5

y = 3

Step-by-step explanation:

x + 4y = 17

2x + 5y = 25

We multiply the first equation by -2

-2x - 8y = -34

2x + 5y = 25

-3y = -9

y = 3

Now we put 3 in for y and solve for x

x + 4(3) = 17

x + 12 = 17

x = 5

Let's Check the answer

5 + 4(3) = 17

5 + 12 = 17

17 = 17

So, x = 17 and y = 3 is the correct answer.

1. Maximum height of the Function H(t) = -12cos( πt/45 ) + 18   is  30 units.

2. For the given sinusoidal function the values of the following are as follow :

amplitude = 6ft, period = π/3 , Maximum = 9ft,

Equation of the midline y = 6, Minimum = 3 ft.

Function with height 'H' is given by:

H(t) = -12cos( πt/45 ) + 18

Here 't' represents the time in seconds.

As we know that range of cosine trigonometric function is ,

-1 ≤ cosα ≤ 1

This implies cos function lies between  -1 and 1.

Replace cos( πt/45 ) by 1 or -1

For cos( πt/45 ) = 1

H(t) = -12(1) + 18

      = 6 units

For cos( πt/45 ) = -1

H(t) = -12(-1) + 18

      = 30 units

Maximum height is equals to 30 units.

Therefore, function H(t) = -12cos( πt/45 ) + 18  representing maximum height is equal to 30 units.

2. In general sinusoidal function is given by :

   y = Asin(Bx + C) + D

A is amplitude

A = High tide - low tide

   = 9 - 3 /2

   = 3ft

Time = 12:30 p.m.  - 6: 39 a.m.

        = 6 : 09 minutes

         = 6hours(approximately)

period B = 2π /T

              = 2π/6

              = π/3

Vertical shift = 9 - 3

                     = 6

Equation of the midline is

y = c

⇒ y = 6

Function is y = 3sin (π/3)x + 6

Maximum sin (π/3)x = 1

y = 9

Minimum sin (π/3)x = -1

⇒ y = 3

Therefore, the values of the following for the given function is :

amplitude = 6ft, period =  π/3 , Maximum = 9ft,

Equation of the midline y = 6, Minimum = 3 ft.

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To evaluate the definite integral of 1/(1+x^2), we can use the substitution method. Let u=1+x^2, then du/dx=2x and dx=du/2x. Substituting these into the integral, we get:
∫1/(1+x^2) dx = ∫1/u * (du/2x)
= (1/2) * ∫(1/u) du
= (1/2) * ln|u| + C
= (1/2) * ln|1+x^2| + C

To evaluate the definite integral from 0 to 1, we can plug in the limits of integration and subtract the results:
∫(0 to 1) 1/(1+x^2) dx = [(1/2) * ln|1+1^2|] - [(1/2) * ln|1+0^2|]
= (1/2) * ln(2) - (1/2) * ln(1)
= (1/2) * ln(2)

To get an approximate answer rounded to 4 decimal places, we can use a calculator to evaluate (1/2) * ln(2) which gives 0.3466 (rounded to 4 decimal places). Therefore, the exact answer is (1/2) * ln(2) and the approximate answer rounded to 4 decimal places is 0.3466.

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Answer:

$8.49

Step-by-step explanation:

Amount Saved = $8.49 (answer). In other words, a 50% discount for a item with original price of $16.98 is equal to $8.49 (Amount Saved).

Since we know that an object is 16.98, all we need to do is find what 50% is off the cost. Since 50% is half of the price, all we need to do is come up with the equation:

\(16.98/2= 8.49 + 16.98 = 25.47\)

I added 16.98 at the end because you have to buy One *object* and get it with half price. The total with the discounted object is 25.47

Thank you! btw can i please get brainly :3

Answer:

x<-2

Step-by-step explanation:

17+4x<9

4x<-8

x<-2

The solution is:

Work/explanation:

Recall that the process for solving an inequality is the same as the process for solving an equation (a linear equation in one variable).

Make sure that all constants are on the right:

\(\bf{4x < 9-17}\)

\(\bf{4x < -8}\)

Divide each side by 4:

\(\bf{x < -2}\)

Answer:

Given that the correlation between stock A and stock B is 0.46, we can substitute the values to calculate the expected return and standard deviation of the portfolio.

Step-by-step explanation:

To calculate the expected returns and standard deviations of the two stocks, we can use the given return data.

a. Expected Returns:

The expected return for a stock is the average of its returns. Using the given data:

Expected return of stock A = (0.10 + 0.07 + 0.15 - 0.05 + 0.08) / 5

Expected return of stock A ≈ 0.07 or 7% (rounded to three decimal places)

Expected return of stock B = (0.06 + 0.02 + 0.05 + 0.01 - 0.02) / 5

Expected return of stock B ≈ 0.024 or 2.4% (rounded to three decimal places)

b. Standard Deviations:

The standard deviation measures the volatility of returns. Using the given data:

For stock A:

Calculate the variance:

Variance of stock A = [(0.10 - 0.07)^2 + (0.07 - 0.07)^2 + (0.15 - 0.07)^2 + (-0.05 - 0.07)^2 + (0.08 - 0.07)^2] / 5

Variance of stock A ≈ 0.00476 (rounded to five decimal places)

Calculate the standard deviation:

Standard deviation of stock A = √(0.00476)

Standard deviation of stock A ≈ 0.069 or 6.9% (rounded to three decimal places)

For stock B:

Calculate the variance:

Variance of stock B = [(0.06 - 0.024)^2 + (0.02 - 0.024)^2 + (0.05 - 0.024)^2 + (0.01 - 0.024)^2 + (-0.02 - 0.024)^2] / 5

Variance of stock B ≈ 0.00056 (rounded to five decimal places)

Calculate the standard deviation:

Standard deviation of stock B = √(0.00056)

Standard deviation of stock B ≈ 0.024 or 2.4% (rounded to three decimal places)

c. Portfolio of 70% stock A:

To calculate the expected return and standard deviation of a portfolio that consists of 70% stock A and 30% stock B, we use the weighted averages:

Expected return of the portfolio = (0.70 * Expected return of stock A) + (0.30 * Expected return of stock B)

Standard deviation of the portfolio = √[(0.70^2 * Variance of stock A) + (0.30^2 * Variance of stock B) + (2 * 0.70 * 0.30 * Correlation * Standard deviation of stock A * Standard deviation of stock B)]

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Answer:

1740

Step-by-step explanation:

1,160 is what she made for the 40 hours.  You have to add the 10 extra hours at double pay.

(10)(29)(2) is 580.  Add that to the number that you got (1160) and you will have your total.

580 + 1160 = 1740

Answer:

$1740

Step-by-step explanation:

See attached worksheet.

Answer:

it's the bottom right!! TRUST MR I PROMISE

Step-by-step explanation:

IT IS THE ONLY LINE GOING DOWN which proves it's negative!!!

Answer:

angle PSQ=25°

Step-by-step explanation:

angle RQS=angle PSQ.......... alternate angle

so angle PSQ=25°

Answer:

25 degrees

Step-by-step explanation:

If it is a parallelogram, then the sides PS and QR will be parallel, then ∠PSQ and ∠RQS are alternate interior angles, and hence they will be congruent. That is, ∠PSQ ≅ ∠RQS = 25°.

But this is not the confirmation that this would be parallelogram as it could be trapezoid. The given condition is must but not sufficient to prove it.

Hope this helps. Do mark me as BRAINLY. thanks

Answer:

4 dolls and 6 cars

Step-by-step explanation:

let c represent the number of cars and d the number of dolls bought , then

c + d = 10 ( subtract c from both sides ) ← total of 10 toys

d = 10 - c → (1)

10c + 15d = 120 → (2) cost of toys

substitute d = 10 - c into (2)

10c + 15(10 - c) = 120

10c + 150 - 15c = 120

- 5c + 150 = 120 ( subtract 150 from both sides )

- 5c = - 30 ( divide both sides by - 5 )

c = 6

substitute c = 6 into (1)

d = 10 - c = 10 - 6 = 4

the customer bought 6 cars and 4 dolls

Answer:

GB xbxnxnjdndjdjsjsjjsjansnsnbsnsbddjndjdjsj

Answer:

£166 : £581

Step-by-step explanation:

sum the parts of the ratio, 2 + 7 = 9 parts

Divide the amount by 9 to find the value of one part of the ratio

£747 ÷ 9 = £83 ← value of 1 part of the ratio, then

2 parts = 2 × £83 = £166

7 parts = 7 × £83 = £581

£747 = £166 : £581 in the ratio 2 : 7

Answer:

\({ \tt{circumference \approx\pi \: d}} \\ \approx{ \tt{3.14 \times 15}} \\ \\ \approx47.124 \: inches\)

The number of commercials in which Avery's songs were played is 5.

The number of movies in which Avery's songs were played is 5.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

The number of times the song played in commercials = x

The number of times the song played in a movie = y

Now,

Avery will earn $40 every time one of her songs is played in a commercial and earn $140 every time one of her songs is played in a movie.

We can make two equations.

x + y = 7 ____(1)

x = 7 - y _____(2)

40x + 140y = 480 _____(3)

Substituting (2) in (3) we get,

40(7 - y) + 140y = 480

280 - 40y + 140y = 480

100y = 480 - 280

100y = 200

y = 2

Now,

x = 7 - 2

x = 5

Thus,'

The number of commercials and the number of movies in which Avery's songs were played are 5 and 2.

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The constant speed of Fast Freddy is 0.25 miles per minute and the constant speed of Speedy Sam is 0.125 miles per minute

The question is incomplete as the graphs and the tables are missing.

However, the points given in the question can be used to represent the graph and the table

By interpreting the points, we have:

Graph

(x, y) = (0, 0) and (4, 1)

Table

x           y

4           0.5

20         2.5

32         4

The slope is calculated using:

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

So, we have:

Graph: \(m = \frac{1 -0}{4 -0} = 0.25\)

Table: \(m = \frac{4 -2.5}{32 -20} = 0.125\)

Freddy's speed is represented by the graph, while Sam's speed is represented by the table

Hence, the constant speed of Fast Freddy is 0.25 miles per minute and the constant speed of Speedy Sam is 0.125 miles per minute

Freddy ran faster because 0.25 is greater than 0.125

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Answer:

1. Freddy ran a speed of 1/4 miles

2. Sam ran a speed of 1/8 miles

3. Freddy ran faster

Step-by-step explanation:

Your welcome :)

flash is the best show to ever exist