Multiply numbers with decimals
2.34 x 1.6

Answer: (x, y) → (x, y - 7)

Step-by-step explanation:

The line integral of the given vector field F along the curve r(t) is 0. To evaluate the line integral (CF. dr for the vector field F = sin(x)i+yvtj + zk along the curve given by r(t) = { i++j+tk,1, we need to parameterize the curve and then compute the integral.

First, let's find the derivative of r(t):

r'(t) = i + j + t k

Next, we need to find the limits of integration. The curve is given by r(t) = { i+j+tk,1 for 0 ≤ t ≤ 1. Therefore, our limits of integration are 0 and 1.

Now, we can compute the line integral using the formula:

CF.dr = ∫(CF).r'(t) dt

= ∫(sin(x)i+yvtj + zk).(i+j+tk) dt

= ∫(sin(i+j+tk) + vt) dt

= -cos(i+j+tk) + 1/2v(t^2)

Evaluating the integral from t=0 to t=1, we get:

CF.dr = [-cos(1+i+j+k) + 1/2v] - [-cos(1+i+j) + 1/2v(0)]

= [-cos(1+i+j+k) + cos(1+i+j)] + 1/2v

Therefore, the value of the line integral is:

CF.dr = [-cos(1+i+j+k) + cos(1+i+j)] + 1/2v.
To evaluate the line integral of the vector field F = sin(x)i + y√tj + zk along the curve r(t) = ti + tj + tk, where t is in the range [1, 1], follow these steps:

1. Differentiate r(t) with respect to t to obtain the tangent vector dr/dt:
dr/dt = (di/dt)i + (dj/dt)j + (dk/dt)k = 1i + 1j + 1k

2. Write the vector field F in terms of the parameter t by substituting x = t, y = t, and z = t:
F(t) = sin(t)i + t√tj + tk

3. Compute the dot product F(t)⋅(dr/dt):
F(t)⋅(dr/dt) = [sin(t)i + t√tj + tk]⋅[1i + 1j + 1k] = sin(t) + t√t + t

4. Evaluate the line integral ∫(CF. dr) over the range [1, 1]:
Since the integral range is [1, 1], the result of the integral will be 0, as there is no difference in the range.

So, the line integral of the given vector field F along the curve r(t) is 0.

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The given statement "if you try to match a slope and an intercept at the same time, their mistakes will be related" is TRUE.

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis.

This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y.

These points satisfy x = 0 because of this.

The errors of a slope and an intercept will be connected if you fit them simultaneously.

By changing Y to 0 in the equation and figuring out X, you can always determine the X-intercept.

Similarly, by putting X to 0 in the equation and solving for Y, you can always determine the Y-intercept.

Therefore, the given statement "if you try to match a slope and an intercept at the same time, their mistakes will be related" is TRUE.

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James' total earnings would be $51.25 if he worked 5 hours.

The equation that correctly relates James' total earnings, d, to the number of hours he worked, h, can be expressed as:

d = 10.25h

In this equation, "d" represents James' total earnings, and "h" represents the number of hours he worked. The equation states that the total earnings, "d," can be determined by multiplying the hourly rate of $10.25 by the number of hours worked, "h."

For each hour James worked, he earned $10.25, so to find his total earnings, we multiply his hourly rate by the number of hours he worked. This equation allows us to calculate his total earnings based on the number of hours he worked.

For example, if James worked 5 hours, we can substitute "h" with 5 in the equation:

d = 10.25 * 5

d = 51.25

Hence, James' total earnings would be $51.25 if he worked 5 hours.

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Answer:

The linear equation is y = 450 - 30 x, where y is the number of pages

Lourdes has left to read after x days

Step-by-step explanation:

Each day, Lourdes reads 30 pages of a 450-page book

- We need to write a linear equation to represent the number of pages

 Lourdes has left to read after x days

∵ Lourdes reads 30 pages each day

∵ Lourdes will read for x days

∴ The number of pages Lourdes will read in x day = 30 x

- The left pages will be the difference between the total pages of the

 book and the pages Lourdes read

∵ The book has 450 pages

∵ Loured will read 30 x in x days

∴ The number of pages left = 450 - 30 x

- Assume that y represents the number of pages Lourdes has left

 to read after x days

∴ y = 450 - 30 x

The linear equation is y = 450 - 30 x, where y is the number of

pages Lourdes has left to read after x days

Answer:

pendrive, memory, chip

the location of the g point is 3.

Two ratios are set to be equal in an equation called a proportion. You might express the ratio as 1: 3 for instance, if there is 1 boy and 3 girls.

Point G Partition the directed line segment form d to f into a

5:4 ratio

so,

g - d = (5/9) x (f - d)

We have that d = -2 and f = 7, Therefore

g - d = (5/9) x (f - d)

g + 2 = (5/9) x (7 + 2)

g + 2 = 5

g = 3

Therefore the location of the g point is 3.

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Answer: OPTION D

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

1) 9*8=72

2) 8*3=24

3)72-24=48

Answer: The box is large enough to ship the coat.

15000cm to the power of 3>10000cm to the power of 3

Step-by-step explanation:

V box=25x30x20

         =750+20

         =15000cm to the power of 3

So the box is large enough to ship the coat

Answer:

the angle which is equal to its supplement is 90 degree

The area of the top of the rhombus-shaped pastry is 12 cm². To find the area of the top of the rhombus-shaped pastry, we can use the formula for the area of a rhombus, which is equal to half the product of its diagonals.

The area of a rhombus can be calculated by multiplying the lengths of its diagonals and dividing the result by 2. In this case, the horizontal diagonal length is 4 centimeters, and the vertical diagonal length is 6 centimeters.

In this case, the horizontal diagonal length is 4 centimeters, and the vertical diagonal length is 6 centimeters.

To find the area of the top of the rhombus-shaped pastry, we can use the formula for the area of a rhombus.

The area of a rhombus is equal to half the product of its diagonals. In this case, the horizontal diagonal has a length of 4 centimeters, and the vertical diagonal has a length of 6 centimeters.

Using the formula:

Area = (1/2) × (horizontal diagonal) × (vertical diagonal)

Substituting the given values:

Area = (1/2) × 4 cm × 6 cm

= 12 cm².

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Comparing the values of sine and cosine for the two angles, we can see that:-

sin(θ₁) is positive while sin(θ₂) is negative.

cos(θ₁) is negative while cos(θ₂) is positive.

To solve this problem, we first need to plot the points (-2, 3) and (3, -2) on the coordinate plane to form the two terminal sides of the angles of rotation.

To find the values of sine and cosine for each angle, we can use the coordinates of the points where the terminal sides intersect the circle centred at the origin.

For angle θ₁:

x-coordinate of a point on circle = -2

y-coordinate of the point on circle = 3

Using the Pythagorean theorem, we can find the length of the hypotenuse of the right triangle formed by the terminal side of angle θ1 and the x-axis:

h² = (-2)²+ 3²

h² = 13

h = √13)

Therefore, we can find the values of sine and cosine for angle θ1 as follows:

sin(θ1) = y-coordinate / hypotenuse = 3 / √(13)

cos(θ1) = x-coordinate / hypotenuse = -2 / √(13)

For angle θ₂:

x-coordinate of a point on a circle = 3

y-coordinate of the point on the circle = -2

Using the Pythagorean theorem, we can find the length of the hypotenuse of the right triangle formed by the terminal side of angle θ₂ and the x-axis:

h₂ = 3₂ + (-2)₂

h²= 13

h = √(13)

Therefore, we can find the values of sine and cosine for angle θ2 as follows:

sin(θ₂) = y-coordinate / hypotenuse = -2 / √(13)

cos(θ₂) = x-coordinate / hypotenuse = 3 / √(13)

sin(θ₁) is positive while sin(θ₂) is negative.

cos(θ₁) is negative while cos(θ₂) is positive.

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Based on the provided question, it seems like you are asking about the most efficient evaluation method, either by hand or using a computer. To determine which method is the most suitable, you need to consider the complexity of the evaluation process and the number of alternatives.

Using a computer is generally faster and more accurate when dealing with large datasets or complex calculations. On the other hand, evaluating by hand may be more suitable for smaller datasets or simpler calculations. It can provide a more hands-on approach, allowing for a deeper understanding of the evaluation process. However, this method is generally more time-consuming and prone to human error.

To select the most appropriate evaluation method, consider the complexity of the task and the available resources. If the evaluation involves a large amount of data or complex calculations, using a computer would likely be the most efficient choice. However, if the task is relatively simple or involves a smaller dataset, evaluating by hand may suffice. In conclusion, the choice between evaluating by hand or using a computer depends on the complexity of the task and the available resources. Consider these factors to determine the most suitable method.

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Answer:

8.4 cm^3 to the nearest tenth.

Step-by-step explanation:

The ratio of the volumes of the 2 cones is the ratio of the cubes of their radii.

So:

5^3 / 2^3 = 131 / v

v = 2^3 * 131 / 5^3

= 8 * 131 / 125

= 8.384.

The volume of smaller cone is 8.4 cm³

The volume of a cone formula is given as one-third the product of the area of the circular base and the height of the cone. According to the geometric and mathematical concepts, a cone can be termed as a pyramid with a circular cross-section. By measuring the height and radius of a cone, you can easily find out the volume of a cone. If the radius of the base of the cone is "r" and the height of the cone is "h", the volume of cone is given as V = (1/3)πr²h.

By applying Pythagoras theorem on the cone, we can find the relation between volume and slant height of the cone.

We know, h² + r² = L²

⇒ h = √(L² - r²)

where,

h is the height of the cone,

r is the radius of the base, and,

L is the slant height of the cone.

The volume of the cone in terms of slant height can be given as V = (1/3)πr²h = (1/3)πr²√(L² - r²).

Given:

The ratio of the volumes of the 2 cones is the ratio of the cubes of their radii.

Then,

5³ / 2³ = 131 / v

v = 2³ * 131 / 5³

v = 8 * 131 / 125

v = 8.384 cm³

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The options are given as follows:

a. H0: fragrance opinion is not independent of gender; Ha: fragrance opinion is independent of gender

b. H0: gender = fragrance opinion; Ha: gender \(\neq\) fragrance opinion

c. H0: fragrance opinion is independent of gender; Ha: fragrance opinion is not independent of gender

d. H0: gender \(\neq\) fragrance opinion; Ha: gender = fragrance opinion

The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

The answer is option (d).

H0: gender \(\neq\) fragrance opinion

Ha: gender = fragrance opinion

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Answer:

A hexagon

Step-by-step explanation:

A hexagon - - - the allen wrench has 2 hexagonal heads. See attached pic.

The geometric shape that forms the hole that fits an allen wrench is a hexagon, which is a six-sided polygon with straight sides and angles.

The geometric shape hexagon-shaped hole in an allen wrench, also known as a hex key, is designed to fit tightly over the hexagonal socket of a screw or bolt head. A hexagon is a six-sided polygon, meaning it has six straight sides and angles. In the case of an allen wrench, the hexagon has internal angles of 120 degrees and opposite sides that are parallel.

The hexagonal shape of the hole in the wrench allows for a tight and secure fit onto the corresponding hexagonal socket of the screw or bolt head. This design ensures that the wrench can apply a significant amount of torque to the fastener without slipping, which is essential for many applications in construction, mechanics, and other industries.

The use of a hexagonal shape also allows for greater precision and control when turning the screw or bolt, making it easier to achieve the desired level of tightness. Overall, the hexagon is an ideal shape for the hole in an allen wrench due to its strength, stability, and precision.

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I think Mr. Han is around the 60 or 70 age.

I am really sorry that I couldn't answer this problem.  Try starting with 21 and multiply that by 3.  To check if you can do it, add 43 to the number you multiply 3 with.  Again, i am really sorry that i only wrote a hint.  Good luck finding the answer!

Now the age of Mr. Han will be 54 years old.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Let x be the age of Mr. Han and y be the age of Alice.

She found that Han is 36 years older than her. Then the equation will be

x = y + 36     ...1

7 years later, Han will be 3 times as old as her. Then the equation will be

(x + 7) = 3(y + 7)

x = 3y + 14   ...2

From equations 1 and 2, we have

3y + 14 = y + 36

2y = 22

y = 11

Then the value of x will be

x = 11 + 36

x = 47

The age of Mr. Han will be

⇒ 47 + 7

⇒ 54

Now the age of Mr. Han will be 54 years old.

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Answer:  E. square root of 2

We can write that in shorthand as sqrt(2)

sqrt(2) = 1.41421 approximately

======================================================

Explanation:

Step 1)

Add up the values to get 18+19+20+21+22 = 100

Divide by n = 5, since there are 5 items in the list. So 100/n = 100/5 = 20

The sample mean is xbar = 20

--------------

Step 2)

Subtract the mean from each data value

The results we get are: -2, -1, 0, 1, 2

---------------

Step 3)

Square the results from the previous step

The results here are: 4, 1, 0, 1, 4

---------------

Step 4)

Add up those squares from the previous step: 4+1+0+1+4 = 10

Now divide by n = 5 to get 10/n = 10/5 = 2

The result 2 represents the population variance. Applying the square root to the population variance leads to the population standard deviation. So we end up with the final answer of sqrt(2). The answer is choice E.

sqrt(2) = 1.41421 approximately

---------------

Note: if you want the sample standard deviation, then you divide by n-1 = 5-1 = 4, but the other steps are the same as before.

Answer k = 3 + 6x

note that 27 = 3³ and 9 = 3²

27 ×9 to the power 3x  = 3³ × (3²)^3x = 3³ ×  =  

hence k = 3 + 6x

The Projection of v onto w is (-3/2, 3/2).

The projection of v onto w is found by using the formula:proj_w(v) = (v · w / ||w||²) * w

Where v is the vector to be projected, w is the vector onto which we want to project v, and ||w||² is the magnitude of w squared.

To find the projection of v onto w if v = (-5,-2) and w = (1,-1), we first need to calculate the magnitude of w squared.||w||² = 1² + (-1)²= 2

Next, we need to calculate the dot product of v and w.v · w = (-5)(1) + (-2)(-1)= -5 - (-2)= -3

Now, we can use the formula above to find the projection of v onto w.proj_w(v) = (v · w / ||w||²) * w= (-3 / 2) * (1,-1)= (-3/2, 3/2)

Therefore, the projection of v onto w is (-3/2, 3/2).

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A, b and c can do a piece of work in 24, 30 and 40 days respectively. the work is completed in 13 days.

Let's calculate the work done by each person per day:

A completes 1/24 of the work per day.

B completes 1/30 of the work per day.

C completes 1/40 of the work per day.

Let's assume the total work is represented by "W".

When all three, A, B, and C, work together, their combined work rate per day is:

1/24 + 1/30 + 1/40 = (5 + 4 + 3) / 120 = 12/120 = 1/10

This means that when all three work together, they complete 1/10 of the total work per day.

Now, let's calculate the number of days it takes for them to complete the work. Let's represent this number of days by "D".

Since C leaves 4 days before the completion of the work, the remaining work is 1 - 1/10 = 9/10.

We can set up the equation:

(D - 4) * (1/10) = 9/10

Simplifying the equation:

D - 4 = 9

D = 9 + 4

D = 13

Therefore, the work is completed in 13 days.

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Answer:

It’s the last one

Step-by-step explanation:

Did this before on a test

The equation to determine the number of visits, x, Anthony must make to earn a free movie ticket is: 85 + 2.5x = 100.


Anthony receives 85 rewards points just for signing up for the movie theater's points card. He earns 2.5 points for each visit to the movie theater. To determine the number of visits, x, needed to earn a free movie ticket (which requires 100 points), we can set up an equation.

The initial 85 points received when signing up are added to the product of 2.5 points per visit and the number of visits, x.

This sum should equal 100 points, as that is the requirement for a free movie ticket.

The equation to solve for x is therefore 85 + 2.5x = 100. By solving this equation, we can find the number of visits, x, that Anthony needs to make in order to accumulate enough points for a free movie ticket.


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To solve this problem, we can use the concept of rates and the formula:

Rate = Work / Time

Let's denote the rate of work for the first robot as R1 (in units of tasks per minute) and the rate of work for the second robot as R2 (in units of tasks per minute).

We are given that when both robots work together, they can complete the task in 5 minutes. So, their combined rate of work is:

R1 + R2 = 1 task / 5 minutes

We are also given that the first robot working alone can complete the task in 15 minutes. Therefore, its rate of work is:

R1 = 1 task / 15 minutes

Now, we can solve the system of equations:

R1 + R2 = 1/5

R1 = 1/15

To find R2, we substitute the value of R1 into the first equation:

1/15 + R2 = 1/5

To combine the fractions on the left side, we need a common denominator:

(1 + 3R2)/15 = 1/5

Cross-multiplying gives:

5 + 15R2 = 15

Subtracting 5 from both sides:

15R2 = 10

Dividing both sides by 15:

R2 = 10/15 = 2/3

Therefore, the rate of work for the second robot is 2/3 tasks per minute.

To find the time it would take for the second robot to complete the task alone, we can use the formula:

Time = Work / Rate

Time = 1 task / (2/3 tasks per minute) = 3/2 minutes

So, the second robot can complete the task alone in 3/2 minutes, which is equivalent to 1 minute and 30 seconds.

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The expected value of the discrete distribution is given by:

µ = 2.36

It is given by the sum of each value multiplied by it's respective probability.

In this problem, the distribution is as follows, considering the amounts of each chip:

P(X = 1) = 2/11

P(X = 2) = 3/11

P(X = 3) = 6/11

Hence, the expected value is given by:

\(\mu = \frac{2}{11} + 2\frac{3}{11} + 3\frac{6}{11} = \frac{2 + 6 + 18}{11} = 2.36\)

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Answer:

5 hours

Step-by-step explanation:

A service call would have to be 5 hours for both companies to charge the exact same amount.

Answer:

443

Step-by-step explanation:

hib9