when it is 4:00, the hour hand on an analog clock is 120$^\circ$ ahead of the minute hand. how many minutes elapse (to three significant digits) before the minute hand next points in the same direction as the hour hand? 21.82 min

Answer:

b=15

Step-by-step explanation:

8²+b²=17²

b²=225

b=15

To determine if the linear system corresponding to an augmented matrix [a1 a2 a3 b] has a solution, we can check whether the vector b is in the span of the vectors {a1, a2, a3}.

In linear algebra, the augmented matrix represents a system of linear equations. The columns a1, a2, and a3 correspond to the coefficients of the variables in the system, while the column b represents the constants on the right-hand side of the equations. To check if the system has a solution, we need to determine if the vector b is a linear combination of the vectors a1, a2, and a3.

If the vector b lies in the span of the vectors {a1, a2, a3}, it means that b can be expressed as a linear combination of a1, a2, and a3. In other words, there exist scalars (coefficients) that can be multiplied with a1, a2, and a3 to obtain the vector b. This indicates that there is a solution to the linear system.

On the other hand, if b is not in the span of {a1, a2, a3}, it implies that there is no linear combination of a1, a2, and a3 that can yield the vector b. In this case, the linear system does not have a solution.

Therefore, determining whether the vector b is in the span of {a1, a2, a3} allows us to determine if the linear system corresponding to the augmented matrix [a1 a2 a3 b] has a solution or not.

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Answer:

sometimes

Step-by-step explanation:

greetings that person is wrong the answer is always

2/5 of an hour long will they take to mow the lawn together.

Additive identity is the value when added to a number, results in the original number. When we add 0 to any real number, we get the same real number. For example, 5 + 0 = 5. Therefore, 0 is the additive identity of any real number.

This is easy to do when you realize the the speed of mowing is additive. This is if John mows at 1 lawn / (2/3) hour and George mows at 1 lawn /  1hour, the total speed of mowing is:

1 / (2/3) + 1 = 3/2 + 1 = 5/2

=> 5/2 of lawn per hour

Now, the time is calculated as the amount of lawn divided by the speed:

1 lawn / (5/2 lawn/hour) = 2/5 hour

2/5 of an hour.

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The given question is incomplete, complete question is;

If Jorge can mow the lawn in 2/3 of an hour and George can mow the lawn in 1 hour, how long will they take to mow the lawn together? 2/5 of an hour 3/5 of an hour 3/4 of an hour

The gas station serves 16 vehicles per hour, and 72 vehicles arrive in 4 hours. The vehicles will spend 4.50 hours at the gas station.



To find the total time the vehicles will spend at the gas station, we need to calculate the total number of vehicles that arrive and then divide it by the rate at which the gas station serves vehicles.

Given:

Arrival rate: 18 vehicles per hour

Service rate: 16 vehicles per hour

Time: 4 hours

First, let's calculate the total number of vehicles that arrive during the 4-hour period:

Total number of vehicles = Arrival rate * Time

                      = 18 vehicles/hour * 4 hours

                      = 72 vehicles

Since the gas station can serve 16 vehicles per hour, we can determine the time it takes to serve all the vehicles:

Time to serve all vehicles = Total number of vehicles / Service rate

                         = 72 vehicles / 16 vehicles/hour

                         = 4.5 hours

Therefore, the vehicles will spend 4.5 hours at the gas station. Rounded to 2 decimal places, the answer is 4.50 hours.

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Answer:

Step-by-step explanation:

b) Diameter of Mercury = 4.88 * 10³ = 4.88 * 1000 = 4880 km

Radius of Mercury = 4880÷ 2 = 2440 km

c) Mass of Jupiter = 1.898 * 10²⁷ = 18.98 * 10²⁶

Mass of Saturn = 5.68 * 10²⁶

Difference  = 18.98 * 10²⁶ - 5.68*10²⁶

                   = (18.98 - 5.68) * 10²⁶

                   = 13.30 * 10²⁶

                   = 1.330 * 10²⁷

Answer The small triangles each have an area of 12m^2 and the big rectangle had an area of 80m^2. This would mean that the combined area is 104m^2

Step-by-step explanation: The rectangle shape can be found by multiplying 8 by 10 to get 80m^2. The two triangles can be found by multiplying 4 (half of 8) by 6 and then dividing it by two. This would mean that the small triangles each have an area of 12.

Answer:

Angles 2, 3, 6, and 7 will be the same with 41 degrees!

Angles 1, 4, 5, and 8 are the same with 139 degrees!

Step-by-step explanation:

Opposite angles are the same so that makes angles 2, 3, 6, and 7 the same at 41 degrees!

The same rule applies to angles 1, 4, 5, and 8 and we have to subtract!

180 - 41 = 139 degrees!

Have an amazing day!!

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Kirsten had to drive 5 miles north, and then turn to the east for 12 miles where she found a nice parking spot at the Movie Theater :)

If the image represents the road she drove, she did travel 5 + 12 miles, thus she finally travelled 17 miles.

2580 grams is 2.58 kilograms

Answer:

y < -7

Step-by-step explanation:

add 4 to both sides to get y<-7

Answer:

add 4 to both side

y-4+4>-11+4

y>-7

It looks like you did a great job solving the equation, and your final answer is correct. Here is a brief summary of the steps you took:
your final answer is correct\(: x = 1 - (pm - pn) / 4t\)

Mathematics has been classified into many branches. Arithmetic is the branch that handles numbers and their operations. Arithmetic taught us addition, subtraction, multiplication and divisions of two or more numbers. Geometry is all about shapes and their construction using different tools like a compass, ruler and pencil. Algebra is another interesting branch where we express our daily life situations in numbers and letters (variables).
1. Expanded the equation: \(12 - tx^2 - pn = 12 - t(2 - x)^2 - pm\)
2. Simplified: \(12 - tx^2 - pn = 12 - 4t + 4tx - tx^2 - pm\)
3. Eliminated the 12 and tx^2 terms: -pn = -4t + 4tx - pm
4. Rearranged the equation:\(-4tx = -4t + pn - pm\)
5. Divided both sides by \(-4t: x = 1 - (pm - pn) / 4t\)
So, your final answer is correct\(: x = 1 - (pm - pn) / 4t\)

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Given information:v.magnitude = 3v makes an angle with positive x-axis.The angle made by v with the positive x-axis is 150°.v is in the direction 4i + 3j.Solution: We have to find the component form of v.

Let's represent the given information on a graph:From the above graph, we can say that v makes an angle of 30° with negative y-axis.The angle between v and the negative y-axis = 180° - 30° = 150°Let's find the magnitude of v:Let v be (x,y).v = x i + y j

Magnitude of v, |v| = √(x² + y²) = 3 Therefore, x² + y² = 3² = 9 ...(1)Angle made by v with negative y-axis, θ = 30°∴ The angle made by v with positive x-axis, α = 150° - 90° = 60°sinθ = y/|v|y = 3 sinθ = 3 sin(30°) = 1.5From equation (1),x² + 1.5² = 9x² = 9 - 2.25 = 6.75x = ± √6.75Since v makes an angle of 150° with the positive x-axis, the vector v lies in the second quadrant. Therefore, x is negative.So, x = - √6.75 and y = 1.5Hence, the component form of v is:(- √6.75, 1.5).Thus, the component form of v is (- √6.75, 1.5).

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Step-by-step explanation:

The compound inequality that represents the values at which Jason will sell his stocks is:

x < 8 OR x > 25

This means that Jason will sell his stocks if the value per share is less than $8 or greater than $25.

Answer:

-1

Step-by-step explanation:

The formula for finding a slope is: m = (change in y)/(change in x)

Find the change in each value

Y: 9 - 6 = 3

X: -3 - 0 = -3

Input the values

m = 3/-3

m = -1

I would start this problem by setting up a table.

In the left column, we will have our x values

and in the right column, we have our y values.

Put our first ordered pair on the top and second on bottom.

We can see the y values go from 6 to 9 so change in y is 3.

The x values go from 0 to -3 so change in x is -3.

The slope is equal to the rate of change or change in y / change in x.

So our slope is 3/-3 of -1.

Answer:

73 degrees

Step-by-step explanation:

Alternate interior angles: 123 is angle ACS, so that means PAC has the same value as this because PQ and RS are parallel.

So, now just subtract 50 from 123 to get x.

If A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6. If the rank of A is less than 6, then the dimension of the row space will be less than 6.

The row space of a matrix is the span of its row vectors. Therefore, the dimension of the row space is equal to the number of linearly independent rows of the matrix.

For a 9x6 matrix A, the largest possible dimension of the row space is 6. This is because there can be at most 6 linearly independent rows in a 9x6 matrix. If there were more than 6 linearly independent rows, then the matrix would have rank greater than 6, which is impossible since the maximum rank of a 9x6 matrix is 6.

For a 6x9 matrix A, the largest possible dimension of the row space is also 6. This is because the number of linearly independent rows cannot exceed the number of columns in the matrix.

Therefore, if A has rank 6, then it has 6 linearly independent rows and its row space has dimension 6.

However, if the rank of A is less than 6, then the dimension of the row space will be less than 6.

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a) The magnitude of Pˉ is P.  b) The direction cosine of Pˉ with respect to the x-axis is 110/P.  c) The directional angle of Pˉ with respect to the z-axis is arctan(60/√(110^2+(-0.58P)^2)).

a) To find the magnitude of vector Pˉ, we use the formula for the magnitude of a vector in three dimensions, which is the square root of the sum of the squares of its components.

b) The direction cosine of a vector with respect to a specific axis is the ratio of the component of the vector along that axis to its magnitude. In this case, the x-component of Pˉ is 110, so the direction cosine with respect to the x-axis is 110 / P.

c) The directional angle of a vector with respect to a specific axis can be found using the arctan function. In this case, we use the y-component and z-component of Pˉ to find the angle between Pˉ and the z-axis.

Therefore, the magnitude of Pˉ is given by P, the direction cosine with respect to the x-axis is cos(θ_x), and the directional angle with respect to the z-axis is θ_z.

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It's the 4th option.

Step-by-step explanation:

Corresponding angles are congruent, so x =43. I hope this helps, have a great day!

Answer:

3.2z + 5y  - 70

Step-by-step explanation:

Answer:

Step-by-step explanation:

i need it too :(

Boulder takes 4.13 seconds to reach its maximum height.

The boulder's maximum height is 282.38 feet.

Velocity is a physical quantity that describes the rate of change of an object's position over time. Velocity has both magnitude as well as direction that's why it is a vector quantity.

Given that:

Upward velocity of the boulder = 132 ft/s

Function for the height of the boulder as a function of time, t:

h(t) = -16\(t^{2}\) + 132t + 30

We can find the maximum height of the boulder and the time it takes to reach that height by finding the vertex of the parabolic function h(t) using the formula:

t = -b/2a

where a = -16 and b = 132.

First, we need to find the time it takes the boulder to reach its maximum height, t:

t = -b/2a = -132/(2*(-16)) = 4.125 seconds

So, it takes the boulder 4.125 seconds to reach its maximum height.

Next, we need to find the maximum height of the boulder, h:

h = h(t) = -16t^2 + 132t + 30 = -16(4.125)^2 + 132(4.125) + 30 = 282.375 feet

So, the boulder's maximum height is 282.375 feet.

Rounding to the nearest hundredth, the time it takes the boulder to reach its maximum height is 4.13 seconds and the boulder's maximum height is 282.38 feet.

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Answer:

A(4,0) B(4,4)

Step-by-step explanation:

graph the points it easy put them together- AB(4,4)

Answer:

c. y = 2/3x + 6

Step-by-step explanation:

If you look closely, the line goes up two and right three so the slope is 2/3. The 6 represents the y intercept.

Answer:

Yes

Step-by-step explanation:

Answer:  yes is the answer bro hopefully this helps you

Step-by-step explanation:

Answer:

x= -2

Step-by-step explanation:

3(2x-4)= -24

expand

6x-12= -24

6x= -24+12

6x= -12

x= -12/6

x= -2

Answer:

x=-2

Step-by-step explanation:

To solve the equation, we must get x isolated on one side of the equation.

\(3(2x-4) = -24\)

3 is being multiplied by 2x -4. The inverse of multiplication is division. Divide both sides of the equation by 3.

\(\frac{3(2x-4)}{3} = -\frac{24}{3}\)

\((2x-4)= -\frac{24}{3}\)

\((2x-4)= -8\)

4 is being subtracted from 2x. The inverse of subtraction is addition. Add 4 to both sides of the equation.

\(2x-4 +4 = -8+4\)

\(2x= -8+4\)

\(2x= -4\)

x is being multiplied by 2. The inverse of multiplication is division. Divide both sides by 2.

\(\frac{2x}{2} =\frac{-4}{2}\)

\(x=\frac{-4}{2}\)

\(x= -2\)

Let's check our solution. Plug -2 in for x and solve.

\(3(2x-4)= -24\)

\(3(2(-2)-4)= -24\)

\(3(-4-4) = -24\)

\(3(-8)= -24\)

\(-24=-24\)

The statement above is true, so we know our solution is correct.

The answer to the equation is x= -2.

The expected size of the largest gap between adjacent cars (as a function of l) is l/(n + 1), and the expected size of the smallest gap between adjacent cars is 2.

Let us consider that cars of length 2 try to park on a length l road. Each minute, a new car parks at a uniformly random spot on the road without crashing into another car or running off the road.

When no more cars fit, the expected size of the largest gap between adjacent cars is l/(n + 1) and the smallest gap is 2.

The expected size of the largest gap between adjacent cars (as a function of l) is l/(n + 1).

Let n be the number of cars parked on the road. Then the total length of the cars parked is 2n.

If the largest gap is a distance g, then the total length of the gaps is l − 2n. Then,gap length:

g (n + 1) ≤ l - 2ng ≤ l − (n + 1)g

Dividing through by (n + 1)g and rearranging:

g ≤ l/(n + 1) (largest gap)g ≥ 2 (smallest gap)

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Answer: 38

Step-by-step explanation:

Answer:

34

Step-by-step explanation:

Answer:

34 customers.

Step-by-step explanation:

57-23=34

The value of the time premium is $100.

According to the statement

we have to find the time premium from the given information.

So, For this purpose, the given information is:

a strike price of $25 when the option price is $2 and the underlying common stock sells for $24

And

Time premium is the amount by which an option price exceeds its intrinsic value. The value of an option beyond its current exercise value representing the option holder's control until expiration, the risk of the underlying asset, and the risk less return.

So, From the given information and the formula

The value of the time premium is $100.

So, The value of the time premium is $100.

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