Nolan drives 15 miles in 30 minutes. How far would Nolan go in 180 minutes?

By using the elimination approach, the system of linear equations x + 2y = 13 and -x + y = 5 may be solved as (3, 8)

In calculus, a linear function is one that of the form y=mx+b. The slope is B, and the y-intercept is m. Since y and x are variables, the previous sentence is frequently referred as a "equation with two variables." Bivariate linear equations are linear equations with two parameters. Linear equations can be found in many places, including 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the structure y=mx+b, where m denotes the slope and b the y-intercept, it is considered to as being linear. A mathematical equation is said to be cubic if its solution has the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

x + 2y = 13

-x + y = 5

In 1

5 - y + 2y = 13

y = 8

- x + 8 = 5

-x = 5 - 8

-x = -3

x = 3 by multiplying the value of x by 2.

By using the elimination approach, the system of linear equations x + 2y = 13 and -x + y = 5 may be solved as (3, 8)

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The equation that can be used to find the number of weeks it will take for Susi and Thuy to have the same amount in their accounts is 50 + 5w = 15 + 12w, where w represents the number of weeks.

In this equation, 50 represents the initial amount Susi has in her account, and 5w represents the additional amount she adds each week. Similarly, 15 represents the initial amount Thuy has in her account, and 12w represents the additional amount she adds each week.

To find the number of weeks when both accounts will have the same amount, we set the two expressions equal to each other: 50 + 5w = 15 + 12w.

By solving this equation, we can determine the value of w, which represents the number of weeks it will take for Susi and Thuy to have the same amount in their accounts.

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The answer to the question "Is the dependent variable continuous?" would be a. Yes, it is measured in interval form.

The question asks whether the dependent variable is continuous. In this context, a continuous variable is one that can take on any value within a certain range. The options provided are: (a) Yes, it is measured in interval form, (b) No, it is measured in variance form,

(c) Yes, it is measured, and (d) The error occurs when you reject the correct hypothesis during a hypothesis test. Among these options, the most appropriate answer is (a) Yes, it is measured in interval form.

This indicates that the dependent variable is continuous and can be measured on an interval scale, where the values can have a meaningful order and the differences between them are consistent.

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The parametric equations and symmetric equations of the line are:

(x, y, z) = (-2, 3, 5) + t(u, v, w)

(x + 2) / u = (y - 3) / v = (z - 5) / w

Let's first consider the case where the line is parallel to a given vector.

If the line is parallel to a vector v = (a, b, c), then any point on the line can be represented as:

(x, y, z) = (x₀, y₀, z₀) + t(a, b, c)

where (x₀, y₀, z₀) is a point on the line and t is a parameter that varies over all real numbers.

Now, suppose we want the line to pass through a point P = (-2, 3, 5) and be parallel to a vector v = (u, v, w). Then we can choose P as our point on the line and write:

(x, y, z) = (-2, 3, 5) + t(u, v, w)

These are the parametric equations of the line.

To find the symmetric equations of the line, we can eliminate the parameter t by solving for it in each equation:

x + 2 = tu

y - 3 = tv

z - 5 = tw

Then, we can eliminate t by setting the ratios of these equations equal to each other:

(x + 2) / u = (y - 3) / v = (z - 5) / w

These are the symmetric equations of the line.

Alternatively, if the line is parallel to another line L that passes through a point Q = (x₁, y₁, z₁) and has direction vector d = (d₁, d₂, d₃), then any point on the line can be represented as:

(x, y, z) = (x₁, y₁, z₁) + t(d₁, d₂, d₃)

where t is a parameter that varies over all real numbers.

To find the parametric equations and symmetric equations of the line that passes through P and is parallel to L, we can set Q = P and d = v, giving:

(x, y, z) = (-2, 3, 5) + t(u, v, w)

(x + 2) / u = (y - 3) / v = (z - 5) / w

These are the parametric equations and symmetric equations of the line.

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a) No length that is the same as AD.

b) No length that is the same as BC.

a) To find a length definitely the same as AD, we need to identify a line segment that shares the same properties with AD.

Since the circle is centered at O, and A and D are points on the circle, we can conclude that AD is a chord of the circle. Another chord in the circle is BC, as both B and C are points on the circle as well.

However, without further information about the circle or the angles, we cannot determine if AD and BC are definitely the same length.

So, there is no length that is definitely the same as AD.
b) To find a length definitely the same as BC, we need to identify a line segment that shares the same properties with BC. As mentioned earlier, BC is a chord of the circle.

Another chord in the circle is AD, but as stated previously, we cannot determine if AD and BC are definitely the same length without additional information.

So, there is no length that is definitely the same as BC.

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Answer:

94/45

Step-by-step explanation:

(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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The null hypothesis would be that the mean time between failures has not increased, and it remains the same.

A null hypothesis is a statement about the population that a researcher wishes to test. It is used to evaluate the significance of the results of an experiment. It is often abbreviated as H0 in statistics.A null hypothesis always assumes that the population's statistical parameters are unchanged from a previous study or a known value.

A researcher may reject or fail to reject the null hypothesis based on the results of the test. If the null hypothesis is not rejected, it does not indicate that the alternative hypothesis is accurate. Rather, it demonstrates that there is not enough statistical evidence to support the claim made by the alternative hypothesis.

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Displacement is the length of the straight line drawn from an object’s initial position to the object’s final position

The term "displacement" refers to a change in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial position to the ending position. For instance, if an object shifts from position A to position B, its position changes.

If an object moves with respect to a reference frame, such as when a passenger moves to the back of an airplane or a professor moves to the right with respect to a whiteboard, the object's position changes. This change in location is described as displacement.

The displacement is the shortest distance between an object's initial and final positions. Displacement is a vector. It is visualized as an arrow that points from the initial position to the final position, indicating that it has both a direction and a magnitude.

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Answer:

Solution = (-8,-28)

Step-by-step explanation:

The largest taco contained approximately 1 kg of onion for every 6. 6 kg grilled teak. then Amount of grilled steak used: 6.6 (79.17) = 538.356 kg

What is a unit amount in math?

When a price is expressed as a quantity of 1, such as $25 per ticket or $0.89 per can, it is called a unit price. If you have a non-unit price, such as $5.50 for 5 pounds of potatoes, and want to find the unit price, divide the terms of the ratio

1 k + 6.6 k = 617.3

Where “k” is a constant value, a multiplier.

Solving for k:

7.8 k = 617.3

k = 617.3 /7.8  

k= 79.17

So:

Amount of onion used:

1 (79.17) = 79.17 kg

Amount of grilled steak used:

6.6 (79.17) = 538.356 kg

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The total mass of the paperclips in the box is 6. 144 × 10^1 mg. Option C

1 mass of a paperclip = 8.0 × 10−4 mg

But there are 7.68 × 104 paperclips = x mg

cross multiply

x = 7.68 × 104 × 8.0 × 10−4 mg

Multiply through

x = 61. 44 × 10^ 4 -4

x = 61. 44 × 1

x = 6. 144 × 10^1 mg

Thus, the total mass of the paperclips in the box is 6. 144 × 10^1 mg. Option C

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Answer:

x=26

Step-by-step explanation:

Simplify both sides of the equation.

16+

x

13

=18

16+

1

13

x=18

1

13

x+16=18

Step 2: Subtract 16 from both sides.

1

13

x+16−16=18−16

1

13

x=2

Step 3: Multiply both sides by 13.

13*(

1

13

x)=(13)*(2)

x=26

Answer:

B=28

Step-by-step explanation:

The speed of train A and train B will be 50 miles per hour and 25 miles per hour. Train A traveled 50 miles less than train B. And graph B is steeper than the graph of train A.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

From the graph, train A travels 150 miles in 3 hours and train B travels 100 miles in 4 hours.

The speed of train A is given as,

S = 150 / 3

S = 50 miles per hour

The speed of train B is given as,

S = (125 - 25) / 4

S = 25 miles per hour

The speed of train A and train B will be 50 miles per hour and 25 miles per hour.

Train A traveled 50 miles less than train B. And graph B is steeper than the graph of train A.

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Answer:

0.354882mL

I don't know how much they let you/want you to round it up.

Step-by-step explanation:

1 cup = 236.588mL

236.588 x 1.5 = 354.882mL

354.882/1000 to convert mL to L

0.354882mL

Answer:

A trapezoid is a quadrilateral, meaning 4 sides. It is similar to a square but with longer lines. It also has 1 pair of parallel lines, the other pair are not.

Step-by-step explanation:

hope this helps :)

In the given set of figures, figures, 2, 3, and 4 are trapezoids.

Since we know that,

A trapezoid is a four-sided polygon with two parallel sides that are usually called bases. The other two sides are called legs.

Trapezoids have a wide range of applications in mathematics, especially in geometry.

They can be used to calculate the area and perimeter of various objects.

Trapezoids can also be classified as isosceles or scalene, depending on whether or not the legs have the same length.

To determine whether a given figure is a trapezoid,

it is important to check for a few specific features.

The first step is to ensure that the figure has four sides - this is a prerequisite for it to be considered a trapezoid.

Once this is established, the next step is to look for two parallel sides.

If there are two sides that are parallel, then the figure could be a trapezoid.

The next step is to check the angles formed by the sides.

If the two non-parallel sides slant towards each other, then the figure is a trapezoid.

However, if they slant away from each other, it is not a trapezoid.

Finally, it is important to make sure that the two non-parallel sides are of different lengths, as a trapezoid must have two parallel sides of different lengths.

By following these steps, we can easily recognize whether a given figure is a trapezoid or not.

Hence figures, 2, 3, and 4 are trapezoids.

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The complete question is attached below:

Given:

P = $10000

r= 5%

Find:

we have to find the time for which initial bank deposit of $10,000 grow to $23,750 at 5% annual compound interest.

Explanation:

The formula for compound interest is

First, convert R as a percent to r as a decimal

r = R/100

r = 5/100

r = 0.05 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(23,750.00/10,000.00) / ( 1 × [ln(1 + 0.05/1)] )

t = ln(23,750.00/10,000.00) / ( 1 × [ln(1 + 0.05)] )

t = 17.729 years

Summary:

The time required to get a total amount of $23,750.00 with compounded interest on a principal of $10,000.00 at an interest rate of 5% per year and compounded 1 times per year is 17.729 years.

(about 17 years 9 months)

Answer:

B and C

Step-by-step explanation:

Jane found multiples of 8 instead of factors and should've gotten 1, 2, 4, and 8 as her answer.

Hope this helps :)

Answer:

B& C

Step-by-step explanation:

hope it helps

Answer: The angle C measures 120 degrees.

Step-by-step explanation:

For a polygon of n side, the sum of internal angle, in degrees  is given by:

S = (n - 2) x 180

Parallelogram

4 sides, so

S = ( 4 - 2) * 180 = 360

Two pair of equal angles

B and D measure 60

A and C measure x. so

2ₓ + 2 * 60 = 360

2× = 240

× = 240/2

× = 120

The angle C measures 120 degrees

Hope this helps! :)

The man worked approximately 10 hours of overtime that week.

Let's assume the man worked "x" hours of overtime.

Regular hours = 36

Overtime hours = x

Total hours worked = Regular hours + Overtime hours = 36 + x

Regular pay = $10.49 per hour

Overtime pay = $15.74 per hour

Total pay = Regular pay + Overtime pay

$535.04 = ($10.49 × 36) + ($15.74 × x)

Now, let's solve this equation to find the value of x:

535.04 = $377.64 + (15.74x)

Subtracting 377.64 from both sides:

535.04 - 377.64 = 15.74x

157.40 = 15.74x

Dividing both sides by 15.74:

157.40 / 15.74 = x

x ≈ 10

Therefore, the man worked approximately 10 hours of overtime that week.

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The prefrontal cortex is responsible for regulating higher cognitive functioning of the brain.

What is prefrontal cortex?

In the frontal lobe of the brain, there is a structure called the prefrontal cortex. It carries out cognitive functions like memory, attention, planning, flexibility, etc. It is regarded as the region of the brain that develops the least quickly

Prefrontal cortex is located in the frontal lobe.

The prefrontal cortex is responsible for regulating higher cognitive functioning of the brain.

Mid-twenties is when it reaches maturity. This explains why teenagers are more likely to establish harmful behaviours than younger kids and why adults are better at planning and thinking. An attention deficit and trouble remembering details can be brought on by prefrontal cortex (PFC) damage. Moreover, it may result in psychological changes, a diminished capacity for feeling, and bodily impairments associated with daily activities.

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Answer:

Step-by-step explanation:

When doing synthetic division, if the remainder is zero, we know that the divisor is a root of the polynomial.  If the remainder is not zero, the remainder is the function vaue for that divisor.

The area of the rectangular pasture is found to be 80,000 ft².

Given:

Let the pasture's rectangular length be l feet.

Given that the rectangular pasture's length being 200 feet longer than its breadth, its width must be w = l200 feet.

The pasture's boundary is;

2(l + w) = 1200

2(l + l - 200) = 1200

2l - 200 = 600

l = 400 feet

Width; w = l - 200

w = 400 - 200 = 200 feet

Rectangular area;

A = l x w

A = 400 x 200

A = 80,000 ft²

Thus, the area of the rectangular pasture is found to be 80,000 ft².

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The velocity vector of the path is (-2sin(2t), -4, 0).

To determine the velocity vector of the path (cos(2t), 7-4t, -7), we need to take the derivative of each component with respect to time:

dx/dt = -2sin(2t)
dy/dt = -4
dz/dt = 0

So the velocity vector is (dx/dt, dy/dt, dz/dt) = (-2sin(2t), -4, 0). However, since we are not given a specific value of t, we cannot simplify this any further. Therefore, the velocity vector of the path is (-2sin(2t), -4, 0).

The velocity vector gives us information about the direction and magnitude of the movement of an object along a path. In this case, the object moves with a changing horizontal component and a constant vertical component.

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a) √2 t |1, -1>

b ) t√0 |0, 1>=0

c) 2t² |1, -1> are the eigenstates of S² with the appropriate eigen value.

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes by a scalar factor when the linear transformation is applied to it. The associated eigenvalue, generally indicated by lambda, is the factor by which the eigenvector is scaled.

Eigenvalues and eigenvectors play an important role in the analysis of linear transformations. The prefix eigen- comes from the German word eigen, which means "property," "characteristic," or "own."

a) S- |1,0>= t√(1+0)(1-0+1) |1, 0-1>

=t√2 |1, -1>

=√2 t |1, -1>

∴S±(s, m>=t√(s±m)(s±m+1) |s, m±1>

b) S₊ |0, 0>= t√(0-0)(0+0+1) |0, +1>

=t√0 |0, 1>=0

S₋ |0, 0>=t√(0+0)(0-0+1_) |0. -1>

c) S² |1, 1>= 1(1+1)t² |1, 1>

=2t² |1, -1>

∴ S² |s, m>=s(s+1)t² |s, m>

Hence, |1, -1> and |1, -1> are eigen function of S² with eigen value 2t²s.

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Answer:

2n+7

Step-by-step explanation:

First lets find the common difference which is 2, now we can use this formula to find the nth term.

an = a1 + (n - 1 ) d

an= 9+(n-1)2

=9+2n-2

=2n+7

To check let's insert n=5, 2(5)=10+7=17.

15+2=17!

The equation of the magnitude of the force applied at the back of otter is F is (P+P0)A F is ( P + P 0 ) A .

The amount that encapsulates the force's power is known as its magnitude. Consider the following scenario: the force is 10 N in the east. The direction is indicated by "towards east," while the force is indicated by "10." Magnitude may be thought of as simply the "value" or "amount" of any physical quantity.

The surface area of the otter's back is A = 0.55 m2.

The fluid pressure at the depth of the otter is P = 11500 Pa.

Thus, the equation of the magnitude of the force applied at the back of otter is F=(P+P0)A F = ( P + P 0 ) A .

The complete question is

An otter is swimming in the deep area of his tank at the zoo. The surface area of the otter's back is A = 0.55 m2. The fluid pressure at the depth of the otter is P = 11500 Pa.

Write an equation for the magnitude of the force F on the back of the otter in terms of the pressure P and the atmospheric pressure P0.

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