Three pigs entered a race around a track. Piggly takes 6 minutes to run one lap. Piglet takes 3 minutes
to run one lap and it takes Wiggly 5 minutes to run one lap. If all three pigs begin the race at the same
time, how many minutes will it take for all three pigs to be at the starting point again?

What is the LCM

Answer:

At the end of first 12 hours = 22.5mg

At the end of the first day = 45mg

At the end of the tenth day = 450mg

Step-by-step explanation:

Hello,

Sophia's doctor prescribed 500mg of drug for her every 12hrs.

At the end of 12 hours, she found out she has 4.5% of the drug in her blood.

What is the amount of the drug in her blood after 12 hours?

After 12 hours = 4.5 / 100 = x / 500mg

x = (4.5 × 500) / 100

x = 22.5mg

At the end of the first 12 hours, she has 22.5mg of the antibiotic in her body.

2. At the end of the second dose, she has

22.5mg + 22.5mg = 45mg of the drug in her body

3. at the end of the third dose, she has (22.5 + 22.5 + 22.5)mg in her body = 67.5mg

4. At the end of the fourth dose, she has (22.5 + 22.5 + 22.5 + 22.5)mg in her body = 90mg

Since 1 day contains 24hrs = 2 × 12hrs

The amount of drug present in her body at the end of the first day = (22.5 + 22.5)mg = 45mg

Assuming the concentration of the drug does not decrease over the course of the 10 days, there's an increase of 45mg of the antibiotic in her body every day

First day = 45mg

Second day = 45mg × 2 = 90mg

Third day = 45mg × 3 = 135mg

Fourth day = 45mg × 4 = 180mg

Fifth day = 45mg × 5 = 225mg

Sixth day = 45mg × 6 = 270mg

Seventh day = 45mg × 7 = 315mg

Eighth day = 45mg × 8 = 360mg

Ninth day = 45mg × 9 = 405mg

Tenth day = 45mg × 10 = 450mg

At the end of the tenth day, the amount of antibiotic present in her blood would be 450mg

Answer:

2x - 8 = 12  has the same solution as 12/x-4 = 2

Step-by-step explanation:

They both equal 10

The length, breadth and height will be 78 cm, 78cm, 78cm each.

let consider the length = l

breadth = b

height = h

we are provided that

l + b + h = 234cm .......(1)

Also we have to maximize the volume , provided length is equal to breadth

∴ eqn (1) becomes

2b + h = 234

h = 234 - 2b

also ,

volume(v) = lbh

v = b²(234 - 2b)

v = b²234 - 2b³

now to maximize the volume we take the first derivative of the volume wrt 'b' and place it equal to zero. ( lagrange method )

i.e. d( v)/db = 0

∴  468b - 6b² = 0

 6b² - 468b = 0

6b( b - 78 ) = 0

∴  b = 78 cm

now as length = breadth

l = b = 78 cm

also putting this value in eqn (1)

h = 234 - 2b

h =  78 cm

So , the dimensions will be equal and will be 78cm , 78cm, 78cm each .

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In conclusion, we have shown that the norms of U+αV and V+αU are equal. This result holds for any real number α and any unit vectors U and V.

To prove that ∥U+αV∥=∥V+αU∥, we will use the definition of vector norms and properties of vectors.

Let's start by calculating the norm of U+αV:
∥U+αV∥ = sqrt((U+αV)·(U+αV))     (1)

Expanding the dot product in equation (1):
∥U+αV∥ = sqrt(U·U + 2αU·V + α²V·V)     (2)

Similarly, let's calculate the norm of V+αU:
∥V+αU∥ = sqrt((V+αU)·(V+αU))     (3)

Expanding the dot product in equation (3):
∥V+αU∥ = sqrt(V·V + 2αV·U + α²U·U)     (4)

Now, we will show that equations (2) and (4) are equal by comparing their components:

U·U = V·V (as U and V are unit vectors, their norms are both equal to 1)

2αU·V = 2αV·U (dot product is commutative)

α²V·V = α²U·U (as U·U = V·V = 1, α²V·V = α²U·U)

Therefore, equation (2) is equal to equation (4). This proves that ∥U+αV∥=∥V+αU∥.

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Answer:

Abbey lane is parallel with brittney drive

collin street is perpendicular with brittney drive

Doltan road is parallel with abbey lane

Edward street is perpendicular to doltan road

From the given conditions the map can be constructed in many ways,

we can construct the map as,

Answer:

He plans to drive it every day to work. The equation to the data is y = 20x + 30,000. How many miles does this car have when Mr. Dash bought .-by-step explanation:

Answer:

\(x^2 - 8x + 7 = 0\)

Step-by-step explanation:

Let the boy's present age be x.

Let his dad's present name be y.

Last year, his dad was 8 times as old as him. Subtract one year from each their ages and multiply the son's age by 8:

(y - 1) = 8(x - 1) ______ (1)

Now, his dad's age is the square of his age:

y = \(x^2\) _________(2)

From (1):

y = 8x - 8 + 1

y = 8x -7

Put this in (2):

\(8x - 7 = x^2\\\\=> x^2 - 8x + 7 = 0\)

This problem has been represented in the form of a quadratic equation.

Answer:

V=1080

Step-by-step explanation:

It's simple enough.  Just do LxWxH! :D

\((12)(15)(6)\)

\((12)(90)\)

\(1080\)

Therefore, the estimated average length of the line is 3 customers.

We can approach this problem by using the M/M/1 queueing model, which assumes a Poisson arrival process, an exponential service time distribution, and a single server.

In this case, the arrival rate (lambda) is 10 customers per hour, the service rate (mu) is 5 customers per hour (since the average servicem time is 14 minutes or 0.2333 hours), and there is one server.

The utilization factor (rho) is given by rho = lambda / mu = 10 / 5 = 2, which is greater than 1. This means that the system is not stable, and the queue will grow indefinitely.

To find the average length of the line, we can use Little's Law, which states that the long-term average number of customers in a stable system is equal to the long-term average arrival rate multiplied by the long-term average time spent in the system:

L = lambda * W

where L is the average number of customers in the system, lambda is the arrival rate, and W is the average time spent in the system.

In this case, since the system is not stable, we cannot use Little's Law directly. However, we can still estimate the average length of the line as follows:

Let's assume that the queue is at its steady-state when there are N customers in the system (i.e., being served plus waiting in the line). Then, the average length of the line (Lq) is:

Lq = N - 1

since one customer is being served and the remaining N-1 customers are waiting in the line.

The steady-state condition requires that the arrival rate equals the departure rate, which is the service rate in this case. Therefore, we can use the following formula to estimate N:

N = lambda / (mu - lambda)

Plugging in the values, we get:

N = 10 / (5 - 10) = -2

This negative value indicates that the system is not stable, and there are more customers arriving than the system can handle. However, we can still estimate the average length of the line as:

Lq = |N - 1| = |-2 - 1| = 3

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As per definition

In. a function every domain has an unique range of it

Here

f(10) has two corresponding values hence it's not a function

Answer:

18/5

Step-by-step explanation:

hope this helps!!!

Answer:

x = 5

Step-by-step explanation:

first of all, the two given angles are alternate angles, meaning they are of the same value in terms of degrees so that means we can write it as 21x - 5 = 100 and then we can work out x from here. we can ads 5 to the left to get rid of -5 but then we would also have to add 5 to the right. we are left with 21x = 105 so now we have to divide both sides by 21 to get x = 5 because 105 ÷ 21 = 5 and 21x ÷ 21 = x

The expression which represents the amount of money Chloe owes is

amount = 14c - 3c. where 'c' is the cost per box.

What is a linear equation in one variable?

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable with the form an x + b = 0 are solved using basic algebraic operations.

Chloe ordered 14 boxes and per box 'c' dollars charged

Hence the total amount of money she has to pay is $14c

But 3 of the boxes are damaged so their price will be deducted from the total amount she was supposed to pay:

Now equation will become,

amount = 14c - 3c.

Hence, the expression which represents the amount of money Chloe owes is

amount = 14c - 3c. where 'c' is the cost per box.

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Answer:

one solution

Step-by-step explanation:

3x + 9 = 25x + 14

-3x         -3x

9 = 22x + 14

-14         - 14

-5 = 22x

Answer: 2

Step-by-step explanation:

Answer: 2 is the correct answer

Step-by-step explanation:

The coordinates (2,1) will be on graph but (1,3) is not on graph.

What is a coordinate?

A coordinate is a set of two or more numbers or variables that identify the position of a point, line, or plane in a space of a given dimension. Coordinates are used to pinpoint a particular location, such as a specific point on a map or a specific point in a mathematical equation.

This means that for every 1.5 cups of dried fruit, there is 1 pound of granola. The graph of this proportional relationship would be a line that goes through the origin and has a slope of 1.5. For the point (2,1), the x-coordinate (2) is exactly 1.5 times the y-coordinate (1). This means that if you used 2 cups of dried fruit, you would get 1 pound of granola. Therefore, this point would be on the graph of the proportional relationship, so the answer is Yes. However, for the point (1,3), the x-coordinate (1) is not 1.5 times the y-coordinate (3). This means that if you used 1 cup of dried fruit, you would not get 3 pounds of granola.

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Answer:

Its none of the above because the scale factor is 1/5.

Step-by-step explanation:

But Im not sure I might be wrong. I'm just saying the scale factor is 1/5. Because my homework said the scale factor is 1/5. but I don't know if you doing the same thing. I just wanted to correct ya'll. GOOD DAY! :)

Answer:

give picture

Step-by-step explanation:

Solving inequalities with addition is similar to solving equations with addition in the initial steps, but it differs in the final answer due to the inequality sign. In both cases, you use addition to isolate the variable. However, with inequalities, you must consider the direction of the sign throughout the process.

When solving inequalities with addition, like equations, the goal is to isolate the variable on one side. You use addition to simplify the expression. Begin by treating the inequality like an equation, adding or subtracting the same value to both sides to eliminate constants and isolate the variable.

For example, if you have \(\(2x + 5 > 10\)\), subtract 5 from both sides to get \(\(2x > 5\)\).

Here's where it diverges: since inequalities involve the relationship between two quantities, you need to be mindful of the inequality sign. When you multiply or divide both sides by a negative number, the inequality direction flips.

For example, if you multiply \(\(x < 3\)\) by -2, the sign changes to \(\(x > -6\)\).

Remember, you're looking for a range of values that satisfy the inequality. So, when representing your final answer, use the appropriate inequality sign. For instance, if \(\(3x + 2 \leq 8\)\), after simplifying, you'll have \(\(x \leq 2\)\), indicating that any value of \(\(x\)\) less than or equal to 2 satisfies the inequality.

In summary, while solving inequalities with addition is akin to solving equations with addition in the initial steps, the crucial distinction lies in managing the inequality sign throughout the process and representing the solution as a range of values that satisfy the inequality.

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Complete Question:

How is solving inequalities with addition is similar to or different from solving equations with addition ?

The following are the offered rational exponents in expression form:

• (A) the fourth root's tenth root = \(\sqrt[10]{4}\)

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations. This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: The following rational exponents are expressed in the expression form (Math Operator, Number/Variable, Math Operator): (A) the tenth root of four= \(\sqrt[10]{4}\)

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Answer:

2688 cm³

Step-by-step explanation:

2058×704/539 = 2688 cm³

Answer:

Rational

Step-by-step explanation:

A rational number is a number that can be represented a/b where a and b are integers and b is not equal to 0. Since 7.12467 is an integer or decimal it's rational

So, it takes Hillary and Bill approximately 4.35 hours to complete 1 puzzle together and the speed of the boat in still water is approximately 12 mph.

a. Let's call the time it takes for Hillary and Bill to complete the puzzle together "t." We know that in 5 hours, Hillary can do 1 puzzle, so her rate is 1/5 puzzles per hour. Bill can do 1 puzzle in 7 hours, so his rate is 1/7 puzzles per hour. When they work together, their combined rate is (1/5 + 1/7) puzzles per hour. To find the time it takes them to complete 1 puzzle together, we set up an equation: t = 1 / (1/5 + 1/7). Solving for t, we find that it takes them approximately 4.35 hours to complete 1 puzzle together.

b. Let's call the speed of the boat in still water "s." When the boat is going against the current, its speed is s - 3 mph, and when it is going with the current, its speed is s + 3 mph. We know that it takes the same amount of time for the boat to go 10 miles against the current and 15 miles with the current, so we can set up an equation: 10 / (s - 3) = 15 / (s + 3). Solving for s, we find that the speed of the boat in still water is approximately 12 mph.

Therefore, it takes Hillary and Bill approximately 4.35 hours to complete 1 puzzle together and the speed of the boat in still water is approximately 12 mph.

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Answer:

1/6 is the slope since you have to flip it

Step-by-step explanation:

Answer:

This is perpendicular because it is the reciprical of the other equation

Step-by-step explanation:

y=-6x+4.

the slope intercept form is y=mx+b

m is the slope

m=-6

for the equation to be perpendicular then the slope is the reciprical

Knowing this lets find a line perpendicular to this equation

Equation:

y=1/6x+2/3

or

y=x/6+2/3

The 95% confidence interval for population mean is (19.8, 22.2).

The confidence interval for population mean using the Student's t-distribution is:

CI = x ± \(t_{\frac{\alpha }{2}, (n -1) }\) \(\frac{s}{\sqrt{n} }\)

Given:

x = 22

s = 3

n = 27

α = n - 1 = 26

The critical value of t for α = 0.05 and degrees of freedom, (n - 1) = 19 is:

\(t_{\frac{\alpha }{2} , (n -1)}\) = \(t_{\frac{0.05}{2,19} }\)

            = 2.093

Compute the 95% confidence interval for population mean as follows:

   CI = X + \(t_{\frac{\alpha }{2}, (n -1) }\frac{s}{\sqrt{n} }\)

⇒ CI = 21± 2.093 × 3/√27

        = 21 ± 1.20

        = (22.2, 19.8)

Thus, the 95% confidence interval for population mean is (19.8, 22.2).

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We can prove that if the diagonals of a quadrilateral bisect each other and one angle of a quadrilateral is a right angle, then the quadrilateral is a rectangle.

Let ABCD = a quadrilateral such that its diagonals AC and BD bisect each other at point O.

Let ∠A = a right angle.

Required: Prove that ABCD is a rectangle.

First, quadrilateral ABCD is a parallelogram. Since the diagonals bisect each other, we have:

OA = OC (diagonals bisect each other)

OB = OD (diagonals bisect each other)

Therefore, triangle AOB is congruent to triangle COD by SAS (Side-Angle-Side) congruence:

AB = CD (corresponding sides of congruent triangles)

Next, triangle BOC is congruent to triangle DOA, as:

BC = AD (corresponding sides of congruent triangles)

So, we have proved that opposite sides of quadrilateral ABCD are congruent, which implies that ABCD is a parallelogram.

Next, we show quadrilateral ABCD has right angles at both B and D. Since ∠A is a right angle, we have:

∠BOC = 180° - ∠A (linear pair)

∠BOC = 180° - 90° (since ∠A is a right angle)

∠BOC = 90°

Again, we show that ∠AOD = 90°. So, we have shown that quadrilateral ABCD has right angles at both B and D.

Finally, we can prove that quadrilateral ABCD is a rectangle.

Since ABCD is a parallelogram with opposite angles B and D, both right angles, then ABCD is a rectangle.

Therefore, if the diagonals of a quadrilateral bisect each other and one angle of the quadrilateral is a right angle, then the quadrilateral is a rectangle.

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The real-valued general solution of the system (3) is:

\(y(t) = (c_1 - 2c_2) ~e^t sin(t) + (c_1 + 2c_2) e^t cos(t).\)

The solution to the initial value problem is:

\(y(t) = (c_1 - 2c_2) e^t~sin(t) + (c_1 + 2c_2) ~e^t ~ cos(t),\)

where \(c_1 ~and ~c_2\) are determined by the initial condition equation

\(c_1 + c_2 = 3.\)

We have,

(a)

To determine the real-valued general solution of the system (3) using the complex eigenvector/eigenvalue pair (4), we can use the fact that complex eigenvalues and eigenvectors come in conjugate pairs for real coefficient matrices.

Given the complex eigenvalue λ = 1 + i, its conjugate is λ* = 1 - i.

Similarly, the complex eigenvector v = (2 + 1)i has a conjugate eigenvector v* = (2 - 1)i.

We can write the general solution as a linear combination of the eigenvector and its conjugate:

\(y(t) = c_1 v e^{\lambda t} + c_2 v e^{\lambda t},\)

where \(c_1 ~and~ c_2\) are arbitrary real constants.

Substituting the given values, we have:

\(y(t) = c_1 (2 + 1)i e^{(1 + i)t} + c2 (2 - 1)i * e^{(1 - i)t},\)

Simplifying this expression, we get:

\(y(t) = (c_1 + 2c_2) i ~e^t cos(t) + (c_1 - 2c_2) e^t sin(t),\)

where we used Euler's formula \(e^{ix} = cos(x) + isin(x).\)

So, the real-valued general solution of the system (3) is:

\(y(t) = (c_1 - 2c_2) ~e^t sin(t) + (c_1 + 2c_2) e^t cos(t).\)

(b)

To solve the initial value problem given by (3) and (4) subject to

y(0) = (3), we substitute t = 0 and y(0) = (3) into the general solution obtained in part (a).

At t = 0, we have:

\(y(0) = (c_1 - 2c_2) ~e^0 ~ sin(0) + (c_1 + 2c_2) ~ e^0 ~ cos(0)\\= c_1 + c_2.\)

Setting this equal to the initial condition y(0) = (3), we have:

\(c_1 + c_2 = 3.\)

So, the constants\(c_1 ~and ~c_2\) must satisfy this equation.

Therefore, the solution to the initial value problem is:

\(y(t) = (c_1 - 2c_2) e^t~sin(t) + (c_1 + 2c_2) ~e^t ~ cos(t),\)

where \(c_1 ~and ~c_2\) are determined by the initial condition equation

c_1 + c_2 = 3.

Thus,

The real-valued general solution of the system (3) is:

\(y(t) = (c_1 - 2c_2) ~e^t sin(t) + (c_1 + 2c_2) e^t cos(t).\)

The solution to the initial value problem is:

\(y(t) = (c_1 - 2c_2) e^t~sin(t) + (c_1 + 2c_2) ~e^t ~ cos(t),\)

where \(c_1 ~and ~c_2\) are determined by the initial condition equation

\(c_1 + c_2 = 3.\)

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The perimeter of the triangle is (30+x) cm

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.

Perimeter is the distance around the edge of a shape.

To find the perimeter of a triangle , we add all the sides together.

Two sides are 22 cm and 8cm

Represent the other sides of the triangle by x

therefore the perimeter will be calculated as:

22+8+x

P = (30+x)cm

therefore the perimeter of the triangle is( 30+x)cm for any value of x

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Answer:

Cómo se vería si estuviera graficado:

2x−y=−2

3x−3y=15

Cómo se vería si lo resolviera graficando:

(−7,−12)

Answer:

Step-by-step explanation:

2x - y = -2

3x - 3y = 15

-6x + 3y = 6

3x - 3y  = 15

-3x = 21

x = -7

2(-7) - y = -2

-14 - y = -2

-y = 12

y = -12

(-7, -12)