Explain why 10 x 2 is equivalent to 10 ÷ 1/2??

Answer:

numbers don't stop. The multiplication table is just basic facts

Step-by-step explanation:

The length of the hypotenuse is 4√3 units.

Given that hypotenuse is 4 times the length of one leg of a triangle. So here we can assume that length to be x. Hence the hypotenuse length is 4x. To calculate hypotenuse we have the formula a²=b² + c², where b and c are two sides of the triangle and a is the hypotenuse. If we put these values in the formula we get,

16x² = x² + (3√5)²

15x² = 45

x² = 3

x = ±√3

Since length cannot be negative, the final value of x = √3, and since the length of the hypotenuse was 4x, the final value of the hypotenuse is 4√3.

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Answer:

Mean (Average):

7.6

Median (Middle):

9

Mode (Most Common):

9

Range (Biggest - Smallest):

7

Step-by-step explanation:

To figure the mean, add up the numbers,  then divide it by the number of data points.

Step-by-step explanation:

all I know is the answer and it's c

Knowing that the number of victims by femicide shows an approximately linear behavior, a mathematical model can be obtained through the following equation:

y - y₀ = [(y₁ - y₀) / (x₁ - x₀)]·(x - x₀)

Considering that the behavior is linear, a mathematical model can be obtained from the following equality that allows us to find the equation of a straight line:

y - y₀ = [(y₁ - y₀) / (x₁ - x₀)]·(x - x₀)

Where P(x₀, y₀) and Q(x₁, y₁) are points that belong to the line, that is, they belong to linear behavior.

¡Hope this helped!

a) The probability that the bank is empty is approximately 0.0026.

b) the average time the customer spends waiting to be called is approximately -0.25 c) hours the average number of customers in the bank is -1.5 d) the average number of customers waiting to be served is approximately 9.

To answer these questions, we can use the M/M/4 queuing model, where the arrival rate follows a Poisson distribution and the service time follows an exponential distribution. In this case, we have four bank tellers, so the system is an M/M/4 queuing model.

Given information:

Arrival rate (λ) = 12 customers per hour

Service rate (μ) = 1 customer every 15 minutes (or 4 customers per hour)

(a) To calculate the probability that the bank is empty, we need to find the probability of having zero customers in the system. In an M/M/4 queuing model, the probability of having zero customers is given by:

P = (1 - ρ) / (1 + 4ρ + 10ρ² + 20ρ³)

where ρ is the traffic intensity, calculated as ρ = λ / (4 * μ).

ρ = (12 customers/hour) / (4 customers/hour/teller) = 3

Substituting ρ = 3 into the formula, we have:

P = (1 - 3) / (1 + 4 * 3 + 10 * 3² + 20 * 3³) ≈ 0.0026

Therefore, the probability that the bank is empty is approximately 0.0026.

(b) The average time the customer spends waiting to be called is given by Little's Law, which states that the average number of customers in the system (L) is equal to the arrival rate (λ) multiplied by the average time a customer spends in the system (W). In this case, we want to find W.

L = λ * W

W = L / λ

Since the average number of customers in the system (L) is given by L = ρ / (1 - ρ), we can substitute this into the equation to find W:

W = L / λ = (ρ / (1 - ρ)) / λ

W = (3 / (1 - 3)) / 12 ≈ -0.25

Therefore, the average time the customer spends waiting to be called is approximately -0.25 hours, which is not a meaningful result. It seems there might be an error in the given data.

(c) The average number of customers in the bank (L) can be calculated as:

L = ρ / (1 - ρ) = 3 / (1 - 3) = -1.5

Therefore, the average number of customers in the bank is -1.5, which is not a meaningful result. It further suggests an error in the given data.

(d) The average number of customers waiting to be served can be calculated as:

\(L_q\) = (ρ² / (1 - ρ)) * (4 - ρ)

Substituting ρ = 3, we have:

\(L_q\\\) = (3² / (1 - 3)) * (4 - 3) ≈ 9

Therefore, the average number of customers waiting to be served is approximately 9.

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Answer:

x = -3

Step-by-step explanation:

An extraneous equation is just an equation that you can solve, but the answer won't work when you check it.

x - 9 = 4x

-3 - 9 = 4(-3)

|-12| \(\neq\) -12

Answer:

120 cubic cm

Step-by-step explanation:

If you look at the picture you will see.

The half-range cosine expansion of f(x) = sin(x), for 0 < x < π, simplifies to f(x) = (2/π).

To find the half-range cosine expansion of the function f(x) = sin(x) for 0 < x < π, we can utilize the half-range Fourier series expansion. The half-range expansion represents the function as a sum of cosine terms.

The half-range Fourier series expansion of f(x) can be expressed as:

f(x) = a₀/2 + ∑[n=1 to ∞] (aₙ * cos(nx))

To find the coefficients a₀ and aₙ, we can use the following formulas:

a₀ = (2/π) ∫[0 to π] f(x) dx

aₙ = (2/π) ∫[0 to π] f(x) * cos(nx) dx

Let's calculate the coefficients:

a₀ = (2/π) ∫[0 to π] sin(x) dx

= (2/π) [-cos(x)] [0 to π]

= (2/π) [-cos(π) + cos(0)]

= (2/π) [1 + 1]

= 4/π

For aₙ, we have:

aₙ = (2/π) ∫[0 to π] sin(x) * cos(nx) dx

= 0 [since the integrand is an odd function integrated over a symmetric interval]

Now, we can rewrite the half-range cosine expansion of f(x):

f(x) = (4/π) * (1/2) + ∑[n=1 to ∞] (0 * cos(nx))

= (2/π) + 0

Therefore, the half-range cosine expansion of f(x) = sin(x), for 0 < x < π, simplifies to:

f(x) = (2/π)

In this expansion, all the cosine terms have coefficients of zero, and the function is represented solely by the constant term (2/π).

It's worth noting that the half-range cosine expansion is valid for the given interval (0 < x < π), and outside this interval, the function would need to be extended or expressed differently.

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The following parts can be solved by the concept of Area.

1. The area of the sprinkled lawn is 9π square feet, where π is approximately 3.14.

2. The area that the storm will affect is 113.1 square miles, where the value of π is approximately 3.14.

1. To find the area of the sprinkled lawn, we need to find the area covered by the sprinkler in one rotation and then multiply it by the number of rotations. The sprinkler sprays water 3 feet in every direction, so it covers a circular area with a radius of 3 feet. The area of a circle with a radius of 3 feet is given by the formula A = πr^2, where r is the radius of the circle.

Therefore, the area covered by the sprinkler in one rotation is 9π square feet (A = π x 3^2 = 9π). If the sprinkler rotates n times, then the total area covered by the sprinkler is n times the area covered in one rotation.

2. To find the area that the storm will affect, we need to find the area of the circle with a radius of 6 miles. The area of a circle is given by the formula A = πr^2, where r is the radius of the circle. Therefore, the area that the storm will affect is 36π square miles (A = π x 6^2 = 36π). To get a numerical value, we can use the approximation of π as 3.14, which gives us an area of approximately 113.1 square miles (A = 3.14 x 36 = 113.1).

Thus, the storm will affect an area of approximately 113.1 square miles.

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a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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Answer:

1.25 x 10^-8

Step-by-step explanation:

The equation of the quartic function is:

f(x) = -3(x + 2)²(x - 1)²

This type's quartics have the general form y = a(x h)4 + k. The pivotal moment occurs at (h, k). Determine the turning point before drawing quartic graphs of the type y = a(x h)4 + k. The x-axis and y-axis intercepts are discovered to provide the graph with further detail.

The given function can be expressed in factored form as: since it has x-intercepts at orders 2 and 2, at positions -2 and 1, respectively.

f(x) = a(x + 2)

²(x - 1)²

where an is a fixed value. We use the knowledge that the function passes through the position (0, -12) to determine the value of a:

f(0) = -12

When we enter x = 0 into the previous equation, we obtain:

a(2²)(-1)² = -12

If we simplify, we get:

4a = -12

a = -3

As a result, the quartic function's equation is:

f(x) = -3(x + 2)

²(x - 1)²

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Answer:

some

Step-by-step explanation:

Answer:

Some, since naturals number are essentially counting numbers / any whole number excluding zero: 1, 2, 3, 4, 5, 6, 7, ............

For instance, you can't have 0 of a person so natural numbers can represent a set of people.

Answer: 4th week

Step-by-step explanation:

You just keep adding 150 to 250 for Sarah and subtract 200 from 1,650 for Felicia until they both have the same amount which would be 850.

At the end of 4th week Sarah and Felicia have same amount of money equals to $850.

"Amount is defined as representation of total of two or more quantities."

According to the question,

Amount with Sarah at the beginning of the week = $250

Amount save per week by Sarah = $150

Amount with Felicia at the beginning of the week = $1650

Amount save per week by Felicia = $200

As per the given conditions,

Sarah amount for different weeks:

At the end first week = $250 + $150

                                   = $400

At the end second week = $400 + $150

                                         = $550

At the end third week = $550 + $150

                                    = $700

At the end fourth week = $700 + $150

                                       = $850

Felicia amount for different weeks:

At the end first week = $1650 - $200

                                   = $1450

At the end second week = $1450- $200

                                         = $1250

At the end third week = $1250 - $200

                                    = $1050

At the end fourth week = $1050- $200

                                       = $850

Hence, at the end of 4th week Sarah and Felicia have same amount of money equals to $850.

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Answer:

y=5

Step-by-step explanation:

Answer:

-1/3

Step-by-step explanation:

rise over run and its a negative slope

Answer:

-1/3

Step-by-step explanation:

Use Rise/Run. Since the line goes down from left to right, it is negative. Also, since it goes down 1 unit and over 3 units it is -1/3

The measures of KM, KQ, LK, LR, NK and PM are 2, 2, 4, 4, 6 and 2 respectively.

1) KM: Since N is the midpoint of QR, we know that QN = NR, so QN + NR = QN + QN = 2QN = 26 = 12. Therefore, KM = KR - QN = (PK+KQ) - QN = 4 - 6 = -2.

2) KQ: Since PK = 4 and KM = -2, we have KQ = PK + KM = 4 + (-2) = 2.

3) LK: The median of a triangle connects a vertex to the midpoint of the opposite side, and it's length is 2/3 the length of the hypotenuse of the right triangle formed by the median and the two segments from the vertex to the endpoints of the median.

In this case, LK = (2/3)(PQ) = (2/3)(4+2) = (2/3)*6 =4

4)LR: In this case, LR = LK = 4

5) NK: NK = QN = 6

6) PM: PM = PK - KQ = 4 - 2 = 2

Please note, that in order to be able to calculate all these lengths and measures, it is assumed that the triangle PQR is a valid triangle i.e, the sum of the lengths of any two sides of the triangle is greater than the length of the third side.

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Step-by-step explanation:

1) The width of the rectangle is 10.2 in.

2) The perimeter of the rectangle is 71.4 in.

3) The area of the rectangle is 260.1 sq.in

Answer:

21

Step-by-step explanation:

Richard's gross pay for the month was $ 4,512.5.

It is required to find the gross pay for the month.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

commission rate: 3.00% for oil changes, 5.00% for tune ups and 6.25% on auto part sales.

salary = $2,450.00 per month

Last month salary= $2,500.00 in oil changes,

tune ups=$4,500.00  

sold =$28,200.00 in parts.

According to given question we have,

2,450 + (2,500 x 0.03) + (4,500 x 0.05) + (28,200 x 0.0625) = X

2,450 + 75 + 225 + 1,762.5 = X

2,450 + 2,062.5 = X

4,512.5 = X

Therefore, Richard's gross pay for the month was $ 4,512.5.

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The height of the tree is 16 feet if it casts a 24 feet shadow at the same time of the day when 4 feet wall casts a 6-foot shadow.

The shadows at the same time of the day can be compared for the garden wall and a tree as follows;

tree shadow / tree height = wall shadow / wall height

As the height of the wall is given to be 4 feet and it has a 6-foot shadow, and the tree casts a 24-foot shadow, substituting these values in the equation;

24 / x = 6 / 4

Here x represents the height of the tree

Solving for x;

24 / x = 1.5

24 = 1.5 x

x = 24 / 1.5

x = 16

Therefore the height of the tree is calculated to be 16 feet.

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The height of the tree is 16 feet when it casts a 24 feet shadow at the same time of the day when 4 feet wall casts a 6-foot shadow.

An equation is an expression that shows the relationship between two or more numbers and variables.

The shadows at the same time of the day can be compared for the garden wall and a tree is given by;

tree shadow / tree height = wall shadow / wall height

Since we know that the height of the wall is given to be 4 feet and it has a 6-foot shadow, and the tree casts a 24-foot shadow, substituting these values in the equation;

24 / x = 6 / 4

Here x represents the height of the tree

Solving for x,

24 / x = 1.5

24 = 1.5 x

x = 24 / 1.5

x = 16

Therefore, the height of the tree is calculated to be 16 feet.

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(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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We need to find the equation relating P to N. Also, we need to find P when N = 26.

We know that N is the number of copies of "history is fun" she sells and that she makes an additional $40 for every copy she sells.

Thus, the total additional she receives for selling those N copies is, in dollars:

Also, we know that her base salary is $2500. Thus, her total pay P, in dollars, is given by:

Now, when she sells 26 copies of "history is fun", N = 26, and we have:

Answer

Equation: P = 2500 + 40N

Total pay if Lenna sells 26 copies: $3540

The number of hours for the tortoise to walk 1 mile will be 1.5 hours.

Speed:

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration. The pie divides the dimension of distance by time. The SI unit of speed is meter per second (m/s), but the most common unit of speed in everyday use is kilometer per hour (km/h), or in the US and UK United, the mile per hour (mph). air And for sea travel, knots are commonly used.

We know that the speed formula

Speed = Distance/Time

A tortoise takes 1 1/4​ hours to walk 5/6 miles.

Convert the mixed fraction number into a decimal number.

1 ¹/₄ = 1.25 hours

Then the speed of the tortoise will be calculated as,

⇒ Speed = (5/6) / 1.25

⇒ Speed = 0.667 miles per hour

The number of hours for the tortoise to walk 1 mile will be calculated as,

⇒ T = 1 / 0.667

⇒ T= 1.5 hours

The number of hours for the tortoise to walk 1 mile will be 1.5 hours.

Complete Question:

A tortoise takes 1 1/4​ hours to walk 5/6 miles. At this rate, how long does it take her to walk 1 mile?

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Answer:

5x-4y = -32

Step-by-step explanation:

We can first get an equation in point slope form since we have a point and a slope

y-y1 = m ( x-x1) where m is the slope and (x1,y1) is a point on the line

y- -2 = 5/4(x- - 8)

y+2 = 5/4 (x+8)

Multiply each side by 4 to get rid of fractions

4(y+2) = 5/4 *4 (x+8)

4(y+2) = 5(x+8)

Distribute

4y+8=5x+40

Subtracy 4y from each side

8 = 5x-4y+40

Subtract 40 from each side

8-40 = 5x-4y

-32 = 5x-4y

5x-4y = -32

Answer:

(2r-1)(2r-5)

Step-by-step explanation:

4r^2-10r-2r+5=0

2r(2r-5)-(2r-5)

(2r-1)(2r-5)

Answer:

\(P = 58\)

Step-by-step explanation:

The image if the circle and triangle can be found online

Given

\(JA = 8\)

\(AL = 8\)

\(CK = 10\)

Required

The perimeter of JKL

Since the mid-points of the tangents are A, B and C respectively.

\(JK = JB + BK\)

Where

\(JB = JA = 8\)

\(BK = CK = 10\)

So:

\(JK =8+10 =18\)

\(JL = JA + AL\)

\(JL = 8+11 = 19\)

\(KL = CL + CK\)

Where

\(CL =AL = 11\)

So:

\(KL = 11+10 = 21\)

So, the perimeter (P) is:

\(P = JK+ KL +JL\)

\(P = 18 + 19 + 21\)

\(P = 58\)

the term to term rule is that every next term becomes 2 times of the previous term and the 11th term is 5120 for the sequence 5, 10, 20, 40, 80.

We have a sequence:

5, 10, 20, 40, 80

We need to find the term to term rule of the sequence.

We get that:

10 / 5 = 2

20 / 10 = 2

40 / 20 = 2

80 / 20 = 2

Term to term rule is that every next term becomes 2 times of the previous term.

10th term = 2560

11th term = 2 × 2560

11th term = 5120

Therefore, we get that, the term to term rule is that every next term becomes 2 times of the previous term and the 11th term is 5120 for the sequence 5, 10, 20, 40, 80.

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