4. The period, T, of a pendulum can be approximated by the formula ~ 2π√L/g, where L is the length of the pendulum and g is the gravitational constant. What is the approximate length of the pendulum if it has a period of 2 s? Note: On Earth the gravitational constant is 9.8 m/s^2

Answer:

Simplify the expression? Is it:   2 x 10 '' + 707 x   ....?

Answer:

m = 2

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Perpendicular lines have a negative reciprocal slope.

Step-by-step explanation:

Step 1: Define

y = -1/2x + 4

Step 2: Identify

Slope m = -1/2

Step 3: Solve

Reciprocate and multiply by negative

m = 2

Algebra I

Slope-Intercept Form: y = mx + b

Perpendicular lines have a negative

reciprocal slope.

\(\pink:\implies\)Define

y= -1/2x +4

\(\:\)

\(\pink:\implies\)ldentify

Slope m = -1/2

\(\:\)

\(\pink:\implies\)Solve

Reciprocate and multiply by negative

\(\dashrightarrow\) m = 2

Answer:

5

Step-by-step explanation:

The expression of "Twice the length (l) less three times the width (w)" in algebraic notation is 3w - 2l

From the question, we have the following parameters that can be used in our computation:

Twice the length (l) less three times the width (w)

Represent the length with l and the width with w

So the statement can be rewritten as follows:

Twice l less three times w

three times w is 3w

So, we have

Twice l less 3w

Twice l is 2l

So, we have

2l less 3w

less here means subtraction

So, we have the following

3w - 2l

Hence, the expression in algebraic notation is 3w - 2l

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Part a: y = -6x + 5 is : Not proportional.

Part b: y = 7/8x proportional:  proportionality constant = 7/8.

For the stated question;

Part a: y = -6x + 5

To check the proportional relation, put value of 'x' and find the corresponding value of 'y'.

The ratio = y/x must be same.

For x = 1, y = -1

y/x = -1

And, for x = 2, y = 7

y/x = 7/2

Thus, ratio is not equal, Not proportional.

Part b:  y = 7/8x

For x = 1, y = 7/8

y/x = 7/8

Now, For x = 2, y = 14/8

y/x = 7/8, both ratios are equal.

Thus,  y = 7/8x proportional:  proportionality constant = 7/8.

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a) The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.

b) The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.

Exponents are mathematical notation used to indicate that a quantity is being multiplied by itself a certain number of times. The exponent is usually written as a superscript to the right of the base number.For example, in the expression 2³, the base number is 2 and the exponent is 3. This means that 2 is being multiplied by itself three times, resulting in a value of 8. Exponents can also be negative or fractional, indicating that the base number is being divided by itself a certain number of times.

In the given question,

a) The value of -42 is different from the value of (-4)². The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.

b) The value of -23 is different from the value of (-2)³. The brackets serve to indicate that the exponent applies to the entire quantity within the brackets.

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Answer: Assuming that the missile is launched vertically upward and neglecting air resistance, we can use conservation of energy to determine the missile's velocity at the peak of its trajectory. At the launch point, the missile has kinetic energy due to its speed and potential energy due to its height above the ground. At the peak of its trajectory, the missile has no kinetic energy (since it momentarily comes to a stop) but has maximum potential energy.

The total energy of the missile at any point in its trajectory is given by the sum of its kinetic and potential energies:

E = 1/2 mv^2 + mgh

where m is the mass of the missile, v is its velocity, g is the acceleration due to gravity, and h is its height above the ground.

At the launch point, the missile has a height of zero and a velocity of 6.0 km/s, so its total energy is:

E_launch = 1/2 m (6.0 km/s)^2 + mgh = 1/2 m (6.0 km/s)^2

At the peak of its trajectory, the missile has a height of 1000 km and a velocity of zero, so its total energy is:

E_peak = mgh = mg (1000 km)

Since energy is conserved, the total energy of the missile at the launch point must be equal to its total energy at the peak of its trajectory:

E_launch = E_peak

1/2 m (6.0 km/s)^2 = mg (1000 km)

Solving for v, the velocity at the peak of the trajectory, we get:

v = sqrt(2gh) = sqrt(2*9.81 m/s^2 * 1000 km) = 7.91 km/s

Therefore, the missile is moving at a speed of 7.91 km/s at the peak of its trajectory.

Step-by-step explanation:

The notation that shows the relationship between sets C and D is C ⊆ D, which means that set C is a subset of set D. This is because all the elements of set C are also present in set D.

Set D contains only even numbers from 1 to 8, and as a result, set C, which contains all the integers from 1 to 8, is a subset of set D. In other words, all the elements of set C are also present in set D. Therefore, we use the subset notation to show the relationship between sets C and D.

The relationship between Set C and Set D can be described using the notation D = C ∩ 2n, where n is a positive integer.

This notation shows that Set D contains elements from Set C that are equal to 2 times an integer (n). In other words, Set D consists of even numbers from Set C. The relationship between the two sets is that Set D is a subset of Set C, including only the even numbers from Set C, which are 2, 4, 6, and 8.

This notation helps us understand the connection between the two sets in a concise and clear manner.

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Answer:

the answer is f(2)= - 1

Step-by-step explanation:

i took the test i failed it but i get that right.

Answer:

f(2) = -1

Step-by-step explanation:

took the test

The monthly repayment on the following hire-purchase agreement is £22.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a colour TV costs £640. The deposit was £200. The interest rate was 10% p.a. and it was paid off in two years.

The monthly repayment will be calculated as,

Total interest for two years = ( 640 - 200 ) x 1.2

Total interest for two years = ( 440 x 1.2 )

Total interest for two years = £528

The value of monthly repayment = 528 / 24 = £22

Therefore, the monthly repayment on the following hire-purchase agreement is £22.

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The ratio of the price of an orange to the price of a pear to the price of an apple is: 10 : 6 : 3.

Let's assume that the price of an orange is x.

The price of a pear at the fruit seller is 3/5th the price of an orange. In other words, for every 5 units of the price of an orange, the price of a pear would be 3 units.

The price of an apple is half the price of a pear. This means that the price of an apple is,

So, we have the following:

The price of a pear would be 3/5 * x.

The price of an apple would be half the price of a pear, or 1/2 * (3/5 * x) = 3/10 * x.

The ratio of the price of an orange to the price of a pear to the price of an apple would be:

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Answer:

-3,8

Step-by-step explanation:

B. This quantity might be the optimal order quantity, but we also need to consider the company’s attitude toward risk.

Simulation models are useful tools for predicting the outcomes of different scenarios, but they are not always accurate representations of reality. Running a simulation model several times with different order quantities can give an indication of the order quantity that maximizes the output, but it does not guarantee that this is the optimal order quantity.

There are many factors that can affect the outcome of a simulation model, such as the model's assumptions, limitations, and inputs. Additionally, simulation models are subject to randomness and variability, so the results of different runs may vary.

For this reason, it is important to consider other factors, such as the company's attitude toward risk, when making decisions based on the results of a simulation model. The company's attitude toward risk can influence the choice of order quantity and affect the overall outcome of the simulation.

Therefore, while the order quantity that maximizes the output in a simulation model might be a good starting point, it is not necessarily the optimal order quantity. Further analysis and consideration of other factors is necessary to determine the best order quantity for the company.

A ratio is a mathematical expression that compares the relative size of two or more values. It is a way of expressing the relationship between two or more quantities in terms of their relative size.

A ratio can be expressed in different ways, such as a fraction, decimal, or percentage. For example, the ratio of 2 to 4 can be expressed as 2/4, 0.5, or 50%.

Ratios are used in many areas of mathematics and science, such as finance, economics, engineering, and physics, to describe and analyze relationships between quantities. For example, in finance, ratios are used to measure a company's financial performance, such as its profitability, liquidity, and debt-to-equity ratios. In engineering, ratios are used to describe the relationship between the size and power of a machine, such as the gear ratio in a car's transmission.

In general, ratios are useful for comparing quantities and understanding the relationships between them, and they play a key role in many aspects of mathematics and science.

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Answer:

The 12 ounce

Step-by-step explanation:

When you buy two twelve ounces you will be receiving 24 oz. for the same price as the 20 oz.

Hope This Helped

The distance between C and D is 17.26 units

What is meant by distance?

Distance is a numerical or qualitative measurement of the distance between two objects or places. Distance can refer to a physical length or an estimate based on other factors in physics or common use (e.g. "two counties over"). Because spatial cognition is a rich source of conceptual metaphors in human thought, the term is frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between text strings) or a degree of separation (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalize most such conceptions of measurement, both real and metaphorical.

Distance CD = √{(-9-8)² + (-6+3)²}

                      = √{(-17)² + (-3)²}

                      = √{289 + 9}

                      = √298

                      = 17.26 units

Hence, the distance between C and D is 17.26 units

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Answer: 17.3

Step-by-step explanation:

Answer:

58

Explanation:

|58| = positive 58

Answer: x2+10x-75= (x-5)(x+15)

Step-by-step explanation:

Ok so we factor by thinking of numbers that can add to 10 and multiple to get -75. so those 2 numbers were -5 and 15. Hope this helps xD

Answer:

(x+15)(x-5)

Step-by-step explanation:

x²+10x-75= x²+15x-5x-75

=x(x+15)-5(x+15)

=(x+15)(x-5)

The direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

To find the maximum rate of change of the function f at the given point (5, 6, -1) and the direction in which it occurs, we can calculate the gradient of f at that point.

The gradient vector represents the direction of maximum increase of the function, and its magnitude represents the rate of change in that direction.

The gradient vector (∇f) of f(x, y, z) = (8x + 5y)/z can be found by taking the partial derivatives with respect to each variable:

∂f/∂x = 8/z

∂f/∂y = 5/z

∂f/∂z = -(8x + 5y)/z^2

Evaluated at the point (5, 6, -1), we have:

∂f/∂x = 8/(-1) = -8

∂f/∂y = 5/(-1) = -5

∂f/∂z = -((8(5) + 5(6))/(-1)^2) = -46

So, the gradient vector (∇f) at the point (5, 6, -1) is (-8, -5, -46).

The maximum rate of change of f at this point is given by the magnitude of the gradient vector:

|∇f| = √((-8)^2 + (-5)^2 + (-46)^2) = √(64 + 25 + 2116) = √2205 = 47.

Therefore, the maximum rate of change of f at the point (5, 6, -1) is 47.

To determine the direction in which this maximum rate of change occurs, we normalize the gradient vector by dividing it by its magnitude:

Direction vector = (∇f) / |∇f| = (-8/47, -5/47, -46/47).

Hence, the direction in which the maximum rate of change of f occurs at the point (5, 6, -1) is approximately (-0.17, -0.11, -0.98).

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The  function f(x) = ln(x – 5) is increasing and has a vertical asymptote at x= 5

What is a vertical asymptote?

A vertical line that appears to coincide with a function's graph but never actually does so is known as a vertical asymptote. When graphing a function, a function's vertical asymptote is crucial.

Consider the function:

f(x) = ln(x – 5)

As the  x values increase, the y values also increase. So this is increasing .

Find vertical asymptote:

Set the expression x-5 to zero  and solve for x

x-5 = 0

=> x= 5

The  function f(x) = ln(x – 5) is increasing and has a vertical asymptote at x= 5

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Which function is increasing and has a vertical asymptote at x = 5?

A. f(x) = -In x + 5

B. f(x)= - In (x – 5)

C. f(x) = ln(x – 5)

D. f(x) = ln x + 5

Answer:

10 units

Step-by-step explanation:

Of course you have to graph the two points to find out the answer.

Then you count the units or squares to find out how far they are.

So it was basically 6 units to the right and 4 units up :)

Hope this helped plz mark brainliest :))

Answer:

use a calculator to find 3x3x7 for step one and for step 2 times 3x3 in a calculator

Step-by-step explanation:

Therefore, the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM is approximately 0.1755, rounded to four decimal places.

To calculate the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM, we need to use the Poisson distribution formula. The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space. In this case, the mean (λ) is given as 5. The formula for the Poisson distribution is:

P(X = k) = (e*(-λ) * λ\(^k\)) / k!

Where:

P(X = k) is the probability of getting exactly k calls

e is the base of the natural logarithm (approximately 2.71828)

λ is the mean number of calls (given as 5)

k is the number of calls (in this case, 4)

k! is the factorial of k

Let's calculate the probability using the formula:

P(X = 4) = (e*(-5) * 5⁴) / 4!

P(X = 4) ≈ 0.1755

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Answer:

x = 20

Step-by-step explanation:

if a line is parallel to a side of a triangle and intersects the other two sides, it divides those sides proportionally.

QR is parallel to ST and intersects the other two sides of the triangle, then

\(\frac{PQ}{QS}\) = \(\frac{PR}{RT}\) ( substitute values )

\(\frac{x}{45-x}\) = \(\frac{16}{30-16}\)

\(\frac{x}{45-x}\) = \(\frac{16}{20}\) ( cross-  multiply )

20x = 16(45 - x)

20x = 720 - 16x ( add 16x to both sides )

36x = 720 ( divide both sides by 36 )

x = 20

Step-by-step explanation:

Let's call the number of girls in the school "g". We know that there are 1000 boys, so the total number of students is 1000 + g.

The problem states that 48% of the total number of students were successful in the examination. Therefore, we can write an equation:

0.48(1000 + g) = 0.5(1000) + 0.4(g)

Simplifying and solving for g:

480 + 0.48g = 500 + 0.4g

0.08g = 20

g = 250

Therefore, the number of girls in the school is 250.

Answer:

250

Step-by-step explanation:

Hi dear,

Firstly, let the girls be G

1000 + G = Total number of students

50% of boy = 1000 × 0.5 = 500

40% of girls = G × 0.4 = 0.4G

0.48 • (1000 + G) = 480 + 0.48G

480 + 0.48G = 500 + 0.4G

Collect Like Terms

0.48G - 0.4G = 500 - 480

0.08G = 20

G = 20/0.08

G = 250

Therefore, the girls are 250( two hundred and fifty)in the school

The probability level used by researchers to indicate the cutoff probability level (highest value) that will allow them to reject the null hypothesis is called the alpha level.

Alpha level refers to a threshold value which is used to determine if a test statistic is statistically significant.  In a statistical test, it demonstrates an acceptable probability of a Type I error. As alpha corresponds to a probability, it lies in the range of 0 to 1. The alpha level denoted as alpha or α refers to the probability of rejecting the null hypothesis when it is true. For example, a alpha level of 0.05 demonstrate a 5% risk of concluding that a difference exists when there is no actual difference.

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a) The set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

To find the set of values of k for which the line and curve meet at two distinct points, we need to solve the equation:

x^2 - kx + 2 = 3kx - 2k

Rearranging, we get:

x^2 - (3k + k)x + 2k + 2 = 0

For the line and curve to meet at two distinct points, this equation must have two distinct real roots. This means that the discriminant of the quadratic equation must be greater than zero:

(3k + k)^2 - 4(2k + 2) > 0

Simplifying, we get:

5k^2 - 8k - 8 > 0

Using the quadratic formula, we can find the roots of this inequality:

\(k < (-(-8) - \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = -2/5\\ or\\ k > (-(-8)) + \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = 2\)

Therefore, the set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

b) To find the two values of k for which the line is a tangent to the curve, we need to find the values of k for which the line is parallel to the tangent to the curve at the point of intersection. For m to be the slope of the tangent at the point of intersection, we need to have:

2x - 4 = m

3k = m

Substituting the first equation into the second, we get:

3k = 2x - 4

Solving for x, we get:

x = (3/2)k + (2/3)

Substituting this value of x into the equation of the curve, we get:

y = ((3/2)k + (2/3))^2 - k((3/2)k + (2/3)) + 2

Simplifying, we get:

y = (9/4)k^2 + (8/9) - (5/3)k

For this equation to have a double root, the discriminant must be zero:

(-5/3)^2 - 4(9/4)(8/9) = 0

Simplifying, we get:

25/9 - 8/3 = 0

Therefore, the constant term is 8/3. Solving for k, we get:

(9/4)k^2 - (5/3)k + 8/3 = 0

Using the quadratic formula, we get:

\(k = (-(-5/3) ± \sqrt{((-5/3)^2 - 4(9/4)(8/3)))} / (2(9/4)) = -1/3 \\or \\k= 4/3\)

Therefore, the two values of k for which the line is a tangent to the curve are k = -1/3 and k = 4/3. To show that the two tangents meet on the x-axis, we can find the x-coordinate of the point of intersection:

For k = -1/3, the x-coordinate is x = (3/2)(-1/3) + (2/3) = 1

For k = 4/3, the x-coordinate is x = (3/2)(4/3) + (2/3) = 3

Therefore, the two tangents meet on the x-axis at x = 2.

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Answer:

28(27)(26) assuming that nobody can get multiple designations.

Step-by-step explanation:

True, a random sample is selected so that every element in the population has the same chance of being included in the sample.

This is an important aspect of random sampling, as it helps to ensure that the sample is representative of the entire population and that there is no bias in the selection process. By giving every element in the population an equal chance of being included in the sample, random sampling helps to reduce the potential for error and increases the likelihood that the results of the study will be accurate and reliable.

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Answer: 52

There are 52 weeks in a year, because 365 ÷ 7 is 52.

It is a whole number, so you do not need to do the next following steps according to your question.

So, the answer is 52.

The number of weeks is 52 in a year 52 is not a whole number and the remainder is 1.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that are +, -, ×, and ÷.

It is given that:

There are 365 days in a non-leap year. There are 7 days per week.

Let x be the number of weeks x:

x = 365/7

x = 52.14

52 is not the whole number.

The remainder is 1

Thus, the number of weeks is 52 in a year and 52 is not a whole number and the remainder is 1.

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Answer:

126 cents, or $1.26

Step-by-step explanation:

First you divide 42 by 12 and get 3.5, then you multiply that by 36 and get you answer.