Please help me with inequalitys

In essence, a function is a rule that assigns to each value of the input set (also known as the domain), a unique value of the output set (also known as the range).

A function is a fundamental mathematical concept that is used to describe the relationship between two sets of values.

To understand the idea of a function, imagine a machine that takes in an input and produces an output. The input values are the domain of the function, and the output values are the range. A function can be represented as an equation, a graph, or a table. For example, the equation f(x) = x + 3 represents a function that takes in an input value x and produces an output value that is 3 greater than the input value.

One of the key features of a function is that each input value must have a unique output value. This means that if you input the same value into the function twice, you should get the same output value both times. In mathematical terms, we say that a function is well-defined if it has a unique output value for each input value.

Functions are used in a wide range of mathematical applications, from algebra and calculus to statistics and data analysis. They provide a powerful tool for describing and analyzing relationships between different sets of values.

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Answer:

Yeah

Step-by-step explanation:

\(\sqrt{3} - \frac{2}{\sqrt{3} } = \frac{3}{\sqrt{3} } - \frac{2}{\sqrt{3} } = \frac{1}{\sqrt{3} } = \frac{\sqrt{3} }{3}\)

ok done. thank to me :>

Seraphina's speed has increased by a factor of around 23% compared to the first hour.

What Is a Change in Percentage?

The ratio of the difference in the amount to its starting value multiplied by 100 is known as the percentage change. When a number's final value is determined by increasing or decreasing a percentage of its starting value, the percentage change of that quantity will always change.

How can you determine the percentage to the closest tenth?

Rounding to the closest tenth entails adding one integer after the decimal point. The number in the thousandths place, or the second number from the right of the decimal, must be considered while rounding. If the amount is five or more, we add one percent to the number in the tenth position.

Percent Change Formula = \(\frac{ (Final value -Initial value)}{ (Initial value)}\)× 100

Percent Change               = \(\frac{(74-60)}{60}\)× 100

…                                     = \(\frac{14}{60}\) × 100

...                                     ≈ 0.23333 × 100

Percent Change             ≈ 23.33%

The pace of Seraphina increased by around 23% in the second hour compared to the first.

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The area of the cottonwood leaf. height 4in, base is 5in is 10 inches².

Based on the information given, it should be noted that the leaf is in the shape of a triangle.

It is important to note that the area of a triangle will be:

= 1/2 × base × height

Base = 5 inches

Height = 4 inches..

Area = 1/2 × base × height

= 1/2 × 5 × 4

= 10 inches²

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The number of possible orderings of appointments is 720.

The number of possible orderings of appointments can be calculated using the formula n!/(n-r)! where n is the number of teaching assistants (7) and r is the number of appointments (7). Therefore, the total number of possible orderings of appointments is 5040.

To explain this formula, we can think of it in terms of permutations. A permutation is an arrangement of a set of items in a specific order. In this case, the set of items are the 7 teaching assistants (4 men and 3 women). The number of possible permutations (orderings) of these 7 teaching assistants is 7!. This is because there are 7 possible choices for the first appointment, 6 for the second, 5 for the third, and so on. This simplifies to 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040.

However, since each appointment is a unique one-time meeting, the order in which the teaching assistants are appointed does not matter, so the number of possible orderings of appointments is reduced to 7!/7 = 5040/7 = 720.

Therefore, in this case, the number of possible orderings of appointments is 720.

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The formula for the uncertainty of x, Δx, can be derived using partial derivatives as follows:

Δx = √((Δa/a)² + (Δb/b)² + (Δc/c)²)

To derive the formula for the uncertainty of x, Δx, we can use the concept of partial derivatives. The general formula for the uncertainty propagation of a function involving multiple variables is given by:

Δf = √((∂f/∂x₁)²Δx₁² + (∂f/∂x₂)²Δx₂² + ... + (∂f/∂xₙ)²Δxₙ²)

In this case, we have x = ab/c, and we want to find Δx. We can assign x as a function of a, b, and c:

f(a, b, c) = x = ab/c

To find Δx, we need to calculate the partial derivatives (∂f/∂a), (∂f/∂b), and (∂f/∂c) and substitute them into the general formula.

∂f/∂a = b/c

∂f/∂b = a/c

∂f/∂c = -ab/c²

Now, we can substitute these partial derivatives into the uncertainty propagation formula:

Δx = √((∂f/∂a)²Δa² + (∂f/∂b)²Δb² + (∂f/∂c)²Δc²)

= √((b/c)²Δa² + (a/c)²Δb² + (-ab/c²)²Δc²)

= √((b²Δa² + a²Δb² + a²b²Δc²)/c²)

= √((a²b²Δc² + b²Δa² + a²Δb²)/c²)

Simplifying further, we get:

Δx = √(a²b²Δc² + b²Δa² + a²Δb²)/c

Thus, the formula for the uncertainty of x, Δx, is:

Δx = √(a²b²Δc² + b²Δa² + a²Δb²)/c

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Answer:

36 inches.

There are 12 inches in 1 foot, and snce there are 3, then you will multiply:

12 * 3 = 36

Step-by-step explanation:

Hope it helps! =D

The measure of angle BCA is 81 degrees.                                            

On the first day, the members earned 90% of their daily goal of $50.00 which is equal to $45.00 (0.9 x $50.00 = $45.00).

On the second day, the members earned 6% more than their daily goal of $50.00 which is equal to $53.00 ($50.00 + 0.06 x $50.00 = $53.00).

On the third day, the members earned 14% less than their daily goal of $50.00 which is equal to $43.00 ($50.00 - 0.14 x $50.00 = $43.00).

Therefore, the members earned a total of $45.00 + $53.00 + $43.00 = $141.00 from ticket sales on all three days.

The members of the school club earned $141.00 from ticket sales over the three days.

percentage, a relative value indicating hundredth parts of any quantity.

To find out how much money the members of the school club earned from ticket sales on all three days

Let us calculate the amount of money earned each day and then add them together.

On the first day, the members earned 90% of their daily goal, which is:

0.9 x $50.00 = $45.00

On the second day, they earned 6% more than their daily goal, which is:

$50.00 + 0.06 x $50.00 = $53.00

On the third day, they earned 14% less than their daily goal, which is:

$50.00 - 0.14 x $50.00 = $43.00

To find the total amount of money earned over the three days, we simply add the amounts earned on each day:

$45.00 + $53.00 + $43.00 = $141.00

Therefore, the members of the school club earned $141.00 from ticket sales over the three days.

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Answer:

Greetings from Brasil...

According to the statement of the question, we conclude that the area of a square is requested, whose value is 171 in²

The area of a square is given by the expression:

A = S²

where S is the side of the square - just what we want to know

So:

A = S²

171 = S²

√171 = S

The number of wins is 68 ad losses is 26.

Let the number of losses = l

Therefore, the number of wins will be: = (2 × l) + 16 = 2l + 16

Total games = 94

Therefore we will add the equation

l + 16 + 2l = 94

3l + 16 = 94

3l = 94 - 16

3l = 78

Divide

l = 78/3

l = 26

Losses = 26

Number if wins = 2l + 16 = 2(26) + 16 = 52 + 16 = 68

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Outstanding balance = Invoice amount - CreditInvoice amount = $1,205Credit = $611.25Outstanding balance = $1,205 - $611.25Outstanding balance = $593.75Therefore, Vail's outstanding balance is $593.75.

a. To determine the credit that Vail should receive, we need to use the formula for partial payment: Payment / (1 - Discount%)The calculation for the credit that Vail should receive is:Discount% = 2/10 = 0.2Credit = 489 / (1 - 0.2)Credit = 489 / 0.8Credit = $611.25The credit that Vail should receive is $611.25.b.

To calculate Vail's outstanding balance, we need to subtract the credit from the invoice amount. The calculation is:Outstanding balance = Invoice amount - CreditInvoice amount = $1,205Credit = $611.25Outstanding balance = $1,205 - $611.25Outstanding balance = $593.75Therefore, Vail's outstanding balance is $593.75.

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Answer:yes they are

Step-by-step explanation:

Answer:

25% on question one

Step-by-step explanation:

For example, on question one, 5 students drink more than half a dozen sodas a week. If there is a total of 20 students you'd divide 5 by 20 and that should be the answer.

Answer:

64%

Step-by-step explanation:

A coin contains 9 grams of nickel and 16 grams of copper for a total weight of 25 grams.

What percentage of the metal in the coin is copper

Solution:

The total weight of the coin = weight of copper in coin + weight of nickel in coin

The total weight of the coin = 9 g + 16 g = 25 g

The percentage of copper in the coin is the ratio of the weight of copper in the coin to the total weight of the coin expressed in percentage. It is given by the formula:

The percentage of copper in the coin = (weight of copper in the coin / total weight of the coin) * 100%

The percentage of copper in the coin = (16 g / 25 g) * 100% = 64%

x = 1 is not an extraneous solution.

✓(x² + 3) = x + 1

Taking square on both the sides of the equation, we get

(✓(x² + 3))² = (x + 1)²

x² + 3 = (x + 1)²

Using the identity (a+b)²= a² + b² + 2ab on the right hand side of the equation, we get

x² + 3 = x² + (1)² + 2(x)(1)

x² + 3 = x² + 1 + 2x

2x = 2

x = 1

Confirming the value is extraneous solution or not

Putting the root x = 1 in the original equation ✓(x² + 3) = x + 1, we get

✓(1² + 3) = 1 + 1

✓4 = 2

2 = 2

⇒ LHS = RHS

∴ x = 1 is not an extraneous solution.

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The standard form of the equation of the line

The equation of the line can be expressed in several forms. One of them is the standard form:

Ax + By = C

Where A, B, and C are constants, and x and y are the variables.

We have the equation:

Multiplying by 3:

Subtracting 4x:

Is the required standard form of the line

The answer is: f′(1) = 7 f′(2) = 5 f′(3) = 3. We have found the values of f′(1), f′(2), and f′(3) where the derivative exists using the definition of the derivative.

The given function is

\(f(x) = −x² + 9x − 5\)

and we need to find f′(x) using the definition of derivative. The definition of the derivative is given by

\(f′(x) = lim(h → 0) (f(x + h) − f(x))/h.\)

Now, let’s use the above definition of derivative to find f′(x).

\(f′(x) = d/dx [−x² + 9x − 5]= -2x + 9.At x = 1, f′(x) = -2(1) + 9 = 7.At x = 2,f′(x) = -2(2) + 9 = 5.At x = 3,f′(x) = -2(3) + 9 = 3.\)

The derivative of a function measures how fast the function is changing at each point of the function. In this problem, we have been given a function

\(f(x) = −x² + 9x − 5\)

and we have to find the derivative of this function, i.e., f′(x) using the definition of the derivative. The definition of the derivative is given by

\(f′(x) = lim(h → 0) (f(x + h) − f(x))/h\).

Substituting the given function

\(f(x) = −x² + 9x − 5\), we get

\(f′(x) = lim(h → 0) (f(x + h) − f(x))/h= lim(h → 0) [−(x + h)² + 9(x + h) − 5 + x² − 9x + 5]/h= lim(h → 0) [−x² − 2xh − h² + 9x + 9h − 5 + x² − 9x + 5]/h= lim(h → 0) [-2xh − h² + 9h]/h= lim(h → 0) [-h(2x + h + 9)]/h= -2x - 9.\)

Therefore,

\(f′(x) = -2x + 9\).

Now, we have to find the value of f′(1), f′(2), and f′(3) where the derivative exists.

Using

\(f′(x) = -2x + 9\), we get

\(f′(1) = -2(1) + 9 = 7\)

\(f′(2) = -2(2) + 9 = 5\)

\(f′(3) = -2(3) + 9 = 3.\)

Hence, the required values of f′(1), f′(2), and f′(3) are 7, 5, and 3, respectively when the derivative exists. Therefore, the answer is: f′(1) = 7, f′(2) = 5, f′(3) = 3. Therefore, we have found the values of f′(1), f′(2), and f′(3) where the derivative exists using the definition of the derivative.

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The value of the test statistic is -8.2542.

We have,

p'= 0.87, p= 0.93 and n= 1232

We know, the equation for the Test statistic for a population proportion  is mathematically given as

z = (p' - p)/ √p(1-p)/ n

So, z= (0.87 - 0.93)/ √0.93(1-0.93)/ 1232

z = (-0.06) / 0.007269

z = -8.2542

So, the value of the test statistic is -8.2542.

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a)The chance that no call will be handled in 10 seconds  is 0.0067

b) 0.2642 percent of classes will be processed in two seconds at least.

A figure or ratio that reflects a fraction of 100 is known as a percentage in mathematics. In addition to ratios, fractions, and decimals, it is one of the ways to depict a dimensionless connection between two numbers. Frequently, the symbol "%" is used after the number to indicate percentages.

given,

The number of phone calls handled by the communications switch in a 10-second period is represented by the Poisson random variable n.

a)the chance that no call will be handled in 10 seconds is

for 10 sec= λ= 10*0.5 = 5 calls per sec

P(X=0) \(e^{-5}\)(5)° / 0!

P(X=0)= 0.0067

b) percent of classes will be processed in two seconds at least is

for 2 sec =λ = 0.5 *2 = 1

P(X≥2) = 1- P(X<2)

= 1-[P(X=2) + P(X=1)]

=0.2642

a)The chance that no call will be handled in 10 seconds  is 0.0067

b) 0.2642 percent of classes will be processed in two seconds at least.

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Answer:

-1.00000425998

Step-by-step explanation:

Answer:

\(\frac{1}{x-1}\)

Step-by-step explanation:

(x - 1) × \(\frac{1}{x-1}\) ( cancel the factor (x - 1) on numerator and denominator

= 1

[ In the same way 2 × \(\frac{1}{2}\) = 1 ]

The required rational expression is \(\frac{1}{x-1}\)

Check the picture below.

so we only want the area in pink.

\(\stackrel{\textit{left and right}}{2(4)(11)}~~ + ~~\stackrel{\textit{front and back}}{2(4)(11)}\implies \text{\LARGE 176}~cm^2\)

Answer:

81.64 yards

Step-by-step explanation:

The formula to find the circumference is:

Circumference = 2 · π · r

r = 13 yards

π = 3.14

C = 2 · 3.14 · 13 = 81.64 yards

So, the circumference is 81.64 yards.

To answer this question, first, we will compute the intensity of each earthquake.

Recall that:

Therefore, using the given formula we get:

Then, the intensity of an earthquake that measures 7.5 on the Richter scale is:

and the intensity of an earthquake which measures 2.3 on the Richter scale is:

Now, notice that:

We know that:

Answer:

Answer:

XY = 8 cm

Step-by-step explanation:

PQ is a midsegment and is half the length of the 3rd side XY , then

XY = 2 × PQ = 2 × 4 = 8 cm

The monthly contribution is increased by $10.25 each month if the Stafford Loan taken by Jessica is not subsidized.

By dividing the loan amount by the number of months, one may determine the formula for calculating the monthly loan payments.

The compound interest can be calculated as follows,

Compounded Annuity = P \((1+ r/n)^{nt\)

Given:

P= $7175

R= 6.3%

So, Compounded Annuity = 7175 \((1+ 0.063/12)^{120\)

Compounded Annuity = $13449

As, the loan was subsidized at 5.28% interest rate.

Compounded Annuity = 7175 \((1+ 0.0044)^{120\)

Compounded Annuity = 12151

The monthly payments can be calculated as,

unsubsidized monthly payments = 13499/120

                                                        = $112

and, subsidized monthly payments = 12151 /120

                                                            = $101.75

So, the difference of the monthly payments is calculated as $10.25 on the subsidization of the Stafford loan.

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