Find x in this 45°-45°-90° triangle.

x=

This is the same as g(x) which, therefore the functions are inverse of each other.

What does a math inverse mean?

for any point (x, y), that appears in one function, the point (y, x) must appear in the other function. for any point (x, y), that doesn't appear in one function, the point (y, x) must not appear in the other function.  

so if you find any point that doesn't meet the above rules, you can prove that the functions are not inverses of each other.  

to prove that they are inverses of each other, you need to check all points in the functions, and there is an infinity of them, so instead, you can write f(x) like this:  

y = 3x - 5  

solve for x:  

y + 5 = 3x  

x = (y + 5) / 3  

swap x and y:  

y = (x + 5) / 3  

this is the same as g(x) which, therefore the functions are inverse of each other.

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1) The event is considered as rare.

2) It is called a rare event event because the probability is less than 5% and is well below threshold.

1) The probability of winning the grand prize is 0.005, which means there is a 0.5% chance of winning the prize.

Since this probability is low, Michele winning the grand prize is considered a rare event.

The term "rare event" is often used to describe an event with a low probability of occurrence.

A rare event typically has a probability of less than 5%, and in this case, the probability is well below that threshold. A probability of less than 0.05 is generally considered a rare event.

The fact that Michele won the grand prize means that she defied the odds, which makes the event rare.

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Answer:

yellow

Step-by-step explanation:

cus it sorta lookes like it

The value of x on the given sides of the rectangles is 4.

The area of a rectangle is the product of its length and width.

The perimeter of a rectangle is the sum of the lengths of all the sides.

Given, The area of the shaded region is 39.

As the smaller rectangle is inside the whole larger rectangle,

∴The area of the smaller rectangle subtracted from the area of the whole larger rectangle is the area of the shaded region.

So, (2x - 1)(x + 3) - (x - 2)(x + 1) = 39.

2x² + 6x - x - 3 - x² - x + 2x + 2 = 39.

x² + 6x - 1 = 39.

x² + 6x - 40 = 0.

x² + 10x - 4x - 40 = 0.

x(x + 10) - 4(x + `10) = 0.

(x + 10)(x - 4) = 0.

(x + 10) = 0 Or (x - 4) = 0.

x = - 10 Or x = 4.

Now if we put x = - 10 the lengths will be negative which is inappropriate.

So, the value of x that satisfies is 4.

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She will pay $12.75 for each shirt and $12.50 for each pair of jeans.

Only (d) 1 equation can you write to represent a single line using a point-slope equations

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

Equation = Linear equation

A linear equation can only be represented with one equation

When it is represented with multiple equations, the equations are equivalent equations

This means that the equations can be converted to one another

Hence, the solution is (d) 1 equation

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The logical equivalence of the statement ¬p∧(p→q) is option b. ¬p, which is the negation of p.

To determine the logical equivalence of the statement ¬p∧(p→q), we can simplify it using logical equivalences and truth tables.

Using the definition of the implication (p→q ≡ ¬p∨q), we can rewrite the statement as ¬p∧(¬p∨q).

Applying the distributive law (¬p∧(¬p∨q) ≡ (¬p∧¬p)∨(¬p∧q)), we get (¬p∧¬p)∨(¬p∧q).

Using the idempotent law (¬p∧¬p ≡ ¬p) and the distributive law again ((¬p∧¬p)∨(¬p∧q) ≡ ¬p∨(¬p∧q)), we simplify it to ¬p∨(¬p∧q).

From the truth table, we can see that the expression ¬p∨(¬p∧q) evaluates to T (true) only when p is false (F) regardless of the value of q. Otherwise, it evaluates to F (false).

Therefore, Option b, which is the negation of p, is the logical equivalent of the statement "p" (pq).

Now, let's analyze the truth table for the expression ¬p∨(¬p∧q):

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Answer:

a. 0.17

b. 0.95

Step-by-step explanation:

The key to answering both questions is that we should understand that the probability of an event happening = 1 - the probability of the event not happening

Firstly, we want to calculate the probability of less than four

Probability of less than four = 1 - probability of four or more heads

that is 1 - 0.83 = 0.17

Probability of less than 8 = 1 - probability of 8 or more = 1-0.05 = 0.95

To modify the spreadsheet model and find the optimal product mix considering the new VXP product, you would need to make the following changes: Update the spreadsheet to include a new row for the VXP product, with columns for assembling time, testing time, component cost, selling price, and maximum sales quantity.

To obtain a feasible solution that is close to optimal, you can try different approaches: Relax the integer constraints, Implement a rounding or adjustment strategy, Analyze the sensitivity of the solution.

Adjust the constraints to account for the maximum sales quantity of 50 VXPs.

Update the objective function to include the contribution of the VXP product sales.

Once you have made these modifications, you can use Solver to find the optimal product mix. However, it's important to note that the optimal solution may not result in integer values for the product quantities. If the optimal solution is not integer-valued, rounding the values in the changing cells to the nearest integers may result in an infeasible solution.

To obtain a feasible solution that is close to optimal, you can try different approaches: Relax the integer constraints, Implement a rounding or adjustment strategy, Analyze the sensitivity of the solution.

Relax the integer constraints: Allow non-integer values for the product quantities and see if the resulting solution is feasible and close to the optimal solution. This may be acceptable depending on the context and specific requirements of the problem.

Implement a rounding or adjustment strategy: Instead of rounding to the nearest integer, you can try rounding up or down or applying specific adjustment rules to the non-integer values. This can help ensure feasibility while still getting a solution close to the optimal.

Analyze the sensitivity of the solution: Check the sensitivity of the objective function to changes in the product quantities. If the solution is not sensitive to small changes in the quantities, you can manually adjust the quantities to obtain a feasible solution that is close to the optimal.

Ultimately, the approach to obtain a feasible solution that is close to optimal will depend on the specific requirements and constraints of the problem, as well as the acceptable trade-offs between optimality and feasibility.

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The power series expansion of the function f(x) = sinx. The correct answer is (b) 1-x^2/2 +x^4/24 -x^6/720.

To obtain this answer, we can use the power series expansion formula for sinx, which is given by

sinx = x - x^3/3! + x^5/5! - x^7/7! + ... .

Evaluating the first four terms of this expansion around x=0, we get

sinx = x - x^3/3! + x^5/5! - x^7/7! + ...

= x - (x^3/6) + (x^5/120) - (x^7/5040) + ...

= 1-x^2/2 +x^4/24 -x^6/720 + ...,

which is equivalent to option (b).

Therefore, the first four nonzero terms in the power series expansion of f(x) = sinx about x=0 are 1-x^2/2 +x^4/24 -x^6/720. The correct option is B).

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Answer:

There would be no value to the laptop. If you’re looking for the actual value, it would be worth $-375.

Step-by-step explanation:

When air expands adiabatically, its pressure and volume are related by the equation PV^1.4 = C, where C is a constant. This equation describes the specific relationship between pressure and volume changes during adiabatic expansion, without any heat transfer.

When air expands adiabatically, the relationship between its pressure (P) and volume (V) is given by the equation PV^1.4 = C, where C is a constant. This equation is derived from the adiabatic process, which means that no heat is transferred into or out of the system during expansion.

In an adiabatic process, the air expands and does work on its surroundings without exchanging heat with the surroundings. As the volume of the air increases, the pressure decreases. The exponent 1.4 in the equation is a constant specific to air and is known as the adiabatic index or the heat capacity ratio. It represents the relationship between the change in pressure and volume during adiabatic expansion.

The equation PV^1.4 = C indicates that as the volume increases, the pressure decreases in a specific manner determined by the adiabatic index. This relationship is commonly used in thermodynamics to analyze the behavior of gases during adiabatic processes. It helps to understand how changes in volume affect the pressure of a gas when no heat is added or removed from the system.

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To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

The domain of the function f(x) = ln(x-3) is x > 3, since the natural logarithm is undefined for non-positive values. The x-intercept occurs when f(x) = 0, so ln(x-3) = 0, which implies x - 3 = 1. Solving for x gives x = 4 as the x-intercept.

There are no vertical asymptotes for the function f(x) = ln(x-3) since the natural logarithm is defined for all positive values. However, the graph approaches negative infinity as x approaches 3 from the right, indicating a vertical asymptote at x = 3.

To sketch the graph of f(x) = ln(x-3), we start with the x-intercept at (4, 0). We can plot a few more points by choosing values of x greater than 4 and evaluating f(x) using a calculator.

As x approaches 3 from the right, the graph approaches the vertical asymptote at x = 3. The graph will have a horizontal shape, increasing slowly as x increases. Remember to label the axes and indicate the asymptote on the graph.

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⇒Let that number unknown number be represented by letter x.

⇒ Mathematically this can be written as

⇒\(x^{2} =13x-22\\\)

Note that this can help you find the unknown value by solving for x

\(x^{2} -13x+22=0\\\\(x-11)(x-2)=0\\x-11=0\\or \\x-2=0\\\\x=11\\\\or\\x=2\)

Note there are two solutions for this question. the answer is 11 and 2

GOODLUCK!!

Answer:

3x=9

3x*1/3=9*1/3 [reciprocal mean switching the fraction so 3/1--->1/3]

x=3

\(\huge\text{Hey there!}\)

\(\large\textsf{3x = 9}\)

\(\large\text{DIVIDE 3 to BOTH SIDES}\)

\(\mathsf{\dfrac{3x}{3}=\dfrac{9}{3}}\)

\(\large\text{CANCEL out: } \mathsf{\dfrac{3}{3}} \large\text{ because that gives you 1}\)

\(\large\text{KEEP: } \mathsf{\dfrac{9}{3}}\large\text{ because that helps us solve for x }\)

\(\large\text{New equation: x = } \dfrac{9}{3}\)

\(\mathsf{\dfrac{9}{3} = \bf 3}\)

\(\boxed{\boxed{\large\textsf{Therefore, your \underline{answer} is: \huge \bf x = 3 }}}\huge\checkmark\)

\(\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

The answer is

\(y =1 \\ x = 25\)

Step-by-step explanation:

\(.5 + .02x = .25 + .03 \\ .01x = .25 \\ x = 25 \\ then \\ y = .5 + .02 \times 25 = 1\)

Answer:

BD= 12

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

20 Plates

Step-by-step explanation:

Given that :

Sally's kitchen :

Setup cost = $60

Cost per plate = $12

Jimmy's BBQ :

Setup cost = $100

Cost per plate = $10

Let number of plates = x

Equate both and solve for x :

Sally's kitchen = Jimmy's BBQ

60 + 12x = 100 + 10x

12x - 10x = 100 - 60

2x = 40

x = 40/2

x = 20

20 plates

The order in which the kids sit is an illustration of arrangement.

We understand that: Bella is two seats away from Ella.

This arrangement is represented as: (E)_ (B)

Freddy sits between Bella and Ella.

This arrangement is represented as: (E) (F) (B)

Danielle does not sit next to Ella, and Charlie is at the end of the table.

This arrangement is represented as: (D) _ (E) (F) (B) (C)

So, Adam will occupy the seat between Danielle and Ella

This arrangement is represented as: (D) (A) (E) (F) (B) (C)

Hence, the order in which the 6 kids sit is: Danielle, Adam, Ella, Freddy, Bella and Charlie

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The statement is true.

An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process.

Given that,

From a linearly independent collection of {x₁, x₂,..., xp}, the gram-Schmidt process creates an orthogonal set of {v₁, v₂,..., vp} with the feature that for each k, the vectors v₁...vk span the same subspace as that spanned by x₁...xk.

Whether the claim is true or false must be determined.

The statement is true.

An orthogonal set with the same dimension as the initial collection of vectors is created by the Gram-Schmidt process. An orthogonal set is further linearly independent. The orthogonal set produced by the Gram-Schmidt process and the original set will cover the same subspace if their dimensions are the same.

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Answer:

x=2

Step-by-step explanation:

you'll have to take my word for it

Answer:

10 : 3

Step-by-step explanation:

15 : 4.5 (divide both parts by 1.5 )

= 10 : 3

ANSWER

My Answer is in the photo above by the way I thought you had made a mistake in the question that's why I gave answers for both 15:4.5 and 15:4:5

The solution is: x = 10/3 hours

What is the equations with one variable?

An equation with one variable is a mathematical statement that involves an unknown quantity represented by a letter, usually x, and an equal sign, where the expressions on both sides of the equal sign have the same value.

We need to set up an equation using the given information to solve for x.

Let's start with Dwayne's formula:

Cost = 30x + 50

And Ivor's formula:

Cost = 45x

Since a job of x hours costs the same for both Dwayne and Ivor, we can set their formulas equal to each other:

30x + 50 = 45x

Simplifying and solving for x:

50 = 15x

x = 50/15

x = 10/3 hours

Therefore, the solution is: x = 10/3 hours

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Answer:

I believe it's c.

Step-by-step explanation:

Starts and includes 2, goes until and includes 5.

Answer:

C

Step-by-step explanation:

Domain represents the possible x-values and the line on the graph only runs through x-values between 2 and 5.