Select the correct answer.

Answer:

  (b) When a vertical line intersects the graph of a relation more than once, it indicates that for that input there is more than one output, which means the relation is not a function.

Step-by-step explanation:

You want to know why the vertical line test tells us whether the graph of a relation represents a function.

A relation maps a set of inputs to a set of outputs. A function maps a set of unique inputs to a set of outputs. That is, the elements of the input set of a function are not repeated, but appear only once.

On the graph of a relation, the input values are mapped to the horizontal coordinate(s) of the point(s) on the graph. If the relation has repeated input values, then those points will have the same x-coordinate on a graph, and will lie on a vertical line. So, we can conclude ...

When a vertical line intersects the graph of a relation more than once, it indicates that for that input there is more than one output, which means the relation is not a function.

__

Additional comment

You can narrow the choices by considering their vocabulary. The question asks about the graph of a relation. Choices A and D talk about the graph of a function, so can be rejected immediately.

The subject of the question is a vertical line. As you know, a vertical line is of the form x = constant, where an (x, y) ordered pair is an (input, output) pair of a relation. Thus a vertical line will be referring to one input value that is a constant. Choice C talks about "more than one input", which has no relationship to a vertical line. Hence the only choice that makes any sense in the context of the question is B.

A lot of multiple choice questions can be answered appropriately just by considering the way the question and answers are worded.

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the left side of this equation equal the right side through the process of completing the square that establishes the equality between the left side and the right side of the Gaussian integral equation.

using  completing the square method:

Starting with the left side of the equation:

∫[tex]e^(^-^x^2)[/tex] dx

[tex]e^(^-^x^2) = (e^(^-x^2/2))^2[/tex]

∫[tex](e^(^-^x^2/2))^2 dx[/tex]

let  u = √(x²/2) =  x = √(2u²).

dx = √2u du.

∫ [tex](e^(^x^2/2))^2 dx[/tex]

= ∫ [tex](e^(^-2u^2)[/tex]) (√2u du)

The integral of [tex]e^(-2u^2)[/tex]= √(π/2).

∫ [tex](e^(-x^2/2))^2[/tex] dx

= ∫  (√2u du) [tex](e^(-2u^2))\\[/tex]

= √(π/2) ∫ (√2u du)

We substitute back  u = √(x²/2), we obtain:

∫ [tex](e^(-x^2/2))^2[/tex]dx

= √(π/2) (√(x²/2))²

= √(π/2) (x²/2)

= (√π/2) x²

A comparison  with the right side of the equation  shows that they are are equal.

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Answer:

The expression 20!/1! is not directly related to the binomial distribution.

The expression 20!/1! represents the number of ways to arrange 20 distinct objects in a specific order, where each object is used exactly once. This is known as a permutation, and the number of permutations of n objects is given by n!.

On the other hand, the binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success. The probability of getting k successes in n trials, each with probability p of success, is given by the binomial probability mass function:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

where (n choose k) represents the number of ways to choose k items from a set of n items, and is given by the formula:

(n choose k) = n!/k!(n-k)!

So, while the expression 20!/1! is not directly related to the binomial distribution, the binomial distribution does involve calculating combinations (i.e., choosing k items from a set of n items), which are related to permutations.

Given statement solution is :- Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages: Simplification and abstraction, Prediction and simulation, Cost and time efficiency, Insight and understanding.

Mathematical models are extremely valuable tools in various fields, including chemistry, biology, and physics. They offer several advantages:

Simplification and abstraction: Mathematical models allow complex systems or processes to be represented using simplified mathematical equations or algorithms. This simplification helps in understanding the underlying principles and relationships of the system, making it easier to analyze and predict outcomes.

Prediction and simulation: Models enable scientists to make predictions about the behavior of a system under different conditions. They can simulate scenarios that are difficult or impossible to observe in the real world, allowing researchers to explore various hypotheses and make informed decisions.

Cost and time efficiency: Models can be used to explore different scenarios and test hypotheses in a relatively quick and cost-effective manner compared to conducting real-world experiments. They can help guide experimental design by providing insights into the most relevant variables and parameters.

Insight and understanding: Mathematical models often reveal underlying patterns and relationships that may not be immediately apparent from experimental data alone. They provide a framework for organizing and interpreting data, leading to a deeper understanding of the system being studied.

However, mathematical models also have limitations and potential disadvantages:

Simplifying assumptions: Models are based on assumptions and simplifications, which may not fully capture the complexity of the real-world system. If these assumptions are incorrect or oversimplified, the model's predictions may be inaccurate or misleading.

Uncertainty and error: Models are subject to uncertainties and errors stemming from the inherent variability of the system, limitations in data availability or quality, and simplifying assumptions. It is crucial to assess and communicate the uncertainties associated with model predictions.

Validation and verification: Models need to be validated and verified against experimental data to ensure their accuracy and reliability. This process requires rigorous testing and comparison to real-world observations, which can be challenging and time-consuming.

Mathematical models are closely linked to the fields of chemistry, biology, and physics, providing valuable insights and predictions in these disciplines. Here are some examples:

Chemistry: Mathematical models are used to study chemical reactions, reaction kinetics, and molecular dynamics. One example is the use of rate equations to model the kinetics of a chemical reaction, such as the reaction between reactants A and B to form product C.

Biology: Mathematical models play a crucial role in understanding biological systems, such as population dynamics, gene regulation, and the spread of infectious diseases. For instance, epidemiological models like the SIR (Susceptible-Infectious-Recovered) model are used to simulate and predict the spread of diseases within a population.

Physics: Mathematical models are fundamental in physics to describe physical phenomena and predict outcomes. One well-known example is Newton's laws of motion, which can be mathematically modeled to predict the motion of objects under the influence of forces.

Quantum mechanics: Mathematical models, such as Schrödinger's equation, are used to describe the behavior of particles at the quantum level, providing insights into atomic and molecular structures and the behavior of subatomic particles.

Fluid dynamics: Mathematical models, such as the Navier-Stokes equations, are employed to study the behavior of fluids, including airflow, water flow, and weather patterns.

These examples demonstrate the wide range of applications for mathematical models in understanding, predicting, and simulating various phenomena in the fields of chemistry, biology, and physics.

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Answer:

3√2/2

Step-by-step explanation:

4 1/2 = 9/2

Now we can express this fraction in radical form by finding the square root of the numerator and denominator separately:

√(9/2) = √9 / √2

Since the square root of 9 is 3, we can simplify further:

√(9/2) = 3 / √2

To rationalize the denominator (i.e., eliminate the radical from the denominator), we can multiply both the numerator and denominator by √2:

3 / √2 * √2 / √2 = 3√2 / 2

Therefore, 4 1/2 in radical form is 3√2/2.

It will take approximately 28.67 years for Talwar's investment of R5,800 to grow to R26,100 at a simple interest rate of 12.2% per annum.

To calculate the number of years it will take for Talwar's investment to grow to R26,100 at a simple interest rate of 12.2% per annum, we can use the formula for simple interest:

Simple Interest = Principal × Rate × Time

Given that the principal (P) is R5,800, the rate (R) is 12.2% (or 0.122 as a decimal), and the desired amount (A) is R26,100, we need to find the time (T) it will take. Rearranging the formula, we get:

Time = (Amount - Principal) / (Principal × Rate)

Plugging in the values, we have:

Time = (R26,100 - R5,800) / (R5,800 × 0.122)

= R20,300 / R708.6

≈ 28.67 years

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The percent profit will be 15.5%.The formula used to calculate the percentage profit is:Percentage Profit = (Profit / Cost Price) x 100%.

Let's assume that the retailer has an item with a wholesale price of $100. After a 54% increase in the wholesale price, the new wholesale price is $154.Now, when the retailer provides a 25% discount off the ticket price, the new price of the item becomes: $154 x 75% = $115.5.

The cost of producing the item is $100, but the retailer sells it for $115.5. Hence, the profit made by the retailer is:$115.5 - $100 = $15.5 or 15.5% profit.The percent profit that the retailer will realize is 15.5%. Therefore, the percent profit will be 15.5%.The formula used to calculate the percentage profit is:Percentage Profit = (Profit / Cost Price) x 100%.

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Answer:

345, 678, 823

Step-by-step explanation:

Ascending means increasing (lowest to highest)

The distance from Trinidad to Tobago via the ferry is approximately 158 kilometers, but when rounded to the nearest tens, it is approximately 160 kilometers.

The distance from Trinidad to Tobago via the ferry is approximately 158 kilometers. To determine the distance to the nearest tens, we need to round this value to the nearest multiple of 10.

To round a number to the nearest tens, we look at the digit in the ones place. If it is 0 to 4, we round down, and if it is 5 to 9, we round up.

In this case, the digit in the ones place is 8. Since 8 is closer to 10 than to 0, we round up to the nearest tens. Thus, the distance from Trinidad to Tobago can be rounded to 160 kilometers.

Rounding to the nearest tens gives us a value that is easier to work with and provides a rough estimate. It is important to note that this rounded value is not exact and may differ slightly from the actual distance. However, for practical purposes, rounding to the nearest tens is often sufficient.

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Answer:opposite side has side length of 11. One of the angle is 27 degrees.

Step-by-step explanation:

Answer:

when x=-9, y=1

Step-by-step explanation:

the graph shows when the x is at -9, the y is at 1

743 general admission tickets and 304 reserved seat tickets were sold.

Let's solve this problem using a system of equations. Let's assume that x represents the number of general admission tickets sold and y represents the number of reserved seat tickets sold.

According to the given information, we have two equations:

Equation 1: The total number of tickets sold is 1047.

x + y = 1047

Equation 2: The total revenue from ticket sales is $4576.50.

3.50x + 6.50y = 4576.50

Now, we can solve this system of equations.

We can start by multiplying Equation 1 by 3.50 to eliminate x:

[tex]3.50(x + y) = 3.50(1047)\\3.50x + 3.50y = 3664.50[/tex]

Now we have the following system of equations:

[tex]3.50x + 3.50y = 3664.50 (Equation 3)\\3.50x + 6.50y = 4576.50 (Equation 2)[/tex]

By subtracting Equation 3 from Equation 2, we can eliminate x:

[tex](3.50x + 6.50y) - (3.50x + 3.50y) = 4576.50 - 3664.50\\3.00y = 912.00[/tex]

Dividing both sides of the equation by 3.00, we find:

y = 304

Now, substitute the value of y into Equation 1 to find x:

x + 304 = 1047

x = 743

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Answer: its B

Step-by-step explanation: because its C ur welcome

Answer:

We can simplify the expression under the cube root first:

3∛(125a^6) = 3∛(5^3 * a^6) = 3 * 5 * a^2 = 15a^2

Therefore, the cube root of 3 square root 125 a^6 is equal to 15a^2.

Answer:

Part A:

Using the Factor Theorem, we know that f(x) can be written as:

f(x) = a(x - 6)(x + 1)(x + 3)

where a is a constant that we need to determine.

To find the value of a, we can use one of the given zeros of f(x), for example, x = 6. When x = 6, we know that f(x) = 0, so we can substitute these values into the equation above:

0 = a(6 - 6)(6 + 1)(6 + 3)

Simplifying, we get:

0 = 189a

Therefore, a = 0.

So, the polynomial f(x) is:

f(x) = 0(x - 6)(x + 1)(x + 3)

Simplifying, we get:

f(x) = 0

Part B:

To divide f(x) by (x² - x - 2), we can use long division:

0

___________

x² - x - 2 | 0x³ + 0x² + 0x + 0

- (0x³ - 0x² - 0x)

_______________

0x² + 0x

- (0x² - 0x - 2)

_______________

2x + 2

Therefore, the rational function g(x) in simplest factored form is:

g(x) = (2x + 2)/(x² - x - 2)

To find the vertical asymptotes, we need to find the roots of the denominator:

x² - x - 2 = 0

(x - 2)(x + 1) = 0

Therefore, the vertical asymptotes are x = 2 and x = -1.

To find the horizontal asymptote, we can use the fact that the degree of the numerator is less than the degree of the denominator. Therefore, the horizontal asymptote is y = 0.

Part C:

The function g(x) has two vertical asymptotes at x = 2 and x = -1.

To check for any holes, we can simplify the function by factoring the numerator:

g(x) = 2(x + 1)/(x - 2)(x + 1)

Since we factored the numerator and denominator of g(x), we can see that there is a hole in the graph at x = -1. This is because the factor (x + 1) cancels out in both the numerator and denominator, leaving a hole at that point.

To find the x-intercepts, we need to solve for when the numerator is equal to zero:

2x + 2 = 0

x = -1

Therefore, the x-intercept is (-1, 0).

To find the y-intercept, we can substitute x = 0 into the equation for g(x):

g(0) = 2(0 + 1)/(0 - 2)(0 + 1)

g(0) = -1

Therefore, the y-intercept is (0, -1).

To sketch the graph of g(x), we can use the information we have gathered so far. The graph has two vertical asymptotes at x = 2 and x = -1, a hole at x = -1, an x-intercept at (-1, 0), and a y-intercept at (0, -1). The horizontal asymptote is y = 0.

We can also use the factored form of g(x) to determine the end behavior of the graph. As x approaches positive or negative infinity, the function approaches zero. Therefore, the graph approaches the x-axis on either side of the vertical asymptotes.

Putting all of this information together, we can sketch the graph of g(x) as follows:

[insert graph of g(x) here]

Answer:

a. The cost at 3% is $46.57 b. The cost at 4% is $49.33 c. The cost at 5% is $52.21

Step-by-step explanation:

Step-by-step explanation:

Given:

f(x) = x² + 3

To find:

f(a + 7),

Replace x with (a + 7) in the function f(x) = x² + 3:

→ f(a + 7) = (a + 7)²+ 3

Now,simplify by expanding the square:

→ f(a + 7) = a² + 14a + 49 + 3

→ f(a + 7) = a² + 14a + 52

Therefore, f(a + 7) = a²+ 14a + 52.

Answer:

[tex]h'(1)=4\sec^2(8)[/tex]

[tex]h''(1)=32\sec^2(8)\tan(8)[/tex]

Step-by-step explanation:

Given the following function.  

[tex]h(x)=\tan(4x+4)[/tex]

Find the following:

[tex]h'(1)= \ ??\\\\h''(1)= \ ??\\\\\\\hrule[/tex]

Taking the first derivative of h(x). We will use the chain rule and the rule for tangent.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{The Chain Rule:}}\\\\\dfrac{d}{dx}[f(g(x))]=f'(g(x)) \cdot g'(x) \end{array}\right}\\\\\\\boxed{\left\begin{array}{ccc}\text{\underline{The Tangent Rule:}}\\\\\dfrac{d}{dx}[\tan(x)]=\sec^2(x) \end{array}\right}[/tex]

[tex]h(x)=\tan(4x+4)\\\\\\\Longrightarrow h'(x)=\sec^2(4x+4) \cdot4\\\\\\\therefore \boxed{h'(x)=4\sec^2(4x+4)}[/tex]

Now plugging in x=1:

[tex]\Longrightarrow h'(1)=4\sec^2(4(1)+4)\\\\\\\Longrightarrow \boxed{\boxed{h'(1)=4\sec^2(8)}}[/tex]

Taking the second derivative of h(x). Using the chain rule again and the secant rule.

[tex]\boxed{\left\begin{array}{ccc}\text{\underline{The Secant Rule:}}\\\\\dfrac{d}{dx}[\sec(x)]=\sec(x) \tan(x) \end{array}\right}[/tex]

[tex]h'(x)=4\sec^2(4x+4)\\\\\\\Longrightarrow h''(x)=(4\cdot 2)\sec(4x+4) \cdot \sec(4x+4)\tan(4x+4) \cdot 4\\\\\\\therefore \boxed{h''(x)=32\sec^2(4x+4)\tan(4x+4)}[/tex]

Now plugging in x=1:

[tex]\Longrightarrow h''(1)=32\sec^2(4(1)+4)\tan(4(1)+4)\\\\\\\therefore \boxed{\boxed{ h''(1)=32\sec^2(8)\tan(8)}}[/tex]

Thus, the problem is solved.

[tex](8.2 \times 10^(^-^1^0^))[/tex][tex](5.3\times 10^(^-^9^))[/tex]The sum of [tex](5.3 \times 10^(^-^9^))[/tex] and [tex](8.2 \times 10^(^-^1^0^))[/tex] in scientific notation is 1.35 x 10^−8.

To find the sum of [tex](5.3 \times 10^(^-^9^))[/tex] and [tex](8.2 x 10^(^-^1^0^))[/tex], we can add the coefficients and keep the same base, which is 10. Adding 5.3 and 8.2 gives us 13.5. Since both numbers are expressed in scientific notation, we need to adjust the decimal point to have one digit to the left of it.

The exponent in scientific notation represents the number of decimal places we need to move the decimal point to the left (for negative exponents) or to the right (for positive exponents). In this case, the exponents are -9 and -10.

Since -9 is larger than -10, we need to adjust the decimal point by 1 place to the left. Therefore, the sum of [tex](5.3 x 10^(^-^9^))[/tex] and [tex](8.2 \times 10^(^-^1^0^))[/tex] in scientific notation is [tex]1.35 \times 10^-^8^[/tex].

Note: Scientific notation is a concise way of representing very large or very small numbers by using powers of 10. It consists of a coefficient (a decimal number between 1 and 10) multiplied by 10 raised to an exponent.

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Answer::x= -2x= 2Step-by-step explanation:First, identify the problem.l x+3 l = 5Secondly, plug in the value for x. l -

Step-by-step explanation:

To determine the probability of having a specific number of phone calls within a given minute, we can use the Poisson distribution, assuming that the calls follow a Poisson process.

The average number of phone calls per minute is 2.5, which indicates that the rate parameter (λ) is also 2.5, as it represents the average number of events occurring in a given interval.

To calculate the probability of having 4 or fewer calls in one minute, we sum the probabilities of having 0, 1, 2, 3, or 4 calls using the Poisson distribution formula. The probability is given by:

P(X ≤ 4) = Σ(k=0 to 4) (e^(-λ) * λ^k / k!)

Similarly, to find the probability of having more than 6 calls, we sum the probabilities of having 7, 8, 9, and so on, up to infinity. The probability is calculated as:

P(X > 6) = 1 - P(X ≤ 6)

By plugging in the values and performing the calculations, we can determine the probabilities for both scenarios.

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To find the value of Az in the geometric sequence, we can use the given information. The geometric sequence is represented as follows: A3, 60, 160, 06 = 9.

From this, we can see that the third term (A3) is 60 and the common ratio (r) is 160/60.

To find Az, we need to determine the value of the nth term in the sequence. In this case, we are looking for the term with the value 9.

We can use the formula for the nth term of a geometric sequence:

An = A1 * r^(n-1)

In this formula, An represents the nth term, A1 is the first term, r is the common ratio, and n is the position of the term we are trying to find.

Since we know A3 and the common ratio, we can substitute these values into the formula:

60 =[tex]A1 * (160/60)^(3-1)[/tex]

Simplifying this equation, we have:

[tex]60 = A1 * (8/3)^260 = A1 * (64/9)[/tex]

To isolate A1, we divide both sides of the equation by (64/9):

A1 = 60 / (64/9)

Simplifying further, we have:

A1 = 540/64 = 67.5/8.

Therefore, the first term of the sequence (A1) is 67.5/8.

Now that we know A1 and the common ratio, we can find Az using the formula:

Az = A1 * r^(z-1)

Substituting the values, we have:

Az =[tex](67.5/8) * (160/60)^(z-1)[/tex]

However, we now have the formula to calculate it once we know the position z in the sequence.

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Answer:

That's a great point! It's important to continue to encourage others to recycle and to educate people on the benefits of recycling to help achieve that 100% goal.

Answer:

d. creating

Step-by-step explanation:

Random numbers are useful for creating real words situations that involve chance.

A.being

B.selling

C.modeling

D.creating

Answer:

x = [tex]\frac{-11}{4}[/tex]

Step-by-step explanation:

x - 8 + 5x + 3  Subtract 1x from both sides

-8 = 4x + 3  Subtract 3 from both sides

-11 = 4x  Divide both sides by 4

[tex]\frac{-11}{4}[/tex] = x

Helping in the name of Jesus.

Answer:

5 + m^3 n^2

----------------------

m^2 n^2

Step-by-step explanation:

To add fractions, we need to get a common denominator:

The common denominator is m^2 n^2.

Multiply the second term by m^2n/ m^2n

m/n * m^2n / m^2 n = m^3n / m^2n^2

Now we can add the two terms

5                               m^3 n^2

------                 + ---------------------------

m^2 n^2                      m^2 n^2

5 + m^3 n^2

----------------------

m^2 n^2

Answer:

Step-by-step explanation:

Remeber, if we have some fraction,

[tex]\frac{x-y}{d}[/tex]

We can rewrite this as a difference of quotients:

[tex]\frac{x}{d} -\frac{y}{d}[/tex]

So essentially,

the first step becomes

[tex]\frac{sec(\alpha )}{sec(\alpha )(tan(\alpha )} -\frac{tan(\alpha )}{sec(\alpha )(tan(\alpha )}[/tex]

Next, remember that we can cancel out common factors in the numerator and denominator.

[tex]\frac{1}{tan(\alpha )} -\frac{1}{sec(\alpha )}[/tex]

Next in order to match the RHS, we would apply the Reciprocal Identity and get

[tex]cot(a)-cos(\alpha )[/tex]

Let me know if you need any further clarification. These types of problems involve math ingenuity so I suggest you  to work on recognizing perfect squares, differences of squares, properties of fractions, canceling common factors, etc.

The present value (PV) of the investment today is approximately $2,965.05.

To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.

The formula for the present value of an annuity is given by:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

C = Cash flow per period

r = Interest rate per period

n = Number of periods

In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.

Let's plug in these values into the formula and calculate the present value (PV):

PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]

Using a calculator, we can evaluate the expression inside the brackets:

PV = $500 * [(1 - 0.376889) / 0.105]

Simplifying further:

PV = $500 * [0.623111 / 0.105]

PV = $500 * 5.930105

PV = $2,965.05

Therefore, the present value (PV) of the investment today is approximately $2,965.05.

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