If f(x)=(x-2)(x+3), then f(1)=

Answer:

The answer is $9.67.

Step-by-step explanation:

Notebooks: 5 * 1.29 = 6.45

Pens: 2 * 1.19 = 2.38

Pencils: 12 * 0.05 = 0.60

Erasers: 6 * 0.15 = 0.90

Total: 6.45 + 2.38 + 0.60 + 0.90 = 10.33

Change: 20 - 10.33 = 9.67

The functions are as follows:

Function f: R → R, f(x) = x²

Onto function: The function f is not an onto function since some negative numbers do not have square roots in real numbers.

One-to-one function: The function f is not a one-to-one function since for each positive number "x", there exist two values that we can input and get that positive number "x" output.

Example: Consider -4 which is a negative number. It doesn't have a square root in real numbers.

Function g: R → R, G(x) = x³

On to function: The function g is onto since every real number can be obtained by the function g.

One-to-one function: The function g is one-to-one since for each input "x" there is only one output.

Example: Consider the values x = 2 and x = -2. On inputting these values into the function, we get outputs 8 and -8 respectively. Thus, we get two different outputs for the same value h(x) = x³Function h: Z → Z, h(x) = x³On to function: The function h is onto since every integer has a cube root.

One-to-one function: The function h is not a one-to-one function since for each negative number "x", there exist two values that we can input and get that negative number "x" output.

Example: Consider the input -2. On input this value into the function, we get the output -8. But -(-2)³ = -8. Thus, we get two different inputs for the same value h(x) = x³.

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Answer:

-7

Step-by-step explanation:

Hope this helped! :)

Answer:

CDF is 52° and DEF is 76°

I hope this helps you, im sorry if it's wrong

Answer: 3 - x

Step-by-step explanation: With

Subtraction be careful. 3 - x is not the same as x - 3. You have to keep the values given in order.

In order to estimate the population proportion within 5%, a sample size of at least 384 is needed.

The number of individuals or observations included in a study is referred to as the sample size. Two statistical properties are influenced by the sample size: 1) The accuracy of our estimates, and 2) The ability to draw conclusions from the study.

This can be calculated using the formula:

n = (z^2 * p * (1-p)) / (e^2)

where z is the z-score corresponding to a 95% confidence level, p is the estimated proportion of people in favor of legalizing marijuana, and e is the margin of error (5%).

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The equation of the sine function is: y = 4 sin(1/4 x).

What is a sine function?

A sine function is a type of trigonometric function that relates the angle of a right triangle to the ratio of the length of its opposite side to its hypotenuse. It is defined as the ratio of the length of the opposite side of an angle in a right triangle to the length of the hypotenuse.

The general form of a sine function is:

y = A sin(Bx + C) + D

where A is the amplitude, B determines the period (B = 2π/period), C is the phase shift, and D is the vertical shift.

Substituting the given values, we get:

A = 4 (amplitude)

Period = 8π

B = 2π/Period = 2π/(8π) = 1/4

C = 0 (no phase shift)

D = 0 (no vertical shift)

the equation of the sine function is:

y = 4 sin(1/4 x)

Note that the value of B is the reciprocal of the period, since the formula for period is T = 2π/B, which can be rearranged to get B = 2π/T.

Hence, the equation of the sine function is: y = 4 sin(1/4 x).

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Answer:

8.50 dollars

Step-by-step explanation:

1.25 per mile ==> 5 dollars for 4 miles

5+3.50(original cost) = 8.50

Answer:

Only 1 flavour ??

Only 1 flavour ??anyway ....

Only 1 flavour ??anyway ....number of different ice cream desserts

desserts= 3 x 1 x 4

= 12

The level of confidence, variability estimates, and sample size can help determine the accuracy (sample error) and estimate the costs of the sample.

Explanation: The level of confidence (e.g., 95%) indicates the probability that the sample accurately represents the population. It determines the range within which the population parameter is estimated. The variability estimates, such as the standard deviation or variance, provide information about the spread of the data. By combining the level of confidence, variability estimates, and sample size, one can estimate the accuracy or sample error, which represents how closely the sample statistics reflect the population parameters.

Determining the costs of the sample involves factors beyond the provided information, such as data collection methods, analysis procedures, and logistical considerations. The representativeness of the sample depends on the sampling method used and how well it captures the characteristics of the target population.

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For a rectangular granite slab purchased by Bob with area 18 sq. feet who replacing the laminate countertop, the width of slab is three feet.

We have a homeowner is replacing the laminate countertop with granite. For this he purchased a slab of granite that is 18 square feet. That is area of slab = 18 sq. feet

Length of slab, l = 6 feet

We have to determine the wide of slab. The shape of slab is rectangular. So, we have calculate the width of rectangular slab. Let the width be equal to ' x feet' . As we know, area of rectangle is written as product of length and width of rectangle. Thus, Area = l × x

=> 18 feet² = 6 feet × x

dividing both sides by 6

=> x = 3 feet

Hence, required width is 3 feet.

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Answer:

see below

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

A = pi (5)^2

A = 25 pi

Using 3.14 for pi

A = 78.5 ft^2

Using the pi button

A =78.53981634 ft^2

Answer:

Y = W + 5yk^3 / h

Step-by-step explanation:

Answer:

B

There is no friction

Step-by-step explanation:

if the object is stationary , it's not moving, no forces acting on it how can it produces friction ?

The values of x that make the function undefined are x = 2 and x = -2. These values make the denominator equal to zero, causing the function to be undefined. Note that x = 3 does not make the denominator zero, so the function is defined for x = 3.

To determine the values that would make the function f(x) = (3-x) / (x^2 - 4) undefined, we need to find the values of x for which the denominator of the fraction becomes zero.

The denominator of the function is x^2 - 4. To find the values of x that make the denominator zero, we'll set x^2 - 4 equal to zero and solve for x:

x^2 - 4 = 0

We can factor this expression as a difference of squares:

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

Now, we'll solve for x by setting each factor equal to zero:

1) x + 2 = 0
  x = -2

2) x - 2 = 0
  x = 2

So, the values of x that make the function undefined are x = 2 and x = -2. These values make the denominator equal to zero, causing the function to be undefined. Note that x = 3 does not make the denominator zero, so the function is defined for x = 3.

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The total distance travelled by the ball after dropping from a height of 16 feet and rebounds 0.81 feet is equal to 168.4 feet.

Balls from a height = 16 feet

Rebounds = 0.81feet

It form a geometric progression pattern :

16 + 16(0.81) + 16(0.81)² + 16(0.81)³ + ......+ ∞

Using sum of geometric progression :

S = a / 1 - r

here a = 16

r = 0.81

S represents the sum .

The total distance travelled by the ball is double of the sum .

S = 16 / ( 1 - 0.81 )

  = 16 / ( 0.19)

  = 84.2 feet

Total distance travelled by the ball  = 2 × 84.2 feet

                                                           = 168.4 feet

Therefore, the total distance travelled by the ball as per given situation is equal to 168.4 feet.

The above question is incomplete, the complete question is:

A ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.81h feet. Find the total distance traveled by the ball .

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The key underlying assumption of the single index model is that the return of a security can be explained by the return of a broad market index.

This assumption forms the basis of the single index model, also known as the market model or the capital asset pricing model (CAPM).

In this model, the return of a security is expressed as a function of the return of the market index. The single index model assumes that the relationship between the returns of a security and the market index is linear.

It suggests that the risk and return of a security can be explained by its exposure to systematic risk, which is represented by the market index.

The single index model assumes that the return of a security can be decomposed into two components: systematic risk and idiosyncratic risk.

Systematic risk refers to the risk that cannot be diversified away, as it affects the entire market. Idiosyncratic risk, on the other hand, is the risk that is specific to a particular security and can be diversified away by holding a well-diversified portfolio.

The single index model assumes that the systematic risk is the only risk that investors should be compensated for, as idiosyncratic risk can be eliminated through diversification.

It suggests that the expected return of a security is determined by its beta, which measures its sensitivity to the market index. A security with a higher beta is expected to have a higher return, as it is more sensitive to market movements.

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It would take approximately 2.86 gallons of standard interior latex paint to cover 1000 square feet with one coat, but this estimate may vary depending on several factors.

To determine the amount of paint needed to cover 1000 square feet, several factors must be considered, including the type of paint being used, the surface being painted, and the number of coats required.

Assuming a standard interior latex paint with a coverage rate of approximately 350 square feet per gallon, it would take approximately 2.86 gallons of paint to cover 1000 square feet with one coat. However, it is important to note that this is just an estimate and may vary depending on the specific circumstances of the project.

Factors such as the porosity and texture of the surface being painted, as well as the color and quality of the paint being used, can all affect the coverage rate. Additionally, if multiple coats are required or if there are areas that require more than one coat for complete coverage, more paint will be needed.

It is always recommended to consult with a professional painter or refer to the manufacturer's instructions for specific guidance on how much paint is needed for a particular project.

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the particular solution xp(t) = 0 satisfies the given system.

What is a Particular Solution?

a particular solution to the given system using the method of undetermined coefficients, we assume that the particular solution has the same form as the nonhomogeneous term. In this case, the nonhomogeneous term is "3e^(-2t)". Let's denote the particular solution as xp(t).

To find a particular solution to the given system using the method of undetermined coefficients, we assume that the particular solution has the form:

xp(t) = A*e^(-2t)

where A is a constant that we need to determine.

Given the system:

x' = 5x - 7y + 12

y' = x - 3y - 3e^(-2t)

Differentiating xp(t) with respect to t:

xp'(t) = -2A*e^(-2t)

Substituting xp(t) and xp'(t) into the system equations, we have:

-2Ae^(-2t) = 5x - 7y + 12

x - 3y - 3e^(-2t) = Ae^(-2t)

Now, we equate the coefficients of e^(-2t) on both sides of the equations:

-2A = 0 (from the first equation)

A = 0

Since -2A = 0, we can conclude that A must be zero.

Therefore, the particular solution xp(t) = 0 satisfies the given system.

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The type of loan that Brady most likely getting  is option (a) conventional loan

Conventional loans are typically not guaranteed or insured by the government and often require a higher down payment compared to government-backed loans such as FHA or VA loans. The down payment requirement of $5,250, which is 3.5% of the purchase price, is lower than the typical down payment requirement for a conventional loan, which is usually around 5% to 20% of the purchase price.

ARM (Adjustable Rate Mortgage) loans have interest rates that can change over time, which can make them riskier for borrowers. FHA (Federal Housing Administration) loans are government-backed loans that typically require a lower down payment than conventional loans, but they also require mortgage insurance premiums.

VA (Veterans Affairs) loans are available only to veterans and offer favorable terms such as no down payment requirement, but not everyone is eligible for them. Fixed-rate loans have a fixed interest rate for the life of the loan, but the down payment amount does not indicate the loan type.

Therefore, the correct option is (a) Conventional loan

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In the given graph, the independent variables represent those factors that are manipulated by the researcher. On the other hand, the dependent variable represents the effect of the independent variable(s).Let's first understand the given graph - it shows data from the light-colored soil enclosure.

There is one dependent variable and more than one independent variable on the graph. Based on this information, it can be concluded that the graph represents the result of an experiment where multiple factors were tested to observe their impact on the dependent variable. Now, coming to the question, we need to identify the independent variables from the graph. Unfortunately, the graph is not available here to analyze and provide an accurate answer. Suppose the experiment aimed to study the effect of different factors on the growth of plants in light-colored soil. Some independent variables that could be manipulated by the researcher are:

Amount of water provided to the plants Type of fertilizer used for the soil Temperature of the enclosure Humidity level inside the enclosure Intensity and duration of light exposure. Amount of water provided to the plants, type of fertilizer used for the soil, temperature of the enclosure, humidity level inside the enclosure, intensity, and duration of light exposure.

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Travis ate 1/12 of the whole cake the next day

A fraction represents a part of a whole. In this case, the whole cake represents the whole, and the part that was eaten represents the fraction. When we say that 3/4 of the cake was eaten, it means that out of the whole cake, 3/4 or three-fourths of the cake was consumed.

Travis ate 1/3 of the remaining cake the next day.

This means that after 3/4 of the cake was eaten, there was 1/4 of the cake remaining. Travis ate 1/3 of that remaining 1/4 of the cake, which can be written as

=> 1/3 x 1/4.

To simplify this fraction, we multiply the numerators (1 x 1) and the denominators (3 x 4), giving us 1/12.

We can write this fraction as a percentage, which is 8.33%. To summarize, fractions are used to represent parts of a whole, and in this case, Travis ate 1/12 or 8.33% of the whole cake the next day.

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Answer:

Three choice

Step-by-step explanation:

I think.

Answer:

120 degrees

Step-by-step explanation:

vertical angle of isoceles = 180 - 2(base angles) = 180 - 2(30) = 120

Answer:

isosceles triangle means both angle or sides equal so in this way

unknown angle + 30 + 30 = 180°

unknown angle+60=180

so unknown angle=120°

which is vertical angle

The equation of function for the given problem is y = 3x + 12.

What is point slope form of the line?

For linear equations, the general form is y - y1 = m(x - x1).

It draws attention to the line's slope and one of the line's points (that is not the y-intercept).

Given:

A bathtub has some water in it. Mia turns on the faucet to add more water.

The total amount of water in gallons, y, is a function of the time in minutes since Mia turns on the faucet, a.

The graph of the linear function passes through the points (4, 24) and

(6, 30).

We have to find the equation of function.

Let the linear function passes through the points (4, 24) and (6, 30).

First to find the slope of equation using given points.

\(m = \frac{y_2-y_1}{x_2-x_1} = \frac{30-24}{6-4} = \frac{6}{2} = 3\)

Now to find the equation of function.

Consider the point slope form of the line,

\(y-y_1=m(x-x_1)\)

Plug the values of m = 3 and \((x_1,, y_1) = (4, 24)\)

⇒

\(y-24=3(x-4)\\y-24=3x-12\\y=3x-12+24\\y=3x+12\)

Hence, the equation of function for the given problem is y = 3x + 12.

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Answer:56.66 mi/h

Step-by-step explanation:

210 + 130 / 3.5 + 2.5 = 340 / 6

Divide by 6 and you get 56.66

Rounding to the nearest tenth 56.7 mi/h

Given a function of two variables, n and k, denoted as h(n, k), the function describes a mathematical relationship or operation that depends on the values of both n and k. Further details about the specific function, its definition, or purpose are required to provide a more comprehensive explanation.

A function of two variables, h(n, k), typically represents a mathematical relationship or operation that involves two independent variables, n and k. The specific form and purpose of the function can vary widely depending on the context or problem at hand.

To understand the behavior and properties of the function h(n, k), additional information is needed. This may include the mathematical expression defining the function, any constraints or conditions on the variables, and the intended interpretation or application of the function.

The function h(n, k) could represent various scenarios, such as a cost function in economics, a probability distribution in statistics, or a mathematical model in a scientific context. Without more details, it is challenging to provide a specific explanation or analysis of the function and its implications.

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Answer:

4*32=128

Step-by-step explanation:

Answer:

0.1

Step-by-step explanation:

10,000 * (1/100,000) = 0.1