Writing and evaluating a function that models a real world

Step-by-step explanation & Answer:

It's easier to compare two functions if you can compare them by graphs.

The first function is a polynomial function - try your best to put these in standard form so that you can see where the roots/x-intercepts are. You can set the function equal to zero to find the roots, as well as set x=0 to find our y-intercept.

The second function is an exponential function.  These always diverge ("shoot off") to positive infinity on the y-axis, and are asymptotic on the x axis, diverging to negative infinity. The only difference is made by a +5 here...that is a ENTIRE vertical shift up of 5 units <— Answer! Exponential functions also have a special y-intercept...think about what will happen if this intercept is shifted up 5 units.

! Know the forms of these two functions and how to graph them and it will make them much easier to compare !

Answer:

23 degrees

Step-by-step explanation:

Sum of all angles in a triangle add up to 180.

Right triangle consists of three angles, one a right angle which is a 90 degree angle and two other angles.

Therefore, 67+90 = 157. 180-157 = 23.

23 degrees

A violation of substantive due process (B)A new law fines book publishers for printing content that is considered unpatriotic. A drug dealer with several prior convictions is sent to prison without a trail.

The procedural rights guaranteed by the United States Constitution ensure that all citizens are treated equally before the law. For example, all citizens have the right to a lawyer, to a public and speedy trial, to have their case judged by a jury of their peers, etc.

In Scenario B, the drug dealer's rights are violated by law enforcement. Even if he has a criminal record, law enforcement has no right to immediately throw him in jail.

Due process is the application of all legal rules and principles relating to a case by the state to uphold all legal rights of individuals. Due process balances the power of the laws of the land and protects individuals against the laws. When the government harms a person without following the exact procedure of the law, it is a violation of due process and violates the rule of law.

It is the constitutional process in which the federal government before denying a citizen the right to life, liberty, or freedom, must give proper notice to the person, the opportunity of being heard, and the decision is taken without any discrimination. The act which violates the Procedural due process is giving a driver a traffic ticket without telling him, his right, i.e, can appeal in court against it.

Learn more about Trial:

https://brainly.com/question/2635763

#SPJ4

When x + 2 is plugged into the number machine, the output y is 5x + 7.

The number machine can be expressed mathematically as z = 5w - 3, where w is an input value and z is the output value. In this case, the input value is x + 2 and the output value is y.

To calculate y in terms of x, we can substitute x + 2 for w in the equation:

z = 5(x + 2) - 3

y = 5x + 10 - 3

y = 5x + 7

Therefore, when x + 2 is plugged into the number machine, the output y is 5x + 7.

Learn more about output value here:

https://brainly.com/question/28787935

#SPJ1

Answer:

The Summer Blue Uniform.

Step-by-step explanation:

NJROTC contains many different policies and guidelines for cadets.

It is TRUE that If you want to calculate the total magnification, take the power of the objective (4X, 10X, 40x) and multiply by the power of the eyepiece, usually 10X.

If you want to get the total magnification of a microscope, you need to multiply the magnification of the objective lens by the magnification of the eyepiece lens. The objective lens typically has a magnification of 4X, 10X, or 40X, and the eyepiece lens usually has a magnification of 10X. So, for example, if you are using a 10X objective lens and a 10X eyepiece lens, the total magnification would be 10 × 10 = 100X.

On the other hand, these numbers may be the total magnification for a lower powered stereomicroscope. 10X and 40X are achievable with 10X eyepieces and 1X or 4X objective lenses. Or it can be a zoom stereomicroscope with zoom set to 1X and 4X and 10X eyepieces. To get a total of 4X, you can use the 0.8X zoom setting (which is common) plus the 5X eyepiece. Or you can use the 0.5x auxiliary lens, 0.8x zoom and 10x eyepieces.

Learn more about total magnification

brainly.com/question/14668612

#SPJ4

Complete Question:

True, or False

To get the total magnification take the power of the objective (4X, 10X, 40x) and multiply by the power of the eyepiece, usually 10X.

The solutions to the equation 2x² + 12x = 26 are x = -7 and x = 1.

How to solve equation?

To solve the equation 2x² + 12x = 26, we need to bring all the terms on one side of the equation and then factorize or use the quadratic formula to find the values of x that satisfy the equation.

First, we can simplify the equation by dividing both sides by 2 to get:

x² + 6x = 13

Now, we can bring all the terms to one side by subtracting 13 from both sides:

x² + 6x - 13 = 0

To factorize the quadratic expression, we need to find two numbers that multiply to give -13 and add to give 6. These numbers are 7 and -1, since 7 * -1 = -7 and 7 + (-1) = 6. So we can rewrite the equation as:

(x + 7)(x - 1) = 0

Now we can use the zero product property to find the values of x that satisfy the equation:

x + 7 = 0 or x - 1 = 0

Solving for x in each equation, we get:

x = -7 or x = 1

Therefore, the solutions to the equation 2x² + 12x = 26 are x = -7 and x = 1.

To know more about equations visit :-

https://brainly.com/question/22688504

#SPJ1

Answer: B. -1.4

Step-by-step explanation:

 To find the residual, we need to first calculate the predicted height of the son using the given regression equation:

ŷ = -2.8 + 1.1x

where x is the height of the father. For the given father who is 72 inches tall, we have:

ŷ = -2.8 + 1.1(72) = 75.6

So the predicted height of the son is 75.6 inches.

The residual is then calculated by subtracting the predicted height from the actual height of the son:

residual = actual height - predicted height

= 75 - 75.6

= -0.6

Therefore, the residual for the son's height is -0.6, which is closest to answer B after rounding to one decimal place.

The statement "the coefficient of determination measures the variation in the dependent variable that is explained by the regression model" is true because coefficient of determination, or R-squared, measures the proportion of variance in the dependent variable that is explained by the independent variables in a regression model.

The coefficient of determination, or R-squared, is a statistical measure that evaluates the goodness of fit of a regression model. It quantifies the amount of variance in the dependent variable that can be explained by the independent variables in the model. R-squared ranges from 0 to 1, where a value of 0 means that none of the variation in the dependent variable is explained by the model, while a value of 1 indicates that all the variation is explained.

Therefore, R-squared is useful in assessing the predictive power of a model, and higher values are generally preferred. However, it is important to note that R-squared alone does not guarantee a good model, and other factors such as model assumptions and outliers should also be considered.

Learn more about coefficient of determination here

brainly.com/question/14115325

#SPJ4

The null hypothesis of the research is that there is no relationship between gratitude and prosocial attitudes.

A study has been carried out to determine the relationship between gratitude and prosocial attitudes. JASP is used to run a Pearson correlation test between gratitude and prosocial attitudes. The null hypothesis of this study is that there is no correlation between gratitude and prosocial attitudes.

In this investigation, the Pearson correlation is used. This research aims to identify the relationship between gratitude and prosocial attitudes. It can be difficult to determine whether or not there is a correlation between two variables. Pearson's correlation is a statistical method that can be used to examine the correlation between two variables.

This research is carried out with the hypothesis that there is a relationship between gratitude and prosocial attitudes. In this study, the null hypothesis of the research is that there is no relationship between gratitude and prosocial attitudes.

See more information about null hypothesis in: https://brainly.com/question/4436370

#SPJ11

Answer: (x,y) = (-6, 6)

Step-by-step explanation: I'm not very good at explaining but if you you follow this equation, (x1-x2, y1-y2) with (x1,y1) (5,5) and (x2,y2) being the function, that's how you get (-1,11)

The required probability of randomly selected person to be a man or a heavy smoker is given by 0.5525.

Total number of people is equals to 1124

Total number of men is equals to 531

Total number of heavy smoker is equals to 90

Man and Heavy smoker are mutually exclusive events.

Let 'M' represents man

And 'H' represents heavy smoker

Probability of randomly selected person is a man or a heavy smoker

= P( M ∪ H )

= Probability of a man  + Probability of a heavy smoker

= P( M ) + P (H)

= ( 531 / 1124 ) + ( 90 / 1124 )

= ( 621 / 1124 )

= 0.5525

Therefore, the probability of a person to be a man or a heavy smoker is equals to 0.5525.

Learn more about probability here

brainly.com/question/28142365

#SPJ4

The above question is incomplete, the complete question is:

If one of the 1124 people is randomly selected, find the probability that the person is a man or heavy smoker.

table is attached.

Answer: A

Step-by-step explanation:

A polygon is a plane figure with at least three straight sides and angles, and typically five or more. A matches with the description best.

(Sorry if you get this wrong..)

If the diagonals of a parallelogram PQRS intersect at z, then the correct statements are:

A. QZ ≅ SZ

D. ∠QRP ≅ ∠SPR

The diagonals of a parallelogram which is a quadrilateral are known to bisect each other. The diagonals of a parallelogram form an angle of 90 degrees with each other.

These diagonals are formed from congruent angles and can also separate into congruent angles. So, for the parallelogram above whose sides intersect at z, we can conclude that QZ is approximately equal to SZ  and angle QRP is approximately equal to angle SPR.

Learn more about parallelograms here:

https://brainly.com/question/970600

#SPJ1

Answer:179 cm3

there you go :)

Step-by-step explanation:

V = πr^2h

V = π7^2•18
V = π49•18

V = 2770.88472

= 2770.88472 • 0.004

= 11.083538

Thus, the container holds 11.08 gallons of juice.

Answer:

3 Pounds

Step-by-step explanation:

If 1 slice of pie = 8 ounces that means that 6 slices would be 48 ounces because of 6 slices * 8 ounces. Now we have to take the 48 ounces and divide them by 16 because 16 ounces = 1 pound. And in doing so, 6 slices would = 3 Pounds.

The statement that must be true is: Carter withdrew or spent $150 during the month.

Deposit is money held in a bank account or with another financial institution that requires a transfer from one party to another.

If Carter had a total of $50 in his bank account at the start of the month and made deposits totaling $150 during the month, then he had a total of $200 in his account during the month.

Since he still had a total of $50 in his account at the end of the month, it means that he must have spent or withdrawn $150 during the month, which is equal to the total amount of deposits he made.

Therefore, the statement that must be true is: Carter withdrew or spent $150 during the month.

Learn more about deposit here : brainly.com/question/29053212

#SPJ1

The variable that 360 represents in this context is the sample size or the number of credit card holders in the sample.

The fact that the average late fee was calculated based on the data from 360 credit card holders implies that a sample of 360 credit card holders was selected from a larger population of credit card holders, and the average late fee was calculated from this sample.

The sample size is an important variable in statistics because it affects the accuracy and precision of the estimates we make based on the sample data. In general, larger samples tend to provide more reliable estimates of population parameters, such as the population mean or the population standard deviation.

Learn more about Sample Size at:

brainly.com/question/28583871

#SPJ4

In linear equation, 12 is the constant of proportionality that relates number of chairs, y, to the number of tables, x.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Number of tables, x = 3  

number of chairs , y = 36   = 36/3  = 12

Row 2 says the same thing = 72/6 = 12

Row 2 says the same thing = 108/9 = 12

Learn more about linear equation

brainly.com/question/11897796

#SPJ1

[tex]x=95.04\div0.0132[/tex]

[tex]95.04\div0.0132=7,200[/tex]

[tex]\bold{x=7,200}[/tex]

Answer:

7200

Step-by-step explanation:

Use the numbers given divide, move the decimal place to the right of 0.0132 until you get 132.

Then divide 95.04 over 132

When 95.04/132=0.72

Then move the decimal four times because 0.0132 to 132 takes times 10000

So 0.72 move the decimal four times or times 10000 you will get 7200

Final answer 7200

After answering the provided question, we can conclude that Therefore, cuboid the cost of the gymnastic block is $225.

A cuboid is a solid or three-dimensional shape in geometry. A cuboid is a convex polyhedron with 8 coordinates, 12 sides, but rather 6 rectangular faces. A cuboid is another name for it. A box is a cuboid because it has six square faces. Objects unearthed in boxes include bricks and books. The following are the primary distinctions between cubic and cubic: In contrast to a cube's rectangular faces, the faces of a capsule are perfectly straight and equal in size. But even though the structures of both the cube and cuboid are similar, they differ significantly in terms of side length, horizontal, and area.

the volume of the block is:

Volume = length x width x height

Volume = 2 ft x 3 ft x 1.5 ft

Volume = 9 cubic feet

Now, to find the cost of the block, we can multiply its volume by the cost of foam per cubic foot:

Cost of block = Volume x Cost per cubic foot

Cost of block = 9 cubic feet x $24.99 per cubic foot

Cost of block = $224.91

Therefore, the cost of the gymnastic block is $225.

To know more about cuboid visit:

https://brainly.com/question/29568631

#SPJ1

The cost of 12 custom-made T-shirts with 12 words in the design is 149.88 dollars.

The cost for 12 custom-made T-shirts can be represented by the simplified expression 0.75n + 119.88, where n is the number of words in the design. For example, if the design has 12 words, the cost of the 12 T-shirts is 0.75*12 + 119.88 = 149.88 dollars. This expression means that for each T-shirt, there is an additional cost of 0.75 dollars for each word in the design, plus a flat fee of 9.99 dollars per T-shirt. This can be interpreted as the cost of each T-shirt increases with the complexity of the design.

Learn more about total cost here:

https://brainly.com/question/6506894

#SPJ4

On solving and factorizing the equation;

1). 2(3x+2y)

2.) 2(5x+4y)

3.) 3(2x+3y)

Factorization is the process of expressing a number or an algebraic expression as a product of its factors, which are numbers or expressions that multiply together to give the original number or expression. In other words, factorization involves breaking down a larger number or expression into smaller factors.

2(4x+3y)-2x-2y

Solving the expression

8x+6y-2x-2y

6x+4y

Factorizing the expression , we get

2(3x+2y)

2(4x+3y)+2(x+y)

Solving the expression

8x+6y+2x+2y

10x+8y

Factorizing the expression , we get

2(5x+4y)

2(4x+4y)-2x+y

Solving the expression

8x+8y-2x+y

6x+9y

Factorizing the expression , we get

3(2x+3y)

To know more about factors, visit:

https://brainly.com/question/14209188

#SPJ1

The approximate length of the pendulum is 255.96 feet.

Calculus is a branch of mathematics that deals with the study of change and how things change over time.

We have the equation for the period of a pendulum as:

T = 2π√(L/32)

We need to find the length of the pendulum, L, if the period is 10 seconds. Rearranging the equation, we get:

L = 32(T/2π)²

Substituting T = 10, we get:

L = 32(10/2π)²

L ≈ 255.96 feet

Hence, the approximate length of the pendulum is 255.96 feet.

To learn more about time period, Visit

https://brainly.com/question/27651512

#SPJ1

Answer:

92 cm

Step-by-step explanation:

From (-20, 14) to (8, 14) the distance is 20 + 8 = 28

From (-20, 14) to (-20, -4) the distance is 14 + 4 = 18

perimeter = 2(length + width)

perimeter = 2(28 + 18)

perimeter = 2(46)

perimeter = 92

Answer: 92 cm