Following is a statement of a theorem which can be proven using calculus or precalculus mathematics. For this theorem, a, b, and c are real numbers. Theorem If f is a quadratic function of the form f (x) = ax^2 + bx + c and a < 0, then the function f has a maximum value when x = -b/2a. Using only this theorem, what can be concluded about the functions given by the following formulas? ? (a) g (x) = -8x^2 + 5x - 2 (b) h (x) = -(1/3)x^2 + 3x (c) k (x) = 8x^2 - 5x - 7 (d) j (x) = -(71/99)x^2 + 210 (e) f (x) = 4x^2 - 3x + 7 (f) F (x) = -x^4 + x^3 + 9

All of the trains scheduled to leave from the Concert Hall station are listed in Keiko's record for the population, and a random selection of 70 train records are listed in Keiko's record for the sample. As a result, statement II is true for the population, whereas statement I is true for the sample. The total population or all trains is regarded as a parameter, while the random group is regarded as a statistic.

In statistics, when we talk about population, we are talking about the entire population from which we want to draw a conclusion about. And when we talk about sample, we are talking about a particular or specific group from which we want to collect data from. So the size of sample will be less compared to the total size of the population.

a) In the given scenario, when we discuss population, we are referring to all of the trains that were scheduled to depart the Concert Hall station in the previous year. So statement II is correct.

And, when we discuss samples, we are referring to the random sample of 70 train records that Keiko audited. So statement I is correct.

b) When we talk about parameters, we are talking about the data of an entire population or all trains. And, when we are talking about statistics, we are talking about the sample data or random group.

The complete question is -

The records for all trains scheduled to depart from the Concert Hall train station last year showed that the average delay for these trains was 13.1 minutes, 18.6% of the trains had been delayed, and 12 trains had been canceled. Keiko is a traffic engineer helping the Concert Hall station improve its performance. She audited a random group of 70 records of trains scheduled to depart from the Concert Hall station last year. In her group the trains were late an average of 22.5 minutes, 30% of the trains had been delayed, and 4 trains had been canceled.

a. For Keiko's audit of train records, identify the population and the sample

Population:

I. The random group of 70 records of trains audited by Keiko.

II. The records of all the trains scheduled to depart from the Concert Hall station last year.

Sample:

I. The random group of 70 records of trains audited by Keiko.

II. The records of all the trains scheduled to depart from the Concert Hall station last year

b. Choose whether each number described below is a parameter or a statistic for Keiko's audit.

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The  percentage of community service Joe still need to complete is 45%,

the correct option is C

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

We need to Write the percent as a fraction in simplest form

16.24%

So, we can rewrite it as;

16.24 / 100

16 and 24/100 or 16 6/25

So the percent as a fraction is 16 6/25.

Given;

Total number of hours joe has to perform= 40

Number of hours joe has already performed= 18

Now;

Percentage;

=18*100/40

=18*5/2

=45

Therefore, the percentage will be 45%

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It will take them 28 minutes to fill the tank.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

The first pipe alone can fill the tank in 84 minutes.

So, the rate at which the first pipe fills the tank = 1/84

and, The second pipe can fill the tank in 42 minutes by itself.

So, the rate at which the second pipe fills the tank =1/42

If they work together, they would work simultaneously and their individual rates are additive.

= 1/84 + 1/42

let it takes t hours for both pipes to fill the tank working together, the working rate per minute would be 1/t. Therefore,

1/84 + 1/42 = 1/t

3/84 = 1/t

t = 84/3

t = 28 minutes

Hence, 28 minutes will take to fill.

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True, The Laffer curve shows the exclusively direct relationship that exists between tax rates and tax revenues

The Laffer Curve was developed by Arthur Laffer. Arthur, a supply side economist used this curve to show the relationship that existed between tax rates and also the amount of tax revenue which the government takes or collects. This curve provides an illustration to his argument that sometimes when tax rates are cut there could be increase in total tax revenue.

True, The Laffer curve shows the exclusively direct relationship that exists between tax rates and tax revenues

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The bearing of B from S = 63.8 + 180 = 243.8°

To calculate the distance that the boys walked, you would need to know their speed and the duration of their walk.

Speed is typically measured in units such as miles per hour (mph) or kilometers per hour (kph). If you know the speed of the boys and the duration of their walk in hours, you can calculate the distance they walked using the formula: distance = speed x time.

To calculate the bearing of S from B, you can use the following steps:

Calculate the distance between S and B using the Pythagorean theorem. The distance is the hypotenuse of a right triangle, where one side is 8.6 km (the north-south distance) and the other side is 12.5 km (the east-west distance).

Calculate the angle formed by the distance between S and B and the north-south line. To do this, you can use the arctangent function (atan), which returns the angle in radians.

To convert radians to degrees, multiply by 180/π

The bearing of S from B = atan(12.5/8.6) x 180/π = 63.8°

To calculate the bearing of B from S, you just need to add 180 degrees to the bearing of S from B

The bearing of B from S = 63.8 + 180 = 243.8°

b. 243.8

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Complete question:

A bank B is 8.6 km north and 12.5 km west of a school S.

Calculate correct to 3 significant figures:

a the bearing of S from B

b the bearing of B from S.

The probability that you select a gold marble is, 1/21.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

We have to given that;

A bag contains 2 gold marbles, 10 silver marbles, and 30 black marbles.

Here, Number of gold marbles = 2

And, Number of total marbles = 2 + 10 + 30

                                              = 42

Hence, The probability that you select a gold marble is,

⇒ Number of gold marbles / Total number of marbles

⇒ 2 / 42

⇒ 1 / 21

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Harris ate (n - 4)/4 number of  slices of pizza.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given:

4 friends evenly divided up an n-slice pizza.

That means,

n / 4.

One of the friends, Harris, ate 1 fewer slice than he received.

That means,

n/4 - 1

= (n - 4)/4

Therefore, Harris ate  (n - 4)/4.

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Answer:

$155.56

Step-by-step explanation:

S.I=(PRT)÷100

$144=(P×9×1)÷100

crossmultiply

$144×100=9P

P=$14400÷9

P=$155.56

Answer:

yes

Step-by-step explanation:

9(b_5)

multiply 9 with everything in the bracket:

9×b=9b

9×5=45

:9(b-5)

Answer:

D. {x | x > 2}

Step-by-step explanation:

Separately solve inequalities:

[tex]\displaystyle{3x-2 > -11 \ \: \text{and} \ \: -2x+1 < -3}[/tex]

For left inequality, add 2 both sides. For right inequality, subtract 1 both sides:

[tex]\displaystyle{3x-2 +2 > -11+2 \ \: \text{and} \ \: -2x+1-1 < -3-1}\\\\\displaystyle{3x > -9 \ \: \text{and} \ \: -2x < -4}[/tex]

For left inequality, divide both sides by 3. For right inequality, divide both sides by -2 and also switch from < to > since the coefficient of x is negative:

[tex]\displaystyle{\dfrac{3x}{3} > \dfrac{-9}{3} \ \: \text{and} \ \: \dfrac{-2x}{-2} > \dfrac{-4}{-2}}\\\\\displaystyle{x > -3 \ \: \text{and} \ \: x > 2}[/tex]

Since both are in form of x > a and x > b, consider for highest value (since putting value below than 2 would make the other inequality false but if we put value higher than 2 then it'd make both inequalities true) which is x > 2.

The scale will register a weight greater than 80 pounds due to Newton’s Third Law

Given that there is a 1-liter container filled with 500 milliliters of water placed on top of a scale displaying 80 pounds.will register a weight greater than 80 pounds

When a body is submerged in a water an upward force acts on the body known as buoyant force which is equal to weight of the water displaced by the body. Since water exerts Buoyant force on the body and according to Newton's third law there must be equal and opposite force exerted by the body on the water. This additional force equal and opposite to the Buoyant force will cause the reading of the scale to increase. Therefore the scale will register a weight greater than 80 pounds due to Newton’s Third Law.

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The complete question is :

There is a 1-liter container filled with 500 milliliters of water placed on top of a scale displaying 80 pounds. When a metal cube is submerged tied to a string end into the container, which of the following statements accurately describes the result?

The cube’s density must be provided to predict what will happen

The scale will remain at 80 pounds until the cube is floating on top of the water fully submerged.

The scale will register a weight greater than 80 pounds due to Newton’s Third Law

The scale will register a weight greater than 80 pounds due to Newton’s Third Law

The answer for the blank is we can use a dive table or computer.

When planning a subsequent dive, it is important to take into account the dive time, depth, and surface interval from the previous dive in order to safely plan for the next dive. To determine the required surface interval, one can use a dive table or a dive computer.

A dive table is a printed or electronic table that provides information about the safe amount of time that can be spent at certain depths, based on the previous dive. The table will take into account the dive time, depth, and surface interval from the previous dive, and provide a recommended surface interval to ensure safe diving.

A dive computer, on the other hand, is an electronic device that is worn by the diver and calculates the safe amount of time that can be spent at a certain depth, based on the diver's previous dive. The dive computer takes into account the dive time, depth, and surface interval from the previous dive, and provides a recommended surface interval to ensure safe diving.

In summary, to determine the required surface interval before returning to the same site and depth for another 60 minutes dive, one can use a dive table or a dive computer. These tools will give you the recommended time for your surface interval, based on your previous dive profile, so you can ensure you have enough no-stop time for your next dive.

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You should order 197.5 hats and 12.5 pairs of sunglasses to lose the least amount of money in the sales promotion.

This is a linear programming problem, which can be solved using a system of equations.

Let x be the number of hats sold and y be the number of pairs of sunglasses sold.

From the problem, we know the following constraints:

x >= 2y (since for every pair of sunglasses sold, two hats must be sold)

x + y >= 210 (to ensure that the items fill out the display)

y <= 100 (the maximum number of pairs of sunglasses that can be ordered)

We also know that the profit per hat sold is -$3 and the profit per pair of sunglasses sold is -$2.

So, the objective function is:

-3x - 2y (to minimize the loss)

Now we can use the equations and inequalities to find the optimal solution.

x >= 2y

x >= 4y

y <= 100

x + y >= 210

x >= 8y

y <= 100

x + y >= 210

Now we can use the equation to find the optimal solution

x = 8y

y <= 100

x + y >= 210

8y <=100

y <= 12.5

x + y >= 210

x >= 210 - y

Now we can find the value of x, y

y = 12.5

x = 210 - y

x = 210 - 12.5

x = 197.5

So the optimal solution is to order 197.5 hats and 12.5 pairs of sunglasses.

You should order 197.5 hats and 12.5 pairs of sunglasses to lose the least amount of money in the sales promotion.

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A linear combination of the values of a1 = (1,-2,0), a2 = (0,1,2), and a3 = (5,-6,8) with the corresponding weights is b = (2,-1,6).

We may construct a system of equations using the coefficients of the linear combination and the elements a1, a2, and a3 to determine whether b is a linear combination of a1, a2, and a3.

It is possible to write the equation for a linear combination of the type b = k1a1 + k2a2 + k3a3 in the following way:

b = k1 × (1,-2,0) + k2 × (0,1,2) + k3 × (5,-6,8) (5,-6,8)

So,

x = k1 + 5k3

y = -2k1 + k2 - 6k3

z = 2k2 + 8k3

From b =, we know the values of x, y, and z. (2,-1,6)

Thus, we can construct the equations in the following system:

x = k1 + 5k3 = 2

y = -2k1 + k2 - 6k3 = -1

z = 2k2 + 8k3 = 6

To determine the values of k1, k2, and k3, we can solve the system of equations using techniques like substitution or elimination.

k1 = 1, k2 = 3, k3 = 1

As a result, we can write b as a linear combination of the variables a1, a2, and a3 with the respective weights of (1, 3, and 1) for k1, k2, and k3.

b = 1a1 + 3a2 + 1 × a3

This indicates that b is a linear combination of the three variables a1, a2, and a3 with the weights (1, 1, and 3, respectively).

The Complete Question  linear combination.

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In a case whereby Dominic is making and  uses 3/4 cup of breadcrumbs for every 11/4 pounds of ground beef the number of  cups of breadcrumbs he need when he uses 1 pound of ground beef is 3/5.

The concept that will be used here is fraction. fraction: A number that is stated as a quotient in mathematics, when the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Since Dominic is using 3/4 cup of breadcrumbs for every 11/4 pounds of ground beef

The amount that will be needed for  1 pound of ground beef will now be:

11/4 pounds =  3/4 cup

we can convert to improper fraction as

5/4 * 3/4

12/ 20= 3/5

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complete question:

Dominic is making meatballs. He uses 3/4 cup of breadcrumbs for

every 11/4 pounds of ground beef. How many cups of breadcrumbs

does he need when he uses 1 pound of ground beef? *

The expression of (9 * 10⁶)(8 * 10⁸) in scientific notation is; 72 * 10¹⁴

Scientific notation is defined as a way of writing very large or very small numbers. A number is usually written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 750,000,000 can be written in scientific notation as 7.5 * 10⁸.

We want to multiply the expression given as;

(9 * 10⁶)(8 * 10⁸)

Now, we can rewrite this as;

(9 * 8) * (10⁶ * 10⁸)

According to laws of exponents, x² × x³ = x²⁺³

Thus;

(9 * 8) * (10⁶ * 10⁸) = 72 * 10⁶⁺⁸

= 72 * 10¹⁴

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The relationship between factors and multiples from the equation  6 x 7 = 42 are given below.

Factorization in mathematics is the process of dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the process of dividing a number into its components or divisors.

Given:

An equation,

6 x 7 = 42.

Multiples are what you receive after multiplying a factor, which is what you can multiply to produce a number.

1 x 42 = 42

2 x 21 = 42

3 x 14 = 42

6 x 7 = 42

So the factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

The multiples of 42 are 1,2,3,4,5,6 etc.

Therefore, the relationship between factors and multiples are given

above.

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Taking k as a common factor on the first expression, we can rewrite that into the second one, thus, the expressions are equivalent.

Two expressions are equivalent only of we can, using algebra, rewrite one of the expressions into the other one.

The two given expressions are:

k + 0.10k

and

1.1k

Now let's take the first expression:

k + 0.10k

We can take k as a common factor, then we will get:

k + 0.10k = (1 + 0.10)k = 1.1k

So yea, the two expressions are equivalent.

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The solution for the expression is (35y - 22)/(5y-8)(10y+1). The solution has been obtained by solving the algebraic expression.

What is algebraic expression?

An algebraic expression is one that uses variables, constants, and algebraic operations (addition, subtraction, etc.).

The four primary categories of expressions are as follows:

We are given

⇒(2/5y -8)+ (3/10y+1)

⇒(2(10y+1) + 3(5y -8))/(5y-8)(10y+1)

⇒(20y + 2 + 15y - 24)/(5y-8)(10y+1)

⇒(35y - 22)/(5y-8)(10y+1)

Hence, the solution for the expression is (35y - 22)/(5y-8)(10y+1).

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Answer:

32%

Step-by-step explanation:

1552 / 4850 = 0.32

The larger angle between the pair of supplementary angles is 126 degrees.

Supplementary angles are simply angles that sum up to 180 degrees.

Given the data in the question;

Since, they both form a supplementary angle, their sum gives a total of 180 degree.

Angle 1 + Angle 2 = 180

(4x+30) + (2x+6) = 180

Solve for x

4x + 2x + 30 + 6 = 180

6x + 36 = 180

6x = 180 - 36

6x = 144

x = 144 / 6

x = 24

Now, we determine the measure of the angles.

Angle 1 = (4x+30)

Angle 1 = 4(24) + 30

Angle 1 = 126 degrees

Angle 2 = (2x+6)

Angle 2 = 2(24) + 6

Angle 2 = 54 degrees.

Therefore, the larger angles measures 126 degree.

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The code chunk to add is summarize(mean(Rating)), and the mean rating is 3.185933 according to the ratings system, summarize(), and mean() functions.

Now, According to the question:

The full code should be trimmed flavors df%>% summarize(mean(Rating)) to determine the mean rating.

In order to present summary statistics, this code combines the summarize() and mean() functions to show the mean rating of your data.

The statistic that will be displayed due to the "mean()" method is the mean rating, which in this instance would be 3.185933.

The mean scale score represents the overall effectiveness of a group of students on a test. A mean scale score is calculated specifically by adding up the scores of each individual student and dividing that total by the number of scores. It is additionally known as an average.

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A 1.5 standard deviations above the mean IQ score is 122.5.

An expression that depicts the relationship between two or more numbers and variables is called an equation.

A dependent variable is one that depends on another variable, whereas an independent variable does not depend on any other variable for its value.

Giving the z score are:

z is calculated as (raw score - mean) / standard deviation.

with a standard deviation of 15 and a mean of 100. The z-score of 1.5 is equal to the IQ score that is 1.5 standard deviations above the mean, so:

1.5 = (x - 100)/15

x = 122.5

A 1.5 standard deviations above the mean IQ score is 122.5.

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The order of rotational symmetry of a square about its center is 4.

Geometrically speaking, a shape has rotational symmetry when it retains its appearance following a small amount of rotation by a partial turn. The number of different orientations in which an object appears exactly the same for each rotation is known as the degree of rotational symmetry.

The number of times a square fits onto itself during a full rotation of 360 degrees determines a square's rotational symmetry. The square in the images above can be seen to fit four times on top of itself during a full 360-degree rotation.

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Answer:

Step-by-step explanation:

I think anyone needs to care about the school bus, it's just a bus, and maybe the people inside are like you, so relax, keep calm on a school bus

The length of the road after D days of construction (L) is equal to the original length of the road (10 miles) plus the number of miles added by the construction crew each day (1 mile/day) times the number of days the construction has been going on (D).

So the equation relating L to D is:

L = 10 + 1D

This equation can be graph on a Cartesian plane with D on the x-axis and L on the y-axis. The graph will be a straight line passing through the point (0,10) and having a slope of 1, meaning that for every one increase in D there is a one increase in L.

It will look like this:

graph{10+x [-12, 12, -6, 6]}

Where D=x and L=y.

Answer: L - 10 = D

Step-by-step explanation:

1 Day = 1 Mile
After 1 Day of construction a 1 Mile is added to the road
Original length is 10 miles
Length (e.g. 11 miles) - 10miles = Day 1
So:
L - 10 = D

The inequality that represents the situation in this problem is given as follows:

x + 3 < 16

The inequality symbols are given as follows:

In three years, your friend's age is given as follows:

x + 3.

To apply for the driver's license, an age of 16 is needed, and your friend will be younger than 16, as he/she cannot apply, hence the inequality is:

x + 3 < 16

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The force the road exerts on the car as the car passes the highest point of the bump n=mg−mv²/R

Newton's second law of motion defines the behavior of objects for which all existing forces are not balanced.

The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object.

The acceleration of an object depends directly upon the net force acting upon the object, and inversely upon the mass of the object.

The free-body diagram given below shows the forces on the car in the vertical direction. Newton’s second law then gives

∑F y=may = mv²/R

mg−n=mv²/R

n=mg−mv²/R

When n=0, mg=mv²/R​

Then, v= √gR

A more gently curved bump, with a larger radius, allows the car to have a higher speed without leaving the road. This speed is proportional to the square root of the radius.

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The interval of time that has the average rate of change being the smallest is 1. 2002 - 2004.

From the information given, the table shows the year and the number of households in a building that had high-speed broadband internet access.

In this case, the average rate of change from 2002-2004 will be:

= 23 - 11

= 12

The average rate of change from 2004-2006 will be:

= 47 - 23

= 24

The average rate of change from 2003-2005 will be:

= 33 - 16

= 17

The smallest is from 2002 to 2004.

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