Students get two grades for a test in an introductory psychology course: a letter grade, and a numerical equivalent (weighted value). So an A is worth 4 points, a B is worth 3 points, a C is worth 2 points, a D is worth 1 point, and an F is worth 0 points.


The results for the test are listed in the table below.


Score F (=0) D (=1) C (=2) B (=3) A (=4)

Number of students 11 18 52 13 6

Using the numerical equivalents (weighted values), what is the average grade for this test?


Rounded to the nearest hundredth, the average grade is

.

Answer:

y = 6x

Step-by-step explanation:

[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

[tex]\frac{24-6}{4-1}[/tex]

[tex]\frac{18}{3}[/tex]

m = 6

y = mx + b

y = 6x + b

6 = 6(1) + b

6 = 6

b = 0

By using the concept of rotation, it can be inferred that

New coordinate of C (C') = (12, -6)

What is rotation?

Rotation is a mathematical transformation in which an object is turned about a fixed point called the center of rotation. Rotation is a very important tool in mathematics, especially in coordinate geometry.

In this problem, 90° rotation clockwise about the origin has been applied.

We need to find the new coordinate of C after rotation.

Coordinate of C = (6, 12)

C is in the first quadrant

On rotating 90° clockwise, point C will go to fourth quadrant

New coordinate of C (C') = (12, -6)

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The cost of admission to the library for each student will be $0.3125. And the admission cost of the zoo will be $156.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Mrs. Hudson's class of 18 understudies is going to the zoo. Every understudy will pay for confirmation and purchase lunch. Mr. Weaver's class of 24 understudies is going to the library. Every understudy will pay for affirmation and pay for transport passage.

Let 'x' be the cost of admission to the library for each student. Then the equation is given as,

$7.50 + $8.25 × 18 + $5.75 × 18 = 24x + $10.50 × 24

Simplify the equation, then we have

$7.50 + $8.25 × 18 + $5.75 × 18 = 24x + $10.50 × 24

$7.50 + $148.5 + $103.5 = 24x + $252

$259.5 - $252 = 24x

x = $0.3125

And the admission cost of the zoo will be given as,

⇒ $7.50 + $8.25 × 18

⇒ $156

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The function's standard form equation is equivalent to

y=(1/2)x²+(-7x)+24.

A mathematical expression (equation) that can be used to define and represent the relationship between two or more variables on a graph is known as a quadratic function.

The standard form of a quadratic equation in mathematics is represented by;

ax² + bx + c = 0

y=ax² + bx + c

The information in the table above would then be used to create a set of equations:

The points are (4, 4), (6, 0), (8, 0), (10, 4)

4=a(4)²+b(4)+c

16a+4b+c=4 ------(1)

0=a(6)²+b(6)+c

36a+64b+c=0  ------(2)

0=a(8)²+b(8)+c

64a+8b+c=0  -------(3)

By solving 2 and 3 equations, we get

Eq2-Eq3,

We get b= -14a

By substituting b value in eq2 we get,

36a+6b+c=0

36a+6(-14a)+c=0

35a-84a+c=0

c=48a

By substituting a, b values in eq1 we get,

16a+4(-14a)+48a=4

16a-56a+48a=4

-40a+48a=4

8a=4

a=1/2

Then, b=-14a

b= -7

c=48a

c=24

Now, by substituting these a, b, c values in,

y=ax² + bx + c

y=(1/2)x²+(-7x)+24

By  checking the above equation is correct or not,

We consider the fourth value x=10

When x=10,

y=(100/2)-70+24

y=50-70+24

y=4

From the given table if x=10 then y=4,

So it satisfies with the equation we get.

Therefore, the function's standard form equation is equivalent to

y=(1/2)x²+(-7x)+24.

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Answer:

Since the slope is undefined, this is a vertical line. Vertical lines have no y-intercept. No y-intercept.

Step-by-step explanation:

hope this helped:)

Answer:

To write the equation of a line in slope-intercept form, we need to first find the slope of the line. The slope is a measure of the steepness of the line, and is calculated as the rise over the run between two points on the line. In this case, we can use the points (-6,-3) and (6,-7) to calculate the slope.

To find the slope, we first need to find the difference between the y-coordinates of the two points, which is -3 - (-7) = 4. We then need to find the difference between the x-coordinates of the two points, which is 6 - (-6) = 12. The slope is then calculated as the rise over the run, which is 4/12 = 1/3.

Once we have the slope, we can use the point-slope formula to write the equation of the line in slope-intercept form. The point-slope formula is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, we can use the point (-6,-3) and the slope 1/3 to write the equation of the line.

The equation of the line in slope-intercept form is then y - (-3) = 1/3(x - (-6)), which simplifies to y + 3 = 1/3x + 2. This is the equation of the line that passes through the points (-6,-3) and (6,-7) in slope-intercept form.

Therefore, the correct answer is y + 3 = 1/3x + 2.

Step-by-step explanation:

Landon is a high school basketball player. In a particular game, he made some two point shots and some three point shots. Landon scored a total of 24 points and made 2 more two point shots than three point shots. Graphically solve a system of equations in order to determine the number of two point shots made, x, and the number of three point shots made, y.

x = the number of two point shots made

y = the number of three point shots made

Each two point shot scores 2 points, so x two point shots would score 2x points. Each three point shot scores 3 points, so y three point shots would score 3y points.

Therefore, the total number of points scored 2x + 3y equals 24 :
2x+3y=24

Since Landon made 2 more two point shots than three point shots, if we add 2 to the number of three point shots made, we will get the number of two point shots made, meaning x equals y + 2.

                                                                                    x = y + 2

Write System of Equations:

​2x + 3y = 24

         x = y + 2

Solve for y in each equation:

The narrowest graph of the quadratic function is y = 5x² + 1.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

We know the graph a quadratic function y = ax² + bx + c is narrower and narrower with an increase in the value of a > 1.

From the given options we conclude that y = 5x²+ 1 has the narrowest graph.

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Answer: 8 + 5i

Step-by-step explanation:  P + Q so insert each equation

5 - 2i + 3 + 7i

combine like terms

5 + 3 and 7i - 2i

leaving you with 8 + 5i   in a + bi form

The measure of x is 22.5 and the angle ADE is 67.5 degrees

The complete question is added at the end of this solution as an attachment

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

Angle A = x

Angle B = 3x

The sum of angles in a triangle is 180

So, we have

x + 3x + 90 = 180

Evaluate the like terms

4x = 90

Divide by 4

x = 22.5

From the attached figure, we have

Angle ADE = Angle B

So, we have

Angle ADE = 3x

This gives

Angle ADE = 3 x 22.5

Evaluate

Angle ADE = 67.5

Hence. the angle is 67.5 degrees

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Answer:

[tex]\frac{-r}{2} +12\\[/tex]

Step-by-step explanation:

Combine multiplied terms into a single fraction, find the common denominator, then combine fractions with the common denominator.

The speed of the ball after one second is given as follows:

9.175 m/s.

The speed function is the derivative of the position function, which is graphed in this problem.

The position function, in meters, for a projectile's height, is given as follows:

h(t) = -4.9t² + v(0)t + h(0).

In which:

From the graph, the initial height is given as follows:

h(0) = 6.

When t = 4, h = 2.5, hence the initial velocity is obtained as follows:

2.5 = -4.9(4)² + 4v(0) + 6

4v(0) = 2.5 - 5 + 4.9(4)²

4v(0) = 75.9

v(0) = 75.9/4

v(0) = 18.975.

Then the position function is of:

h(t) = -4.9t² + 18.975t + 6.

The velocity function is the derivative of the position, hence:

v(t) = -9.8t + 18.975.

Then the velocity after one second is of:

v(1) = -9.8 + 18.975 = 9.175 m/s.

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The combined mass of the Earth and Moon is 6.07342 × 10^24.

Scientific notation is a method of displaying very large or very small numbers in a more simplified format. We know that entire numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper.

Mass of Earth = 6 × 10^24

Mass of Moon = 7.342 × 10^22

The combined mass of the Earth and Moon will be:

= (6 × 10^24) + (7.342 × 10^22)

= 6.07342 × 10^24

The mass is 6.07342 × 10^24.

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Answer:

x= 3.5 and x= -3.5

Step-by-step explanation:

4x^2 -49=0

x^2=49/4

x= 3.5 and -3.5

Answer: 5 small bags and 3 large bags

Step-by-step explanation:  5+5+5+5+5=25    7+7+7=21    21+25=46

The equivalent equation for the given equation m = ca is a = m/c. The equivalent equation has no effect on the original equation's actual function.

An equivalent equation is one that yields the same solution as the original equation.

The equivalent equation is obtained by removing a variable from the given equation. There will be the same number of equivalent equations as there are variables in an equation.

Given that,

m = ca

Here m, c, and a are the three variables in the given equation.

We can write the equation into two more forms as follows:

W.r.t variable 'c',

m = ca

Dividing both sides by 'a'

⇒ ca/a = m/a

c = m/a

W.r.t variable 'a',

m = ca

Dividing both sides by 'c'

⇒ ca/c = m/c

a = m/c

The missing image is attached with the answer.

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221 pages are read in an average reader's time of 6.1 hours. Depending on your Speed, it can take you longer or less period than 6.1 hours you read 221 pages.

You should try to complete the Speed Problems on your own before checking where you are falling behind. We are aware that an object's speed is just how far it travels in one unit of time. 1. A 25 km (6 h) stroll by a man Find the man's speed, please. 2. A railway travels 70 km 30 minutes, compared to a car's 420 m in a minute.

If you're driving your car at 60 km/h, that indicates that the vehicle will cover 60 kilometres per hour. The total distance of 120 km would have been traveled after two hours of driving at a speed of 60 km/h. Because of this, distance equals speed times time, and understanding the connection between speed, time, and distance is essential to figuring out any questions about speed.

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The value of the expression given as 7/4 of 66 is 231 / 2 or 115.5.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

Given:

7/4 of 66

The above expression is represented by of operation, which means multiplication

7/4 of 66 = 7 / 4 × 66

7/4 of 66 = 7 / 2 × 33

7/4 of 66 = 231 / 2

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x ≥ 3, the value of x is greater than or equal to 3 is the solution of inequality (7x-3)/9 ≥ 8-2x, correct option is C.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

(7x - 3)/9 more than or equal to 8 - 2x

(7x-3)/9 ≥ 8-2x

7x-3 ≥ 9(8-2x)

7x-3 ≥ 72-18x

Add 18x on both sides

7x+18x-3 ≥ 72

25x-3 ≥ 72

Add 3 on both sides

25x ≥ 75

Divide both sides by 25

x ≥ 3

Hence, x ≥ 3, the value of x is greater than or equal to 3 is the solution of inequality (7x-3)/9 ≥ 8-2x, correct option is C.

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Answer:

The school ordered more than enough concrete to completely fill in the court, so the number of bags of concrete ordered, represented by x, must be greater than the number of cubic yards of concrete needed to fill the court. This can be represented by the inequality x > 60 cubic yards / 0.5 cubic yards/bag. Solving for x, we get x > 60 * 2 = 120. Therefore, the inequality that describes the problem is x > 120.

The midsegment has length 25 then the value of x exists 14.

The length of the midsegment is half that of the base, according to the theorem.

A segment that joins the midpoints of two triangle's sides is referred to as a midsegment. According to the midsegment theorem, the third side of a triangle is parallel to the middle two sides of the triangle, and the midsegment is half its length.

Find the midpoints of two of any triangle's sides. A section joins these midpoints. This section will then be half the length of the third side and parallel to it.

The midsegment has length 25.

The base has length x.

x/2 = 25

simplifying the above equation, we get

x = 12.5

Therefore, the value of x exists 12.5.

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Answer: 1/10 of a pound

Step-by-step explanation: The original block of cheese was 1/2 a pound, then she cut the block into 5 equal parts. Divide 1/2 by 5 and you get 1/10

Answer:

1/10 of a pound

Step-by-step explanation:

Using this word problem, we can tell that the problem is a division problem:

1/2 ÷ 5 = x

To solve a division problem with fractions, you multiply the first number with the reciprocal (reverse) of the second number:

Now you get the equation:

1/2 x 1/5

To solve this you multiply the numerators together and the denominators together:

1/10 is the answer

Answer:

Step-by-step explanation:

            400                            ÷                                           80

Number of cookies        Divde by         Number of peanut butter cookies

= 5 Total cups

Using an algebraic equation to represent the word problem, the smallest integer is 1

This is a way of representing mathematical problems with words. To solve this, we have to use algebraic equations or expressions.

Let the integers be represented as

We can write an equation from the word problem given as

7 × (x + 2) = 15 + [x + (x + 4)]

7x + 14 = 15 + x + x + 4

7x + 14 = 15 + 2x + 4

collect like terms

7x - 2x = 15 - 14 + 4

5x = 5

Divide both sides by coefficient of x

5x / 5  = 5 / 5

x = 1

The smallest integer is 1

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Translation:

Find the smallest of three consecutive odd integers such that 7 times the middle integer is 15 more than the sum of the first and third integers

Answer: first, second, and third images.

Step-by-step explanation:

to determine if something is a function, the domain must not have more than one answer in the range. My class calls it the y axis test, if you were to graph it, you cannot draw a line straight down that will go through two points. it's easy to understand with images like these, because all you need to know is that arrows cannot go from one number on the left to multiple on the right. Vice versa is a function, because it passes the y axis test.

The taxi can travel a maximum distance of 11 miles if we have at most $10 to spend on the cab ride.

What is distance?

The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line.

The formula for measuring distance between two lines, the total length of all a polygon's sides, the perimeter of a polygon on a coordinate plane, the area of a polygon, and many other things are all found in analytical geometry. For instance, we can use the distance formula to find the lengths of a triangle's sides and decide if it is scalene, isosceles, or equilateral.

It is given that, a taxi charges a flat rate of $1.75 plus an additional fee of $0.75 per mile.

We have to find the maximum distance it could travel at most with $10

Let the maximum distance be x miles.

Thus, the fare would be

$(1.75 + 0.75x) = 10

⇒ 0.75x = 8.25

⇒ x = 8.25/0.75

⇒ x = 11

The taxi can travel a maximum distance of 11 miles if we have at most $10 to spend on the cab ride.

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Answer:

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

Let the missing side be x.

Use Pythagorean to find its value:

Answer:

Step-by-step explanation:

no

Answer: y= mb + xe

Step-by-step explanation:

If the two bikes are racing a distance of 100 feet, the bike that will win the race is: D. Bike 1 will win because the slope of the line for Bike 1 is 3/2, which is greater than the slope of the line for Bike 2.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would calculate the slope of the line representing the distance covered by each of the bikes based on the data points on their graph.

For Bike 1, the slope is given by;

Slope, m = (6 - 3)/(4 - 2)

Slope, m = 3/2

Slope, m = 1.5.

For Bike 2, the slope is given by;

Slope, m = (10 - 5)/(8 - 4)

Slope, m = 5/4

Slope, m = 1.25.

Therefore, the slope of Bike 1 is greater than the slope of Bike 2.

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