There are five people competing in the track meet this weekend. They are competing for 1st, 2nd, and 3rd place ribbons. How many different ways can the winners be chosen? A. 30 B. 60 C. 120 D. 150

y = x²-2x+1, 2x-y=2 is the system of equations represented by the graph

By examining the graph, you will notice that the straight and the curve meet at (3,4) and (1,0) as indicated. The x values of these points of intersection give the solution of the system. Thus:

We have x = 3 and x = 1

These values can be used to form the equation of the system. Thus:

(x-3)(x-1) = 0         (Clear the parenthesis)

x² -x-3x +3 = 0

x² -4x +3 = 0

Next, we are going to check for the option that gives the x² -4x +3 = 0

Given:  y = x²-2x+1, 2x-y=2

Rewrite 2x-y=2 to be in form y: y =2x-2

We now have  y = x²-2x+1 and  y =2x-2

Equate the two y: x²-2x+1 =2x-2

x²-2x+1 -2x+2 = 0

x²- 4x+ 3 = 0

Since y = x²-2x+1, 2x-y=2 gives the same equation, therefore, the system of equations represented by the graph is y = x²-2x+1, 2x-y=2. So option D is the answer

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The number 74.9963 would round down to 70

Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.

Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.

We need to round  74.9963 to the nearest 10

We can see that the 74.9963 is below 75 so it goes down, and it rounds down to 74.9963 instead of, 74.9 then that would round up to the decimal is higher than 70.

The answer would be 70

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g(x) = (x+2-3) + 4 = (x-1)+4

When charging $15 for a key chain, it is discovered that his maximum profit is $75 using the vertex of the quadratic function.

The vertex of a quadratic equation,

A quadratic equation is given by, [tex]ax^{2} +bx +c[/tex]

The vertex is given by [tex]A (x_{1} ,y_{1} )[/tex]

[tex]x_{1} = \frac{-b}{2a}\\ \\y_{1} = \frac{-b^{2} +4ac }{4a}[/tex]

Considering the coefficient a, we have that:

If a < 0, the vertex is a maximum point.

If a > 0, it will be a minimum point.

The function given is (x -10 ) (60 -3x)

f(x) = (x -10 ) (60 -3x)  = 60x -3[tex]x^{2}[/tex] -600 +30x = -3[tex]x^{2}[/tex] +90x -600

So, here a = -3, b = 90 and c = -600

So,

[tex]x_{1} = \frac{-b}{2a}\\ \\x_{1} = \frac{-90}{2*(-3)} = 15[/tex]

[tex]y_{1} = \frac{-b^{2} +4ac }{4a} = \frac{(-90)^{2} + 4*(-3)*(-600) }{4*(-3)} = 75[/tex]

Hence, He can make up to $75 in profit when he charges $15 for a key chain.

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a. The set in set builder form A = {x : x ∈ N}

b. the set in descriptive form, A = {set of natural numbers}

A set is a collection of well defined items.

Set builder form is a way of enumerating a set by using a set of rules which define its elements.

Descriptive form is a way of enumerating the elements of a set in words.

Since we have the set A = {1, 2, 3, 4, 5, …}, which is the set of natural numbers ,N, we identify each element of the set as x and give it a rule that x is an element of N. That is x ∈ N.

So, in set builder form A = {x : x ∈ N}

Since we have the set A = {1, 2, 3, 4, 5, …}, which is the set of natural numbers ,N.

In descriptive form, we write that A = {set of natural numbers}

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The amount you pay for the items is C. $41.42.

The amount that the customer pays for the two items is determined by first discounting the second item by 60%.

The result after the discount is added to the cost of the first item before the sales tax is added to get the final cost of the items.

Discount on second item = 60%

The price of the first item purchased = $30

The price of the second item purchased = $20

Discounted price on the second = $8 ($30 x (1 - 60%)

Total cost before sales tax = $38 ($30 + $8)

Sales tax = 9%

Total cost after sales tax = $41.42 ($38 x 1.09)

Thus, after discounting the second item by 60% and adding the sales tax of 9%, the customer will pay $41.42 for the items.

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Answer:

c. 41.42 my teacher told me the answer

Step-by-step explanation:

The greatest possible number of total points for each of the top three teams is 24.

Given;

Six teams compete against one another twice in a tournament. A team receives three points for a victory, one point for a tie, and no points for a defeat. The top three clubs ended up with the same total number of points when all the games were completed.

After fully understanding the problem, we immediately know that the three top teams, say team A, team B, and team C, must beat the other three teams D, E, F. Therefore, A, B, and C must each obtain (3 + 3 + 3 ) = 9 points. However, they play against each team twice, for a total of 18 points against D, E, and F. For games between A, B, and C, we have 2 cases. There is an equality of points between A, B, and C in the following cases.

Case (I): A team ties the two other teams. For a tie, we have 1 point, so we have (1 + 1) * 2 = 4 points (they play twice).

Therefore, this case brings a total of 4 + 18 = 22 points.

Case (II): A team beats one team while losing to another. This gives equality, as each team wins once and loses once as well. For a win, we have 3 points, so a team gets 3 * 2 = 6 points if they each win a game and lose a game.

This case brings a total of 18 + 6 = 24 points.

Therefore, we use case (II) since it brings the greater amount of points as 24.

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Answer:

DEFG = (1/2)a^2

Step-by-step explanation:

tells us ∠FDG = 45° and ∠EGD = 45° and by corresponding angles related to parallel lines ∠FBD = 45°. Then ∠DFB = 90°!

So DFB- (1/2)(DF)(FB)=(1/2)a2

The relationship between height and vertical jump is High positive correlation.

What is a correlation?

A statistical indicator of the relationship between the relative motions of two variables is the correlation. If the variables are correlated, a line or curve will be formed by the points. The points will touch the line more closely the better the correlation.

Main body:

To find the relation we need to draw a line passing closely to all the points , if we are able to draw such line , it has high positive correlation.

If the line doesn't pass through all points it has low positive correlation.

hence this has high positive correlation .

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Answer:

-positive

-linear

-strong

-no.

Step-by-step explanation:

edge 2023

The random variable in given problem is "x" . The possible values of random variable x are 0,1,2 and 3..

All possible values of random variable is numrical in nature.

We have a table to right lists probabilities for the corresponding number of girls in three live births.

from the table we cleary see that the random variable is x which represents the number of girls in three live births.

Random variable is a variable whose value is unknown or a variable which assigns a numerical value to each trials in Sample Space.

Also, we can see in list that the number of girls in three live birth values are 0, 1 ,2 and 3 ( 3 live birth)

So, the possible values of random variable x is 4 i.e., 0, 1, 2 and 3..

From data we get a result that all possible values of random variable and it's probabilities are numrical in nature.

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The sum of the geometric progression with the features stated in the text is given as follows:

S = 2.62 x 10^(43).

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

The sum of a finite geometric sequence with n terms is given as follows:

[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]

In this problem, the first term and the common ratio are given as follows:

[tex]a_1 = 2, n = 3[/tex]

Hence the equation is:

[tex]a_n = 2(3)^{n - 1}[/tex]

The nth term is of 1458000, hence the number of terms of the sequence is obtained as follows:

[tex]a_n = 2(3)^{n - 1}[/tex]

[tex]1458000 = 2(3)^{n - 1}[/tex]

[tex]3^{n - 1} = 729000[/tex]

[tex]3^{n - 1} = 3^{90}[/tex]

Then:

n - 1 = 90

n = 91.

Thus the sum of the sequence is given as follows:

[tex]S_n = \frac{a_1(1 - r^n)}{1 - r}[/tex]

[tex]S_{91} = \frac{2(1 - 3^{91})}{1 - 3}[/tex]

S = 2.62 x 10^(43).

The problem is solvable with an nth term of 1,450,800, not 145,800, as 145,800/2 is not a root of 3.

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Answer: 4x+10

simplified: 2x+5

Step-by-step explanation:

Answer: 4x+10

You multiply 2 by (2x) = 4x

You multiply 2 by (5) = 10

Answer:

the answer Is 6 .........

Reflection in geometry means the type of transformation that flips a shape in a mirror line.

What is reflection ?

Reflection is a type of transformation that flips a shape in a mirror line so that each point is the same distance from the mirror line as its reflected point.

Let us suppose that the triangle with one coordinate  [tex](3,-5)[/tex] and the other two are unknown and we do not even want to know them but it would be better if we do know them:-

And we have a graph.

Let us draw a line [tex]y=-2[/tex] on the graph and draw the triangle

Now the coordinates [tex](3,-5)[/tex] are three boxes away from the line [tex]y=-2[/tex], so we plot this coordinate three boxes up from the line [tex]y=-2[/tex] and do the same for other coordinates so [tex](x,y)[/tex] is one box up from the line [tex]y=-2[/tex] so we plot the coordinates one box up from the line [tex]y=-2[/tex]

Hence, the image is located at [tex]G[/tex] is plotted above.

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The expressions that show the distance between P and Q are option (d) |-6| + (-2) and option (e) 6 - 2

From the given number line

The distance between P and Q = 4 units

Now we have to solve each expression

Expression 1

|-6| + |-2| = 6 +2

Add the terms

= 8

Expression 2

|2-(-6)| = | 2 + 6|

= |8|

= 8

Expression 3

|-2| - (-6) = 2 + 6

Add the terms

= 8

Expression 4

|-6| + (-2) = 6 - 2

Subtract the term

= 4

Expression 5

6 - 2 = 4

Hence, the expressions that show the distance between -6 and -2 are option (d) |-6| + (-2) and option (e) 6 - 2

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The required increasement of height of tree is 33 centimeters annually

Function of time is defined as the change of abject or expression of variables with time. As the time increases, there is change in shape, height, etc. is called function of time.

we have given an expression of height of tree,

H = 210 + 33t

Where t represent the time and H is height of tree.

So, Changes in the height of the tree with years,

for t = 1 year

⇒ H = 210 + 33×1 = 210 + 33 = 243 centimeters

Thus, the height of tree in increases by 33 centimeters yearly.

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The amount received by Charis on Simple interest in 2 years will be $8.4

What is Simple Interest?

The process of figuring out how much interest will accrue on a given principal sum of money is known as simple interest (S.I.).

It's formula is given by S.I. = PRT/100  where P = principle amount

R= rate and T = time.

Main Body:

P= $140

R= 3%

T= 2 years

so S.I. = 140*2*3/100

S.I. = $ 8.4

Hence total amount received by Charis at the end of 2 years will be $8.4

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The correct statement regarding the proportional relationships is given as follows:

Boat A travels at a faster rate than Boat B.

A proportional relationship is a special case of a linear function with intercept zero in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:

y = kx

The function for boat A is:

d = 10.5t.

Hence the rate is:

10.5 miles per hour.

From the graph, the rate for boat B is obtained as follows:

k = 90/10 = 9 miles per hour.

A higher constant means a faster rate, 10.5 is greater than 9, hence boat A travels faster.

The problem is given by the image shown at the end of the answer.

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Answer:

The absolute difference is 1050

The relative percentage is 32.3076%

Step-by-step explanation:

We are given

The population of a town increased from 3,250 in 2008 to 4,300 in 2010

In 2008:

In 2010:

Absolute difference:

we know that

absolute difference =

absolute difference =

absolute difference is 1050

Relative increase:

we know that

Relative percentage is

now, we can plug values

=32.3076

So, the relative percentage is 32.3076%

The principle investment necessary to obtain a total sum of $400.00 from simple interest at an annual rate of 8% for 8 years is $243.90.

Arithmetic operations is a field of mathematics that studies numbers and the operations on numbers that are helpful in all other disciplines of mathematics. It consists mostly of operations like addition, subtraction, multiplication, and division. Arithmetic Operator is used to conduct mathematical operations on the supplied operands such as addition, subtraction, multiplication, division, modulus, and so on.

Here,

First, converting R percent to r a decimal

r = R/100 = 8%/100 = 0.08 per year.

Solving our equation:

P = 400 / ( 1 + (0.08 × 8)) = 243.90243902439

P = $243.90

The principal investment required to get a total amount, principal plus interest, of $400.00 from simple interest at a rate of 8% per year for 8 years is $243.90.

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The probability that the student takes statistics given that he or she is a business major is 0.04.

The probability that an event will occur is determined by the probability formula. The ratio of positive outcomes to all possible outcomes is used as the formula to determine an event's probability. Probabilities are always in the 0 to 1 range. A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to express probabilities.

Given,

The probability that a student takes statistics and is a business major is 0.036. the probability that a student takes statistics is 0.9. the probability that a student is a business major is 0.12

Students who have taken both:

P( statistics ∩ business) = 0.036

Only a statistics major:

P( statistics/ business) = 0.9

P( student is business major)

P ( statistics / business) ÷ P( statistics/ business)

0.036/0.9

0.04

The probability that the student takes statistics given that he or she is a business major is 0.04.

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Answer:

Step 2 is incorrect

Step-by-step explanation:

Step 2 is where you are distributing out -5. Step 2 should be distribution rather than division property of equality.

Answer:  [tex](g \circ f)(x)=9\text{x}^2-36\text{x}+50\\\\[/tex]

=====================================================

Explanation:

The notation (g∘f)(x) is the same as g(f(x))

We'll start with the outer function g(x). Then replace each x with f(x). Afterward plug in f(x) = -3x+5 for the right hand side only.

This is what the steps look like

[tex]g(\text{x})=\text{x}^2+2\text{x}+15\\\\g(f(\text{x}))=(f(\text{x}))^2+2f(\text{x})+15\\\\g(f(\text{x}))=(-3\text{x}+5)^2+2(-3\text{x}+5)+15\\\\g(f(\text{x}))=9\text{x}^2-30\text{x}+25-6\text{x}+10+15\\\\g(f(\text{x}))=9\text{x}^2-36\text{x}+50\\\\[/tex]

Therefore,

[tex](g \circ f)(x)=9\text{x}^2-36\text{x}+50\\\\[/tex]

You can use tools like WolframAlpha, GeoGebra, and Desmos as ways to confirm the answer.

Answer:

Answer is: 8 2/3 but improper is 26/3

The area of the figure created by Brianna is  [tex]33\frac{3}{4}[/tex] square feet.

Explain area in mathematics.

Area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area or, it can be simply defined as the total amount of space occupied by a flat (2-D) surface or an object's shape.

Solution Explained:

A square with a side of 4 1/2 feet and two parallelograms with bases of 4 1/2 feet and heights of 1 1/2 feet make up the figure.

Therefore, the total area of the figure is
Area of Square + 2 X Area of Parallelogram
= (side)^2 + 2(b X h)
= (4 1/2)^2 + 2(4 1/2 X 1 1/2)
= 81/4 + 27/2    
=  135/4
= [tex]33\frac{3}{4}[/tex] square feet

Area of the figure is [tex]33\frac{3}{4}[/tex] square feet.

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The number of student like at least one kind of ice cream is given by (d) 275.

Let C be the student who like chocolate ice cream and P be the student who like Pistachio ice cream.

Now given that, n(C) = 145, n(P) = 150

Also given that, 123 students do not like neither chocolate or pistachio ice cream.

So, n(P' and C') = 123

The required number of student like at least one kind of ice cream is given by,

N = 398 - n(P' and C') = 398-123 = 275

Hence the correct option is (d).

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Answer:

(2,1)

Step-by-step explanation:

The x-value stays the same since we are only moving up/down and the y-value becomes the opposite

(x,y)--> (x,-y)

So the point becomes (2,1)

Answer:

(2,-1) hope this helps you understand

By taking the product between the mass and the acceleration, we will see that the force is:

F = 640 N

By the second Newton's law, we know that a force can cause motion on a body by accelerating it, such that the force is equal to the product between the mass of the object and the acceleration.

F = m*a

Here we know that:

m = 80kg

a = 8 m/s^2

Replacing that we get:

F = (80 kg)*( 8 m/s^2) = 640 N

Where N is the unit Newton.

1 N = 1 kg*m/s^2

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