Three runners are training for a marathon. one day, they all run about ten miles, each at their own constant speed. which of the three runners has the fastest pace?

The probability of selecting 2 red marbles in a row is 1/12.

A bag contains 6 blue marbles, 5 red marbles, 3 green marbles, and 2 yellow marbles. Two marbles are removed from the bag one at a time without being replaced. We need to find the probability of selecting 2 red marbles in a row. Let the probability be represented by the variable "P".

The probability that the first selected marble will be red is given below :

P1 = 5/(6 + 5 + 3 + 2) = 5/16

The probability that the second selected marble will be red is given below :

P2 = 4/(6 + 4 + 3 + 2) = 4/15

The probability that both of the selected marbles will be red is given below :

P = P1*P2 = (5/16)*(4/15) = 1/12.

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1/2 fraction of the day will the clock show the correct time when  it is supposed to display a 1 , it mistakenly displays a 9.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where 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.

Here,

=2/3(1-15/60)

=2/3(3/4)

=2/4

=1/2

When the clock should be displaying a 1, but instead shows a 9, the correct time will be displayed for 1/2 of the day.

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The coordinates of the translated of the image is as below

(-3, -3), (-2, -6), and (-5,-3)

Transformation is a term used in mathematics to refer to the movements made by objects.

Translation refers to a type of transformation that involve a linear movement.

Movements as seen in translation includes

The up and down movements are on the vertical direction controlled by the y coordinate. While the left and right movements are on the horizontal direction controlled by the x coordinate.

Applying the translation rule (x-3, y-4) the coordinates of the image is calculates as below

(0, 1) ⇒  (0-3, 1-4) ⇒ (-3,-3)

(1, -2)  ⇒  (1-3, -2-4) ⇒ (-2,-6)

(-2, 1) ⇒  (-2-3, 1-4) ⇒ (-5, -3)

preimage          image

(0, 1)                  (-3, -3)

(1, -2)                 (-2, -6)

(-2, 1)                 (-5, -3)

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The giveaway cost is $600   and the direct product cost is  $300    .

In the question ,

it is given that ,

number of baskets that are planned to give away = 10 basket

price = $60

gross margin percentage = 50%

The give away cost is calculated using the formula

give away cost = number of basket × price

give away cost = 10 × 60 = $600.

the direct product cost can be calculated using the formula

direct product cost = Number of basket x Price x (1-margin%)

direct product cost = 10 × 60 × (1-50%)

= 10 × 60 × 0.5

= 600 × 0.5

= 300

Therefore , The giveaway cost is $600   and the direct product cost is  $300    .

The given question is incomplete , the complete question is

To promote your basket business, you plan to give away 10 baskets. Your price is $60 in your normal gross margin percentage is 50%. How much will the give away cost you and direct product costs ?

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The triangle-shaped array of numbers known as Pascal's triangle has a top number of 1 and a line of 1s going down each of the other two sides. Each new number is situated between two other numbers and below them; its value is the product of the numbers immediately above it.

What is Pascal's Triangle?

What is the purpose of Pascal's triangle?

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The graph of y-2=-3(x-1) is shown in the figure below;

Graphing functions is the process of drawing the graph (curve) of the corresponding function. Graphing basic functions like linear, quadratic, cubic, etc is pretty simple, graphing functions that are complex like rational, logarithmic, etc, needs some skill and some mathematical concepts to understand.

Given;

y-2= -3(x-1)

When x=0

y-2= -3(0-1)

y-2=0

y=0

When y=0

0-2= -3(x-1)

x=1.667

Hence, the graph of these coordinates is as follows;

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The set of coordinates after the reflection is (c) M' = (-3, -4) N' = (2, -3) O' = (1, -1) P' = (-2, -2)

The graph represents the given parameter

On the graph, we have the following coordinate points

M = (-3, 4)

N = (2, 3)

O = (1, 1)

P = (-2, 2)

The rule of the reflection is given as:

Reflection across the x-axis

Mathematically, this is represented as

(x, y) ⇒ (x, -y)

When this is applied to the points, we have the following representation

M' = (-3, -4)

N' = (2, -3)

O' = (1, -1)

P' = (-2, -2)

Hence, the set of coordinates is (c)

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Answer:The equation of the solution 4x + 5y = 22 and 2x + 3y = 12 will be (3, 2).

What is the solution of the equation?

The solution of the equation means the value of the unknown or variable.

The equations are given below.

4x + 5y = 22   …1

2x + 3y = 12    …2

The degree of the equation is one, then the equations will be the linear equation.

Multiply the equation 2 by 2, then subtract the equation 1 from 2. Then the equation will be

 4x + 6y = 24

–4x – 5y = –22

6x -  5y = 24 – 22

Then simplify the equation, then the equation will be

y = 2

Substitute the value of y in equation 1, then the value of x will be

4x + 5(2) = 22

 4x + 10 = 22

        4x = 22 – 10

        4x = 12

          x = 12 / 4

          x = 3

Then the equation of the solution will be (3, 2).

Step-by-step explanation:

The equation of the line passing through the point (2,6)  and perpendicular to the given line is y = 6.

Given data;

The line is horizontal, and the slope of the line is infinity.

The slope of the line perpendicular will be expressed as [tex]\frac{-1}{∞}[/tex] = 0

To get the equation of the line and passes through the point (2,6),

A line's equation in point-slope form is written as;

[tex]m = \frac{y-yo}{x-xo}[/tex]

As m is the slope of the line then,

The required equation will be:

y - 6 = 0*(x-2)

y - 6 = 0

y = 6

Hence, the equation of the line that is perpendicular to the given line and passes through the point (2,6) is y = 6.

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The system of inequalities is

x + y ≥ 14

5x + 2.5y ≤ 60

Given, that Yaritza and her children went into a restaurant that sells hamburgers for $5 each and tacos for $2.50 each.

Yaritza has $60 to spend and must buy at least 14 hamburgers and tacos altogether.

As, x represents the number of hamburgers purchased and y represents the number of tacos purchased

Now, according to the question

x + y ≥ 14

as, she must buy at least 14 hamburgers and tacos altogether.

Now, 5x + 2.5y ≤ 60

as, she has $60 to spend.

So, we have two inequalities

x + y ≥ 14

5x + 2.5y ≤ 60

Hence, the system of inequalities for the given problem is

x + y ≥ 14

5x + 2.5y ≤ 60

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The average rate of change from x=2 to x=6 is 0.

What is the average rate of change?

The average rate of change is a measurement of how much the function changed on average per unit during that time period.

The average rate of change of function f over the interval a≤x≤b, is less than or equal to, x, is less than or equal to, b is given by this expression:

[tex]f'(x) = \frac{f(b)-f(a)}{b-a}[/tex]

Given, for x = 2 to x = 6 , we get a = 2 and b = 6

Then, from the figure,

f(a) = f(2) = -2

f(b) = f(6) = -2

Now,

Average rate of change = [tex]\frac{f(6)-f(2)}{6-2}[/tex] = [tex]\frac{-2-(-2)}{4}[/tex] = 0

Hence, the average rate of change is 0.

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Answer:

The amount of the ticket will be $531.

Step-by-step explanation:

If the driver is charged $30 for every mile above the speed limit, than :
diff = 52.7 - 35

     =  17.7 miles
which leads to say that he owes 17.7 * $30 = $531

The ordered pair that is a solution of the system of inequalities:

4x + 2y > 8

x - y ≥ 2

is (7, 2)

Here we have the following system of inequalities:

4x + 2y > 8

x - y ≥ 2

The points (x, y) are solutions only if make both inequalities true. For example let's use the first pair (2, 4)

Replacing that in the inequalities we get:

4*2 + 2*4 > 8

2 - 4 ≥ 2

Simplify the left side:

16 > 8

-2  ≥ 2

The second inequality is false, so (2, 4) is not a solution.

The correct option is the second one, (7, 2), evaluating the inequalities we get:

4*7 + 2*2 = (32) > 8

7 - 2 = 5 ≥ 2

You can see that both are true.

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The total dollar amount saved by Mo is y = $90 + $8h. The y-intercept is the amount of money he has already saved, $90. The slope is the rate at which the amount saved would increase, $8.

The total dollar amount saved by Merv is y = $50 + $8.50h. The y-intercept is the amount of money he has already saved, $50. The slope is the rate at which the amount saved would increase, $8.50.

Mo would reach the goal. Because the total amount of money he would have saved is $154.

A linear equation is an equation that has a single variable that is raised to the power of one. When drawn on a graph, a linear equation is a straight line.

The general form of a linear equation is:

y = mx + b

Where:

The equation that would be used to represent the total amount of money saved is:

Equation that represents the amount that should be saved by Mo:

y = $90 + $8h

Substitute h with 8

y = $90 + $8(8)

y = $90 + $64 = $154

The total dollar amount saved by Merv is:

y = $50 + $8.50h

Substitute h with 8

y = $50 + (8.50 x 8)

y = $50 + 68

y = 118

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Answer:

Step-by-step explanation:

From the series,  2, 8, 18, 32, 50,...

By observation and by trial and error.

The first term, n = 1    = 2*1*1 = 2

Second term, n =2,     = 2*2*2 = 8

Third, n =3,                = 2*3*3 = 18

Third term, n = 4,       = 2*4*4 = 32

Fourth term, n =5,     2 * 5* 5 = 50

For nth term,        2 *n *n = 2n²

Therefore nth term =  2n²

I hope this helps.

The same circle's radii. parallelogram, rectangle, square, and rhombus opposite sides, sides of a triangle with equal sides.

What is congruent segments?

Segments of the same length are said to be congruent. Collinear points are those that share a line. A mathematical assertion that can be validated is known as a theorem. A point that divides a segment into two congruent segments is the segment's midpoint.

Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments.

When two lines are the same length, they are said to be congruent. Superimposable figures that entirely enclose each other when stacked one atop the other are congruent segments.

The congruent segments continue to be congruent even after being turned, flipped, or rotated. Congruence between any two congruent line segments is represented by the symbol.

Look at the illustration below that shows congruent line segments:

Here, the double vertical bars on each line segment, PQ and XY, represent their equality, resulting in the line segment PQ ≅ XY.

We shall examine the congruent line segments' qualities in order to learn more about them. Congruent lines in geometry possess the following characteristics:

(i) Reflexive

(ii) Symmetric

(iii) Transitive

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The answer shown is incorrect as it doesn't follow the rules of indices? Unless that was your attempt?

A power outside the bracket should multiply with the inner powers not add, so the first part should be

(3 x^2 y^5)^4

= 3^4 x^(2*4) y^(5*4)

= 81 x^8 y^20

Then you have

81 x^8 y^20 + x^6 y^9 - 12 x^8 y^20

The powers that equal can be taken away to give

69 x^8 y^20 + x^6 y^9

I hope it's clear enough

The hydrogen atoms are on the reactant side in the reaction is 2 atoms.

Reaction is defined as when atoms' chemical bonds are created or ruptured. The substances that start a chemical reaction are known as reactants, and the compounds that are produced as a result of the reaction are known as products. Now that the chemicals had been combined, bonds would be rearranged, resulting in the production of a new product.

We are aware that one of the requirements for formulating a balanced chemical reaction equation is that the quantity of each element's atoms on the reactant side must match the quantity of that element's atoms on the products side. By performing an atom count, we may determine the number of hydrogen atoms present on the reactants side of the reaction when we examine the reaction as it is proved to be balanced.

Thus, the hydrogen atoms are on the reactant side in the reaction is 2 atoms.

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These are the numbers that can be generated which are 3, 5, 4, 1/4, -11, 20, -8, 64, 1/2, etc.

What is arithematic operartions?

Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.

We have,

signs + , − , × , ÷ , ( , )

the digits 4 4 4

By putting suitable signs + , − , × , ÷ , ( , ) in-between the digits 4 4 4

4 − (4 ÷ 4) = 3.

4 + (4 ÷ 4) = 5.

4 × (4 ÷ 4) = 4.

4 ÷ (4 × 4) = 1/4.

4 - (4 × 4) = -11.

4 + (4 × 4) = 20.

4 - (4 + 4) = -8.

4 × (4 + 4) = 64.

4 ÷ (4 + 4) = 1/2.

Hence, these are the numbers that can be generated which are 3, 5, 4, 1/4, -11, 20, -8, 64, 1/2, etc.

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The expression that represents this scenario would be l(t) = 0.28t. This expression states that the amount of liquid that has leaked at any given time is equal to 0.28 times the number of seconds that have passed.

Linear equations are mathematical equations of the type y = mx + b, with   and x and y being variables. These equations represent a straight line on a graph and are referred to be "linear" since the maximum power of the variable is 1. For example, the equation y = 2x + 3 is a linear equation since the maximum power of the variable x is 1. Linear equations are useful for representing a broad range of real-world events, such as the link between the distance an object travels and the time it takes to traverse that distance. They are a common tool in many disciplines, including physics, engineering, and economics. They are also quite simple to answer.

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When  [tex]x^3[/tex]+4x-24 is divided by x-2 then the remainder is -8.

What is remainder theorem?

 Remainder Theorem is a method for dividing polynomials according to Euclidean geometry. This theorem states that when a polynomial P(x) is divided by a factor (x - a), which isn't really an element of the polynomial, a smaller polynomial is produced along with a remainder. The remainder theorem asserts that when a polynomial p(x) is divided by (x - a), the remainder equals f. (a). Using Euclid's Division Lemma, this may be demonstrated. To put it another way, p(x) = q(x) (x - a) + r if q(x) is the quotient and 'r' is the remainder.

Here the given [tex]x^3[/tex]+4x-24 and x-2

When a function f(x) is divided by x+a, then the remainder is given by f(−a):

So, in this case remainder will be f(2) .

=> f(x)= [tex]x^3[/tex]+4x-24

put x=2 then

=> f(2)= [tex]2^3[/tex]+4(2)-24

=> f(2) =8+8-24

=> f(2) = 16-24 =-8

Hence the remainder is -8.

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Answer:

154

Step-by-step explanation:

The difference is 8.

Answer: The answer is d 1 23/25

Step-by-step explanation: if you where to rewrite 1.92 as a improper fraction you would get 48/25 so the next step would be to rewrite 48/25 as a mixed number then you would get 1 23/25 there you go :))

Answer:

-5/6

Step-by-step explanation:

1. Label X1 AND Y1 and X2 AND Y2  (9(x1),5(x2))  (21(x2),-5(y2))

2.  Use this formula  [tex]\frac{y2-y1}{x2-x1}[/tex]=slope

3. Plug the numbers into the formula [tex]\frac{-5-5}{21-9}[/tex][tex]= - \frac{10}{12}[/tex]

4. Find the simplest form.

[tex]slope= - \frac{5}{6}[/tex]

Answer:

The answer is 40

Step-by-step explanation:

You are counting by 4's

Answer:

$540,000

Step-by-step explanation:

250000 + .2(1250000) + .1(400000)

250000 + 250000 + 40000

540,000