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The table shows the relationship between the participants walking and running for the week's cross-country practices.



Walk (laps) 3 B 15

Run (laps) 5 10 D

Total (laps) A C 40



At this rate, how many laps will the participants walk if the total distance is 32 miles? How many miles will they run?

They will walk 7 laps and run 17 laps for a total of 32 miles.

They will walk 12 laps and run 20 laps for a total of 32 miles.

They will walk 14 laps and run 18 laps for a total of 32 miles.

They will walk 10 laps and run 22 laps for a total of 32 miles.

Calculating the LCM of all these, one gets  2^2. 3^2 . 5^4 .7^5. Using the factor counting formula, the answer is 3.3.5.6 = {270}

Step-by-step explanation:            

Note that for all n, 149^n-2^n  is divisible by 149-2=147  by difference of nth powers. That is 3.7^2, so now we can clearly see that the smallest n to make the expression divisible by 3^3  is just 3^2 Similarly, we can reason that the smallest n to make the expression divisible by 7^7 is just 7^5.
       

Finally, for 5^5, take (mod {5}) and ( mod {25} )of each quantity (They happen to both be -1 and 2 respectively, so you only need to compute once). One knows from Fermat's theorem that the maximum possible minimum n for divisibility by 5 is 4, and other values are factors of 4. Testing all of them(just 1,2,4 using mods-not too bad), 4 is indeed the smallest value to make the expression divisible by 5, and this clearly is NOT divisible by 25. Therefore, the smallest (n) to make this expression divisible by 5^5 is $2^2 .5^4.    

Using the factor counting formula, 2^2. 3^2 . 5^4 .7^5 = 3.3.5.6 = {270}

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The y-intercept in this situation means A. When the cab travels 0 miles, the total fee will be $14.00.

The formula to find the y-intercept is y = f(x), where x = 0, and then solve for y.

The equation for a linear relationship is y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope of the line, and b is the y-intercept.

Cab Fare

Number of Miles Total Fee

2                             $17.00

5                             $21.50

7                            $24.50

10                          $29.00

15                          $36.50

Difference between 7 and 5 = 2

Difference between $24.50 and $21.50 = $3

Variable cost per mile (Slope) = Rise/Run

= $1.50 ($3/2)

y = mx + b

y-intercept, b = 24.50 - 7(1.5)

= 14

= $14.00

Thus, the y-intercept in this situation means Option A while the slope shows that for every additional mile, the total fee increases by $1.50.

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Answer:

The y-intercept in this situation means A. When the cab travels 0 miles, the total fee will be $14.00.

Step-by-step explanation:

If we assume that Cal lives between Beverly and Alex: so the distance between the two of them is 11-4 = 7 miles.

Number line is a line contain every real numbers which includes all rational and irrational number. Generally we use it for determining ranges of a set. Using number line we can understand range and domain of function easily. A number line is a picture representation of real numbers evenly laid out on a straight line.

The distance from zero of a positive number r is simply r. But if r is negative, then we make a positive number by multiplying by -1, in other words -r is the distance in that case.

There is a standard mathematical function that does this, called the modulus function.

And whether r is positive or negative we write it like this |r|

So for example |100|=100 and |-100|=100 as well.

Alex is 11 miles away, and Cal is 4 miles away, so the distance between the two of them is 11-4 = 7 miles.

If we assume that Cal lives on the opposite side of Beverly from Alex:

Alex is 11 miles away from Beverly, and Cal is 4 miles away from Beverly in the opposite direction from Alex, so the distance between Alex and Cal is 11 + 4 = 15 miles.

The easiest way to see this is by creating a number line.

(for the first possible solution) If you put Beverly as a point, let's call it 0, then we would put Alex at 11 and Cal at 4, and the distance between them is 7.

(for the second possible solution) If you put Beverly as a point, 0, then we would put Alex at 11 and Cal at -4, and the distance between them is 15.

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5 is not an algebraic expression.

Since it is obvious that 5 is a constant, even if constants constitute a component of the algebraic equation, they do not finish it. A variable and an operator are also necessary for an expression to qualify as an algebraic expression. Any unknown term, such as x, y, or z, can be a variable, and the operators + and - can be used. Terms with no associated variables are known as constants. A variable and an operator are also necessary for an expression to qualify as an algebraic expression.

It follows that 5 cannot be an algebraic expression.

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Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤. To ‘solve’ an inequality means to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality.

Suppose we want to solve the inequality x + 3 > 2.

We can solve this by subtracting 3 from both sides:

x + 3 > 2

x > −1

So the solution is x > −1. This means that any value of x greater than −1 satisfies x + 3 > 2.

Inequalities can be represented on a number line such as that shown in the image attached below. The solid line shows the range of values that x can take. We put an open circle at −1 to show that although the solid line goes from −1, x cannot actually equal −1.

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The slope of 5x 2y =- 3 is -5/2.

To find the slope of the equation 5x 2y =- 3, we need to rearrange it into the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

We start by rearranging the equation 5x 2y = -3 so that all the terms with y are on one side and all the terms with x are on the other side.

5x -2y = -3

Now, we divide both sides by -2 to isolate y.

-5x/2 = y + 3/2

Finally, we subtract 3/2 from both sides to get the equation in the slope-intercept form.

-5x/2 = y - 3/2

Therefore, the slope of the equation 5x 2y = -3 is -5/2.

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Answer:

C) The total fixed cost.

Answer:

not directly proportional

Step-by-step explanation:

if the cost is directly proportional to number of rolls , then the unit cost for both will be equal.

first

one roll costs $1.99 ÷ 6 = $0.33 ( to 2 decimal places )

second

one roll costs $2.69 ÷ 9 = $0.30 ( to 2 decimal places )

since the unit costs are different there is not a directly proportional relationship.

Answer:

No because to buy nine rolls would be $2.69 but to buy six and then three to make nine then it would be $2.985 which is more expensive.

Step-by-step explanation:

$1.99 divided by 2 = 0.995

$1.99 + 0.995 = $2.985

$2.985 > $2.69

Answer:

2) The estimated weight, in pounds, of the beaver on June 1.

Step-by-step explanation:

Given function:

[tex]w(t) = 29 + 0.0674t \quad t < 90[/tex]

where:

When t = 0:

[tex]\begin{aligned}\implies w(0)&=29+0.0674(0)\\&=29+0\\&=29\end{aligned}[/tex]

Therefore, the constant of the equation (29) is the estimated weight of the beaver, in pounds, when t = 0.

As t = 0 is June 1:

Answer:

2.

Step-by-step explanation:

There are more boxes towards the highest numbers which means that the medians for northbound cars are generally high while the medians for southbound cars are located more on the smaller numbers representing the speed.

Answer: B

Step-by-step explanation: These lines are parallel. If you count over then down from point to point, then the slope for both lines is negative since it is going down, the slop is -2/1

To change logarithmic form to exponential form, spot the logarithmic equation's base and move the base to another side to the equal sign. Moving the base will make the current number or variable into the exponent.

Do not move something but the base: the other numbers or value will not change sides, and the word "log" will be release.

Log Rules:

1. the first rule is logb(mn) = logb(m) + logb(n)

2. the second rule is logb(m/n) = logb(m) – logb(n)

3. the third rule is: log b (mn) = n · logb(m)

1. Multiplication can be turned outside the log into addition and vice versa can be turned.

2. Division can be spin outside the log into a subtraction, and vice versa.

3. An exponent can be proceeded as a multiplier outward on all within a log, and vice versa.

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50 cm is the required perimeter of shape B.

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter.

A circle's or an ellipse's circumference is referred to as its perimeter.

There are numerous uses in real life for perimeter calculations.

We must sum up the lengths of the rectangle's four sides in order to get its perimeter.

So, according to the given figures:

Shape A's circumference is 60 cm.

Let x cm be the length of each square.

The total length of shape A's free bounds is equal to 12x.

Consequently, 12x = 60.

x = 5 cm

Currently, the length surfaces of form B equal 10x.

Shape B's perimeter equals 10x.

= 10(5)

= 50 cm

Therefore, 50 cm is the required perimeter of shape B.

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Correct question:
Shape A and Shape B are each made from 5 identical squares.

The perimeter of shape A is 60cm. Work out the perimeter of Shape B

0.01 is not the way of expressing the relationship because it does not represent the correct ratio between 10 square and 100 square

A ratio tells the relationship between two or more quantities by comparing their relative sizes.It is typically written as two or more numbers separated by a colon (:), such as 2:4, or expressed as a fraction, such as 2/4. The numbers in a ratio represent the relative amounts of the quantities being compared. A ratio can be used to compare any type of quantity, such as length, weight, or time.

A) 10 square is 1/10th of the area of 100 square. It can be represented as a fraction, where the numerator is the area of the smaller square (10) and the denominator is the area of the larger square (100). The fraction would be 1/10.

B) Another way of expressing the relationship is as a percentage, where the smaller area (10) is divided by the larger area (100), and the result is multiplied by 100 to get the percentage. So 10 square is 10% of 100 square.

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On solving the provided question, we can say that - the value of the linear equation is 2y+8x = 140

The algebraic equation y=mx+b is known as a linear equation. B is the y-intercept, and m is the slope. The previous sentence, where y and x are variables, is commonly referred to as a "linear equation in two variables." Bivariate linear equations are those that contain two variables in them. The linear equations 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3 are examples. When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

here, we have 2y + 8x

and x = 10 ; y = 15

2y + 8x

20 + 120 = 140

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A 9-sided shape is called a nonagon.

Therefore the answer is nonagon.

A nonagon is a polygon with nine sides and nine angles. A nonagon can be regular or irregular, depending on the lengths of its sides and angles. A regular nonagon has equal sides and angles, while an irregular nonagon has sides and angles of different lengths.

Nonagons are two-dimensional shapes, and they can be described by their number of sides, angles, and vertices. They are considered a type of polygon, which is a closed geometric figure that is made up of straight lines. In addition to nonagons, there are other types of polygons such as triangles, quadrilaterals, pentagons, hexagons, heptagons, and so on.

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Answer:

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

The two triangles have 2 sides marked as congruent and the included angles are congruent as vertical angles:

This gives us SAS congruence postulate.

The matching choice is B.

The average speed of the plane from Winnipeg to Red Deer is 400 km/h

Average speed is total distance travelled over total time taken.

Since a plane flew from Red Deer to Winnipeg, a flying distance of 1260 km. On the return journey, due to a strong head wind, the plane travelled 1200 km in the same time it took to complete the outward journey. On the outward journey, the plane was able to maintain an average speed 20 km/hr greater than on the return journey.

Let

Since the plane travels 1260 km on the outward journey, we have that

1260 = vt  (1)

Also,  the plane travels 1200 km on the inward journey, we have that

1200 = v't  (2)

Since the plane was able to maintain an average speed 20 km/hr greater than on the return journey, we have that

v = v' + 20 (3)

Substituting equation (3) into (1), we have that

1260 = (v' + 20)t  (4)

The required equations are

1260 = v't + 20t  (4)

1200 = v't  (2)

Subtracting equations, (2) from (4), we have that

1260 = v't + 20t  (4)

-

1200 = v't  (2)

60 = 20t

t = 60/20

t = 3 h

From equation (2), we have that the average speed

v' = 1200/t

Substituting t = 3 into the equation, we have that

v' = 1200/3

v' = 400 km/h

So, the average speed is 400 km/h

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Answer:

1.0833333333333333333333333333333333 (repeats)

Step-by-step explanation:

use a calculator

The measure that would be most useful to determine if the people can safely use the elevator is B. Mean

The most useful measure to determine if the people can safely use the elevator would be the mean weight of the people, as it would give an idea of the average weight of the group and if it is below 4,500 pounds.

The mode is the most common value in a set of data and does not give information about the weight of the entire group. The interquartile range is a measure of the spread of the middle 50% of the data and does not give information about the average.

In conclusion, the correct option is B.

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Answer:

Step-by-step explanation:

Given Line equation is 4x+3y=12 and point (3,4)

Given condition two line are parallel

Parallel means two straight lines having same slope.

From the above condition we can use "point-slope"  equation.

[tex]y-y_{1} =m(x-x_{1} )[/tex]    

From the given line equation we can find slope easily.

We can rewrite the line equation as [tex]y=-\frac{4}{3} x+4[/tex]

We can compare the above equation as  y=mx+b

slope [tex]m=-\frac{4}{3}[/tex] and point [tex](x_{1} ,y_{1} )[/tex]=(3,4) submit in slope-point equation.

Becareful while submit point in the slope point equation.

Note:(Many students do mistakes while submitting point.

[tex]y-4=-\frac{4}{3}(x-3)[/tex]

solve and get the answer

Equation of line is 4x+3y=24

Answer:

the bus will take approximately 33.33 minutes to cover 5km at a speed of 9 km/h.

Step-by-step explanation:

To find out how many minutes it will take for a bus to cover 5km at a speed of 9km/h, we need to use the formula:

time = distance / speed

In this case, the distance is 5 km, and the speed is 9 km/h. To convert the speed to km/min we can divide 9 by 60.

9 km/h = 0.15 km/min (by dividing 9 by 60)

Now we can substitute the distance and speed into the formula:

time = 5 km / 0.15 km/min = 33.33 min

So, the bus will take approximately 33.33 minutes to cover 5km at a speed of 9 km/h.

It's important to note that in this problem km/h is the speed and the distance is given in km, so you need to convert it to km/min in order to find the time. Also the time you get will be in minutes.

The value of 'a' for which the system of equations has a unique solution is a = 4/3.

The given system of equations can be written as:

Ax = 2

6x – 2y = 3

To find the value of 'a' for which the system has a unique solution, we can solve the equations for 'x' and 'y' and equate them.

Solving for 'x' in the first equation, we get:

x = 2/a

Solving for 'y' in the second equation, we get:

y = (3 + 6x)/2

Substituting the value of 'x' in the above equation, we get:

y = (3 + 6(2/a))/2

Equating the two equations, we get:

2/a = (3 + 6(2/a))/2

Multiplying both sides of the equation by 'a', we get:

2 = 3a + 6

Subtracting 2 from both sides of the equation, we get:

3a = 4

Dividing both sides of the equation by 3, we get:

a = 4/3

Therefore, the value of 'a' for which the system of equations has a unique solution is a = 4/3.

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Answer:

6000.000 + 900.000 + 0 + 5 + 3/10 + 2/100 + 7/1000

six thousand nine hundred and five ones point(.) three tenths two hundredths and seven thousandths

Step-by-step explanation:

right!!!

Answer:

Step-by-step explanation:

You want to find the measure of the angle designated as ∠1, given the other two have measures of 40° and 30°. You also want the classification of the triangle based on its angles.

The sum of angles in a triangle is 180°.

  40° +∠1 +30° = 180°

  ∠1 = 110° . . . . . . . . . . . . subtract 70°

The classification of a triangle as acute, right, or obtuse is based on the measure of its largest angle. If that angle is 90°, the triangle is a right triangle. If it is less, the triangle is acute; if it is more, the triangle is obtuse.

The angle measure 110° is more than 90°, so this triangle is an obtuse triangle.

Answer:

y = x + 1/3

Step-by-step explanation:

We know

You drank x ounces of juice and someone drank 1/3 more than what you think

Let's y represent the total, we have the equation

y = x + 1/3

Answer: 4/3x (or 1/3 + x, since your wording's pretty odd)

Step-by-step explanation:

i can't tell if the one-third you're referring to is a third of how many ounces of juice you drank (meaning it will change if you drank 1, 2, 3 oz of juice and so on) or if it's always going to be a third of an ounce more than the amount of oz of juice you drank (in which case it'd be 1/3 + x). anyway just choose whichever answer you're looking for :3

Answer: m = -1/10

Step-by-step explanation:

Use the slope formula to find the slope m.

m = −1/10

Equation for the sentence's inequality are $7.62 and necklaces are $15.67, which means that 7.62x + 15.67y >= 450.

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal symbol (). Different inequalities are used to contrast values, no matter how small or large. Many simple inequalities can be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

given

let X =  the number of bracelets

let Y =  the number of necklaces

The inequality equation = 7.62x + 15.67y >= 450

Equation for the sentence's inequality She needs to generate at least $450 in revenue because bracelets are $7.62 and necklaces are $15.67, which means that 7.62x + 15.67y >= 450.

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Answer: The Seed Calculator app is used to calculate the amount of seed required in order to produce a desired crop yield.

Step-by-step explanation:

The best description of the figure with the vertices given is, C. Quadrilateral

The figure given is a Quadrilateral firstly because it has 4 vertices and therefore 4 points. A Quadrilateral has four points as well which means this figure is a Quadrilateral.

The figure is not a Parallelogram because no two values of y are the same. A Parallelogram would have two points that have the same y value as there would be parallel lines involved.

To find out if the shape is a rectangle or square, find the lengths of the vertices using a distance calculator.

The length of (1, -4), and  (-2, 1) is:

=  5.83 units

The length of (-2, 1), and   (3, 4) is:

= 5.83 units

The length of (5, 2) and  (3, 4) is:

= 2.82 units

The length of (5, 2) and  (1, -4 ) is:

= 7.21 units

The shape is neither a square nor a rectangle so it is a quadrilateral.

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