This line plot shows the number of laps students ran in gym class.

Select the three true statements about the line plot.

OPTIONS:
Most of the students ran more than 3 laps.


None of the students ran more than 3 1/2 laps.


The same number of students ran 1 lap as ran 2 laps.


Most of the students ran 2 1/2 laps.


The greatest number of students ran 1 1/2 laps.

Answer:

15. -3 1/4

16. -4 1/2 OR -4 2/4

17. 1 1/4

18. -5 3/4

19. 1/2 OR 2/4

20. -2 1/2 OR -2 2/4

Step-by-step explanation:

Answer:

15) -3.25

16) -4.5

17)1.25

18)-5.75

19).5

20)-2.5

In the year 1582, January 1st was adopted for the new year celebration

An equation is used to show the relationship between numbers and variables.

Polynomials consist of exponents of variables and numbers forming an equation using operations of addition and subtraction. The degree of a polynomial determines it type such as linear, quadratic, cubic and so on.

The polynomial having a degree of 3 is cubic while that with a degree of 2 is quadratic and that with degree of 1 is linear

The year that January 1st was adopted as new year can be gotten using the function:

f(x) = 3x³ - 7x² - 5x + 7

f(9) gives the year that it was adopted. Substituting x = 9 gives:

f(9) = 3(9)³ - 7(9)² - 5(9) + 7

f(9) = 1582

In the year 1582, the new year was celebrated at January 1st

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Therefore , the solution of the given problem of expression comes out to be √14q × 2√4q = 4q√14.

combinations of numbers, symbols, and operations (such + and) that show how much something is worth. Examples: • 2 + 3 is the formula.

• 3 x/2 variable  is another formula.There is no equals sign in the expression. A mathematical expression is a sentence made up of variables, numbers, or both. There is never an equal symbol in an expression. These expressions are examples. An equation is a mathematical statement proving the equality of two expressions.

Here,

The simplified expressions are 20 = 25, 56x2 = 2x14, [150x3k4] = 5xk26x, and 14q 24q = 4q14 given the facts from the question.

Simplifying the surd

A perfect square must be one of the components for a number to be written as just surds.

How to Make 20 Recall Simpler

20 = 4 × 5

Thus,

√20 = √(4 × 5)

√20 = 2√5

simple methods √(56x²)\s√(56x²) = √56 × √x²

Recall

√56 = √(4 × 14) = 2√14

√x² = x

Thus,

√(56x²) = 2√14 × x

√(56x²) = 2x√14

simple methods [150x3k4] = [150x3k4] = [150x3k4]

Recall

√150 = √(25 × 6) = 5√6

√x³ = √(x² × x) = x√x

√k⁴ = k²

Thus,

√[150x³k⁴] = 5√6 × x√x × k²

√[150x³k⁴] = 5k²x√6x

How to simplify 14q 2 4q: 14q 2 4q = 2

(14q × 4q)

√14q × 2√4q = 2 × 2q√14

√14q × 2√4q = 4q√14

Therefore , the solution of the given problem of eexpression comes out to be √14q × 2√4q = 4q√14.

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The bake sale sign has a 6 ft2 space.

An object's area is how much space it takes up in two dimensions.

It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure.

The word "area" refers to a free space.

A shape's length and width are used to compute its area. Unidimensional length is expressed in terms of feet (ft), yards (yd), inches (in), etc.

But a shape's area is a two-dimensional measurement. In order to measure something in a square, it is done so using measurements like square inches (in2), square feet (ft 2), square yards (yd2), etc.

The majority of forms and things have corners and edges. 

According to our question-

The opposite sides of a rectangle's quadrilateral (it has four sides and four angles) are equal and parallel.

Area of a rectangle equals length times width.

The area of the bake sale sign = length * breadth

Hence, The bake sale sign has a 6 ft2 space.

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Answer:

3.23, -1.23

Step-by-step explanation:

Draw the line y=1

See where it intersects x^2-2x-3

The x coordinates of the intersections are your answer

The length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in is 12.73 in.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the square of the length of the other two sides (a and b).

In this case, a = b = 9 in, so:

c2 = 92 + 92

c2 = 81 + 81

c2 = 162

c = √162

c = 12.73 in

The length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in is 12.73 in, calculated using the Pythagorean theorem.The length of the hypotenuse of a 45 90 45 triangle whose leg measures 9 in is 12.73 in.

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On solving the provided question, we got to know that -  to plot the graph, required equation is 3x +y -8 = 0

a collection of numbers, symbols, and operators (like + and ) that represent a value. Examples -  2 + 3 is a formula and there is also the statement 3 x/2. The equals symbol does not appear in expressions. Actually, none of these = ≠ < > ≤ ≥

We frequently have to understand a written phrase in order to write an expression. For instance, the notation x + 6 can be used to represent the phrase "6 added to some number," where x stands for the unknown value. To plot the graph,we need to find the equation first.

and to find the equation -

(y - y1) = m( x - x1)

y1 = -4

x1 = -2

y = 3

x = -5)

equation  -

(-3)(x-1) = y-5

-3x + 3 = y-5

3x - 3 = 5-y

3x +y -8 = 0

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Answer: To find an equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35, we can use the fact that two lines are parallel if and only if they have the same slope.

The slope of the line 4x−5y=35 is -4/5. Therefore, we can find an equation of the line that passes through (-5,-6) and is parallel to 4x−5y=35 by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

Substituting the values into the slope-intercept form, we get:

y = (-4/5)x + b

To find the value of b, we can substitute the coordinates of the point (-5,-6) into the equation:

-6 = (-4/5)(-5) + b

-6 = 8/5 + b

-6 - 8/5 = b

-24/5 = b

Therefore, the equation of the line that passes through the point (-5,-6) and is parallel to the line 4x−5y=35 is:

y = (-4/5)x - 24/5

This can also be written as:

y = -4/5x - 24/5

Step-by-step explanation:

To find the values of b and c, we can use the quadratic formula:

[tex]x = (-b ± \sqrt{ (b^2 - 4ac)}) / 2a[/tex] which will give us the value B = -6 & C = -4

A quadratic equation is a second-order polynomial equation in one variable using the formula [tex]x = ax2 + bx + c = 0[/tex] and a 0. The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

So the equation that she get is [tex]x^{2} -6x-4[/tex]

this means that x=3+√13 or 3-√13

which also equals to x=3+√13 & x-3-√13=0 and

x=3-√13

x-3+√13=0

which if you try to find the quadratic equation for this. you need to do it by this

(x-3+√13)(x-3-√13)

which will get you

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The graph of the linear equation 2x + 3y = 6 is a straight line that cuts the Y-axis at the point (0,2).

A linear equation is an equation in which the highest power of the variable is 1.

The general form of a linear equation is:ax + by = c where a, b and c are constants and x and y are variables. This equation represents a straight line when plotted on a graph.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept

To find the points at which the line will intersect y-axis,

take x=0 and substitute in the linear equation 2x+3y=6

2(0) + 3y = 6

3y = 6

y = 2

So the point where the line cuts the Y-axis is (0,2)

The straight line of the linear equation 2x+3y=6 intersects the y-axis at (0,2).

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The length of the rectangle is 4 units.

A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle.

Let n be the length of the rectangle.

The width of a rectangle is the length minus 2 units.

The width = n - 2

The area of the rectangle is 8 square units.

The area of the rectangle = length x width

8 = n (n-2)

n²-2n - 8 = 0

n²-4n+2n - 8 = 0

n(n-4)+2(n-4) = 0

(n+2)(n-4) = 0

n = 4 and -2.

So the length is 4 units.

Therefore, 4 units are the length of the rectangle.

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Its slope is m = 1 on the right side of the vertex, and m = - 1 on the left side of the vertex.

Absolute Value Function:

An absolute value function is a function that contains an algebraic expression within the absolute value sign. Remember that the absolute value of a number is its distance from 0 on the number line. To graph the absolute value function, select some values ​​of x and find some ordered pairs.

In mathematics, the absolute value or modulus of the real number x, represented as.

|x| is the non-negative value of x, regardless of sign.

x is positive and |xI =-x}.  For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3. The absolute value of a number can be thought of as the distance from zero.

Generalizations of the absolute value of real numbers are made in a variety of mathematical contexts. For example, absolute value is also defined for complex numbers, quaternions, ordinal rings, fields, and vector spaces. Absolute value is closely related to the concepts of magnitude, distance, and norm in various mathematical and physical contexts.

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Answer: not enough to answer

The total surface area of the cuboid is 2 (lh + lw+ hw) square units.

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Answer:

1:3

Step-by-step explanation:

The total profit P in terms of x can be expressed as

P(x) =  (a - c) (a/(x-c) + b(95-x))

The selling price that will maximize profit is the positive constant, a in dollars.

To find the selling price that will bring a maximum profit, we need to find the derivative of the profit function P(x) and set it equal to 0.

The profit function P(x) is given by P(x) = nx - nc,

where n is the number of backpacks sold and c is the cost to manufacture and distribute each backpack.

Substituting the given expression for n into the profit function gives:

P(x) = (a/(x-c) + b(95-x))x - c(a/(x-c) + b(95-x))

P(x) = (a - c) (a/(x-c) + b(95-x))

To find the selling price that will maximize profit, we need to find the critical points of P(x) by taking the derivative of P(x) with respect to x and setting it equal to 0:

P'(x) = (a - c) (-a/(x - c)² - b) = 0

Thus P'(x) = 0 at c = a or (x - c)² = -a/ b

a and b are positive constants, so -a/ b is negative but (x - c)² is never negative, so it is not a possible solution.

So only solution is c = a, that is for maximum profit selling price, c should be equal to the positive constant, a.

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When you see a graphed cluster of dots depicting the values and relationship of two different variables, you are seeing a visual description of relatedness called a scatter-plot or scatter-gram.

Scatter-plot: A scatter-plot is a form of mathematical diagram or plot that employs Cartesian coordinates to illustrate distinct values associated to two variables for a specific set of data. It is also known as a scatter-gram, scatter-graph, scatter-chatter, or scatter-diagram.

It is being utilized to determine how one variable influences the other.

The supplied statement in the question above represents the scatter plot.

Here,

When you observe a graphed cluster of dots reflecting the values and relationship of two separate variables, you are looking at a scatter-plot or scatter-gram, which is a visual explanation of relatedness.

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Answer:

y = -3x +20

Step-by-step explanation:

Equation of line: y =mx + b

Where m is the slope and b is the y-intercept.

3x + y = 17

Write the above equation in y = mx +b form.

      y = -3x + 17

m = -3

Parallel lines have same slope.

So, slope of the required line is (-3).

     y = -3x + b

This line is passing through (4,8). Substitute in the above equation and find the value of 'b'.

       8 = -3*4 + b

        8 = -12 + b

  8 + 12 = b

          b = 20

Equation of the line:

               [tex]\sf \boxed{ y = -3x + 20}[/tex]

Latitude 36°30′ was designated by the Missouri Compromise of 1820 as the northern limit for the legalization of slavery in the western territories.

By Stephen A. Douglas's Kansas-Nebraska Act of 1854, the Missouri Compromise's prohibition on slavery in the former Louisiana Territory north of the parallel 36°30′ north had been essentially removed. Latitude 36°30′ was designated by the Missouri Compromise of 1820 as the northern limit for the legalization of slavery in the western territories.

The expansion of slavery into the western lands was addressed by the Missouri Compromise, the Compromise of 1850, and "Bleeding Kansas." The balance between "free" and "slave" states in the Union was a factor in each of them.

Slavery was proposed to be outlawed in the remaining Louisiana Territory above the 36° 30' latitude line in the Missouri Compromise. The Kansas-Nebraska Act of 1854 abolished this clause after it had been in effect for 34 years.

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The Missouri Compromise of 1820 established latitude 36°30′ as the northern boundary for the legalisation of slavery in the western territories.

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At this rate, the ratio or proportion of red balloons to the total balloons, the number of red balloons out of 48 is 6.

Proportion describes the two or more ratios equated to each other.

Proportions are depicted as fractional values in decimals, fractions, or percentages.

In this situation, we equate the ratio or proportion of red balloons to the sample to determine the number that will likely be red.

The total number of balloons thrown in a water balloon fight = 6,960

The number of the balloons that are red = 870

The proportion of the red balloons to the total = 0.125 or 12.5% (870/6,960)

In a sample of 48 balloons, the number of red balloons will be 6 (48 x 0.125)

Thus, out of 48 balloons, there are 6 red balloons at this constant rate.

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Kaiser roll packet cost $1 more than the price of a pepperoni roll at Luis's store.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that the graph shows the prices, in dollars, of different numbers of pepperoni rolls at Luis's store. The table shows the prices, in dollars, of different numbers of Kaiser roll packets at the same store.

The price of a Kaiser roll packet = {C1} = (48 - 24)/(8 - 4) = 24/4 = 6

The price of a Kaiser roll  = {C2} = (40 - 20)/(8 - 4) = 20/4 = 5

$6 - $5 = 1

Therefore, Kaiser roll packet cost $1 more than the price of a pepperoni roll at Luis's store.

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On solving the provided question we can say that - the probability of the event will be there are two red sides, thus multiplying 16.6667 by two results in 33.3333%.

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1. the proportion between the number of events in a comprehensive collection of equally likely outcomes that lead to a certain occurrence and the entire number of outcomes.

Each side would be 50%, and if one side were divided among three people, it would equal 16.6667 per person.

Given that there are two red sides, you can multiply 16.6667 by 2 to get 33.3333%.

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Answer:-14°F

Step-by-step explanation:

-2°F -12°F is basically the same as 12°F+2°F which is 14°F and then you inverse it

when the input r, is 4, then the output g, is 13.

The function g = 25 - 3r gives the output g when the input r is given.

If we substitute r = 4 into the equation, we get:
g = 25 - 3×4
g = 25 - 12
g = 13

Therefore, when the input, r is 4, the output g, is 13.


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Each person will pay $49.056. The value must be divided by the entire value, and the resulting number must then be multiplied by 100 to get the percentage.

A percentage, often known as percent, is a division by 100. Percentage, which meaning "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.

Amount of bill = $124.72

and tip they left = 18% of $124.72

total amount is =$124.72 + $124.72*18%=$147.1696

so, each person pay= $147.1696/3=$49.056

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Answer:

  b)  250,000

Step-by-step explanation:

You want to estimate the product of 5,398 and 47 by rounding to the nearest thousand and ten.

Rounding 5,398 to the nearest thousand gives 5000.

Rounding 47 to the nearest ten gives 50.

The product of these is the estimate you want:

  5000·50 = 250,000

To solve this we must be knowing each and every concept related to probability and its calculations. Therefore, the  probability of tossing heads is 0.000976.

Probability is the branch of mathematics concerned with the outcomes of random occurrences. Probability refers to the chance or potential of an outcome. It describes the likelihood of a specific occurrence occurring.

Probability denotes the possibility of something happening. It is a statistical discipline that deals only with probability of such a random event. The number ranges from 0 to 1, with 0 being an improbable event and 1 representing a certain event.

P(getting heads on one toss) = 1/2

P(getting all heads in 10 tosses)=(1/2)¹⁰

                                                     =1/1024

                                                   =0.000976

Therefore, the  probability of tossing heads is 0.000976.

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Answer:

$27

Step-by-step explanation:

If we know that %25 is equal to 1/4, or 0.25, then we can use an equation that look like this:
108 × 0.25 = 27

Therefore, the amount of the discount was $27

Solving for percentages can be tricky, and you may need help on trying to solve a problem including one. If you need to find a percentage of a number, the easiest way to do that is to convert the percentage into a fraction or decimal and multiply the total by that number.

For ex.

What is 15% of 60?

To do this, convert the percentage into a decimal.

15% converted into a decimal is 0.15.

Now multiply 60 by 0.15.

60 ÷ 0.15 = 9

So, the answer to this example would be 9.