Find the equivalent measures. Express as a decimal
(a) 250 cm =

Answer:

1 [tex]\frac{1}{4}[/tex] miles

Step-by-step explanation:

the routes from Lexington to Somerville are

Lexington → Brookfield → Somerville with distance

[tex]\frac{3}{8}[/tex] + [tex]\frac{7}{8}[/tex] = [tex]\frac{3+7}{8}[/tex] = [tex]\frac{10}{8}[/tex] = 1 [tex]\frac{2}{8}[/tex] = 1 [tex]\frac{1}{4}[/tex] miles

the other route is

Lexington → Brookfield → Yardley → Somerville with distance

[tex]\frac{3}{8}[/tex] + [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{3}{8}[/tex] + [tex]\frac{4}{8}[/tex] + [tex]\frac{4}{8}[/tex] = [tex]\frac{3+4+4}{8}[/tex] = [tex]\frac{11}{8}[/tex] = 1 [tex]\frac{3}{8}[/tex] miles

the shortest distance is

Lexington → Brookfield → Somerville , a distance of 1 [tex]\frac{1}{4}[/tex] miles

The equation of a line is y = 7/9x -3.5. using exact numbers from the graph.

A straight line is produced by a linear function. Therefore, the slope has a constant value. If the slope was variable, a straight-line graph would not exist. When you know the slope of the line to be investigated and the given point is also the y-intercept, you can utilize the slope-intercept formula, y = mx + b. (0, b). The y value of the y-intercept point is denoted by the symbol b in the formula.

Given a line in the graph in that we can see that,

At x = 0, y is -3.5 and at y = 0, x is 4.5 thus,

coordinates of the given line are (0, -.35) and (4.5, 0)

Therefore the slope of the line (m) = (y₂-y₁)/ (x₂ -x₁)

The slope of the line = 3.5/4.5 = 7/9

therefore equation of the line in the slope-intercept form:

y = 7/9 x +  c

Since this line passe from (0, -3.5)

hence, -3.5 = c

therefore, using exact numbers equation of the line is y = 7/9x -3.5.

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Limits of the functions shown in the graph are limx +f(x) = 0 and limx -f(x) = 0. The link between a group of inputs, each of which has a related output, is known as a function.

The study of mathematics covers a variety of topics, including numbers, formulas and related structures, forms and the environments in which they exist, quantities and their variations, and the environments in which they exist.  An easy way to think of a function is as a relationship between inputs and outputs, where each input leads to a single, distinct result. Each function has a respective domain and a codomain, or scope. Functions are typically represented by the letter f. (x). input is x. The accessible functionalities fall into four categories. based on the following elements: on functions, one-to-one functions, many-to-one functions, and within functions.

given

We first take into account how f(x) behaves as x increases unboundedly for the function in the graph below. As x can always increase because the function has no limit, it can never be zero. However, the function's behavior when x rises.

Similar to how x decreases without bound or how we move leftward on the graph, f(x) also seems to be approaching zero.

So in this case we can write:

limx → +∞f(x) = 0

limx → - ∞f(x) = 0

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Answer:

96

Step-by-step explanation:

24 divided by 1/4 is 96

you turn 24 into a fraction by putting a one under is and then you keep it change it flip it

24/1 Divided by 1/4

24/1 times 4/1

24 times 4= 96

1 times 1= 1

96/1=96

Answer:

18

Step-by-step explanation:

36-10-2-6

26-8

18

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{6^2 - 2(5 + 1 + 3)}\\\mathsf{= 6^2 - 2(5) - 2(1) - 2(3)}\\\mathsf{= 6^2 - 10 -2(1) - -2(3)}}\\\mathsf{= 6\times 6 - 10 - 2(1) - 2(3)}\\\mathsf{= 36 - 10 - 2(1) - 2(3)}\\\mathsf{= 26 - 2(1) - 2(3)}\\\mathsf{= 26 - 2 - 2(3)}\\\mathsf{= 24 - 2(3)}\\\mathsf{= 18}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{18}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer: 12

Step-by-step explanation: Because of the ratio we know that half of the screens will be showing action films. Half of 24 is 12, so 12 screens will be playing action.

Answer: It is not possible for me to draw a slope triangle or dilate it along the graph without more information about Sara's monthly savings.

To determine whether the amount Sara saves each month is constant, you can choose any two points on the graph and use them to calculate the slope of the line connecting them. If the slope is constant for all pairs of points, then the amount Sara saves each month is constant. If the slope is not constant, then the amount Sara saves each month is not constant.

To calculate the slope of the line connecting two points, you can use the following formula:

slope = (y2 - y1)/(x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

You can then use the slope triangle to visualize the slope of the line connecting the two points. If you dilate the slope triangle along the graph and the slope remains constant, then the amount Sara saves each month is also constant.

Step-by-step explanation:

Answer: slope=-5 and y-intercept=1

Step-by-step explanation:

The equation given is in slope-intercept form. Slope-intercept for is y=mx+b, where m is slope and b is y-intercept.

This gives m=-5 and b=1.

Answer: y = 85 - 6x

Step-by-step explanation:

Number of napkins remaining: y

Number of tables set: x

Akira starts out with 85 napkins. So, every time she sets a table, she is losing 6 napkins. The steady rate of napkins lost can be written with the following expression, as she is losing 6 napkins per table.

[tex]-6x[/tex]

These napkins are being removed from the total of 85 napkins:

[tex]85 - 6x[/tex]

The above equation also expresses the number of napkins remaining. Writing it as a proper equation:

[tex]y = 85 - 6x[/tex]

The final answer is: y = 85 - 6x

Answer:

Step-by-step explanation:

You want to solve graphically the system of inequalities expressing that Rashaad has no less than a total of 18 dimes (x) and nickels (y) with a combined value of at most $1.50, of which at least 4 are dimes.

An inequality can be written for each of the constraints:

  x + y ≥ 18 . . . . . . . no less than 18 coins

  0.10x +0.05y ≤ 1.50 . . . . . . at most $1.50 in value

  x ≥ 4 . . . . . . . . . . at least 4 dimes

A graph of these inequalities is attached. The marked points are the vertices of the triangular solution space. Each is a possible solution, along with all of the grid points inside the triangle.

One possible solution is 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50.

Using graph to solve the system of linear inequality the most likely solutions will be 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50

Systems of linear inequalities are equations with two or more linear inequalities that contain two or more variables. These equations can be used to represent real-world problems and to find the solutions of such problems. The solutions of a system of linear inequalities are all the points that are common to all of the linear inequalities in the system.

In this problem, we have to define our variables and then solve this using graphical method. The point of intersection between the two lines lies the solution to the linear inequality.

Let;

x + y ≥ 18

0.1x + 0.05y ≤ 1.50

x ≥4

Using a graphing calculator to solve this,

The possible solutions is 4 dimes and 22 nickels, for a total of 26 coins with a value of $1.50.

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Answer:

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

Slope-intercept form:

Point-slope form:

Use the point-slope form to find the equation and then convert it to slope-intercept form:

A line that crosses the origin is symbolized by the equation y=mx. The line going through the origin equation is also y=2x.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

given

The line going through the origin equation is also y=2x.

A line that crosses the origin is symbolized by the equation y=mx.

Also, y=2x satisfies the point (0,0)

A line that crosses the origin is symbolized by the equation y=mx. The line going through the origin equation is also y=2x.

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Answer: 18.1666666667

Step-by-step explanation:

The complete statement is f(2) = 8+5√7

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here f(x)=2x²+5√7

Thus f(1) = 2×4+5√7

              = 8+5√7

Hence, The complete statement is f(2) = 8+5√7

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The Correct answer while simplifying the given algebraic expression is: 4a²+1/2a+7

The concept of algebraic expressions is the use of letters or alphabets to represent numbers without providing their precise values. We learned how to express an unknown value using letters like x, y, and z in the fundamentals of algebra. Here, we refer to these letters as variables. Variables and constants can both be used in an algebraic expression. A coefficient is any value that is added before a variable and then multiplied by it.

Method to simplify any algebraic Expressions are :

Given:

=3a²+1/4a+3+a²+4+1/4a

=(3a²+a²)+(1/4a+1/4a)+(3+4)

=4a²+1/2a+7

So the Answer is

=4a²+1/2a+7

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Answer:

There are 5 people working and each person works 8 hours per day, so there are a total of 58 = <<58=40>>40 hours of work per day.

Over the course of the week, the total number of hours worked is 405 = <<405=200>>200 hours.

The total number of toys assembled is 400 and the total number of hours worked is 200, so the average number of toys assembled per hour per person is 400/200 = <<400/200=2>>2 toys per hour per person.      Answer:{2}.

Step-by-step explanation:

The total surface area of the cube will be 37.5 cm²

Here the edge of the cube is given

Edge = 2.5 cm

We have to find out the total surface area of the cube

Total surface area of cube = 6a², where a is the edge of the cube

                                            = 6 × 2.5 × 2.5

                                            = 37.5 cm²

Hence, the total surface area of the cube will be 37.5 cm²

The complete question is,
Find the surface area of a cube of Edge 2.5 CM​

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Answer:

4^5 = 1024

4×4×4×4×4 = 1024

Step-by-step explanation:

An exponential expression is going to have an exponent representing the repeated multiplication. 4 times itself 5 times over is 4^5.

A product of factors is going to show the multiplication written out sort of in a long format:

4 × 4 × 4 × 4 × 4

4^5 = 1024

4×4×4×4×4 = 1024

Answer:

6

Step-by-step explanation:

Let the number of hours be [tex]x[/tex].

[tex]125+7x<110+10x \\ \\ 15+7x<10x \\ \\ 15<3x \\ \\ x>5[/tex]

So, the minimum is 6 hours.

The lines with a slope larger than f(x) are:

option 4) y = (25/3)*x - 1/2

option 5) (4/5)*y - 16x = -1/2

A general linear equation can be written as:

y = a*x + b

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

First, you can see that the line crosses the y-axis at y = -4, so the line is something like:

y = a*x - 4

And we can see that it crosses the x-axis at x = 2, then we can write the equation:

0 = a*2 - 4

4 = a*2

4/2 = a

2 = a

So the linear equation on the graph is:

y = 2*x - 4

The slope is 2, the linear equations with a slope larger than that are:

option 4) y = (25/3)*x - 1/2

option 5) (4/5)*y - 16x = -1/2

Which can be rewritten as:

y = (5/4)*16x - (5/4)*(1/2)

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The equation to represent the cost of renting the car, given the cost per week and the cost per mile, is y = 42 + 0.25x.

The total cost of renting the car at any given point, would be:

= Cost to rent per week + ( Cost per mile x Number of miles driven)

If we assume the number of miles driven is denoted by x, then the equation becomes :
= 42 + 0. 25 x

If we further take y to be the total cost, the equation then becomes :

y = 42 + 0. 25 x

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Answer:

0.16 or 0.2 if rounded

Step-by-step explanation:

4 gallons divided by 25 chairs equals 0.16 gallons for each chair

hope this helps <3

The number of guests, g, coming for dinner is not 8, is g ≠ 8.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

Given:

The expression,

the number of guests, g, coming for dinner is not 8.

That means,

Let the number is g.

According to the question,

the number is not equals to 8.

That means,

the expression in the numerator form,

g ≠ 8.

Therefore, the term in the mathematical form g ≠ 8.

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The angle that the golfer has between the spectator and the hole is 60°. Therefore, option A is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

Given that, in a tournament, a professional golfer knows that she is 200 yards from the hole. A spectator is watching her play and is 140 yards away from the golfer.

Let the angle that the golfer has between the spectator and the hole be x

Here, sin 120°/200 =sin x/140

0.8660/200 =sin x/140

0.00433 = sin x/140

sin x=0.866

x=60°

Therefore, option A is the correct answer.

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Hi hi! The answer would be 22.7°, I took the test a while ago.

Answer: Gloria will need 14 cups of flour

Step-by-step explanation: 2 1/3 x 6 = 14

As a result, $1600 is the answer to the problem equation comes out to be stated problem, which is the estimated rent.

A mathematical statement known as an equation is created by joining two expressions using the equivalent sign. For instance, 2x - 5 = 15 is an equation. We can find that the variable x has a value of 5 by resolving this equation.

Here,

In New York City, a one-bedroom apartment will cost $1600 in 2020.

Y = mx + c is frequently used as the formula for a straight line graph, where;

gradient = m

The vertical intercept is given by c.

With this knowledge, it is evident from the graph that y = 40x + 800 is the best line of fit for the data presented.

This indicates how much a one-bedroom apartment in New York City will cost in 2020, or 20 years after the year 2000.

y = 40(20) + 800 = $1600

As a result, $1600 is the answer to the problem equation comes out to be stated problem, which is the estimated rent.

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25 coins represent 25 percent of Jocelyn's collection.

A percentage is a quantity or ratio that, in mathematics, represents a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The symbol "%" is frequently written after the number to indicate percentages.

given, Jocelyn has a collection of 100 coins.

100% of her collection represents = 100 coins

1 %  of her collection represents = 100/100 coins

1%  of her collection represents = 1 coin

thus,

25%  of her collection represents = 1*25 coins

25%  of her collection represents = 25 coins

therefore, 25 percent of the collection of Jocelyn represents 25 coins.

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The vertex of the parabola -x² - 2x + 10 = 0 occurs at (-1,11), It is a maximum value.

Given the equation of the parabola;

-x² - 2x + 10 = 0

First, the maximum of a quadratic function occurs at;

x = -b/a, if a is negative, the maximum value of the function is f( -b/2a)

f_max(x) = ax² + bx + c occurs at;

x = -b/2a

Now, find the value of x = -b/2a

Plug in a = -1 and b = -2

x = -( -2/2(-1) )

x = -( -2/-2) )

x = -( 1 )

x = -1

Hence;

f(x) = -x² - 2x + 10

f( -1 ) = -( -1 )² - 2( -1 ) + 10

f( -1 ) = -1 + 2 + 10

f( -1 ) = -1 + 12

f( -1 ) = 11

Therefore, maximum occurs at (-1,11).

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The test statistic from the factory population is 2.12. The p value is given as .017003.

We have the following values to solve the problem with

n = 58

sample mean x = 12.07

standard deviation = 0.25 meters

u = length = 12

The formula is given by

[tex]z= \frac{x-u}{sd/\sqrt{n} }[/tex]

when we insert the values we would have:

[tex]z= \frac{12.07-12}{0.25/\sqrt{58} }[/tex]

z = 0.07 / 0.033

z = 2.12

we have to find the p value when z = 2.12

The p value is 0.017003 using a statistical calculator

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-560° in radian is -28π/9 radian and the positive and negative coterminals are 8π/9 and -10π/9 respectively.

170° in radian is  17π/18 radian and the positive and negative coterminals are 53π/18 and -19π/18 respectively

An angle can be converted from degree to radian by multiplying it by π/180.

1. -560°

-560° × π/180 = -28π/9 radian

2. 170°

170° × π/180 = 17π/18 radian

In general, if θ is any angle in radian, then θ + n(2π) is coterminal angle with θ, for all nonzero integer n.

coterminal of -28π/9:

positive: -28π/9 =  -28π/9 + 2(2π) = 8π/9

negative: -28π/9 =  -28π/9 + 2π = -10π/9

coterminal of 17π/18:

positive: 17π/18 =  17π/18 + 2π = 53π/18

negative: 17π/18 =  17π/18 - 2π = -19π/18

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