a recipe for fizzy grape juice, the ratio of cups of sparkling water to cups of grape
ice concentrate is 3 to 1.
a. Find two more ratios of cups of sparkling water to cups of juice concentrate that
would make a mixture that tastes the same as this recipe.
b. Describe another mixture of sparkling water and grape juice that would taste
different than this recipe.

Lesson 3 Practice Problem

The revolution per minute done by the wheel of a bicycle is 16.9 rev/min.

Velocity is the rate at which a moving object's direction changes as perceived from a certain vantage point and measured by a particular unit of time. Kinematics, the area of special relativity that investigates how bodies move, starts with the fundamental idea of speed.

In order to be explained, the scientific vector quantity known as velocity needs to have both a magnitude and a direction.

As per the given information in the question,

Diameter of wheel = 20 inch

Radius, r = 10 inch

The velocity of the bicycle, v = 13 mi/h.

Revolution, R = v²/r

R = 13²/10

R = 16.9 rev/min

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The trigonometric ratios for angle A are measured below.

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a right angled triangle as shown in the image attached.

The six trigonometric ratios are -

sin (A) = 10/√116

cos (A) = 4/√116

tan (A) = 10/4

cosec (A) = √116/10

sec (A) = √116/4

cot (A) = 4/10

Therefore, the trigonometric ratios for angle A are measured above.

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The value of f after solving the expression, 2-f/4 = f-3f/4+3, is -2.

According to the question,

We have the following expression:

2-f/4 = f-3f/4+3

We know that to find the value of f we will have to move the terms with the same variable on one side. Now, moving f and 3f/4 from the right hand side to the left hand side will result in the change of their signs.

3f/4-f/4-f +2 = 3

Moving 2 from the left hand side to the right hand side:

3f/4-f/4-f = 3-2

Taking the least common factor as 4:

(3f-f-4f)/4 = 1

(-2f)/4 = 1

Using the cross multiplication method:

-2f = 4

f = -4/2

f = -2

Hence, the value of f for the given expression is -2.

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Answer:

B

Step-by-step explanation:

The  simple or compound interest will be

a. $120

b. $12,000

c. $15,000

d. $18,000

e. Option B is better as it is giving us more interest.

Formula of total simple interest is

SI = (P * R * T) /100  where

P = initial principal balance

r = annual interest rate

t = time (in years)

Formula of compound interest is

C.I.= P × [tex](1 + r/n)^{nt}[/tex] - P  where

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

a. By applying the formula given above we will get

SI = (3000 * 0.4 * 10) / 100

SI = $120

b. Formula to find total value is P * R * T. By applying this we will get

I = 3000 * 0.4 * 10

I = $12,000

c.  By putting values in the formula we will get

CI = 3000 * [tex](1 + 0.2)^{10}[/tex] - 3000

CI = 18000 - 3000

CI = $15,000

d. formula to find total compound value is P * [tex](1 + r/n)^{nt}[/tex]. By applying this in the formula we get

A = 3000 [tex]( 1 + 0.2 )^{10}[/tex]

A = $18,000

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The size of the moose population, 65 + (48-14)=99.

acc to our question-

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As per the system of linear equations concept, the solution of x is -1.282

Linear equations:

Linear equation is referred as the algebraic equation in which each term has an exponent of 1 and when graphed, the result is always a straight line.

Given,

Here we have the equations -4x - 1 = 5ˣ + 4

Now, we need to find the value of x by using the graph.

In order to plot the graph for the given linear equation,

First, we have to split the equation into two,

Like the following:

y = -4x - 1

y = 5ˣ + 4

Now, we plot the graph of both equations

Then we get the graph like the following.

Where the red line represents the equation y = -4x - 1 and the green line represents the equation y = 5ˣ + 4.

While we looking into the graph, we have identified the solution is,

x = -1.282

Therefore, the solution of x is -1.282

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After simplifying an equation the value of x is x = 3.

What is solving an equation?

Unifying Principle for Equation Solving

By deleting parenthesis and grouping like terms, each side of the equation can be made simpler.

The variable term on one side of the equation can be separated using addition or subtraction.

To find the variable, use multiplication or division.

Consider, the given equation

     5(2x - 4) = 10

      10x - 20 = 10                                  Removing parenthesis

10x -20 + 20 = 10 + 20                         Adding 20 on both sides

              10x = 30                                 Simplifying

                  x = 3                                    Dividing both sides by 10

Hence, the value of x is, x = 3.

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The intersection of A and I, A ∩ I = {-2, -1, 1}

The intersection of two sets A and B is the set of all common elements, it is denoted with A ∩ B.

Whereas the union of those two sets is the set of all elements that are either in A or in B, it is denoted by A ∪ B.

The given sets are,

A = {-2, -1, 0, 1, 7}

And I = {-2, -1, 1, 2, 8}

Intersection of A and I,

A ∩ I = {-2, -1, 1}

The intersection of A and I is {-2, -1, 1}.

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The coordinate of point B is such that M (1,-8) is the midpoint of A(-6,-12) and B will be (5,-2).

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).

The coordinate of midpoint between two points  (x₁, y₁) and (x₂, y₂) is given by,

( (x₁ + x₂)/2 ,(y₁+ y₂)/2)

Given that, M is the midpoint of A and B.

Let's say the coordinate of point B is B(x,y).

Then,

1 = (-3 + x)/2

x = 2 + 3 = 5

And,

(-6 + y)/2 = -4

y = -8 + 6 = -2

Hence "The coordinate of point B is such that M (1,-8) is the midpoint of A(-6,-12) and B will be (5,-2)".

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The given polynomial solved as same as RHS is x^3/3(x^2- 1/x^2)

Polynomial is defined as the sum of variable terms in the form of k×x^n, where k is constant and x variable and n is an integer.

we have given a polynomial,

(x-1/x)(x^4/3+x^2/3) = (x^3/3)(x²-1/x²)

Take LHS

⇒  (x-1/x)(x^4/3+x^2/3)

⇒  (x^2-1/x)×(x^4 + x^2/3)

⇒  (x^2-1/x) x^2(x^2+1/3)

⇒  x^2/3x (x^2-1)(x^2+1)

⇒​x^2/3x(x^4-1)                                  ∴(a^2-b^2 = (a+b)(a-b))

multiply numerator and denominator by x

⇒x^3/3 (x^4-1/x^2)

⇒x^3/3(x^2- 1/x^2) = RHS

Hence, given problem has solved.

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The composition f(4) has a value of -27

The definition of the functions is given as

f(x) = -2x^2 + 5

Rewrite the above function properly

So, we have the following representation

f(x) = -2x² + 5

To find the function f(4), we set the value of x in the equation f(x) = -2x² + 5

This is represented by

Calculate f(x), when x = 4

Substitute 4 for x in the equation f(x) = -2x² + 5

So, we have the following equation

f(4) = -2(4)² + 5

Evaluate the exponents

This gives

f(4) = -2 * 16 + 5

Evaluate the products

This gives

f(4) = -32 + 5

Evaluate the sum

f(4) = -27

Hence, the value of the function is -27

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Answer:

A square is an sqaure.

Step-by-step explanation:

circle is a circle. :) happy to help

Equation of a line that has a slope of 4 and passes through point (1, 6) is  y = 4x + 2 . Hence, C is the correct option.

To represent the standard form of equation of a line are:

Slope-intercept form:

y = mx + c

Here m represent the slope of the given line and c is the y intercept.

Intercept form:

x/a + y/b = 1

Generic way of representing the straight line, i.e. Ax+By+C = 0

x/(-C/A) + y/(-C/B) = 1

Hence a = -C / A and b = – C / B

Normal form:

The equation of the line whose length of the normal from the origin is p and the angle made by the normal with the positive x-axis is given by α is given by:

x cos α+y sin α = p

General equation of the line is represented in the form:-

y - y1 = m (x-x1) ,

Where x1, y1 represents a point on the line whereas,

m represents the slope of the line.

    = (1 , 6) point on the line

    = Slope (m) = 4

Putting all the required values in general equation:-

y - 6 = 4 ( x-1 )

Hence, we get y = 4x + 2

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Answer:

y=4x+1

Step-by-step explanation:

Our slope is 4/1 or 4, so we know 4x is our slope. Then our y intercept is at (0,1), so we know our b=1. So we know our equation is y=4x+1.

-Hope this helped.

The Linear equation used is x -y = 1; to find the age of Isabelle's age.

What is Linear Equation?

An equation is said to be linear if the maximum power of the variable is consistent Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present. A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason.

Let the age of Ben be x;

Let the age of Amara be y;

According to the question:

It is given that:

Ben is one year younger than Amara. That means we have to form a linear equation such that Amara is one year older than Ben.

So,

We have assumed the Age of Ben is x;

we have assumed the Age of Amara is y;

So, According to the question,

Framing the linear equation,

x -1 =y;

⇒x -y = 1;

Hence, We can find the age of Isabelle using the linear equation: x -y = 1;

where x is ben's age;

where y is Amara's age.

Therefore, The Linear equation used is x -y = 1; to find the age of Isabelle's age.

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The expressions are:

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

Given:

15 x squared minus 18 end quantity over 6.

= 15x² - 18 / 6

= 3(5x² - 6)/ 6

= (5x² - 6)/ 2

and, 5 x squared minus 18 end quantity over 2

= 5x² - 18/2

and, 5 x squared minus 6 end quantity over 2

= 5x² -6 /2

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The number of people that are seated in the buses is 425

From the information, there are 5 buses and there are 85 people in each. Therefore, the total number of people will be:

= 85 × 5.

= 425

Since 3/5 of those people are seated, the number of people seated will be:

= Fraction of those seated × Total number of people.

= 3/5 × 425

= 255

Therefore, there are 255 people.

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Answer:

21 + 3x

Step-by-step explanation:

Its simple really. Just expanding the brackets by bringing the 3 inside the bracket :

3 × 7 = 21

3 × x = 3x

So our answer will 21 + 3x

Hope this helped and have a good day

The constant of proportionality in the equation y = 11x is  11 , the correct option is (a) .

in the question ,

it is given that

the equation is y = 11x

also given that the equation is proportional relationship ,

we need to find constant of proportionality .

we know that the proportional equation is written as y = k*x

where k is the constant of proportionality , on comparing it with the equation y = 11x

, we get k = 11 ,

So , the constant of proportionality is = 11 .

Therefore , The constant of proportionality in the equation y = 11x is  11 .

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Answer:

  3

Step-by-step explanation:

You want the value of f(2) for the graphed function.

The value of the function f(a) is the y-coordinate of the point that has 'a' as its x-coordinate.

Finding the function value requires you locate x=a on the horizontal axis. Where the graph crosses that vertical line, the y-coordinate is the function value.

Here, the vertical line x=2 meets the function graph at the dot with coordinates (2, 3). The y-value there is 3, so ...

  f(2) = 3

Answer:  [D]:  " 3 " ;  [that is; f(2) = 3 ].
____
We are asked to:

Evaluate the given function for f(2) ; within the given image.

By examination of the graph, we can verify that the graph is, in fact, a function—by using the vertical line test.
  We find that no value for x shares more than one y-value; which means that the graph is a function.

____

Note that for a function:   f(x) = y .  

So;  To find f(2) :
____
Note:  f(2)  =  the "[ y - coordinate/corresponding value for y ]" ;  

                       ⇒  when " x = 2 ".

So; looking at the graph:   We see that when  " x = 2 " ;  →  " y = 3 " .
        → {Examine the co-ordinate/point:  (2, 3) —that is part of the graph.}

So;  f(2) = 3 ;  which is Answer choice:  [D]:  " 3 ."
______

Hope this is helpful to you.  Best wishes!
______

Step-by-step explanation:

The base of the separated triangle is (x+5) - (2x - 4) = x + 5 - 2x + 4 = 9 - x

So, area of the separated triangle would be:-

1/2 * b* h

or, 1/2 * (9-x)* (x+3)

or, (6x + 27 - x² )/2

Total area of trapezium = (6x + 27 - x²)/2 + (2x-4)(x + 3)

or, 60 = (6x + 27 - x²)/2 + 2x² + 2x - 12

or, 60 = (6x + 27 - x² + 4x² + 4x - 24)/2

or, 120 = 10x + 3x² + 3

or, 0 = 3x² + 10x + 3 - 120

hence, 3x² + 10x - 117 = 0 (proved)

Again,

Use quadratic formula to figure out value of x.

(It woun't be a natural number)

Write the value of x with only one digit after it's decimal.

wa can rewrite it as 12/1 which is A

The equation of the parabola whose focus is at (3, 0) and directrix at x = - 3 is y² = 12 · x. (Correct choice: D)

In this problem we need to determine the equation of a parabola based on the information of the focus and the directrix. The vertex form of the parabola is described below:

4 · p · (x - h) = (y - k)²

Where p is the distance from the vertex to the focus. The coordinates of the vertex is the midpoint of the line segment of the least distance between the directrix and the focus.

First, determine the coordinates of the vertex:

(h, k) = 0.5 · (- 3, 0) + 0.5 · (3, 0)

(h, k) = (0, 0)

Second, calculate the distance from the vertex to the focus:

p = 3 - 0

p = 3

Third, write the vertex form of the parabola:

y² = 12 · x

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Answer:

$22,106.28

Step-by-step explanation:

[tex]CI=P(1+(\frac{r}{12}) )^{12t}[/tex], where [tex]P[/tex] is the principal, [tex]r[/tex] is the interest rate in decimal form, and [tex]t[/tex] is the time in years.

[tex]CI=\$11000.00(1+(\frac{0.07}{12}) )^{12(10)}[/tex]

[tex]CI=\$22106.28[/tex]

Answer:

B. -6.08 x 10^-8

Answer:d

Step-by-step explanation:d

The addition property used by Bill in finding the actual December temperature is the commutative property of addition.

According to the question,

We have the following information:

Bill claims that he found the actual December temperature by adding either -5 + 3 or 3 +-5.

We know that are five properties of addition: closure property, commutative property, associative property, additive identity property of addition and additive inverse property.

The commutative property of addition means that if two numbers are added and their order is inversed then  the result of addition will always be the same.

For example, we get -2 by adding -5+3 and 3+(-5). The change in order of digits does not affect the final result.

Hence, the addition property used by Bill in finding the actual December temperature is the commutative property of addition.

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Answer:

  XY is tangent to circle Z

Step-by-step explanation:

You want to know if segment XY, measuring 3.6 units, is tangent to circle Z at point X. Segment YZ has length 1.8 units outside the circle, which has radius 2.7 units.

If the triangle XYZ is a right triangle, then we have ...

  XY² +XZ² = YZ²

  3.6² +2.7² = (1.8 +2.7)²

  12.96 +7.29 = 20.25 . . . . . true

Segment XY is a tangent.

If segment YZ is extended across the circle, the lengths of the segments from Y to the circle intersection points are 1.8 and (1.8 +2·2.7) = 7.2. The relation between the secant and the "tangent" will be ...

  3.6² = (1.8)(7.2) . . . . . true

This means XY is a tangent.