Harley has 6 pints of lemonade. Rosie has 3 times as many pints of
lemonade as Harley.
a) How many pints of lemonade does Rosie have?
b) How many more pints of lemonade does Rosie have than Harley?
Give your answers as whole numbers or as fractions in their simplest form.

The scale factor of the dilation is the ratio of the lengths of the corresponding sides of the two triangles. Since triangle ABC and triangle A'B'C' both have side lengths of AB, BC, and CA, the scale factor is 1.

1. Calculate the length of the sides of triangle ABC:

AB = length of side AB of triangle ABC

BC = length of side BC of triangle ABC

CA = length of side CA of triangle ABC

2. Calculate the length of the sides of triangle A'B'C':

A'B' = length of side A'B' of triangle A'B'C'

B'C' = length of side B'C' of triangle A'B'C'

C'A' = length of side C'A' of triangle A'B'C'

3. Calculate the scale factor of the dilation:

Scale factor = (AB/A'B') x (BC/B'C') x (CA/C'A')

= (length of side AB of triangle ABC / length of side A'B' of triangle A'B'C')

x (length of side BC of triangle ABC / length of side B'C' of triangle A'B'C')

x (length of side CA of triangle ABC / length of side C'A' of triangle A'B'C')

= 1 x 1 x 1

= 1

Therefore, the scale factor of the dilation is 1.

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T(60) > T(10) + T(30) means that the number of tenants living on 60th floor is greater than the sum of tenants that are living in 10th and 30th floor.

n = number of floor of the Princess Tower (Floor Number)

T(n) is a function of n (floor number) which tells how many tenants are beings living on the nth floor

Tenant means a person occupying a rented land or property (A resident for simple understanding)

Therefore:

The statement:  T(60) > T(10) + T(30)

Means that: The number of tenants living on 60th floor is greater than the sum of tenants living on 10th and 30th floor.

Just for an example If we have T(60) = 30, T(10) = 10, T(30) = 5

Then T(60) > T(10) + T(30) means that 30 > 10 + 5 which becomes 30 > 15

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A triangle with given lengths 4cm , 5cm , and 6cm is scalene and acute angled triangle.

As given in the question,

In the given triangle ,

Lengths of the sides of a triangle is given by :

4cm , 5cm , and 6cm.

All the sides are of different measure , it is a scalene triangle.

Apply cosine rule to find the measure of largest angle:

c = 6cm is the longest side opposite to largest angle.

c² = a² + b²- 2abcosα

⇒ 6² = 4² + 5² - 2(4)(5)cosα

⇒cosα = ( 16 + 25 - 36 ) / 40

⇒ cosα = 5/40

⇒ α = cos⁻¹( 1/8)

⇒ α = 82.8° < 90°

It is an acute angled triangle.

Therefore, for the given lengths of the triangle it is a scalene and acute angled triangle.

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The radius of the circle is 48 feet.

Circle:

The round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center)

The arc length of a circle is given by the formula arc length = (angle/360) * 2 * pi * radius.

In this case, the angle is 75 degrees, and the arc length is 10* pi feet.

So, we can set up the equation: (75/360) * 2 * pi * r = 10 * pi

Solving this equation for the radius, we get: r = (10pi) / ( (75/360) * 2 * pi) = (10360) / 75 = 48 feet. So, the radius of the circle is 48 feet.

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Correct option is A, the cost of the meal plan is non-linear.

The simplest approach to tell if a function is linear is to look at its graph. A linear function produces a straight line on a graph. A nonlinear function is not straight and is curved in some way. A linear function results in a straight line on a graph. As a result, non-linear functions can be of any kind. Although determining a function's linearity from its input/output table or equation is the simplest method, it is also possible to do so.

Based on the given conditions, formulate:

The definition of linear function

8-10 meals = (135-123) = (10-8) =10/2=5

10-12 meals: (155-135) = (12-10)

=20/2

= 10

12-21 meals: (220-155) = (21-12)

= 65/9

=7 2/9

5 < 7 2/9 < 10

So the cost of the meal plan is non-linear.

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Complete question -

The graph of the proportional relation is the one in the second option.

"a graph of a line that passes through the points 0 comma 0 and 4 comma negative 1"

A general linear equation can be written as:

y = a*x +b

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

Particularly, if the y-intercept is 0, then we have:

y = a*x

We have a proportional relationship.

Notice that when x = 0 we have:

y = a*0

y = 0

So the proportional relationships always pass through the point (0, 0).

Then the correct option is the second one:

"a graph of a line that passes through the points 0 comma 0 and 4 comma negative 1"

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Answer:0.5

Step-by-step explanation:

According to the given measurement, the total amount of intake is 621.0435 ml

Here we have given the following measurements they are listed as follows:

=> 1/2 cup of orange juice,

=> 2/3 glass of milk, full cup of lemonade,

=> full glass of water,

=> 1 popsicle (3 ounces) and

=> 4 ounces ice chips.

Here we also know that

1 cup = 8 oz

1 glass = 6 oz

And as per the Si measurements,

1 oz = 29.5735 ml.

To order to calculate the total amount of intake we have to sum all the given measurements, then we get,

=> 1/2(8) + 2/3(6) + 6 + 3 + 4

When we simplify this one then we get,

=> 4 + 4 + 6 + 3 + 4 = 21

Now, we have to convert ounce into milliliter, for that we have multiply 29.5735 with the total measurement, then we get,

=> 21 x 29.5735 = 621.0435 ml

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If a forest covers 51,000 acres. A survey finds that 0.4​% of the forest is​ old-growth trees. The number of  acres of​ old-growth trees that are​ there is: 204 acres.

Using this formula to find the number of acres that are there.

Number of acres = Number of forest covers acres × Forest old growth tree percentage

Where:

Number of forest covers acres = 51,000 acres

Forest old growth tree percentage = 0.4% or 0.004

Let plug in the formula

Number of acres = 51,000 acres × 0.004

Number of acres = 204 acres

Therefore we can conclude that the number of acres  is 204 acres.

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You need to deposit $55,555 each year until your retirement to achieve your retirement goal.

To find the amount you need to deposit each year, you need to calculate the present value of your future withdrawals, considering the time value of money and taking into account the interest rate.

One way to do this is to use the formula for present value:

PV = FV/(1 + r)^t

where PV is the present value, FV is the future value, r is the interest rate, and t is the number of years until the future value.

In this case, FV is $50000 per year for 30 years, so the total future value is $50000 × 30 = $1,500,000. And t is 15 years, so the present value is:

PV = $1,500,000/(1 + 0.04)^15 = $1,500,000/1.8 = $833,333

So, you need to deposit $833,333/15 = $55,555 each year until you retire to achieve your goal.

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The probability that none of the five students chosen at random are mechanical engineering majors is 0.0111 or about 1.11%.

The probability that none of the five students chosen at random are mechanical engineering majors is

=(51/100) * (50/99) * (48/98) * (47/97) * (46/96)

= 0.0111

This means that the probability is about 1.11%

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

The probability means that the chances of an event to occur or do not occur and it lies between the range of 0 and 1.

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De acuerdo con la información del enunciado, el resultado de esta operación matemática (división) es 0,13

Esta división da como resultado un número decimal de varios valores por lo que podemos repetir este procedimiento tantas veces sea necesario dependiendo de la exactitud de nuestras necesidades.

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The equation of the curve in the XY-plane that passes through (0,3) and whose tangent line at a point (x,y) has slope 2x/y^2 is y^2 = 2x*F(x,y) or y^2 = 2x*F(x,y) + C where C is constant.

The equation of a curve in the xy-plane is given by F(x,y) = 0. To find such a curve that passes through the point (0,3) and whose tangent line at a point (x,y) has a slope of 2x/y^2, we can use the method of implicit differentiation.

First, we can find the equation of the tangent line at a point (x,y) on the curve by computing the derivative of F(x,y) with respect to x and setting it equal to 2x/y^2. This gives us:

F_x(x,y) = 2x/y^2

Next, we can use the fact that the curve passes through the point (0,3) to set up the following equation:

F(0,3) = 0

Solving for F(x,y) in terms of x and y and substituting in the equation for F_x(x,y) gives the implicit equation of the curve is

y^2 = 2x*F(x,y) or y^2 = 2x*F(x,y) + C where C is constant

This is the equation of a curve in the XY-plane that passes through the point (0,3) and whose tangent line at a point (x,y) has a slope of 2x/y^2.

Therefore, The equation of the curve in the XY-plane that passes through (0,3) and whose tangent line at a point (x,y) has slope 2x/y^2 is y^2 = 2x*F(x,y) or y^2 = 2x*F(x,y) + C where C is constant.

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Answer:

To solve the simultaneous equations by substitution, we can first solve one equation for one of the variables, and then substitute that expression into the other equation. Here is one way to solve the given equation:

2x - 3y = 8

We can solve for x by adding 3y to both sides:

2x = 3y + 8

We can divide both sides by 2 to get x by itself:

x = (3y + 8)/2

Now we can substitute this expression for x into the other equation:

2((3y + 8)/2) - 3y = 8

Simplifying and solving for y:

3y + 8 - 3y = 8

8 = 8

So the solution for y is any value.

Now we can substitute the value of y into the equation x = (3y + 8)/2 and we'll get the value of x.

x = (3 * y + 8) / 2

For example if we substitute y = 2

x = (3 * 2 + 8) / 2 = 14/2 = 7

So the solution for the simultaneous equations is x = 7, y = 2

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To graph an absolute value function, choose several values of x and find some ordered pairs. Plot the points on a coordinate plane and connect them.

Absolute value equations are the equations in which the absolute value operator is used.

To graph such an equation, we must first get rid of the absolute value equation by dividing the equation into different parts. Then graph the equations of these parts separately.

If the value of the expression or the number inside the operator is negative, then the result is the negative of the expression or the number.

Suppose we have an expression: |x+1|

If (x+1) is positive or equal to 0, then  |x+1| =x+1

However, if (x+1) is negative, then |x+1| =-(x+1)=-x-1.

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Answer:

[tex]df = \sqrt{ {29}^{2} - {20}^{2} } = 21 \\ \sin(d) = \frac{20}{29} \\ \cos(d) = \frac{21}{29} \\ \tan(d) = \frac{20}{21} \\ \sin(e) = \frac{21}{29} \\ \cos(e) = \frac{20}{29} \\ \tan(e) = \frac{21}{20} [/tex]

Answer:

Step-by-step explanation:

First, use the pythagorean theorem to complete the vales of each sides of the triangle. Then, use the respective trigonometric formulas and inverse the answer to compute the degree of every corners.

7019 gallons of water will be in the pool.

Initial volume of water = 8000 gal

Daily reduction = 1.3%

Time = 10 days

Required equation:

=8000*(1- 0.013)^10

=8000*0.987^10

=7018.7781 ≈ 7019 rounded to the nearest gallon.

An expression that uses constant algebraic numbers, variables, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

In contrast, since they are not derived from integer constants and algebraic operations, transcendental numbers like and e are not algebraic. The definition of e necessitates an infinite number of algebraic operations, while the construction of is typically done as a geometric relationship.

Any expression that can be converted into a rational fraction using the properties of the arithmetic operations is said to be rational (commutative properties and associative properties of addition and multiplication, distributive property and rules for the operations on the fractions).

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It can be concluded that -

Given are the questions as shown in the image.

[1] -

Greater is the value of amount of tablespoon of sugar per oz of tea, sweetest it will be.

For table {1}, we can write -

m₁ = (12/18) = 2/3

For table {2}, we can write -

m₂ = 6/16 = 3/8

m₁ = 2/3 = (2 x 8)/(3 x 8) = 16/24

m₂ = 3/8 = (3 x 3)/(8 x 3) = 9/24

m₁ > m₂

Version A of iced tea will be sweetest.

[2] -

Greater is the value of amount of strawberry puree per unit of the total amount of liquid, stronger will be the strawberry flavor.

For Nick -

m₁ = 8/12 = 80/120

For Sam -

m₂ = 12/20 = 72/120

m₁ > m₂

Hence, Nick's claim is true.

Therefore, it can be concluded that -

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Answer:

y = 136

x=15

Step-by-step explanation:

to work this question out you must know the angles on a straight line add up to 180 degrees. By doing that we can find the top angle inside of the triangle.

180 - 104 = 76

to find x we need to know that angles in a triangle add up to 180 degrees.

180 =  (3x-1) + 4x + 76

To solve for x, we can first simplify the equation.

180 = (3x-1) + 4x + 76

This can be re-arranged as:

(3x-1) + 4x = 104

and then combined as:

7x = 105

Finally, we can solve for x by dividing both sides by 7:

x = 105/7

x = 15

So the value of x that satisfies the equation is 15

to find y we need to know that angles on a line equal 180

180 = (3(15)-1) + y

180 = 44 + y

To find the value of y, we can subtract 44 from both sides

y = 180-44

y = 136

Answer:

36.3 units²

Step-by-step explanation:

Area of a trapezoid = A = ((a+b)/2)h = [tex]\frac{a+b}{2}[/tex]h

a = 4

b = 1.5+7=8.5

solve for h using pythagorean theorem:

1.5² + h² = 6²

h² = 36 - 2.25 = 33.75

h = [tex]\sqrt{33.75}[/tex] = 5.81

A = [tex]\frac{4+8.5}{2}[/tex](5.81) = 36.3125

A. 73.91% of respondents were under the age of 30 and did not snore.

B. Data show that snoring is not age-independent as most snorers are over 30 years of age.

A. The first step is to convert all percentage population groups into numbers. This helps make things clearer.

Total number of adults surveyed = 995 adults

Number of adults over the age of 30 = 81.5% of 995

                                                              = 81.5/100 × 995

                                                              = 810.925

                                    ≈ 811(part of the population can be counted).

Number of adults under 30 = 995 - 811 = 184 adults.

Number of all adults who snore = 36.8% of 995

= 36.8/100 × 995 ≈ 366 adults who snore

Of the total 995, 32% of the snorers were over 30 was.

Number of snorers over 30 × 995 ≈ 318 adults

Snorers under 30 = 366 - 318 = 48 adults

Number of under 30s recorded 30 - under 30 snorers

= 184 - 48 = 136

Converting this to percentage: 136/184× 100 = 73.91%

so 73

B. From the data, snoring is not independent of age as most of the people that snored were above 30 years. Snoring is related to the age. This is because that the most of the younger adults did not snore, while more of the older adults snored.

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On solving the provided question, we can say that The probability of a person purchasing both a beverage and gasoline is 0.060, or 6%.

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

At a gas station, 84% of customers buy gasoline

[tex]P (A) = 0.84[/tex]

5% of customers buy gasoline and a beverage

[tex]P (B) = = 0.05[/tex]

conditional probability = P (A and B) = P(A) × P(B/A)

[tex]P(B/A) = P (A and B) / P(A)\\P ( B/A ) = 0.0595 = 0.060 or 6%\\[/tex]

The likelihood of a person purchasing both a beverage and gasoline is 0.060, or 6%.

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a) The unit prices to determine the best buy are as follows:

b) The best buy is the 14-ounce bottle of salad dressing with a unit cost of $0.24 since they are all Grade A products.

The unit price or cost is the cost for an item or a unit.

The unit price can be compared to the unit rate, which is the quotient of the total cost and the number of units.

                              6 ounces   14 ounces   20 ounces

Total costs               $1.56           $3.36          $5.60

Unit cost                  $0.26          $0.24          $0.28

                            ($1.56/6)      ($3.36/14)     ($5.60/20)

Thus, buying a 14-ounce bottle of salad dressing is more economical than others.

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Answer:

Step-by-step explanation:

The equation given:

[tex]15 + \left(3x\right) = 24[/tex]

Our goal is to find x. To find x, what I like to do is add the given values together, then subtract them by 24 to find x's value.

[tex]15 + 3 = 18\\24 - 18 = x\\x = 6[/tex]

Hope this helps!

The area covered by the roller in one full revelation is 1674 square inches.

Step-by-step explanation:

Given that You are using a 9 inch paint roller to paint a wall of your bedroom. The roller has a dimension of 158 inches as diameter and a nap thickness of 14 inch, as shown,

The nap is the fuzzy materials on the surface roller. How much area does the roller cover in one full revelation

The parameters to be considered are:

Diameter = 158 inches

Thickness = 14 inches

After one revolution rolling, the dimensions of the length will be:

L = 14 + 158 + 14

L = 186 inches.

Let the width be equal to 9 inches

The area covered = L × W

Substitute L and W into the formula

Area = 186 × 9

Area = 1674 square inches.

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The product of two rational numbers is a rational number.

In any field containing integers, rational numbers, along with addition and multiplication, produce a field that also contains the integers. In other words, a field only has characteristic zero if and only if it contains the field of rational numbers as a subfield. The field of rational numbers is a prime field.

"A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator 'p' and a non-zero denominator 'q'."

Therefore, when we are multiplying two rational numbers, their product must be a rational number.

This is because, numerators of both rational numbers are integers and denominators of both the numbers are non-zero integers.

Hence, the product is a rational number.

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The absolute value of a number is always positive, but the number itself can be positive or negative, and there are always two possible solutions for the absolute value equation, one positive and one negative, that are the same distance from 0.

An absolute value equation of the form |x| = k (where k is a constant) will have two solutions, one positive and one negative, that are the same distance from 0 on the number line.

For example, if the equation is |x| = 5, the two solutions of the equation are x = 5 and x = -5.

This is because the absolute value of a number represents the distance of that number from 0 on the number line, and this distance is the same regardless of whether the number is positive or negative. Therefore, for any non-negative value k, there are two numbers that are that distance away from 0, one positive and one negative.

For example, the distance of 5 from 0 is 5 units, and the distance of -5 from 0 is also 5 units. Therefore, |5| = |-5| = 5.

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The number of candy bars that Beth has sold, given the total they have sold and the amount sold by Carly, is 125 candy bars

To find the number of candy bars that Beth has sold, you can assume that the amount of candy sold by Carly is denoted as x.

This means that the amount of candy bars sold by Beth is:

= 2x - 1

The total sold by both Beth and Carly is therefore:

= 2x - 1 + x

The number of candy bars sold by Carly is:

188 = 2x - 1 + x

188 = 3x - 1

3x = 188 + 1

x = 189 / 3

x = 63

This means that the candy bars sold by Beth is:

= 2 ( 63 ) - 1

= 126 - 1

= 125 candy bars

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The total time taken by the experienced bricklayer to complete the job as per given condition is equal to 13 hours.

As given in the question,

Let the time taken by experienced bricklayer be 't' hours

Then time taken by apprentice bricklayer be '2t' hours

Time to complete 1 complete work is

Experienced bricklayer worked for 4 hours

Apprentice bricklayer worked for ( 4 + 14 ) = 18 hours

Required equation to complete 1 work is :

( 4/x) + ( 18 /2x) = 1

⇒( 8 + 18 )/ 2x = 1

⇒26/2 = x

⇒ x = 13 hours

Therefore, time taken by the experienced bricklayer to complete the job is equal to 13 hours.

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The domain and range for the function W = 15T + 400 is domain = set of all real numbers from 0 to 90 and range = set of all real numbers from 400 to 1750.

What is the range and domain of a function?

A function's range includes all conceivable values for y. Y = f(x) is the formula to determine a function's range. It is only a function in a relation if each x value has exactly one y value.

The collection of all potential inputs for a function is its domain.

The function for Total amount of water in the tank is given as -

W = 15T + 400

Where, T is the total number of minutes when the water is added.

So, according to the definition of range and domain -

T = domain = Number of minutes when the water is added

W = range = Total amount of water in the tank

W was a function of T for the next 90 minutes.

So, the domain will be the set of all real numbers from 0 to 90.

At, T = 0 -

W = 15(0) + 400

W = 400

At, T = 90 -

W = 15(90) + 400

W = 1350 + 400

W = 1750

So, the range will be set of all real numbers from 400 to 1750.

Therefore, the domain and range is (0,90) and (400,1750) respectively.

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