The time,
T
(seconds), it takes for a pot of water to boil is proportional to the amount,
A
(litres), of water.
It takes 200 seconds to boil 2.7 litres of water.
Work out how much water is in the pot if it boils in 220 seconds.

Equation for each situation are A = 59 -7t and B = 34 -2t and t<5 is the interval of time.

Two or more expressions with an Equal sign is called as Equation.

Snowman A starts at 59 inches and decreases height at 7 inches per hour.

The height can be represented as A = 59 -7t

Snowman B starts at 34 inches and decreases height by 2 inches per hour. That height can be represented by B = 34 -2t

A is taller than B.

A > B

59 -7t > 34 -2t

add 7t-34

25 > 5t

Divide by 5

5 > t

A will be taller than B when t < 5.

Hence,  A = 59 -7t and B = 34 -2t are equation for each situation and t< is the interval.

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The value of the unknown side y for the given triangle will be 46.15.

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

The sine law, also known as the law of sines, states that the ratio of a triangle's side length to the sine of its opposite angle is constant for all three sides. It's sometimes referred to as the sine rule.

We have to find the value of the side as y.

Apply Sin law in the given triangle,

SinA/a=SinB/b=SinC/c

Sin42/31=sin85/y

0.6691/31=0.9962/y

y=30.8822/0.6691

y=46.15

Thus, the value of the unknown side y for the given triangle will be 46.15.

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The equation for the line connecting the two points is as follows y = 2x + x.

A mathematical statement known as an equation is comprised of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

Equation of a line:

y = mx +b

Where;

m = slope

b = y-intercept

You are given the y-intercept from the point (0,2). When x = 0, y = 1

You can then see from the Eq: y = mx + b  

that b = 1

By dividing the change in y by the change in x, or "rise over run," one may get the slope, m.

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

One of the points is (x1, y1) and the other (x2, y2)

m = (1-(2)) / (0 -(2))

m = (-1)/(-2) = 1/2

The equation for the line connecting the two points is as follows:

y = 2x + x.

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Answer:

sometimes used to distinguish between the measure of the angle

Step-by-step explanation:

Answer:

Step-by-step explanation:

The scatter plot shows positive correlation because as the plotted values of x increase, the values of y generally increase.

When x and y both increase, you have a positive correlation. When one increases and the other decreases then you have a negative correlation.

It explains that people don't want to donate their organs in opt out  because the probability of non donation public are greater.

As we know people who wants to donates their is organs opt out are approximately around 15 %

And we also know that people who don't want to donate their organs are approx. 90 %

In countries such as Australia, laws make organ donation the default option at the time of death, and so people must explicitly “opt out” of organ donation. In these so-called opt-out countries, more than 90% of people register to donate their organs.

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Answer:

is that geometry

Step-by-step explanation:

Answer: -2.2y - 1.8

Step-by-step explanation:

Combine like terms

1.2y+(-3.4y)

4.5+(-6.3)

-2.2y - 1.8

The given triangles are congruent following the side angle side (SAS) congruency .

Given,

∴ ∠ A = ∠ B = ∠ C = ∠ D =90°

In Δ ABC and Δ CDA

AB =  CD

∠ BAC= ∠ DAC

AB= AD

∴ By Side Angle Side congruent property

Δ ABC ≅ Δ CDA

Congruent refers to figures that are similar in all respects, primarily in terms of size and shape. Congruence describes how two congruent figures relate to one another.

The relationship between two figures that are congruent is referred to as congruence. Let's talk about the triangle SAS congruence now. We don't necessarily need to look into all the sides and angles to determine whether the two triangles are identical.

Triangles must be congruent to mean,

There are no different comparable angle pairs.

It is equal on all comparable sides.

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Answer:

f = 3

g = -1

h = 6

r = 18

Step-by-step explanation:

Box 1

f(x) = [tex]2x^{4}[/tex]-[tex]12x^{3}[/tex]+[tex]16x^{2}[/tex]+4x+15 with x = 3

f(3) = [tex]2(3^{4)}[/tex] - [tex]12(3^{3} )[/tex] + [tex]16(3^{2})[/tex]+ 4(3) + 15

Reorder

Evaluate

Multiply

3f = 2 x 81 - 12 + 27 +16 x 9 + 12 +15

3f = 162 - 324 + 144 + 12 + 15

3f =  9

3  ÷  3

f = 3

Box 1

g(x) = [tex]3x^{3}[/tex] - [tex]16x^{2}[/tex] - 7x - 36 with x = 6

g(6) = [tex]3(6^{3} )[/tex] - [tex]16(6^{2})[/tex] - 7(6) - 36

g6 = 3 x 216 - 576 - 42 - 36

g6 = -6

6   ÷ 6

g = -1

Box 2

h(x) = [tex]5x^{3}[/tex] - [tex]2x^{2}[/tex] - 3 with x = -1

h(-1) = [tex]5(-1^{3} )[/tex] - [tex]2(-1^{2})[/tex] -3

h-1 = -5 + 2 -3

h-1 = -6

-1    ÷  - 1

h = -6

Box 2

r(x) = [tex]4x^{4}[/tex] - [tex]9x^{2}[/tex] + 5x - 2 with x = 2

r(2) = [tex]4(2^{4} )[/tex] - [tex]9(2^{2} )[/tex] + 5(2) - 2

r2 = 64 - 36 + 10 - 2

r2 = 36

2   ÷  2

r = 18

If a square has an area of 450 square inches then according to Area = 2(length of a side), the length of one side of that square will be 225 inches.

The formula of Area of a Square is ,

area = side × side = side² square units

whereas the perimeter of square is = 4 x side

A square is a quadrilateral with four equal sides and four equal angles that is a regular quadrilateral. The square's angles are at right angles or at 90 degrees.

let the length of a side of a square is x

area of square is = 450 square inches

as area of square is found as

Area = 2(length of a side)

2x = 450 square inches

x =450/2

x=225 inches

so the length of each side of square is 225 inches.

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The number of subscribers in 2008 will be 110845988.

From the information, in 1985, there were 285 cell phone subscribers in the small town of glenwood. the number of subscribers increased by 75% per year after 1985.

It should be noted that the number of years between 1985 and 2008 will be:

= 2008 - 1985

= 23 years.

Therefore, the number of subscriber in 2008 will be:

= 285 × (1 + 75%)^23

= 285 × 1.75^23

= 285 × 388933.29

= 110845988

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Answer: A

Step-by-step explanation: To solve this problem, we can set up a system of equations to represent the information given in the problem. Let x represent the cost of a plate of spring rolls, y represent the cost of a plate of chicken tenders, and z represent the cost of a plate of pretzel dippers.

The first group spent $23 on 2 plates of chicken tenders and 1 plate of pretzel dippers, so the equation for this group is:

2y + z = $23

The second group spent $30.75 to buy 3 plates of spring rolls and 1 plate of chicken tenders, so the equation for this group is:

3x + y = $30.75

The third group spent $22.25 on one of each appetizer, so the equation for this group is:

x + y + z = $22.25

Now that we have three equations, we can use algebraic techniques to solve for the value of x, which represents the cost of a plate of spring rolls.

First, we can solve the second equation for y:

y = $30.75 - 3x

Substituting this expression for y into the first equation, we get:

2($30.75 - 3x) + z = $23

Solving for x, we find that x = $7.75.

Therefore, the cost of a plate of spring rolls is $7.75, so the answer is A.

Answer:

No.

Step-by-step explanation:

No.

In a proportional relationship, every minute has the same charge.

The probability distribution that she or he is on duty on Saturday or Sunday will be 0.7

What is probability distribution ?

A frequency distribution that has been idealised is a probability distribution.

An individual sample or dataset is described by its frequency distribution. It's the number of times in the dataset that each potential value of a variable appears.

The probability of occurrence of a value determines how frequently it appears in a sample. Probability is a value between 0 and 1 that indicates the likelihood that something will happen:

A value will occur more frequently in a sample the higher its likelihood.

The probability of a value is more particularly the relative frequency in an indefinitely large sample.

Probability distributions are theoretical since it is not feasible to obtain infinitely large samples in practise.

Let the people work on Sunday = sun = 4

Let the people work on Saturday = sat = 3

total no. of doctors are 10

so the probability distribution of people work on either Sunday or Saturday will be :

= Sun + sat / total no of doctors

= 3+4/10

=0.7

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△X'Y'Z' is transformed form △XYZ. If △XYZ rotated 90 degrees counterclockwise about the origin, then YZ ⊥ Y'Z'. Hence option B is the correct option.

What is transformation?

A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object. Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.

Given that,

△XYZ is rotated 90 degrees counterclockwise about the origin to form △X'Y'Z'.

Each side of △XYZ is rotated 90 degrees counterclockwise.

Then the angle between corresponding sides of △XYZ and △X'Y'Z' are 90 degrees.

Therefore

XY⊥X'Y'

YZ ⊥Y'Z'

ZX ⊥ Z'X'.

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Geometry is a topic that deals with shapes, lines and angles. The explanation below is required to show the reasons for the statements are given below:

A triangle has three straight sides and three internal angles. The sum of the internal angles of a triangle is [tex]180^{o}[/tex]. Triangles can generally be classifies with respect to the size of angles, or according to the length of sides. Some common types are; right angles, obtuse angled, acute angle, isosceles, equilateral and scalene.

A right angled triangle is a type which has two of its sides at [tex]90^{o}[/tex] to each other.

Therefore, the required statements and reasons to prove that <JLK ≅ <LJM are:

                 STATEMENT                                         REASON

1. ΔJKL and ΔLMJ are right triangles                  Given

2. JK ≅ LM                                                             Hypotenuse-Leg (HL)

3. Jl ≅ LJ                                                                Reflexive property

4. ΔJKL ≅ ΔLMJ                                                    CPCTC

5. <JLK ≅ <LJM                                                     Symmetric property

Thus,  <JLK ≅ <LJM

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By solving linear inequation, it can be calculated that

x = 60 , y = 70 is one possible solution.

What is linear inequation?

Inequation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by <, >, ≤, ≥

A one degree inequation is known as linear inequation

Let the number of tacos sold be $x and the number of burrito sold be $y

He only has enough supplies to make 130 tacos or burritos.

x + y [tex]\leq[/tex] 130 ... (1)

He sells each taco for $4.25 and each burrito for $8.50.

Isaac must sell a minimum of $850 worth of tacos and burritos each day.

4.25x + 8.5y [tex]\geq[/tex] 850

x + 2y [tex]\geq[/tex] 200 ... (2)

The inequalities has been solved graphically

One possible solution is x = 60, y = 70

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The constant of proportionality of y and x in the graph is given as follows:

k = 3/4.

In a proportional relationship, the ratio between the output variable y and the input variable x is constant, and is called constant of proportionality, given as follows:

k = y/x.

A proportional relationship is a special case of a linear function, which has an intercept of zero, as is the case for the graph in this problem.

The marked point on the graph has the coordinates given as follows:

(4,3).

Meaning that the constant of proportionality of y and x in the graph is calculated as follows:

k = y/x = 3/4.

(division of the value of the y-coordinate by the value of the x-coordinate).

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The equation of line parallel to y = -3 passing through (2,6) is y = 6

The slope-intercept form of straight line is used to find the equation of line. It is given as y =mx + b

where m is a slope of line

b is y-intercept

According to the question,

The required line is parallel to line y = -3

Slope of given line : m₁

m₁ = 0

When two lines are parallel to each other then their slopes are equal

Therefore , slope of required line is m₂ =  m₁ = 0

Also , given that the line is passing through the coordinate (2,6)

So , 6 = 0(2) + b

=> b = 6

Substituting the values of slope and intercept

y = 6 is required equation of line

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The kind of sequence shown 2, -1, -4, -7, -10, is definitely an arithmetic sequence.

In mathematics, a sequence is a collection of numbers or items that have been organised in a certain order in accordance with a set of rules. These sequences, which might be endless or finite, are useful for simulating a variety of real-world processes. In addition to its practical uses, sequences are an essential mathematical notion that allows us to analyse patterns and relationships between numbers. We may edit and examine sequences to better understand their characteristics and behaviour by applying mathematical operations. Sequences are frequently used to investigate patterns and relationships between numbers, as well as to solve problems in a variety of mathematical disciplines such as algebra, calculus, and geometry. Arithmetic sequences, geometric sequences, recursive sequence are a few examples of frequent sequence types.

How to solve?

In an arithmetic sequence, the difference between any two consecutive terms is constant.

In the given sequence, the difference between any two consecutive terms is -3. i.e.,

d = -10 - (-7) = -7 -(-4) = -4 - (-1) = -1 - (2) = -3

Therefore, the sequence is an arithmetic sequence.

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Following is the geometric progression of Nelson's debt after each month: (E) 950,967.1, 984.51, 1002.23, 1020.27

A geometric progression sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

So, in this issue, the interest rate is as follows: 1.8%.

The debt will therefore be equal to the debt from the previous month multiplied by 100 + 1.8 = 101.8% = 1.018 each month, and the common ratio is as follows: 1.018.

In light of this, the terms of the series are as follows:

2nd term: 950 x 1.018 = $967.1

3rd term: 967.1 x 1.018 = $984.51

4th term: 984.51 x 1.018 = $1002.23

5th term: 1002.23 x 1.018 = $1020.27

Therefore, the following is the geometric progression of Nelson's debt after each month: (E) 950,967.1, 984.51, 1002.23, 1020.27

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Complete question:
Many credit card companies chard a compound interest rate of 1.8% per month Nelson owes 950 on a credit card. If he makes no purchases or payments he will go deeper and deeper into debt.

Answer:

Interest rate = 7 percent

Step-by-step explanation:

i = prt

r = [tex] \frac{i}{pt} [/tex]

r = [tex] \frac{1400}{20000 \times 1} [/tex]

r = 0.07

0.07 x 100 = 7

The value of the inequality is ( 45/4 , 19/4 )

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

According to the given information

Number of hours spent in washing cars = x

Number of hours spent in clearing tables = y

Amount paid per hour for washing the car = $7

Amount paid per hour for clearing the tables = $15

Earnings

7x + 15y ≥ 150

x + y ≤ 16

7x + 15y = 150 ........ (i)

x + y = 16 ........(ii)

Multiply (ii) by 7

7x + 7y = 112 ..... (iii)

Subtract (i) and (iii)

8y = 38

y = 19/4

Putting the value of y in (ii)

x + 19/4 = 16

x = 16 - 19/4

x = 45/4

The value of the inequality is ( 45/4 , 19/4 )

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Answer:

12

Step-by-step explanation:

Answer:

Step-by-step explanation:    3?    

Answer: d.) 6

Step-by-step explanation:

Since Chris runs 1. 2 as fast as his usual running speed, he runs at 5 km/h, and so will take 6 hours to complete the 30 km run. Since Pat runs at 11. 2 times her usual speed.

The expression for 60 decreased by twice Jenny's score 60 - 2x.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.

Let Jenny's score be x.

Twice Jenny's score will be 2x.

Therefore, the expression will be:

= 60 - 2x

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