I think this is an elimination problem:

12x-20y=-32
x+20y=10

Step-by-step explanation

:We have to prove that (a + b + c)³ - a³ - b³ - c³ = 3(a + b ) (b + c) (c + a).

Considering LHS,

LHS : (a + b + c)³ - a³ - b³ - c³

= [(a + b + c)³ - a³] - (b³ + c³)

Using the algebraic identity,

a³ - b³ = (a - b)(a² + b² + ab)

(a + b + c)³ - a³ = ((a + b + c) - a)((a + b + c)² + a² + (a + b + c)a)

Using the algebraic identity,

(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)

= (b + c)(a² + b² + c² + 2(ab + bc + ca) + a² + a² + ab + ac)

= (b + c)(3a² + b² + c² + 3ab + 2bc + 3ac)

Using the algebraic identity,

a³ + b³ = (a + b)(a² + b² - ab)

b³ + c³ = (b + c)(b² + c² - bc)

So, [(a + b + c)³ - a³] - (b³ + c³) = (b + c)(3a² + b² + c² + 3ab + 2bc + 3ac) - [(b + c)(b² + c² - bc)]

= (b + c)[3a² + b² + c² + 3ab + 2bc + 3ac - (b² + c² - bc)]

= (b + c)[3a² + b² + c² + 3ab + 2bc + 3ac - b² - c² + bc]

= (b + c)[3a² + 3ab + 3bc + 3ac]

= (b + c)[3(a² + ab + bc + ac)]

= (b + c)[3(a(a + b) + c(b + a)]

= (b + c)[3(a + c)(a + b)]

= 3(a + b)(b + c)(a + c)

= RHS

The amount of Chemical  B needed is 1.6 g.

This refers to a diagram that shows a series of one or more points, lines, line segments, curves, or areas that represents the variation of a variable when compared with that of one or more other variables.

The quantity of Chemical B is plotted against the quantity of  Chemical A.

Chemical B  is plotted on the vertical axis using the scale of 1 cm to represent 2 units. Chemical A is plotted on the horizontal axis using the scale of 1 cm to represent 1 unit.

Therefore, on the graph, the line passing through the origin of the graph shows that when  1.4 g of Chemical A is used  1.6 g of Chemical B is needed.

Chemical B  is plotted on the vertical axis using the scale of 1  cm to represent 2 units.

To get the amount of Chemical B is  on vertical axis =  2 grams

                                                                                             5 boxes

                                                                                       =0.4 g

Tracing the mass of Chemical A used 1.4 g it meets the line passing through the center at 4th line (4th box).

To get the amount of Chemical B is  on vertical axis = amount of Chemical B per box * the number of line (boxes).

To get the amount of Chemical B is  on vertical axis = 0.4 g * 4 lines (boxes)

                                                                                        = 1.6 g

Hence The amount of Chemical  B needed is 1.6 g.

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Answer:

Step-by-step explanation:

1000-520=480

480/6=80

x+6+520=1000 (-6)

x+514=1000

x=486

Answer:

140 hamburgers

Step-by-step explanation:

to find the answer we must first use a let statement and write an equation

let x = hamburgers

hamburgers * 2 is cheeseburgers and added together that is 420

so

x + 2x = 420

now solve

3x = 420

x = 140

140 hamburgers were sold

Answer:

Step-by-step explanation:

240 divided by 3= 80

80+80=160

160 hamburgers sold altogether on Wednesday.

Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%

One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified. As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

Here,

Given: Total number of freshman =500

mean =75 and standard deviation =7

a) the percentage of scores that fell between 68 and 82

340 is the number of freshman whose  scores that fell between 68 and 82

thus,

percentage = 340 /500 * 100

=> percentage = 68%

b)the percentage of scores that fell between 61 and 75

237 is the number of freshman whose  scores that fell between 61 and 75

thus,

percentage = 237/500 * 100

=> percentage = 47.4%

Therefore , the percentage of case 1 is 68% and percentage of case 2 is 47.4%

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The probability that the first household speaks French, but the second household speaks English, is 0.1449. The correct option is a.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

In Canada, 63% of households speak English as their primary language, and 23% speak French as their primary language.

Let A be the event that the household speaks French and B be the event that the household speaks English.

Converting percentage to decimals,

63% = 0.63

and 23% = 0.23

According to the question,

P (A) = 0.23 and P (B) = 0.63.

Then, the probability that the first household speaks French, but the second household speaks English is,

Probability =(0.23) x (0.63)

                  =0.1449

Therefore, the probability that the first household speaks French, but the second household speaks English is 0.1449.

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Probability of drawing bad potatoes = 0.1

The probability of drawing a bag with bad potatoes is less than 1.

The probability of drawing a bag with good potatoes is greater than 0

The probability of drawing a bag with bad potatoes as a decimal .

The probability is 20% which means 20 by hundred , which means there is a chance of being its ok.

probability of bad potatoes = 2/20

=1/10

=0.1

To find the probability of the outcomes = Number of favourable outcome / Number of total outcome.

Probability of event 1 and 2

probability of event 1 =Number of favourable outcome / Number of total outcome.

probability of event 2 = 1 -( probability of event 1)

probability of good potatoes = 1- ( probability of bad potatoes)

Probability of the given event( probability of the bad potatoes = 1-(0.1)

Thus,

Probability of the bad potatoes in the 2 of the bags are=0.9

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By adding the given fractions, we can see that 11/15 of the friends bought food, and 4/15 bought drinks.

We know that 2/5 of the group bought a hamburger, and 1/3 of them bought chips.

Then the total fraction of friends who bought food is given by the addition of the two fractions above.

2/5 + 1/3

finding a common denominator we will get:

(3/3)*(2/5) + (5/5)*(1/3)

6/15 + 5/15

11/15

So 11/15 of the friends bought food, and the rest:

4/15 bought drinks.

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Answer:

none

Step-by-step explanation: if the person driving is one of the five people than none

Answer:

2

Step-by-step explanation:

it says 3 times the sum of x and 7 equals 27 so 1st divide 27 by 3 which gives you 9 and then subtract 7 which is given and that gives you 2 for your answer

The complete model will be;

⇒ 0.5 × 0.1 = 0.05

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A 10 by 10 grid is shown.

And, 5 columns and 1 row are shaded.

Now,

Since, 5 columns and 1 row are shaded.

Hence, The complete model will be;

⇒ 0.5 × 0.1 = 0.05

Thus, The complete model will be;

⇒ 0.5 × 0.1 = 0.05

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If there is another element of the same set between any two members of a set, we can say that the set is dense.

We'll show that the first choice—3.14 and pi—is the right one.

To prove that the set of irrational numbers contains a lot of real numbers, we must first discover an irrational number that lies between two specified real numbers.

In order to extend this to the real set, which is the union of irrational numbers and rational numbers, we should be able to find an irrational number between a rational number and an irrational number (or between an irrational number and a rational number). This is because we know that irrational numbers are dense (between two irrational numbers we can find another irrational number).

The first option, which has one of each, will then be the right choice.

Pi is irrational, while 3.14 is rational.

Finding an irrational number between these two indicates that the real set contains many irrational numbers.

(Note that the third option likewise has an irrational and a rational number, but the first one, [tex]e^{2}[/tex], is larger than the second one[tex]\sqrt{54}[/tex], thus it is written wrongly; for this reason, we did not choose it.)

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Answer:

y = -5x -2

Step-by-step explanation:

Equation y=mx+b

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

Slope m=(-7- -2)/(1 - 0)

Slope m=(-7 + 2)/(1 - 0)

Slope m=(-5)/(1)

Slope m= -5

Point-slope form = y − y 1 = m ( x − x 1 )

Point-slope form = y − -2 = -5 ( x − 0 )

Point-slope form = y + 2 = -5x − 0

Point-slope form = y = -5x -2

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Answer:

48 minutes

Step-by-step explanation:

6 : 16 = 18 : x

x = 16 * 18 / 6

x = 16 * 3

x = 48

There are 720 different ways can a race with 6 runners be completed.

What is a combination?

The process of combining or the condition of combining. a combination of things; an amalgamation of concepts. a grouping of notes: A chord is a grouping of notes. a grouping of people or entities acting together to impede commerce.

Here, we have

The winner can be chosen from all 6 runners, the second person can be chosen from 5 people, the third - from 4, and so on.

So the total number of possible results can be calculated as:

n = 6×5×4×3×2×1= 6!

= 720

Hence, there are 720 different ways can a race with 6 runners be completed.

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He took 7.616 hours for victory at the speed of 131.3009 and cover 1000 miles.

What is distance?

The distance between two sites is the length of the route. The metre is the SI unit for distance.

What is speed?

The speed at which an object’s location changes in any direction. The distance travelled divided by the time it took to travel that distance is how fast something is moving.

What is time?

The amount of time that something happens, goes through a process, or remains the same.

Speed= 131.3009 mph

Total distance= 1000 miles

Speed = distance/ time

time= distance/ speed

time= 1000/131.3009

(nearest thousandth means round off upto 3 decimal places)

time= 7.616 hours

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Answer:

8 is the answer

The answers are 1) Distributive property 2) Combining like terms 3)    Subtraction property of equality 4)  Subtraction property of equality 5)  Subtraction property of equality

An identity is an equality that holds true regardless of the values chosen for its variables. They are used in simplifying or rearranging algebra expressions.

Given; 4x-2(3+2x) = 2x+11

1) 4x-6-4x = 2x+11 = Distributive property

2) 4x-4x-6 = 2x-11 = Combining like terms

3) -6 = 2x-11 = Subtraction property of equality

4) -17 = 2x = Subtraction property of equality

5) -8.5 = 2 =  Subtraction property of equality

Hence, the answers are 1) Distributive property 2) Combining like terms 3)    Subtraction property of equality 4)  Subtraction property of equality 5)  Subtraction property of equality

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Answer:

Step-by-step explanation:

B is the answer

Create a line from-6,-5 to the x axis to -6 and draw a line from -1,3 down to x axis because that is your domain. Make sure to look at your open circles or closed circles at end of the line, if closed there are block brackets, If open then it is parenthesis. If it is a coordinate it is curly brackets. So therefore the answer is B

The degrees of freedom in the denominator of the f-statistic calculation is 2.

The number of distinct bits of information required to construct a statistic is called the degrees of freedom, which is frequently denoted by the letters v or df.

For the stated question-

degrees of freedom df = n - 1

n = 3 groups

df = 3 - 1

df = 2

Thus, the degrees of freedom in the denominator of the f-statistic calculation is 2.

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The decimal 0.000000836 in scientific notation is 8. 36 × 10^-7

Scientific notation can be defined as a way of expressing numbers too small or too large to be conveniently written in decimal form.

It is also referred to as standard index form,  standard form and scientific form.

It is commonly used for complex calculations with lengthy numbers.

It is also described as a method of expressing numbers in the terms of a decimal number that is between 1 and 10, and not 10 itself multiplied by a power of 10.

Given the decimal;

0.000000836

In scientific notation, it is written as;

8. 36 × 10^-7

The power is negative because the zeros are counted towards the right side.

Hence, the value is 8. 36 × 10^-7

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Answer:

103

Step-by-step explanation:

[tex]\frac{75}{310} = \frac{25}{p}\\ 25 X \frac{310}{75} = 103[/tex]

Increasing the given sample size will decreases the probability because σx will decreases as n value increases.

In Statistitics whenever we test a hypothesis for testing a statistic, we use confidence interval. Confidence interval is on either side of an assumed value a margin of error. Margin of error is calculated as critical value * sigma/sqrt of n. Thus we find that whenever n increases, margin of error decreases.

Thus making confidence interval narrower and thus making probability for accepting null hypothesis a less value. As the pattern sizes increase, the range of every sampling distribution decreases so they emerge as more and more leptokurtic. The variety of the sampling distribution is smaller than the variety of the authentic populace. Therefore, as a pattern length increases, the pattern imply and general deviation might be nearer in fee to the populace imply μ and general deviation σ.

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Answer:

12

Step-by-step explanation:

14 + 7 = 21

14 / 21 = ⅔

AE = 18

x / 18 = ⅔

x = 18 x ⅔

x = 12

The result of 45.8*10^3 is going to be 45800. Using mental math, 45.8*0.1 will be 4.58.

A set of abilities known as mental math enable people to perform calculations "in their heads" without the aid of paper and pencil or a calculator. Recalling math information, such as 8 x 5 = 40, is one of these abilities. Rounding numbers and estimating calculations are additional abilities. Mathematical calculations made solely with the human brain, without the aid of any materials or tools like a calculator, are referred to as mental calculations. When computing tools are not available, when mental calculation is quicker than other methods, or even in a competitive setting, people may use it.

Here,

45.8*10³=45800

45.8*0.1=4.58

The value of 45.8*10³ will be 45800. The value of 45.8*0.1 will be 4.58 using mental math.

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Answer:

The answer is 37.5.

Step-by-step explanation:

The expression after simplifying with the first rule of radicals is 9√5.

A square is a two-dimensional figure that has four sides and all four sides are equal.

The area of a square is side²

We have,

Area of a square = side² _______(1)

Area = 405 square feet _______(2)

From (1) and (2) we get,

405 square feet = Side²

Side = √405 feet

[ 405 = 81 x 5 ]

Side = √(81 x 5)

[ 9² = 81 ]

Side = 9√5

Thus,

The side length is 9√5 feet.

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