(3.6 x 105) / (1.2 x 103) =

[tex]\boldsymbol{\sf{(x-6)^{2}-5=0 }}[/tex]

[tex]\boldsymbol{\sf{x-6=\pm\sqrt{5} }}[/tex]

[tex]\boldsymbol{\sf{x-6=\sqrt{5} }}[/tex]

[tex]\boldsymbol{ \sf{x=\sqrt{5}+6 }}[/tex]

[tex]\boldsymbol{\sf{x-6=-\sqrt{5} }}[/tex]

[tex]\boldsymbol{\sf{x=-\sqrt{5}+6 }}[/tex]

[tex]\boldsymbol{\sf{x=\sqrt{5}+6,-\sqrt{5}+6 }}[/tex]

    [tex]\huge \red{\boxed{\boldsymbol{\sf{Answer \ \ \longmapsto \ \ \ x=\pm\sqrt{5}+6 }}}}[/tex]

The number of possible outcomes is 81

Count of Outcomes :

In the domain of Statistics, the number of possible outcomes for a given help in determining the overall size of the universe of outcomes. From such a universe, one can ascertain the probability or likelihood of desirable outcomes in terms of percentage or fraction.

Let's come to the solution of the question:

Here, the number of possible outcomes for each game is 3 (win, lose, tie).

The total number of possible outcomes is given by:

= Number of outcomes for 1st game * Number of outcomes 2nd game

= 3*3*3*3

=81

Hence, The number of possible outcomes is 81

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Answer:

It is everything that's bigger then (0,-3),

Picture under ↓

It's a bad drawing.

The solution region for the given pair of inequalities is found to be the common shaded region in the graph attached.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

For drawing the graph of any inequality, we first have to assume the inequality as an equation and draw the graph of the resulting equation. Hence, finding the points for the inequality , we let the inequality as:

Putting y=0, we get:

The point will be: (-2,0)

Now, putting x=0, we get:

The point will be: (0,4)

Now as the sign of inequality is >, the line of graph will be dotted.

Taking a test point (0,0) to find the shaded region, substituting this in the inequality,

So, the shaded region will be away from the test point.

Similarly, finding the points for the inequality , we let the inequality as:

Putting y=0, we get:

The point will be: (6,0)

Now, putting x=0, we get:

The point will be: (0,6)

Now, as the sign of inequality is of , the line of graph will be solid.

Taking a test point (0,0) to find the shaded region, substituting this in the inequality,

So, the shaded region will be towards the test point.

The resulting graph is attached after the solution.

The solution to the pair of given inequalities will be the shaded region that is common between both the individual inequality's shaded regions.

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The values of x and y are;

If a, b, and r are all real numbers that are not equal to zero, then;

ax + by = c depicts a two-variable linear equation.

For the given equations;

(7y-4)° = 59⁰ and (3y - 5)° = (12x + 3)º

Consider (7y-4)° = 59⁰;

Simplifying;

7y = 59 + 4

7y = 63

y = 9

Put y = 9 in the second equation;

(12x + 3)º = (3y - 5)°

12x + 3 = 3×9 - 5

Further simplifying;

12x = 27 - 8

12x = 19

x = 19/12

Thus, the values obtained for x and y are  x = 19/12° and y = 9°.

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The correct question is-

Find the values of x and y.

(7y-4)° = 59⁰

(3y - 5)° = (12x + 3)º

Answer:

c

Step-by-step explanation:

because 7 of the 12 sections are shaded in blue.

Answer:

-3

Step-by-step explanation:

4+(-7), In math you always have to do parentheses first. But, 4+(-7) equals -3 because -7 is bigger than 4. So it equals -3.

Answer:

y = [tex]\frac{16}{11}[/tex]x - [tex]\frac{-56}{11}[/tex]

Step-by-step explanation:

First find the slope.  The slope is the change in y over the change in x

[tex]\frac{8 - (-8)}{9 - (-2)}[/tex] = [tex]\frac{8+8}{9+2}[/tex] = [tex]\frac{16}{11}[/tex]

Next, find the y-intercept.  Use the slope and one of the points.  It does not matter which point that you use.  I will use the point (9,8)

y = mx + b

8 = [tex]\frac{16}{11}[/tex](9) + b

8 = [tex]\frac{144}{11}[/tex] + b  Subtract 144/11 from both sides

[tex]\frac{-56}{11}[/tex] = b

The graph of the given piecewise function is plotted at the end of the answer.

A piecewise function is a function that has different definitions, depending on the input.

From the definition in the problem, we have that:

Considering these three definitions, the graph is given at the end of the answer, with the legend of the closed interval given in the text.

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The interest owed is $40

Interest is the amount of money paid when a loan is collected

The amount is $500

The interest rate is 8%

Therefore the interest owed can be calculated as follows

= 8/100 × 500

= 0.08 × 500

= 40

Hence the interest owed is $40

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The post image coordinates are - A'(12,3), B'(10, -5) and C'(7,0)

Here, we are given 3 points A (-6, 15), B (-8,7) and C (-11, 12)

We are given the following translation rule- (x + 18) and (y - 12)

Let us take each point one by one-

A (-6, 15)

here x = -6

⇒ x + 18 = -6 + 18 = 12

and y = 15

⇒ y - 12 = 15 - 12 = 3

Thus the post image of A is (12, 3)

B (-8,7)

here x = -8

⇒ x + 18 = -8 + 18 = 10

and y = 7

⇒ y - 12 = 7 - 12 = -5

Thus the post image of B is (10, -5)

C (-11, 12)

here x = -11

⇒ x + 18 = -11 + 18 = 7

and y = 12

⇒ y - 12 = 12 - 12 = 0

Thus the post image of C is (7, 0)

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Answer:

-1, 2

Step-by-step explanation:

Plug the "x" on the top row into the "x" on the equation.

y = 3(0) - 1 = -1

y = 3(1) - 1 = 2

The number of glasses of lemonade that can be poured from the cooler is 45.

Given that, an insulated cooler holds 558 ounces of lemon.

We need to find how many full 12.4-ounces glasses of lemonade can be poured from the cooler.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Now, the number of glasses of lemonade = 558/12.4

=45

Hence, the number of glasses of lemonade that can be poured from the cooler is 45.

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Answer:

k = 1.75

Step-by-step explanation:

5 - 4k = -7

k = 1.75, because if you subtract 4 from both sides, you are left with 1.75 = -7.

Answer:

k = 3

Step-by-step explanation:

5 - 4k = - 7 ( subtract 5 from both sides )

- 4k = - 12 ( divide both sides by - 4 )

k = 3

Answer:

12 1/2

1/6

Step-by-step explanation:

5/6 x 15/1

2/3 x 1/4

The derivative of the function y = (sin(7x))ln(x) is [tex]\frac{Sin(7x)}{x} +7*ln(x)*Cos(7x)[/tex]

Derivative of a function f(x) is defined as the rate of change of that function with respect to x at a point in its domain.

For Example , Derivative of [tex]3x^{2} =6x[/tex].

Product Rule of Differentiation

Let f(x) and g(x) be any two function. The derivative of their will be

F(x)=f(x)*g(x)

[tex]F'(x)=f(x)*g'(x)+g(x)*f'(x)[/tex]

Given y=(sin(7x))ln(x)

[tex]y'=Sin(7x)*\frac{d}{dx} ln(x)+ln(x)*\frac{d}{dx}Sin(7x)[/tex]

[tex]y'=Sin(7x)*\frac{1}{x} +ln(x)*Cos(7x)*7[/tex]

[tex]y'=\frac{Sin(7x)}{x} +7*ln(x)*Cos(x)[/tex]

Therefore , the derivative of the function y = (sin(7x))ln(x) is [tex]\frac{Sin(7x)}{x} +7*ln(x)*Cos(7x)[/tex]

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Answer:

First term = 53,

Step-by-step explanation:

a10 = a1 + (10 - 1)d so:

98 = a1 + 9*5

a1 = 98 - 45

    = 53,

The amount of money in sales that Nolvia needs to earn a salary that exceeds $40,000 is greater than or equal to $19,000.

Given that:-

Fixed salary of Nolvia = $21,000

Commission tax that Nolvia gets = 4 %

Linear equation of Nolvia's salary and commission tax = 21000 + 0.04x

Where,

s represents her salary

x represents total sales

We have to find the amount of money in sales that Nolvia needs to earn a salary that exceeds $40,000.

The amount of money in sales that Nolvia needs to earn a salary that exceeds $40,000 = 40000 - 21000 ≥ $ 19,000

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Natural number multiplication is commutative.

The given number is commutative as -

7.4.1.5 = 5.1.4.7

The answer will always be same irrespective of the order in which it is multiplied

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Answer: 20

Step-by-step explanation:

The midpoint of line segment AB is (2, 5)

The coordinates are given as:

A= (-1,3)

B = (5.-7)

The midpoint of line segment AB is calculated as

Midpoint = 0.5 * (x1 + x2, y1 + y2)

So, we have:

Midpoint = 0.5 * (-1 + 5, 3 + 7)

Evaluate

Midpoint = (2, 5)

Hence, the midpoint of line segment AB is (2, 5)

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The original price of the bed was £330.

From the question, we are to determine the original price of the bed.

Let the original price of the bed be x

From the given information,

The current sale price of the bed is £257.40, and this price is a saving of 22% on the original price

Then,

We can write that

x - 22% of x = £257.40

Thus,

x - 0.22x = £257.40

0.78x = £257.40

x = £257.40/0.78

x = £330

Hence, the original price of the bed was £330.

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Answer:330

Step-by-step explanation:

easy way to do this:

1. ok so you know 100%=x and 100-22=73 so that means that 73%=2570.40

2. so write them with the known above the unknown: 100%=x

                                                                                          78%=2457.40

3. no cross multiply like this [tex]\frac{100X257.40}{78}[/tex] imagine the multiplication sign is the X here( the app didn't let me change that?)

4. the solution equals 330 which the answer

5. YOU DID IT!!

The scores of two groups can be compared using coefficient of variation;

Coefficient of variation (C.V.) = (Standard Deviation/ Mean) × 100%;

For Data set 1;

Standard deviation = 3.6

Mean = 35.3

C.V. = (3.6/35.3) × 100%;

       = 10.19%

For Data set 2;

Standard deviation = 0.5

Mean = 34.1

C.V. = (0.5/34.1) × 100%;

       = 1.46%

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Answer:

y=8,x=-3

Step-by-step explanation:

1/3×+1/4y=1

lcm=12

multiply through by lcm to get equation 1

4x+3y=12

equation 2

2×-3y=-30

equation 2 by 2

using the substitution method

y=8

x=-3

The volume required for a 5% solution is 5.7 L, while a 40% solution requires 4.3 L for the experiment.

A percentage is a fraction of a whole represented as a number ranging from 0 and 100.

The equation should be as follows:

If 'x' is the volume of a 40% solution, then the volume of a 5% solution is:

10 L = 40% solution volume + 5% solution volume

10 L = x + 5% volume of solution

10 L - x = 5% solution volume

The volume would then be calculated as follows:

(volume 20% × concentration 20%) = (volume 40% × concentration 40%)           + (volume 5% × concentration 5%)

10 litre × 20% = x litre × 40% + (10- x) litre × 5%

10 L ×  20% = x litre  × 35% + 10 litre × 5%

x litre × 35 = 10 L × 20 - 10 L × 5

                 = 10 L × 15

x litre = 10 L × 15/35

x litre = 4.28 L

x litre = 4.3 L

40% solution volume = 4.3 L

The volume of 5% solution is equal to 10 L - 4.3 L = 5.7 L.

Thus, the volume of 5% solution  requires is 5.7 L and volume of 40% solution required is 4.3 L.

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Answer:

good question it is very hard question

Answer:

0

Step-by-step explanation:

As x aproaches a, (x-a) will aproach 0, so the numerator will aproach 0, and because 0 divided by anything=0, the whole function will become 0. So, the answer is 0.