{10x + 7y= - 12
9x+ 5y = -16

The Fundamental Counting Principle, choosing from 3 sizes of bottled water and from distilled, filtered, or spring water is 9 ways.

The Basic Counting Principle is a technique used in mathematics, more especially in probability theory and combinatorics, to determine how many combinations of options, items, or outcomes are possible. The Rule of Multiplication, the Product Rule, the Multiplication Rule, and the Basic Counting Rule are some of its alternate names.

It has a connection to the Sum Rule, often known as the Rule of Sum, which is a fundamental counting method used to calculate probabilities.

According to the Basic Counting Principle, if a decision or event has a potential result or set of options, and a different decision or event has b possible outcomes or choices, then the sum of all the unique combinations of outcomes for the two is ab.

Using the fundamental counting principle, if an event occurs in m ways and another event occurs in n ways then the total occurrence is given as (m)(n).

Given that,

m = 3 for choosing between sizes.

n = 3 for distilled, filtered, or spring water.

Thus, the total number of occurrence is given as:

T = (3) (3) = 9

Hence, the Fundamental Counting Principle, choosing from 3 sizes of bottled water and from distilled, filtered, or spring water is 9 ways.

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[tex]\log _6 \sqrt[3]{6} \quad[/tex]=0.3 i.e 1/3

[tex]\log _2 64[/tex] =6

[tex]-3 \log _5 25 \quad[/tex]=-6

[tex]\log _2 \sqrt[4]{8} \quad[/tex] = 0.75

[tex]\log _3 \frac{1}{81}[/tex]=-4

Generally, A logarithm is a mathematical function that determines the power to which a given number (called the base) must be raised to obtain a certain value. In other words, a logarithm is the inverse operation of exponentiation.

For example, if we take the base 2 and the value 8, the logarithm of 8 to the base 2 (written as log2 8) is 3, because 2 raised to the power of 3 (i.e., 2^3) equals 8.

Logarithms are widely used in many fields of science, engineering, and mathematics, particularly in areas where large numbers or very small numbers are involved. They are also used in data analysis, signal processing, and many other applications.

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The area of the shape is given as 24.52 cm2

We have two triangles and 1 rectangle

we have to find the area of the triangles first and then solve for the area of the rectangle.

The area of a triangle = 1/2bh

for first triangle

area = 1/2 * 2.7 * 3

= 4.05

for second triangle

height = 6.8 - 2.7

= 4.1

area = 1/2 * 3.4 * 4.1

= 6.97

For the rectangle

area = l * w

= 2.7 * 5 = 13.5

The area = 13. 5 + 6.97 + 4.05

= 24.52 cm2

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Answer: A: Yes. The input and output are both feasible.

Step-by-step explanation:

To determine whether the solution (29.5, $212.50) makes sense for the function c(x), we need to evaluate whether the input and output are feasible and make sense in the context of the problem.

The input is given as 29.5, which represents the number of students. It is unclear from the information given whether a non-integer value for the number of students is feasible or not. However, if we assume that 29.5 students means 29 students and 1 child attending the carnival, then the input of 29.5 students is feasible.

The output is given as $212.50, which represents the amount of money spent at the carnival. It is reasonable to assume that a school group on a field trip would spend a certain amount of money at a carnival, and $212.50 is not an unreasonable amount to spend.

Therefore, based on the information given, we can conclude that the solution (29.5, $212.50) makes sense for the function c(x). So the answer is A: Yes. The input and output are both feasible.

Answer: 5/8

Step-by-step explanation:

We can make the fractions easier to read by changing 1/4 to 2/8, simply by multiplying the fraction by 2/2.

2/8 : 7/8

now you can see how much more George ate.

7/8 - 2/8 = 5/8

George ate 5/8 more than Grace.

Using a system of equations, Company A charges 25 + 0.06x more than Company B.

A system of equations involves two or more equations whose solutions are found concurrently or at the same time.

A system of equations is also known as simultaneous equations.

                                   Company A     Company B    Difference

Fixed charge                  $75.50             $50.50        $25 ($75.50 - $50.50)

Variable charge per mile $0.16               $0.10         $0.06 ($0.16 - $0.10)

Let the number of miles covered = x

The total cost of Company A (Equation 1) = 75.50 + 0.16

The total cost of Company B (Equation 2) = 50.50 + 0.1

The difference in total cost for x miles      = 25 + 0.06w

Thus, for each mile of travel that the family rents the car, Company A will charge more than Company B by exactly 25 + 0.06w.

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The required population of the city is approximately 44,44.44.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Let's use algebra to solve for the population of the city.

Let P be the population of the city. We know that 27% of the population is from 50 to 64 years old.

The number of people from 50 to 64 years old is 27% of the whole population, which can be expressed as,

0.27P

We can set up an equation to relate the number of people from 50 to 64 years old to the number of eligible voters,

0.27P = x

where x is the number of people from 50 to 64 years old who voted.

We can solve for P by multiplying both sides of the equation by the reciprocal of 0.27,

P = x / 0.27

Substituting x with 1200,

P = 12,00 / 0.27 = 4444.44

Therefore, the population of the city is approximately 44,44.44.

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Complete quesiton,

'if 12,00 people voted in the election how many were from 50 to 64 years which is 27% of the whole population, calculate the population of the city?

The number of new phone sold is 1 and the number of old phone sold is 5, if the sales for the day totals $625.

It is given that

A new phone sells for $250

and a used one sells for $75

Let number of new phone is sold = x

and number of old phone is sold = y

Here the total profit for the day is $625

So, 250x + 75y = 625

or 10x + 3y = 25

Now the value of x  and y satisfy the above equation, if we take x = 2 and more than 2, it is clear that it not satisfy the above equation. So we made a conclusion here x must be equal to 1 here.

Now, if x = 1

10(1) + 3y = 25

3y = 15

y = 5

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Answer:

Step-by-step explanation:

The factors of 96 are the integers that divide evenly into 96. To find the factors of 96, you can divide 96 by integers starting from 1 and increasing until you reach 96.

The factors of 96 are:

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.

These are all the integers that divide evenly into 96.

Answer:

[tex]y-8=3(x+2)[/tex]

Step-by-step explanation:

The equation of the line with slope [tex]m[/tex] passing through [tex](x_1, y_1)[/tex] in point-slope form is [tex]y-y_1=m(x-x_1)[/tex].

Reason:

-2 * 2 = -4

-2 + 2 = 0

These values are found through trial and error. The order of -2 and 2 doesn't matter.

Answer:

Step-by-step explanation:

There are 5 cans left over after painting the walls.

Let x represent the maximum number of trims that can be painted

Since each trim requires 1/2 a can, x trims will take x/2 cans

This cannot exceed 5 cans so we get the inequality:
x/2 ≤  5

Multiplying by 2 both sides of inequality:
x  ≤ 10

In words:
Maximum number of trims that can be painted with 5 cans is 10

Number line attached

The constant 0.9965 is the rate of change per hour. Specifically, it represents the factor by which the quantity changes every hour. In this case, the factor is less than 1, indicating that the quantity is decreasing over time.

To see how this rate of change works, consider an example:

If the initial quantity is 930, after one hour the quantity will be:

f(1) = 930(0.9965) ≈ 926.20

That is, the quantity has decreased by a factor of 0.9965, or about 0.35%.

After two hours, the quantity will be:

f(2) = 930(0.9965)^2 ≈ 922.42

That is, the quantity has decreased by a factor of 0.9965 twice, or about 0.70%.

So the constant 0.9965 reveals the rate of change of the quantity, which is a decrease of about 0.35% per hour.

Answer:

9.8

Step-by-step explanation:

two angles are given, 35 and 90. subtract these from 180 to get 55, the corresponding angle of x. we can then use law of sin to solve.

sin90/12 = sin55/x

sin55 * 12 = 9.8 , 9.8 = sin90x  , 9.8/sin90

=9.8

The limit as x approaches -2 is equal to 0. The correct option is B.

The limit of the function f(x) = x² - 4 / x + 2 as x approaches 2 is equal to 0. This can be evaluated by plugging in x = -2 into the expression for f(x) and simplifying it:-

The limit of the function f(x) = x² - 4 / x + 2 as x approaches -2 is equal to 4. This can be evaluated by plugging in x = -2 into the expression for f(x) and simplifying it:

f(-2) = (-2)² - 4 / -2 + 2 = 4 - 4 / 0 = 0

So, the limit as x approaches -2 is equal to 0.

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The airline fees was $41 each

The over the weight limit of the bag is 3 pounds

Number pounds of Natalie's bag = x

Airline 1:

29 + 4x

Airline 2:

23 + 6x

Equate airlines 1 and 2

29 + 4x = 23 + 6x

collect like terms

29 - 23 = 6x - 4x

6 = 2x

divide both sides by 2

x = 6/2

x = 3 pounds

Hence,

Airline 1:

29 + 4x

= 29 + 4(3)

= 29 + 12

= $41

Airline 2:

23 + 6x

= 23 + 6(3)

= 23 + 18

= $41

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The measure of ∠A is 37.6°. Angle is a geometric figure that can be described as the amount of rotation.

A figure produced by two rays, line segments, or lines that have a same endpoint is called an angle. It is measured in degrees, with a complete 360-degree angle. The Greek letter theta is commonly used to represent it. An angle can be acute (less than 90 degrees), right (90 degrees), obtuse (greater than 90 degrees but less than 180 degrees), straight (180 degrees), or reflex (more than 180 degrees).

∠A is an angle measure and is commonly represented by the symbol "∠A".  calculate the measure of ∠A, an angle must be given in degrees. The answer is then rounded to the nearest hundredth. For example, if the angle measure of ∠A is 37.58°, then the answer would be 37.6°.

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Answer:10[tex]\sqrt{7}[/tex]

Step-by-step explanation:

Answer:

(f,g)=(1,-2)

Step-by-step explanation:

72f-12g=96, 6f-2g=10

72f-12g=96

f=5/3+1/3g

72(5/3+1/3g)-12g=96

g=-2

f=5/3+1/3x(-2)

f=1

(f,g)=(1,2)

The total surface area of the cylinder is S = 45π units²

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the surface area of the cylinder be represented as S

Now , the equation will be

The height of the cylinder h = 4.5 units

The radius of the cylinder r = 3 units

So , Surface area of cylinder = 2πr ( r + h )

Substituting the values in the equation , we get

Surface area of cylinder S = 2π ( 3 ) ( 3 + 4.5 )

On simplifying the equation , we get

Surface area of cylinder S = 2π ( 3 ) ( 7.5 )

Surface area of cylinder S = 45π units²

Hence , the surface area of cylinder is 45π units²

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The extraneous values of the rational function are given as follows:

x = 7 and x = -3.

The extraneous values of a function are the values of x that are outside the function's domain.

In this problem, we have a rational function, hence the extraneous values are the values that make the denominators zero, as follows:

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Since Hong made 162 dollars for 9 hours of work, we can set up the proportion:

162 dollars / 9 hours = x dollars / 13 hours

where x is the amount of money Hong would make for 13 hours of work.

To solve for x, we can cross-multiply and simplify:

162 dollars × 13 hours = 9 hours × x dollars

2106 = 9x

x = 234

Therefore, at the same rate, Hong would make 234 dollars for 13 hours of work.

The simplified form of the expression 2( ³√64 + √25 ) is 18.

Given the expression in the question;

2( ³√64 + √25 )

First, simplify each term.

2( ³√64 + √25 )

Rewrite 64 as 4³

2( ³√( 4³ ) + √25 )

Also, rewrite 25 as 5²

2( ³√( 4³ ) + √( 5² ) )

Now, pull the terms out of the radical, assuming positive real numbers.

Take the cube root of 4³

2( 4 + √( 5² ) )

Take the square root of 5²

2( 4 +  5  )

Add 4 and 5

2( 9 )

Multiply 2 and 9

18

Therefore, the simplified form is 18.

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The graph of the system is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x) = 2x + 8 for x < -1

      -2x + 7 for x > 3

The above system is a piece wise fucntion that include

Two linear equations

Next, we plot the graph

See attachment for the graph of the equation

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The perimeter of the triangle is 36√2

From the question, we have the following parameters that can be used in our computation:

height = 12

Also, we understand that the triangle is an equilateral triangle

This means that the other sides are

Sides = 12√2

The perimeter is then calculated as

Perumeter =3 * Sides

So, we have

Perimeter =3 * 12√2

Evaluate

Perimeter = 36√2

Hence, the perimeter is 36√2

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The value of the expression is [tex]\frac{63}{20}[/tex].

An expression contains more than two variables or numbers with the mathematical operation.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[tex]\frac{1}{4}[/tex] and [tex]\frac{4}{5}[/tex]

Now,

Simplify.

= 7 x [tex]\frac{1}{4}[/tex] + [tex]\frac{1}{5}[/tex]

= 7 x [tex]\frac{5+4}{20}[/tex]

= 7 x [tex]\frac{9}{20}[/tex]

= [tex]\frac{63}{20}[/tex]

Thus,

[tex]\frac{63}{20}[/tex] is the expression.

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The perimeter of the figure is 68+24=92 cm.

The area of Rectangle is length times of width.

In the given figure there is a rectangle and right angle triangle.

The length of rectangle is 16 cm and width is 18 cm

Perimeter=2(length+Breadth)

=2(16+18)

=68 cm

Now let us find perimeter of triangle

Base of height is 6cm and base is 8

P=a+b+√a²+b²

=6+8+√6²+8²

=24

Hence, the perimeter of the figure is 68+24=92 cm.

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Since the fish was share evenly amongst the 3 dolphins, and each one got 6, the equation will be:

f = d x n

where

f represents the fish

d represents the dolphin

n represents the number of fish each got.

Let's assume that the number of fish in the bucket before Colleen feeds the dolphins is "f". To find out how many fish there were in the bucket, you can use the following equation:

f = 3 * 6

where 3 is the number of dolphins and 6 is the number of fish each dolphin gets. Solving for "f", you get:

f = 3 * 6

f = 18

So there were 18 fish in the bucket before Colleen fed the dolphins.

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Answer:

Step-by-step explanation:

x=12wb+rb

probability of rb=5/11

12+11=23

5/23

rb=5/23

Answer: 1m/s

Step-by-step explanation: Accleration = Speed/Time

10/10 = 1