5x4> 12
AND 12x +5 ≤-4

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)

Answer:

Maths

Step-by-step explanation:

We find the percent equivalent of each test.

Maths: 14 out of 17

percent = part/whole × 100%

percent = 14/17 × 100%

percent = 82.35%

English: 31 out of 39

percent = part/whole × 100%

percent = 31/39 × 100%

percent = 79.49%

Since 82.35% > 79.49%, she did better in Maths.

Answer: Maths

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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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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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 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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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?

a) The vertex is, (20, 800) and its mean at the length of 20 the area is 800.

b) At 0 and 40 length the area is zero.

c) At length interval (20, 40), the area is decreasing.

d) At the area 600 the length is 30.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The graph is shown in figure.

Hence, By the figure we have;

a) The vertex is, (20, 800) and its mean at the length of 20 the area is 800.

b) At 0 and 40 length the area is zero.

c) At length interval (20, 40), the area is decreasing.

d) At the area 600 the length is 30.

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use pythagorean theorem : a²+b²=c²

Answer

4x6=24

24x1 ml=24ml

Answer:

 the answer to your question is 24 milliliters!

Step-by-step explanation:

good luck!

Other things constant, how will an increase in the wage of teenagers affect the market for fast food hamburgers will cause the supply of fast food hamburgers will increase, leading to an increase in price of hamburgers. Option A

supply is the amount of a resource that firms, producers, laborer, providers of financial assets, or other economic agents are willing and able to provide to the marketplace or to an individual.

The law of supply in economics states that supply will increase as price increases, due to the fact that producers want to maximize profits. In this instance, the law assumes that all other factors are equal and price is the only independent element, meaning supply is completely dependent on the price.

Hence, an increase in the wages of teenager will lead to an increase in the quantity of hamburgers demanded, which will also leads to an increase in supply.

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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: 1m/s

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

10/10 = 1

a. The type of figure shown is a triangular prism.

b. The surface area of the figure is 118.5 sq. in.

A triangular prism is a 3 dimensional shape which has 2 triangular surfaces and a rectangular base. It has 5 surfaces in total.

Considering the given figure in the question, we have;

a. The type of figure shown is a triangular prism.

b. The surface area of the prism can be deduced as follows;

area of one of its triangular surfaces = 1/2*base*height

                                       = 1/2*5*1.7

                                       = 4.25 sq. in.

area of its base = length x width

                   = 10x 5

                   = 50 sq. in.

area of one of its slant sides = length x width

                      = 10 x 3

                      = 30 sq. in.

Therefore, the surface area of the figure = (2*4.25) + 50 + (2*30)

                                    = 8.5 + 50 + 60

                                     = 118.5 sq. in.

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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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Reason:

-2 * 2 = -4

-2 + 2 = 0

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

So the solution of the given question is,  the correct answer is D) Both data sets represent multiplicative relationships. from the given conditions.

In mathematics, a multiplicative relationship between two variables means that the ratio of their values remains constant as the values of the variables change. In other words, the product of the two variables is a constant. For example, if we have two variables x and y such that xy = k, where k is a constant, then x and y have a multiplicative relationship. If we increase the value of one variable, we must decrease the value of the other variable proportion in order to maintain the constant product. This type of relationship is often seen in situations involving rates, ratios, and proportions, such as in growth or decay processes, population dynamics, and financial calculations.

In Table A, y is 2.5 times x, and in Table B, y is 3 times x. In both tables, the relationship between x and y is a constant ratio, which is a characteristic of multiplicative relationships. In Table A, the ratio of y to x is always 2.5, meaning that y is always 2.5 times greater than x. In Table B, the ratio of y to x is always 3, meaning that y is always 3 times greater than x. Therefore, both tables represent multiplicative relationships between x and y.

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Answer:

they are both circles

Step-by-step explanation:

Answer:

A=a+b/2 x h

Step-by-step explanation:

The area for a trapezoid is a+b divided by 2, multiplied by the height.

Since there are no lengths given, I cannot be solved.

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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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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 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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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:

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 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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In this using the knowledge of computational language in python, we have that this code will be written as:

Here's an algorithm in pseudocode that you can use to find all the common elements in two sorted lists of numbers:

Input: two sorted lists A and B of size N and M respectively.

Output: a list C of all common elements in A and B.

C = [ ]

i = j = 0

while i < N and j < M:

   if A[i] == B[j]:

       C.append(A[i])

       i += 1

       j += 1

   else if A[i] < B[j]:

       i += 1

   else:

       j += 1

return C

In this algorithm, two pointers i and j are used to traverse both lists A and B. At each step, the algorithm compares the elements at the current positions of i and j in A and B respectively. If they are equal, it means the element is common to both lists, so it is added to the result list C. If the element in list A is less than the element in list B, i is incremented to move to the next element in list A. Similarly, if the element in list B is less, j is incremented to move to the next element in list B.

The algorithm continues this process until either one of the lists is fully traversed.

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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.

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 price after the discount but before tax, to the nearest dollar and cent is $24.

Discounts are price reductions that store owners make on items or services that are otherwise priced as marked. This portion of the refund is typically provided to boost sales or get rid of excess inventory. The price of an item as stated by the manufacturer or seller, without any price decrease, is known as the List price or Marked Price. After any discounts or price reductions from the list price, the selling price is the final price at which an item is actually sold. "Off",

Discount is equal to List Price – Selling Price.

Given that, the store was offering a 40% discount.

The discount on the price tag of $40 is:

Discount = 40 (40/100) = $16.

The new price after the discount but before tax is:

New price = 40 - 16

New price = $24.

Hence, the price after the discount but before tax, to the nearest dollar and cent is $24.

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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