The table below shows the cost of mailing a postcard in different years. During
which time interval did the cost increase at the greatest average rate?

Step-by-step explanation:

a)

any prime number has only 2 (1 and the number itself).

almost every even number has 1, 2, a factor of 2 and the number itself. so that did not work either.

following that line of thought, the only possible solutions are square numbers of prime numbers :

4, 9, 25, 49

they have only 1, its square root and the number itself as factors.

b)

in the same line of thinking it must be powers of 4 of prime numbers :

2⁴ = 16

with the factors 1, 2, 4, 8, 16

3⁴ = 81

with the factors 1, 3, 9, 27, 81

c)

and so, it must be a power of 6 of a prime number.

the only one possible is

2⁶ = 64

with the factors 1, 2, 4, 8, 16, 32, 64

Number of child tickets were sold on Wednesday is 33 if three times as many adult tickets as child tickets were sold.

According to the question

At the city museum, child admission is $6.30 and adult admission is $9.80. On Wednesday, three times as many adult tickets as child tickets were sold, for a total sales of $ 1178.10

Number of Child admission = x

Number of Adult admission = y

On Wednesday ;

y = 3x

9.80y + 6.30x = 1178.10

9.80(3x) + 6.30x = 1178.10

29.40x + 6.30x = 1178.10

35.70x = 1178.10

x = 1178.10 / 35.70

x = 33

So, 33 child tickets were sold on Wednesday.

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The complete question is

At the city museum, child admission is $6.30 and adult admission is $9.80. On Wednesday, three times as many adult tickets as child tickets were sold, for a total sales of $ 1178.10 . How many child tickets were sold that day?

Answer:

So the polynomial function is

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

Step-by-step explanation:

A polynomial function of lowest degree in standard form with roots x = 1, 3, and 2i can be written as (x - 1), (x - 3), and (x - 2i),

From the above data we can get,

k(x) = (x - 1)(x - 3)(x - 2i)

After expanding the equation ,

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

So the polynomial function is

k(x) = x^3 - 6x^2 + 11x - 6 - 6i

Answer:

Step-by-step explanation:

make the inequality y=3x-7 to get the linear line then find x=0 with is -7 and anything below that line or on the line is not part of the inequality therefore remember to graph with a dotted line instead of a solid.

Answer:

Step-by-step explanation:

The required equation that can be used to determine the price of each gallon of gas is 8.4x = 23.94. Option A is correct.What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.here,Let the cost of gas per gallon be x,Now according to the question,Cost of 8.4 gallons of fuel = 8.4xfrom the question,8.4x = 23.94Thus, the required equation that can be used to determine the price of each gallon of gas is 8.4x = 23.94. Option A is correct.

Answer: 825 workers altogether

Step-by-step explanation:

well, if the ratio is 4.5 men to every woman, we just have to multiply 150 by 4.5, which means there will be 675 male workers and 150 female workers.

One solution exists for the following system of equations. In this question, correct answer is option (5) which states the solution is point

(3 , 2).

There are many various ways to define an equation. The definition of an equation in algebra is a mathematical statement that illustrates the equality of two mathematical expressions.

As we know that when the system of equations are given in graph form ,

then the solution to them is the number of points they intersect each other.

Now in the given question,

In the given graph it can be clearly seen that graphs of equations meet at one point. The point at which the graph meets is (3 , 2).

We can see that option (5) is correct.

So the given system of equations have one solution.

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Answer:

n = 3

Step-by-step explanation:

Starting equation:

2n + 4 = n + 7

Subtract by n on both sides:

n + 4 = 7

Subtract 4 on both sides

n = 3

Check to see if the answer works:

2(3) + 4 = 3 + 7

6 + 4 = 3 + 7

10 = 10

The solution works

n = 3

Answer: x = -3, 1/2

Step-by-step explanation:

Using the given linear equation, we found the altitude of the plane at different time periods and the altitude of airplane at 5 and 30 minutes is found to be 250 feet and 0 feet respectively.

What is a linear equation?

A linear equation is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear equation with exponents greater than 1. A linear equation's graph almost always takes the shape of a straight line.

The linear equation which shows the altitude of an airplane is as follows,

y = -10x + 300

where y = altitude (in feet)

           x = time of descend ( minutes)

a) when x = 0

     y = 300 feet

  when x = 5 minutes

    y = -10 * 5 + 300 = 250 feet

 when x = 8 minutes

   y = -10 * 8 + 300 = 220 feet

when x = 10 minutes

 y = -10 * 10 + 300 = 200 feet

when x = 30 minutes

y = -10 * 30 + 300 = 0 feet.

the table is as follows:

x (minutes)     0         5          8          10       30

y(feet)            300    250     220     200       0

b) From the above table, we can see that at 5 minutes the altitude is 250 feet and at 30 minutes, the altitude is 0 feet. There is a decrease in altitude, which suggests the plane is descending and finally landed when the time was 30 minutes.

Therefore using the given linear equation, we found the altitude of the plane at different time periods and discussed the altitude of airplane at 5 and 30 minutes.

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The measure of the other angle of the parallelogram is 22 degrees.

Opposite angles of a parallelogram are equal (or congruent).

Let the missing angle be represented by x.

Since the opposite angles of a parallelogram are equal (or congruent).

x = 2x - 22

Solve for x

2x - 22 = x

2x = 22 + x

2x - x = 22

x = 22°

Therefore, 22 degrees is the measure of the other angle.

Option C) 22° is the correct answer.

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Answer:

1.25 laps per minute

Step-by-step explanation:

5 laps in 4 minutes so distance over time is equal to rate so

5/4=1.25

Answer:

x=10

Step-by-step explanation:

First, add 5 to both sides of the equation, getting rid of the -5 on the left side but still making them equal.

5x=3x+20

Then, do the same with 3x, Subtract from both sides.

2x=20

Lastly, Divide both sides by 2 and you'll get your answer

x=10

Answer:

[tex] \sf \: x = 10[/tex]

Step-by-step explanation:

Now we have to,

→ Find the required value of x.

The equation is,

→ 5x - 5 = 3x + 15

Then the value of x will be,

→ 5x - 5 = 3x + 15

→ 5x - 3x = 15 + 5

→ 2x = 20

→ x = 20 ÷ 2

→ [ x = 10 ]

Hence, the value of x is 10.

The addition of two numbers is 410+210 is 620.

From the given numbers,

First number is 410

Second number is 210.

One of the arithmetic operations is addition. The total of the numbers is provided. In other words, addition refers to the operation of adding the numbers together. "+" is the symbol used to denote addition. The outcome of the adding procedure is referred to as the sum. Addends are the numbers that are added together.

The following are the rules of addition operation:

Now,

⇒410+210=620

Therefore, the value is 620.

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The number of pieces in a jigsaw puzzle and the number of minutes required for a person to complete are not directly related. The time it takes for a person to complete a jigsaw puzzle depends on several factors, including the person's experience with puzzles, the level of difficulty of the puzzle, the size of the puzzle pieces, and the person's level of concentration.

For example, a 500-piece puzzle might take one person several hours to complete, while another person might be able to finish it in just a few hours. Similarly, a 1000-piece puzzle might take one person a full day to complete, while another person might be able to finish it in just a few hours.

In general, the larger the number of pieces in a puzzle, the more time it will take to complete. However, the actual time required can vary greatly depending on the individual and the specific puzzle.

Answer:

Step-by-step explanation:

Advantages of Fifth Generatin of Computer:These computers are much faster than other generation computers. Development of true artificial intelligence.

Development of Natural language processing.

Advancement in Parallel Processing. Advancement in Superconductor technology. More user-friendly interfaces with multimedia features. Availability of very powerful and compact computers at cheaper rates.

Disadvantages of Fifth Generatin of Computer: They tend to be sophisticated and complex tools. ...

Example of Third Generation of Computer: Desktop.

Sarah should blend 80.5 pounds of the high-quality beans and 39.5 pounds of the cheaper beans to make 120 pounds of blended coffee.

In this problem, we are given that Sarah Meeham needs to prepare 120 pounds of blended coffee beans to sell at a rate of $4.17 per pound. She plans to blend two types of coffee beans: a high-quality bean costing $5.25 per pound and a cheaper bean costing $2.00 per pound.

Let x be the number of pounds of the high-quality coffee beans needed and y be the number of pounds of the cheaper coffee beans needed. Since we need 120 pounds of the blended coffee, we have:

x + y = 120

The cost of the blended coffee is $4.17 per pound. This means that the total cost of the blended coffee is:

4.17(120) = 501.6

We can also find the cost of the high-quality and cheaper beans in terms of x and y:

5.25x is the cost of the high-quality beans

2.00y is the cost of the cheaper beans

The total cost of the two types of beans is the sum of their individual costs:

5.25x + 2.00y

Since we need 120 pounds of the blended coffee, we can set up the following equation using the above expressions for total cost:

5.25x + 2.00y = 501.6

Now, we can use the system of equations consisting of x + y = 120 and 5.25x + 2.00y = 501.6 to solve for x and y. One way to do this is by substitution:

x = 120 - y (from the first equation)

5.25(120 - y) + 2.00y = 501.6 (substituting x in the second equation)

Simplifying and solving for y, we get:

630 - 5.25y + 2.00y = 501.6

3.25y = 128.4

y ≈ 39.5

Now we can use this value of y to find x:

x = 120 - y

x = 120 - 39.5

x ≈ 80.5

Therefore, Sarah needs to blend approximately 80.5 pounds of the high-quality coffee beans and 39.5 pounds of the cheaper coffee beans to make 120 pounds of blended coffee that she can sell for $4.17 per pound.

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The area of the right triangular puppy pen found using the formula 1/2(b.h²) is 4900.90 feet².

What is a triangle?

A polygon with three edges and three vertices is called a triangle. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. A right triangle is a specific kind of triangle that has one angle that is exactly 90 degrees.

Given,

 The length of OY = 12 feet

The length of DY = 31 feet

m∠OYD = 65°

Since SDOG is a rectangle, m∠DOY = 90°.

So the ΔDOY is a right triangle.

Area of right triangle = 1/2 * b * h²

where b = base length

          h = height

From the given figure,

b = OY = 12

h = OD

h can be found using Pythagoras' theorem.

DY² = OD² + OY²

OD² = DY² - OY² = 31² - 12²  = 817

OD = √817 = 28.58 feet = h

Therefore the area of the right triangle ΔDOY is

area =  1/2 * b * h² = 0.5 * 12 *28.58² = 4900.90 feet².  

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The dimensions will be as follows;

width is 5cm while the length is 20cm.

Let width = w

Let length = 4w (according to question)

Perimeter = 50cm

Perimeter formula for a rectangle = 2 (l +w)

Substituting in the variables (width and length)

2(w + 4w) = 50

2(5w) = 50

10w = 50

w = 5

Remember that length = 4w

length = 4w

length = 4(5)

length = 20cm

Therefore, the dimensions of the rectangle are 5cm by 20 cm.

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Answer:

-----------------------

Given measurements:

Bring all to same unit, grams, then compare;

Order them from smallest to largest:

Answer:

The order of the measurements from smallest to largest is:

Step-by-step explanation:

The three given measurements of mass are:

Therefore, to be able to order the three given measurements from smallest to largest, first convert them to the same unit of mass (grams):

⇒ 3,000 g = 3,000 g

⇒ 60,000 mg = 60,000 × 0.001 = 60 g

⇒ 1.5 kg = 1.5 × 1000 = 1,500 g

Therefore, the order of the measurements in grams from smallest to largest is:

So, the order of the measurements in their original units from smallest to largest is:

Answer:

Area = 15a^3b^6

Perimeter: 10a^2b^4+6ab^2

Step-by-step explanation:

Formula For Area: L*W

Input The Numbers: 5a^2b^4 * 3ab^2

5a^2b^4 * 3ab^2 = 15a^3b^6

Area = 15a^3b^6

Formula for perimeter: P=2(l+w)

Input the Numbers: P = 2(5a^2b^4 + 3ab^2)

2(5a^2b^4 + 3ab^2) = 10a^2b^4+6ab^2

Perimeter: 10a^2b^4+6ab^2

Hope this helped!

The function g(x) can be written as -

g(x) = f(x - 1)

Graph translation is a process of moving the graph over the dimensional plane either vertically, horizontally or both.

A translation can take place either horizontally or vertically as -

Given are the graphs of exponential functions f(x) and g(x).

We can write the exponential function g(x) as -

g(x) = f(x - 1)

Therefore, the exponential function g(x) can be written as -

g(x) = f(x - 1).

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The required weight of a hippo in pounds is given as 3,000 pounds.

What is a unit of measurement?

Unit of measurement is defined as every entity having its measures in dimensions, weight, and time. Such as for length we have a meter, for liquid we have liters, and so on.

Here,
One ton is equal to 2,000 pounds, so a hippo that weighs 1.5 tons would weigh,

1.5 tons × 2,000 pounds/ton = 3,000 pounds

Therefore, the hippo at the zoo weighs 3,000 pounds.

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If the sales tax rate is 6% and if Sally buy rowboat priced at $842, the amount of tax she will pay,  $50.52

Percentage is a way to express a number as a fraction of 100. It is often used to represent ratios and proportions in a more convenient and understandable form, especially in financial and statistical contexts. For example, 50% means 50 per 100, or half of a given quantity. It is denoted using the symbol "%".

To calculate the sales tax on the purchase of a sailboat priced at $842 with a sales tax rate of 6%, you can follow these steps:

1. Convert the sales tax rate from a percentage to a decimal by dividing by:

= 100: 6% ÷ 100

= 0.06.

2. Multiply the price of the sailboat by the sales tax rate to find the amount of tax:

= $842 × 0.06

= $50.52.

Therefore, Sally will pay $50.52 in sales tax for the purchase of the sailboat.

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A helium tank shaped like a cylinder has 2,401π in³ of space inside the tank. If the diameter of the helium tank is 14 inches,  its height is 1 inch.

Volume is a measure of the amount of space occupied by a three-dimensional object or a region of space. It is usually measured in units such as cubic meters (m³), cubic centimeters (cm³), cubic inches (in³), or liters (L).

For a solid object, such as a cube, cylinder, or sphere, volume is calculated by measuring the length, width, and height of the object and using a formula that is specific to that shape. For irregularly shaped objects, such as rocks or trees, volume can be determined by using techniques such as water displacement.

The volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

In this case, we are given the diameter of the cylinder, which is 14 inches. The radius of the cylinder is half of the diameter, so r = 7 inches.

We are also given the volume of the cylinder, which is 2,401π cubic inches.

Using the formula for the volume of a cylinder, we can set up the following equation:

2,401π = π(7)²h

Simplifying this equation, we get:

2,401 = 49h

Dividing both sides by 49, we get:

h = 49/49 = 1

Therefore, the height of the helium tank is 1 inch.

However, this answer seems unlikely since the height of the tank should be greater than its radius. Therefore, there may be an error in the given volume or diameter of the tank.

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the answer is A its height is 49

Answer:

Step-by-step explanation:

The perimeter of the rectangle: We know that the frame is equal to 2(L+B)

therefore, the edge of a rectangle is 2[5a^2b^4 + 3ab^2]

                        = 2[ab^2(5ab^2 + 3)]

The area of a rectangle is L * B

                       =  (5a^2b^4) * (3ab^2)

                       =  15a^3b^6

Answer:

69 meters

Step-by-step explanation:

Answer:

1. The formula for the area of a circle is given by A = πr^2, where r is the radius of the circle. To find the area of the 12" pizza, we first need to find the radius:

r = 12 / 2 = 6 inches

The area of the pizza is then:

A = πr^2 = π * 6^2 = 36π square inches

2. To find the radius of a pizza that is 25% larger, we can first find the amount by which the radius will increase:

increase = 6 * 0.25 = 1.5 inches

The new radius will then be:

new_r = 6 + 1.5 = 7.5 inches.

Step-by-step explanation:

Answer:

113.1, 8

The equation to find the area of a circle is:

Now we can input 12 into the equation:

To find the radius of a pizza that is %25 larger, we can use this equation:

Well, that's a good question! If we were to multiply by 0.25, the radius would get smaller, instead of bigger. We add the 1.0 because we have to add the original radius, not just the added length.

Fitting the radius into the equation:

Therefore, the area of the pizza is 113.1, and the radius of a pizza that is %25 larger is 8.