By what percent will a fraction change if its numerator is increased by 60% and its denominator is decreased by 20%?

Final answer:

To find the number of children wearing helmets correctly, multiply 2/5 by 8,159 to get the number of children wearing helmets, then multiply that result by 13/20 to get the number of children wearing helmets correctly, which is approximately 2,134.

Explanation:

The student's question involves mathematical computations to determine how many children were wearing helmets correctly out of a surveyed group. The data provided indicates that 2/5 of the 8,159 children were wearing helmets, and out of those, 13/20 were wearing the helmets correctly. To calculate the exact number of children wearing helmets correctly, we should perform the following steps:

Calculate the number of children wearing helmets: (2/5) × 8,159 = 3,263.6, which we can round down to 3,263 children, since we cannot have a fraction of a child.

Calculate the number of children wearing helmets correctly: (13/20) × 3,263 = 2,134.95, which we can round down to 2,134 children wearing helmets correctly.

Therefore, approximately 2,134 children were wearing helmets correctly.

To find the volume of a paperweight given its mass of 50g and density of 2.5g/cm³, you can use the formula Volume = Mass/Density. After substituting the given values into the formula the result is 20 cm³.

The question is asking to find the volume of a paperweight given its mass and density. The formula used to find the volume when mass and density are given is: Volume = Mass/Density. Given that your paperweight has a mass of 50g and a density of 2.5g/cm³, you can use this formula to find volume.

First, substitute the values into the formula:

Volume = 50g / 2.5g/cm³

This calculation gives you a volume of 20 cm³. So, your paperweight takes up 20 cubic centimeters of space.

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The number -√17 is an irrational number and is part of the set of real numbers.

The number -√17 belongs to the set of real numbers. However, because this number is the square root of a positive number (17) and is multiplied by negative sign, it is not a rational number, but rather an irrational number.

It is part of the real numbers because the set of real numbers includes all numbers that can be plotted on a number line, including integers, rational numbers (numbers that can be expressed as a quotient of two integers), and irrational numbers (numbers that cannot be expressed as a quotient of two integers).

It is specifically an irrational number because the square root of 17 is a non-repeating, non-terminating decimal, and when we multiply this by a negative sign, the numerical value itself does not change, only its direction on the number line.

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Answer:

The graph in the attached figure

Step-by-step explanation:

we have

[tex]5x-9\leq 21[/tex]

solve the inequality

[tex]5x\leq 21+9[/tex]

[tex]5x\leq 30[/tex]

[tex]x\leq 30/5[/tex]

[tex]x\leq 6[/tex]

The solution is the interval----------> (-∞,6]

All real numbers less than or equal to [tex]6[/tex]

The solution of the inequality is the shaded area to the left of the solid line

see the attached figure

Rory's change in elevation over time is described by the equation e = 300 - 10t. Viable points are (0, 300), (10, 200), (20, 100), and (30, 0) feet, indicating that she reaches sea level after 30 minutes.

Understanding Rory's Change in Elevation:

Rory is walking down a hill from a cabin that is 300 feet above sea level. The equation describing her elevation over time is given by e = 300 - 10t, where e represents elevation regarding sea level, and t is the time in minutes since she started her journey.

Calculating Elevation Points:

To determine the viable points, we'll plug in different values of t into the equation to get corresponding values of e:

When t = 0,
e = 300 - 10(0) = 300 feet

When t = 10,
e = 300 - 10(10) = 200 feet

When t = 20,
e = 300 - 10(20) = 100 feet

When t = 30,
e = 300 - 10(30) = 0 feet

These values suggest that at t = 30 minutes, Rory reaches sea level.

Creating a Table:

The viable points and their corresponding values of e can be summarized in the following table:

(t = 0, e = 300 feet)

(t = 10, e = 200 feet)

(t = 20, e = 100 feet)

(t = 30, e = 0 feet)

The improper fraction of the given expression is [tex]\frac{44}{9}[/tex].

A fraction with a numerator greater than or equal to the denominator is said to be improper. The denominator is the lower number, and the numerator is the top number. When you have wholeness or more than one whole, you can have improper fractions. Here are a few instances of incorrect fractions:

7/5 18/18 100/13

We can see the number of pieces we have in the numerator and the number of parts we are dividing by in the denominator. In the case of an improper fraction, like the first one mentioned above, there are seven parts, each of which is a fifth of the whole.

The improper fraction of [tex]4 \frac{8}{9}[/tex]  [tex]=[/tex] [tex]\frac{(9*4)+8}{9}[/tex]  

                                               [tex]=[/tex] [tex]\frac{36+8}{9}[/tex]

                                               [tex]=[/tex] [tex]\frac{44}{9}[/tex]

Hence, the improper fraction of the [tex]4 \frac{8}{9}[/tex] is [tex]\frac{44}{9}[/tex] .

To learn more about improper fractions

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Final answer:

There are 7,750 different ways the two winners can be chosen from the 125 students volunteering for the prom committee, calculated using the combination formula C(n, k) = n! / (k!(n-k)!).

Explanation:

To determine how many different ways the two winners can be chosen from the 125 students, we need to use the concept of combinations, because the order in which we choose the winners doesn't matter. The formula for combinations is given by:

C(n, k) = n! / (k!(n-k)!)

where:

n represents the total number of items,

k represents the number of items to choose.

For this situation:

n = 125 (total students),
k = 2 (winners to choose).

Therefore,

C(125, 2) = 125! / (2!(125-2)!)

= 125! / (2! * 123!)

= 125 * 124 / (2 * 1)

= 7750

So, there are 7,750 different ways the winners can be chosen to win free tickets to the prom.

we know that

The number [tex]9.125*10^{10}[/tex] is equal to

[tex]9.125*10^{10}=9.125*(10,000,000,000)=91,250,000,000[/tex]

therefore

the answer is

The number in standard form is equal to

[tex]91,250,000,000[/tex]

Answer:

The answer is 1.5

Step-by-step explanation:

Answer:

Part 1 : 29.75

Part 2: 0.75

Part 3: less

Step-by-step explanation:

Floor: 24 * 48 = 1152 square inches

Tile: 8^2 = 64 square inches each

1152/64 = 18 

 18 tiles are needed

Answer:

[tex]\frac{8}{45}[/tex]

Step-by-step explanation:

We are given that

[tex]0.1\bar 7[/tex]

We have to find the value in fraction of given rational number

Let x=[tex]0.1\bar 7[/tex]

Multiply on both side by 10 then we get

[tex]10 x=1.77...[/tex]

[tex]10x=1.6+0.1\bar 7[/tex]

Substitute the value then we get

[tex]10x=1.6+x[/tex]

[tex]10x-x=1.6[/tex]

[tex]9x=1.6[/tex]

[tex]x=\frac{1.6}{9}[/tex]

[tex]x=\frac{16}{90}[/tex]

[tex]x=\frac{8}{45}[/tex]

Hence, the fraction =[tex]\frac{8}{45}[/tex]

Answer:

X = 3

Step-by-step explanation:

to answer this question you must isolate the X. Meaning you must get it by itself.

To get the x by itself you must minus 5 from BOTH sides. This will get the x by itself. That will be your answer

X = 3

Answer:

In the division problem,

The number which is divided is called dividend,

While, the number which divides, is called divisor,

Let dividend = 150 ( a three digit number ),

Divisor = 15 ( a number between 10 and 12 ),

So, the problem would be,

[tex]150\div 15[/tex]

In the below figure,

Take a grid that shows 150,

Divide this grid such that each box represents 15,

Thus, there are such 10 boxes,

That is,

[tex]150\div 15 = 10[/tex]

Answer:the answer is The statement is true, but the inverse is false.

Step-by-step explanation: