It takes Awan 8 1/3 minutes to run a mile, it takes Kate 1 1/5 time longer. How long does it take Kate to run one mile?

The absolute value equation that represents the range of a category 1 hurricane's wind speed is |V - 84.5| ≤ 10.5. 84.5 is the average of the range and 10.5 is the difference from the range's center to the end.

The absolute value equation that represents the minimum and maximum sustained wind speeds of a category 1 hurricane can be written as |V - 84.5| ≤ 10.5. Here, V stands for the wind speed. The middle value of 74 and 95 is 84.5 (the average of 74 and 95). And the distance from 84.5 to either end of the range (74 or 95) is 10.5. So, the range of speeds is represented by the absolute difference from the center of the range is less than or equal to 10.5.

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[tex]\boxed{{\mathbf{40\% }}}[/tex] of the first 10 natural numbers are prime numbers.

Further explanation:  

The prime numbers are the numbers that is only divisible by 1 and itself and greater than 1.

Natural numbers are the numbers that is easily countable as their successors can be defined and its starts from 1.

The natural number can be expressed as,

[tex]1,2,3,4,5,6,7,8,9,10 \ldots[/tex]  

Step by step explanation:

Step 1:

First determine the first ten natural numbers.

[tex]1,2,3,4,5,6,7,8,9,10[/tex]  

Step 2:

Now determine the prime numbers among the first ten natural numbers.

The prime numbers among the first ten natural number are [tex]2,3,5,7[/tex].

Therefore, there are 4 prime numbers.

Step 3:

Now, find the percentage of the first 10 natural numbers are prime numbers.

In general the percentage of any number can be calculated as,

[tex]{\text{percent of  }}x = \dfrac{x}{{{\text{total number}}}} \times 100[/tex]  

The percentage of the prime numbers can be calculated as,

[tex]\begin{aligned}{\text{percent of  prime number}}& = \frac{4}{{{\text{10}}}} \times 100\\ &= 40\% \\\end{aligned}[/tex]  

Therefore, [tex]40\%[/tex] of the first 10 natural numbers are prime numbers.

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Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Percentage

Keywords: Integers, expression, natural numbers, prime numbers, percentage, denominator, numerator, fractions, divisible, total number, the required number

The inequality representing '15 is no more than a number T divided by 5' is written as 15 <= T/5, which means T divided by 5 should be greater than or equal to 15.

The phrase '15 is no more than a number T divided by 5' can be translated into an inequality. When we interpret 'no more than', it means 'less than or equal to'. Therefore, the statement can be translated into the inequality 15 <= T/5. This expresses that when you divide the number T by 5, the result should be at least 15 or any value less than 15. The interpretation of "no more than" as "less than or equal to" clarifies the inequality's meaning, emphasizing that the resulting quotient from dividing T by 5 should not exceed 15. Thus, the inequality encapsulates the relationship between the number 15 and T when considering their division by 5.

The solution after divide is,

⇒ 0.893

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

To divide the numbers,

⇒ 25 divided by 28

Now, We can divide the numbers as;

⇒ 25 divided by 28

⇒ 25 ÷ 28

⇒ 25 / 28

⇒ 0.893

Thus, The solution after divide of the numbers is,

⇒ 0.893

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Tony is not correct. The midway point between 4,000 and 5,000 is found by calculating the average of the two numbers, which is 4,500. Therefore, the halfway point is 4,500, not 4,400.

Tony states that 4,400 is halfway between 4,000 and 5,000. To determine if Tony is correct, we need to find the midpoint between the two numbers. The midpoint can be found by adding the two numbers together and dividing by 2:

(4,000 + 5,000) / 2 = 9,000 / 2 = 4,500.

Therefore, the exact halfway point between 4,000 and 5,000 is 4,500. This means that Tony's assertion that 4,400 is halfway between these two numbers is not correct; the correct halfway point is actually 4,500.

No, Tony is not correct. Halfway between 4,000 and 5,000 would be the average of the two numbers, which is 4,500.

No, Tony is not correct. Halfway between 4,000 and 5,000 would be the average of the two numbers. To find the average, we add the two numbers together and divide by 2. In this case, the average of 4,000 and 5,000 would be (4,000 + 5,000) / 2 = 9,000 / 2 = 4,500. Therefore, 4,400 is not halfway between 4,000 and 5,000.

Infinite is the answer

Answer:

23

Step-by-step explanation:

Imagine that each person is assigned one wall, and all 6 people begin painting at the same time.

Since everyone will finish painting their assigned wall after 23 minutes, it takes one person 23 minutes to paint one wall.

If we have 9 people and 9 walls, we can again assign one wall to each person.

Everyone will take 23 minutes to paint their assigned wall.

In other words, it takes 23 minutes for 9 people to paint 9 walls.

Let x denotes the number of days and y denotes the total change in gas price ( in dollars).

Given : During the past seven days the price of regular gas is decreased by $0.2 each day.

Rate of decrease =$0.2 per day

Then , Total change in gas price = Rate of decrease x Number of days

i.e.[tex]y= 0.2 \times x[/tex]

i.e. [tex]y=0.2x[/tex]         (1)

To find the total change in gas price in 7 days , we put x= 7 in (1) , we get

[tex]y=0.2(7)=1.4[/tex]    

Hence, the total change in gas price in 7 days = $1.4

Answer:

0.14

Step-by-step explanation:

Let t be the total reduction. Then ...  

t = daily change * number of days  

t = 7 * 0.02  

t = $0.14!

Answer:

The rate of the area increasing for square is 24cm²/ s

            Rate of increasing side ?

    Changing the length of side with respect to time is the rate of increasing side .

    Given each side of square is increasing at a rate 3cm/s.

          Area of square = sides²

           Side length = a

       (dA/dt) = (dA/da)×(da/dt) { chain rule of differentiation}

             Differentiation of area w.r.t. t is

                dA/da= 2a (da/dt)

                dA/dt = 2a *(da/dt)

                 da/dt = 3 cm/s

              When A=16 cm²

                      16 = a²

                         a= 4

                (dA/dt) = 2x4 x 3

                           = 24 cm²/ s

Hence, the rate of the area increasing for square is 24cm²/s

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Answer: its the third option

There are 2 glasses of full water would be needed to fill the baking pan.

What is an expression?

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

Given that;

A drinking glass has height of 4 inches ,in a length of 2 inches and 2 inches in width.

And, A baking pan has a width of 4 inches length of 8 inches and a depth of 2 inches.

Now,

The volume of drinking water = 4 x 2 x 2

                                              = 16 inches³

And, The volume of baking pan = 4 x 8 x 2

                                                 = 64 inches³

So, Half depth of baking pan =  64 / 2

                                             = 32 inches³

Here, The volume of drinking water = 16 inches³

Thus, Number of glass of full water would be needed to fill the baking pan = 32 / 16 = 2

Therefore, There are 2 glasses of full water would be needed to fill the baking pan.

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Let the first integer be represented by: 2k

the second integer by: 2(k+1)

and the third by: 2(k+2)

Then, 2k + 2(k+1) = 2(k+2) + 30

2k + 2k + 2 = 2k + 4 + 30

4k + 2 = 2k + 34

2k = 32

k = 16

first integer: 2k = 2(16) = 32

second integer: 2(k+1) = 2(16+1) = 2(17) = 34

third integer: 2(k+2) = 2(16+2) = 2(18) = 36

Answer: 32, 34, 36

Final answer:

To find the two numbers, we set up two equations, solve for one variable, and find the other. The numbers that satisfy the condition of one exceeding the other by 1 with their sum being 29 are 14 and 15.

Explanation:

The student's question involves finding two numbers where one number exceeds the other by 1 and their sum is 29. To solve this, let's set up a system of equations. We'll call the first number x and the second number y. Based on the question:

x = y + 1 (one number exceeds the other by 1)

x + y = 29 (the sum of the numbers is 29)

Substituting the first equation into the second gives us:

(y + 1) + y = 29

2y + 1 = 29

2y = 28

y = 14

Now that we have the value of y, we can find x:

x = y + 1

x = 14 + 1

x = 15

Therefore, the two numbers are 14 and 15.

To find out how many DVDs you can buy for the same price at both stores, you create a formula incorporating the cost per DVD and the shipping cost at the online store. Solving this equation will give you the number of DVDs where the cost will be equal at both stores. However, this might not always result in a whole number, indicating that there is no exact count of DVDs resulting in the same cost.

To determine how many DVDs you can buy for the same amount at both stores, you can set up a mathematical equation accounting for the cost of each DVD and the shipping cost in the online store. The equation would look like this:

15.49 x = 13.99 y + 6

where x and y represent the number of DVDs bought from the local and online store respectively. By solving this equation we're finding out for which number of DVDs the total costs at both stores are equal.

To find the exact number of DVDs where the total cost will be the same, the equation needs to be solved for a whole number. This may result in no exact integer solution, showing that there's no exact number of DVDs for which the cost will be the same at both stores.

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