free-falling body: h = -15t + 1/2at^2 + 5 (Solve for a)

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!

Final answer:

The donations in 2012 had a more dispersed distribution than in 2013, as indicated by a higher coefficient of variation of 20% compared to 15% in 2013.

Explanation:

To determine which year had a more dispersed contribution distribution, we examine the coefficient of variation (CV), which is calculated by dividing the standard deviation by the mean and then multiplying by 100 to express it as a percentage. A higher CV indicates a more dispersed distribution.

For 2012:

For 2013:

Comparing the coefficients of variation, we can conclude that the donations in 2012 had a more dispersed distribution than in 2013 since the CV in 2012 was higher.

[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

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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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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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

xm-2m

x=-2, m = -3

xm = -2 *-3 = 6

2m = 2*-3 = -6

6- -6 = 6+6 = 12

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.

Answer: its the third option

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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The mean travel distance for the sample of 100 customers surveyed by the manager at First City Bank is considered a statistic.

The mean travel distance for the sample of 100 customers surveyed by the manager at First City Bank is considered a statistic.

In statistics, a parameter is a numerical characteristic of the whole population that can be estimated by a statistic. Since the manager is surveying only a sample of customers, the mean travel distance calculated from this sample is a statistic, not a parameter.

For example, if the manager had surveyed all customers of First City Bank, then the mean travel distance calculated from that data would be a parameter.

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.