David and his two friends

                [tex]c=30d[/tex]

    Number of days     Cost

          3                         90

          5                         150

           7                         210

          10                        300    

It is given that:

The cost to rent a car is $30 per day.

Now, the expression which is used to represent the cost for renting a car d days is:

  [tex]c=30d[/tex]

where c is the cost of renting a car.

when d=3 we have:

     c=90

( Since, 30×3=90 )

when d=5

      c=150

( Since, 30×5=150 )

when d=7

     c=210

( Since, 30×7=210 )

when d=10

     c=300  

( Since, 30×10=300 )          

Final answer:

The given set contains 10 elements. Subsets with at least one vowel can be found by considering different combinations of vowels in the set which is 3 + 3 + 0 = 6.

Explanation:

The given set m,a,t,h,c,o,u,r,s,e contains 10 elements.

In order to find the number of subsets that contain at least one vowel, we need to consider the possible combinations of vowels in the set.

Therefore, the total number of subsets that contain at least one vowel is 3 + 3 + 0 = 6.

To find the number of subsets of the set m,a,t,h,c,o,u,r,s,e that contain at least one vowel, we can count the number of subsets that have no vowels and subtract it from the total number of subsets.

To find the number of subsets of the set m,a,t,h,c,o,u,r,s,e that contain at least one vowel, we can count the number of subsets that have no vowels and subtract it from the total number of subsets. The given set contains 9 consonants and 5 vowels. So, the number of subsets with no vowels is equal to the number of subsets of the 9 consonants, which is 2^9 = 512.

The total number of subsets of the given set is 2^14 = 16384. Therefore, the number of subsets that contain at least one vowel is 16384 - 512 = 15872.  

Answer:

Step-by-step explanation:

Postulates are suggestion or assumptions that something is true based on reasoning, for example, the definition of a point in Euclidian Geometry.

Therefore, mathematics is grounded in systems of postulates that are tacitly true. Those postulates are used to define and demonstrate theorems, which are the strong structure of every law in Mathematics.

The postulates are helpful as they are  taken to be true without proof and  are basic structure from which lemmas and theorems are derived .

A statement, also known as an axiom, which is taken to be true without proof. Postulates are the basic structure from which lemmas and theorems are derived. The whole of Euclidean geometry, for example, is based on five postulates known as Euclid's postulates.

According to the question

Postulates are helpful because they are basic structure from which lemmas and theorems are derived and they are also known as an axiom, which is taken to be true without proof.  

Hence, postulates are helpful as they are  taken to be true without proof and  are basic structure from which lemmas and theorems are derived .

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Answer: THAT MAKES NO SENCE

Step-by-step explanation:

The entire group will need 3 buses to transport them on the field trip.

Let total number of people in the group be represented by 'P'

We are told that 1/9 of the group can fit on 1/3 of a school bus.

So, this shows 1/9 of P = (1/3) of a bus; we will write an equation to find the total number of buses needed

==>

(1/9)P = (1/3) bus

P = (1/3) bus * 9

P = 9/3

P = 3 buses.

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Final answer:

The probability of picking a bronze medal is found by subtracting the probabilities of picking a gold and a silver medal from 1. As the probability of picking gold is 5/12 and silver is 1/3 (or 4/12), the probability of picking bronze is 1 - (5/12 + 4/12) = 1/4 or 0.25.

Explanation:

The probability of picking each type of medal from the sack adds up to 1 since one of the medals must be picked. Given the probability of picking a gold medal is 5/12 and the probability of picking a silver medal is 1/3, we can calculate the probability of picking a bronze medal by subtracting the probabilities of picking a gold or silver medal from 1.

First, let's find a common denominator for 5/12 and 1/3, which is 12. The probability of picking a silver medal expressed with the denominator 12 is 4/12 (since 1/3 equals 4/12).

Now, we add the probabilities of picking a gold or silver medal: 5/12 + 4/12 = 9/12.

Finally, we subtract this sum from 1 to find the probability of picking a bronze medal:
1 - 9/12 = 3/12, which simplifies to 1/4.

Therefore, the probability of picking a bronze medal is 1/4, or 0.25 when expressed as a number between 0 and 1.

Answer:

[tex]8.76\times 10^6[/tex] is 10,000 times [tex]8.76\times 10^2[/tex].

Step-by-step explanation:

Let [tex]8.76\times 10^6[/tex] be n times [tex]8.76\times 10^2[/tex].

We have been given two numbers [tex]8.76\times 10^6[/tex] and [tex]8.76\times 10^2[/tex].

We can represent this information in an equation as:

[tex]8.76\times 10^2\cdot n=8.76\times 10^6[/tex].

[tex]\frac{8.76\times 10^2\cdot n}{8.76\times 10^2}=\frac{8.76\times 10^6}{8.76\times 10^2}[/tex]

[tex]n=\frac{8.76\times 10^6}{8.76\times 10^2}[/tex]

Using exponent property of fractions [tex]\frac{a^m}{a^n}=a^{m-n}[/tex], we will get:

[tex]n=\frac{8.76\times 10^{6-2}}{8.76}[/tex]

[tex]n=1\times 10^{4}[/tex]

[tex]n=10,000[/tex]

Therefore, [tex]8.76\times 10^6[/tex] is 10,000 times [tex]8.76\times 10^2[/tex].

Answer:

5,378,000,000

Step-by-step explanation: