solve (6-5x)/10-(2x+1)/5+x/3=2x/15

Answer:

The mistake is the sing of the "3" on the second term.

a=1

Step-by-step explanation:

The mistake was changing the sing of the second term in the first step. You could found it highlighted below.

4a-5=2a-3

4a-2a-5=3  ( the correct expression will be 4a-2a-5=-3)

2a-5=3

2a=8

So ,  the correct answer is

4a-2a-5=-3

2a=5-3

2a=2

a=1

Answer:

[tex]2d+35[/tex]

Step-by-step explanation:

Let d represents the number of dogs that will attend the event.

She wants to have 2 biscuits per dog plus an additional 35 dog biscuits.

So, the expression that represents the number of dog biscuits Nicole will need for the event is :

[tex]2d+35[/tex]

2d because 2 biscuits for each dog where 'd' is the number of dogs. And 35 is constant because she will be taking extra 35 with her.

Answer:

look at the screenshots below! all correct test answers!

Step-by-step explanation:

The sum of the charges in the neon atom is 0 if the neon atom has 10 protons and 10 electrons and the 10 protons have a charge of +10 and the 10 electrons have a charge of −10.

It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.

It is given that:

A neon atom has 10 protons and 10 electrons. The 10 protons have a charge of +10 and the 10 electrons have a charge of −10.

No other particles in the atom have a charge.

Total charge:

= sum of the charge on the electron + sum of the charge of the protons

As we know, the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

Total charge = +10 + (-10)

Total charge = +10 -10

Total charge = 0

If we plot the above situation on a number line we will get the total charge is zero.

Thus, the sum of the charges in the neon atom is 0 if the neon atom has 10 protons and 10 electrons and the 10 protons have a charge of +10 and the 10 electrons have a charge of −10.

Learn more about the number line here:

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The expression 8⋅54 can be rewritten as 8⋅(50 + 4) using the distributive property. This mathematical property allows us to break down the sum and perform the multiplication individually.

The expression 8⋅54 can be rewritten using the distributive property in mathematics as 8⋅(50 + 4). This property allows you to multiply a sum by breaking it into two parts - in this case, 54 is broken down into 50 and 4. The multiplication is then performed on both these parts separately. When using the distributive property, we follow the steps:

1. Identify the number to be distributed, in this case, it's 8.

2. Break down the other number into two simpler components we can easily multiply with, like 50 and 4 for 54.

3. Multiply the distributing number with each of these parts separately. That gives us: 8⋅50 and 8⋅4.

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The distance covered by an airplane flying at 300mph for 7 hours is 2100 miles.

Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement.

Given that, an airplane flying at 300mph for 7 hours,

Speed = distance/time

Distance = speed×time

Distance covered in 7 hours = 300×7 = 2100

Hence, the distance covered by the airplane is 2100 miles.

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Final answer:

There are 800 possible area codes and exchange numbers each, following the given digit restrictions. The total number of unique 10-digit phone numbers given these rules is 6,400,000,000, which is sufficient considering a population of about 400,000,000.

Explanation:

The question addresses how many different area codes and phone numbers are possible given certain digit restrictions for both the United States and Canada. For the area code, the first digit can be any from 2 to 9, which gives us 8 possibilities, and the second and third digits can be any from 0 to 9, which provides 10 possibilities each. Therefore, the number of different area codes is 8 × 10 × 10 = 800.

Applying the same rules to the exchange number, which also has three digits, we have another 800 possibilities. Considering there are 10,000 combinations for the last four digits (from 0000 to 9999), we can calculate the total number of unique 10-digit phone numbers by multiplying the possibilities for the area code, exchange number, and the last four digits: 800 × 800 × 10,000 = 6,400,000,000 possible phone numbers.

Since the combined population of the United States, Canada, and a few islands is about 400,000,000, this amount of possible phone numbers is more than sufficient to provide a unique phone number for every individual.

Answer:

B. 33 years.

Step-by-step explanation:

Let N represent Nia's age in years.

We have been given that Nia is 3 years younger than Jordan. So Jordan's age would be 3 years more than Nia's age that is [tex]N+3[/tex] years.

We are told that Jordan is 36 years old.  We can represent this information in an equation as:

[tex]N+3=36[/tex]

[tex]N+3-3=36-3[/tex]

[tex]N=33[/tex]

Therefore, Nia's age is 33 years.

5 1/2 gallons of water is equivalent to 88 cups of water. This is calculated by understanding that one gallon equals 16 cups, and therefore multiplying 5.5 (5 1/2 in decimal form) by 16.

The subject of this question is a simple conversion in mathematics. To make this conversion, we need to understand the basic relationship between gallons and cups. In U.S. standard measurements, one gallon is equivalent to 16 cups. So, if we have 5 1/2 gallons, we would multiply this by 16 to get the equivalent number of cups. Hence, 5.5 (which is 5 1/2 in decimal form) multiplied by 16 equals 88. So, 5 1/2 gallons of water is equivalent to 88 cups of water.

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To find the distance Drake walked, calculate 2/3 of 7/8 mile, which results in 14/24, and simplify this fraction to 7/12 mile. Therefore, Drake walked 7/12 mile when he met Scott.

Drake lives 7/8 mile from the park. To find out how far he walked when he met Scott after walking 2/3 of the way to the park, you need to calculate 2/3 of 7/8 mile. The calculation is as follows:

Distance walked = (2/3) * (7/8)

First, multiply the numerators together: 2 * 7 = 14.

Then, multiply the denominators together: 3 * 8 = 24.

Now, put it together:
Distance walked = 14/24

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

So, 14 / 2 = 7 and 24 / 2 = 12.

Therefore, the simplified fraction is 7/12 mile.

Drake walked 7/12 mile when he met Scott.

Answer:  The required percentage is 40%.

Step-by-step explanation:  We are given to find the percentage of the first 20 natural numbers that are prime.

We know that

first 20 natural numbers are 1, 2, 3, 4,  .  .  .  , 19, 20.

And, the prime numbers among them are 2, 3, 5, 7, 11, 13, 17 and 19.

So, if S be the sample space for the experiment and A be the event of selecting a prime number.

Then, we have

n(S) = 20  and  n(A) = 8.

Therefore, the probability of event A is given by

[tex]P(A)=\dfrac{n(A)}{n(S)}=\dfrac{8}{20}=\dfrac{2}{5}\times100\%=40\%.[/tex]

Thus, the required percentage is 40%.  

Final answer:

Multiplying two negative integers always results in a positive integer because the negatives cancel each other out.

Explanation:

When you multiply two negative integers, the result will always be a positive integer. Each negative sign cancels the other out, leading to a positive product. For example, if you take two negative integers such as -2 and -3, when you multiply them (-2) x (-3), you obtain 6, which is a positive integer. This is a consistent rule in mathematics, so whenever you multiply two negatives, you can expect the result to be positive.

By breaking down each number into its place value parts, performing six separate multiplications, and then adding those products together, you can multiply a three-digit number by a two-digit number.

The multiplication of a three-digit number by a two-digit number can be accomplished via place value and partial products. To illustrate, consider multiplying 123 by 25. Begin by breaking down 123 into 100 + 20 + 3 and 25 into 20 + 5.

Next, multiply each part of the three-digit number by each part of the two-digit number, which gives us 100 * 20, 20 * 20, 3 * 20, 100 * 5, 20 * 5, and 3 * 5. When you add these six products together, you get: 2000 + 400 + 60 + 500 + 100 + 15 = 3075, which is the result of 123 * 25.

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1) convert 7% into a decimal by divinding 7 by 100 

7 / 100 = 0.07

multiply that number by 350

350 x 0.07 = 24.5

3) add that number to 350

350 + 24.5 =

174.5

350+174.5= 524.5