Write the correct answer in the blank at the right of each question.Keisha’s family is planning a trip to Europe. If they want to visit each of the cities listed in the table under, in how many different orders can they do so?
City:
-Athens
-Berlin
-London
-Paris
-Rome

Answers

Answer 1

Answer:

Answer: They can visit all 5 cities in 120 different ways

Step-by-step explanation: If the family has the option of visiting five different cities in Europe, and they intend to visit all of them, then they can visit any one first and go on to another one, and so on till they exhaust all their options.

However, there is the option of which to visit first, which to visit second, and so on. This means if they decide for example, to start with Athens then they may decide to visit any of the four other cities afterwards in more than one way, and this is because all the other four cities equally have the option of being number two. So with Athens at number one, we have the other four equally likely to be number two, and so on.

To make this less cumbersome, we shall apply the formula for permutations. Rather than counting numbers of arrangements like described above, Keisha's family can use the permutation formula which is;

Pₙ = n!

Where n is the number of available options,

P₅ = 5!

P₅ = 5 x 4 x 3 x 2 x 1

P₅ = 120

Hence, the family can arrange their trip to Europe in 120 different orders

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A rectangular shoebox has a volume of 728 cubic inches. The base of the shoebox measures 8 inches by 6.5 inches. How long is the shoe box?

Answers

Divide the volume by the two measures. 728 ÷ 8 = 91 ÷ 6.5 = 14 so, the shoe box is we inches long.

Own arranges 48 beads into an array. There are 6 rows of beads. How many columns are there.

Answers

Answer:

There will be 8 columns

Step-by-step explanation:

So first you get 48 and divide it by 6 then you get 8 as your answer

You were planning to spend $12 on a pizza. Write and solve an inequality to represent the additional amount you must spend to get free delivery.Free Delivery — for orders of $30.00 or more

Answers

You have $12, and need at least x more dollars to spend $30 total. So the inequality is 12 + x ≥ 30, where x is the number of dollars needed to get free delivery. To solve for x, subtract 12 from each side of the sign. x ≥ 30 - 12, x ≥ 18. You must spend at least 18 more dollars to qualify for free delivery.

The total weight of 6 pieces of butter and a bag of sugar is 3.8lb. If the weight of the bag of sugar is 1.4 lbs what is the weight of each piece of butter

Answers

the total weight of 6 pieces of butter and bag of sugar is 3.8 lb

lets name a piece of butter as x

there are 6 pieces of butter - then x * 6 = 6x

if we write an equation for the total cost

6x + bag of sugar = 3.8 lb

weight of bag of sugar = 1.4 lb

6x + 1.4 lb = 3.8 lb

6x = 3.8 - 1.4

6x = 2.4 lb

x = 2.4/6

x = 0.4 lbs

therefore weight of a piece of butter is 0.4 lbs

The weight of each piece of butter is $\boxed{\bf0.4{\text{ lbs}}}$ .

Further explanation:

Given:

The total weight of 6 pieces of butter and the weight of a bag of sugar is equal to 3.8 lbs.

The weight of the bag of sugar is 1.4 lbs.

Our aim is to find the weight of each piece of butter.

Calculation:

Let the weight of each piece of butter to be $x$ lbs.

Also consider the weight of a bag of sugar to be $y$ lbs.

Then the weight of 6 pieces of butter is $\boxed{6x}$ .

Therefore, the total weight of 6 pieces of butter and one bag of sugar is calculated as.

${\text{Total weight}}=6x+y$

Given that total weight of 6 pieces of butter and one bag of sugar is equal to 3.8.

Now, the total weight in the form of an equation can be written as,

$6x+y=3.8$ ……(1)

Since, the weight of one bag of sugar is equal to 1.4 lbs., then substitute 1.4 for $y$ in equation (1) to obtain the value of $x$ as follows:

$6x+1.4=3.8$

Subtract 1.4 on both sides of above equation as follows:

$\begin{aligned}6x+1.4-1.4&=3.8-1.4\n6x&=2.4\n\end{aligned}$

Now, divide both sides of above equation by 6 to obtain the value of $x$ as follows:

$\begin{aligned}\frac{{6x}}{6}&=\frac{{2.4}}{6}\nx&=0.4\n\end{aligned}$

Therefore, the weight of each piece of butter is equal to $\boxed{\bf0.4{\text{ lbs}}}$ .

Learn more:

1. Learn more about equations brainly.com/question/788903

2. Learn more about algebraic expression brainly.com/question/5533462

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Linear equations

Keywords: Weight, pieces, butter, bag, sugar, total, lbs., equations, algebraic equations, linear, subtract, 6x+y=3.8, x=0.4.

a cereal box is 19 cm long 6 cm wide and 28 cm cm high. an artist is trying to create a design for the box. what is the surface area the artist needs to cover?

Answers

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then 28 x 19 x 2 = 1064
then 28 x 6 x 2 = 336
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What's 5 divided by x squared explain

Answers

5 divided by x squared is a fraction.
written mathematically would look like this
5/x^2
In order for this fraction to be true, x CANNOT equal zero. If it does, the fraction is then simply equal to 0.
In any other case, x can be both negative and positive because a negative value squared will always be positive.
For example
if x=1
5/(1)^2=5/1=5
simple.
If x=2 though, then the result is much different
5/(2)^2=5/4

Answer:

what is x

Step-by-step explanation:

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