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
Answer: 175.
Step-by-step explanation:
Since, Let there could be total number of vehicle parked = x
And, According to the question, 2/5 of the parking spaces are for cars.
Therefore, Number of cars are 2x/5
But, there were 200 car parked.
So 2x/5 = 200 ⇒x=500
That is, 500 vehicle can be parked in the parking lot.
And, Again from the question, The parking lot was 3/4 full.
The total vehicle that parked = 3/4 of 500 = 375
Therefore total number of buses= The total vehicle that parked - the total number of car that parked = 375-200=175.
The measure of ∠E = 87° and ∠F = 93°.
<h3>What is Parallelogram? What is triangle?</h3>
In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a parallelogram in which EFGH the measure of angle E is (2x+3) and the measure of angle F is (3x - 33).
We can write -
2(2x + 3) + 2(3x - 33) = 360°
4x + 6 + 6x - 66 = 360°
10x - 60 = 360
10x = 420
x = 42
∠E = 2 x 42 + 3 = 84 + 3 = 87°
∠F = 3 x 42 - 33 = 126 - 33 = 93°
Therefore, the measure of ∠E = 87° and ∠F = 93°.
To solve more questions on 2 -D figures, visit the link below-
brainly.com/question/25950519
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i think the answer is 96,628