In a 20% off sale a coat was £220. work out the original price

An instructor gives her class the choice to do 7 questions out of the 10 on an exam.

Maksim231197 [3]

Answer:

(a) 120 choices

(b) 110 choices

Step-by-step explanation:

The number of ways in which we can select k element from a group n elements is given by:

$nCk=\frac{n!}{k!(n-k)!}$

So, the number of ways in which a student can select the 7 questions from the 10 questions is calculated as:

$10C7=\frac{10!}{7!(10-7)!}=120$

Then each student have 120 possible choices.

On the other hand, if a student must answer at least 3 of the first 5 questions, we have the following cases:

1. A student select 3 questions from the first 5 questions and 4 questions from the last 5 questions. It means that the number of choices is given by:

$(5C3)(5C4)=\frac{5!}{3!(5-3)!}*\frac{5!}{4!(5-4)!}=50$

2. A student select 4 questions from the first 5 questions and 3 questions from the last 5 questions. It means that the number of choices is given by:

$(5C4)(5C3)=\frac{5!}{4!(5-4)!}*\frac{5!}{3!(5-3)!}=50$

3. A student select 5 questions from the first 5 questions and 2 questions from the last 5 questions. It means that the number of choices is given by:

$(5C5)(5C2)=\frac{5!}{5!(5-5)!}*\frac{5!}{2!(5-2)!}=10$

So, if a student must answer at least 3 of the first 5 questions, he/she have 110 choices. It is calculated as:

50 + 50 + 10 = 110

6 0

2 years ago

PLEASE HELP

lutik1710 [3]

Neagative six plus r is less than or equal to negative three point five

5 0

2 years ago

A right prism has height 7½ and triangular bases with sides of length 5, 12, and 13 What is the: Total Surface Area of the Prism

sdas [7]

Given:

A right prism has height 7½ and triangular bases with sides of length 5, 12, and 13.

To find:

The total surface area of the prism.

Solution:

We have,

Height of prism = 7½ = 7.5

Sides of triangular base are 5, 12, 13. These sides of Pythagorean triplets because

$5^2+12^2=13^2$

$25+144=169$

$169=169$

So, the base of the prism is a right triangle.

Area of a triangle is

$Area=\dfrac{1}{2}\times base \times height$

$A_1=\dfrac{1}{2}\times 5\times 12$

$A_1=30$

The area of the base is equal to the area of the top, i.e., $A_2=30$ sq units.

Perimeter of the base is

$P=5+12+13$

$P=30$

The curved surface area of the prism is

$CSA=\text{Perimeter of the base}\times \text{Height of the prism}$

$CSA=30\times 7.5$

$CSA=225$

Now, the total area of the prism is

$A=A_1+A_2+CSA$

$A=30+30+225$

$A=285$

Therefore, the total surface area of the triangular prism is 285 square units.

5 0

2 years ago

a rectangular prism has a volume of 300 cm squared if the scale factor of the second rectangular prism is 3.5 what is the volume

velikii [3]

Volume of rectangular prism= 30 cm³
Formula for volume of rectangular prism:
V=whl
Scale factor of second prism= 3.5
Which is 3 and a half times greater than the 1st one.
So volume of 2nd prism = 3. 5 x 300
V= 1050 cm³

Answer: Volume of second Rectangular Prism is 1050 cm³

6 0

2 years ago

75 cm x 50 cm HELP 61 POINTS

katen-ka-za [31]

3,750 cm its simple math really

3 0

3 years ago

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