There are 8 students in a small class. To make a team, the names of the 2 of them will be drawn from a hat. How many different teams of 2 students are

Answers

Answer 1

Answer: use slot method
2 slots

8 choices for first slot
7 choices for second (since 1 is in 1st slot)
8 times 7=56

56 ways to make 2 person teams

Answer 2

Answer: The first name can be any one of the 8.
   For each of those . . .
The second name can be any one of the remaining 7.

Total number of ways that 2 names can be drawn = (8 x 7) = 56 .

But . . .

Each team can be drawn in two different ways . . .
   -- Smith first, then Cohen
   -- Cohen first, then Smith.

So, among the 56 ways to draw 2 names, you will find
each possible pair of names drawn twice, in the opposite
order.

The number of different 2-member teams is (56 / 2) = 28 .

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How to multiply 25 by 5 without using calculator?

Answers

Hey There

In multiplication you have to know the process of regrouping, which means to take away from tens. Also, you multiply from left to right.

Steps
1. First multiply 5*5=25, the two adds to the product of 5*2

2. Now you have to multiply 5*2=10, now you have to add two because of regrouping, 10+2=12, so you're final answer is 125.

In conlusion, 25*5=125

Hope this helps :)

2 5

× 5
___________
1 2 5
____________

1st step: 5 × 5 = 25. Put down 5 . Keep 2 aside.

2nd step: 5 × 2 = 10. 10 plus the 2 kept aside = 12

3rd step : write down 12.

That brings the answer to 125.

What type of angle is <CEB?

Answers

Answer:

obtuse angle

Step-by-step explanation:

m(<CEA)=m(<BED)=88 (vertically opposite angles)

So m(<CEB)+m(<AED)=360-(88+88)=182

m(<CEB)=m(<AED)= 182÷2=92

The product of 13 and m plus the product of 2.7 and n

Answers

Answer:

13 m + 2.7 n.

Step-by-step explanation:

Given : the product of 13 and m plus the product of 2.7 and n

To find : Write expression .

Solution : We have given

Product of 13 and m = 13 * m

Product of 2.7 and n = 2.7 * n

According to question :

Sum of Product of 13 and m and Product of 2.7 and n

13 *m + 2.7 *n

13 m + 2.7 n.

Therefore, 13 m + 2.7 n.

13m+2.7n

If thats what you need

Nancy does 5 loads of washing per week using a box of a 1.2kg box of Fab using 60 grams per wash.How many weeks should the box of washing powder last.

Answers

So 1.2 Kg = 1200 g
5 washes per week = 60 grams x 5 times = 300 grams per week
1200 grams total divided by 300 grams per week
= 4 weeks

So the answer is 4 weeks

if the sides of a square are increased by 3m,the area becomes 64m2. find the length of a side of the original square

Answers

$a-the\ length\ of\ a\ side\ of\ the\ original\ sqare\n\n(a+3)^2=64\Rightarrow a+3=√(64)\n\na+3=8\n\na=8-3\n\na=5\ (m)\leftarrow solution$

A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?a. (-7, -1), 36 units
b. (7, 1), 36 units
c. (7, 1), 6 units
d. (-7, -1), 6 units

Answers

Answer:

option d is correct.

center = (-7, -1)

r = 6

Step-by-step explanation:

The general equation of the circle is given by;

$(x-h)^2+(y-k)^2 = r^2$

where;

(h, k) is the center of the circle

r is the radius of the circle respectively.

As per the statement:

A circle is described by the equation $x^2 + y^2 + 14x + 2y + 14 = 0$

then;

$(x^2+14x)+(y^2 + 2y) + 14 = 0$

Using the completing the square:

$(x^2+14x+7^2-7^2)+(y^2 + 2y+1^2-1^2) + 14 = 0$

⇒ $(x+7)^2 - 49 + (y+1)^2 - 1 + 14 = 0$

⇒ $(x+7)^2+(y+1)^2 -36 = 0$

Add 36 to both sides we have;

$(x+7)^2+(y+1)^2=36$

On comparing with the general equation of circle:

we get;

h = -7 , k = -1 and $r^2 = 36$

⇒ $r = 6$

Therefore, the coordinate of the center of the circle is (-7, -1) and length of the radius of the circle is 6

The equation of a circle:
$(x-h)^2+(y-k)^2=r^2$
(h,k) - the coordinates of the center
r - the radius

$x^2+y^2+14x+2y+14=0 \nx^2+14x+49+y^2+2y+1+14-49-1=0 \n(x+7)^2+(y+1)^2+14-49-1=0 \n(x+7)^2+(y+1)^2-36=0 \n(x+7)^2+(y+1)^2=36 \n(x-(-7))^2+(y-(-1))^2=6^2 \n \Downarrow \nh=-7 \nk=-1 \nr=6$

The center is (-7,-1), the length of the radius is 6 units.
The answer is D.

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