An angle measures 56° less than the measure of a complementary angle. What is the measure of each angle?

Answer:

1. 617.5 cm³

2. 335.6 in³

3. 151.6 m³

4. 3479.1 ft³

Step-by-step explanation:

1.

B1: 19.5 × 9 = 175.5

B2: 6 × 13 = 78

sqrt(B1 ×B2) = 117

h = 5

Volume = ⅓ × 5 × [175.5 + 78 + 117]

617.5

2.

B1: 3.14 × 4.5² = 63.585

B2: 3.14 × 3² = 28.26

sqrt(B1 ×B2) = 42.39

h = 7.5

Volume = ⅓ × 7.5 × [63.585 + 28.26 + 42.39]

335.5875

3.

B1: ½(8+12) × 6 = 60

B2: ½(3+4.5) × 2.25 = 8.4375

sqrt(B1 ×B2) = 22.5

h = 5

Volume = ⅓ × 5 × [60 + 8.4364 + 22.5]

151.5625

4.

B1: 3.14 × 12² = 452.16

B2: 3.14 × 7² = 153.86

sqrt(B1 ×B2) = 263.76

h² = 13² - (12-7)²

h² = 13² - 5²

h² = 144

h = 12

Volume = ⅓ × 12 × [452.16 + 153.86 + 263.76]

3479.12

The correct answer is 9

What is permutation and combination?

• A permutation is an act of arranging the objects or numbers in order.
• Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter.

How to solve this problem?

The steps are as follow:

• We need to select any one from pizza , hamburger or hotdog = 3C1
• We need to select any one from pear , grapes or an apple = 3C1

Therefore the possibilities are 3C1*3C1 = 3!/1!(3-1)!*3!/1!(3-1)!

= 3*2!/1*2! *3*2!/1*2! = 3*3 = 9

Therefore , the number of possibilities is 9

Learn more about Permutation and combination here

brainly.com/question/11732255

#SPJ2

Answer:

x = 33/5

Step-by-step explanation:

x - 3/5 = n.......n = 6

so we sub

x - 3/5 = 6......add 3/5 to both sides

x = 6 + 3/5...convert using common denominator of 5

x = 30/5 + 3/5

x = 33/5 <===

check...

x - 3/5 = 6

33/5 - 3/5 = 6

30/5 = 6

6 = 6 (correct)...so it checks out

Answer:

66.67 ml of 5% solution and 133.33 ml of 6.5% solution are mixed.

Step-by-step explanation:

Let 200 ml of 6% solution is formed by mixing x ml of 5% solution and y ml of 6.5% solution.

We can write the equation x + y = 200 ........ (1)

Now, x ml of 5% solution will contain ml of acid  

Again, y ml of 6.5% solution will contain ml of acid.

So, mixing them together will give (0.05x + 0.065y) ml of acid in 200 ml of solution.

So, from the condition given we can write  

⇒ 0.05x + 0.065y = 12  

⇒ x + 1.3 y = 240 ........... (2) {Dividing both sides by 0.05}

Now, solving equations (1) and (2), we get

0.3y = (240 - 200) = 40

⇒ y = 133.33 ml  

From equation (1) we get, x = 200 - 133.33 = 66.67 ml

Therefore, 66.67 ml of 5% solution and 133.33 ml of 6.5% solution are mixed. (Answer)