Match the trigonometric ratios with their values based on the triangle shown in the diagram.

Susie has a bag with 10 hair pins, 7 pencils , 2 snacks and 4 books. What is the ratio of books to pencils?

MA_775_DIABLO [31]

Answer:

4:7 i think, bc its books to pencils so books go first, which is 4, put the ratio sign, then 7

6 0

3 years ago

A 0.25 mL sample of water drawn from a 5 liter flask contains 1.25 x 10^8 bacteria. Give the approximate number of bacteria in t

vazorg [7]

Answer:

The number of bacteria in 0.25 mL is 6.25 x 10^3.

Step-by-step explanation:

5 liter flask contains 1.25 x 10^8 bacteria.

So, 1liter flask contains = $\frac{1.25 \times 10^8}{5} =2.5\times 10^7$

Now

0.25 mL contains = $2.5\times 10^7 \times0.25\times 10^{-3} = 6.25\times 10^3$

7 0

3 years ago

What is the volume of this rectangular prism?

tankabanditka [31]

Answer:

There is not enough info to solve this. And if 4/3 is the base you do

(4/3)(4/3) which equals 16/9 = 1 7/9

8 0

3 years ago

A speedometer has a percent error of 10%. The actual speed of the car is 40 mph. Select from the drop-down menus to correctly co

rodikova [14]

Answer

The speedometer is likely to show the speed is either 36.0 mph or 44.0 mph.

To prove

Formula

$Percentage\ error = \frac{error\times 100}{Exact\ value}$

Where error = |Approx value - Exact value |

First case

As given

A speedometer has a percent error of 10%. The actual speed of the car is 40 mph.

Here

Percentage error = 10%

Exact value = 40 mph

error = - (Approx value - Exact value )

= - (Approx value - 40 )

= - Approx value + 40

Put in the formula

$10 = \frac{(-Approx\ value + 40)\times 100}{40}$

$400 = {(-Approx\ value + 40)\times 100}$

$\frac{400}{100} =-Approx\ value + 40$

$\4 =-Approx\ value + 40$

Thus

Approx value = 40 - 4

Approx value = 36 mph

Therefore Option (b) is correct .

Second Case

error = (Approx value - Exact value )

= (Approx value - 40 )

= Approx value - 40

Put in the formula

$10 = \frac{(Approx\ value - 40)\times 100}{40}$

$400 = {(Approx\ value - 40)\times 100}$

$\frac{400}{100} = Approx\ value - 40$

$\4 = Approx\ value - 40$

Thus

Approx value = 40 + 4

Approx value = 44 mph

Therefore Option (c) is correct .

4 0

3 years ago

Express z = square root (4 + 3i) in the form p + qi , where p and q and are rational numbers.

Gwar [14]

Answer:

z = (3/√2) + (1/√2)î = (1/√2) [3 + i] = (2.1213 + 0.7071i)

OR

z = -(3/√2) + i(1/√2) = (1/√2) [-3 + i] = (-2.1213 + 0.7071i)

p = (3/√2) = 2.1213

q = (1/√2) = 0.7071

OR

p = (-3/√2) = -2.1213

q = (1/√2) = 0.7071

Step-by-step explanation:

z = √(4 + 3i)

Let the complex number z be equal to

z = p + qi

So, we can write

z = p + qi = √(4 + 3i)

p + qi = √(4 + 3i)

Square both sides

(p + qi)² = [√(4 + 3i)]²

p² + pqi + pqi + (qi)² = (4 + 3i)

p² + 2pqi + q²i² = 4 + 3i

note that i² = -1

p² + 2pqi - q² = 4 + 3i

(p² - q²) + 2pqi = 4 + 3i

Comparing both sides, and them equating the real parts on both sides to each other and the complex parts to each other

(p² - q²) = 4 (eqn 1)

2pq = 3 (eqn 2)

From eqn 2

p = (3/2q)

p² = (9/4q²)

Substituting this into eqn 1

(9/4q²) - q² = 4

multiplying through by 4q²

9 - 4q⁴ = 16q²

4q⁴ + 16q² - 9 = 0

let q² = x, q⁴ = x²

4x² + 16x - 9 = 0

Solving the quadratic equation

x = 0.5 or -4.5

q² = 4

q² = 0.5 or q² = -4.5

q = √0.5 or √-4.5

q = (1/√2) = (√2)/2 = 0.7071

Or q = i(3/√2) = i(3√2)/2 = 2.1213I

p = (3/2q)

If q = (1/√2) = (√2)/2 = 0.7071

p = (3/√2) = (3√2)/2 = 2.1213

if q = i(3/√2) = i(3√2)/2 = 2.1213I

p = i(1/√2) = i(√2)/2 = 0.7071i

z = p + qi

If q = (1/√2) = (√2)/2 = 0.7071

p = (3/√2) = (3√2)/2 = 2.1213

z = (3/√2) + (1/√2)î = (1/√2) [3 + i]

= 2.1213 + 0.7071i

if q = i(3/√2) = i(3√2)/2 = 2.1213I

p = i(1/√2) = i(√2)/2 = 0.7071i

z = i(1/√2) + [i(3/√2) × i]

z = i(1/√2) - (3/√2)

z = -(3/√2) + i(1/√2)

z = (1/√2) [-3 + i]

z = -2.1213 + 0.7071i

Hope this Helps!!!

8 0

4 years ago