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AnnZ [28]
3 years ago
15

Find part "b". =_4____

Mathematics
2 answers:
harina [27]3 years ago
6 0

Answer:

11.25

Step-by-step explanation:

Mamont248 [21]3 years ago
4 0

Value of b is 11.25

<u>Step-by-step explanation:</u>

Step 1:

Use the trigonometric ratio sine to find z.

⇒ sin 60° = opposite side/hypotenuse = z/15

∴ z = 15 sin 60° = 15√3/2

Step 2:

Use the trigonometric ratio sine to find y.

⇒ sin 30° = opposite side/hypotenuse = y/z

∴ y = z sin 30° = 15√3/2 × 1/2 = 15√3/4

Step 3:

Use Pythagoras theorem to find value of b.

⇒ y² + b² = z²

⇒ b² = z² - y² = (15√3/2)² - (15√3/4)²

                      = (15 × 15 × 3/4) - (15 × 15 × 3/4²)

                      = 15²×3/4 [1 - 1/4]   (taking common factor out)

                      = 15² × 3/4 × 3/4 = 15² × 3²/4²

∴ b = √15² × 3²/4² = 15 × 3/4

     = 45/4 = 11.25

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As an estimation we are told £3 is €4.<br> Convert £18 to euros.
Yuri [45]

Answer:

€24

Step-by-step explanation:

We can use ratios to solve this.

3:4 = 18:x

Cross multiply: 3x = 18*4

Divide: x = 18*4/3

Simplify: x = 6*4 = 24

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What statement describes the decimal equivalent of 3/ 8 ?
HACTEHA [7]

Answer:

0.375

Step-by-step explanation: All you need to do is divide 3 and 8

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At a construction job for a house there are 16 painters. Of these painters, 4 of them are painting the
Nikolay [14]

For this case, we have the total of painters is 16, so to determine what percentage is painting the interior of the house, we make a rule of three:

16 ---------------> 100%

4 -----------------> x

Where "x" represents the% of painters who paint the interior of the house.

x = \frac {4 * 100} {16}\\x = 25

Thus, 25% of painters are painting the interior of the house.

Answer:

25%

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Identify the graph and describe the solution set of this system of inequalities. Y&gt;x+5, y
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This is the answer for graph

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3 years ago
The annual birth rate for a population of a given country is represented by the function y= 918397(0.9763)^t where “t” represent
viktelen [127]

Answer:

<em>The initial number of annual births in 2018 is 918,397</em>

<em>The percent decrease in birth rates is 2.37%</em>

<em>The expected number of births in 2021 is 834,379</em>

Step-by-step explanation:

<u>Exponential Decay Function</u>

The exponential function is frequently used to model natural decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function is expressed as:

C(t)=C_o\cdot(1-r)^t

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

We are given the function that models the annual birth rate for a population of a given country:

y= 918,397(0.9763)^t

Where t represents the number of years since 2018.

a.) We can identify the variables with the actual model by comparing with the general equation, thus: Co=918,397 and 1-r=0.9763.

Solving for r we have r=1-0.9763=0.0237.

This means the initial number of annual births in 2018 (t=0) is 918,397

b.) The percent decrease in birth rates is r=0.0237 = 2.37%

c.) To find the expected number of births in 2021 (t=4 years), we substitute the value of t in the equation of the model:

y= 918,397(0.9763)^4

Calculating:

y = 834,379

The expected number of births in 2021 is 834,379

5 0
3 years ago
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