What is the probability that the employee is less than 175 cm tall- chosen from those with brown hair

Find the average value of the function f(t)=cos13(5t)sin(5t) f(t)=cos13⁡(5t)sin⁡(5t) on the interval [4,10].

Vilka [71]

The average value is given by

$\displaystyle\frac1{10-4}\int_4^{10}\cos^{13}5t\sin5t\,\mathrm dt$

Setting $y=\cos5t$ , you get $\mathrm dy=-5\sin5t\,\mathrm dt$ , and the integral becomes

$\displaystyle-\frac1{30}\int_{\cos20}^{\cos50}y^{13}\,\mathrm dy$
$=-\dfrac1{30}\dfrac{y^{14}}{14}\bigg|_{y=\cos20}^{y=\cos50}$
$=-\dfrac{\cos^{14}50-\cos^{14}20}{420}\approx-0.00145$

6 0

3 years ago

If a new soccer ball is labeled $45, what would the new price be if the sign above it says "63% off"?

Paul [167]

Answer:

New price of the ball after discount = $16.65

Step-by-step explanation:

Selling price of the soccer ball = $45

Discount labeled on the ball = 63% off

Therefore, selling price after the discount = Original selling price - %discount

= $45 - (63% of $45)

= $45 - $28.35

= $16.65

New price of the ball after discount = $16.65

3 0

2 years ago

11-Across plus 28-Down

Art [367]

Answer:

(11,-28)

Step-by-step explanation:

8 0

3 years ago

In the Pi Corporation, 4/5 of the managers are female. If there are 64 female managers, how many managers in total are there? Ho

oksano4ka [1.4K]

Step-by-step explanation:

$\frac{4}{5} = 64 \\ \frac{1}{5} = 64 \div 4 \\ \: \: \: \: \: \: = 16 \\ total \: managers \: = 16 \times 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 80 \\ number \: of \: male \: \: managers \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{5}{5} - \frac{4}{5} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{5} = 16$

hope this helps you.

5 0

3 years ago

The school is planting a circular garden. If the

Tatiana [17]

Answer:

The area of the circular garden is 28.3 square feet

Step-by-step explanation:

Let's recall that the area of a circle is π * r², therefore if the diameter of the circular garden is 6 feet, the area is:

Diameter = 6 feet ⇒ radius = (6/2) = 3 feet

Area of the circular garden = π * 3²

Area of the circular garden = 3.1416 * 9

Area of the circular garden = 28.2744

Area of the circular garden = 28.3 square feet

8 0

3 years ago