All categories

3 years ago

A bag contains 7 red, 4 blue, and 6 white marbles.

Mathematics

1 answer:

Leno4ka [110]3 years ago

4 0

Answer:

28/289

Step-by-step explanation:

7 red, 4 blue, and 6 white = 17 marbles

P ( red ) = number of red / total

= 7/17

Replace the marble

7 red, 4 blue, and 6 white = 17 marbles

P ( blue ) = number of blue / total

= 4/17

P (red, replace, blue) = 7/17* 4/17

=28/289

You might be interested in

Find the values of the sine, cosine, and tangent for ZA C A 36ft B 24ft

Reptile [31]

<h2>Question:</h2>

Find the values of the sine, cosine, and tangent for ∠A

a. sin A = $\frac{\sqrt{13} }{2}$ , cos A = $\frac{\sqrt{13} }{3}$ , tan A = $\frac{2 }{3}$

b. sin A = $3\frac{\sqrt{13} }{13}$ , cos A = $2\frac{\sqrt{13} }{13}$ , tan A = $\frac{3}{2}$

c. sin A = $\frac{\sqrt{13} }{3}$ , cos A = $\frac{\sqrt{13} }{2}$ , tan A = $\frac{3}{2}$

d. sin A = $2\frac{\sqrt{13} }{13}$ , cos A = $3\frac{\sqrt{13} }{13}$ , tan A = $\frac{2 }{3}$

<h2>Answer:</h2>

d. sin A = $2\frac{\sqrt{13} }{13}$ , cos A = $3\frac{\sqrt{13} }{13}$ , tan A = $\frac{2 }{3}$

<h2>Step-by-step explanation:</h2>

The triangle for the question has been attached to this response.

As shown in the triangle;

AC = 36ft

BC = 24ft

ACB = 90°

To calculate the values of the sine, cosine, and tangent of ∠A;

i. First calculate the value of the missing side AB.

Using Pythagoras' theorem;

⇒ (AB)² = (AC)² + (BC)²

Substitute the values of AC and BC

⇒ (AB)² = (36)² + (24)²

Solve for AB

⇒ (AB)² = 1296 + 576

⇒ (AB)² = 1872

⇒ AB = $\sqrt{1872}$

⇒ AB = $12\sqrt{13}$ ft

From the values of the sides, it can be noted that the side AB is the hypotenuse of the triangle since that is the longest side with a value of $12\sqrt{13}$ ft (43.27ft).

ii. Calculate the sine of ∠A (i.e sin A)

The sine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the hypotenuse side of the triangle. i.e

sin Ф = $\frac{opposite}{hypotenuse}$ -------------(i)

In this case,

Ф = A

opposite = 24ft (This is the opposite side to angle A)

hypotenuse = $12\sqrt{13}$ ft (This is the longest side of the triangle)

Substitute these values into equation (i) as follows;

sin A = $\frac{24}{12\sqrt{13} }$

sin A = $\frac{2}{\sqrt{13}}$

Rationalize the result by multiplying both the numerator and denominator by $\sqrt{13}$

sin A = $\frac{2}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }$

sin A = $\frac{2\sqrt{13} }{13}$

iii. Calculate the cosine of ∠A (i.e cos A)

The cosine of an angle (Ф) in a triangle is given by the ratio of the adjacent side to that angle to the hypotenuse side of the triangle. i.e

cos Ф = $\frac{adjacent}{hypotenuse}$ -------------(ii)

In this case,

Ф = A

adjacent = 36ft (This is the adjecent side to angle A)

hypotenuse = $12\sqrt{13}$ ft (This is the longest side of the triangle)

Substitute these values into equation (ii) as follows;

cos A = $\frac{36}{12\sqrt{13} }$

cos A = $\frac{3}{\sqrt{13}}$

Rationalize the result by multiplying both the numerator and denominator by $\sqrt{13}$

cos A = $\frac{3}{\sqrt{13}} * \frac{\sqrt{13} }{\sqrt{13} }$

cos A = $\frac{3\sqrt{13} }{13}$

iii. Calculate the tangent of ∠A (i.e tan A)

The cosine of an angle (Ф) in a triangle is given by the ratio of the opposite side to that angle to the adjacent side of the triangle. i.e

tan Ф = $\frac{opposite}{adjacent}$ -------------(iii)

In this case,

Ф = A

opposite = 24 ft (This is the opposite side to angle A)

adjacent = 36 ft (This is the adjacent side to angle A)

Substitute these values into equation (iii) as follows;

tan A = $\frac{24}{36}$

tan A = $\frac{2}{3}$

6 0

3 years ago

In New York City at the spring equinox there are 12 hours 8 minutes of daylight. The

slamgirl [31]

Answer:

independent: day number; dependent: hours of daylight

d(t) = 12.133 +2.883sin(2π(t-80)/365.25)

1.79 fewer hours on Feb 10

Step-by-step explanation:

a) The independent variable is the day number of the year (t), and the dependent variable is daylight hours (d).

b) The average value of the sinusoidal function for daylight hours is given as 12 hours, 8 minutes, about 12.133 hours. The amplitude of the function is given as 2 hours 53 minutes, about 2.883 hours. Without too much error, we can assume the year length is 365.25 days, so that is the period of the function,

March 21 is day 80 of the year, so that will be the horizontal offset of the function. Putting these values into the form ...

d(t) = (average value) +(amplitude)sin(2π/(period)·(t -offset days))

d(t) = 12.133 +2.883sin(2π(t-80)/365.25)

c) d(41) = 10.34, so February 10 will have ...

12.13 -10.34 = 1.79

hours less daylight.

5 0

3 years ago

Find the surface area. Use 3.14 for pie

antoniya [11.8K]

Answer:

3,165.12 square meters

Step-by-step explanation:

To find the surface area of a cylinder, first separate the shapes you must find the area of. In this case, you need to find the areas of two circles and one rectangle (the height).

The two circles can be found using the equation: a = pi(r^2). r means radius!

12 squared is 144, which, multiplied by pi, is 452.16 square units. Because there are two circles, you can multiply this area by two to get the area of both: 904.32.

The rectangle can be found by multiplying the circumference of the circle by the height of the cylinder. The circumference can be found with the equation: c = 2pi(r). The circumference of this cylinder's base is 75.36, which, multiplied by the height of the cylinder, is 2,260.8.

Now that you have both the area of the circles and the side, you can add them both together and get the surface area.

6 0

3 years ago

??????????????????????

Mariana [72]

Hmmm... try subtracting or multiplying the other numbers??

3 0

3 years ago

Read 2 more answers

There are many cylinders with a height of 9 inches. Let r represent the radius in inches and V represent the volume in cubic inc

romanna [79]

Answer:

lol

Step-by-step explanation:

4 0

3 years ago