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2 years ago

9

A fair die is rolled 360 times. Find the probability that: a) less than50 results are a 6. B) between 55 and 65 results (inclusi

ve) are a 6

1 answer:

Karolina [17]2 years ago

8 0

For this problem, you haven = 360p = 1/6q = 5/6 E[x] = np = 360*1/6 = 60SD[x] = √(npq) = √(360*1/6*5/6) = √(50) ≈ 7.07

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A cell tower is located 3 miles east and 4 miles north of the center of a small town. The cell tower has a coverage radius of 3

butalik [34]

Answer:

The answer is below

Step-by-step explanation:

A cell tower is located 3 miles east and 4 miles north of the center of a small town. The cell tower has a coverage radius of 3 miles.

a) Start by drawing a diagram of this situation. Your diagram might include a coordinate plane, the cell tower, and a circle representing the cell tower's coverage boundary.

a) A house is located 5 miles north of the center of the town and is to the east of the cell tower. If the house lies on the boundary of the cell tower's coverage, how far east of the center of the town is the house?

Answer:

Let the center of the town represent the origin (0,0). Also 1 unit = 1 mile. Since the cell tower is located 3 miles east and 4 miles north of the center of a small town, it is represented by A(3, 4)

The cell tower has a coverage of radius 3 miles. This can be represented by a circle with equation:

(x - a)² + (y - b)² = r². where (a,b) is the center of the circle and r is the radius. Hence:

(x - 3)² + (y - 4)² = 3²

(x - 3)² + (y - 4)² = 9

The diagram is drawn using geogebra.

b) The house is 5 miles north. It can be represented by y = 5 line.

To find the distance east of the house we have to substitute y = 5 and solve for x, hence:

(x - 3)² + (y - 4)² = 9

(x - 3)² + (5 - 4)² = 9

(x - 3)² + 1 = 9

(x - 3)² = 8

(x - 3) = √8

x - 3 = ±2.83

x = 3 ± 2.83

x = 5.83 or 1.83

Since it is to the east to the cell tower, hence x = 5.83.

Therefore the house is located 5.83 miles to the east of the cell tower

8 0

2 years ago

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is defined as L = 10 lo

butalik [34]

Answer:

The approximate loudness of a rock concert with a sound intensity of $10^{-1}$ is 110 Db.

Step-by-step explanation:

The loudness, L, measured in decibels (Db), of a sound intensity, I, measured in watts per square meter, is : $L=10 log (\frac{I}{I_0})$

$I_0=10^{-12}$

We are supposed to find What is the approximate loudness of a rock concert with a sound intensity of $10^{-1}$

So, $I = 10^{-1}$

Substitute the values in the formula :

$L=10 log (\frac{10^{-1}}{10^{-12}})$

$L=10 log (10^{11})$

L=110 Db

So, the approximate loudness of a rock concert with a sound intensity of $10^{-1}$ is 110 Db.

7 0

2 years ago

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A cook needs 5 cups of vegetable stock for a soup recipe. How much is this in pints? Write your answer as a whole number or a mi

sineoko [7]

2.5 pints. Look it up. That's what I would do

4 0

2 years ago

Susan charges $8 per hour walking her neighbor’s dog. She charges $12 per hour babysitting. Part A: Define the variables. Part B

Anna35 [415]

Answer:

the total she earns with "d" hours of dog walking and "b" hours of babysitting is given by: 8 d + 12 b

Step-by-step explanation:

If we use "d" to represent the number of hours that Susan walks the dog, and we define "b" as the number of hours she babysits, then the expression that represents the amount she earns by walking the dog is: $8 times d = 8 d

Similarly, the amount she earns by babysitting is $12 times b = 12 b

Then the total she earns with "d" hours of dog walking and "b" hours of babysitting is: 8 d + 12 b

7 0

2 years ago

What are the vertex and x-intercepts of the graph of the function given below?

madreJ [45]

VERTEX
To determine the vertex (coordinate x) of parabola y = ax² + bx + c, use this following formula
x vertex = $-\dfrac{b}{2a}$

y = x² - 2x - 48
a = 1, b = -2, c = -48
plug in the numbers
x vertex = $-\dfrac{b}{2a}$
x vertex = $-\dfrac{(-2)}{2(1)}$
x vertex = $\dfrac{2}{2}$
x vertex = 1

To find y vertex, substitute the value of x vertex to the parabola equation
y = x² - 2x - 48
y = 1² - 2(1) - 48
y = 1 - 2 - 48
y = -49

The vertex is (1, -49)

X-INTERCEPT
x-intercept located in x axis, that means y = 0. Substitute y = 0 to the parabola equation
x² - 2x - 48 = y
x² - 2x - 48 = 0
(x - 8)(x + 6) = 0
x = 8 or x = -6
The x-intercepts are (8,0) and (-6,0)

The answer is first option

5 0

2 years ago

Read 2 more answers