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3 years ago

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sin x = -1/2, and the cos y = √3/2. if angle x is in the fourth quadrant and angle y is in the first quadrant, the value of cos(

x-y) is

2 answers:

Gnom [1K]3 years ago

7 0

X is 11pi/6 and y is pi/6. So cos(10pi/6) = cos(5pi/3)=1/2. 1/2 is the answer

skad [1K]3 years ago

5 0

Answer:

More info

Step-by-step explanation:

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Customers arrive at a grocery store at an average of 2.1 per minute. Assume that the number of arrivals in a minute follows the

Black_prince [1.1K]

Answer:

a) P(2)=0.270

b) P(X>3)=0.605

c) P=0.410

Step-by-step explanation:

We know that customers arrive at a grocery store at an average of 2.1 per minute. We use the Poisson distribution:

$\boxed{P(k)=\frac{\lambda^k \cdot e^{-\lambda}}{k!}}$

a) In this case: $\lambda=2.1$

$P(2)=\frac{2.1^2 \cdot e^{-2.1}}{2}\\\\P(2)=0.270$

Therefore, the probability is P(2)=0.270.

b) In this case: $\lambda=2\cdot 2.1=4.2$

$P(X>3)=1-P(X\leq 3)\\\\P(X>3)=1-\sum_{x=0}^3 \frac{4.2^x \cdot e^{-4.2}}{x!}\\\\P(X>3)=1-0.395\\\\P(X>3)=0.605$

Therefore, the probability is P(X>3)=0.605.

c) We know that two customers came in in the first minute. That is why we calculate the probability of at least 5 customers entering the other 2 minutes.

In this case: $\lambda=2\cdot 2.1=4.2$

$P(X\geq 5)=1-P(X$

Therefore, the probability is P=0.410.

4 0

3 years ago

As part of a new advertising campaign, a beverage company wants to increase the dimensions of their cans by a multiple of 1.12.

olga_2 [115]

Answer:

The new can can hold upto volume of 476.69 cubic centimeters.

Step-by-step explanation:

Diameter of the can = d = 6 cm

Radius of the can = r = 0.5d = 0.5 × 6 cm = 3 cm

Height of the can = h = 12 cm

Company wants to increase the dimensions of their cans by a multiple of 1.12. So, the new dimension will be:

r'= 3 cm × 1.12 = 3.36 cm

h' = 12 cm × 1.12 =13.44 cm

Volume of the = can = V

Volume of a cylinder = $\pi r^2h$

$V=\pi r'^2h'$

$=3.14\times (3.36 cm)^2\times 13.44 cm=476.6808 cm^3\approx 476.68 cm^3$

The new can can hold upto volume of 476.69 cubic centimeters.

3 0

3 years ago

Solve the quadratic inequalities, by either graphing, or pure algebraic method:

BlackZzzverrR [31]

Answer:

less than/equal to -2

Or, greater than/equal to 2.5

Step-by-step explanation:

2x² - x - 10 ≥ 0

2x² - 5x + 4x - 10 ≥ 0

x(2x - 5) + 2(2x - 5) ≥ 0

(x + 2)(2x - 5) ≥ 0

Roots: -2, 5/2

x《 -2 or x》5/2

6 0

3 years ago

Neo could choose from 3 different pants, 5 different shirts, and 4 sweaters. How many different combinations of 1 pant, 1 shirt

Sidana [21]

To answer you do 5 times 4 times 3 to get 60

7 0

3 years ago

I really need help! I'm stuck.

Dovator [93]

y-axis = altitude in feet

x-axis = minutes

slope = y/x = feet/minute

According to above data, we know that 1800 feet is y-intercept and slope is -300 feet per minute (why slope is negative? because its approaching ground at a constant speed)

a. slope = -300

y-intercept = 1800

b. y = -300 x + 1800

c. Here we are given x = 2 minutes

y = -300(2) + 1800

y = -600 + 1800

y = 1200

The balloon will be 1200 feet high above the ground in 2 minutes.

d. Here we are given 300 feet which is y, and find x minutes.

y = -300 x + 1800

300 = -300x + 1800

300 - 1800 = - 300x

-1500 = -300x

1500 = 300 x

x = 1500 / 300

x = 5

The balloon will reach 300 feet above the ground in 5 minutes.

e. It asking when the balloon will reach the ground, if the balloon reaches the ground than the height will be 0, therefore x-intercept (y=0).

y = -300 x + 1800

0 = -300 x + 1800

-1800 = -300x

1800 / 300 = x

x = 6

The balloon will reach the ground in 6 minutes.

<em>//Hope this helps</em>

3 0

3 years ago