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Mamont248 [21]
3 years ago
13

How to determine if vectors are parallel?

Mathematics
1 answer:
sattari [20]3 years ago
3 0
One could use the relation

\mathbf a\cdot\mathbf b=\|\mathbf a\|\|\mathbf b\|\cos\theta

where \mathbf a,\mathbf b are two vectors, \|\mathbf a\| denotes the norm of that vector, and \theta is the angle between the two vectors.

Then the two vectors will be parallel if \theta=0 or \pi.
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Gardener Tony has a 49 cm row of mini roses. He also has a row of daises that is 27 cm longer than the row of mini roses.
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Miranda's garden has three rows. There are 13 rose plants in the first row, 7 lily plants in the second row, and 12 daisy.
8 0
3 years ago
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What is the solution set for 7x – 3 = 18, given the replacement set {0, 1,2,3,4} ? O
yawa3891 [41]

Answer:

X = 3

Step-by-step explanation:

Given the expression :7x - 3 = 18

To obtain the solution set ; we solve for X in the equation ;

7x - 3 = 18

Add 3 to both sides

7x - 3 + 3 = 18 + 3

7x = 21

Divide both sides by 7

7x / 7 = 21 / 7

x = 3

Hence, x = 3

4 0
3 years ago
Which is the best interpretation of the solution set for the compound inequality? 3(2x + 1) > 21 or 4x + 3 4 D. all real numb
loris [4]

D

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5 0
3 years ago
At a certain coffee shop, all the customers buy a cup of coffee; some also buy a doughnut. The shop owner believes that the numb
Zinaida [17]

Answer:

a) 0.2514

b) No

c) 0.2611

Step-by-step explanation:

For coffee cups sold daily

Mean(μ) = 320 cups

Standard deviation (σ) = 20 cups

For doughnut sold daily

Mean(μ) = 150 doughnut

Standard deviation (σ) = 12 doughnut

Let X be the random variable representing the number of cups.

Let y be the random variable representing the number of doughnuts.

a) The shop is opened everyday except Sunday's. This means that the shop is opened 6 times in a week.

The probability that he will sell more 2000 cups of coffee in a week = Pr(x>2000)

Using normal distribution

Z = (x - μ)/σ

Z = (2000 - 6(320))/6(20)

Z = (2000 - 1920) / 120

Z = 80/120

Z = 0.67

From the normal distribution table, 0.67 = 0.2486

Φ(z) = 0.2486

Recall that if Z is positive,

Pr(x>a) = 0.5 - Φ(z)

Pr(x>2000) = 0.5 - 0.2486

= 0.2514

b) On each cup of coffee, he makes a profit of 50 cents and makes a profit of 40 cents on each doughnut. We have 0.5x + 0.4y

Z = (x - μ) / σ

Z = (300 - (0.5*320 + 0.4*150)) / √0.5^2*20^2 + 0.4^2*12^2

Z = (300 - (160+60)) / √100+23.04

Z = (300 -220)/√123.04

Z = 80/11.09

= 7.02

Since 300 is more than 7 standard deviation from the mean and the value of z cannot be found in the normal distribution table, then he has NO reasonable chance to earn a profit more than 300.

c) The probability that on any given day he will sell a doughnut to more than half of his coffee customers = Pr(y - 0.5x > 0)

From normal distribution,

Z = (x - μ) / σ

Z = (0 - (150 - 0.5*320)) / √12^2 + 0.5^2*20^2

Z = (0 - (150 - 160)) / √144 + 100

Z = (0 -(-10))/√244

Z = 10/15.62

= 0.64

From the normal distribution table, 0.64 = 0.2389

Φ(z) = 0.2389

Recall that if Z is positive,

Pr(x>a) = 0.5 - Φ(z)

Pr(y - 0.5x >0) = 0.5 - 0.2389

= 0.2611

6 0
3 years ago
A high rise building has a sink on the fourth floor located 2-feet above the floor. Each floor is 10-feet above the other. Calcu
kap26 [50]
The pressure at a certain height is the pressure at sea level plus the hydrostatic pressure.

P = 80 psi + ΔP
where
ΔP = ρgh
ρ is the density of water equal to 62.4 lbm/ft³
ΔP = (62.4 lbm/ft³)(1 lbf/lbm)(4*10 + 2 ft)(1 ft/12 in)² = 18.2 psi

Thus,
P = 80 + 18.2
<em>P = 98.2 psi</em>
8 0
3 years ago
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