One-third of the result of three times a number that is increased by 12.

Write the equation of a line that goes the through the point (4 , -2) and is parallel to the line y = 3x - 1/3.

nataly862011 [7]

Answer:

y = 3x - 14

Step-by-step explanation:

If a line is parallel to another, it will have the same slope

So, the line's slope will be 3

Plug in the given point and the slope into y = mx + b, and solve for b

y = mx + b

-2 = 3(4) + b

-2 = 12 + b

-14 = b

Plug in the slope and b into y = mx + b

y = 3x - 14

So, the equation is y = 3x - 14

4 0

3 years ago

___________________

strojnjashka [21]

Answer:

The answer is A

Step-by-step explanation:

6 0

3 years ago

In October of 2012, Apple introduced a much smaller variant of the Apple iPad, known at the iPad Mini. Weighing less than 11 oun

sveticcg [70]

Answer:

a. $f_X(x) = \dfrac{1}{3.5}8.5$

b. the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. 86 should have a battery life of at least 9 hours

Step-by-step explanation:

From the given information;

Let X represent the continuous random variable with uniform distribution U (A, B) . Therefore the probability density function can now be determined as :

$f_X(x) = \dfrac{1}{B-A}A$

where A and B are the two parameters of the uniform distribution

From the question;

Assume that battery life of the iPad Mini is uniformly distributed between 8.5 and 12 hours

So; Let A = 8,5 and B = 12

Therefore; the mathematical expression for the probability density function of battery life is :

$f_X(x) = \dfrac{1}{12-8.5}8.5$

$f_X(x) = \dfrac{1}{3.5}8.5$

b. What is the probability that the battery life for an iPad Mini will be 10 hours or less (to 4 decimals)?

The probability that the battery life for an iPad Mini will be 10 hours or less can be calculated as:

F(x) = P(X ≤x)

$F(x) = \dfrac{x-A}{B-A}$

$F(10) = \dfrac{10-8.5}{12-8.5}$

F(10) = 0.4286

the probability that the battery life for an iPad Mini will be 10 hours or less is 0.4286 which is about 42.86%

c. What is the probability that the battery life for an iPad Mini will be at least 11 hours (to 4 decimals)?

The battery life for an iPad Mini will be at least 11 hours is calculated as follows:

$P(X\geq11) = \int\limits^{12}_{11} {\dfrac{1}{3.5}} \, dx$

$P(X\geq11) = {\dfrac{1}{3.5}} (x)^{12}_{11}$

$P(X\geq11) = {\dfrac{1}{3.5}} (12-11)$

$P(X\geq11) = {\dfrac{1}{3.5}} (1)$

$P(X\geq11) = 0.2857$

the probability that the battery life for an iPad Mini will be at least 11 hours is 0.2857 which is about 28.57 %

d. What is the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours (to 4 decimals)?

$P(9.5 \leq X\leq11.5) =\int\limits^{11.5}_{9.5} {\dfrac{1}{3.5}} \, dx$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} \, (x)^{11.5}_{9.5}$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (11.5-9.5)$

$P(9.5 \leq X\leq11.5) ={\dfrac{1}{3.5}} (2)$

$P(9.5 \leq X\leq11.5) =0.2857* (2)$

$P(9.5 \leq X\leq11.5) =0.5714$

Hence; the probability that the battery life for an iPad Mini will be between 9.5 and 11.5 hours is 0.5714 which is about 57.14%

e. In a shipment of 100 iPad Minis, how many should have a battery life of at least 9 hours (to nearest whole value)?

The probability that battery life of at least 9 hours is calculated as:

$P(X \geq 9) = \int\limits^{12}_{9} {\dfrac{1}{3.5}} \, dx$

$P(X \geq 9) = {\dfrac{1}{3.5}}(x)^{12}_{9}$

$P(X \geq 9) = {\dfrac{1}{3.5}}(12-9)$

$P(X \geq 9) = {\dfrac{1}{3.5}}(3)$

$P(X \geq 9) = 0.2857*}(3)$

$P(X \geq 9) = 0.8571$

NOW; The Number of iPad that should have a battery life of at least 9 hours is calculated as:

n = 100(0.8571)

n = 85.71

n ≅ 86

Thus , 86 should have a battery life of at least 9 hours

3 0

3 years ago

Help!! I’ll give brainlist !

iren [92.7K]

Divide each one out to see which is cheaper. 4.39/12 = .37 cents per pint while 2.89/8 = .36 cents per pint. These are cost per unit problems.The second choice is the cheaper of 2 by a cent.

4 0

3 years ago

Latasha is younger than Andrea. The sum of their ages is 28. The difference between their ages is 10

antoniya [11.8K]

Latasha is 9 years old

Explanation: 9+19=28
19-9=10

8 0

3 years ago