Write the slope- intercept form of the equation

(Round to the nearest tenth of a percent.) In 2011, the IRS increased the deductible mileage cost to

RUDIKE [14]

Answer:

$\%Change = 8.8\%$

Step-by-step explanation:

Given

$Initial = 51\ cents$

$Final = 55.5\ cents$

Required

Determine the percentage change

Percentage change is calculated as;

$\%Change = \frac{Final - Initial}{Initial} * 100\%$

$\%Change = \frac{55.5 - 51 }{51 } * 100\%$

$\%Change = \frac{4.5}{51} * 100\%$

$\%Change = \frac{4.5* 100\%}{51}$

$\%Change = \frac{450\%}{51}$

$\%Change = 8.8\%$

<em>Hence, the percentage change is approximately 8.8%</em>

6 0

2 years ago

Write an expression for "7 less than y."

lisov135 [29]

Answer:

(y - 7)

Step-by-step explanation:

"7 less than y" means just that.... that you have 7 fewer units then the value of y.

3 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

I really need help and i need to solve this one that says solve & simplify:3/4×2/3

VARVARA [1.3K]

3/4 2/3

This is a multiplication of fractions

1.- Multiply the numerators and the denominators

3/4 x 2/3 = (3x 2) / (4 x 3)

= 6/12

2.- Simplify

= 3/6

= 1/2

4 0

11 months ago

jose jumped 8 1/3 feet. this was 2 1/3 feet farther than lila jumped. how far did lila jump TELL MEH AFTER THIS I GET ON IXL

nika2105 [10]

In this scenario Jose jumped the distance Lila jumped plus 2 1/3 ft, so...

Lilia + 2 1/3 = 8 1/3

subtract 2 1/3 from each side to get Lila by herself

Lila = 8 1/3 - 2 1/3
Lila = 6

Lila jumped 6 feet

5 0

3 years ago