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3 years ago

6

When Aiden left his house in the morning, his cell phone battery was partially charged. The charge remaining in Aiden's battery,

as a percentage, can be modeled by the equation B = -2t + 26, where t is the number of hours since Aiden left his house. What is the slope of the equation and what is its interpretation in the context of the problem?

1 answer:

andre [41]3 years ago

5 0

Answer:

The slope is -2

It means that the battery decreases by 2% each hour since Aiden left his house

Step-by-step explanation:

In the equation y = mx + b, m is the slope.

This equation's slope is -2, since it is the coefficient for t.

In the context of this problem, this means that the battery will decrease by 2% each hour since Aiden has left his house.

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Which values, when placed in the box, would result in a system of equations with no solution? Check all that apply.

s2008m [1.1K]

Y = -2x + 4
6x + 3y = 6x + 3(-2x + 4) = 6x - 6x + 12 = 12
⇒ y = -2x + 4 == 6x + 3y = 12 ⇒ invinite solutions: 12
⇒ no solutions -12, -4, 0, 4

6 0

4 years ago

In a survey of women in a certain country the mean height was 62.9 inches with a standard deviation of 2.81 inches answer the fo

Natasha2012 [34]

The question is incomplete. The complete question is :

In a survey of women in a certain country ( ages 20-29), the mean height was 62.9 inches with a standard deviation of 2.81 inches. Answer the following questions about the specified normal distribution. (a) What height represents the 99th percentile? (b) What height represents the first quartile? (Round to two decimal places as needed)

Solution :

Let the random variable X represents the height of women in a country.

Given :

X is normal with mean, μ = $62.9$ inches and the standard deviation, σ = $2.81$ inches

Let,

$Z=\frac{X - 62.9}{2.81}$ , then Z is a standard normal

a). Let the $99th$ percentile is = a

The point a is such that,

$$P(X$

$P \left( Z < \frac{a-62.9}{2.81} \right) = 0.99$

From standard table, we get : $P( Z < 2.3263) =0.99$

∴ $\frac{(a-62.9)}{281} = 2.3263$

$a= (2.3263 \times 2.81 ) +62.9$

= 6.536903 + 62.9

= 69.436903

= 69.5 (rounding off)

Therefore, the height represents the $99th$ percentile = 69.5 inches.

b). Let b = height represents the first quartile.

It is given by :

$P( X < b) =0.25$

$P \left( Z < \frac{(b-62.9)}{2.81} \right) = 0.25$

From the standard normal table,

$P( Z < -0.6745) =0.99$

∴ $\frac{(b-62.9)}{2.81}= 0.6745$

$b=(0.6745 \times 2.81) +62.9$

= 1.895345 + 62.9

= 64.795345

= 64.8 (rounding off)

Therefore, the height represents the 1st quartile is 64.8 inches.

8 0

3 years ago

At a certain breakfast restaurant, the probability of a customer ordering coffee is 0.8. When the restaurant seats two new custo

exis [7]

The probability of both of two new customers not ordering coffee is:
$P(X=0)=0.2\times 0.2=0.04$

3 0

3 years ago

Read 2 more answers

Can you check my work please?

maks197457 [2]

Your answer is correct. Indeed:

- In order to find the degrees per minute, you have to divide the full rotation angle (which is 360deg) by the number of minutes (which is 60):
360deg ÷ 60min = 6 deg/min

- In order to find how many minutes have passed, you subtract the times:
1h50m - 1h25m = 0h25m

- You then find how many degrees correspond to 25minutes:
6 deg/min × 25 min = 150deg

- Lastly, you transform degrees into radiants, through the proportion:
deg : 180 = rad : π
Therefore,
150 : 180 = rad : π
rad = (150×π)/180 = 5π/6

4 0

4 years ago

A. 530 ft^2<br><br> B. 500 ft^2<br><br> C. 470 ft^2<br><br> D. 450 ft^2

Angelina_Jolie [31]

Answer: OPTION A.

Step-by-step explanation:

Find the length scale factor by dividing the known length of the larger triangle by the known length of the smaller triangle:

$lenght\ scale\ factor=\frac{35}{25}=\frac{7}{5}$

Then, the area scale factor is:

$area\ scale\ factor=(\frac{7}{5})^2=\frac{49}{25}$

To find the area of the the larger triangle, multiply the area of the smaller triangle by the area scale factor. Then:

$A_{(larger)}=(270ft^2)(\frac{49}{25})=529.2ft^2$

So, the option that shows an approximation of the area of the larger triangle is the option A:

$A_{(larger)}$ ≈ $530ft^2$

4 0

3 years ago