Solve for x. x/7 - y = a<br><br> Please help as soon as possible. Thanks! =D

Faye has a drink with 120 milligrams of caffeine. Each hour, the amount of caffeine in her body will be 80% of the amount from t

Ray Of Light [21]

Answer:

<em>12 hours </em>are required to be less than 10 milligrams of caffeine in Faye's body

Step-by-step explanation:

<u>Geometric sequences </u>

We can recognize a geometric progression, when we can get each member n as the previous member n-1 multiplied or divided by a constant value, called the common ratio.

Faye holds 120 milligrams of caffeine. We know each hour the amount of caffeine in her body will be 80% of the amount from the previous hour. For example, the first hour she will hold 80%(120)=96 milligrams of caffeine. Next hour it will be 80%(96)=76.8 and so on

We can see the sequence of contents of caffeine follows the rule of a geometric sequence and the common ratio is 80%, i.e. 0.8. The first term is 120, so the general term of the sequence is

$a_t=120(0.8)^t\ ,\ t>=0$

We are required to find how much time is needed to be less than 10 milligrams of caffeine remaining in Faye's body. It can be stated that

$120(0.8)^t$

Let's solve for t. Operating

$(0.8)^t$

Taking logarithms in both sides

$ln(0.8)^t$

Applying the power property of logarithms

$t\ ln(0.8)$

Solving for t. Since ln0.8 is negative, the direction of the inequality changes

$t>\frac{ln\frac{10}{120}}{ln(0.8)}$

$t>11.14$

Rounding to the next integer

12 hours are required to be less than 10 milligrams of caffeine in Faye's body

8 0

3 years ago

Read 2 more answers

Andre has 60% of his goal of $70 saved for his trip. How much has he saved so far?

dmitriy555 [2]

Answer:

42$

Step-by-step explanation:

So there's an easy way to know this.

100%--$70

60%--x

<em>cross multiply </em>

100x=4200

÷100 ÷100

______________

x=42

So he saved 42$. Hope this helps :D

5 0

3 years ago

What is the surface area of the given figure

Ad libitum [116K]

Answer:

1,728cm square

Step-by-step explanation:

Surface area=sum of all faces of a polygon

Let's do the biggest ones: 32•20=640

32•16=512

Now the rest:

12•32=384

16•12=192 192÷2=96

Now add it all up: 640+512+384+96+96=1,728cm square

5 0

3 years ago

Which set of ordered pairs has point symmetry with respect to the origin (0, 0)? (5, 4), (-5, -4) (5, 4), (5, -4) (5, 4), (4, 5)

Sidana [21]

The set of ordered pair that has point symmetry in respect to origin is (5, 4), (-5, -4).

<h3>What is the point of symmetry?</h3>

This is a term that is used to refer to the points that are on the same distance from the origin but are on opposite sides.

The line that connects the points are known to move through the origin such that when measured on the graph, the distances between these points but they are opposite because they are in negatives and positives on the two sides.

Read more on point of symmetry here:

brainly.com/question/1553710

#SPJ1

4 0

2 years ago

A marine sales dealer Önds that the average price of a previously owned boat is $6492. He decides to sell boats that will appeal

Anuta_ua [19.1K]

Answer:

The maximum price that the dealer will sell is $7471 and the minimum is $5513.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 6492, \sigma = 1025$