Miguel's family drove 357 miles on their weekend trip. Their car's average gas mileage was 25.5 miles per gallon, How

The extract of a plant native to Taiwan has been tested as a possible treatment for Leukemia. One of the chemical compounds prod

True [87]

Answer:

a) 57.35%

b) 99.99%

c) 68.27%

Step-by-step explanation:

When we have a random variable X that is normally distributed with mean $\large\bf \mu$ and standard deviation $\large\bf \sigma$ , then

The probability that the random variable has a value less than a, P(X < a) = P(X ≤ a) is the area under the normal curve with mean $\large\bf \mu$ and standard deviation $\large\bf \sigma$ to the left of a.

The probability that the random variable has a value greater than b, P(X > b) = P(X ≥ b) is the area under the normal curve with mean $\large\bf \mu$ and standard deviation $\large\bf \sigma$ to the right of b.

The probability that the random variable has a value between a and b, P(a < X < b) = P(a ≤ X ≤ b) = P(a < X ≤ b)= P(a ≤ X < b) is the area under the normal curve with mean $\large\bf \mu$ and standard deviation $\large\bf \sigma$ between a and b.

In this case, the random variable is the collagen amount found in the extract of the plant. The mean is 63 g/ml and the standard deviation is 5.4 g/ml

(a) What is the probability that the amount of collagen is greater than 62 grams per mililiter?

As we have seen, we need to find the area under the normal curve with mean 63 and standard deviation 5.4 to the right of 62 (see picture).

You can find this value easily with a calculator or a spreadsheet. If you prefer the old-style, then you have to standardize the values and look up in a table.

If you have access to Excel or OpenOffice Calc, you can find this value by introducing the formula:

1- NORMDIST(62,63,5.4,1) in Excel

1 - NORMDIST(62;63;5.4;1) in OpenOffice Calc

and we will get a value of 0.5735 or 57.35%

(b) What is the probability that the amount of collagen is less than 90 grams per mililiter?

Now we want the area to the left of 90

NORMDIST(90,63,5.4,1) in Excel

NORMDIST(90;63;5.4;1) in OpenOffice Calc

You will get a value of 0.9999 or 99.99%

(c) What percentage of compounds formed from the extract of this plant fall within 1 standard deviations of the mean?

You can use either the rule that 68.27% of the data falls between $\large\bf \mu -\sigma$ and $\large\bf \mu +\sigma$ or compute area between 63 - 5.4 and 63 + 5.4, that is to say, the area between 57.6 and 68.4

In Excel

NORMDIST(68.4,63,5.4,1) - NORMDIST(57.6,63,5.4,1)

In OpenOffice Calc

NORMDIST(68.4;63;5.4;1) - NORMDIST(57.6;63;5.4;1)

In any case we get a value of 0.6827 or 68.27%

3 0

2 years ago

Sarah sells fruit trays at a salad shop. Last week, she sold 450 fruit trays for $8 per tray. In previous weeks, she found that

Mamont248 [21]

Sarah's income = Number of trays × Rate per tray

y = 450 × 8

If there is an increase of 0.85 in price,

New price = 8 + 0.85

For x number of increases,

new price = 8 + 0.85x.

Number of trays reduced = 450 - 15x.

So, Sarah's income in this case is y = (450 - 15x) (8 + 0.85x).

4 0

2 years ago

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You are playing a video game. For each diamond you collect, you earn 80 points. You also earn 100 bonus points by completing the

Karo-lina-s [1.5K]

Given

For each diamond you collect, you earn 80 point

earn 100 bonus points by completing the level in less than 2 minutes.

earn more than 1220 points to continue on to the next level

Find the inequality that represents the numbers dd of diamonds you must collect in less than 2 minutes to advance to the next level.

To proof

As given in the question

For each diamond earn point = 80

bonus points by completing the level in less than 2 minutes = 100

earn more than 1220 points to continue on to the next level

Let us assume that the number of diamond = d

The inequality written in the form

we get

$80d + 100 \geq 1220$

now solving the above equation

$80d \geq1120$

$d \geq14$

Thus the numbers of diamonds you must collect in less than 2 minutes to advance to the next level be 14.

Hence proved

3 0

2 years ago

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Triangle BCD is isosceles and BC ≅ BD. Circle A is shown. Isosceles triangle C B D has points on the circle. The lengths of C B

Masja [62]

Answer:

130

Step-by-step explanation:

since bc and bd equal the same thing, plug in every answer option until you get to 360.

(130 x 2) = 260

plus cd = 100.

260 + 100 = 360.

3 0

2 years ago

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Jeanne babysits for $6 per hour. She also works as a reading tutor for $10 per hour. She is only allowed to work 20 hours per we

Maru [420]

A) System of inequalities

Income from babysitting: 6x
Income from tutoring: 10y

Goal for this week: at least $ 75 => 6x + 10y ≥ 75
Number of hours: maximum $20 => x + y ≤ 20

x and y have to be zero or positvie => x≥0 and y ≥ 0

Answer of part A.

6x + 10y ≥ 75
x+y ≤ 20
x ≥ 0
y ≥ 0

Part B. Graph

The solution is a region closed by 4 lines and you can find it in the file attached.

In that graph:

1) the line x + y = 20 is the upper limit
2) the line 6x + 10 y = 75 is the lower incclined line
3) y = 0 is the botton horizontal line it is the x-axis
4) x = 0 is the left vertical line, in is the y-axis

Part C.

Use, for example the point (7,10).

It is in the region of the graph limited by the above equations.

It implies:

Number of hours worked = 7 + 10 = 17 which is less than 20.

Income: 6(7) + 10(10) = 42 + 100 = 142, which is greater than 75

Of course, both are greater than 0.

In this way we proved that the point (7,10) is a true solution for the model.

Download pdf

8 0

2 years ago