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Butoxors [25]
2 years ago
7

The mean sat verbal score is 486, with a standard deviation of 95. use the empirical rule to determine what percent of the score

s lie between 391 and 486. (assume the data set has a bell-shaped distribution.)

Mathematics
1 answer:
Pavel [41]2 years ago
8 0
Find the z-scores for the two scores in the given interval.

z=\frac{x-\mu}{\sigma}

For the score x =391, z=\frac{391-486}{95}=\frac{-95}{95}=-1.

For the score x = 486, z=\frac{486-486}{95}=0

Now you want the area (proportion of data) under the normal distribution from z = -1 to z = 0. The Empirical Rule says that 68% of the data falls between z = -1 to z = 1. But the curve is symmetrical around the vertical axis at z = 0, so the answer you want is HALF of 68%.

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2 years ago
Suppose that the concentration of a bacteria sample is 100000 bacteria per milliliter. If the concentration doubles every 2 hour
Aliun [14]

Answer:

3.85 hours

Step-by-step explanation:

We have that the model equation in this case would be of the following type, being "and" the concentration of bacteria:

y = a * e ^ (b * t)

where a and b are constants and t is time.

We know that when the time is 0, we know that there are 100,000 bacteria, therefore:

100000 = a * e ^ (b * 0)

100000 = a * 1

a = 100000

they tell us that when the time is 2 hours, the amount doubles, that is:

200000 = a * e ^ (b * 2)

already knowing that a equals 100,000

e ^ (b * 2) = 2

b * 2 = ln 2

b = (ln 2) / 2

b = 0.3465

Having the value of the constants, we will calculate the value of the time when there are 380000, that is:

380000 = 100000 * (e ^ 0.3465 * t)

3.8 = e ^ 0.3465 * t

ln 3.8 = 0.3465 * t

t = 1.335 / 0.3465

t = 3.85

That is to say that in order to reach this concentration 3.85 hours must pass

4 0
2 years ago
Which of the following are necessary when proving that the opposite angles of a parallelogram are congruent? A. Opposite sides a
Misha Larkins [42]

Answer:

C and B

Step-by-step explanation:

The correct option is option B and C. The necessary condition to prove that the opposite angles of a parallelogram are congruent:

C. Angle Addition Postulate.

B. Opposite sides are congruent

8 0
2 years ago
Read 2 more answers
James has to fill 40 water bottles for the soccer team. Each bottle holds 500 milliliters of water. How many liters of water doe
zhenek [66]

Answer:

20 litter

Step-by-step explanation:

40 \: bottels \:  \times 500 \times  ({10}^{ - 3} ) \: litters \:  = 20 \: litters

5 0
2 years ago
A rocket is divided into three sections. The top section is one-eighth the length of the bottom section. The middle section is o
Ahat [919]

Answer:

312 ft

Step-by-step explanation:

The steps are as follows :

1. The problem can be described as an equation

x +  \frac{1}{2}x +  \frac{1}{8}x = 312

2. Convert all values on the left side into their equivalent fractional values

\frac{8}{8}x  +  \frac{4}{8}x +  \frac{1}{8} x = 312

3. Combine like terms

\frac{13}{8} x = 312

4. Multiply both sides by the reciprocal of 13/8 to isolate variable X

concept \:  \:  \: ({ \frac{8}{13}  \times  \frac{13}{8} }) = 1

\frac{8}{13} \times  \frac{13}{8}x  = 312 \: \times  \frac{8}{13}

5. Simplify

x = 192

6. Check answer by using it in the original equation

(192) +  \frac{1}{2}(192) +  \frac{1}{8} (192) = 312

4 0
2 years ago
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