MATHEMATICS HIGH SCHOOL

A marine biologist collects data on the length of rainbow trout on a protected western river. She finds that the length of adult trout in her study are approximately normally distributed with mean 14 inches. She also reports that the minimum length was 10 inches and the maximum was 18 inches. Based on this information what is the most likely value of the standard deviation?

Answers

Answer 1

Answer:

Answer:

The standard deviation of the data is 2 inches.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 14

We are given that the distribution of length of adult trout is a bell shaped distribution that is a normal distribution.

Minimum length = 10 inches

Maximum length = 18 inches

Range

= Maximum length - Minimum length = 18 - 10 = 8

Thumb Rule of Standard Deviation:

The Range Rule of Thumb says that the range is about four times the standard deviation.
$\text{Range} = 4* \text{Standard Deviation}$
The standard deviation tells us how data is clustered around the mean.

Thus, by thumb rule, we get,

$\text{Standard Deviation} = \displaystyle\frac{\text{Range}}{4} = (8)/(4) = 2$

Thus, the standard deviation of the data is 2 inches.

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The LCF of 4 and 9 is_____. (2pionts)
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What is ? + 38 = 60

A bag contains blue and yellow marbles. Two marbles are drawn without replacement. The probability of selecting a blue marble and then a yellow marble is 0.37, and the probability of selecting a blue marble on the first draw is 0.55. What is the probability of selecting a yellow marble on the second draw, if the first marble drawn was blue?
A) 18%
B) 20%
C) 46%
D) 67%

Answers

Let b = blue marbles
y = yellow marbles
Sum = b+y
The chance of a blue marble being drawn first is:
b / (b+y) = 0.55
The chance of a blue marble being drawn first then a yellow next is:
b / (b+y) * y / (b+y-1) = 0.37
This can be solve easily by using a theorem of Bayes
0.37/0.55 = .67 or 67%

If f(x)=1/2 x-6 what is the equation for f–1(x)? A. f–1(x) = 2x + 6

B. f–1(x) = 2x – 6

C. f–1(x) = 2(x + 6)

D. f–1(x) = 2(x – 6)

Answers

Answer:

Option C $f^(-1)(x)=2(x+6)$

Step-by-step explanation:

we have that

$f(x)=(1)/(2)x-6$

Let

$y=f(x)$

$y=(1)/(2)x-6$

Exchange the variables x for y and y for x

$x=(1)/(2)y-6$

Isolate the variable y

$x+6=(1)/(2)y$

$y=2(x+6)$

Let

$f^(-1)(x)=y$

$f^(-1)(x)=2(x+6)$

I hope this helps you

Solve for x.
y=(2 + x)m

Answers

Answer:

x = $(y-2m)/(m)$

Step-by-step explanation:

Given

y = (2 + x)m ← distribute parenthesis by m

y = 2m + mx ( subtract 2m from both sides )

y - 2m = mx ( divide both sides by m )

$(y-2m)/(m)$ = x

What is the standard form of the equation of a parabola is y = 5x^2 + 20x + 14. What is the vertex form of the equation

Answers

vertex form is $y=a(x-h)^2+k$

comlpete the square

$y=5x^2+20x+14$

group x terms

$y=(5x^2+20x)+14$

factor quadratic coefient

$y=5(x^2+4x)+14$

take 1/2 of linear coefient and square it

4/2=2, 2^2=4

add positive and negative of it inside the parentheasees

$y=5(x^2+4x+4-4)+14$

factor perfect squarer trinomial

$y=5((x+2)^2-4)+14$

expand

$y=5(x+2)^2-20+14$

$y=5(x+2)^2-6$ is vertex form

Find the sum of the geometric sequence –3, 15, –75, 375, … when there are 9 terms and select the correct answer below.A. -976,563
B.976,563
C.1,464,843
D.976,562

Answers

The correct answer to the question presented above would be letter A. -976, 563. I got this through solving with the first number of the set, then getting the ratio of the data set (which is -5) and the number of terms in the set. Thus, I arrived with the answer, -976, 563.

Answer:

Find the sum of the geometric sequence −3, 15, −75, 375, … when there are 9 terms and select the correct answer below.

-The answer is A. ( −976,563)

Explanation:

Took the test and got it correct.

Which is bigger, 40% of 180 or ¼ of 320?

Answers

'of' in mathematics means multiplication.

40% of 180 means 40/100 * 180

40/100 * 180
= 0.40 * 180
= 72

1/4 of 320 means 1/4 * 320

1/4 * 320
= 320/4
= 80

40% of 180 is 72
1/4 of 320 is 80

1/4 of 320 is bigger than 40% of 180

You could also say that as:

1/4 of 320 is greater than 40% of 180.

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