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Oksanka [162]
2 years ago
5

A new version of the Medical College Admissions Test (MCAT) was introduced in spring 2015 and is intended to shift the focus fro

m what applicants know to how well they can use what they know. One result of the change is that the scale on which the exam is graded was modified, with the total score of the four sections on the test ranging from 472 to 528. In spring 2015, the mean score was 500.0 with a standard deviation of 10.6.
Required:
What are the median and the first and third quartiles of the MCAT scores?
Mathematics
1 answer:
katrin [286]2 years ago
6 0

Answer:

The median of the MCAT scores was of 500.

The first quartile of MCAT scores was of 492.845.

The third quartile of MCAT scores was of 507.155.

Step-by-step explanation:

When the distribution is normal, we use 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.

The mean score was 500.0 with a standard deviation of 10.6.

This means that \mu = 500, \sigma = 10.6

Median:

In a normal distribution, the median is the same as the mean, so the median of the MCAT scores was of 500.

First quartile:

This is the 100*(1/4) = 25th percentile, which is X when Z has a pvalue of 0.25. So X when Z = -0.675.

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

-0.675 = \frac{X - 500}{10.6}

X - 500 = -0.675*10.6

X = 492.845

The first quartile of MCAT scores was of 492.845.

Third quartile:

This is the 100*(3/4) = 75th percentile, which is X when Z has a pvalue of 0.75. So X when Z = 0.675.

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

0.675 = \frac{X - 500}{10.6}

X - 500 = 0.675*10.6

X = 507.155

The third quartile of MCAT scores was of 507.155.

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FORMULA:

  • Volume of cylinder = πr²h
  • Volume of sphere = 4/3πr³

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Volume of capsule = 4/3πr³ + πr²h

πr²(4/3r + h)

  • 3.14 × 2²(8/3 + 5.6)
  • 3.14 × 4(2.6 + 5.6)
  • 12.56(8.2)
  • 102.99 or 103 rounded.

Now, Density = 0.7mg/mm³

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2 years ago
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2 years ago
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The center of a circle lies on the line y = 4x + 1 and is tangent to the x-axis at (−3,0) . What is the equation of the circle i
Hunter-Best [27]

Answer:

(x+3)^2+(y+11)^2=121

Step-by-step explanation:

Consider a sketch of the problem as shown in the picture, where:

  • Blue line is given by y = 4x + 1.
  • Point B is the center of the circle.
  • Point A is (-3, 0).

Since the center of the circle lies on the line y = 4x +1 and is tangent to the x-axis at point A, then its radius BA is perpendicular to the x-axis. To find the coordinates of point B, we must replace x = -3 into the blue line equation: y = 4x(-3) + 1 = -11.

So, we know that the center of the circle is at B=(-3, -11). And furthermore, the radius BA is of length r=11.

Since the <em>general equation of the circle</em> of radius lenght r centered at (h, k) is given by

(x-h)^2+(y-k)^2=r^2

then with h = -3, k = -11 and r= 11, the equation of our circle is

(x+3)^2+(y+11)^2=121

5 0
3 years ago
Let $a$ and $b$ be nonzero real numbers such that
algol [13]
<h3>Answer:   -7/2</h3>

=========================================================

Explanation:

Let's expand out (2 - 7i)(a + bi) using the FOIL rule

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7bi^2

(2 - 7i)(a + bi) = 2a + 2bi - 7ai - 7b(-1)

(2 - 7i)(a + bi) = 2a + 2bi - 7ai + 7b

(2 - 7i)(a + bi) = (2a+7b) + (2bi-7ai)

(2 - 7i)(a + bi) = (2a+7b) + (2b-7a)i

We're told the result is purely imaginary. What this means is that the real part (2a+7b) is zero, while the imaginary part (2b-7a) is nonzero. If both are zero, then we have 0+0i = 0 which is purely real.

For example, the complex numbers 0-7i and 0+2i are purely imaginary.

Let's use the fact that 2a+7b must be zero to do the following steps:

2a+7b = 0

2a = -7b

a = -7b/2

a/b = -7/2 which is the final answer

We must check to see if 2b-7a is nonzero

2b - 7a = 2b - 7(-7b/2)

2b - 7a = 2b + 24.5b

2b - 7a = 26.5b

The result is nonzero if and only if b is nonzero. Luckily we're told b is nonzero at the top of the problem. So we don't have any worries that (2b-7a) is zero.

Therefore, (2a+7b) + (2b-7a)i will be purely imaginary with a/b = -7/2

------------------

A concrete example:

Let a = -14 and b = 4

a/b = -14/4 = -7/2

(2-7i)(a+bi) = (2-7i)(-14+4i) = 0 + 106i which is purely imaginary.

I'll let you do the steps in expanding that out using the FOIL rule.

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Answer:

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Step-by-step explanation:

It looks to be asking "Is Jesse correct in saying that he has EXACTLY one liter left?" That would be a no because even though 10L-7L= 3L, the problem asks if he does have exactly ONE liter left, and Jesse says he DOES. But, according to my little equation above, if he drank 7L, he would have 3L left, NOT 1L. Soo, my answer would be "No, Jesse is not correct because 10L-7L=3L and if he says there is 1L left, he would not be correct because there are 3L left." Hope that helps!

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3 years ago
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