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Elden [556K]
3 years ago
15

Scores on the mathematics part of the SAT exam in a recent year were roughly Normal with mean 455 and standard deviation 120. Yo

u choose an SRS of 100 students and average their SAT math scores. If you do this many times, with a sample of size 100 each time, the standard deviation of the average scores will get close to:A. 120 B. 1.2 C. 12 D. None of the above.
Mathematics
1 answer:
laila [671]3 years ago
7 0

Answer:

its a

Step-by-step explanation:

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Find the function value. tan 240°
ivanzaharov [21]

Answer:

Step-by-step explanation:

240 has a reference angle of 60 in the third quadrant. The side across from 60 is going to be negative in this quadrant, measuring -√3; the side adjacent to the angle is also negative in this quadrant, measuring -1. The tangent ratio is the side opposite the angle over the side adjacent to the angle, so

tan(240) = √3

7 0
3 years ago
Find the absolute extrema of the function over the region R. (In each case, R contains the boundaries.) Use a computer algebra s
algol [13]

<em>f(x, y)</em> = <em>x</em> ² - 4<em>xy</em> + 5

has critical points where both partial derivatives vanish:

∂<em>f</em>/∂<em>x</em> = 2<em>x</em> - 4<em>y</em> = 0   ==>   <em>x</em> = 2<em>y</em>

∂<em>f</em>/∂<em>y</em> = -4<em>x</em> = 0   ==>   <em>x</em> = 0   ==>   <em>y</em> = 0

The origin does not lie in the region <em>R</em>, so we can ignore this point.

Now check the boundaries:

• <em>x</em> = 1   ==>   <em>f</em> (1, <em>y</em>) = 6 - 4<em>y</em>

Then

max{<em>f</em> (1, <em>y</em>) | 0 ≤ <em>y</em> ≤ 2} = 6 when <em>y</em> = 0

max{<em>f</em> (1, <em>y</em>) | 0 ≤ <em>y</em> ≤ 2} = -2 when <em>y</em> = 2

• <em>x</em> = 4   ==>   <em>f</em> (4, <em>y</em>) = 12 - 16<em>y</em>

Then

max{<em>f</em> (4, <em>y</em>) | 0 ≤ <em>y</em> ≤ 2} = 12 when <em>y</em> = 0

max{<em>f</em> (4, <em>y</em>) | 0 ≤ <em>y</em> ≤ 2} = -4 when <em>y</em> = 2

• <em>y</em> = 0   ==>   <em>f</em> (<em>x</em>, 0) = <em>x</em> ² + 5

Then

max{<em>f</em> (<em>x</em>, 0) | 1 ≤ <em>x</em> ≤ 4} = 21 when <em>x</em> = 4

min{<em>f</em> (<em>x</em>, 0) | 1 ≤ <em>x</em> ≤ 4} = 6 when <em>x</em> = 1

• <em>y</em> = 2   ==>   <em>f</em> (<em>x</em>, 2) = <em>x</em> ² - 8<em>x</em> + 5 = (<em>x</em> - 4)² - 11

Then

max{<em>f</em> (<em>x</em>, 2) | 1 ≤ <em>x</em> ≤ 4} = -2 when <em>x</em> = 1

min{<em>f</em> (<em>x</em>, 2) | 1 ≤ <em>x</em> ≤ 4} = -11 when <em>x</em> = 4

So to summarize, we found

max{<em>f(x, y)</em> | 1 ≤ <em>x</em> ≤ 4, 0 ≤ <em>y</em> ≤ 2} = 21 at (<em>x</em>, <em>y</em>) = (4, 0)

min{<em>f(x, y)</em> | 1 ≤ <em>x</em> ≤ 4, 0 ≤ <em>y</em> ≤ 2} = -11 at (<em>x</em>, <em>y</em>) = (4, 2)

5 0
3 years ago
The value of 4 less than the product of 0.25 and x is greater than 6. What are all the possible values of x? SHOW YOUR WORK!
seraphim [82]

Answer:

0.25x - 4 > 6

Step-by-step explanation:

First, we would like to thank you for all of the additional support you offer at home. ... Subtract the absolute values. Multiply the denominators. 4. Reduce if necessary. 3. 10 x. 2. 3. 6. 30. = 1. 5. 3 ... 1 less than the product of 3 and m 3m – 1.

6 0
3 years ago
Anwar is thinking of a number. He gives three clues about his number: It is an odd number; The number is less than -12; and The
tigry1 [53]

Answer:

-13

Step-by-step explanation:

it must be either -11 or -13. -13 is less  than -12.

6 0
2 years ago
Write an equation that could be used to solve the given problem: if twice a number is increased by 15 , the result is the same a
Semmy [17]
Equation 2X+15= X-10

X=-25
7 0
3 years ago
Read 2 more answers
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