So we are given that the mean is 42% and the sd (standard deviation) is 8%
Assuming our data is normal we can use the 68-95-99 rule
So one thing you should realize is that 42% + 8% is 50% which is passing. That is one standard deviation higher. So we use:
100 - 68 - 13.5 - 2.35 - 0.15 = 16. That means 16% of students passed the test. Which is terrible. They probably need to hit the books more.
Anyways if you have any question feel free to message me!
Hopes this helps!
Answer:
x=-4
Step-by-step explanation:
(x+4) ^ (1/3) + (2x+8) ^ (1/3) = 0
Subtract (x+4) ^ (1/3) from each side
(x+4) ^ (1/3) - (x+4) ^ (1/3)+ (2x+8) ^ (1/3) = -(x+4) ^ (1/3)
(2x+8) ^ (1/3) = -(x+4) ^ (1/3)
Cube each side
(2x+8) ^ (1/3) ^3= -(x+4) ^ (1/3)^3
2x+8 = -(x+4)
Distribute the negative sign
2x+8 = -x -4
Add x to each side
2x+8 +x =-x+x-4
3x+8 = -4
Subtract 8 from each side
3x+8-8 =-4-8
3x =-12
Divide by 3
3x/3 = -12/3
x = -4
Answer: 117.6° ; 32.4° .
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Explanation:
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Note: ALL triangles, by definition, have exactly 3 (THREE) sides and exactly 3 (THREE) angles.
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We are given the following:
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We have a triangle.
Angle 1: m∡1 = (8x) ;
Angle 2: m∡2 = (2x + 3) ;
Angle 3: m∡3 = 30.
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We are asked to find: "m∡1" and " m∡2" .
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Note: In ALL TRIANGLES, the measurements of all THREE (3) angles ALWAYS add up to 180 degrees.
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So, " m∡1 + m∡2 + m∡3 = 180 " .
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Let us substitute our given values for the measurements in EACH of
the THREE (3) angles — on the left-hand side of the equation; then solve for "x" ; then substitute that solved value for "x" into the given expressions for BOTH "m∡1" AND "m∡2" ; to find the values for " m∡1" AND " m∡2 " ; which are the values asked for in this very question ;
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m∡1 + m∡2 + m∡3 = 180 ;
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8x + (2x + 3) + 30 = 180 ;
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8x + 2x + 3 + 30 = 180 ;
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Combine the "like terms" on the 'left-hand side" of the equation; to simplify:
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+8x + 2x = +10x ;
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+3 + 30 = +33 ;
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Rewrite the entire equation, as:
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10x + 33 = 180 ;
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Now, subtract "33" from EACH SIDE of the equation:
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10x + 33 − 33 = 180 −<span> 33 ;
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to get:
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10x = 147 ;
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Now, divide EACH side of the equation by "10" ; to isolate "x" on ONE SIDE of the equation; and to solve for "x" :
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10x / 10 = 147 / 10 ;
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to get:
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x = 14.7 ;
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Now, given the following, we plug in our solved value, "14.7", for "x", into the expression given for "m</span>∡1" and "m∡2"; as follows:
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Angle 1: "(8x)" = 8*(14.7) = 117.6° ;
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Angle 2: "2x + 3" = 2*(14.7) + 3 = 29.4 + 3 = 32.4° ;
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These are the two answers; that is the 2 (TWO) values asked for in the question: 117.6° ; 32.4° .
<span>____________________________________</span><span>
Do they make sense? That is, do the measurements of ALL 3 (THREE) angles; that is, our two solved measurements added together, and then added to the value of the third angle (given: "m</span>∡3 = 30°); all add up to 180° ?
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Let us check:
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m∡1 + m∡2 + m∡3 = 180 ;
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Plugging in our solved values for "m∡1" and "m∡2" ; and our given value: "30" — for "m∡3 — does the equation hold true?
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→ 117.6 + 32.4 + 30 = ? 180 ??
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→ 117.6 + 32.4 = 150 ; → 150 + 30 =? 180 ? Yes!
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Answer:
A. h(x)= -5.86x^2 + 23.37x + 34
Step-by-step explanation:
If the scientist uses the same amount of pesticide on the two farms then the x's of the functions are the same.
Then, the combined yield 
of the two farms is just the yield of the first farm plus the yield of the second farm:
.
Now, since
and
,
then
we add the coefficients of the corresponding terms to get:
Which is choice A.
