Answer:
C -1
Step-by-step explanation:
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.
2 answers:
You might be interested in
Answer:
a) 0.283 or 28.3%
b) 0.130 or 13%
c) 0.4 or 40%
d) 30.6 mm
Step-by-step explanation:
z-score of a single left atrial diameter value of healthy children can be calculated as:
z= where
- X is the left atrial diameter value we are looking for its z-score
- M is the mean left atrial diameter of healthy children (26.7 mm)
- s is the standard deviation (4.7 mm)
Then
a) proportion of healthy children who have left atrial diameters less than 24 mm
=P(z<z*) where z* is the z-score of 24 mm
z*= ≈ −0.574
And P(z<−0.574)=0.283
b) proportion of healthy children who have left atrial diameters greater than 32 mm
= P(z>z*) = 1-P(z<z*) where z* is the z-score of 32 mm
z*= ≈ 1.128
1-P(z<1.128)=0.8703=0.130
c) proportion of healthy children have left atrial diameters between 25 and 30 mm
=P(z(25)<z<z(30)) where z(25), z(30) are the z-scores of 25 and 30 mm
z(30)= ≈ 0.702
z(25)= ≈ −0.362
P(z<0.702)=0.7587
P(z<−0.362)=0.3587
Then P(z(25)<z<z(30)) =0.7587 - 0.3587 =0.4
d) to find the value for which only about 20% have a larger left atrial diameter, we assume
P(z>z*)=0.2 or 20% where z* is the z-score of the value we are looking for.
Then P(z<z*)=0.8 and z*=0.84. That is
0.84= solving this equation for X we get X=30.648
Step-by-step explanation:
use Pythagoras theorem,
1) The function is 3(x + 2)³ - 3
2) The end behaviour is the limits when x approaches +/- infinity.
3) Since the polynomial is of odd degree you can predict that the ends head off in opposite direction. The limits confirm that.
4) The limit when x approaches negative infinity is negative infinity, then the left end of the function heads off downward (toward - ∞).
5) The limit when x approaches positive infinity is positivie infinity, then the right end of the function heads off upward (toward + ∞).
6) To graph the function it is important to determine:
- x-intercepts
- y-intercepts
- critical points: local maxima, local minima, and inflection points.
7) x-intercepts ⇒ y = 0
⇒ <span>3(x + 2)³ - 3 = 0 ⇒ (x + 2)³ - 1 = 0
</span>
<span>⇒ (x + 2)³ = -1 ⇒ x + 2 = 1 ⇒ x = - 1
</span>
8) y-intercepts ⇒ x = 0
y = <span>3(x + 2)³ - 3 = 3(0 + 2)³ - 3 = 0 - 3×8 - 3 = 24 - 3 = 21
</span><span>
</span><span>
</span><span>9) Critical points ⇒ first derivative = 0
</span><span>
</span><span>
</span><span>i) dy / dx = 9(x + 2)² = 0
</span><span>
</span><span>
</span><span>⇒ x + 2 = 0 ⇒ x = - 2
</span><span>
</span><span>
</span><span>ii) second derivative: to determine where x = - 2 is a local maximum, a local minimum, or an inflection point.
</span><span>
</span><span>
</span><span>y'' = 18 (x + 2); x = - 2 ⇒ y'' = 0 ⇒ inflection point.
</span><span>
</span><span>
</span><span>Then the function does not have local minimum nor maximum, but an inflection point at x = -2.
</span><span>
</span><span>
</span><span>Using all that information you can graph the function, and I attache the figure with the graph.
</span>
2) The end behaviour is the limits when x approaches +/- infinity.
3) Since the polynomial is of odd degree you can predict that the ends head off in opposite direction. The limits confirm that.
4) The limit when x approaches negative infinity is negative infinity, then the left end of the function heads off downward (toward - ∞).
5) The limit when x approaches positive infinity is positivie infinity, then the right end of the function heads off upward (toward + ∞).
6) To graph the function it is important to determine:
- x-intercepts
- y-intercepts
- critical points: local maxima, local minima, and inflection points.
7) x-intercepts ⇒ y = 0
⇒ <span>3(x + 2)³ - 3 = 0 ⇒ (x + 2)³ - 1 = 0
</span>
<span>⇒ (x + 2)³ = -1 ⇒ x + 2 = 1 ⇒ x = - 1
</span>
8) y-intercepts ⇒ x = 0
y = <span>3(x + 2)³ - 3 = 3(0 + 2)³ - 3 = 0 - 3×8 - 3 = 24 - 3 = 21
</span><span>
</span><span>
</span><span>9) Critical points ⇒ first derivative = 0
</span><span>
</span><span>
</span><span>i) dy / dx = 9(x + 2)² = 0
</span><span>
</span><span>
</span><span>⇒ x + 2 = 0 ⇒ x = - 2
</span><span>
</span><span>
</span><span>ii) second derivative: to determine where x = - 2 is a local maximum, a local minimum, or an inflection point.
</span><span>
</span><span>
</span><span>y'' = 18 (x + 2); x = - 2 ⇒ y'' = 0 ⇒ inflection point.
</span><span>
</span><span>
</span><span>Then the function does not have local minimum nor maximum, but an inflection point at x = -2.
</span><span>
</span><span>
</span><span>Using all that information you can graph the function, and I attache the figure with the graph.
</span>