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BartSMP [9]
3 years ago
12

The grades on a language midterm at Oak Academy are roughly symmetric with = 67 and 0 = 2.5. Ishaan scored 70 on the exam. Find

the z-score for Ishaan's exam grade. Round to the nearest tenth.
Mathematics
1 answer:
rodikova [14]3 years ago
3 0

Answer:  1.2

Step-by-step explanation:

Let X denotes the grades on a  language midterm at Oak Academy.

As per given ,

X follows normal distribution ( because it has symmetric graph)

\mu=67,\ \ \ \ \sigma= 2.5

Formula for z : z=\dfrac{X-\mu}{\sigma}

For X = 70, we have

z=\dfrac{70-67}{2.5}=\dfrac{3}{2.5}=1.2

Hence, the z-score for Ishaan's exam grade = 1.2

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8 0
3 years ago
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Find the critical points of the function f(x, y) = 8y2x − 8yx2 + 9xy. Determine whether they are local minima, local maxima, or
NARA [144]

Answer:

Saddle point: (0,0)

Local minimum: (\frac{3}{8}, -\frac{3}{8})

Local maxima: (0,-\frac{9}{8}), (\frac{9}{8},0)

Step-by-step explanation:

The function is:

f(x,y) = 8\cdot y^{2}\cdot x -8\cdot y\cdot x^{2} + 9\cdot x \cdot y

The partial derivatives of the function are included below:

\frac{\partial f}{\partial x} = 8\cdot y^{2}-16\cdot y\cdot x+9\cdot y

\frac{\partial f}{\partial x} = y \cdot (8\cdot y -16\cdot x + 9)

\frac{\partial f}{\partial y} = 16\cdot y \cdot x - 8 \cdot x^{2} + 9\cdot x

\frac{\partial f}{\partial y} = x \cdot (16\cdot y - 8\cdot x + 9)

Local minima, local maxima and saddle points are determined by equalizing  both partial derivatives to zero.

y \cdot (8\cdot y -16\cdot x + 9) = 0

x \cdot (16\cdot y - 8\cdot x + 9) = 0

It is quite evident that one point is (0,0). Another point is found by solving the following system of linear equations:

\left \{ {{-16\cdot x + 8\cdot y=-9} \atop {-8\cdot x + 16\cdot y=-9}} \right.

The solution of the system is (3/8, -3/8).

Let assume that y = 0, the nonlinear system is reduced to a sole expression:

x\cdot (-8\cdot x + 9) = 0

Another solution is (9/8,0).

Now, let consider that x = 0, the nonlinear system is now reduced to this:

y\cdot (8\cdot y+9) = 0

Another solution is (0, -9/8).

The next step is to determine whether point is a local maximum, a local minimum or a saddle point. The second derivative test:

H = \frac{\partial^{2} f}{\partial x^{2}} \cdot \frac{\partial^{2} f}{\partial y^{2}} - \frac{\partial^{2} f}{\partial x \partial y}

The second derivatives of the function are:

\frac{\partial^{2} f}{\partial x^{2}} = 0

\frac{\partial^{2} f}{\partial y^{2}} = 0

\frac{\partial^{2} f}{\partial x \partial y} = 16\cdot y -16\cdot x + 9

Then, the expression is simplified to this and each point is tested:

H = -16\cdot y +16\cdot x -9

S1: (0,0)

H = -9 (Saddle Point)

S2: (3/8,-3/8)

H = 3 (Local maximum or minimum)

S3: (9/8, 0)

H = 9 (Local maximum or minimum)

S4: (0, - 9/8)

H = 9 (Local maximum or minimum)

Unfortunately, the second derivative test associated with the function does offer an effective method to distinguish between local maximum and local minimums. A more direct approach is used to make a fair classification:

S2: (3/8,-3/8)

f(\frac{3}{8} ,-\frac{3}{8} ) = - \frac{27}{64} (Local minimum)

S3: (9/8, 0)

f(\frac{9}{8},0) = 0 (Local maximum)

S4: (0, - 9/8)

f(0,-\frac{9}{8} ) = 0 (Local maximum)

Saddle point: (0,0)

Local minimum: (\frac{3}{8}, -\frac{3}{8})

Local maxima: (0,-\frac{9}{8}), (\frac{9}{8},0)

4 0
3 years ago
Two figures are similar, and the scale factor is 2/3
d1i1m1o1n [39]

Answer:

The answer is 8.

Step-by-step explanation:

The scale factor between the figures is 2/3, this means that the ratio of the smaller figure to the larger figure is 2/3:

\frac{smaller\:figure}{larger\:figure}=\frac{2}{3}.

So when a side of the the larger figure is 12 then:

\frac{smaller\:figure\: side}{12}=\frac{2}{3}

Therefore

smaller\:figure\:side=\frac{2}{3}*12=8.

Thus the length of the corresponding smaller side is 8.

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[3 - (4 + 32 * 8) ÷ 4] =
serg [7]
<span>[3 - (4 + 32 * 8) ÷ 4] 
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= 3 - 8 ÷ 4
= 3 - 2 
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3 years ago
Translate the word problem using an inequality and solve and graph it.
galben [10]

Answer:

ok

Step-by-step explanation:

6 0
3 years ago
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