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3 years ago

Find the new cost including Sales Tax $99 headphones; 5% tax

Mathematics

1 answer:

sveticcg [70]3 years ago

4 0

The new price is $103.95.
99 + 0.05(99)= $103.95

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PLEASE HELP ME ASAP!! I had trouble with this and it is now over due

erica [24]

Answer:

Shira: x = 8

Samuel: m = 0

Step-by-step explanation:

Shira's mistake was that she subtracted 2 from both sides instead of adding to on both sides.

Correct Solving:

2x - 2 = 14

Add 2 to both sides;

2x = 16

Divide both sides by 2;

x = 8

Samuel's mistake was that when he distributed -2 to 8m and 8 he put the wrong sign for -2 * 8.

Correct Solving:

-2(8m + 8) = -16

Distribute;

-16m - 16 = -16

Add 16 to both sides;

-16m = 0

Divide both sides by -16;

m = 0

3 0

3 years ago

Amy is planning the seating arrangement for her wedding reception. Each round table can sit 10 guests. The head table can sit th

Zigmanuir [339]

236-6 because of head table

230 divided by 10 because of 10 per table

Answer: 23

3 0

2 years ago

P(Q) = 12/17<br> P(R) = 3/8<br> If Q and Rare independent events, find the PQ and R).

kodGreya [7K]

Answer:

9/34

Step-by-step explanation:

P(QnR) = P(Q) * P(R)

= 12/17 * 3/8

= 9/34

6 0

2 years ago

Help help help pls :)

kykrilka [37]

Answer:

$opposite\approx 70.02$

Step-by-step explanation:

The triangle in the given problem is a right triangle, as the tower forms a right angle with the ground. This means that one can use the right angle trigonometric ratios to solve this problem. The right angle trigonometric ratios are as follows;

$sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}$

Please note that the names ( $opposite$ ) and ( $adjacent$ ) are subjective and change depending on the angle one uses in the ratio. However the name ( $hypotenuse$ ) refers to the side opposite the right angle, and thus it doesn't change depending on the reference angle.

In this problem, one is given an angle with the measure of (35) degrees, and the length of the side adjacent to this angle. One is asked to find the length of the side opposite the (35) degree angle. To achieve this, one can use the tangent ( $tan$ ) ratio.

$tan(\theta)=\frac{opposite}{adjacent}$

Substitute,

$tan(35)=\frac{opposite}{100}$

Inverse operations,

$tan(35)=\frac{opposite}{100}$

$100(tan(35))=opposite$

Simplify,

$100(tan(35))=opposite$

$70.02\approx opposite$

4 0

2 years ago

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