MATHEMATICS COLLEGE

A fine fabric was selling for $ 10.50 a yard. Joni bought 2 1/3 yards. How much did she spend?

Answers

Answer 1

Answer:

Answer:

$24.50

Step-by-step explanation:

10.50 * 2 1/3 = 24.50

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To make a specific shade of green paint, Timia mixes 2 cups of blue paint with 10 cups of yellow point. How many cups of yellow paint should she mix with one cup of blue paint to make the same shade of green.

consider the quadratic form q(x,y,z)=11x^2-16xy-y^2+8xz-4yz-4z^2. Find an orthogonal change of variable that eliminates the cross product in q(x,y,z) and express q in the new variables.

Answers

Answer:

$q(x,y,z)=16x^(2)-5y^(2)-5z^(2)$

Step-by-step explanation:

The given quadratic form is of the form

$q(x,y,z)=ax^2+by^2+dxy+exz+fyz$ .

Where $a=11,b=-1,c=-4,d=-16,e=8,f=-4$ .Every quadratic form of this kind can be written as

$q(x,y,z)={\bf x}^(T)A{\bf x}=ax^2+by^2+cz^2+dxy+exz+fyz=\left(\begin{array}{ccc}x&y&z\end{array}\right) \left(\begin{array}{ccc}a&(1)/(2) d&(1)/(2) e\n(1)/(2) d&b&(1)/(2) f\n(1)/(2) e&(1)/(2) f&c\end{array}\right) \left(\begin{array}{c}x&y&z\end{array}\right)$

Observe that $A$ is a symmetric matrix. So $A$ is orthogonally diagonalizable, that is to say, $D=Q^(T)AQ$ where $Q$ is an orthogonal matrix and $D$ is a diagonal matrix.

In our case we have:

$A=\left(\begin{array}{ccc}11&((1)/(2))(-16) &((1)/(2)) (8)\n((1)/(2)) (-16)&(-1)&((1)/(2)) (-4)\n((1)/(2)) (8)&((1)/(2)) (-4)&(-4)\end{array}\right)=\left(\begin{array}{ccc}11&-8 &4\n-8&-1&-2\n4&-2&-4\end{array}\right)$

The eigenvalues of $A$ are $\lambda_(1)=16,\lambda_(2)=-5,\lambda_(3)=-5$ .

Every symmetric matriz is orthogonally diagonalizable. Applying the process of diagonalization by an orthogonal matrix we have that:

$Q=\left(\begin{array}{ccc}(4)/(√(21))&-(1)/(√(17))&(8)/(√(357))\n(-2)/(√(21))&0&\sqrt{(17)/(21)}\n(1)/(√(21))&(4)/(√(17))&(2)/(√(357))\end{array}\right)$

$D=\left(\begin{array}{ccc}16&0&0\n0&-5&0\n0&0&-5\end{array}\right)$

Now, we have to do the change of variables ${\bf x}=Q{\bf y}$ to obtain

$q({\bf x})={\bf x}^(T)A{\bf x}=(Q{\bf y})^(T)AQ{\bf y}={\bf y}^(T)Q^(T)AQ{\bf y}={\bf y}^(T)D{\bf y}=\lambda_(1)y_(1)^(2)+\lambda_(2)y_(2)^(2)+\lambda_(3)y_(3)^(2)=16y_(1)^(2)-5y_(2)^(2)-5y_(3)^2$

Which can be written as:

$q(x,y,z)=16x^(2)-5y^(2)-5z^(2)$

-1/2 + (3/4 x 4/9) =

Answers

-.1666667
You can use khan academy or Socratic if you still not sure.

How does 3.71 round up to 3.7

Answers

Answer:

Step-by-step explanation:

cuz 7 is greater then 5

An ESP experiment used the "Ten Choice Trainer." This is like the Aquarius, but with 10 targets instead of 4. Suppose that in 1,000 trials, a subject scores 173 correct guesses. Required:
a. Set up the null hypothesis as a box model.
b. The SD of the box is:_______
c. Make the z-test.
d. What do you conclude?

Answers

Answer:

a. The H0 is number of correct guesses is 173

b. Standard Deviation of box is 0.3

c. z-test value is 7.70

d. The difference does not appear due to chances of Variation.

Step-by-step explanation:

The standard deviation is :

$√(0.1 * 0.9)$ = 0.3

The standard deviation of the box is 0.3 approximately.

Z-score is $(x-u)/(standard error)$

Z-score = $(173-100)/(9.4868)$

the value of z-score is 7.70.

farmer ed has 3000 meters of fencing and wants to enclose a rectangle plot that borders on a river. if farmer ed does not fence the side along the river what is the largest area that can be enclosed

Answers

Answer:

area = 1500× 750 = $1125000 m^2$

Step-by-step explanation:

we know area of rectangle

for length = l m

and width = b m

$A = lb$

and perimeter

$Perimeter = 2 (length + width)$

but one side length measures is not required because of the river so

He does not use the fence along the side of the river

so we use this formula

Perimeter = P = L + 2 b

Perimeter is 3000 m

$so \ \ 3000 = l +2b$

$l = 3000 - 2b$

so area will be

$A = (3000-2b)b$

it is a quadratic function whose max or min will

occur at the average of the Solutions.

on Solving (3000 - 2b)b = 0

3000 - 2b = 0 or b=0

2b =3000

$b =(3000)/(2) \nb = 1500 m$

or $b = 0 m$

The average of the values are $((0+1500))/(2) = 750$

so for max area we use b= $750 m$

The Length is then L=3000 - 2(750) = 3000 - 1500 = 1500

for max area

length = 1500 m

bredth = 750 m

area = 1500× 750 = $1125000 m^2$

Final answer:

The largest area that can be enclosed by Farmer Ed with 3000 meters of fencing along a river (with only three sides fenced) equals 1,125,000 square meters by using principles of mathematical optimization.

Explanation:

In this question, Farmer Ed wants to maximize the area of a rectangle with only three sides fenced, since one side borders on a river. We can use the principles of optimization in mathematics to solve this problem.

With 3000 meters of fencing for three sides, if we denote one side perpendicular to the river as X and the side parallel to the river (which forms the base of the rectangle) as Y, then, the perimeter would be Y+2X which is equal to 3000 meters. So, Y = 3000-2X.

The area A of a rectangle is length times width, or, in this case, A = XY. Substituting Y from the equation above: A = X(3000-2X) = 3000X - 2X^2. To maximize this area, we need to find values of X for which this equation has its maximum value.

The maximum or minimum of a function can be found at points where its derivative is zero. So, we take the derivative of A with respect to X, set it equal to zero, and solve for X.

The derivative, dA/dX is 3000 - 4X. Setting this equal to 0 gives X = 3000/4 = 750. So, the maximum area that Farmer Ed can enclose is when X is 750, and Y is 3000 - 2X = 1500, so the maximum area is 750 * 1500 = 1,125,000 square meters.

Learn more about Mathematical Optimization here:

brainly.com/question/32199704

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Consider the following system of equations:Equation 1: 82 + 2y = 30
Equation 2: 70 + 2y = 24
Which variable pair should we try to eliminate?
The x's because the coefficients are the same.
The y's because the coefficients are the same.
The x's because the coefficients are different?
The y's because the coefficients are different?

Answers

The correct answer is: "The y's because the coefficients are the same."

Further explanation:

we always try to eliminate the variable from the system of equations which involves lesser calculations and complexity.

Assuming that Given equations are:

Equation 1: 82x + 2y = 30

Equation 2: 70x + 2y = 24

we can see that the coefficients of x are very large and different. While the coefficients of y are same. We can only subtract the equations to eliminate y.

Hence,

The correct answer is: "The y's because the coefficients are the same."

Keywords: Linear equations, variables

Learn more about linear equations at:

#LearnwithBrainly

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