Juanita drive 40 miles in 48 minutes At this rate, she will drive ______

What does the term American Dream mean to you?

iragen [17]

The American dream that means to me is being rich and famous

7 0

3 years ago

All vectors are in Rn. Check the true statements below:

Oduvanchick [21]

Answer:

A), B) and D) are true

Step-by-step explanation:

A) We can prove it as follows:

$Proy_{cv}y=\frac{(y\cdot cv)}{||cv||^2}cv=\frac{c(y\cdot v)}{c^2||v||^2}cv=\frac{(y\cdot v)}{||v||^2}v=Proy_{v}y$

B) When you compute the product Ax, the i-th component is the matrix of the i-th column of A with x, denote this by Ai x. Then, we have that $||Ax||=\sqrt{(A_1 x)^2+\cdots (A_n x)^2}$ . Now, the colums of A are orthonormal so we have that (Ai x)^2=x_i^2. Then $||Ax||=\sqrt{(x_1)^2+\cdots (x_n)^2}=||x||$ .

C) Consider $S=\{(0,2),(2,0)\}\subseteq \mathbb{R}^2$ . This set is orthogonal because $(0,2)\cdot(2,0)=0(2)+2(0)=0$ , but S is not orthonormal because the norm of (0,2) is 2≠1.

D) Let A be an orthogonal matrix in $\mathbb{R}^n$ . Then the columns of A form an orthonormal set. We have that $A^{-1}=A^t$ . To see this, note than the component $b_{ij}$ of the product $A^t A$ is the dot product of the i-th row of $A^t$ and the jth row of $A$ . But the i-th row of $A^t$ is equal to the i-th column of $A$ . If i≠j, this product is equal to 0 (orthogonality) and if i=j this product is equal to 1 (the columns are unit vectors), then $A^t A=I$

E) Consider S={e_1,0}. S is orthogonal but is not linearly independent, because 0∈S.

In fact, every orthogonal set in R^n without zero vectors is linearly independent. Take a orthogonal set $\{u_1,u_2\cdots u_p\}$ and suppose that there are coefficients a_i such that $a_1u_1+a_2u_2\cdots a_nu_n=0$ . For any i, take the dot product with u_i in both sides of the equation. All product are zero except u_i·u_i=||u_i||. Then $a_i||u_i||=0$ then $a_i=0$ .

5 0

3 years ago

A rectangular room has a perimeter of 70m and is 20m long write an equation to represent the area

sveta [45]

Do you have any answer choices

4 0

3 years ago

An unfair coin with Pr[H] = 0.2 is flipped. If the flip results in a head, a marble is selected at random from a urn containin

satela [25.4K]

Normally when dealing with coins the probability of getting heads or tails is 0.5 each. However in this case since its an unfair coin, the probability of getting heads is 0.2.
H - head
T - tails
R - red marble
pr (H) = 0.2
urn
6 red and 4 blue
pr (T) = 0.8
urn
3 red and 5 blue

when heads is obtained
red - 6/10 -0.6
blue - 4/10 - 0.4
therefore when multiplying with 0.2 probability of getting heads
pr (R ∩ H) red - 0.6*0.2 = 0.12

when tails is obtained
red - 3/8 - 0.375
blue - 5/8 - 0.625
when multiplying with 0.8 probability of getting tails
pr (R ∩ T) red - 0.375 * 0.8 = 0.3

using bayes rule the answer can be found out,
the following equation is used;
pr (H | R) = pr (R ∩ H) / {pr (R ∩ H) + pr (R ∩ T)}
= 0.12 / (0.12 + 0.3)
= 0.12 / 0.42
= 0.286
the final answer is 0.286

6 0

3 years ago

789/548x-89/887=688/8724 find x

Olin [163]

$\frac{789}{548}x- \frac{89}{887}=\frac{688}{8724}$

first we try to semplify as much as possible the fractions.

First we decompose the numbers

789 = 3 * 263

548 = 2 * 2 * 137 = 2^2

they have nothing in common, so the first fraction remains so

89 = 89 (prime number)

887 = 887 (prime number)

they have nothing in common, so the second one remains so

688 = 2 * 2 * 2 * 2 * 43 = 2^4 * 43

8724 = 2 * 2 * 3 * 727 = 2^2 * 3 * 727

they have 2^2 (=4) in common, so the numerator and the denominator can be devided by 4

$\frac{688}{8724}= \frac{688:4}{8724:4}=\frac{172}{2181}$

so:

$\frac{789}{548}x- \frac{89}{887}=\frac{172}{2181}$

now we calculate the common denominator

take the scomposition:

548 = 2^2 * 137

887 = 887

2181 = 3 * 727

take every number one time

so the common denominator is 2^2 * 137 * 887 * 727 * 3 = 1'060'131'756

now calculate every single numerator: first we divide each denominator by the common denominator, then we moltiply the result with each numerator

first fraction: 789/548

1060131756 / 548 = 1934547

1934547 * 789 = 1526357583

second fraction: 89/887

1060131756 / 887 = 1195188

1195188 * 89 = 106371732

third one: 172/2181

1060131756 / 2181 = 486076

486076 * 172 = 83605072

now we can delete the common denominator

1526357583x - 106371732 = 83605072

solve it

1526357583x = 83605072 + 106371732

1526357583x = 189976804

x = 1526357583 / 189976804

decompose

1526357583 = 887 * 3 * 3 * 727 * 263

189976804 = 137 * 2 * 2 * 211 * 53 * 31

nothing in common

x = 1526357583 / 189976804

8 0

3 years ago

Juanita drive 40 miles in 48 minutes At this rate, she will drive _______ miles in 6 minutes