What is a unit vector

If one of the non-right angles in a right triangle is equivalent to an angle in another right triangle, what can you say about t

Vitek1552 [10]

The triangles are similar, they aren't congruent (identical) though as we don't know if they share a common side

7 0

3 years ago

Read 2 more answers

Solve for x. 6(x – 1) = 9(x + 2)

bazaltina [42]

Let's solve your equation step-by-step.
6(x−1)=9(x+2)
Step 1: Simplify both sides of the equation.
6(x−1)=9(x+2)
Simplify:
(6)(x)+(6)(−1)=(9)(x)+(9)(2)(Distribute)
6x+−6=9x+18
6x−6=9x+18
Step 2: Subtract 9x from both sides.
6x−6−9x=9x+18−9x
−3x−6=18
Step 3: Add 6 to both sides.
−3x−6+6=18+6
−3x=24
Step 4: Divide both sides by -3.
−3x−3=24−3
x=−8
Answer: x= -8

-Hope I helped.

8 0

3 years ago

Read 2 more answers

One year Roger had the lowest ERAâ€‹ (earned-run average, mean number of runs yielded per nine inningsâ€‹ pitched) of any male p

baherus [9]

Answer:

(a) The z-score of Roger is -1.56 and the z-score of Amber is -1.13.

(b) Roger had a better year relative to his peers.

Step-by-step explanation:

If X follows N (µ, σ₂), then $z=\frac{x-\mu}{\sigma}$ , is a standard normal variate with mean, E (Z) = 0 and Var (Z) = 1. That is, Z follows N (0, 1).

Let X = ERA of male pitchers and Y = ERA of ERA of female pitchers.

It is provided that the mean and standard deviation of X are:

$\mu_{X}=4.371\\\sigma_{X}=0.787$

Also, the mean and standard deviation of Y are:

$\mu_{Y}=4.363\\\sigma_{Y}=0.869$

ER of Roger is 3.14 and ERA of Amber is 3.38.

(1)

Compute the z-score of Roger as follows:

$z=\frac{x-\mu_{X}}{\sigma_{X}}=\frac{3.14-4.371}{0.787}=-1.56$

Thus, the z-score of Roger is -1.56.

Compute the z-score of Amber as follows:

$z=\frac{x-\mu_{Y}}{\sigma_{Y}}=\frac{3.38-4.363}{0.869}=-1.13$

Thus, the z-score of Amber is -1.13.

(2)

Compute the probability of ERA's that are greater than Roger's ERA as follows:

$P(X>3.14)=P(\frac{X-\mu}{\sigma}>\frac{3.14-4.371}{0.787})\\=P(Z>-1.56)\\=P(Z$

This implies that 94% of the other male pitchers had an ERA higher than 3.14.

Compute the probability of ERA's that are greater than Amber's ERA as follows:

$P(Y>3.38)=P(\frac{Y-\mu_{Y}}{\sigma_{Y}}>\frac{3.38-4.363}{0.869})\\=P(Z>-1.13)\\=P(Z$

This implies that 87% of the other female pitchers had an ERA higher than 3.38.

As it is provided that the lower the ERA the better the pitcher, then it can be concluded that Roger had a better year relative to his peers.

4 0

4 years ago

The school band is scheduled to march in the annual parade, but the band’s starting point is changed the day before the parade.

sattari [20]

D. 40

follow the pattern

1 band director calls 3 members. = 4

Each member calls 3 more members 3(3) = 9

Then each of those 9 call 3 more members 9(3) = 27

Add them up

4+9+27 = 40

3 0

3 years ago

Find the projection of the vector A = î - 2ġ + k on the vector B = 4 i - 4ſ + 7k. 15. Given the vectors A = 2 i +3 ſ +6k and B =

Gwar [14]

Answer:

Part 1)

Projection of vector A on vector B equals 19 units

Part 2)

Projection of vector B' on vector A' equals 35 units

Step-by-step explanation:

For 2 vectors A and B the projection of A on B is given by the vector dot product of vector A and B

Given

$\overrightarrow{v_{a}}=\widehat{i}-2\widehat{j}+\widehat{k}$

Similarly vector B is written as

$\overrightarrow{v_{b}}=4\widehat{i}-4\widehat{j}+7\widehat{k}$

Thus the vector dot product of the 2 vectors is obtained as

$\overrightarrow{v_{a}}\cdot \overrightarrow{v_{b}}=(\widehat{i}-2\widehat{j}+\widehat{k})\cdot (4\widehat{i}-4\widehat{j}+7\widehat{k})\\\\\overrightarrow{v_{a}}\cdot \overrightarrow{v_{b}}=1\cdot 4+2\cdot 4+1\cdot 7=19$

Part 2)

Given vector A' as

$\overrightarrow{v_{a'}}=2\widehat{i}+3\widehat{j}+6\widehat{k}$

Similarly vector B' is written as

$\overrightarrow{v_{b'}}=\widehat{i}+5\widehat{j}+3\widehat{k}$

Thus the vector dot product of the 2 vectors is obtained as

$\overrightarrow{v_{b'}}\cdot \overrightarrow{v_{a'}}=(\widehat{i}+5\widehat{j}+3\widehat{k})\cdot (2\widehat{i}+3\widehat{j}+6\widehat{k})\\\\\overrightarrow{v_{a'}}\cdot \overrightarrow{v_{b'}}=1\cdot 2+5\cdot 3+3\cdot 6=35$

7 0

4 years ago