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3 years ago

Evaluate the expression. r = , v = , w = v ⋅ w

Mathematics

1 answer:

FromTheMoon [43]3 years ago

6 0

Answer:

v . w= -13

Step-by-step explanation:

Evaluate the expression: v ⋅ w Given the vectors: r = <8, 1, -6>; v = <6, 7, -3>; w = <-7, 5, 2>

Solution

Given the vectors:

r = <8, 1, -6>

v = <6, 7, -3>

w = <-7, 5, 2>

If you're asking about the dot product.

The dot product is a scalar. It is the sum of the product of the corresponding components.

v.w = (6*-7) + (7*5) + (-3*2)

= -42+35-6

= -13.

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Yesterday, Caitlin swam 20 laps in the pool. Hannah swam 4/5 as many laps As Caitlin. How many laps did Hannah swim?

Misha Larkins [42]

Caitlin = 20 laps

Hannah = 4/5 as many laps

Multiply the laps swan by Caitlin (20) by 4/5

20 x 4/5 = 80/5 = 16

Hannah swam 16 laps

6 0

1 year ago

The mean student loan debt for college graduates in Illinois is $30000 with a standard deviation of $9000. Suppose a random samp

Nataly [62]

Answer:

the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331

Step-by-step explanation:

Given that:

Mean = 30000

Standard deviation = 9000

sample size = 100

The probability that the mean student loan debt for these people is between $31000 and $33000 can be computed as:

$P(31000 < X < 33000) = P( X \leq 33000) - P (X \leq 31000)$

$P(31000 < X < 33000) = P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P( \dfrac{X - 30000}{\dfrac{\sigma}{\sqrt{n}}} \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )$

$P(31000 < X < 33000) = P( Z \leq \dfrac{33000 - 30000}{\dfrac{9000}{\sqrt{100}}} )- P(Z \leq \dfrac{31000 - 30000}{\dfrac{9000}{\sqrt{100}}} )$

$P(31000 < X < 33000) = P( Z \leq \dfrac{3000}{\dfrac{9000}{10}}}) -P(Z \leq \dfrac{1000}{\dfrac{9000}{10}}})$

$P(31000 < X < 33000) = P( Z \leq 3.33)-P(Z \leq 1.11})$

From Z tables:

$P(31000 < X$

Therefore; the probability that the mean student loan debt for these people is between $31000 and $33000 is 0.1331

8 0

3 years ago

Find the accumulated value of an investment $10,000 for 3 years at an interest of 7% if the money is compounded semiannually; co

asambeis [7]

Answer:

Correct answer: 1) AV = 12,290 $, 2) AV = 12,310 $, 3) AV = 12,330 $,

4) AV = 12,337 $

Step-by-step explanation:

Given:

I = 10,000$

n = 3 years

p = 7% = 0.07

Accumulated value of an investment is calculated with next formula:

AV = I · (1 + (p/a))ᵃⁿ where is:

AV - accumulated value

I - investment

p - interest

a - number of calculation parts during one year as the accounting period

n - number of years as the accounting period

1) money is compounded semiannually

a = 2 and a · n = 2 · 3 = 6

AV = I · (1 + (p/a))ᵃⁿ = 10,000 · (1 + (0.07/2))⁶ = 10,000 · 1.229 = 12,290 $

AV = 12,290 $

2) money is compounded quarterly

a = 4 and a · n = 4 · 3 = 12

AV = I · (1 + (p/a))ᵃⁿ = 10,000 · (1 + (0.07/4))¹² = 10,000 · 1.231 = 12,310 $

AV = 12,310 $

3) money is compounded monthly

a = 12 and a · n = 12 · 3 = 36

AV = I · (1 + (p/a))ᵃⁿ = 10,000 · (1 + (0.07/12))³⁶ = 10,000 · 1.233 = 12,330 $

AV = 12,330 $

4) money is compounded continuously

Accumulated value of an investment continuously compounded is calculated with next formula:

AV = I · eⁿᵇ where is:

n - number of years as the accounting period

b = p = 7% = 0.07

n · b = 3 · 0.07 = 0.21

AV = 10,000 e⁰²¹ = 10,000 2.7183⁰²¹ = 10,000 1.2337 = 12,337 $

AV = 12,337 $

God is with you!!!

8 0

3 years ago

This graph displays a linear function. What is the rate of change?

ivolga24 [154]

Answer:

5/1 or 5

Step-by-step explanation: You find two points that the line goes on. So in this it would be 1,1 for the first one, the second one is 2,4. Then you go from the first point up or down to get to the same level at the second point. Then you go over to the left or right to meet the second point, in this graph you will go up 5 times to get to the same level. Then over 1 time to get to the point. Then you divide the rise over the run the rise is 5 and the run is 1, so you would do 5 divided by 1 and the answer of that is 5.

Hope this helps you in the future

Smiles, MysticCryptic (Aka) Jordan

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3 years ago

What is a formula for the nth term of the given sequence?<br> 36, 24, 16...

SpyIntel [72]

Answer:

The formula to find the nth term of the given sequence is 54 · $\frac{2}{3} ^{n}$