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3 years ago

Need help with these answer please and thank you..

Mathematics

1 answer:

Volgvan3 years ago

5 0

Answer:

There were were 30 Buses for a Field Trip. If 18 buses were in transit, 3 still at the school, and 9 that have arrived, and 300 kids at the school, how many kids arrived at the Field Trip? (There are an equal amount of kids in each bus.

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Determine which of the sets of vectors is linearly independent. A: The set where p1(t) = 1, p2(t) = t2, p3(t) = 3 + 3t B: The se

defon

Answer:

The set of vectors A and C are linearly independent.

Step-by-step explanation:

A set of vector is linearly independent if and only if the linear combination of these vector can only be equalised to zero only if all coefficients are zeroes. Let is evaluate each set algraically:

$p_{1}(t) = 1$ , $p_{2}(t)= t^{2}$ and $p_{3}(t) = 3 + 3\cdot t$ :

$\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0$

$\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (3 +3\cdot t) = 0$

$(\alpha_{1}+3\cdot \alpha_{3})\cdot 1 + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot t = 0$

The following system of linear equations is obtained:

$\alpha_{1} + 3\cdot \alpha_{3} = 0$

$\alpha_{2} = 0$

$\alpha_{3} = 0$

Whose solution is $\alpha_{1} = \alpha_{2} = \alpha_{3} = 0$ , which means that the set of vectors is linearly independent.

$p_{1}(t) = t$ , $p_{2}(t) = t^{2}$ and $p_{3}(t) = 2\cdot t + 3\cdot t^{2}$

$\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0$

$\alpha_{1}\cdot t + \alpha_{2}\cdot t^{2} + \alpha_{3}\cdot (2\cdot t + 3\cdot t^{2})=0$

$(\alpha_{1}+2\cdot \alpha_{3})\cdot t + (\alpha_{2}+3\cdot \alpha_{3})\cdot t^{2} = 0$

The following system of linear equations is obtained:

$\alpha_{1}+2\cdot \alpha_{3} = 0$

$\alpha_{2}+3\cdot \alpha_{3} = 0$

Since the number of variables is greater than the number of equations, let suppose that $\alpha_{3} = k$ , where $k\in\mathbb{R}$ . Then, the following relationships are consequently found:

$\alpha_{1} = -2\cdot \alpha_{3}$

$\alpha_{1} = -2\cdot k$

$\alpha_{2}= -2\cdot \alpha_{3}$

$\alpha_{2} = -3\cdot k$

It is evident that $\alpha_{1}$ and $\alpha_{2}$ are multiples of $\alpha_{3}$ , which means that the set of vector are linearly dependent.

$p_{1}(t) = 1$ , $p_{2}(t)=t^{2}$ and $p_{3}(t) = 3+3\cdot t +t^{2}$

$\alpha_{1}\cdot p_{1}(t) + \alpha_{2}\cdot p_{2}(t) + \alpha_{3}\cdot p_{3}(t) = 0$

$\alpha_{1}\cdot 1 + \alpha_{2}\cdot t^{2}+ \alpha_{3}\cdot (3+3\cdot t+t^{2}) = 0$

$(\alpha_{1}+3\cdot \alpha_{3})\cdot 1+(\alpha_{2}+\alpha_{3})\cdot t^{2}+3\cdot \alpha_{3}\cdot t = 0$

The following system of linear equations is obtained:

$\alpha_{1}+3\cdot \alpha_{3} = 0$

$\alpha_{2} + \alpha_{3} = 0$

$3\cdot \alpha_{3} = 0$

Whose solution is $\alpha_{1} = \alpha_{2} = \alpha_{3} = 0$ , which means that the set of vectors is linearly independent.

The set of vectors A and C are linearly independent.

4 0

3 years ago

A fair spinner has 11 equal sections: 4 red, 4 blue and 3 green.

Darina [25.2K]

Answer:

24/121

Step-by-step explanation:

The probability of an event happening is the ratio of the number of possible outcome to the number of total outcome.

The probability of not getting green then green

= rg or bg

Where r is the probability of getting red, g is the probability of green and b is the probability of blue.

= 4/11 * 3/11 + 4/11 * 3/11

= 12/121 + 12/121

= 24/121

4 0

3 years ago

Jazzie runs 5 miles each day.How many days will it take her to jog 57 miles?

kodGreya [7K]

Answer:

It will take her 11.4 days, or 12 whole days to jog 57 miles

Step-by-step explanation:

1 day = 5 miles

? days = 57 miles

57/5 = 11.4 days

4 0

3 years ago

Read 2 more answers

WILL GIVE BRAINEST FOR THE FIRST PERSON TO ANSWER THAT IS CORRECT WITH A FULL EXPLANATION AS TO WHY YOU GOT THAT ANSWER! THANKS

Kryger [21]

Answer:

it would be a rectangle

Step-by-step explanation:

it would be a rectangle because when you cut it in the cross section there will be four parell sides, so therefore it would have to make a rectangle because the side lengths would not be even.

4 0

3 years ago

Read 2 more answers

Please help me with this question!!

nata0808 [166]

Answer:

(4, 3)

Step-by-step explanation:

x = (-2 + 10)/2 = 4

y = (3+3)/2 = 3

(4,3)

6 0

3 years ago

Need help with these answer please and thank you..​

Need help with these answer please and thank you..