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3 years ago

Select the name of the vector and complete its component form.

Mathematics

1 answer:

love history [14]3 years ago

8 0

Answer:

GH = (5, -3)

Step-by-step explanation:

The horizontal extent of the vector is 5 squares; the vertical extent is 3 squares. H has a lower y-value than G, so the vertical component is -3.

GH = (5, -3)

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4 years ago

What is the sum of the first 37 terms of the arithmetic sequence?

lidiya [134]

Answer:

The sum of the first 37 terms of the arithmetic sequence is 2997.

Step-by-step explanation:

Arithmetic sequence concepts:

The general rule of an arithmetic sequence is the following:

$a_{n+1} = a_{n} + d$

In which d is the common diference between each term.

We can expand the general equation to find the nth term from the first, by the following equation:

$a_{n} = a_{1} + (n-1)*d$

The sum of the first n terms of an arithmetic sequence is given by:

$S_{n} = \frac{n(a_{1} + a_{n})}{2}$

In this question:

$a_{1} = -27, d = -21 - (-27) = -15 - (-21) = ... = 6$

We want the sum of the first 37 terms, so we have to find $a_{37}$

$a_{n} = a_{1} + (n-1)*d$

$a_{37} = a_{1} + (36)*d$

$a_{37} = -27 + 36*6$

$a_{37} = 189$

Then

$S_{37} = \frac{37(-27 + 189)}{2} = 2997$

The sum of the first 37 terms of the arithmetic sequence is 2997.

6 0

3 years ago

A very large study showed that aspirin reduced the rate of heart attacks by 44%. A pharmaceutical company thinks they have a dru

Butoxors [25]

Answer: $H_0:\mu=0.44\ ,H_a:\mu$

Step-by-step explanation:

Since we have given that

A very large study showed that aspirin reduced the rate of heart attacks by 44%.

we claim that they have a drug that will be more effective than aspirin.

so, our hypothesis would be

$H_0:\mu=0.44\\\\H_a:\mu$

So, it will be one tail test.

Hence, $H_0:\mu=0.44\\\\H_a:\mu$

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3 years ago

Please help ASAP Meteorologists are planning the location of a new weather station to cover Santa Cruz, Morgan Hill, and Gilroy,

Likurg_2 [28]

Answer:

(-1, -2.5)

Step-by-step explanation:

(3, 0) is the midpoint between (2, 2) and (4, -2)

(-5, -5) (3, 0) the midpoint between these two points is

(-5 + 3) / 2 = -1, (-5 + 0) / 2 = -2.5

4 0

3 years ago

Which expression correctly displays the calculations to find the a^5b^4 term of (a+b)^8

LUCKY_DIMON [66]

Answer:

Step-by-step explanation:

THE BINOMIAL THEOREM shows how to calculate a power of a binomial -- (a + b)n -- without actually multiplying.

For example, if we actually multiplied out the 4th power of (a + b) --

(a + b)4 = (a + b)(a + b)(a + b)(a + b)

-- then on collecting like terms we would find:

(a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4 . . . . (1)

Note: The literal factors are all possible terms in a and b where the sum of the exponents is 4: a4, a3b, a2b2, ab3, b4.

The degree of each term is 4.

The first term is actually a4b0, which is a4 · 1.

Thus to "expand" (a + b)5, we would anticipate the following terms, in which the sum of all the exponents is 5:

(a + b)5 = ? a5 + ? a4b + ? a3b2 + ? a2b3 + ? ab4 + ? b5

The question is, What are the coefficients?

They are called the binomial coefficients. In the expansion of

(a + b)4, the binomial coefficients are

1 4 6 4 1

line (1) above.

Note the symmetry: The coefficients from left to right are the same right to left.

The answer to the question, "What are the binomial coefficients?" is called the binomial theorem. It shows how to calculate the coefficients in the expansion of (a + b)n.

The symbol for a binomial coefficient is The binomial theorem. The upper index n is the exponent of the expansion; the lower index k indicates which term, starting with k = 0.

For example, when n = 5, each term in the expansion of (a + b)5 will look like this:

The binomial theorema5 − kbk

k will successively take on the values 0 through 5.

(a + b)5 = The binomial theorema5 + The binomial theorema4b + The binomial theorema3b2 + The binomial theorema2b3 + The binomial theorem ab4 + The binomial theoremb5

Note: Each lower index is the exponent of b. The first term has k = 0 because in the first term, b appears as b0, which is 1.

Now, what are these binomial coefficients, The binomial theorem ?

The theorem states that the binomial coefficients are none other than the combinatorial numbers, nCk .

The binomial theorem = nCk

(a + b)5 = 5C0a5 + 5C1a4b + 5C2a3b2 + 5C3a2b3 + 5C4ab4 + 5C5b5

= 1a5 + The binomial theorema4b + The binomial theorema3b2 + The binomial theorema2b3 + The binomial theoremab4 + The binomial theoremb5

= a5 + 5a4b + 10a3b2 + 10a2b3 + 5ab4 + b5

The binomial coefficients here are

1 5 10 10 5 1.

8 0

3 years ago