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2 years ago

Carter lives on a street where all the house numbers are a multiple of 6. Name two house numbers between 601 and 650

Mathematics

1 answer:

GarryVolchara [31]2 years ago

7 0

Answer:

606 and 612

Step-by-step explanation:

A number is a multiple of 6 if:

1. the sum of its integers can be divided by 3

2. The number is even (ending in 0, 2, 4, 6, 8

With this rule in mind, you have to play around with the numbers. Of course, all odd numbers are out.

606:

6 is even

6 + 6 = 12

12 divided by 4 is 3

612:

2 is even

6 + 1 + 2= 9

9 divided by 3 is 3

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Which binomial is a factor of49x^2+84xy+36y^2

Alex17521 [72]

Answer:

(7 x + 6 y)^2

Step-by-step explanation:

Factor the following:

49 x^2 + 84 x y + 36 y^2

The coefficient of x^2 is 49 and the coefficient of y^2 is 36. The product of 49 and 36 is 1764. The factors of 1764 which sum to 84 are 42 and 42. So 49 x^2 + 84 x y + 36 y^2 = 49 x^2 + 42 x y + 42 x y + 36 y^2 = 7 x (7 x + 6 y) + 6 y (7 x + 6 y):

7 x (7 x + 6 y) + 6 y (7 x + 6 y)

Factor 7 x + 6 y from 7 x (7 x + 6 y) + 6 y (7 x + 6 y):

(7 x + 6 y) (7 x + 6 y)

(7 x + 6 y) (7 x + 6 y) = (7 x + 6 y)^2:

Answer: (7 x + 6 y)^2

3 0

3 years ago

Let X be a Bernoulli rv with pmf as in Example 3.18. a. Compute E(X2 ). b. Show that V(X) 5 p(1 2 p). c. Compute E(X79).

spayn [35]

The Bernoulli distribution is a distribution whose random variable can only take 0 or 1

The value of E(x2) is p
The value of V(x) is p(1 - p)
The value of E(x79) is p

<h3>How to compute E(x2)</h3>

The distribution is given as:

p(0) = 1 - p

p(1) = p

The expected value of x2, E(x2) is calculated as:

$E(x^2) = \sum x^2 * P(x)$

So, we have:

$E(x^2) = 0^2 * (1- p) + 1^2 * p$

Evaluate the exponents

$E(x^2) = 0 * (1- p) + 1 * p$

Multiply

$E(x^2) = 0 +p$

Add

$E(x^2) = p$

Hence, the value of E(x2) is p

<h3>How to compute V(x)</h3>

This is calculated as:

$V(x) = E(x^2) - (E(x))^2$

Start by calculating E(x) using:

$E(x) = \sum x * P(x)$

So, we have:

$E(x) = 0 * (1- p) + 1 * p$

$E(x) = p$

Recall that:

$V(x) = E(x^2) - (E(x))^2$

So, we have:

$V(x) = p - p^2$

Factor out p

$V(x) = p(1 - p)$

Hence, the value of V(x) is p(1 - p)

<h3>How to compute E(x79)</h3>

The expected value of x79, E(x79) is calculated as:

$E(x^{79}) = \sum x^{79} * P(x)$

So, we have:

$E(x^{79}) = 0^{79} * (1- p) + 1^{79} * p$

Evaluate the exponents

$E(x^{79}) = 0 * (1- p) + 1 * p$

Multiply

$E(x^{79}) = 0 + p$

Add

$E(x^{79}) = p$

Hence, the value of E(x79) is p

Read more about probability distribution at:

brainly.com/question/15246027

5 0

2 years ago

Distance between (-10,9) and (-5,2)

jonny [76]

Answer:

8.60 units (3 s.f.)

Step-by-step explanation:

The distance between 2 points is given by the formula:

$\sqrt{(y1 - y2)^{2} + {(x1 - x2)}^{2} }$

Thus using the above formula,

Distance between (-10, 9) and (-5, 2)

$= \sqrt{ {(9 - 2)}^{2} + {( - 10 + 5)}^{2} } \\ = \sqrt{ {7}^{2} + ( - 5)^{2} } \\ = \sqrt{74} \\ = 8.60 \: units \: (3 \: s.f.)$

8 0

3 years ago

Factorize: x² + 3x + 2

zvonat [6]

Step-by-step explanation:

x² + 3x + 2

x² + x + 2x + 2 because 1+2=3 and 2×1=2

By taking out common terms, we get

x(x+1)+2(x+1)

(x+1)(x+2)

7 0

3 years ago

Twice a number x, minus 17

LekaFEV [45]

Answer:

2x - 7

Step-by-step explanation:

Twice a number x means x times 2, which can be written as 2x

Minus 17 from 2x

7 0

2 years ago