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3 years ago

Between which two consecutive integers does the square root of 53 lie

Mathematics

2 answers:

Fittoniya [83]3 years ago

6 0

53 is between 49 and 64

choli [55]3 years ago

4 0

The square root of 53 will lie between 7 and 8.

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Ship collisions in the Houston Ship Channel are rare. Suppose the number of collisions are Poisson distributed, with a mean of 1

alexandr1967 [171]

Answer:

$a) \simeq 0.3012$ $b) \simeq 0.0494$ c) $\simeq 0.2438$

Step-by-step explanation:

Rate of collision,

1.2 collisions every 4 months

or, $\frac{1.2}{4}$

= 0.3 collisions per month

So, the Poisson distribution for the random variable no. of collisions per month (X) is given by,

P(X =x) = $\frac{e^{-\lambda}\times {\lambda}^{x}}}{x!}
$

for x ∈ N ∪ {0}

= 0 otherwise --------------------------------------(1)

here, $\lambda = 0.3$ collision / month

No collision over a 4 month period means no collision per month or X =0

Putting X = 0 in (1) we get,

P(X = 0) = $\frac{e^{-0.3}\times {\0.3}^{0}}{0!}
$

$\simeq 0.7408182207$ ------------------------------------(2)

Now, since we are calculating this for 4 months,

so, P(No collision in 4 month period)

= $0.7408182207^{4}$

$\simeq 0.3012$ -----------------------------------------------------------(3)

2 collision in 2 month period means 1 collision per month or X =1

Putting X =1 in (1) we get,

P(X =1) = $\frac{e^{-0.3}\times {\0.3}^{1}}{1!}
$

$\simeq 0.2222454662$ ------------------------------------(4)

Now, since we are calculating this for 2 months, so ,

P(2 collisions in 2 month period)

= $0.2222454662^{2}$

$\simeq 0.0494$ -----------------------------------------(5)

1 collision in 6 months period means

$\frac{1}{6}$ collision per month

Now, P(1 collision in 6 months period)

= P( X = 1/6] (which is to be estimated)

= $\frac {P(X=0)\times 5 + P(X =1)\times 1}{6}$

= \frac {0.7408182207 \times 5 + 0.2222454662 \times 1}{6}[/tex]

$\simeq 0.6543894283$ -------------------------------------------(6)

So,

P(1 collision in 6 month period)

= $0.6543894283^{6}$

$\simeq 0.0785267444$ ------------------------------------------------(7)

So,

P(No collision in 6 months period)

= $(P(X =0)^{6}$

$\simeq 0.1652988882$ ---------------------------------(8)

so,

P(1 or fewer collision in 6 months period)

= (8) + (7 ) = 0.0785267444 +0.1652988882

$\simeq 0.2438$ ---------------------------------------------(9)

7 0

3 years ago

Find the sum. Homework: 9.4 arithmetic series

RUDIKE [14]

Answer:

Step-by-step explanation:

a1 = 3(1) - 7 = - 4

a2 = 3(2) - 7 = -1

d = a2 - a1

d = -1 - (-4)

d = -1 + 4

d = 3

a60 = 3(60) - 7

a60 = 180 - 7

a60 = 173

n = 60

Sum = (a1 + a60) * n / 2

Sum = (-4 + 173) * 60/2

Sum = (169)*30

Sum = 5070

==================

Just to check, we'll use the second summation formula

d = 3

n = 60

a1 = -4

Sum = (2*a1 + (n - 1)*d )*n / 2

Sum = (2*(-4) + (60 -1)*3)* 60/2

Sum = (-8 + 59*3) * 30

Sum = (177 - 8)*30

Sum = 169 * 30

Sum = 5070

Same answer.

5 0

3 years ago

6)532 with a remainder

BartSMP [9]

Hello Rebelkid2004, 532 with a remainder is, gives remainder 0 and so are divisible by 1, we get factors of 532 numbers by finding numbers that can divide 532 without remainder or alternatively numbers that can multiply together to equal the target number being converted.

3 0

3 years ago

Can someone please help me. This is an equation for either an arithmetic or geometric sequence.

djyliett [7]

A6 = -8
a15= -62

There are (15 - 6) terms in between, therefore 9 terms in between.
-8 to -62 ... there is a difference of 54
54 ÷ 9 = 6
Therefore it gets -6 each term.
a6 = -8, a7= -14, a8 = -20 ......

4 0

3 years ago

Read 2 more answers

Find the range of the given data set. 5/8, 3/4, 1 1/8, 1 1/4 A)5/8 B)3/4 C)1 1/8

rodikova [14]

Answer:

A)5/8

Step-by-step explanation:

The range of a set of data is the difference between the highest and lowest values in the set.

Given data set:

5/8, 3/4, 1 1/8, 1 1/4

Rewriting the data set in the same denominator to compare:

5/8, 6/8, 9/8, 10/8

As we see the smallest value is 5/8 and the highest value is 10/8, so the difference:

10/8 - 5/8 = 5/8

So, the range of the given data set is 5/8

Correct choice is: A)5/8

6 0

3 years ago