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never [62]
3 years ago
8

The cities of los Angeles and new York are located 35 inches apart on a map. If the actual distance between the two cities is 24

50 miles, then what did the scale in the key of the map read
Mathematics
1 answer:
Vsevolod [243]3 years ago
6 0

2450 miles /  35 inches =  70 miles / inch

(big freaking map!)

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What is the expansion of (3+x)^4
Vlad1618 [11]

Answer:

\left(3+x\right)^4:\quad x^4+12x^3+54x^2+108x+81

Step-by-step explanation:

Considering the expression

\left(3+x\right)^4

Lets determine the expansion of the expression

\left(3+x\right)^4

\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i

a=3,\:\:b=x

=\sum _{i=0}^4\binom{4}{i}\cdot \:3^{\left(4-i\right)}x^i

Expanding summation

\binom{n}{i}=\frac{n!}{i!\left(n-i\right)!}

i=0\quad :\quad \frac{4!}{0!\left(4-0\right)!}3^4x^0

i=1\quad :\quad \frac{4!}{1!\left(4-1\right)!}3^3x^1

i=2\quad :\quad \frac{4!}{2!\left(4-2\right)!}3^2x^2

i=3\quad :\quad \frac{4!}{3!\left(4-3\right)!}3^1x^3

i=4\quad :\quad \frac{4!}{4!\left(4-4\right)!}3^0x^4

=\frac{4!}{0!\left(4-0\right)!}\cdot \:3^4x^0+\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1+\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2+\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3+\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4

=\frac{4!}{0!\left(4-0\right)!}\cdot \:3^4x^0+\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1+\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2+\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3+\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4

as

\frac{4!}{0!\left(4-0\right)!}\cdot \:\:3^4x^0:\:\:\:\:\:\:81

\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1:\quad 108x

\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2:\quad 54x^2

\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3:\quad 12x^3

\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4:\quad x^4

so equation becomes

=81+108x+54x^2+12x^3+x^4

=x^4+12x^3+54x^2+108x+81

Therefore,

  • \left(3+x\right)^4:\quad x^4+12x^3+54x^2+108x+81
6 0
3 years ago
A policyholder has probability 0.7 of having no claims, 0.2 of having exactly one claim, and 0.1 of having exactly two claims. C
Sladkaya [172]

Answer:

0.89.

Step-by-step explanation:

So, we are given the following data or parameters or information which is going to aid in the solution to this question or problem. So, the data or parameters are;

(1). "probability 0.7 of having no claims, 0.2 of having exactly one claim, and 0.1 of having exactly two claims."

(2). " distributed on the interval [0,60] and are independent."

(3). "The insurer covers 100% of each claim."

So, taking (1) above we will have;

(Total probability= 0.7 + 0.2 + 0.1 = 0.1)

A = { (0.7 × 0)^2 + (0.2 × 1)^2 + ( 0.1 × 2)^2 =( 0.4) +( 0.4) = 0.8.

0.8 + total probability = 0.8 + 0.1 = 0.9.

So, from the question, we are to "Calculate the probability that the total benefit paid to the policyholder is 48 or less."

Hence, P< 48/A = P < 48/0.9 = P < 53.33.

Thus, 53.33/60 = 0.89.

6 0
3 years ago
How do you simplify 15/40​
Katyanochek1 [597]

Answer:3/8

Step-by-step explanation:

The simplest form of  

15 /40  is  3 /8 .

Steps to simplifying fractions

Find the GCD (or HCF) of numerator and denominator

GCD of 15 and 40 is 5

Divide both the numerator and denominator by the GCD

15 ÷ 5

40 ÷ 5

Reduced fraction:  

3 /8

Therefore, 15/40 simplified to lowest terms is 3/8.

3 0
2 years ago
Tia cut a 4 meters and 8 centimeters wire in to 10 equal pieces. Marta cut a 540 centimeters wire into 9 equal pieces. How much
Black_prince [1.1K]
540/9 = 60cm

408/10 = 40.8

60-40.8 = 19.2cm longer
5 0
3 years ago
For the questions, imagine a segment in a plane. Use that information to help you answer the questions.
Mars2501 [29]
1 a
2 c
3 a

Hope this help :)
7 0
3 years ago
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