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Sever21 [200]
1 year ago
14

Use the binomial theorem to show that 7^n + 2 is divisible by 3, where n is a positive integer.

Mathematics
1 answer:
masha68 [24]1 year ago
7 0

By the binomial theorem,

7^n=(6+1)^n=6^n+n6^{n-1}+\dbinom n26^{n-2}+\cdots+\dbinom n{n-2}6^2+n6^1+1

Each term containing a factor 6 is divisible by 3, since 3 divides 6. The remaining 1 and 2 sum to 3, which is also divisible by 3.

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The scores of eighth-grade students in a math test are normally distributed with a mean of 57.5 and a standard deviation of 6.5.
Anna11 [10]
Approximately 68% of a normal distribution lies within one standard deviation of the mean, so this corresponds to students with scores between (57.5 - 6.5, 57.5 + 6.5) = (51, 64)
8 0
2 years ago
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A map shows the town where Niko lives. The actual distance from Niko's house to his school is 3 miles, and measures one-half inc
katrin2010 [14]

Answer:

<u>The distance of the library in the map is 0.67 inches (Rounding to two decimal places)</u>

Step-by-step explanation:

1. Let's review all the information given for solving this question:

Scale factor for the map of the town = 0.5 inches: 3 miles

Distance from Niko's house to his school = 3 miles

Distance from Niko's school to the library = 4 miles

2. Let's find the distance of the library in the map

Distance of the library in the map = Distance of the library * Scale factor

Distance of the library in the map = 4 miles * 0.5 inches:3 miles

Distance of the library in the map = (2 miles * inches)/3 miles

Distance of the library in the map = 2 inches/3 (Miles are cancelled in the numerator and in the denominator)

<u>Distance of the library in the map = 0.67 inches (Rounding to two decimal places)</u>

3 0
2 years ago
Read 2 more answers
Simplify 100y^3/98xy pls answer soon hegarty maths lazy
OleMash [197]

Answer:

50y^4x/49

Step-by-step explanation:

y^3/98

((100* y^3/98 * x) * y

2.1 y^3 * y^1=y^(3+1)=y^4

8 0
2 years ago
A triangle’s height is 6c meters and the base is c – 1 meters. Brian knows that the area of the triangle is 18 square meters and
dusya [7]
18= 0.5 (b)(h)
36=(6c)(c-1)
6c^2-6c-36=0
6(c^2-c-6)=0
6(c-3)(c+2)=0
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now plug into the original equation.
base is c-1 3-1=2
height is 6c= 6(3)=18


3 0
2 years ago
Read 2 more answers
"If you switch to the late shift, you will receive a 10% wage increase." Great! I make $12.00 per hour now, and that extra 10% w
maxonik [38]

Answer:

$13.20/hr

Step-by-step explanation:

A 10% wage increase would amount to 0.10($12) = $1.20.  Adding this increase to the starting rate $12/hr results in $13.20/ hr.

A faster way in which to do this is shown below:

Wages after a 10% increase = (1.10)($12/hr) = $13.20/hr

7 0
2 years ago
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