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4 years ago

What is the measure of an interior angle of a regular pentagon?

1 answer:

3 0

We use this formula to calculate the sum of all interior angles of a regular polygon; 180(n-2) , n= number of sides
so 180(5-2) = 540
each interior angle = 540 ÷ 5 = 108

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Enter the explicit rule for the geometric sequence.<br><br> 9,6,4,83,…

soldier1979 [14.2K]

Answer:

a_n = 2^(n - 1) 3^(3 - n)

Step-by-step explanation:

9,6,4,8/3,…

a1 = 3^2

a2 = 3 * 2

a3 = 2^2

As we can see, the 3 ^x is decreasing and the 2^ y is increasing

We need to play with the exponent in terms of n

Lets look at the exponent for the base of 2

a1 = 3^2 2^0

a2 = 3^1 2^1

a3 = 3^ 0 2^2

an = 3^ 2^(n-1)

I picked n-1 because that is where it starts 0

n = 1 (1-1) =0

n=2 (2-1) =1

n=3 (3-1) =2

Now we need to figure out the exponent for the 3 base

I will pick (3-n)

n =1 (3-1) =2

n =2 (3-2) =1

n=3 (3-3) =0

8 0

4 years ago

Make, Dan, Ed, and summer played together on a baseball team. Mike’s batting average was 0.349, dan’s was 0.2, Ed’s was 0.35, an

Harrizon [31]

the highest batting average is of Ed's and that is 0.350 .

<u>Step-by-step explanation:</u>

Here we have , Make, Dan, Ed, and summer played together on a baseball team. Mike’s batting average was 0.349, dan’s was 0.2, Ed’s was 0.35, and sy’swas 0.299. We need to find Who had the highest batting average . Let's find out :

According to question we have following parameters as :

$Mike = 0.349\\Dan's=0.200\\Ed's=0.350\\Sy'swas=0.299$

Arranging these data from decreasing to increasing order we get :

⇒ $0.200$

⇒ $(Dan's)0.200$

Therefore , the highest batting average is of Ed's and that is 0.350 .

6 0

3 years ago

Sherry claims that the expression 1/x will always be equivalent to a repeating decimal whenever x is an odd number greater than

fomenos

Answer:

The correct options are :

b. 5

e. 25

Step-by-step explanation:

The question is incomplete. The missing part is :

'' Which of these values will prove Sherry's claim is false :

a. 3

b. 5

c. 7

d. 11

e. 25 ''

One way to prove that Sherry's claim is false is finding one odd number greater than 1 that when we replace it in the denominator of the expression $\frac{1}{x}$ the result isn't equivalent to a repeating decimal.

Let's analyze each option :

a. 3

3 is an odd number greater than 1 ⇒ If we replace in the expression $\frac{1}{x}$ ⇒

$\frac{1}{3}$ ≅ 0.3333 (repeating decimal)

The option a. 3 won't prove that Sherry's claim is false.

b. 5

5 is an odd number greater than 1 ⇒ If we replace in the expression $\frac{1}{x}$ ⇒

$\frac{1}{5}=0.2$

The result isn't a repeating decimal.

The option b. 5 will prove that Sherry's claim is false.

c. 7

7 is an odd number greater than 1 ⇒ If we replace in the expression $\frac{1}{x}$ ⇒

$\frac{1}{7}$ ≅ 0.1428 (repeating decimal)

The option c. 7 won't prove that Sherry's claim is false.

d. 11

11 is an odd number greater than 1 ⇒ If we replace in the expression $\frac{1}{x}$ ⇒

$\frac{1}{11}$ ≅ 0.0909 (repeating decimal)

The option d. 11 won't prove that Sherry's claim is false.

e. 25

25 is an odd number greater than 1 ⇒ If we replace in the expression $\frac{1}{x}$ ⇒

$\frac{1}{25}$ ≅ 0.04

The result isn't a repeating decimal

The option e. 25 will prove that Sherry's claim is false.

3 0

3 years ago

A country's population in 1992 was 72 million. In 1998 it was 76 million. Estimate the population in 2012 using the exponential

stepan [7]

We assume the annual percentage increase is the same. We will work out the constant k using the formula

We have
P = 76
A = 72
t = 6 years (from 1992 to 1998)

Substitute into the formula
$76=72e^{6k}$
$\frac{76}{72}=e^{8k}$
Take log both sides give
$ln( \frac{76}{72})=ln(e^{6k})$
$0.05406722127=6k$
$k=0.009$

We can now work out the number of population by the end of 2012 using the formula

We have
A = 72 million
k = 0.009
t = 10 years (1992 to 2012)

$P=72e^{0.009*10}$ $P=78.78$ ≈79 million

7 0

3 years ago

For the data set below, calculate the standard deviation to the nearest hundredth decimal place. 27 38 47 42 33 56 37 57 38 52

mihalych1998 [28]

In order to calculate standard deviation, apply the standard deviation formula, which is given in the attached file. In this formula, we are finding the square root of the sum of the square of given values less their mean value (the sum of the given numbers divided to their amount) divided to N-1, where N is the amount of the given numbers. When we calculate the mean, it is 42.7 and the standard deviation is 10.02275

5 0

4 years ago

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