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natita [175]
3 years ago
12

Express 10.9090909091... as a rational number, in the form pq where p and q are positive integers with no common factors.

Mathematics
1 answer:
Alexeev081 [22]3 years ago
4 0
Firts, Let x be the repeated decimal that we are trying to convert , so x=10.9090909090 equation (1)

Next, lets find how many digits are repeating:
It is pretty cleat that 90 is repeating, and 90 has two digits. So we are going to multiply our equation by 100 to move the decimal point two places:
100x=1090.90909090 (2)

Subtract equation (1) from equation (2):
100x-x=1090.90909090-10.90909090
99x=1080

Solve for x
x= \frac{1080}{99}

We can conclude that 10.9090909091... expressed as a rational number, i<span>n the form pq where p and q are positive integers with no common factors, is </span>\frac{1080}{99}.
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Please help me with this #5
shepuryov [24]

\text{Given that,}\\\\a_1 = 10~ \text{ and}~ a_n = a_{n-1} -4~\text{for}~ n\geq 2\\\\a_2 = a_{2-1} -4 = a_1 -4 = 10 -4 = 6\\\\a_3 = a_{3-1} - 4=a_2 -4 = 6 -4  =2\\\\a_4 = a_{4-1} -4 = a_3 -4 = 2 -4 = -2\\\\\text{The first four terms are:}~ 10,~ 6,~ 2~, -2

8 0
2 years ago
What’s the correct answer for this?
Anton [14]

Answer:

A

Step-by-step explanation:

Plate X will result in the lightest place since it's density and thickness both are less.

6 0
3 years ago
A box of oat cereal costs $3.90 for 15 ounces. A box of rice of cereal costs $3.30 for 11 ounces. Which box of cereal costs less
Firlakuza [10]

Answer:

The cost of per ounce of oat cereal is $0.04 less than per ounce cost of rice.

Step-by-step explanation:

Given:

Cost of 15 ounces of oat cereal box = $3.90

Cost of 11 ounces of rice box = $3.30

To compare the unit prices of the the boxes.

Solution:

Using unitary method to find the unit prices:

If 15 ounce of oat box cost =$3.90

∴ 1 ounce of oat cereal would cost = \$\frac{3.90}{15}=\$0.26

∴ Per ounce cost of oat cereal = $0.26

If 11 ounce of rice box cost =$3.30

∴ 1 ounce of rice would cost = \$\frac{3.30}{11}=\$0.3

∴ Per ounce cost of rice = $0.3

Difference in unit costs of oat and rice = \$0.3-\$0.26=\$0.04

On comparing the the unit costs of oats and rice, we find out that the cost of per ounce of oat cereal is $0.04 less than per ounce cost of rice.

3 0
3 years ago
A salesman's commission rate is 6%. What is the commission from the sale of 36,000 worth of furnaces?
borishaifa [10]

Answer:

2160

Step-by-step explanation:

36000*6/100=2160

6 0
3 years ago
Suppose we have an unfair coin that its head is twice as likely to occur as its tail. a)If the coin is flipped 3 times, what is
Alenkinab [10]

Answer: a) 0.2222, b) 0.3292, c) 0.1111

Step-by-step explanation:

Since we have given that

Let the probability of getting head be p.

Since,  its head is twice as likely to occur as its tail.

p+\dfrac{p}{2}=1\\\\\dfrac{3p}{2}=1\\\\p=\dfrac{2}{3}

a)If the coin is flipped 3 times, what is the probability of getting exactly 1 head?

So, here, n  = 3

p=\dfrac{2}{3}

q=\dfrac{1}{3}

Now,

P(X=1)=^3C_1(\dfrac{2}{3})^1(\dfrac{1}{3})^2=0.2222

b)If the coin is flipped 5 times, what is the probability of getting exactly 2 tails?

2 tails means 3 heads.

So, it becomes,

P(X=3)=^5C_3(\dfrac{2}{3})^3(\dfrac{1}{3})^2=0.3292

c)If the coin is flipped 4 times, what is the probability of getting at least 3 tails?

P(X\leq 1)=\sum _{x=0}^1^4C_x(\dfrac{2}{3}^x(\dfrac{1}{3})^{4-x}=0.1111

Hence, a) 0.2222, b) 0.3292, c) 0.1111

8 0
3 years ago
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