What is the name of our number system?

The length of sides x in the simplest radical form is 2√2

Properties of a right angled triangle:

• One of the angle is equals to 90 degree.
• The sides can be found using Pythagoras theorem
• Trigonometric ratios can be used to find the angles.

Let's find x using trigonometric ratios

sin ∅ = opposite / hypotenuse

Therefore,

sin 30° = √2 / x

x sin 30° = √2

x = √2 / sin 30°

x =

x = × 2

x = 2√2

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It is proved that the given decimals are equivalent decimals.

What are equivalent fractions? What is a mathematical function, equation and expression?

• equivalent fractions : Equivalent fractions can be defined as fractions that may have different numerators and denominators but they represent the same value.
• function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

• expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.

• equation : A mathematical equation is used to equate two expressions.

Given are the fractions -

7/10 and 70/100

We have the following fractions -

A = (7/10) = 0.7

B = 70/100 = (7 x 10)/(10 x 10) = (7/10)

B = (7/10) = 0.7

It can be seen that fraction A equals to B.

Therefore, it is proved that the given decimals are equivalent decimals.

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Step-by-step explanation:

7/10 in percentage form is 70%

70/100 in percentage form is 70%

Simple as that

Answer: The lower bound is 0.26 and the upper bound is 0.34.

Step-by-step explanation:

Formula to find the confidence interval for population proportion (p) is given by :_

, where n= sample size

z* = Critical value. (two-tailed)

= Sample proportion.

Let p be the true population proportion of hits to at bats for the entire team during the last season.

As per given , we have

n= 300

By z-table , the critical value for 90% confidence interval : z* = 1.645

Now , 90% confidence interval for the proportion of hits to at bats for the entire team during the last season:

The lower bound is 0.26 and the upper bound is 0.34.

The simplified result of the expression  3-8 divided by 3-2 is -5 .

Let's simplify the expression step by step :

Given expression: (3 - 8) / (3 - 2)

Step 1: Evaluate the numerator and denominator separately:

A fraction is considered to be simplified when it is expressed in the lowest term. That means the only common divisor between the numerator and denominator is .

Numerator: 3 - 8 = -5

Denominator: 3 - 2 = 1

Step 2: Divide the numerator by the denominator:

-5 / 1 = -5

So, the simplified result of the expression is -5 .

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Answer:

-5

Step-by-step explanation:

Answer:

Thus, when both S-jams and C-tunes have 20 songs downloaded in a month  , the cost will be same.

an expression for the cost of S-Jams $0.99n + $16

Step-by-step explanation:

For

S-Jams

cost of 1 song = $1.29

let there be n songs downloaded in a month

then

cost of n songs = n*cost of 1 song  = $1.29n

monthly fee = $10

Total cost of S-Jams = $1.29n+$10

________________________________________

For

C-Tunes

cost of 1 song = $0.99

let there be n songs downloaded in a month

then

cost of n songs = n*cost of 1 song  = $0.99n

monthly fee = $16

Total cost for C-Tunes= $0.99n + $16

we have to find When will the company’s plans cost the same.

Total cost of S-Jams = Total cost of C- Tunes

1.29n+10 = 0.99n + 16

=> 1.29n - 0.99n = 16-10

=> 0.30n = 6

=> n = 6/0.3 = 20

Thus, when both S-jams and C-tunes have 20 songs downloaded in a month  , the cost will be same.

an expression for the cost of S-Jams $0.99n + $16