Step-by-step explanation:
hope thissss helpsss!!!!
Area of the rectangle is 44 in²
Step-by-step explanation:
- Step 1: Find the area of the rectangle.
Length of the rectangle = 5√16 in = 5 × 4 = 20 in
Width of the rectangle = 2 1/5 in = 11/5 in
Area of the rectangle = length × width
= 20 × 11/5 = 44 in²
By definition, a rational number is a precise number: or in other terms, we know its exact value. Irrational numbers are number that has endless digits on the right of the decimal points: in other terms, we can't know its exact value.
First question:
√2.5 = 1.58113.... It's endless, so irrational.
-√64 = -8 it's a whole number, so rational.
4√5 = 8.94427.... Endless, so irrational.
√14.4 = 3.7947... Endless so irrational.
So -√64 is the rational number.
Second:
7.885 is rational because has a defined number of digits after the decimal points.
π² = 9.8696.... Endless, so irrational.
√0.144 = 0.3794.... Endless, so irrational
√91 = 9.5393.... Endless, so irrational
So 7.885 is the rational number.
Third:
-7.8 bar: You can notice the line over the 8, this means that there's an infinite number of 8 after the decimal points. So it's 7.88888888888.... Endless, so irrational.
√25 = 5, whole number so rational
25.8125 Has a definite number of digits after the decimal point, so is rational.
√0.025 = 0.1581... Endless, so irrational.
So -7.8 bar and √0.025 are irrational.
Fourth:
π= 3.1415... Endless, so irrational.
1.425 has a definite number of digits after the decimal point, so rational.
√50 = 7.0710.... Endless, so irrational
√-4 Doesn't exist. Finding the square root of a negative number is mathematically impossible.
So 1.425 is the rational number.
Fifth:
√10 = 3.1622..... Endless, so irrational.
√100 = 10, a whole number so rational.
√1000 = 31.6227..... Endless, so irrational
√100000 = 316.2277...... Endless, so irrational.
√100 is the rational number.
Hope this helps!! :D And I hope you understood the lesson a bit more xD
Answer:
The proportion of defective chips produced by the machine is more than 4% so the machine needs an adjustment.
Step-by-step explanation:
In this case we need to test whether the proportion of defective chips produced by the machine is more than 4%.
The hypothesis can be defined as follows:
<em>H</em>₀: The proportion of defective chips produced by the machine is not more than 4%, i.e. <em>p</em> ≤ 0.04.
<em>H</em>ₐ: The proportion of defective chips produced by the machine is more than 4%, i.e. <em>p</em> > 0.04.
The information provided is:
<em>X</em> = 12
<em>n</em> = 200
<em>α</em> = 0.025
The sample proportion of defective chips is:
Compute the test statistic as follows:
The test statistic value is 1.44.
Decision rule:
We reject a hypothesis if the p-value of a statistic is lower than the level of significance α.
Compute the <em>p</em>-value of the test:
The <em>p</em>-value of the test is 0.075.
<em>p</em>-value = 0.075 > <em>α</em> = 0.025
The null hypothesis was failed to be rejected at 2.5% level of significance.
Thus, it can be concluded that the proportion of defective chips produced by the machine is more than 4% so the machine needs an adjustment.
Answer:
Option (3)
Step-by-step explanation:
Integers are the numbers which don't have a fractional part (having positive of negative notations)
Example; -2, -1, 0, 1, 2,...
Let the two integers are 0 and 2,
Subtraction of these integers will be = 0 - 2
= 0 + (-2)
Here opposite of 2 has been added to 0.
That means subtraction of two integers is to add the opposite of the integer being subtracted.
Option (3) will be the answer.