The options presented are:
(1) division property of equality
(2) factoring the binomial
(3) completing the square
(4) subtraction property of equality
Response: (2) factoring the binomial
Step 1:
Step 2:
In step 2, 'a' is extracted from . Upon factoring out 'a', we divide all terms by 'a', resulting in
.
Step 2 involves the binomial factorization process.
762,508 expressed in expanded form with exponents is:
We need to write 762,508 using expanded notation with exponents.
Expanded form indicates how to represent numbers to highlight the individual digit values.
Let's determine the positional values of each digit:
The concept of place value signifies the worth assigned to each digit based on its location.
For 7, the place value is 700,000
In 762508, the digit 7 is located in the hundred-thousands position.
For 6, the place value is 60,000
In 762508, the digit 6 occupies the ten-thousands position.
For 2, the place value is 2,000
In 762508, 2 is in the thousands position.
For 5, the place value is 500
In 762508, 5 is placed in the hundreds position.
For 0, the place value is 0 x 10 = 0
In 762508, 0 is found in the tens position.
For 8, the place value is 8
In 762508, 8 is positioned in the units place.
Thus, the expanded form is:
700,000 + 60,000 + 2,000 + 500 + 0 + 8
Expressed with exponents, it can be written as:
Answer:
a. 0.82%
b. 71.11%
c. 0.564 micrometer
Step-by-step explanation:
To find the z value for each measurement, we must calculate and determine the percentage they correspond to, and the difference will give us the percentage between those two statistics.
The equation for z is:
z = (x - m) / (sd)
Here, x is the value being evaluated, m denotes the mean, and sd represents the standard deviation.
a.
For 0.62 copies, we calculate:
z = (0.62 - 0.5) / (0.05)
z = 2.4
This translates to 0.9918.
Therefore, p (x > 0.62) = 1 - 0.9918
p (x > 0.62) = 0.0082 = 0.82%
b.
For 0.47 copies, we have:
z = (0.47 - 0.5) / (0.05)
z = -0.6, which equates to 0.2742.
For 0.63 copies:
z = (0.63 - 0.5) / (0.05)
z = -2.6, which yields 0.9953.
Hence, p (0.47 > x > 0.63) = 0.9953 - 0.2742
p (0.47 > x > 0.63) = 0.7211 = 72.11 %
c.
For x copies, we find:
p = 0.9 corresponds to z = 1.28.
Thus, 1.28 = (x - 0.5) / (0.05)
From which we derive:
x = 1.28*0.05 + 0.5
x = 0.564 micrometer
