When you write it as an inequality you get x + 19 ≈ 8.2 and when you solve it it should look like x + 19 ≈ 8.2
19 ≈ - <u>19
</u> x ≈ -10.8<u>
</u>
Answers:
- a) The sample is the set of students Ms. Lee selects from the box.
- b) The population is the set of all students in Ms. Lee's classroom.
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Explanation:
The first sentence tells us what the population is: it's the set of all her students. She's not concerned with any other students in any other classroom. So her "universe", so to speak, is solely focused on this classroom only. Once the population is set up, a sample of it would be a subset of the population.
If set A is a subset of set B, then everything in A is also in B, but not vice versa. For example, the set of humans is a subset of the set of mammals because all humans are mammals. However, a dog is a mammal but not a human. This shows that A is a subset of B, but not the other way around. In this example, A = humans and B = mammals.
Going back to the classroom problem, we have A = sample and B = population. If Ms. Lee has 30 students, and she randomly selects 5 of them, then those 30 students make up set B and the 5 selected make up set A. Selecting the names randomly should generate an unbiased sample. This sample should represent the population overall. If the population is small enough, the teacher could do a census and not need a sample. Though there may be scenarios that it's still effective to draw a sample.
begin by pulling 2 out of the numerator using the distributive property.
numerator: 2(16x^4 - 25) and now factor
numerator: 2(4x^2 - 5)(4x^2 + 5)
Now go to the denominator. It looks messy but it will break down.
Pull out 4x^2 for the first two terms and 5 for the last 2 terms. Use the distributive property.
denominator: 4x^2(x - 3) - 5(x - 3) now x - 3 is the common term.
denominator: (x - 3)(4x^2 - 5)
Put the two results together.
After canceling out 4x^2 - 5 on both the numerator and the denominator, you are left with.
LM is equal to 7.
In order to find this, we need to first set LM and MN equal to each other since M is the midpoint of LN.
LM = MN
3x - 2 = 2x + 1
x - 2 = 1
x = 3
Now that we know x = 3 we can find the value of LM by plugging in to the problem.
LM = 3x - 2
LM = 3(3) - 2
LM = 9 - 2
LM = 7
Answer : The two correct options are,
3.4a + 5.6b
5.6b + 3.4a
Step-by-step explanation :
The given expression is:
(-2.4a - 1.8b) - (-3.8a - 4.4b) + (2.0a + 3.0b)
First we have to open the brackets.
⇒ -2.4a - 1.8b + 3.8a + 4.4b +2.0a + 3.0b
Now keep like terms together.
⇒ -2.4a + 3.8a +2.0a + 3.0b - 1.8b + 4.4b
By subtraction or addition, we get:
⇒ 3.4a + 5.6b
or,
⇒ 5.6b + 3.4a
Hence, the expressions that equivalent to the given expression are, 3.4a + 5.6b and 5.6b + 3.4a
