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3 years ago

Can someone give me a quick algebra lesson and solve this example for me?

Mathematics

2 answers:

Ad libitum [116K]3 years ago

5 0

Answer:

3x- 15+6x+2=41

or, 9x-13=41

or, 9x= 54

: x=6

Karolina [17]3 years ago

5 0

Answer:

See below

Step-by-step explanation:

Hi there!

>>Do I subtract or add the coefficients with variables together?

Add the terms with variables. In this case, the terms with variables are 3x and 6x. The communicative property of addition still holds true, so 3x+6x and 6x+3x are the same.

Do NOT subtract terms. If you do, let's take the 3x and 6x from the example above, doing either 3x-6x or 6x-3x would lead to the wrong answer.

Note: if you encounter a situation where if you have let's say, the terms -3x and 17x, -3x+17 and 17x + -3x are exactly the same (commutative property of addition still holds true). DO NOT do 17x - -3x or -3x-17x! Those would lead to the wrong answer.

Now,

We are given the following equation:

3x-15+6x+2=41

And we want to solve it for x

As stated above, we ADD the terms with coefficients together. So 3x+6x=9x.

The same is true for the numbers without variables; -15+2=-13

On the left, we have:

9x-13=41

Add 13 to both sides to remove it from the left side

9x=54

Divide both sides by 9 to isolate x

x=6

Hope this helps!

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The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systo

PIT_PIT [208]

Answer:

The estimate is

$52.02 < \mu < 55.78$

Step-by-step explanation:

From the question we are told that

The sample mean is $\ = x = 53.9$

The sample size is n = 24

The standard deviation is $\sigma = 5.6$

Given that the confidence level is 90% the level of significance is mathematically represented as

$\alpha = 100 - 90$

$\alpha = 10 \%$

$\alpha = 0.10$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table.The value is

$Z_{\frac{\alpha }{2} } =Z_{\frac{0.10 }{2} } = 1.645$

The reason we are obtaining critical value of $\frac{\alpha }{2}$ instead of $\alpha$ is because $\alpha$

represents the area under the normal curve where the confidence level interval ( $1 - \alpha$ ) did not cover which include both the left and right tail while

$\frac{\alpha }{2}$ is just the area of one tail which what we required to calculate the margin of error

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{ \sqrt{n} }$

substituting values

$E = 1.645 * \frac{5.6 }{ \sqrt{24} }$

$E = 1.880$

The estimate of how much the drug will lower a typical patient's systolic blood pressure(using a 90% confidence level) is mathematically represented as

$\= x - E < \mu < \= x + E$