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2 years ago

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Imagine you are teaching a younger student how to factor. Describe in full sentences what you would say to teach the young stude

nt how to factor the trinomial $x^{2}$ + 4x - 21 into (x - 3)(x + 7). Your description must include at least 3 different steps.

1 answer:

djyliett [7]2 years ago

3 0

Answer:

$x^2+ 4x - 21$ =(x-3)(x+7)

Step-by-step explanation:

To factor the trimonial: $x^2+ 4x - 21$ , we follow these steps:

Step 1: Multiply the first and last term

$-21 \times x^2=-21x^2$

Step 2: List out product factors of the term derived above

$-21=-1 \times 21\\ -21=-3 \times 7\\-21=3 \times -7\\-21=1 \times -21$

Step 3: Determine which of the factors sum up to the middle term 4x

The required product is: -3 and 7

Therefore: -3x+7x=4x

Step 4: Replace the middle term by the expression derived in step 3 and factorize.

$x^2+ 7x -3x- 21\\=x(x+7)-3(x+7)\\=(x-3)(x+7)$

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Find the 95% confidence interval for estimating the population mean μ

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Normally we would check for conditions, but since this is not formulated as a "real-world scenario" type problem, it is hard to check for randomness and independence. Therefore, I will be excluding conditions from this answer.

<h3>Confidence Interval Formula</h3>

The formula for constructing a <u>confidence interval for means</u> is as follows:

$\displaystyle \overline{x} \pm t^*\big{(}\frac{\sigma}{\sqrt{n} } \big{)}$

We are given these variables:

$\overline{x}=50$
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Plug these values into the formula for the confidence interval:

$\displaystyle 50\pm t^* \big{(}\frac{10}{\sqrt{60} } \big{)}$

<h3>Finding the Critical Value (t*)</h3>

In order to find t*, we can use this formula:

$\displaystyle \frac{1-C}{2}=A$

Calculating the z-score associated with "A" will give us t*.

So, let's plug in the confidence interval 95% (.95) into the formula:

$\displaystyle \frac{1-.95}{2}=.025$

Use your calculator or a t-table to find the z-score associated with this area under the curve.. you should get:

$t^*=1.96$

<h3>Constructing Confidence Interval</h3>

Now, let's finish the confidence interval we created:

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We can calculate the confidence interval, using this formula, to be:

$\boxed{(47.4697, \ 52.5303)}$

<h3>Interpreting the Confidence Interval</h3>

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2 years ago

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3 years ago

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zubka84 [21]

I assume the equation is supposed to be

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3 years ago

Two siblings' ages have a sum of 64 years. The older sibling was born 6 years before their young sibling.

Elina [12.6K]

Hi!

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