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SashulF [63]
3 years ago
15

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.
Mathematics
1 answer:
djyliett [7]3 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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In a fruit cocktail, for every 30 ml of orange juice you need 20 ml of apple juice and 50 ml of coconut milk. What proportion of
KengaRu [80]

Answer:

first things first, you need to find out how much juice you have: 30 + 20 + 50 = 100, so 100 ml of juice. all together, the juice is 100%, or 1. separated, the amounts are 30%, 20%, and 50%, therefore the amount of coconut milk in the cocktail you have is 50%, or 1/2.

3 0
3 years ago
The home run percentage is the number of home runs per 100 times at bat. A random sample of 43 professional baseball players gav
Andru [333]

Step-by-step explanation:

(a) Yes, if you enter all 43 values into your calculator, you calculator should report:

xbar = 2.293

s = 1.401

(b)

Note: Most professors say that is sigma = the population standard deviation is unknown (as it is unknown here), you should construct a t-confidence interval.

xbar +/- t * s / sqrt(n)

2.293 - 1.684 * 1.401 / sqrt(43) = 1.933

2.293 - 1.684 * 1.401 / sqrt(43) = 2.653

Answer: (1.933, 2.653)

Note: To find the t-value that allows us to be 90% confident, go across from df = 43-1 = 42 (round down to 40 to be conservative since 42 in not in the table) and down from (1-.90)/2 = .05 or up from 90% depending on your t-table. So, the t-critical value is 1.684.

Note: If you can use the TI-83/84, it will construct the following CI using df = 42 (ie t = 1.681).

2.293 +/- 1.681 * 1.401 / sqrt(43)

(1.934, 2.652)

Note: Some professors want you to construct a z-CI when the sample size is large. If your professor says this, the correct 90% CI is:

2.293 +/- 1.645 * 1.401 / sqrt(43)

(1.942, 2.644)

Note: To find the z-value that allows us to be 90% confident, (1) using the z-table, look up (1-.90)/2 = .05 inside the z-table, or (2) using the t-table, go across from infinity df (= z-values) and down from .05 or up from 90% depending on your t-table. Either way, the z-critical value is 1.645.

(c)

Note: Again, most professors say that is sigma = the population standard deviation is unknown (as it is unknown here), you should construct a t-confidence interval.

xbar +/- t * s / sqrt(n)

2.293 - 2.704 * 1.401 / sqrt(43) = 1.715

2.293 - 2.704 * 1.401 / sqrt(43) = 2.871

Answer: (1.715, 2.871)

Note: To find the t-value that allows us to be 99% confident, go across from df = 43-1 = 42 (round down to 40 to be conservative since 42 in not in the table) and down from (1-.99)/2 = .005 or up from 99% depending on your t-table. So, the t-critical value is 2.704.

Note: If you can use the TI-83/84, it will construct the following CI using df = 42 (ie t = 2.698).

2.293 +/- 2.698 * 1.401 / sqrt(43)

(1.717, 2.869)

Note: Again, some professors want you to construct a z-CI when the sample size is large. If your professor says this, the correct 99% CI is:

2.293 +/- 2.576 * 1.401 / sqrt(43)

(1.742, 2.843)

Note: To find the z-value that allows us to be 99% confident, (1) using the z-table, look up (1-.99)/2 = .005 inside the z-table, or (2) using the t-table, go across from infinity df (= z-values) and down from .005 or up from 99% depending on your t-table. Either way, the z-critical value is 2.576.

(d)

Tim Huelett 2.5

Since 2.5 falls between (1.715, 2.871), we see that Tim Huelett falls in the 99% CI range. So, his home run percentage is NOT significantly different than the population average.

Herb Hunter 2.0

Since 2.0 falls between (1.715, 2.871), we see that Herb Hunter falls in the 99% CI range. So, his home run percentage is NOT significantly different than the population average.

Jackie Jensen 3.8.

Since 3.8 falls above (1.715, 2.871), we see that Jackie Jensen falls in the 99% CI range. So, his home run percentage IS significantly GREATER than the population average.

(e)

Because of the Central Limit Theorem (CLT), since our sample size is large, we do NOT have to make the normality assumption since the CLT tells us that the sampling distribution of xbar will be approximatley normal even if the underlying population distribution is not.

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Answer:

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Write the exact value of the side length of each square. If the value is not a whole number, estimate the length.
Savatey [412]

Given:

The area of the squares are given.

To find:

The exact side length or estimate side length of the square.

Solution:

We know that, the area of a square is

A=a^2

Where, a is the side length of the square.

a=\sqrt{A}

Area of the square is 100 square units. So, the side length is:

a=\sqrt{100}

a=10

Therefore, the side length is 10 units.

Area of the square is 95 square units. So, the side length is:

a=\sqrt{95}

It is not exact. We know that \sqrt{81}.

Therefore, the side length is between 9 and 10.

Area of the square is 36 square units. So, the side length is:

a=\sqrt{36}

a=6

Therefore, the side length is 6 units.

Area of the square is 30 square units. So, the side length is:

a=\sqrt{30}

It is not exact. We know that \sqrt{25}.

Therefore, the side length is between 5 and 6.

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