*19th January 2021*

**Question:**

Convert Ounces to Gallons

The most important thing to remember about changing ounces to gallons is that there are 128 fluid ounces in every gallon.

Another way to think of it is ‘for every 128 ounces you have 1 gallon’. Let’s use *x* to represent the number of ounces and *y* to represent the number of gallons. (Notice that this formula divides the number of ounces into groups of 128 to determine the number of gallons).

*A farmer measures his cows’ milk production by the ounce but sells it by the gallon. If the farmer collected 19,200 ounces of milk in a week, how many gallons of milk will he be able to sell?*

**Answer:**

#### Step 1:

Remember the formula for finding how many fluid ounces are in a gallon.

#### Step 2:

Substitute known values into the formula. Here the number of ounces is 19,200.

#### Step 3:

Calculate the answer.

The equivalent number of gallons is 150. It is most appropriate to answer word problems with full sentences, so the answer to this problem is best written as ‘The farmer will be able to sell 150 gallons of milk this week’. Remember that ounces can be abbreviated as *oz* and gallons can be abbreviated as *gal* in your answers.

hence; 19,200 ounces converts to 150 gallons.

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*14th January 2021*

**Question:**

What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of of 0.1 in the following scenario?

There is no preliminary estimate for *p*

**Answer:**

1. No preliminary estimate for *p … so **p* = 0.5 for maximum margin.

1.96 (0.5) (0.5)

2. n ≥ __________________

(0.1)2

3. n ≥ 49

4. n = 49

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**13th December 2020**

**Question: **

Solve it algebraically or using matrices.

2x (1) + 2x (2) + 9x (3) = 7

**Answer:**

**Step 1: **

2x (1) + 2x (2) + 9x (3) = 7

**Step 2: **

let x (2) = t, X (3) = v

**Step 3:**

7 – 2t – 9v

X (1) = __________________

2

**Step 4:**

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**12th December 2020**

**Question: **

A graph of three functions, *f (x) = x + 6 *in red, *k f (x) *in blue, and *f (hx) *in green. Determine the values of *h* and *k.*

**Answer:**

K f (x) 3 1

_______ = K = _______ —-> K =________

f (x) 6 2

**Part 2: **

f (hx) = 8 (x) = hx+6

**Part 3: **

8 (-3) = h (-3) + 6 = 0 —-> – 3h+6 = 0 —-> -3h = -6

**Part 4:**

– 6

h = ________ = 2

– 3

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**11th December 2020**

**Question: **

Determine whether the given function is even, odd, or neither.

f(x) = 5

**Answer:**

f(x) = 5

f(-x) = 5 =f(x) | The Function is Even

-f(-x) = -5 ≠ 5 – f(x) | The Function is not Odd

Answer: The Function is Even

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**10th December 2020**

**Question: **

Use the given information to find the quadrant in which Ø lies.

tan Ø > 0 and sin Ø < 0

Quadrant 1, 2 3 or 4?

**Answer:**

tan Ø > 0 = Positive

Tangents are positive in 1st and 3rd Quadrant

sin Ø < 0 = Negative

Sines are negative in 3rd and 4th.

Answer: Quadrant 3

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**9th December 2020**

**Question: **

Identify the sampling techniques used.

Every fifth person boarding a plane is searched thoroughly.

A. Convenience

B. Cluster

C. Systematic

D. Stratified

E. Random

**Answer:**

This is systemic sampling

Answer is C) Systemic

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**8th December 2020**

**Question: **

Thirty-five percent of consumers prefer to purchase electronics online. You randomly select 8 consumers. Find the probability that the number of consumers who prefer to purchase electronics online is at most five.

P(x ≤ 5) =

**Answer:**

Mean: *M* = 3.353 (3.4)

Variance: = 3.380391 (3.4)

Standard Deviation: σ = √σ2 = √3.380391 = 1.838583966

= 1.8

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