Let P(n) be the statement that a postage of n cents can be formed using just 4-cent and 7-cent stamps. Use strong induction to prove that P(n) is true for all integers greater than or equal to some threshold x.

Answer:

An interesting experiment is given. We need to address various questions based on our knowledge of calculus.

Step 2

Part (a)

Time taken for the radius to grow to 2 cm = t1 = r/0.5 = 2/0.5 = 4 hours

Time taken for the radius to become 0 = t2 and the same can be obtained by solving:

r = 2 - √t2 = 0

Hence, t2 = 22 = 4 hours

Hence, the time duration of the entire experiment (from the introduction of the bacteria until its disappearance) = t1 + t2 = 4 + 4 = 8 hours

Step 3

Part (b)

r(t) = 0.5t for 0 ≤ t ≤ 4

and

r(t) = 2 - √(t - 4) for t > 2

Step-by-step explanation:

Answer:

80:280

Step-by-step explanation:

Final answer:

To share £360 in the ratio 2:7, you first find the value of one part by dividing £360 by the total number of ratio parts (9). Then, multiply each part of the ratio by this amount, resulting in £80 and £280.

Explanation:

To share £360 in the ratio 2:7, you first need to understand that the sum of the parts of the ratio (2+7) equals to 9 parts. The amount of £360 should be distributed into these 9 parts.

First, you divide the total amount by the total number of parts:
£360 / 9 = £40.

This result £40 is the value of 1 part. To find the amounts for the ratio 2:7, you multiply each part of the ratio by the value of 1 part:

• 2 * £40 = £80 which is the amount for the first part of the ratio, and
• 7 * £40 = £280 which is the amount for the second part of the ratio.

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*see attachment for the dot plot being referred to

Answer:

The data is symmetric and shows that he typically sent about 6 to 8 text messages per day

Step-by-step explanation:

The distribution of the data set on a dot plot can be said to be symmetric when most of the data points in the data are located or are concentrated at the center of the dot plot.

As we can observe from the given dot plot in the attachment, it shows that 6 to 8 text messages per day have more frequencies and are just right at the center of the dot plot. This shows the data is symmetric.

This also shows that Reza dents averagely 6 - 8 text messages per day. Reza can be said to have typically sent 6 - 8 text messages per day.

The rest statements about the dot plot are untrue.

Answer:

1. x=17

2. x=19

3. x=3

4. x=4

Answer:

question 1:

3/11

question 2:

-  7/11

Step-by-step explanation:

in

Final answer:

The part-time shelf stocker's taxable income is calculated by subtracting the exemption of $3650 and the standard deduction of $5700 from her annual income of $8912.03, resulting in a negative number, which means her taxable income was $0.

Explanation:

To calculate the taxable income for the part-time shelf stocker who made $8912.03 last year, we need to subtract the exemption and standard deduction from her annual income. The exemption claimed is $3650, and the standard deduction is $5700.

Here's the calculation:

1. Start with the total annual income: $8912.03.
2. Subtract the exemption amount: $8912.03 - $3650 = $5262.03.
3. Subtract the standard deduction: $5262.03 - $5700 = -$437.97.

Since the taxable income cannot be negative, the correct answer is $0. Thus, her taxable income last year was $0.

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Answer: C) $0

Step-by-step explanation:

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