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2 years ago

The length of a log of wood is 90 in. How many cuts do you need to make to obtain

1 answer:

6 0

The greatest number of pieces will be 12 where each piece will have a different length and the length of each piece is a whole number, in inches and the remaining piece length will be 12 in(90 - 78).

<h3>What is a sequence?</h3>

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

The total length of the wood = 90 in

We have to cut it into the greatest number of pieces, where each piece will have a different length and the length of each piece is a whole number, in inches.

We can cut it like:

1 in, 2 in, 3 in, 4 in, and so on

The above shows the arithmetic sequence,

The sum of the n natural number is given by:

$\rm S_n = \dfrac{n(n+1)}{2}$

$\rm 90 = \dfrac{n(n+1)}{2}$

After solving, we will get a quadratic equation:

n² + n -180 = 0

After solving, we will get:

n = 12.92 and n = -13.92(term can not be negative)

n = 12 (taking whole number)

Thus, the greatest number of pieces will be 12 where each piece will have a different length and the length of each piece is a whole number, in inches and the remaining piece length will be 12 in(90 - 78).

Learn more about the sequence here:

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Complete the input output table for the function y=3^x

egoroff_w [7]

Answer:

Input of x when it is equal to (1,2,3,4,5) gave an output of 3, 9, 27,81 & 243 respectively.

Step-by-step explanation:

Step 1. Substitute for x (1,2,3,4,5) in the functions to solve for the output of y.

y=3^x

when x= 1

y=3¹ = 3

when x= 2

y=3² = 9

when x= 3

y=3³ = 27

when x= 4

y=3⁴ = 81

when x= 5

y=3 ^ 5 = 243.

Input of x when it is equal to (1,2,3,4,5) gave an output of 3, 9, 27,81 & 243 respectively.

6 0

3 years ago

Suppose that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to

polet [3.4K]

Answer:

(a) The probability that X is at most 30 is 0.9726.

(b) The probability that X is less than 30 is 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is 0.7406.

Step-by-step explanation:

We are given that 11% of all steel shafts produced by a certain process are nonconforming but can be reworked. A random sample of 200 shafts is taken.

Let X = the number among these that are nonconforming and can be reworked

The above situation can be represented through binomial distribution such that X ~ Binom(n = 200, p = 0.11).

Here the probability of success is 11% that this much % of all steel shafts produced by a certain process are nonconforming but can be reworked.

Now, here to calculate the probability we will use normal approximation because the sample size if very large(i.e. greater than 30).

So, the new mean of X, $\mu$ = $n \times p$ = $200 \times 0.11$ = 22

and the new standard deviation of X, $\sigma$ = $\sqrt{n \times p \times (1-p)}$

= $\sqrt{200 \times 0.11 \times (1-0.11)}$

= 4.42

So, X ~ Normal( $\mu =22, \sigma^{2} = 4.42^{2}$ )

(a) The probability that X is at most 30 is given by = P(X < 30.5) {using continuity correction}

P(X < 30.5) = P( $\frac{X-\mu}{\sigma}$ < $\frac{30.5-22}{4.42}$ ) = P(Z < 1.92) = 0.9726

The above probability is calculated by looking at the value of x = 1.92 in the z table which has an area of 0.9726.

(b) The probability that X is less than 30 is given by = P(X $\leq$ 29.5) {using continuity correction}

P(X $\leq$ 29.5) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{29.5-22}{4.42}$ ) = P(Z $\leq$ 1.70) = 0.9554

The above probability is calculated by looking at the value of x = 1.70 in the z table which has an area of 0.9554.

(c) The probability that X is between 15 and 25 (inclusive) is given by = P(15 $\leq$ X $\leq$ 25) = P(X < 25.5) - P(X $\leq$ 14.5) {using continuity correction}

P(X < 25.5) = P( $\frac{X-\mu}{\sigma}$ < $\frac{25.5-22}{4.42}$ ) = P(Z < 0.79) = 0.7852

P(X $\leq$ 14.5) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{14.5-22}{4.42}$ ) = P(Z $\leq$ -1.70) = 1 - P(Z < 1.70)

= 1 - 0.9554 = 0.0446

The above probability is calculated by looking at the value of x = 0.79 and x = 1.70 in the z table which has an area of 0.7852 and 0.9554.

Therefore, P(15 $\leq$ X $\leq$ 25) = 0.7852 - 0.0446 = 0.7406.

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3 years ago

Which of these statements is true? A. The interior angles of both a regular and irregular pentagon have a sum of 540o. B. The in

Varvara68 [4.7K]

Answer:

Option A is the correct answer.

Step-by-step explanation:

The sum of interior angles of a polygon is given by (n-2) x 180°, where n is the number of sides.

The sum of interior angles will not affect irregularity of polygon, it is same for regular and irregular polygon.

For a pentagon n =5.

Sum of interior angles = (5-2) x 180 = 3 x 180 = 540°

Option A is the correct answer.

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3 years ago

√7 is between what two consecutive integers?

bulgar [2K]

Answer: √7 is between 2 and 3

Step-by-step explanation:

The next lower number that is a perfect square is 4, the next higher perfect square is 9. Take the roots of those two numbers to find the integers you are looking for.

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3 years ago

Please help Point____is plotted at -4/5

musickatia [10]

Answer:

Step-by-step explanation:

-4/5 is -0.8, which is at point C

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3 years ago

Read 2 more answers