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3 years ago

Disproof by counter example: For all positive integers x: 1/x < 1

Mathematics

1 answer:

xz_007 [3.2K]3 years ago

5 0

Answer:

The given statement is correct for all positive integers.

Step-by-step explanation:

The given inequality is

$\frac{1}{x}$ for all positive integers

$\frac{1}{x}1$

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Simplify (write without the absolute value sign) |x+3|, if x>2

kodGreya [7K]

Answer:

Step-by-step explanation

Note that if x>2, then x+3>3+2=5. Then x+3>0. Recall that the absolute value function is defined as

$|x|=x \text{ if } x\geq 0$

$|x|=-x \text{ if } x< 0$

Since x+3>0, we have that |x+3|=x+3

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3 years ago

What is the y-intercept of f(x) = 1 + log2(11x + 4)?

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Step-by-step explanation:

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3 years ago

Brian, Chris, and Damien took a math test that had 20 questions. The number of questions Brian got right is 14 more than the num

shepuryov [24]

Question:

Brian, Chris, and Damien took a math test that had 20 questions. The number of questions Brian got right is 14 more than 1/4 the number of questions Chris got right. Damien correctly answered 2 less than 5/4 the number of questions Chris answered correctly. If Brian and Damien have the same score, which statement is true?

A) Brian and Damien both answered 2 fewer questions correctly than Chris did.

B) Brian and Damien both answered 4 more questions correctly than Chris did.

C) Brian and Damien both answered 2 more questions correctly than Chris did.

D) Brian and Damien both answered 4 fewer questions correctly than Chris did.

Answer:

Option C

Brian and Damien both answered 2 more questions correctly than Chris did

Solution:

Let "x" be the number of correct answers of Brian

Let "y" be the number of correct answers of Chris

Let "z" be the number of correct answers of Damien

The number of questions Brian got right is 14 more than 1/4 the number of questions Chris got right

$x = 14 + \frac{1}{4}y\\$ ---------- eqn 1

Damien correctly answered 2 less than 5/4 the number of questions Chris answered correctly

$z = \frac{5}{4}y - 2$ ---------- eqn 2

Brian and Damien have the same score

x = z -------- eqn 3

Therefore,

$14 + \frac{1}{4}y = \frac{5}{4}y - 2\\\\\frac{5}{4}y - \frac{1}{4}y = 14+2\\\\y = 16$

Substitute y = 16 in eqn 1

$x = 14 + \frac{16}{4}\\\\x = 14 + 4\\\\x = 18$

Therefore, by eqn 3,

z = 18

Thus we get,

Number of correct answers of Brian = 18

Number of correct answers of chris = 16

Number of correct answers of Damien = 18

Therefore, correct statement is:

Brian and Damien both answered 2 more questions correctly than Chris did

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3 years ago

The national average for the math portion of the College Board’s Scholastic Aptitude Test

Alex73 [517]

Answer:

a) 0.1587

b) 0.023

c) 0.341

d) 0.818

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 515

Standard Deviation, σ = 100

We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(score greater than 615)

P(x > 615)

$P( x > 615) = P( z > \displaystyle\frac{615 - 515}{100}) = P(z > 1)$

$= 1 - P(z \leq 1)$

Calculation the value from standard normal z table, we have,

$P(x > 615) = 1 - 0.8413 = 0.1587 = 15.87\%$

b) b) P(score greater than 715)

$P(x > 715) = P(z > \displaystyle\frac{715-515}{100}) = P(z > 2)\\\\P( z > 2) = 1 - P(z \leq 2)$

Calculating the value from the standard normal table we have,

$1 - 0.977 = 0.023 = 2.3\%\\P( x > 715) = 2.3\%$

c) P(score between 415 and 515)

$P(415 \leq x \leq 515) = P(\displaystyle\frac{415 - 515}{100} \leq z \leq \displaystyle\frac{515-515}{100}) = P(-1 \leq z \leq 0)\\\\= P(z \leq 0) - P(z < -1)\\= 0.500 - 0.159 = 0.341 = 34.1\%$

$P(415 \leq x \leq 515) = 34.1\%$

d) P(score between 315 and 615)

$P(315 \leq x \leq 615) = P(\displaystyle\frac{315 - 515}{100} \leq z \leq \displaystyle\frac{615-515}{100}) = P(-2 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < -2)\\= 0.841 - 0.023 = 0.818 = 81.8\%$

$P(315 \leq x \leq 615) = 81.8\%$

4 0

4 years ago