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djyliett [7]
3 years ago
6

If an integer n has three unique prime divisors, then it follows that the largest prime divisor of n is less than or equal to cu

be root of n. True or False?
Mathematics
1 answer:
TiliK225 [7]3 years ago
4 0

Answer:

False

Step-by-step explanation:

Lets call the three prime divisors of n p, q, and r, being r the largest, we know:

n=q * p * r

Now, if

q * p < r

then

n < r * r = r^2

So:

\sqrt{n} < \sqrt{r^2} = r

Also, for every natural greater than one, we know:

\sqrt[3]{n}

so

\sqrt[3]{n}

from which:

\sqrt[3]{n} < r

So, we see, this means the preposition is false, we can find a particular counterexample:

q=2

p=3

p*q = 6

We need to choose a prime greater than 6

r=7

n= 2 * 3 *7 = 42

\sqrt[3]{42} = 3.4760 < 7

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Step-by-step explanation:

<u>5</u><u>)</u><u> </u>2.4×10^-5 / 4.5×10^-11

  • 2.4×10^-5= 0.000024
  • 4.5×10^-11= 0.000000000045

=0.000024/0.000000000045

=24/1 × 1,000,000/45

=24,000,000/45

=533,333.33°

=5.33333°×10^5

**NOT SURE ABOUT THIS QUESTION

<u>6</u><u>)</u><u> </u>(4,-2)

<u>7</u><u>)</u> --------

<u>8</u><u>)</u>

  1. 2x + 3 = 5x - 2

  • 2x - 5x = - 2 - 3
  • -3x = -5
  • x = -5/-3
  • x = 1.66°

  1. 6x + 4 = 6x + 4
  • 6x - 6x = 4 - 4
  • 0x = 0

  1. 2 (2x + 3) = 8x - 2
  • 4x + 6 = 8x - 2
  • 4x - 8x = -2 - 6
  • -4x = -8
  • x = -8/-4
  • x = 2

  1. -3x + 2 = -3x + 5
  • -3x + 3x = 5 - 2
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Letter be has no solution because it is broken down as "0x = 0"

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3 years ago
The town of Hayward (CA) has about 50,000 registered voters. A political research firm takes a simple random sample of 500 of th
timama [110]

Answer: (0.076, 0.140)

Step-by-step explanation:

Confidence interval for population proportion (p) is given by :-

\hat{p}\pm z_{\alpha/2}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

, where \hat{p} = sample proportion.

n= sample size.

\alpha = significance level .

z_{\alpha/2} = critical z-value (Two tailed)

As per given , we have

sample size : n= 500

The number of Independents.:  x= 54

Sample proportion of Independents\hat{p}=\dfrac{x}{n}=\dfrac{54}{500}=0.108

Significance level 98% confidence level : \alpha=1-0.98=0.02

By using z-table , Critical value : z_{\alpha/2}=z_{0.01}=2.33

The 98% confidence interval for the true percentage of Independents among Haywards 50,000 registered voters will be :-

0.108\pm (2.33)\sqrt{\dfrac{0.108(1-0.108)}{500}}\\\\=0.108\pm2.33\times0.013880634\\\\=0.108\pm0.03234187722\\\\\approx0.108\pm0.032=(0.108-0.032,\ 0.108+0.032)=(0.076,\ 0.140)

Hence, the 98% confidence interval for the true percentage of Independents among Haywards 50,000 registered voters.= (0.076, 0.140)

8 0
3 years ago
Line j has an equation of y - 8 = -2/3(x+5). Line K is perpendicular to line j and passes + through (-6, -2). What is the equati
riadik2000 [5.3K]

Answer:

y = \frac{3}{2} x + 7

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y - 8 = - \frac{2}{3} (x + 5) ← is in point- slope form

with m = - \frac{2}{3}

given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{-\frac{2}{3} } = \frac{3}{2}

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept ) , then

y = \frac{3}{2} x + c ← is the partial equation

to find c substitute (- 6, - 2 ) into the partial equation

- 2 = - 9 + c ⇒ c = - 2 + 9 = 7

y = \frac{3}{2} x + 7 ← equation of line K

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Mademuasel [1]

Answer:

Step-by-step explanation:

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2 years ago
500g of an item costs $12. Use the unitary method to find the equivalent cost of 320g.
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A) 500g=$12 -> 100g=12:5 100g=$2,40
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320g=3x2,40+0,58
320g=7,20+0,58
320g=7,78$
5 0
3 years ago
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