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JulsSmile [24]
2 years ago
5

10 increased by the quotient of a number and 6 is 15

Mathematics
1 answer:
Makovka662 [10]2 years ago
3 0
<h2>Verbal Phrase to Mathematical Phrase</h2><h3>Answer:</h3>

10 +\frac{n}{6} = 15\\

<h3>Step-by-step explanation:</h3>

Let that number be n.

The quotient of a number and 6 is \frac{n}{6}\\.

"Increased" is just another term for "plus (+)" so 10 increased by The quotient of a number and 6 is 10 + \frac{n}{6}\\

And it tells us that it is 15 so it must be 10 +\frac{n}{6} = 15\\

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I want to take a survey of students at my university to find out what proportion like the new bus service on campus. I believe t
tatiyna

Answer:

You will need to sample at least 3108 students.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

In this problem, we have that:

\pi = 0.75

99% confidence level

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

How many students will I need to survey if I want to estimate, with 99% confidence, the true proportion to within 2%?

You need a sample size of at least n.

n is found when M = 0.02. So

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.02 = 2.575\sqrt{\frac{0.75*0.25}{n}}

0.02\sqrt{n} = 1.115

\sqrt{n} = \frac{1.115}{0.02}

\sqrt{n} = 55.75

\sqrt{n}^{2} = (55.75)^{2}

n = 3108

You will need to sample at least 3108 students.

4 0
3 years ago
7. A machine produces memory sticks of varying lengths, distributed uniformly between 3mm and 13 mm. Memory sticks longer than 1
Mars2501 [29]

Answer:

The proportion of memory sticks that will be scrapped is 0.3 = 30%.

Step-by-step explanation:

Uniform probability distribution:

An uniform distribution has two bounds, a and b.  

The probability of finding a value of at lower than x is:

P(X < x) = \frac{x - a}{b - a}

The probability of finding a value between c and d is:

P(c \leq X \leq d) = \frac{d - c}{b - a}

The probability of finding a value above x is:

P(X > x) = \frac{b - x}{b - a}

Distributed uniformly between 3mm and 13 mm.

This means that a = 3, b = 13

Calculate the proportion of memory sticks that will be scrapped:

P(X > 10) = \frac{13 - 10}{13 - 3} = \frac{3}{10} = 0.3

The proportion of memory sticks that will be scrapped is 0.3 = 30%.

6 0
2 years ago
The straight line 2x + 3y = 7 meets the curve
NISA [10]

Step-by-step explanation:

xy + 10 = 0. => y = -10/x.

2x + 3y = 7. => 3y = -2x + 7, y = -2/3 x + 7/3.

When -10/x = -2/3 x + 7/3,

-10 = -2/3 x² + 7/3 x, 2/3 x² - 7/3 x - 10 = 0.

=> 2x² - 7x - 30 = 0

=> (2x + 5)(x - 6) = 0

=> x = -2.5 or x = 6.

dy/dx = d/dx [-10/x] = 10/x².

When x = -2.5, dy/dx = 10 / (-2.5)² = 1.6.

When x = 6, dy/dx = 10 / (6)² = 5/18.

Hence the gradients at the points are 1.6 and 5/18.

5 0
3 years ago
Find the arc length of a central angle of 300° in a circle whose radius is 2inches
Svetradugi [14.3K]
360 degrees is the whole circumference.
300 degrees is 300/360 of the circumference.
The circumference: pi*r*2 = 4*pi = approximately 12.566.
300/360*12.566=10.472 = answer
8 0
3 years ago
2 very important questions
Troyanec [42]

Answer:

yes this is correct

Step-by-step explanation:

and what you wanna talk about

8 0
3 years ago
Read 2 more answers
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