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amm1812
3 years ago
8

Fiona was thinking of a number. Fiona doubles it and adds 5.1 to get an answer of 11.5.

Mathematics
1 answer:
telo118 [61]3 years ago
7 0

Answer:

<h2>3•2</h2>

Step-by-step explanation:

<h2>let X be the unknown number</h2><h2>X × 2 = 2x</h2><h2>2x + 5•1 = 11•5</h2><h2>2x = 11•5 - 5•1</h2><h2>2x = 6•4</h2><h2>divide both sides by 2</h2><h2>X = 3•2</h2>
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10. Contacts. Assume that 30% of students at a university
jonny [76]

Using the <em>normal distribution and the central limit theorem</em>, we have that:

a) A normal model with mean 0.3 and standard deviation of 0.0458 should be used.

b) There is a 0.2327 = 23.27% probability that more than one third of this sample wear contacts.

<h3>Normal Probability Distribution</h3>

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
  • By the Central Limit Theorem, for a <u>proportion p in a sample of size n</u>, the sampling distribution of sample proportion is approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1 - p)}{n}}, as long as np \geq 10 and n(1 - p) \geq 10.

In this problem:

  • 30% of students at a university wear contact lenses, hence p = 0.3.
  • We randomly pick 100 students, hence n = 100.

Item a:

np = 100(0.3) = 30 \geq 10

n(1 - p) = 100(0.7) = 70 \geq 10

Hence a normal model is appropriated.

The mean and the standard deviation are given as follows:

\mu = p = 0.3

s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.3(0.7)}{100}} = 0.0458

Item b:

The probability is <u>1 subtracted by the p-value of Z when X = 1/3 = 0.3333</u>, hence:

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{0.3333 - 0.3}{0.0458}

Z = 0.73

Z = 0.73 has a p-value of 0.7673.

1 - 0.7673 = 0.2327.

0.2327 = 23.27% probability that more than one third of this sample wear contacts.

To learn more about the <em>normal distribution and the central limit theorem</em>, you can take a look at brainly.com/question/24663213

5 0
2 years ago
Calculate the amount of interest on $1200.00 for one year at an annual rate of 4 %.
kodGreya [7K]
Interest = (PRT)/100 = (1200×4×1)/100 = $48
7 0
3 years ago
Read 2 more answers
HELP PLEASE!
olasank [31]

Answer        

Find out the Area of a triangle .

To proof  

Formula

Area of Triangle

= \frac{1}{2}\times( {x_1(y_{2}-y_{3}) +x_{2}(y_{3} - y_{1})+x_{3}(y_{1}-y_{2})})

Now vertices are D(3, 3) , E(3, −1) , and F(−2, −5) .

= \frac{1}{2} (3\times(-1 +5) + 3\times(-5-3)-2\times(3+1))

Solving the above

= \frac{1}{2}(3\times4+3\times-8 -2\times4)

=\frac{1}{2} (12-24-8)\\ =\frac{1}{2} (-32+12)\\=\frac{1}{2} (-20)

= -10 units²

(Neglected the negative sign as area cannot be negative.)

= 10 units ²

Area of  a triangle is 10 units ²

Hence proved

6 0
3 years ago
Factor completely. x 3 + 6x 2 - 4x - 24
Ulleksa [173]
You can factor (x^3 and 6x^2) and (-4x and -24).

So x^2(x+6) - 4(x+6)

(x^2-4)(x+6)

(x-2)(x+2)(x+6)
5 0
3 years ago
Help? Because my teacher doesn't want too
snow_lady [41]
M<ABC = m<EBD = 36 (vertical angles)

78 - x + 36 + 3x - 10 = 180 (straight angle)

Now solve for x

78 - x + 36 + 3x - 10 = 180
2x + 68 = 180
     -  68     -68 (subtract 68 on both sides)
2x        =  58
  x        =  29
7 0
3 years ago
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