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3 years ago

Mary won £5000 in a competition

Mathematics

1 answer:

Ahat [919]3 years ago

5 0

Answer: £833

Step-by-step explanation:

1. Multiply 279 by 9 (equals 2,511)

2. Multiply 184 by 9 (1,656)

3. Add 2,511 and 1,656 together (4,167)

4. Subtract 4,167 from 5,000 (833)

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Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produ

SOVA2 [1]

$y=\ln(6+x^3)\implies y'=\dfrac{3x^2}{6+x^3}$

The arc length of the curve is

$\displaystyle\int_0^5\sqrt{1+\frac{9x^4}{(6+x^3)^2}}\,\mathrm dx$

which has a value of about 5.99086.

Let $f(x)=\sqrt{1+\frac{9x^4}{(6+x^3)^2}}$ . Split up the interval of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [9/2, 5]

The left and right endpoints are given respectively by the sequences,

$\ell_i=\dfrac{i-1}2$

$r_i=\dfrac i2$

with $1\le i\le10$ .

These subintervals have midpoints given by

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4$

Over each subinterval, we approximate $f(x)$ with the quadratic polynomial

$p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

so that the integral we want to find can be estimated as

$\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It turns out that

$\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{f(\ell_i)+4f(m_i)+f(r_i)}6$

so that the arc length is approximately

$\displaystyle\sum_{i=1}^{10}\frac{f(\ell_i)+4f(m_i)+f(r_i)}6\approx5.99086$

5 0

3 years ago

If 588 digits were used to number the pages of a book, how many pages are in this book?

gregori [183]

Answer:

294 pages are in this book

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

The demand for a daily newspaper at a newsstand at a busy intersection is known to be normally distributed with a mean of 150 an

AURORKA [14]

Answer:

171 newspapers.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 150, \sigma = 25$

How many newspapers should the newsstand operator order to ensure that he runs short on no more than 20% of days

The number of newspapers must be on the 100-20 = 80th percentile. So this value if X when Z has a pvalue of 0.8. So X when Z = 0.84.

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

$0.84 = \frac{X - 150}{25}$

$X - 150 = 0.84*25$

$X = 171$

So 171 newspapers.

4 0

3 years ago

Pls help sixowiskosixo

erma4kov [3.2K]

The given question is a quadratic equation and we can use several methods to get the solutions to this question. The solution to the equation are 3/4 and -5/6 and the greater of the two solutions is 3/4

<h3>Quadratic Equation</h3>

Quadratic equation are polynomials with a second degree as it's highest power.

An example of a quadratic equation is

$y = ax^2 + bx + c$

The given quadratic equation is $24x^2 + 2x = 15$

Let's rearrange the equation

$24x^2 + 2x = 15\\24x^2 + 2x - 15 = 0$

This implies that

a = 24
b = 2
c = -15

The equation or formula of quadratic formula is given as

$y = \frac{-b +- \sqrt{b^2 - 4ac} }{2a}$

We can substitute the values into the equation and solve

$y = \frac{-b +- \sqrt{b^2 - 4ac} }{2a}\\y = \frac{-2 +- \sqrt{2^2 -4 * 24 * (-15)} }{2*24} \\y = \frac{-2+-\sqrt{4+1440} }{48} \\y = \frac{-2+-\sqrt{1444} }{48} \\y = \frac{-2+- 38}{48} \\y = \frac{-2+38}{48} \\y = \frac{3}{4}\\ \\or\\y = \frac{-2-38}{48} \\y = \frac{-40}{48} \\y = -\frac{5}{6}$

From the calculations above, the solution to the equation are 3/4 and -5/6 and the greater of the two solutions is 3/4

Learn more on quadratic equation here;

brainly.com/question/8649555

#SPJ1

7 0

2 years ago

2.85 as a mixed number

WARRIOR [948]

The number 2.85 can be writen using the fraction 285/100 which is equal to 57/20 when reduced to lowest terms.
It is also equal to 2 17/20 when writen as a mixed number.
You can use the following approximate value(s) for this number:57/20 =~ 2 6/7 (if you admit a error of 0.250627%)2.85 =~ 2 5/6 (if you admit a error of -0.584795%)2.85 =~ 3 (if you admit a error of 5.263158%)

3 0

3 years ago

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