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3 years ago

Bought three books: 150, if one book cost 50% more than the other two combined what was the price of the more expensive book

Mathematics

1 answer:

EleoNora [17]3 years ago

7 0

Two cheaper books = x
more expensive = 1.5x
so, 2.5x=150
150/2.5=x=60
therefore the more expensive book = 90

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Which of the below descriptions shows a possible HAMILTON PATH?

ra1l [238]

Option B: FECBAD represents the Hamilton path

Explanation:

The vertices in the given graph are A,B,C,D,E and F

We need to determine the Hamilton path of the given graph.

By definition, we know that a Hamilton path touches each and every vertex in a graph exactly once.

Hence, we need to connect the vertices in such a way that the graph touches each and every vertex exactly once.

Option A: EFADECBA

From this description, we can see that the path starts from the vertex E and connects all the vertices but some of the vertices are repeated twice.

Hence, the path EFADECBA is not a Hamilton path.

Therefore, Option A is not the correct answer.

Option B: FECBAD

From this description, we can see that the path starts from the vertex F and connects all the vertices exactly once.

Hence, the path FECBAD is the Hamilton path.

Therefore, Option B is the correct answer.

Option C: ADEFBC

From this description, we can see that the path starts from the vertex A and connects all the vertices but the path from F to B has to touch the vertex A. Thus, the vertices are repeated twice.

Hence, the path ADEFBC is not a Hamilton path.

Therefore, Option C is not the correct answer.

Option D: ADECBAFE

From this description, we can see that the path starts from the vertex A and connects all the vertices but some of the vertices are repeated twice.

Hence, the path ADECBAFE is not a Hamilton path.

Therefore, Option D is not the correct answer.

6 0

3 years ago

I will mark brainliest

matrenka [14]

A: 2,5
B: 3,1
C: -2,4

Explanation:

When you’re moving right and up you would add however many numbers you moved up to the original points because going right on a graph makes the X a larger number, and going up makes it larger.

5 0

3 years ago

Sadie finished her math test in sixteen minutes less than three times the amount of times it took her friend Laura to finish.if

amid [387]

Answer:

Sadie took 47 minutes to finish her test.

Step-by-step explanation:

Let Laura's time be x minutes.

Then we have:

x + 3x - 16 = 68

4x = 84

x = 21 minutes.

So Sadie took 3(21) - 16 = 63-16

= 47 minutes.

3 0

3 years ago

Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral with the specified value of n.

Vera_Pavlovna [14]

Split up the integration interval into 4 subintervals:

$\left[0,\dfrac\pi8\right],\left[\dfrac\pi8,\dfrac\pi4\right],\left[\dfrac\pi4,\dfrac{3\pi}8\right],\left[\dfrac{3\pi}8,\dfrac\pi2\right]$

The left and right endpoints of the $i$ -th subinterval, respectively, are

$\ell_i=\dfrac{i-1}4\left(\dfrac\pi2-0\right)=\dfrac{(i-1)\pi}8$

$r_i=\dfrac i4\left(\dfrac\pi2-0\right)=\dfrac{i\pi}8$

for $1\le i\le4$ , and the respective midpoints are

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{(2i-1)\pi}8$

Trapezoidal rule

We approximate the (signed) area under the curve over each subinterval by

$T_i=\dfrac{f(\ell_i)+f(r_i)}2(\ell_i-r_i)$

so that

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4T_i\approx\boxed{3.038078}$

Midpoint rule

We approximate the area for each subinterval by

$M_i=f(m_i)(\ell_i-r_i)$

so that

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4M_i\approx\boxed{2.981137}$

Simpson's rule

We first interpolate the integrand over each subinterval by a quadratic polynomial $p_i(x)$ , where

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

so that

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It so happens that the integral of $p_i(x)$ reduces nicely to the form you're probably more familiar with,

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

Then the integral is approximately

$\displaystyle\int_0^{\pi/2}\frac3{1+\cos x}\,\mathrm dx\approx\sum_{i=1}^4S_i\approx\boxed{3.000117}$

Compare these to the actual value of the integral, 3. I've included plots of the approximations below.

3 0

3 years ago

28, 33, 88, 81, 40, 25, 41<br> Mean median mode and range

PolarNik [594]

Hello!

Step-by-step explanation:

Mean: 48

Median: 40

Mode: None

Range: 63

Hope this helps!

3 0

2 years ago

Read 2 more answers