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2 years ago

14

There are 12 female students and 18 male students in a class. Which of the following expresses the ratio of female students to m

ale students in simplest form?

1 answer:

svet-max [94.6K]2 years ago

4 0

Answer: 2:3

Step-by-step explanation:

12:18 is like a fraction so you can divide it down on each side to make it simple.

12 and 18 can both be dived by 6 at most

so it would end up being

2:3

You might be interested in

If you roll a fair 10-sided die 7 times, what is the probability that the die lands on "10" exactly 2 times?

nexus9112 [7]

Answer: 2:7 times

Step-by-step explanation: hope it helps u

7 0

2 years ago

The equation of the line passing through the points (3, 16) and (5, 10) can be expressed as y = mx + b. Give the value of b

Alenkinab [10]

we are given two points as

(3, 16) and (5, 10)

firstly , we will find slope

slope is m

so, we can use formula

$m=\frac{y_2-y_1}{x_2-x_1}$

now, we can plug points

$m=\frac{10-16}{5-3}$

$m=\frac{-6}{2}$

$m=-3$

we can plug it in y=mx+b

we get

$y=-3x+b$

now, we can select any one points

and find b

(3,16)

x=3 and y=16

$16=-3*3+b$

we can find b

$b=25$

now, we can plug back b

and we get

$y=-3x+25$

so, equation is

$y=-3x+25$

and

$b=25$ ...............Answer

8 0

2 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

What is the answer explain please

eduard

Answer:

Pattern B

<h3> Explain: </h3>

A quadratic relationship is characterized by constant second differences.

<em><u>Pattern A </u></em>

Sequence: 0, 2, 4, 6

First Differences: 2, 2, 2 . . . . constant indicates a 1st-degree (linear, arithmetic) sequence

__________________________________________________________

<em><u>Pattern B</u></em>

Sequence: 1, 2, 5, 10

First Differences: 1, 3, 5

Second Differences: 2, 2 . . . . constant indicates a 2nd-degree (quadratic) sequence

__________________________________________________________

<em><u>Pattern C</u></em>

Sequence: 1, 3, 9, 27

First Differences: 2, 6, 18

Second Differences: 4, 12 . . . . each set of differences has a common ratio, indicating an exponential (geometric) sequence

__________________________________________________________

Pattern B shows a geometric relationship between step number and dot count.

6 0

2 years ago

Peter is making new cushion covers for a chair. There are three sizes of

Lesechka [4]

Answer:

A 846 square inches

Step-by-step explanation:

Use the net:

Rectangle 1: (21 in + 3 in + 21 in + 3 in) by 15 in.

Rectangle 2: 21 in by 3 in

Rectangle 3: 21 in by 3 in

total area = sum of areas of 3 rectangles above.

total area = (48 in * 15 in) + 2(21 in * 3 in)

total area = 720 in^2 + 126 in^2

total area = 801 in^2

Answer: A 846 square inches

6 0

2 years ago