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3 years ago

15

The conditional relative frequency table was generated using data that compares the number of boys and girls who pack their lunc

h or buy lunch from the cafeteria. 35 total girls and 50 total boys were surveyed. How many students bought their lunch from the cafeteria? Round to the nearest whole number.

2 answers:

slega [8]3 years ago

8 0

Answer:

Its 36 students

Step-by-step explanation:

Kaylis [27]3 years ago

4 0

36 students............................................

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Express 0.7723 as a fraction

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The answer is 3697/4787

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A rectangular prism has a height of 5 yd and a square base with a side length of 8 yd. What is the surface area of the prism? A

pantera1 [17]

Positive the answer should be C.288yd2

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3 years ago

Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficie

Dvinal [7]

For part (a), you have

$\dfrac x{x^2+x-6}=\dfrac x{(x+3)(x-2)}=\dfrac a{x+3}+\dfrac b{x-2}$
$x=a(x-2)+b(x+3)$

If $x=2$ , then $2=b(2-3)\implies b=-2$ .

If $x=-3$ , then $-3=a(-3-2)\implies a=\dfrac35$ .

So,

$\dfrac x{x^2+x-6}=\dfrac 3{5(x+3)}-\dfrac 2{x-2}$

For part (b), since the degrees of the numerator and denominator are the same, you first need to find the quotient and remainder upon division.

$\dfrac{x^2}{x^2+x+2}=\dfrac{x^2+x+2-x-2}{x^2+x+2}=1-\dfrac{x+2}{x^2+x+2}$

In the remainder term, the denominator $x^2+x+2$ can't be factorized into linear components with real coefficients, since the discriminant is negative $(1-4\times1\times2=-7)$ . However, you can still factorized over the complex numbers, so a partial fraction decomposition in terms of complexes does exist.

$x^2+x+2=0\implies x=-\dfrac12\pm\dfrac{\sqrt7}2i$
$\implies x^2+x+2=\left(x-\left(-\dfrac12+\dfrac{\sqrt7}2i\right)\right)\left(x-\left(-\dfrac12-\dfrac{\sqrt7}2i\right)\right)$
$\implies x^2+x+2=\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)$

Then you have

$\dfrac{x+2}{x^2+x+2}=\dfrac a{x+\dfrac12-\dfrac{\sqrt7}2i}+\dfrac b{x+\dfrac12+\dfrac{\sqrt7}2i}$
$x+2=a\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)+b\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)$

When $x=-\dfrac12-\dfrac{\sqrt7}2i$ , you have

$-\dfrac12-\dfrac{\sqrt7}2i+2=b\left(-\dfrac12-\dfrac{\sqrt7}2i+\dfrac12-\dfrac{\sqrt7}2i\right)$
$\dfrac32-\dfrac{\sqrt7}2i=-\sqrt7ib$
$b=\dfrac12+\dfrac3{2\sqrt7}i=\dfrac1{14}(7+3\sqrt7i)$

When $x=-\dfrac12+\dfrac{\sqrt7}2i$ , you have

$-\dfrac12+\dfrac{\sqrt7}2i+2=a\left(-\dfrac12+\dfrac{\sqrt7}2i+\dfrac12+\dfrac{\sqrt7}2i\right)$
$\dfrac32+\dfrac{\sqrt7}2i=\sqrt7ia$
$a=\dfrac12-\dfrac3{2\sqrt7}i=\dfrac1{14}(7-3\sqrt7i)$

So, you could write

$\dfrac{x^2}{x^2+x+2}=1-\dfrac{x+2}{x^2+x+2}=1-\dfrac {7-3\sqrt7i}{14\left(x+\dfrac12-\dfrac{\sqrt7}2i\right)}-\dfrac {7+3\sqrt7i}{14\left(x+\dfrac12+\dfrac{\sqrt7}2i\right)}$

but that may or may not be considered acceptable by that webpage.

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3 years ago

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What is the volume of the figure below?

Alja [10]

Answer:

312

Step-by-step explanation:

Volume of the parallalelepiped:

base x width x height

V = 5 x 4 x 12 = 240

for triangular prism:

base = 8-5 = 3

base area = (base x height)/2 = (3x4)/2 = 6

V = base area x 12

V = 6 x 12 = 72

Total volume = 240 + 72 = 312

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3 years ago

Translate and solve: The difference of n and 1/6 is 1/2.

enyata [817]

<h2>Translating Words into Problems</h2>

We can translate a word equation into a mathematical equation by translating key words into operations.

<em>difference</em> = subtract
<em>is</em> = equals

<h2>Addinng Fractions</h2>

Whenever we need to add one fraction to another, we must find a common denominator, change both the fractions for their denominators to be the same, and then add the numerators. Finally, we reduce the fraction.

<h2>Solving the Question</h2>

We're given:

The difference of n and $\dfrac{1}{6}$ is $\dfrac{1}{2}$ .

Translate the given information into an equation:

⇒ $n-\dfrac{1}{6}=\dfrac{1}{2}$

Solve for <em>n</em>:

⇒ $n-\dfrac{1}{6}=\dfrac{1}{2}\\\\n=\dfrac{1}{2}+\dfrac{1}{6}\\\\n=\dfrac{3}{6}+\dfrac{1}{6}\\\\n=\dfrac{4}{6}\\\\n=\dfrac{2}{3}$

<h2>Answer</h2>

$n=\dfrac{2}{3}$

4 0

2 years ago