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4 years ago

13

A candy maker mixed marshmallows worth $1.80 a pound with rice crisipes worth $3.20 a pound to make 50 pounds of a rice crispie

treats worth $2.92 a pound. Find the number of pounds of each item used.

1 answer:

Orlov [11]4 years ago

4 0

$\bf \begin{array}{lccclll}
&amount&price&\textit{price per amount}\\
&-----&-----&--------\\
\textit{marshmallows}&x&1.80&(1.80)(x)\\
\textit{rice crispies}&y&3.20&(3.20)(y)\\
-----&-----&-----&--------\\
mixture&50&2.92&(50)(2.92)
\end{array}\\\\
-----------------------------\\\\

\begin{cases}
x+y=50\implies \boxed{y}=50-x\\
1.80x+3.20y=(50)(2.92)\\
----------\\
1.80x+3.20\left( \boxed{50-x} \right)=(50)(2.92)
\end{cases}$

solve for "x", to see how many lbs of marshmallows were needed

what about "y"? well, y = 50 - x

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Find the complex fourth roots of 81(cos(3pi/8) + i sin(3pi/8))

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By using <span>De Moivre's theorem:
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∴ The modulus of the fourth root = $\sqrt[4]{z} = \sqrt[4]{81} = 3$

Part (b) find the angle for each of the four roots

The angle of the given complex number = $\frac{3 \pi}{8}$
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The angle of the first root = $\frac{ \frac{3 \pi}{8} }{4} = \frac{3 \pi}{32}$
The angle of the second root = $\frac{3\pi}{32} + \frac{\pi}{2} = \frac{19\pi}{32}$
The angle of the third root = $\frac{19\pi}{32} + \frac{\pi}{2} = \frac{35\pi}{32}$
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Complete Question

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Answer:

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The alternative hypothesis $H_a : \mu < 15.9$

2

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Step-by-step explanation:

From the question we are told that

The population mean value for time citizens remain unemployed is $\mu = 15.9 \ weeks$

The sample size is n = 50

The sample standard deviation is 6.7 weeks.

The sample mean value for time citizens remain unemployed is $\mu = 15.9 \ weeks$

The null hypothesis is $H_o : \mu \ge 15.9$

The alternative hypothesis $H_a : \mu < 15.9$

Generally test statistics is mathematically represented as

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=> $z = \frac{13.4 - 15.9}{\frac{6.7}{\sqrt{50}}}$

=> $z = -2.64$

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-------------------------------$

$\bf \begin{array}{ccll}
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