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3 years ago

Ava has 34 candy bars. If

Mathematics

1 answer:

aliya0001 [1]3 years ago

4 0

$\bf Step-by-step~explanation:$

If Ava has 34 candy bars, and each box can hold 5 bars, then we need to find out how many boxes that are filled up.

$\bf Step~1:$

Divide the number of candy bars (34), by the number each box can hold (5)

$\bf\frac{34}{5}=6.8$

Since we cannot have 6.8 boxes, we have to round down to 6.

$\boxed{\bf Our~final~answer:~6~boxes}$

$\bf Check~our~answer:$

To check our answer, we multiply the number of boxes (6), by the number of bars in each box (5), to get 30. We add Ava's extra bars (4), and we get the number we started off with: 34. This proves our answer is correct!

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Simplify the complex numbers using de Moivre's Theorem and match them with their solutions.

alexandr1967 [171]

For the numbers in $a+bi$ form, convert to polar form:

$1+i=\sqrt2\dfrac{1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)$

By DeMoivre's theorem,

$(1+i)^5=(\sqrt2)^5\left(\cos\dfrac{5\pi}4+i\sin\dfrac{5\pi}4\right)=4\sqrt2\dfrac{-1-i}{\sqrt2}=-4-4i$

$-1+i=\sqrt2\dfrac{-1+i}{\sqrt2}=\sqrt2\left(\cos\dfrac{3\pi}4+i\sin\dfrac{3\pi}4}\right)$

$\implies(-1+i)^6=(\sqrt2)^6\left(\cos\dfrac{18\pi}4+i\sin\dfrac{18\pi}4\right)=8i$

$\sqrt3+i=2\dfrac{\sqrt3+i}2=2\left(\cos\dfrac\pi6+i\sin\dfrac\pi6\right)$

$\implies2(\sqrt3+i)^{10}=2^{11}\left(\cos\dfrac{10\pi}6+i\sin\dfrac{10\pi}6\right)=2^{11}\dfrac{1-i\sqrt3}2=2^{10}(1-i\sqrt3)$

For the numbers already in polar form, DeMoivre's theorem can be applied directly:

$2\left(\cos20^\circ+i\sin20^\circ\right)^3=2\left(\cos60^\circ+i\sin60^\circ\right)=2\dfrac{1+i\sqrt3}2=1+i\sqrt3$

$2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)^4=2(\cos\pi+i\sin\pi)=-2$

At second glance, I think the 2s in the last two numbers should also be getting raised to the 3rd and 4th powers:

$\left(2(\cos20^\circ+i\sin20^\circ)\right)^3=8\left(\cos60^\circ+i\sin60^\circ\right)=4+4\sqrt3$

$\left(2\left(\cos\dfrac\pi4+i\sin\dfrac\pi4\right)\right)^4=16(\cos\pi+i\sin\pi)=-16$

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3 years ago

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larisa86 [58]

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Answer:

(d) 8 cm and 9 cm

Step-by-step explanation:

The sum of the other two side lengths must <em>exceed</em> 13 cm for a triangle to be possible.

8 cm and 9 cm

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2 years ago

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Tcecarenko [31]

Answer: 0.030

Step-by-step explanation:

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The percent of the items produced by machine which are not defective: $Q=1-0.1=0.9$

Sample size : n = 100

Now, the standard error of the proportion is given by :-

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Hence, the the standard error of the distribution of the sample proportions=0.030

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3 years ago

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ss7ja [257]

Answer:

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Step-by-step explanation:

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2 years ago

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Lubov Fominskaja [6]

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3 years ago