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3 years ago

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Suzy has an Etsy store where she sells shirts. Her shirts come in five sizes: small, medium, large, extra-large, or 2XL. Her shi

rts come as long sleeves, short sleeves, or tank tops; The color options are blue, red, pink, or green. Use the counting principle to figure out how many total outcomes there are.

2 answers:

fredd [130]3 years ago

8 0

35. Seven outcomes for each size

Shalnov [3]3 years ago

4 0

Answer:

25

Step-by-step explanation:

You might be interested in

If X= -6 and y=4 what is x² + y²

Rainbow [258]

Answer:

52

Step-by-step explanation:

(-6)x(-6)=36

(4)x(4)=16

36+16=52

6 0

2 years ago

Read 2 more answers

Let z=3+i, <br>then find<br> a. Z²<br>b. |Z| <br>c.<img src="https://tex.z-dn.net/?f=%5Csqrt%7BZ%7D" id="TexFormula1" title="\sq

zysi [14]

Given <em>z</em> = 3 + <em>i</em>, right away we can find

(a) square

<em>z</em> ² = (3 + <em>i </em>)² = 3² + 6<em>i</em> + <em>i</em> ² = 9 + 6<em>i</em> - 1 = 8 + 6<em>i</em>

(b) modulus

|<em>z</em>| = √(3² + 1²) = √(9 + 1) = √10

(d) polar form

First find the argument:

arg(<em>z</em>) = arctan(1/3)

Then

<em>z</em> = |<em>z</em>| exp(<em>i</em> arg(<em>z</em>))

<em>z</em> = √10 exp(<em>i</em> arctan(1/3))

or

<em>z</em> = √10 (cos(arctan(1/3)) + <em>i</em> sin(arctan(1/3))

(c) square root

Any complex number has 2 square roots. Using the polar form from part (d), we have

√<em>z</em> = √(√10) exp(<em>i</em> arctan(1/3) / 2)

and

√<em>z</em> = √(√10) exp(<em>i</em> (arctan(1/3) + 2<em>π</em>) / 2)

Then in standard rectangular form, we have

$\sqrt z = \sqrt[4]{10} \left(\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) + i \sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right)\right)$

and

$\sqrt z = \sqrt[4]{10} \left(\cos\left(\dfrac12 \arctan\left(\dfrac13\right) + \pi\right) + i \sin\left(\dfrac12 \arctan\left(\dfrac13\right) + \pi\right)\right)$

We can simplify this further. We know that <em>z</em> lies in the first quadrant, so

0 < arg(<em>z</em>) = arctan(1/3) < <em>π</em>/2

which means

0 < 1/2 arctan(1/3) < <em>π</em>/4

Then both cos(1/2 arctan(1/3)) and sin(1/2 arctan(1/3)) are positive. Using the half-angle identity, we then have

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1+\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1-\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

and since cos(<em>x</em> + <em>π</em>) = -cos(<em>x</em>) and sin(<em>x</em> + <em>π</em>) = -sin(<em>x</em>),

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{1+\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{1-\cos\left(\arctan\left(\dfrac13\right)\right)}2}$

Now, arctan(1/3) is an angle <em>y</em> such that tan(<em>y</em>) = 1/3. In a right triangle satisfying this relation, we would see that cos(<em>y</em>) = 3/√10 and sin(<em>y</em>) = 1/√10. Then

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1+\dfrac3{\sqrt{10}}}2} = \sqrt{\dfrac{10+3\sqrt{10}}{20}}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)\right) = \sqrt{\dfrac{1-\dfrac3{\sqrt{10}}}2} = \sqrt{\dfrac{10-3\sqrt{10}}{20}}$

$\cos\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{10-3\sqrt{10}}{20}}$

$\sin\left(\dfrac12 \arctan\left(\dfrac13\right)+\pi\right) = -\sqrt{\dfrac{10-3\sqrt{10}}{20}}$

So the two square roots of <em>z</em> are

$\boxed{\sqrt z = \sqrt[4]{10} \left(\sqrt{\dfrac{10+3\sqrt{10}}{20}} + i \sqrt{\dfrac{10-3\sqrt{10}}{20}}\right)}$

and

$\boxed{\sqrt z = -\sqrt[4]{10} \left(\sqrt{\dfrac{10+3\sqrt{10}}{20}} + i \sqrt{\dfrac{10-3\sqrt{10}}{20}}\right)}$

3 0

3 years ago

Read 2 more answers

Kyle is stringing a necklace with beads he puts black beads on 5/8 of the string and white beads on 1/4 of the string Kyle think

Alexeev081 [22]

Answer:Kyle’s claim is not reasonable

Step-by-step explanation:

Total length of the string of the necklace that Kyle covered with black beads is 5/8.

Total length of the string of the necklace that Kyle covered with white beads is 1/4.

Total length of the string of the necklace that Kyle covered with black beads and white beads is would be

1/4 + 5/8 = 7/8 = 0.875

Kyle thought that he will cover 6/12 of the string with beads. 6/12 = 0.5

It means that he covered more than 6/12. Kyle's claim was wrong

3 0

3 years ago

I think of a number. If I divide the sum of 6 and the number by 3,the result is 4 more than one quarter of the number. Find the

Alex17521 [72]

Answer:

24

Step-by-step explanation:

Let the number be x.

Sum of the number and 6: $6+x$

Divide it by 3: $\frac{6+x}{3}$

Result is 4 more than one quarter of the number:

$\frac{6+x}{3} =4+\frac{1}{4} x$

Multiply both sides by 12:

$\frac{6+x}{3}\cdot \:12=4\cdot \:12+\frac{1}{4}x\cdot \:12$

Simplify:

$4\left(x+6\right)=48+3x$

Expand:

$4x+24=48+3x$

Subtract 24 from both sides:

$4x+24-24=48+3x-24$

$4x=3x+24$

Subtract 3x from both sides:

$4x-3x=3x+24-3x$

$x=24$

The number is 24.

7 0

3 years ago

choose the equation below that represents the line passing through the point (1, −4) with a slope of 1/2. a.) y − 4 = 1/2(x − 1)

Ganezh [65]

Point (1, -4)
Slope=1/2
y=mx+c
y=1/2x +c
-4=1/2(1)+c
-4=1/2+c
c=-4-1/2
c=-4 1/2
y= $\frac{1}{2} x- \frac{9}{2}$

3 0

3 years ago