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3 years ago

Students were asked how many hours during the

Mathematics

2 answers:

Natali5045456 [20]3 years ago

6 0

Answer:

mean of samples in row 1: 8

Mean of samples in row 2: 5

Mean of samples in row 3: 6

Mean of samples in row 4: 4

Step-by-step explanation:

Aleks04 [339]3 years ago

5 0

Answer:

mean of samples in row 1: 8

Mean of samples in row 2: 5

Mean of samples in row 3: 6

Mean of samples in row 4: 4

Step-by-step explanation:

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Given the polynomial x7y³ + 2x5y² - 3x³ - 2x4 -2, its degree is equal to?

denis-greek [22]

Answer:

Step-by-step explanation:

its always the highest exponet

4 0

3 years ago

Which of the following is not one of the 8th roots of unity?

Anika [276]

Answer:

1+i

Step-by-step explanation:

To find the 8th roots of unity, you have to find the trigonometric form of unity.

1. Since $z=1=1+0\cdot i,$ then

$Rez=1,\\ \\Im z=0$

and

$|z|=\sqrt{1^2+0^2}=1,\\ \\\\\cos\varphi =\dfrac{Rez}{|z|}=\dfrac{1}{1}=1,\\ \\\sin\varphi =\dfrac{Imz}{|z|}=\dfrac{0}{1}=0.$

This gives you $\varphi=0.$

Thus,

$z=1\cdot(\cos 0+i\sin 0).$

2. The 8th roots can be calculated using following formula:

$\sqrt[8]{z}=\{\sqrt[8]{|z|} (\cos\dfrac{\varphi+2\pi k}{8}+i\sin \dfrac{\varphi+2\pi k}{8}), k=0,\ 1,\dots,7\}.$

Now

at k=0, $z_0=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 0}{8}+i\sin \dfrac{0+2\pi \cdot 0}{8})=1\cdot (1+0\cdot i)=1;$

at k=1, $z_1=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 1}{8}+i\sin \dfrac{0+2\pi \cdot 1}{8})=1\cdot (\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};$

at k=2, $z_2=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 2}{8}+i\sin \dfrac{0+2\pi \cdot 2}{8})=1\cdot (0+1\cdot i)=i;$

at k=3, $z_3=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 3}{8}+i\sin \dfrac{0+2\pi \cdot 3}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2};$

at k=4, $z_4=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 4}{8}+i\sin \dfrac{0+2\pi \cdot 4}{8})=1\cdot (-1+0\cdot i)=-1;$

at k=5, $z_5=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 5}{8}+i\sin \dfrac{0+2\pi \cdot 5}{8})=1\cdot (-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=-\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};$

at k=6, $z_6=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 6}{8}+i\sin \dfrac{0+2\pi \cdot 6}{8})=1\cdot (0-1\cdot i)=-i;$

at k=7, $z_7=\sqrt[8]{1} (\cos\dfrac{0+2\pi \cdot 7}{8}+i\sin \dfrac{0+2\pi \cdot 7}{8})=1\cdot (\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2})=\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2};$

The 8th roots are

$\{1,\ \dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ i, -\dfrac{\sqrt{2}}{2}+i\dfrac{\sqrt{2}}{2},\ -1, -\dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2},\ -i,\ \dfrac{\sqrt{2}}{2}-i\dfrac{\sqrt{2}}{2}\}.$

Option C is icncorrect.

5 0

3 years ago

Fatima paid a $50. Initiation fee to join a gym. She also pays a fee of $25 per month. Write an expression that shows how much F

Morgarella [4.7K]

When it says per month, it means to multiply. In this case, the expression would be;

25x+50

So however many months Fatima has spent at the gym, you would multiply that times 25 and add the initiation fee. Hope this helps.

3 0

3 years ago

Solve for x 4(x-167)=48

bogdanovich [222]

Answer:

x=179

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Please help me #3 in the top and #1 and #2 in the bottom. I'm so confused

nikitadnepr [17]

Question 3
C(1, -7) D(-8, -7)
To find side length DC you count how many units are between the two points. C(1) D(-8) = 9 units

Question 1
Again count the points around the edge of the square. Since this shape is a rectangle, side length WX = YZ and side length XY = WZ.
WX = YZ = 11 units
XY = WZ = 15 units
Perimeter = WX + YZ + XY + WZ = 11(2) + 15(2) = 52 units

5 0

3 years ago