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3 years ago

14

Kayla won 47 super bouncy balls playing hoops at her school's game night. Later, she gave two to each of her friends. She only h

as 7 remaining. How many friends does she have? Write an equation and then solve.

1 answer:

PIT_PIT [208]3 years ago

4 0

Answer: 20 friends

Step-by-step explanation:

47 - 7 = 40

40 ÷ 2 = 20

Just to double check, 2 x 20 = 40 + 7 balls left over = 47

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4. Using the geometric sum formulas, evaluate each of the following sums and express your answer in Cartesian form.

nikitadnepr [17]

Answer:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=1$

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=0$

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})=\frac{1}{2}$

Step-by-step explanation:

$\sum_{n=0}^9cos(\frac{\pi n}{2})=\frac{1}{2}(\sum_{n=0}^9 (e^{\frac{i\pi n}{2}}+ e^{\frac{i\pi n}{2}}))$

$=\frac{1}{2}(\frac{1-e^{\frac{10i\pi}{2}}}{1-e^{\frac{i\pi}{2}}}+\frac{1-e^{-\frac{10i\pi}{2}}}{1-e^{-\frac{i\pi}{2}}})$

$=\frac{1}{2}(\frac{1+1}{1-i}+\frac{1+1}{1+i})=1$

2nd

$\sum_{k=0}^{N-1}e^{\frac{i2\pi kk}{2}}=\frac{1-e^{\frac{i2\pi N}{N}}}{1-e^{\frac{i2\pi}{N}}}$

$=\frac{1-1}{1-e^{\frac{i2\pi}{N}}}=0$

3th

$\sum_{n=0}^\infty (\frac{1}{2})^n cos(\frac{\pi n}{2})==\frac{1}{2}(\sum_{n=0}^\infty ((\frac{e^{\frac{i\pi n}{2}}}{2})^n+ (\frac{e^{-\frac{i\pi n}{2}}}{2})^n))$

$=\frac{1}{2}(\frac{1-0}{1-i}+\frac{1-0}{1+i})=\frac{1}{2}$

What we use?

We use that

$e^{i\pi n}=cos(\pi n)+i sin(\pi n)$

and

$\sum_{n=0}^k r^k=\frac{1-r^{k+1}}{1-r}$

6 0

3 years ago

Three brothers, Andy, Bob, and Curly, take a taxi together home from the

MrRa [10]

Answer:

See explanation

Step-by-step explanation:

not sure what class this is for but I\ll try. Each traveller has a 21 km drive so their fare should be equal.

method 1) each traveller can pay for 21 km worth when they get out

method 2) Curly can pay the full fare and Andy and Bob can pay him back later (they're brothers so this should be easy to manage)

5 0

3 years ago

A 1:35 scale model of a fishing hut is 17 cm tall, 18 cm wide, and 19.7 cm long. What are the dimensions of the actual ice fishi

konstantin123 [22]

Multiply each dimension by 35:-

17*35 = 595 cm

18*35 = 630 cm

19.7 * 35 = 689.5 cm

in meters the dimensions are L = 6.895 m, W = 6.3 m and H = 5.95 m

6 0

3 years ago

In art class, Arthur has created a triangle painting 1/5 of his painting is purple. He decided he wants to Paint 4/8 of the purp

babymother [125]

$\frac{1}{10}$ part of the whole painting is gold colored.

<u>Solution:</u>

Given that , In art class, Arthur has created a triangle painting $\frac{1}{5}$ of his painting is purple.

He decided he wants to Paint $\frac{4}{8}$ of the purple area gold

We have to find what fraction of the whole painting will be painting?

Now, $\frac{1}{5}$ part of whole painting is purple

And, $\frac{4}{8}$ part of the purple area is gold ⇒ $\frac{4}{8}$ part of the $\frac{1}{5}$ part of whole painting is gold

$\text { Then, fraction of gold color }=\frac{4}{8} \times \frac{1}{5}=\frac{1}{2} \times \frac{1}{5}=\frac{1}{10}$

Hence, $\frac{1}{10}$ part of the whole painting is gold colored.

4 0

3 years ago

Can someone please help me with #12?

Genrish500 [490]

4x+12=90

4x=90-12

4x=8

x=8/4

x=2

5 0

3 years ago