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ycow [4]
3 years ago
7

Erica treated her sister to lunch while visiting her in Lowell. Their lunch cost $60, and the sales tax in Lowell is 5%. If Eric

a left a 20% tip on the $60, how much in total did she pay?
Mathematics
1 answer:
Mumz [18]3 years ago
5 0

Answer:

Erica payed a total of $75

Step-by-step explanation:

Step 1: Determine total lunch cost

Total lunch cost=$60

Step 2: Calculate total sales tax

Total sales tax=tax rate×total lunch cost

where;

tax rate=5%

total lunch cost=$60

replacing;

Total sales tax=(5/100)×60=$3

Total sales tax=$3

Step 3: Cost of tip

Cost of tip=20% of 60=(20/100)×60=$12

Step 4: Total she payed

Total she payed=Cost of tip+total sales tax+total lunch cost

where;

Cost of tip=$12

total sales tax=$3

total lunch cost=$60

replacing;

Total she payed=(12+3+60)=$75

Erica payed a total of $75

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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
4 years ago
What is the simplified version of <img src="https://tex.z-dn.net/?f=%282%5Csqrt%7B5%7D%2B3%29%28%5Csqrt%7B5%7D-1%29" id="TexForm
Tpy6a [65]

ANSWER

EXPLANATION

We want to simplify:

(2\sqrt{5}+3)(\sqrt{5}-1)

Recall the distributive property;

(a+b)(c+d)=a(c+d)+b(c+d)

We apply this property to get,

2\sqrt{5}(\sqrt{5}-1) + 3(\sqrt{5}-1)

We expand to get,

2 \times 5-2 \sqrt{5} + 3\sqrt{5}-3

This simplifies to,

10 + \sqrt{5}-3

The simplest form of the given expression is:

7 +  \sqrt{5}

7 0
4 years ago
How do you put this into a decimal equivalent<br><br> 8 4/9=
PSYCHO15rus [73]

Answer:

8.44444444444

Step-by-step explanation:

hope this helped

3 0
3 years ago
Read 2 more answers
The options for number two is
Blizzard [7]
The area of any quad = the base* height
for q 1:
the base=12 in
the height= 3 in
then the area = 12*3 = 36 sq in

for q 2:
the base= 14 in
the height = 4.5 in
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3 0
3 years ago
1) Complete the input-ouput table for the linear equation y = 4x + 2.
monitta

Answer:

5, 42, 15, 82

Step-by-step explanation:

y=4x+2

22=4x+2

20=4x

5=x

y=4(10)+2

y=40+2

y=42

62=4x+2

60=4x

15=x

y=4(20)+2

y=80+2

y=82

4 0
3 years ago
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