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3 years ago

Two-thirds of a number is equal to negative one-fifth. what is the number?

Mathematics

2 answers:

Nataly_w [17]3 years ago

8 0

-7 1/2 just because they said so

elena-s [515]3 years ago

3 0

Answer:

-7 1/2

Step-by-step explanation:

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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

A rectangular flower bed covers an area of 11.76 square feet in the garden. The width of the flower bed is 3.5 feet less than it

Degger [83]

The length and width of the garden will be obtain as follows:
let the length be x ft, the width will be (x+3.5)ft
area of the bed will be:
A=length*width
11.76=x(x+3.5)
11.76=x^2+3.5x
thus
x^2+3.5x-11.76=0
solving this by quadratic formula we get:
x=[-b+/-sqrt(b^2-4ac)]/2a
thus plugging in the values we obtain
x=[-3.5+/-sqrt(3.5^2-4(-11.76*1))]/2
x=[-3.5+/-sqrt59.29]/2
x=[-3.5+/-7.7]/2
x=4.2 or -11.2
thus the length will be x=4.2 ft and the width will be x-3.5=0.7 ft

8 0

3 years ago

Plz help u have to do all 3 parts

Jobisdone [24]

Answer:

all you have too do is 750*750 = 562,500

Step-by-step explanation:

i hope this helps and pleas give me a stare and a heart thank you so much if you do and if you do not still thank you

7 0

2 years ago

According to the Empirical Rule, what percentage of a normal population falls between 1 standard deviations left of the mean and

svlad2 [7]

Answer:

68% of the data falls within one standard deviation, 95% percent within two standard deviations, and 99.7% within three standard deviations from the mean.

Step-by-step explanation:

6 0

2 years ago

In Las Vegas, Nevada, stores charge a 4.6% state sales tax and a 3.65% county sales tax. Yuki is purchasing a handbag priced at

Vitek1552 [10]

Yuki pays tax at a rate 4.6% + 3.65% = 8.25%

The total tax on the handbag is

.0825 (220) = $18.15

5 0

3 years ago

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Two-thirds of a number is equal to negative one-fifth. what is the number?​

Two-thirds of a number is equal to negative one-fifth. what is the number?