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lana66690 [7]
3 years ago
6

The price of a new car is $29,990. If the sales tax rate is 6.5%, then how much sales tax is being charged? What is the total co

st for the car including tax?
Mathematics
1 answer:
Zanzabum3 years ago
8 0
29990
10%=29990/10=2999
1%=2999/10=299.90
0.5%=299.90/2=149.95
6%=299.90x6=1799.40
6.5%=1799.50+149.95=$1949.35 tax

total +tax
29990+1949.35=$31395.35

hope this helps
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Find the complex fourth roots of 81(cos(3π/8)+isin(3π/8)). a) Find the fourth root of 81. b) Divide the angle in the problem by
WARRIOR [948]

Answer:

The answer is below

Step-by-step explanation:

Let a complex z = r(cos θ + isinθ), the nth root of the complex number is given as:

z_1=r^{\frac{1}{n} }(cos(\frac{\theta +2k\pi}{n} )+isin(\frac{\theta +2k\pi}{n} )),\\k=0,1,2,.\ .\ .,n-1

Given the complex number z = 81(cos(3π/8)+isin(3π/8)), the fourth root (i.e n = 4) is given as follows:

z_{k=0}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(0)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(0)\pi}{4} ))=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})] \\z_{k=0}=3[cos(\frac{3\pi}{32} )+isin(\frac{3\pi}{32})]\\\\z_{k=1}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(1)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(1)\pi}{4} ))=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})] \\z_{k=1}=3[cos(\frac{19\pi}{32} )+isin(\frac{19\pi}{32})]\\\\

z_{k=2}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(2)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(2)\pi}{4} ))=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})] \\z_{k=2}=3[cos(\frac{35\pi}{32} )+isin(\frac{35\pi}{32})]\\\\z_{k=3}=81^{\frac{1}{4} }(cos(\frac{\frac{3\pi}{8}  +2(3)\pi}{4} )+isin(\frac{\frac{3\pi}{8}  +2(3)\pi}{4} ))=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})] \\z_{k=3}=3[cos(\frac{51\pi}{32} )+isin(\frac{51\pi}{32})]

3 0
3 years ago
Solve for x and y<br> 7x - 3y =23<br>2x - 4y = -8<br>​
dybincka [34]

Q. 7x - 3y =23

Lets,   \: Find  \: x :-

7x - 3y = 23

7x - 3(0) = 23

x = 3.286

Now, Lets \:  find  \: y :-

7x - 3y = 23

7(0) - 3y = 23

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3 0
3 years ago
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Tony and Ricky spend a certain amount of money from their accounts each week at a pet shelter. The table shows the relationship
andriy [413]
<span>Function 1:

Number of Weeks (x)          Amount Remaining (dollars) (y)

1                                           30
2                                           24
3                                           18
4                                           12

You find the rate of weekley rate of change by calculating the difference of the amont remaing between two weeks:

24 - 30 = - 6

18 - 24  = - 6

12 - 18 = - 6

As you see the rate of change is constant: - 6 dollars per week. 


The equation shows the relationship between the amount of money, y, remaining in Ricky's account and the number of weeks, x:

Function 2: y = –7x + 30 Which statement states and explains which function shows a greater rate of change?

The rate of change is the slope of the linear function, and this is the coefficient of the independent variable, x. Then the rate of change is - 7 dollar per week. Now you know that the two rates are constant and that the second function shows a steeper decreasing.


</span>
7 0
3 years ago
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Alona [7]

Answer:

95% Confidence interval for the variance:

3.6511\leq \sigma^2\leq 34.5972

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Step-by-step explanation:

We have to calculate a 95% confidence interval for the standard deviation σ and the variance σ².

The sample, of size n=8, has a standard deviation of s=2.89 miles.

Then, the variance of the sample is

s^2=2.89^2=8.3521

The confidence interval for the variance is:

\dfrac{ (n - 1) s^2}{ \chi_{\alpha/2}^2} \leq \sigma^2 \leq \dfrac{ (n - 1) s^2}{\chi_{1-\alpha/2}^2}

The critical values for the Chi-square distribution for a 95% confidence (α=0.05) interval are:

\chi_{0.025}=1.6899\\\\\chi_{0.975}=16.0128

Then, the confidence interval can be calculated as:

\dfrac{ (8 - 1) 8.3521}{ 16.0128} \leq \sigma^2 \leq \dfrac{ (8 - 1) 8.3521}{1.6899}\\\\\\3.6511\leq \sigma^2\leq 34.5972

If we calculate the square root for each bound we will have the confidence interval for the standard deviation:

\sqrt{3.6511}\leq \sigma\leq \sqrt{34.5972}\\\\\\1.9108\leq \sigma \leq 5.8819

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fenix001 [56]

Answer:

D. 7%

Step-by-step explanation:

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