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liberstina [14]
3 years ago
7

Original price is $29.99 markdown 33 1/3%

Mathematics
2 answers:
Serga [27]3 years ago
4 0
equation:  \\ 29.99*.67=x \\ answer: 20.09
nikklg [1K]3 years ago
3 0

The <em><u>correct answer</u></em> is:

$19.99.

Explanation:

33 1/3% is equal to taking 1/3 of a number. To take 1/3 of a number, we multiply by 1/3:

29.99(1/3) = 29.99/3 = 9.9966666667 ≈ $10

This means the price is marked down by $10. This makes the new price 29.99-10 = 19.99

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Find the mean, variance &amp;a standard deviation of the binomial distribution with the given values of n and p.
MrMuchimi
A random variable following a binomial distribution over n trials with success probability p has PMF

f_X(x)=\dbinom nxp^x(1-p)^{n-x}

Because it's a proper probability distribution, you know that the sum of all the probabilities over the distribution's support must be 1, i.e.

\displaystyle\sum_xf_X(x)=\sum_{x=0}^n\binom nxp^x(1-p)^{n-x}=1

The mean is given by the expected value of the distribution,

\mathbb E(X)=\displaystyle\sum_xf_X(x)=\sum_{x=0}^nx\binom nxp^x(1-p)^{n-x}
\mathbb E(X)=\displaystyle\sum_{x=1}^nx\frac{n!}{x!(n-x)!}p^x(1-p)^{n-x}
\mathbb E(X)=\displaystyle\sum_{x=1}^n\frac{n!}{(x-1)!(n-x)!}p^x(1-p)^{n-x}
\mathbb E(X)=\displaystyle np\sum_{x=1}^n\frac{(n-1)!}{(x-1)!((n-1)-(x-1))!}p^{x-1}(1-p)^{(n-1)-(x-1)}
\mathbb E(X)=\displaystyle np\sum_{x=0}^n\frac{(n-1)!}{x!((n-1)-x)!}p^x(1-p)^{(n-1)-x}
\mathbb E(X)=\displaystyle np\sum_{x=0}^n\binom{n-1}xp^x(1-p)^{(n-1)-x}
\mathbb E(X)=\displaystyle np\sum_{x=0}^{n-1}\binom{n-1}xp^x(1-p)^{(n-1)-x}

The remaining sum has a summand which is the PMF of yet another binomial distribution with n-1 trials and the same success probability, so the sum is 1 and you're left with

\mathbb E(x)=np=126\times0.27=34.02

You can similarly derive the variance by computing \mathbb V(X)=\mathbb E(X^2)-\mathbb E(X)^2, but I'll leave that as an exercise for you. You would find that \mathbb V(X)=np(1-p), so the variance here would be

\mathbb V(X)=125\times0.27\times0.73=24.8346

The standard deviation is just the square root of the variance, which is

\sqrt{\mathbb V(X)}=\sqrt{24.3846}\approx4.9834
7 0
3 years ago
Each term of the first polynomial is ____________ to each term in the second polynomial
Georgia [21]

9514 1404 393

Answer:

  • multiplied
  • like terms

Step-by-step explanation:

To multiply two polynomials, each term of the first polynomial is <u>multiplied</u> to each term in the second polynomial. Combine any <u>like terms</u> to simplify.

3 0
2 years ago
Gertrude takes out a $5,500 subsidized stafford loan, which must be paid back in ten years. gertrude will graduate four years af
Leno4ka [110]

The total amount of interest will Gertrude pay by the time the subsidized Stafford loan is repaid is $2094.80.

<h3>What is compound interest?</h3>

Compound interest is the amount charged on the principal amount and the accumulated interest with a fixed rate of interest for a time period.

The formula for the final amount with the compound interest formula can be given as,

A=P\times\left(1+\dfrac{r}{n\times100}\right)^{nt}\\

Here, A is the final amount (principal plus interest amount) on the principal amount P of with the rate<em> r </em>of in the time period of <em>t.</em>

Gertrude will graduate four years after taking out the loan. if the loan has an interest rate of 6.8%, compounded monthly, and Gertrude makes monthly payments.

Put the values in the above formula as,

5500=P_{mt}\times\left(1-\dfrac{6.8}{12\times100}\right)^{-12\times10}\\P_{mt}=63.29

In the 10 years, the refund she gets,

A_r=63.29\times12\times100\\A_r=7594.8

Interest paid by her is,

I=7594.8-5500\\I=2094.8

Thus, the total amount of interest will Gertrude pay by the time the subsidized Stafford loan is repaid is $2094.80.

Learn more about the compound interest here;

brainly.com/question/24274034

3 0
2 years ago
The circle passes through the point (-4,-1). What is its radius?
liubo4ka [24]

Answer:

c is the correct answer for this question

Step-by-step explanation:

c is the correct answer for this question

А

1.5

2.5

© 2

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Hope this helps.

4 0
3 years ago
What is the domain of the function f(x) =x+1/<br> X^2-6x+8?
SpyIntel [72]

Answer:

The domain of the function is all real values of x, except x = 4 and x = 2

Step-by-step explanation:

We are given the following function:

f(x) = \frac{x+1}{x^2-6x+8}

It's a fraction, so the domain is all the real values except those in which the denominator is 0.

Denominator:

Quadratic equation with a = 1, b = -6, c = 8

Using bhaskara, the denominator is 0 for these following values of x:

\Delta = (-6)^2 - 4(1)(8) = 36-32 = 4

x_{1} = \frac{-(-6) + \sqrt{4}}{2} = 4

x_{2} = \frac{-(-6) - \sqrt{4}}{2} = 2

The domain of the function is all real values of x, except x = 4 and x = 2

8 0
3 years ago
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