Which is a better deal: A tool that costs $13.99 with 7% tax or the same tool that costs $14.03 with 6.5% tax

InWrite the equation of the line that passes through (7, - 4) and (- 1, 2) slope- intercept form.

blondinia [14]

Answer:

General Equation of a Line

$General Equation \\(y - y_{1} )= m (x-x_{1}) \\Slope=m= \frac{x_{2}-x_{1} }{y_{2}-y_{1} } \\\\Given:\\p_{1}=(7,-4)\\p_{2}=(-1,2)\\Solution:\\m=(\frac{-1-7}{2-(-4)}) =\frac{-8}{6}\\y-(-4) = (\frac{-8}{6} )(x-7)\\y+4=\frac{-8x}{6} + 56\\y=\frac{-8x}{6} + 52 \\\\The\\ equation \\ is \\ y=\frac{-8x}{6} + 52$

Step-by-step explanation:

Find the slope first and then place the values on the general formula. The final step is to solve for y

5 0

2 years ago

When you solve a problem involving money what can a negative answer represent?

kati45 [8]

A negative balance of money could represent debt or money owed.

4 0

3 years ago

A coach travels to the beach which is 576 KM away in 6 hours. If he is only allowed to travel at a maximum speed of 90 kph, did

Whitepunk [10]

Answer:

Yes

Step-by-step explanation:

576Km:6Hrs

576 divided by 6=96 km

6 divided by 6=1

96km:1hr

96 was the coaches speed limit

km=Kilometers

Hrs=Hours

96>90

6 0

2 years ago

Find the mean, variance &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

A rental car agency charges $30.00 per day

lutik1710 [3]

<h2>Answer:</h2><h2>They should travel 120 mils in one day for both rental agencies to cost the same amount to rent</h2>

Step-by-step explanation:

A rental car agency charges $30.00 per day plus per mile $0.15.

Let x be the number of miles travelled by car

Their total cost = 30 + (0.15x) ... (1)

Another rental car agency charges $36.00 per day plus $0.10 per mile

Their total cost = 36 + (0.10x) ... (2)

Equating (1) and (2), we get

30 + (0.15x) = 36 + (0.10x)

36 - 30 = 0.15x - 0.10x

6 = 0.05x

x = 120 miles

They should travel 120 mils in one day for both rental agencies to cost the same amount to rent

5 0

2 years ago