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3 years ago

Determine the distance between the points (-2,3) and (5,- 3).

1 answer:

5 0

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{-3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{[5-(-2)]^2+[-3-3]^2}\implies d=\sqrt{(5+2)^2+(-6)^2} \\\\\\ d=\sqrt{49+36}\implies d=\sqrt{85}\implies d \approx 9.22$

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One member of the Lockport High School will be chosen randomly for a trip over spring break. There are 900 students in the high

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It would be a 50% percent

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3 years ago

Each month, an American household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the standard d

Verdich [7]

Answer:

(a) Between 27 and 31 pounds per month = 0.62465

(b) More than 30.2 pounds per month = 0.1357

Step-by-step explanation:

We are given that each month, an American household generates an average of 28 pounds of newspaper for garbage or recycling. Assume the standard deviation is 2 pounds and the variable is approximately normally distributed.

Let X = generation of newspaper for garbage or recycling

The z-score probability distribution for normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = population average = 28 pounds

$\sigma$ = population standard deviation = 2 pounds

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

(a) Probability of household generating between 27 and 31 pounds per month is given by = P(27 pounds < X < 31 pounds) = P(X < 31 pounds) - P(X $\leq$ 27 pounds)

P(X < 31 pounds) = P( $\frac{X-\mu}{\sigma}$ < $\frac{31-28}{2}$ ) = P(Z < 1.50) = 0.93319

P(X $\leq$ 27 pounds) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{27-28}{2}$ ) = P(Z $\leq$ -0.50) = 1 - P(Z < 0.50)

= 1 - 0.69146 = 0.30854

{Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.50 and x = 0.50 in the z table which has an area of 0.93319 and 0.30854 respectively.}

Therefore, P(27 pounds < X < 31 pounds) = 0.93319 - 0.30854 = 0.62465

(b) Probability of household generating more than 30.2 pounds per month is given by = P(X > 30.2 pounds)

P(X > 30.2 pounds) = P( $\frac{X-\mu}{\sigma}$ > $\frac{30.2-28}{2}$ ) = P(Z > 1.10) = 1 - P(Z $\leq$ 1.10)

= 1 - 0.8643 = 0.1357

Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.10 in the z table which has an area of 0.8643.

3 0

4 years ago

Alexa borrows $10,000 from her aunt and they agree Alexa will pay her back including 5% simple interest. How much more will Alex

zavuch27 [327]

Answer:

46.73

Step-by-step explanation:

10000(5)75/)57)/83)’lsh “32=46.73

3 0

3 years ago

What is the equation of the line in standard form?

madam [21]

Answer:

x+6y=9 - > y= (-1/6)x+(3/2)

x - 6y=-9 - > y= (1/6)x+(3/2)

-9x - 6y = -9 - > y = (-3/2)x +(3/2)

3x - y = - 6 - > y= 3x + 6

-63x - y = - 6 - > y = - 63x + 6

3x + y = 6 - > y = -3x +6

Step-by-step explanation:

The standard form of the equation of a line is: y=ax+b

You seperate y from x and the constant value(the number) and then devide tge equation with the coefficient of y. Obviously it mustnt be division by zero.

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3 years ago

Leanne runs a lap in 12 minutes. Kory runs a lap in 9 minutes. If they

klemol [59]

Kory and Leanne will meet each other again after 36 minutes from starting i.e. at 10:36 am .

Step-by-step explanation:

Here we have , Leanne runs a lap in 12 minutes. Kory runs a lap in 9 minutes. We need to find out that If they both start running at 10 am, at what time will they both cross the start together again . Let's find out:

Kory runs a lap in 9 minutes and , Leanne in 12 minutes , in order to find at what time will they both cross the start together again we will find LCM of 9 & 12 :

⇒ $\frac{9(4)}{12(4)}$

⇒ $\frac{36}{36}$

So ,LCM of 9 & 12 is 36 .That means Kory and Leanne will meet each other again after 36 minutes from starting i.e. at 10:36 am .

In clear way , Kory will run race as :

1st lap = 9 minutes

2nd lap = 18 minutes

3rd lap = 27 minutes

4th lap = 36 minutes , i.e. at 10:36 am he'll complete his 4th lap

For , Leanne

1st lap = 12 minutes

2nd lap = 24 minutes

3rd lap = 36 minutes i.e. at 10:36 am he'll complete his 3rd lap .

This means Kory & Leanne will meet at 10:36 am completing there 4th and 3rd lap respectively .

6 0

4 years ago