On average, 9.8 x 105 drivers visit

Ulleksa [173]

Answer:

D

Step-by-step explanation:

The perpendicular equation can be found by getting the reciprocal of the slope then multiplying it by -1. The slope is the "m" value of y=mx+b; in this case, the slope is $\frac{2}{5}$ .

To find out if it is C or D, you plug in the x value given in the equation (2) and see if it equals the y value given in the equation (-2). C is incorrect, which means that D is correct.

8 0

2 years ago

Read 2 more answers

Taylor wants to install new carpet in her living room. The room length is 15 ft and the width is 15 ft. If the cost of the carpe

irga5000 [103]

Answer:

$1,800.

Step-by-step explanation:

15 x 15 = 225

225 x 8 = 1800

Feel free to let me know if you need more help! :)

7 0

3 years ago

a goat tethered to a stake by a rope has grazed the meadow over an area of 12.56msqare around it stretching the rope. i) what is

Nikolay [14]

Answers:

length of rope = 2 meters

perimeter of meadow = 12.56 square meters

=========================================================

Explanation:

Assuming there are no structures (buildings, fences, etc) to get in the way of the goat, this means the goat's area that it can roam is a circle with radius r

The area of the circle is pi*r^2 which is equal to 12.56 square meters

pi*r^2 = 12.56

3.14*r^2 = 12.56

r^2 = 4

r = sqrt(4)

r = 2

The radius of the circle is 2 meters. This is the length of the rope. If the goat goes out as far as it can go, and tries to move left/right, then it will trace out a circle of radius 2. This is assuming the rope is kept fully taut the entire time.

The perimeter of the circle is the same as the circumference

circumference = 2*pi*r

circumference = 2*pi*2

circumference = 4*pi

circumference = 4*3.14

circumference = 12.56

The circumference and area are the same because r^2 = 4 and 2*r = 4 when r = 2. For any other positive r value, the area and circumference will be different values.

So in short, if a friend says that the area of a circle is the same as its perimeter, then you can immediately conclude the radius is 2.

Side note: throughout all of this solution, I used the approximation pi = 3.14 though pi has more decimal digits

7 0

3 years ago

Read 2 more answers

Just a quick question. Is 21 the right answer for y?

slava [35]

Answer:

I think it is right but not sure

7 0

3 years ago

kicyunya [14]

Answer:

8.69% probability that at least 285 rooms will be occupied.

Step-by-step explanation:

For each booked hotel room, there are only two possible outcomes. Either there is a cancelation, or there is not. So we use concepts of the binomial probability distribution to solve this question.

However, we are working with a big sample. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

In this problem, we have that:

A popular resort hotel has 300 rooms and is usually fully booked. This means that $n = 300$

About 7% of the time a reservation is canceled before the 6:00 p.m. deadline with no pen-alty. What is the probability that at least 285 rooms will be occupied?

Here a success is a reservation not being canceled. There is a 7% probability that a reservation is canceled, and a 100 - 7 = 93% probability that a reservation is not canceled, that is, a room is occupied. So we use $p = 0.93$