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3 years ago

What is the length of the hypotenuse in a right triangle if the legs are 50 and 120

Mathematics

1 answer:

miv72 [106K]3 years ago

5 0

Good evening

Answer:

Step-by-step explanation:

let L represent the length of the hypotenuse :

Since we are in a right triangle case then the Pyth theorem is a valid choice to solve the problem :

the Pythagoren theorem states that :

L² = 50^2+120^2

then

L² = 16 900

then

L = √(16 900)

=130

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The delivery person weighs 150lb and each box of books weigh 40lb the maximum capacity of the elevator is 1020lb how many box of

padilas [110]

Answer:

21 box of books can be brought up by the delivery person at one time

Step-by-step explanation:

Here, we want to know the number of box of books that the delivery person could bring up at one time.

Let the number of boxes be x , so the total mass of the boxes that could come up at a time will be x * 40 = 40x lb

Let’s add this to the mass of the delivery person = 150 lb

So the total mass going inside the lift would be 150 + 40x

So we have to equate this to the maximum capacity of the lift;

150 + 40x = 1020

40x = 1020 - 150

40x = 870

x = 870/40

x = 21.75

Now since we cannot have fractional boxes, the number of boxes that could come into the lift without exceeding the maximum capacity of the lift is 21

5 0

3 years ago

A pair of perpendicular lines intersect at the point (5,9). Write

maw [93]

Answer:

The equation of the line that is perpendicular to the line that passes through the point (-4, 2) is y = -9·x/5 + 18

Step-by-step explanation:

The coordinates of the point of intersection of the two lines = (5, 9)

The coordinates of a point on one of the two lines, line 1 = (-4, 4)

The slope of a line perpendicular to another line with slope, m = -1/m

Therefore, we have;

The slope, m₁, of the line 1 with the known point = (9 - 4)/(5 - (-4)) = 5/9

Therefore, the slope, m₂, of the line 2 perpendicular to the line that passes through the point (-4, 4) = -9/5

The equation of the line 2 is given as follows;

y - 9 = -9/5×(x - 5)

y - 9 = -9·x/5 + 9

y = -9·x/5 + 9 + 9

y = -9·x/5 + 18

Therefore, the equation of the line that is perpendicular to the line that passes through the point (-4, 2) is y = -9·x/5 + 18.

6 0

2 years ago

Jill’s bowling scores are approximately normally distributed with mean 170 and standard deviation 20, while Jack’s scores are ap

miss Akunina [59]

Answer:

a) The probability of Jack scoring higher is 0.3446

b) They probability of them scoring above 350 is 0.2119

Step-by-step explanation:

Lets call X the random variable that determines Jill's bowling score and Y the random variable that determines jack's. We have

$X \simeq N(170,400)\\Y \simeq N(160,225)$

Note that we are considering the variance on the second entry, the square of the standard deviation.

If we have two independent Normal distributed random variables, then their sum is also normally distributed. If fact, we have this formulas:

$N(\lambda_1, \sigma^2_1) + N(\lambda_2, \sigma^2_2) = N(\lambda_1 + \lambda_2,\sigma^2_1 + \sigma^2_2) \\r* N(\lambda_1, \sigma^2_1) = N(r\lambda_1,r^2\sigma^2_1)$

for independent distributions $N(\lambda_1, \sigma^2_1)$ , $N(\lambda_2, \sigma^2_2)$ , and a real number r.

a) We define Z to be Y-X. We want to know the probability of Z being greater than 0. We have

$Z = Y-X = N(160,225) - N(170,400) = N(160,225) + (N(-170,(-1)^2 * 400) = N(-10,625)$

So Z is a normal random variable with mean equal to -10 and vriance equal to 625. The standard deviation of Z is √625 = 25.

Lets work with the standarization of Z, which we will call W. $W = (Z-\mu)/\sigma$ = (Z+10)/25. W has Normal distribution with mean 0 and standard deviation 1. We have

P(Z > 0) = P( (Z+10)/25 > (0+10)/25) = P(W > 0.4)

To calculate that, we will use the <em>known </em>values of the cummulative distribution function Φ of the standard normal distribution. For a real number k, P(W < k) = Φ(k). You can find those values in the Pdf I appended below.

Since Φ is a cummulative distribution function, we have P(W > 0.4) = 1- Φ(0.4)

That value of Φ(0.4) can be obtained by looking at the table, it is 0.6554. Therefore P(W > 0.4) = 1-0.6554 = 0.3446

As a result, The probability of Jack's score being higher is 0.3446. As you may expect, since Jack is expected to score less that Jill, the probability of him scoring higher is lesser than 0.5.

b) Now we define Z to be X+Y Since X and Y are independent Normal variables with mean 160 and 170 respectively, then Z has mean 330. And the variance of Z is equal to the sum of the variances of X and Y, that is, 625. Hence Z is Normally distributed with mean 330 and standard deviation rqual to 25 (the square root of 625).

We want to know the probability of Z being greater that 350, for that we standarized Z. We call W the standarization. W is s standard normal distributed random variable, and it is obtained from Z by removing its mean 330 and dividing by its standard deviation 25.

P(Z > 350) = P((Z - 330)/25 > (350-330)/25) = P(W > 0.8) = 1-Φ(0.8)

The last equality comes from the fact that Φ is a cummulative distribution function. The value of Φ(0.8) by looking at the table is 0.7881, therefore P(X+Y > 350) = 1 - Φ(0.8) = 0.2119.

As you may expect, this probability is pretty low because the mean value of the sum of their combined scores is quite below 350.

I hope this works for you!

Download pdf

6 0

3 years ago

Need ASAP answer because I don’t not understand

dimaraw [331]

Hello there! The correct answer is B.

Note that in functions, x values cannot repeat. The points are given as (x, y) values, and you can see in the second option there are two -7s in the x values, making it not a function!

<em>I hope this was helpful, have a great rest of your day! If you need further help with this question, let me know!</em>

6 0

3 years ago

Read 2 more answers

If the standard deviation of a set of data is zero, what can you conclude about the set of values? The sum of the deviations fro

Rashid [163]

Answer:

All values are identical.

Step-by-step explanation:

We are given the following in the question:

If the standard deviation of a set of data is zero.

Then, all the values in data are identical.