the points A (1, 5), B (5, 5) and C (5, 1) are 3 corners of a square ABCD. what are the coordinates of D, the 4th corner

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

Tanzania [10]

Answer:

Approximately, 159 men weighs more than 165 pounds and 159 men weighs less than 135 pounds.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 150 pounds

Standard Deviation, σ = 15

We are given that the distribution of weights of 1000 men is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P( men weighing more than 165 pounds)

P(x > 165)

$P( x > 165) = P( z > \displaystyle\frac{165 - 150}{15}) = P(z > 1)$

$= 1 - P(z \leq 1)$

Calculation the value from standard normal z table, we have,

$P(x > 165) = 1 - 0.8413 = 0.1587 = 15.87\%$

Approximately, 159 men weighs more than 165 pounds.

P(men weighing less than 135 pounds)

P(x < 135)

$P( x < 135) = P( z < \displaystyle\frac{135 - 150}{15}) = P(z < -1)$

Calculation the value from standard normal z table, we have,

$P(x < 135) = 0.1587 = 15.87\%$

Approximately, 159 men weighs less than 135 pounds.

6 0

2 years ago

Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and Pedro make it to their first pe

muminat

Answer:

15.25% probability that Napoleon and Pedro catch the bus and make it to their first period class on time

Step-by-step explanation:

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this problem, we have that:

Event A: Both Napoleon and Pedro catch the bus, so P(A) = 0.25.

Event B: Making to their first period class on time.

However, the probability that they make it to their first period class on time, given that they catch the bus is 0.61.

This means that $P(B|A) = 0.61$

What is the probability that Napoleon and Pedro catch the bus and make it to their first period class on time

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

$0.61 = \frac{P(A \cap B)}{0.25}$

$P(A \cap B) = 0.61*0.25$

$P(A \cap B) = 0.1525$

15.25% probability that Napoleon and Pedro catch the bus and make it to their first period class on time

8 0

2 years ago

(a) Find a vector-parametric equation r⃗ 1(t)=⟨x(t),y(t),z(t)⟩r→1(t)=⟨x(t),y(t),z(t)⟩ for the shadow of the circular cylinder x2

motikmotik

Answer: (a) r1(t) = <2cost , 0 , 2sint>

(b) <2cost , (1 - 12sint - 10cost)/8 , 2sint>

Step-by-step explanation:

x2+z2=4

a)

Now, in the xz plane, we know that y = 0...

So, x^2 + z^2 = 4 will simply be a circle centered at (0,0)..

This can be easily parameterized as

x = 2cos(t)

z = 2sin(t)

So, the required parameterization is :

r1(t) = <2cost , 0 , 2sint>

b)

Cylinder : x^2 + z^2 = 4

Plane : 5x+8y+6z=1

Easily enough, the x^2 + z^2 = 4 can again be parameterized as

x = 2cost , z = 2sint

With this, we can find y using plane equation...

5x+8y+6z=1

5(2cost) + 8y + 6(2sint) = 1

8y = 1 - 12sint - 10cost

y = (1 - 12sint - 10cost)/8

So, the parameterization is :

<2cost , (1 - 12sint - 10cost)/8 , 2sint>

6 0

2 years ago

For each of the questions below, a histogram is described. Indicate in each case whether, in view of the Central Limit Theorem,

denis-greek [22]

Solution :

a). This histogram is not a bell shaped.

Here we cannot use the theorem of the central limit as the histogram is being plotted by using 365 samples data values of the one sample.

b). This histogram may be bell shaped approximately since the sample size is large.

Here there are 50 sample each having a size of 500 and there is 50 sample proportions. The histogram shows sampling distribution of the sample proportion. Thus the central limit theorem can be used.

The histogram is approximately bell shaped as there is 50 samples of each having 500 size and an average of 50. Thus the central limit theorem can be used.

c). The histogram is not a bell shaped.

In this case central limit theorem cannot be used as the histogram is plotted by using 100 sample data values of one sample.

d). The histogram is a bell shaped since the sample size is large.

In this case 200 samples of each having a size of 50 and a data values of 50. The histogram here shows a sampling distribution of the sample proportion. Thus the central limit theorem can be used.

In the second also the histogram is of bell shaped as the sample size is large.

There are 200 samples of each sample having a size of 40 and they have 40 data values , i.e. sum of rolls.

e). It is not a bell shaped.

The histogram here is plotted using 100 sample data values having one sample. Therefore we cannot use the central limit theorem.

6 0

1 year ago

Tiana has already taken 1 page of notes on her own, and she will take 1 page during each hour of class. In all, how many hours w

Novosadov [1.4K]

Answer:

<u>42 Hours.</u>

Step-by-step explanation:

As an equation where y is the total pages and x is hours of class:

y=1+1x since she started with 1 page and does 1 page per hour.

Setting the total pages she needs as 43 (y=43) we get:

43=1+1x

Subtract one on both sides

42=1x

The 1 doesn't need to be written so

x=42

Therefore, it'll take her 42 hours to write all those notes.

4 0

2 years ago