6 months ago, Juan used his credit card for a transaction of 128 dollars. The bank charges a rate of interest

The distribution of waist circumferences of US adult men randomly selected for a research study was approximately normal with me

kow [346]

Answer: 99cm

Step-by-step explanation:

5 0

2 years ago

Let X denote the temperature (degree C) and let Y denote thetime in minutes that it takes for the diesel engine on anautomobile

BlackZzzverrR [31]

Answer:

Step-by-step explanation:

Given $f_{XY} (x,y) = c(4x + 2y +1) ; 0 < x < 40\,and\, 0 < y$

a)

we know that $\int\limits^\infty_{-\infty}\int\limits^\infty_{-\infty} {f(x,y)} \, dxdy=1$

therefore $\int\limits^{40}_{-0}\int\limits^2_{0} {c(4x+2y+1)} \, dxdy=1$

on integrating we get

c=(1/6640)

b)

$P(X>20, Y>=1)=\int\limits^{40}_{20}\int\limits^2_{1} {\frca{1}{6640}(4x+2y+1)} \, dxdy$

on doing the integration we get

=0.37349

c)

marginal density of X is

$f(x)=\int\limits^2_{0} {\frca{1}{6640}(4x+2y+1)} \, dy$

on doing integration we get

f(x)=(4x+3)/3320 ; 0<x<40

marginal density of Y is

$f(y)=\int\limits^{40}_{0} {\frca{1}{6640}(4x+2y+1)} \, dx$

on doing integration we get

$f(y)=\frac{(y+40.5)}{83}$

d)

$P(01)=\int\limits^{40}_{0}\int\limits^2_{1} {\frca{1}{6640}(4x+2y+1)} \, dxdy$

solve the above integration we get the answer

e)

$P(X>20, 0$

solve the above integration we get the answer

f)

Two variables are said to be independent if there jointprobability density function is equal to the product of theirmarginal density functions.

we know f(x,y)

In the (c) bit we got f(x) and f(y)

f(x,y)cramster-equation-2006112927536330036287f(x).f(y)

therefore X and Y are not independent

4 0

2 years ago

A 96-ft high transmission tower casts a 72-ft long shadow. An anchor wire runs from the top of the tower to the tip of the shado

galben [10]

See attached picture and check solution below.
We are given with the following values:
A = length of transmission line = 96ft
B = length of shadow = 72 feet
C = distance of ladder to base of transmission line = 66 feet

Solve for angle created between the wire and tip of the shadow:
tan x = opposite/ adjacent
tan x = 96 feet / 72 feet
x = 53.13°

Solving for the height of the ladder:
tan x = Ladder length / (72-66)
tan 53.13° * (72-66) = ladder length
ladder length = 8 feet

The answer is letter "B" which is 8 feet.

5 0

2 years ago

In 2010, Rafik bought a house. In 2015, Rafik sold the house to Bianca. He made a 20% profit on the sale. In 2019, Bianca sold t

sweet [91]

Answer:

£170000

Step-by-step explanation:

In 2010, Rafik bought a house. Let us assume Rafik bought the house for $x. In 2015, Rafik sold the house to Bianca and made 20% profit. 20% profit = 20% of x = 0.2 × x = 0.2x. Therefore Rafik sold the house to Bianca at x + 0.2x = 1.2x. Bianca bought the house at 1.2x

The house was sold by Bianca at 5% loss in 2019. 5% loss = 0.05(1.2x) = 0.06x

Therefore the house was sold by Bianca at 1.2x - 0.06x = 1.14x. Since Bianca sold the house at £193800.

⇒ 1.14x = 193800

x = 193800/1.14

x = £170000

Rafik paid £170000 for the house in 2010

7 0

2 years ago

What is the equation of the line that passes through the points (-3,2) and (-5,8)

Debora [2.8K]

<h2>Greetings!</h2>

Answer:

The answer is a. 3x - y = -11

Step-by-step explanation:

Firstly, you must find the gradient. This is found using the following formula:

$\frac{y2 - y1}{x2 - x1}$

Make sure that the x2 and y2 values are in the same coordinate set:

Let's set (-3 , 2) as y1 and x1,

y1 = 2 and x1 = -3

That means that (-5 , 8) is y2 and x2,

y2 = 8 and x2 = -5

Plug the values in:

$\frac{8 - 2}{-5 - - 3}$

Simplified:

$\frac{6}{2}$

Or 3

So the gradient (or slope) is 3

Now, using the following equation of a line formula:

y - y1 = m(x - x1)

Where m is the gradient and y1 and x1 are two coordinates, we can plug these values in:

y1 = 2

x1 = -3

m = 3

y - 2 = 3(x - - 3)

The negative and the subtract makes it a positive:

y - 2 = 3(x + 3)

Now we can multiply the bracket out:

3 * x = 3x

3 * 3 = 9

So:

y - 2 = 3x + 9

The equation is usually in the form:

y = mx + c

So we need to move the -2 over to the other side making it a positive 2:

y = 3x + 9 + 2

y = 3x + 11

Which is the equation of the line.

The one option that this rearranges to is a) because if you move the y over to the 3x, and the + 11 over to the other side, making them both negatives, the result is:

3x - y = -11

So your answer is a.

<h2>Hope this helps!</h2>

4 0

1 year ago