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Setler79 [48]
2 years ago
5

Round 36.319 to the nearest tenth

Mathematics
2 answers:
frozen [14]2 years ago
4 0
The answer is 36.
Explanation
vampirchik [111]2 years ago
3 0
36.3 because the digit in the hundredths place is not 5 or greater
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Each day, X arrives at point A between 8:00 and 9:00 a.m., his times of arrival being uniformly distributed. Y arrives independe
astraxan [27]

Answer:

Y will arrive earlier than X one fourth of times.

Step-by-step explanation:

To solve this, we might notice that given that both events are independent of each other, the joint probability density function is the product of X and Y's probability density functions. For an uniformly distributed density function, we have that:

f_X(x) = \frac{1}{L}

Where L stands for the length of the interval over which the variable is distributed.

Now, as  X is distributed over a 1 hour interval, and Y is distributed over a 0.5 hour interval, we have:

f_X(x) = 1\\\\f_Y(y)=2.

Now, the probability of an event is equal to the integral of the density probability function:

\iint_A f_{X,Y} (x,y) dx\, dy

Where A is the in which the event happens, in this case, the region in which Y<X (Y arrives before X)

It's useful to draw a diagram here, I have attached one in which you can see the integration region.

You can see there a box, that represents all possible outcomes for Y and X. There's a diagonal coming from the box's upper right corner, that diagonal represents the cases in which both X and Y arrive at the same time, under that line we have that Y arrives before X, that is our integration region.

Let's set up the integration:

\iint_A f_{X,Y} (x,y) dx\, dy\\\\\iint_A f_{X} (x) \, f_{Y} (y) dx\, dy\\\\2 \iint_A  dx\, dy

We have used here both the independence of the events and the uniformity of distributions, we take the 2 out because it's just a constant and now we just need to integrate. But the function we are integrating is just a 1! So we can take the integral as just the area of the integration region. From the diagram we can see that the region is a triangle of height 0.5 and base 0.5. thus the integral becomes:

2 \iint_A  dx\, dy= 2 \times \frac{0.5 \times 0.5 }{2} \\\\2 \iint_A  dx\, dy= \frac{1}{4}

That means that one in four times Y will arrive earlier than X. This result can also be seen clearly on the diagram, where we can see that the triangle is a fourth of the rectangle.

6 0
3 years ago
X and y are in direct proportion, when x is 8, y is 12. Which of the following is not a
Nat2105 [25]

Answer:

d.

Step-by-step explanation:

if x varies directly as y,

x = ky

8 = 12k

12k = 8

k = 8/ 12

k = 2/3,

x = 2/3 y

now substitute the value of any of the numbers of each pair, and check if it works:

for e.g, find x when y = 15

x = 2/3y

x = 2/3 × 15

x = 10

since you obtain x = 10 when y = 15, the pair is a possible corresponding value of x and y. now do the same for the rest .

ii) x = 2/3y

x = 2/3 × 3, when y = 3

x = 2

hence, this is also a possible pair of x and y values.

iii) x = 2/3y

x = 2/3 × 9 when y = 9

x = 6

again, a possible pair of x and y values.

iv) x = 2/3y

x = 2/3 × 20 when y = 20

x = 40/3

here, when y = 20, x is not 15. it is 40/3.

thus, it can be determined that this is not a possible pair of x and y values.

please try to understand and have a great day!

8 0
2 years ago
The radii of earth and Pluto are 6,371 kilometers and 1,161 kilometers, respectively. Approximately how many spheres the size of
SCORPION-xisa [38]
Earth volume: (3/4).π.(6371)³ = 1,0832x10¹² km³

Pluto volume: (3/4).π.(1171)³ = 6,555,189,765 km³

How many spheres the size of Pluto does it take to have the same volume as earth?

volume Earth/ volume Pluto = 1,0832x10¹² / 6,555,189,765 = 165.25
3 0
3 years ago
Read 2 more answers
Hiiii.. please help me with this limit question ​
Alenkasestr [34]

Answer:

π

Step-by-step explanation:

Solving without L'Hopital's rule:

lim(x→0) sin(π cos²x) / x²

Use Pythagorean identity:

lim(x→0) sin(π (1 − sin²x)) / x²

lim(x→0) sin(π − π sin²x) / x²

Use angle difference formula:

lim(x→0) [ sin(π) cos(-π sin²x) − cos(π) sin(-π sin²x) ] / x²

lim(x→0) -sin(-π sin²x) / x²

Use angle reflection formula:

lim(x→0) sin(π sin²x) / x²

Now we multiply by π sin²x / π sin²x.

lim(x→0) [ sin(π sin²x) / x² ] (π sin²x / π sin²x)

lim(x→0) [ sin(π sin²x) / π sin²x] (π sin²x / x²)

lim(x→0) [ sin(π sin²x) / π sin²x] lim(x→0) (π sin²x / x²)

π lim(x→0) [ sin(π sin²x) / π sin²x] [lim(x→0) (sin x / x)]²

Use identity lim(u→0) (sin u / u) = 1.

π (1) (1)²

π

Solving with L'Hopital's rule:

If we plug in x = 0, the limit evaluates to 0/0.  So using L'Hopital's rule:

lim(x→0) [ cos(π cos²x) (-2π cos x sin x) ] / 2x

lim(x→0) [ -π cos(π cos²x) sin(2x) ] / 2x

-π/2 lim(x→0) [ cos(π cos²x) sin(2x) ] / x

Again, the limit evaluates to 0/0.  So using L'Hopital's rule one more time:

-π/2 lim(x→0) [ cos(π cos²x) (2 cos(2x)) + (-sin(π cos²x) (-2π cos x sin x)) sin(2x) ] / 1

-π/2 lim(x→0) [ 2 cos(π cos²x) cos(2x) + π sin(π cos²x) sin²(2x) ]

-π/2 (-2)

π

8 0
2 years ago
Can I get an answer?
Reil [10]

coordinate of B= (2+3,0) = (5,0)

by pythagoras' theorem,

height of triangle^2 + half length of AB^2 = AC^2

height of triangle^2 = 3^2-1.5^2

height of triangle ^2= 6.75

height of triangle= √6.75

coordinates of C= (1.5,√6.75)

5 0
3 years ago
Read 2 more answers
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