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2 years ago

Round 154,394 to the nearest hundred thousand

Mathematics

1 answer:

Leviafan [203]2 years ago

6 0

150,000 because its 5 or higher add one more 4 or lower just ignore so since its 4 i just lowered it to 0

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A certain virus infects one in every 400 people. A test used to detect the virus in a person is positive 90% of the time if the

Ahat [919]

Answer:Given:

P(A)=1/400

P(B|A)=9/10

P(B|~A)=1/10

By the law of complements,

P(~A)=1-P(A)=399/400

By the law of total probability,

P(B)=P(B|A)*P(A)+P(B|A)*P(~A)

=(9/10)*(1/400)+(1/10)*(399/400)

=51/500

Note: get used to working in fraction when doing probability.

(a) Find P(A|B):

By Baye's Theorem,

P(A|B)

=P(B|A)*P(A)/P(B)

=(9/10)*(1/400)/(51/500)

=3/136

(b) Find P(~A|~B)

We know that

P(~A)=1-P(A)=399/400

P(~B)=1-P(B)=133/136

P(A∩B)

=P(B|A)*P(A) [def. of cond. prob.]

=9/10*(1/400)

=9/4000

P(A∪B)

=P(A)+P(B)-P(A∩B)

=1/400+51/500-9/4000

=409/4000

P(~A|~B)

=P(~A∩~B)/P(~B)

=P(~A∪B)/P(~B)

=(1-P(A∪B)/(1-P(B)) [ law of complements ]

=(3591/4000) ÷ (449/500)

=3591/3592

The results can be easily verified using a contingency table for a random sample of 4000 persons (assuming outcomes correspond exactly to probability):

===....B...~B...TOT

..A . 9 . . 1 . . 10

.~A .399 .3591 . 3990

Tot .408 .3592 . 4000

So P(A|B)=9/408=3/136

P(~A|~B)=3591/3592

As before.

Step-by-step explanation: its were the answer is

5 0

3 years ago

Write an equation in slope-intercept form of the line that passes through (6, -1) and (3, 47)

katrin2010 [14]

Answer:

Step-by-step explanation:

(47+1)/(3-6) = 48/-3 = -16

y + 1 = -16(x - 6)

y + 1 = -16x + 96

y = -16x + 95

6 0

3 years ago

I need help with the steps. The answer is (5,2)

Elden [556K]

So with this, I will be using the substitution method. With the first equation, substitute (y+3) into the x variable and solve for y:

$y+3+y=7\\2y+3=7\\2y=4\\y=2$

Next, now that we have the value of y, substitute it into either equation to solve for x:

$x+2=7\\x=5\\\\x=2+3\\x=5$

<u>And this is how you get your final answer (5,2).</u>

5 0

3 years ago

PLEASE help me and PLEASE show the work PLEASE.

Dafna1 [17]

20(4×-2)

________

(4 - (-2))²

simplified;

20(-8)

_____

(6)²

simplified;

-160

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simplified;

-4 16/36

simplified;

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3 0

2 years ago

Hi! I need help with the attached question in calc. Thank you:)

Elena L [17]

Answer:

3π square units.

Step-by-step explanation:

We can use the disk method.

Since we are revolving around AB, we have a vertical axis of revolution.

So, our representative rectangle will be horizontal.

R₁ is bounded by y = 9x.

So, x = y/9.

Our radius since our axis is AB will be 1 - x or 1 - y/9.

And we are integrating from y = 0 to y = 9.

By the disk method (for a vertical axis of revolution):

$\displaystyle V=\pi \int_a^b [R(y)]^2\, dy$

So:

$\displaystyle V=\pi\int_0^9\Big(1-\frac{y}{9}\Big)^2\, dy$

Simplify:

$\displaystyle V=\pi\int_0^9(1-\frac{2y}{9}+\frac{y^2}{81})\, dy$

Integrate:

$\displaystyle V=\pi\Big[y-\frac{1}{9}y^2+\frac{1}{243}y^3\Big|_0^9\Big]$

Evaluate (I ignored the 0):

$\displaystyle V=\pi[9-\frac{1}{9}(9)^2+\frac{1}{243}(9^3)]=3\pi$

The volume of the solid is 3π square units.

Note:

You can do this without calculus. Notice that R₁ revolved around AB is simply a right cone with radius 1 and height 9. Then by the volume for a cone formula:

$\displaystyle V=\frac{1}{3}\pi(1)^2(9)=3\pi$

We acquire the exact same answer.

8 0

2 years ago