A circular sinkhole has a radius of 12 meters. A week later, it has a diameter of 48 meters. How much greater is the circumference of the sinkhole compared to the previous week?

Answer:

a. 0.0535 = 5.35% probability that it will not be discovered

b. 0.9465 = 94.65% probability that it will be discovered

Step-by-step explanation:

Conditional Probability

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

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

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

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

a. If it has an emergency locator, what is the probability that it will not be discovered?

Event A: Has an emergency locator.

Event B: Not discovered.

Probability of having an emergency locator:

67% of 76%(discovered).

100 - 88 = 12% of 100 - 76 = 24%(not discovered). So

[tex]P(A) = 0.67*0.76 + 0.12*0.24 = 0.538[/tex]

Probability of having an emergency locator and not being discovered:

12% of 24%. So

[tex]P(A \cap B) = 0.12*0.24[/tex]

Desired probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.12*0.24}{0.538} = 0.0535[/tex]

0.0535 = 5.35% probability that it will not be discovered.

b. If it does not have an emergency locator, what is the probability that it will be discovered?

Event A: Has an emergency locator.

Event B: Discovered.

Probability of having an emergency locator:

67% of 76%(discovered).

100 - 88 = 12% of 100 - 76 = 24%(not discovered). So

[tex]P(A) = 0.67*0.76 + 0.12*0.24 = 0.538[/tex]

Probability of having an emergency locator not being discovered:

67% of 76%. So

[tex]P(A \cap B) = 0.67*0.76[/tex]

Desired probability:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.67*0.76}{0.538} = 0.9465[/tex]

0.9465 = 94.65% probability that it will be discovered

Answer: 1.5

mean: 104

S.D: 6

110-104/6=1.5

Answer:

x=0

Step-by-step explanation:

0/3 = 0

0+5=5

Answer:

(-2, 3).

Step-by-step explanation:

2x + y = -1

3x- 5y = -21

Multiply the first equation by 5:

10x + 5y = -5     Adding this to the second equation:

13x = -26

x = -2.

Substituting this into equation 1:

2(-2) + y = -1

y = -1 + 4 = 3.

Checking this result in the second equation:

3(-2) - 5(3)

= -5 - 15 = -21

- Checks OK.

Answer:10

Step-by-step explanation:

10 because 10 minus 8 would be 2

Answer: GIVEN : f(x)= -3x+1

f(x)= -5

REQUIRE:  x=?

CALCULATION:

f(x)= -3x+1

As, given f(x)= -5.

Hence,

-5= -3x+1

OR

-3x+1= -5

-3x= -5-1

-3x=-6

x= -6/-3

x= 2

Answer:

the speed in 18mph

Step-by-step explanation:

Answer:

n = √108 or 6√3

Step-by-step explanation:

n is the altitude of the right triangle

Based on the right triangle altitude theorem, we would have:

h = √(xy)

Where,

h = n

x = 18

y = 6

Substitute

n = √(18*6)

n = √108

Or

n = 6√3

Answer:

x = 10

Step-by-step explanation:

if two prisms are similar then the side lengths are proportional

2/4 = x/20 cross multiply expressions

40 = 4x divide both sides by 4

10 = x

Answer:

Solution given:

B: 9x - 4/x^2 - 4

Step-by-step explanation:

.k

Answer:

The width of the rectangle is 6,105 yards, and the length of the rectangle is 13,105 yards.

Step-by-step explanation:

Given that a rectangular garden covers 80 square yards, and the length is 7 yd longer than the width, to find the length and width of the rectangle the following calculation must be performed, knowing that the area of a rectangle arises from multiplying its width by its length:

X x (X + 7) = 80

5 x 12 = 60

6 x 13 = 78

8 x 14 = 112

6.1 x 13.1 = 79.91

6,105 x 13,105 = 80

Therefore, the width of the rectangle is 6,105 yards, and the length of the rectangle is 13,105 yards.

Answer:

3rd choice

Step-by-step explanation:

multiply by 9/5: F=9/5 C

then add 32: F = 9/5C +32

Answer:

The right answer is "605 persons".

Step-by-step explanation:

Given that,

⇒ [tex]\frac{dP}{dt} \alpha P[/tex]

or,

⇒ [tex]\frac{dP}{dt} =RP[/tex]

⇒ [tex]\frac{1}{R} \int\limits^{PT}_{500} {\frac{dP}{P} } = \int\limits^{t}_{0} dt[/tex]

⇒ [tex]\frac{1}{R} [log PT-log500]=t[/tex]

⇒                  [tex]log[\frac{PT}{500} ]=Rt[/tex]

At t = 10 years,

⇒ [tex]PT=\frac{110}{100}\times 500[/tex]

          [tex]=550[/tex]

∴ [tex]log[\frac{550}{500} ]=R\times 10[/tex]

            [tex]R=\frac{log(1.1)}{10}[/tex]

At t = 20,

⇒ [tex]log{\frac{PT}{500} }=\frac{log \ 1.1}{10}\times 20[/tex]

        [tex]PT=500\times (1.1)^2[/tex]

              [tex]=605 \ persons[/tex]

Answer:

Total selling price= $663.82

Selling price per liter= $1.69

Step-by-step explanation:

Giving the following information:

Proportion of oil and gasoline:

Oil= 3/14= 0.21

Gasoline= 11/14= 0.79

The oil costs $0.75 per liter.

The gasoline costs $1.60 per liter.

First, we need to calculate the number of liters of oil and gasoline required:

Oil= 0.21*392= 82.32 liters

Gasoline= 0.79*392= 309.68

Now, the total cost to produce 392 liters:

Total cost= 82.32*0.75 + 309.68*1.6

Total cost= $577.23

Finally, the total and unitary selling price:

Total selling price= 577.23*1.15= $663.82

Selling price per liter= 663.82 / 392= $1.69

Answer and Step-by-step explanation:

The answer would be 2x + 2y.

This is because we combine the x's together and the y's together. This is the simplest form of the expression.

#teamtrees #PAW (Plant And Water)

Answer:

2x+y^2

Step-by-step explanation:

Collect like terms and rewrite

2x+y*y

Answer:

26w

Step-by-step explanation:

Answer:wpeleoe

Step-by-step explanation:

Answer:

-27

Step-by-step explanation:

a = 7 and c = -4

- a + 5 c

- ( 7 ) + 5 ( - 4 )

- 7 - 20

- 27

Answer:

m-a = n

Step-by-step explanation:

a=m-n

Subtract m from each side

a-m = m-n-m

a-m = -n

Multiply each side by -1

-a+m = n

m-a = n

Answer:

~ 7 years

Step-by-step explanation:

2 = (1 + .1/4)^(4t)

2 = (1.025)^(4t)

Take the log of both sides

log2 = 4t * log1.025

divide both sides by log1.025

log2/log1.025 = 4t

28.07103452593863 = 4t

Divide both sides by 4

7.017758631484657 = t

~ 7 years

Answer:

4

Step-by-step explanation:

Based on your math expression:

7-15 = -8

-2*(-8) = 16

16 / 4 = 4

Answer:

4

Step-by-step explanation:

-2(7-15)

=-14+30

=16÷4

=4

Answer:

585.57

Step-by-step explanation:

Maya got 286.00

if lian got 192.84 less than we do 286-192.84 which is 93.16

if lian got 93.16, we add 113.25 to 93.16 to get rei's amount.

113.25 + 93.16 = 206.41

Now we add all their amounts, 286+93.16+206.41

585.57

Answer:

65

Step-by-step explanation:

See image below:)

Answer:

C

Step-by-step explanation:

Since Carrie walked 6 miles her day, the function that best suits this relationship is given by [tex]y=6x[/tex] where [tex]x[/tex] is the number of days she walked and [tex]y[/tex] is the number of miles.

Table C represents this function [tex]y=6x[/tex] because all y values are exactly 6 times the x value.

Answer:

The answer is C.

Step-by-step explanation:

18 ÷ 3 = 6 miles a day

36÷6 = 6 miles a day

54÷9 = 6 miles a day

72÷12 = 6 miles a day

Answer: 24- b 25- c 26- b 27- c

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

The median is the middle when the numbers are lined up from smallest to largest

3,4,4,6,7,15

There are 6 number so the middle is the  between the 3rd and 4th number

3,4,4,    6,7,15

Take the 3rd and 4th numbers and average

(4+6)/2 = 10/2 = 5

Answer:

median = 5

Step-by-step explanation:

Arrange the data in ascending order :

3 , 4 , 4 , 6 , 7 , 15

Choose the middle number.

Here there are even number of data. Take the average of the middle

numbers .

4 and 6 are the middle number. average of 4 and 6 = ( 4 + 6 ) /2 = 5

Therefore , median = 5

Answer:

good for them i think

Step-by-step explanation:

this doesnt make any sense