8


Find the circumference of the circle pictured above.

Round your answer to the nearest tenth

By definition of conditional probability,

P(F | E ) = P(F and E ) / P(E )

Then

P(F and E ) = P(F | E ) P(E ) = 0.5 • 0.2 = 0.1

Rounded to the nearest meter, the depth of the pool is 2 meters.

We can use the formula for the volume of a cylinder (which includes a circular pool) to solve for the depth:

Volume of circular pool = π × radius² × depth

We are given that the capacity of the pool is 30,000 liters. Since 1 m³ = 1,000 liters, we can convert the capacity to cubic meters:

30,000 L ÷ 1,000 L/m³ = 30 m³

Now we can plug in the given diameter of the pool (480 cm) to find the radius:

radius = diameter ÷ 2 = 480 cm ÷ 2 = 240 cm

We can convert the radius to meters:

240 cm ÷ 100 cm/m = 2.4 m

Finally, we can solve for the depth:

Volume of circular pool = π × radius² × depth

30 m³ = 3.142 × (2.4 m)² × depth

Solving for depth, we get:

depth = 30 m³ ÷ (3.142 × (2.4 m)²) ≈ 1.9 m

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Answer:sum: -1/6

Step-by-step explanation:

Answer:

\( JM = 60 units \)

Step-by-step explanation:

Given:

\( JM = 9x + 6 \)

\( JK = 5x \)

\( KM = 3x + 12 \)

\( JK + KM = JM \) (segment addition postulate)

\( (5x) + (3x + 12) = (9x + 6) \) (substitution)

Solve for x

\( 5x + 3x + 12 = 9x + 6 \)

Collect like terms

\( 5x + 3x - 9x = -12 + 6 \)

\( -x = -6 \)

Divide both sides by -1

\( x = 6 \)

\( JM = 9x + 6 \)

Plug in the value of x

\( JM = 9(6) + 6 \)

\( JM = 54 + 6 \)

\( JM = 60 units \)

The new coordinates of the reflected point will be (2, 2).

In mathematics, reflection is a transformation that "flips" an object over a line or plane. Reflection is a type of symmetry, where an object appears exactly the same after being reflected as it did before.  

When a point is reflected across the y-axis, its x-coordinate changes sign while its y-coordinate remains the same.  

Here we have

The point (-2, 2) is reflected across the y-axis

When a point is reflected across the y-axis, its x-coordinate changes sign while its y-coordinate remains the same.

The new coordinate of the point = (-(-2), 2) = (2, 2)

Therefore,

The new coordinates of the reflected point will be (2, 2).

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Step-by-step explanation:

a I think if wrong let me kknoww

Answer:

number 12 is A for sure

Answer:

I got an F- on math soo i cannot help i am sorry

Step-by-step explanation:

.-.

A = (0,1)

B = (2,1)

C = (2,-1)

A' = (2,4)

B' = (4,4)

C' = (4,2)

we can conclude that the original image is translated 2 units to the right and 3 units up, therefore:

SOLUTION

Comparing the graphs and the options, it follows that each line on the graph represents 5 points. This means the person 6 obtained a score of 45, comparing this to the person 3, it means the person 3 obtained a score of 35.

So the answer is 35.

For the rating since person 6 has the highest possible score, which is 45, person 3 score becomes

so we can classify person 3 as very good

Answer:

-2/12, -0.1, 1/9

Step-by-step explanation:

Answer:

Least to greatest: -2/12 , -0.1 , 1/9

Greatest to least: 1/9, -0.1, -2/12

Step-by-step explanation:

Change all of the numbers so that they are either fractions or decimals. Usually it is easier to change all the numbers to decimal.

Divide:

1/9 = ~0.111 (rounded)

-0.1 = -0.1

-2/12 = - ~0.167 (rounded)

Put the numbers in number order:

-~0.167 , -0.1 , ~0.111

-2/12 , -0.1 , 1/9

~

Answer:

18:36

Step-by-step explanation:

their are 18 nickels and 12+6+18=36 total coins

so the ratio is 18 to 36  or  18:36

Ones is the place value of the digit 6 in the number 2,016 and 6 is the face value of the digit 6 in the number 2,016.

Given, a number 2,016

we have to find the place and face value of 6 in the given number 2,016.

So, the Place value of 6 in the given number is ones.

Ones is the place value of the digit 6 in the number 2,016

Also, the Face value of 6 in the given number is 6.

6 is the face value of the digit 6 in the number 2,016

Hence, Ones is the place value of the digit 6 in the number 2,016 and 6 is the face value of the digit 6 in the number 2,016.

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Answer:

-11 - z

(-11) - (-11)

= 0

I hope I have helped.

Answer:

C

Step-by-step explanation:

All sides make a cube

Answer:

D

Step-by-step explanation:

Answer: a = 10

Step-by-step explanation:    6a + 12 = 72

                                                       -12    -12

                                                6a = 60

                                                6a/6 = 60/6

                                                a = 10

Answer:

a = 10

Step-by-step explanation:

Hello! :)

6a+12=72

6a = 72 - 12

6a = 60

a = 60 ÷ 6

a = 10

Good luck!!

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1. Table 4 values shows a Linear function.

2. 6 seconds faster were the runner in Group 2 than runners in Group 1.

Linear function are those which are in the form of f(x) = x ( here the line is passing through the origin )

Also Linear function can be in the form of y = mx + c where 'm' is the slope of the given line and 'c' is constant.

1. In the table 4 we conclude that:

y = f(x)

f(2) = 4         -------- point is ( 2, 4)

f(4) = 6         -------- point is ( 4, 6)

f(6) = 8         -------- point is ( 6, 8)

f(8) = 10        -------- point is ( 8, 10)

for the points to be in a line their slope must be equal:

Slope of line from point (2, 4) and (4, 6):

Slope = ( y2 - y1 )/ (x2 - x1)

Slope = ( 6 - 4 )/(4-2)

Slope = 2/2 = 1

Similarly,

Slope of line from point (4, 6) and (6, 8):

Slope = ( 8- 6 )/(6-4)

Slope = 1

Same as for points (6, 8) and (8,10)

Slope = 1

here the slop of the all points are same, so they lie on a single line and forms a linear equation in form of y = mx + c.

Hence, Table 4 values shows a Linear function.

2.  Here we have given the data:

For group 1: 55 68 64 66 70

For group 2: 56 58 59 61 57

Average or Geometric mean :

Sum of all the observation / number of observation

Average for Group 1 = ( 55 + 68 +64 +66 + 70)/5

Average for Group 1 = 64.6

Average for Group 2 = (56 + 58 + 59 + 61 +  57)/5

Average for Group 2 = 58.2

Difference between the Average of group 1 and group 2: 6.4.

in whole number 6 seconds.

Hence,

6 seconds faster were the runner in Group 2 than the runners in Group 1.

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Answer:

10 miles

Step-by-step

The restricted values of x for the given rational expression are all real numbers except for x = −12.

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Answer:

The answer to the question provided is letter c.

The simplified expression can be written as:

\((-\sqrt{6} )*(-2*\sqrt{-42} ) = \sqrt{-1,008}\)

Here you need to remember the property:

\(\sqrt{x} *\sqrt{y} = \sqrt{x*y}\)

Now we have the expression:

\((-\sqrt{6} )*(-2*\sqrt{-42} )\)

First, we can cancel the two first negative signs to get:

\((\sqrt{6} )*(2*\sqrt{-42} )\)

Now we can write the 2 as the square root of 4.

\((\sqrt{6} )*(\sqrt{4} *\sqrt{-42} )\)

Finally, we can use the above property to get:

\((\sqrt{6} )*(\sqrt{4} *\sqrt{-42} ) = \sqrt{6*4*(-42)} = \sqrt{-1,008}\)

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Answer:

y = (-3x/5) +1

Step-by-step explanation:

We know that the line passes through the point (-5 , 4)

AND

the slope is given to be -3/5

let's look at the slope a bit more

we know that the formula for slope of a line is Rise / Run

Which means that the rise of this line is -3 after spanning 5 units to the right

Hence, the line goes down 3 units after moving 5 units to the right

We know that to find the equation of a line through the point-slope equation, we need the slope as well as the y-intercept of the line

since we are already given the slope, we need to find the point where the line intersects the y-axis

Now, back to the given point the line passes through

this point has a x - coordinate of -5 and we know that after moving 5 units to the right, the line moves 3 units downwards

So, if the line moves 5 units to the right from the given point, it will reach the y- axis and we know that it's y-coordinate will decrease by 3

Hence, the y-intercept will be 3 units below the given y -coordinate

y - intercept = (4 - 3) =  1 = y-intercept

Now, using the slope-intercept formula to get the equation:

y =  (slope)*x + (y-intercept )

y = (-3/5)x + (1)

y = (-3x/5) + 1

Answer: B

Step-by-step explanation:

The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.

The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.

For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.

Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

So we have derived p as the result using the Power of a Power Property.

In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.

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Answer: percent: 25% amount: 40 base: unknown

Base after finding it: 160

Step-by-step explanation:

40/x = 25%/100

butterfly method

25x/25 = 4000/25

simplify; cancel out

x (aka the base) = 160

Mean - this is the average. Add up the numbers and divide by the count of the numbers in the data set.

11+13+14+16+17+18+20+20+21+24+25+29 = 228

There are 12 numbers, so divide by 12.

228/12 = 19. The mean is 19.

Median - - - this is the MIDDLE number. Your data is already in numerical order (hooray!) so there are 12 numbers. Since it's even, we'll take the average of the 2 middle numbers. The 6th number is 18 and the 7th number is 20. The average of these is 19. So the median is 19.

(Side note: yes, median and mean can be the same.)

Mode - - - this is repeat/most common numbers! 20 repeats. 20 is the mode.

Range - - - biggest number is 29, littlest is 11. The range is 29-11 = 18.

The weight of the male that has a body surface area of 2.3 would be = 108kg

The body surface area (BSA) is defined as the parameter that can be used to estimate the surface area of a person's body based on body weight and height.

The formula for BSA = √w×h/3600

The weight of the male = X

The height of the male = 176cm

The BSA = 2.3

From the formula, make w the subject of formula;

w = BSA²× 3600/h

w = 2.3²× 3600/176

w= 5.29×3600 /176

w = 19044/176

w = 108kg

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