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Find the volume of the solid.


The volume of the solid is _____cubic centimeters.

Answer:

96 days. Divide 3072 by 32 and you get 96.

μ satisfies the countable additivity property. To prove that μ is a measure on a σ-algebra A, we need to show that it satisfies the following properties:

Non-negativity: For any set E in A, μ(E) ≥ 0.

Null empty set: μ(∅) = 0.

Countable additivity: For any countable sequence {\(E_n\)} of disjoint sets in A, μ(∪\(E_n\)) = Σμ(\(E_n\)).

First, let's prove the non-negativity property. Since μ is a measure, it assigns non-negative values to sets in A. Therefore, μ(E) ≥ 0 for any set E in A.

Next, we prove the null empty set property. Since μ is a measure, it assigns a value of 0 to the empty set. Therefore, μ(∅) = 0.

Now, we prove the countable additivity property. Let {\(E_n\)} be a countable sequence of disjoint sets in A. We want to show that μ(∪\(E_n\)) = Σμ(\(E_n\)).

Since μ₁ and μ₂ are measures on A, they satisfy the countable additivity property individually. Therefore, for any countable sequence {\(E_n\)} of disjoint sets in A:

μ₁(∪\(E_n\)) = Σμ₁(\(E_n\)) (1)

μ₂(∪\(E_n\)) = Σμ₂(\(E_n\)) (2)

Now, consider the measure μ = μ₁ + μ₂. We want to show that μ satisfies the countable additivity property.

By definition, μ(∪\(E_n\)) = μ₁(∪\(E_n\)) + μ₂(∪\(E_n\)).

Substituting equations (1) and (2), we have:

μ(∪\(E_n\)) = Σμ₁(\(E_n\)) + Σμ₂(\(E_n\))

Since the sequences {\(E_n\)} are disjoint, the sum of their measures can be combined:

μ(∪\(E_n\)) = Σ(μ₁(\(E_n\)) + μ₂(\(E_n\)))

Using the distributive property of addition, we get:

μ(∪\(E_n\)) = Σμ₁(\(E_n\)) + Σμ₂(\(E_n\))

This is equivalent to:

μ(∪\(E_n\)) = Σ(μ₁(\(E_n\)) + μ₂(\(E_n\)))

Therefore, μ satisfies the countable additivity property.

Since μ satisfies all three properties of a measure, we can conclude that μ is a measure on A.

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I hope that it helps you..

The new earned value in week 10 can be calculated by multiplying the total planned value of the project by the progress percentage achieved in week 10. To compare the performance at week 10 with week 8, we can calculate the Cost Performance Index (CPI) and Cost Variance (CV).

To calculate the new earned value in week 10, we multiply the total planned value by the progress percentage achieved in week 10. Let's assume the total planned value for the project is RM100,000. The earned value in week 10 would be 75% of RM100,000, which is RM75,000.

To compare the performance at week 10 with week 8, we calculate the Cost Performance Index (CPI) and Cost Variance (CV). The CPI is calculated by dividing the earned value by the actual cost. If the actual cost spent in week 10 is RM6,000, the CPI would be RM75,000 (earned value) divided by RM6,000 (actual cost), which equals 12.5.

The CV is calculated by subtracting the actual cost from the earned value. In this case, the CV would be RM75,000 (earned value) minus RM6,000 (actual cost), which equals RM69,000.

To calculate the FCAC, we add the actual costs incurred in week 9 and week 10 (RM5,000 + RM6,000) to the planned costs for the remaining phases. Let's assume the planned costs for the remaining phases are RM40,000. The FCAC would be RM5,000 + RM6,000 + RM40,000, which equals RM51,000.

The TCPI is calculated by dividing the remaining budget by the remaining work. If the remaining budget is RM40,000 and the remaining work is 25% (100% - 75%), the TCPI would be RM40,000 divided by 25%, which equals RM160,000.

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we know that

The surface area of a square pyramid is given by the formula

where

B is the area of the square base

LA is the lateral area (area of the four triangular faces)

step 1

Find out the area of the square base B

step 2

Find out the area of one triangular face

the area of one triangular face is given by the formula

where

b=96 m

h=?

Applying the Pythagorean Theorem, find out the value of h

where

H=220 m (height of the building)

b/2=96/2=48 m

substitute

substitute

Multiply by 4 to obtain the Lateral Area

The surface area of the building is equal to

step 3

we know that

one gallon of cleaning solution -----> for every 250 square meters of surface

Applying proportion

1/250=x/52,450.56

solve for x

x=52,450.56/250

x=210 gallons

see the figure below to better understand the calculation to obtain the value of

h (the height of each triangular face)

Answer:

He has:

20 quarters : 0.25x20= 5.00

16 dimes: 0.10x 16 = 1.60

20+ 16= 36 coins

5.00 + 1.60 = $6.60

Answer:

a other word for domain is state , zone land ,kingdom

The number of pheasants in 2012 was 1832. The number of pheasants in 2016 was 422. The minimum viable density is 100 pheasants per hectare.

So, we need to find out the year in which the population will fall below 100 pheasants per hectare.

First, we need to find out the rate of decline per year which can be calculated as follows: Rate of decline per year = (1832 - 422) / (2016 - 2012)= 1410 / 4= 352.5 per yearNow, let the number of pheasants per hectare be y after t years from 2012.

Then, y = 1832 - 352.5t (as we know the rate of decline per year)We need to find the year in which the population will fall below 100 pheasants per hectare. So, we need to solve the equation:1832 - 352.5t = 100⇒ 352.5t = 1732⇒ t = 1732 / 352.5⇒ t = 4.91 Therefore, the population will fall below the minimum viable density of 100 pheasants per hectare after 4.91 years from 2012, which is around 2017 or 2018.

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it will take approximately 21 weeks for the blood bank to reach at least 1350 pints of blood, considering their current rate of increasing the supply.

To determine how long it will take for the blood bank to have at least 1350 pints of blood, we can calculate the number of weeks required to reach the desired amount.

Current supply of blood: 72 pints

Target supply of blood: 1350 pints

Increase rate per week: 61 pints

The additional pints of blood needed to reach the target supply is:

Additional pints = Target supply - Current supply

Additional pints = 1350 pints - 72 pints

Additional pints = 1278 pints

To find the number of weeks required, we divide the additional pints needed by the increase rate per week:

Number of weeks = Additional pints / Increase rate per week

Number of weeks = 1278 pints / 61 pints per week

Using division, we find that:

Number of weeks ≈ 20.95

Since we cannot have a fraction of a week, we can round up to the nearest whole number. Therefore, it will take approximately 21 weeks for the blood bank to reach at least 1350 pints of blood, considering their current rate of increasing the supply.

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A fixed ratio schedule is a type of reinforcement schedule in which a response is reinforced after a specific number of responses. In this case, the response of putting money in the machine is reinforced after every 1 response.

If each time you put a dollar in a vending machine you get a snack, then your response is reinforced according to a fixed ratio schedule.

Variable interval, fixed interval, and variable ratio schedules are all different types of reinforcement schedules that are based on different criteria. A variable interval schedule is a type of reinforcement schedule in which a response is reinforced after a random interval of time. A fixed interval schedule is a type of reinforcement schedule in which a response is reinforced after a fixed interval of time. A variable ratio schedule is a type of reinforcement schedule in which a response is reinforced after a random number of responses.

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Answer:

His interest is $2340 his total is $8840

Step-by-step explanation:

Answer:2340$

Step-by-step explanation:

1. Do 6500x 0.09 to get 585

2. Then multiply it by 4 since it is his interest rate for 4

3. 585x4=2340

Answer:

p > 31

Step-by-step explanation:

If their record is 31, and they need to beat it, then it would mean his score needs to be greater than 31, which is written as:

p > 31

Hope this helps

Answer:

p(x) = (x-a)(x-b)(x-7) - a and b can be whatever you want, any real numbers

Step-by-step explanation:

If you plug in 7, you need to multiply the other two numbers by 0, which will result in 0. There are 3 factors since it must be a 3rd degree polynomial

Hope this helps! Please give brainliest!

The components of the vector with initial point (7,−6) and a terminal point at (6,−3) are:

The components of a vector are the vectors that makes up the resultant as described in the problem to have starting point (7,−6) and terminal point (6,−3).

This can be gotten by plotting these points and getting the coordinates of the points that makes the initial point and the terminal point the hypotenuse of the triangle

From the graph, the coordinates are:

component 1: (6, -6) to (3, -6)

component 2: (7, -6) to (6, -6)

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On solving the provided question, by properties of parallel lines we got to know that -  1 - A  2 - C  3 - B  4 - D

When two or more lines cross the intersection line, alternate exterior angles result. These angles are created on a number of sides outside the transverse lines. Any two parallel lines that cross one another create two angles with the horizontal line. In the area between the parallel lines, interior angles are formed, while alternate exterior angles are formed in the area outside the parallel lines.

Matches are -When two parallel lines cross one other, the horizontal line is divided into two angles. Interior angles develop between the parallel lines, whereas alternative outside angles develop outside the parallel lines.

1 - A

2 - C

3 - B

4 - D

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The probability that the basketball player hits all 4 shots is approximately 0.0416 or 4.16%.

To determine the probability that a basketball player hits all 4 shots during a game, when the player hits three-point shots 41% of the time, we have to apply binomial probability distribution.

Let X be the number of successful shots when taking 4 shots, the probability of success in each trial, p = 0.41 and the number of trials, n = 4.

Therefore, we can use the binomial probability distribution as given below: `P(X = k) = (n choose k) × p^k × q^(n-k)

`Where q = 1 - p = 1 - 0.41 = 0.59 is the probability of failure.In this case, k = 4, and we can calculate P(X = 4) as follows:`P(X = 4) = (4 choose 4) × 0.41^4 × 0.59^(4-4)`= (1) × (0.41)^4 × (0.59)^0= 0.0416

Therefore, the probability that the basketball player hits all 4 shots is approximately 0.0416 or 4.16%.

Note: A probability is a number between 0 and 1, and it can be represented as a fraction, decimal or percentage. In this case, we have represented the answer in percentage format.

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Answer:

2 x 3 x 5²

Step-by-step explanation:

The number 150 is a composite and it should have prime factors. Now let us know how to calculate the prime factors of 150.

Step 1: The first step is to divide the number 150 with the smallest prime number, say 2.

150 ÷ 2 = 75

Step 2: You will get a fractional number if you divide 75 by 2. Continue with the next prime number, say 3.

75 ÷ 3 = 25

Step 3: Again you will get a fractional value when you divide 25 by 3 hence, continue with the next prime number say 5.

25 ÷ 5 = 5

5 ÷ 5 = 1

Finally, we received the number 1 at the end of the division process. So that we cannot proceed further. So, the prime factors of 150 are written as 2 x 3 x 5 x 5 or 2 x 3 x 5², where 2, 3 and 5 are the prime numbers.

The solution is, : 150 as a product of primes is, 2 x 3 x 5², where 2, 3 and 5 are the prime numbers.

A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words.

here, we have,

The number 150 is a composite and it should have prime factors. Now let us know how to calculate the prime factors of 150.

Step 1: The first step is to divide the number 150 with the smallest prime number, say 2.

150 ÷ 2 = 75

Step 2: You will get a fractional number if you divide 75 by 2. Continue with the next prime number, say 3.

75 ÷ 3 = 25

Step 3: Again you will get a fractional value when you divide 25 by 3 hence, continue with the next prime number say 5.

25 ÷ 5 = 5

5 ÷ 5 = 1

Finally, we received the number 1 at the end of the division process. So that we cannot proceed further.

So, the prime factors of 150 are written as 2 x 3 x 5 x 5 or 2 x 3 x 5², where 2, 3 and 5 are the prime numbers.

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Based on the histogram, the probabilities are;

The different probabilities are obtained from the data values seen in the histogram.

The modal number of children is 2 and has a probability of 0.37.

Hence, the probability of the most likely outcome of the survey = 0.37

The least likely number of children is 5 and has a probability of 0.03.

Hence, the probability of the least likely outcome of the survey = 0.03

The probability of at least one child = 1 - the probability of no child

Probability of no child = 0.13

The probability of at least one child = 1 - 0.13

The probability of at least one child = 0.87

The probability that a woman has more than 3 children is the sum of the probabilities of 4 or 5 children.

The probability that a woman has more than 3 children = 0.06  + 0.03

The probability that a woman has more than 3 children = 0.09

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The value of the discriminant for the equation -5x^2 - x + 1 = 0 is 21.

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.

To find the discriminant of a quadratic equation in the form ax^2 + bx + c = 0, we use the formula:

Discriminant (D) = b^2 - 4ac

For the given equation -5x^2 - x + 1 = 0, we have a = -5, b = -1, and c = 1. Plugging these values into the discriminant formula, we get:

D = (-1)^2 - 4(-5)(1)

D = 1 + 20

D = 21

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Answer:

Linear pairs add up to 180°

1st angle = x

2nd angle = x+24 (24° more than the first)

The equation would be

1st angle + second angle = 180 Subbing in the expressions we came up with:

x+x+24 = 180

Answer:

-----------------------

40% of the total number is 6.

Find the total number x:

Answer:

To find the missing base, you simply divided the area by the given height

Step-by-step explanation:

hope this help

Note that the volume of the solid is 5,132.32unit³

To find the volume of the solid generated by revolving the region about the line y=14, we can use the method of cylindrical shells.

 We integrate the surface area of each shell from 0 to 13, then multiply by the thickness of ech shell (d x), and finally add up all the shells.

The radius of each shell is given by the distance from the axis of rotation (y =14) to the function y = x, which is r  = 14 - x. The height of each shell is given by the function   y = 13 - x.

Therefore, the volume of the solid is stated as

V = ∫[0,13] 2πrh dx

V = ∫[0,13] 2π(14-x)(13-x) dx

V = 2π ∫[0,13] (182 - 27x + x²) dx

V = 2π [182x - (27/2)x² + (1/3)x³] [0,13]

V = 2π [(182(13) - (27/2)(13)² + (1/3)(13)³) - 0]

V ≈ 5132.32

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Answer:

Shown below.

Step-by-step explanation:

Test Marks          Tally          Frequency          Percentage

1                                                    8                   8/60 = 0.133

2                                                   6                   6/60 = 0.100

3                                                   5                   5/60 = 0.083

4                                                   5                   5/60 = 0.083

5                                                   5                   5/60 = 0.083

6                                                   8                   8/60 = 0.133

7                                                   6                   6/60 = 0.100

8                                                   7                   7/60 = 0.116

9                                                   4                   4/60 = 0.066

10                                                 5                   5/60 = 0.083

Total                                            59                 59/60 = 0.983

For the Tally section, I believe you just fill in tally marks corresponding to the frequency. One of the observations in the table is 0, which is not a column in the frequency table.

The equation of the tangent line to the curve f(x) = x^3 - 5x + 2 at the point (-2,4) is y = 7x + 18.



To find the equation of the tangent line to the curve given by the function f(x) = x^3 - 5x + 2 at the point (-2,4), we can follow these steps:

1. Calculate the derivative of the function f(x) to find the slope of the tangent line. The derivative of f(x) = x^3 - 5x + 2 is f'(x) = 3x^2 - 5.

2. Substitute x = -2 into the derivative f'(x) to find the slope of the tangent line at the point (-2,4). Evaluating f'(-2) gives f'(-2) = 3(-2)^2 - 5 = 7.

3. Now that we have the slope of the tangent line, we can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope.

Plugging in (-2, 4) and the slope 7, the equation of the tangent line is y - 4 = 7(x - (-2)), which simplifies to y - 4 = 7x + 14.

Therefore, the equation of the tangent line to the curve f(x) = x^3 - 5x + 2 at the point (-2,4) is y = 7x + 18.

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Answer:

15xy-6x+5y-2

15xy+5y-6x-2

5y(3x+1) -2(3x+1)

(we pick one out of the (3x+1) brackets.

your final answer becomes:

(5y-2)(3x+1)

Answer:

(5y - 2)(3x + 1)

Step-by-step explanation:

Let's focus on those first two terms, 15xy and 6x. They have two factors in common, an x and a 3, giving them a greatest common factor of 3x. If we factor that out, the expression 15xy - 6x becomes 3x(5y - 2). Substituting that into our original expression, we get the new expression

\(3x(5y-2)+5y-2\)

Let's group those last two terms to make our next step clearer:

\(3x(5y-2)+(5y-2)\)

Now, each term has the factor (5y - 2) in common. We can pull it out to get the fully factored expression

\((5y-2)(3x+1)\)

Answer:

Since  

x

is on the right side of the equation, switch the sides so it is on the left side of the equation.

x

2

−

2

x

+

3

=

G

(

x

)

Multiply  

G

by  

x

.

x

2

−

2

x

+

3

=

G

x

Subtract  

G

x

from both sides of the equation.

x

2

−

2

x

+

3

−

G

x

=

0

Use the quadratic formula to find the solutions.

−

b

±

√

b

2

−

4

(

a

c

)

2

a

Substitute the values  

a

=

1

,  

b

=

−

2

−

G

, and  

c

=

3

into the quadratic formula and solve for  

x

.

−

(

−

2

−

G

)

±

√

(

−

2

−

G

)

2

−

4

⋅

(

1

⋅

3

)

2

⋅

1

Simplify.

Tap for more steps...

x

=

2

+

G

±

√

G

2

+

4

G

−

8

2

The final answer is the combination of both solutions.

x

=

2

+

G

+

√

G

2

+

4

G

−

8

2

x

=

2

+

G

−

√

G

2

+

4

G

−

8

2

Step-by-step explanation: