A = L x W
A = ? X ?
A = ?
The area is ? square centimeters.

The given statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is False.

The union of two events A and B represents the event that at least one of the events A or B occurs. The probability of the union of two events can be calculated using the formula:

P(A or B) = P(A) + P(B) - P(A and B)

On the other hand, the intersection of two events A and B represents the event that both events A and B occur. The probability of the intersection of two events can be calculated using the formula:

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

where P(B|A) is the conditional probability of B given that A has occurred.

It is possible for the probability of the union of two events to be greater than the probability of the intersection of two events if the two events are not mutually exclusive.

In this case, the probability of both events occurring together (the intersection) may be relatively small, while the probability of at least one of the events occurring (the union) may be relatively high.

In summary, the probability of the union of two events occurring can sometimes be greater than the probability of the intersection of two events occurring, depending on the relationship between the events.

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The probability of the two fair six sided dice thrown together and getting sum of shown numbers to 7 is equal to ( 1/ 7).

As given in the question,

Number of times both 6-sided fair dice rolled out = 2

Dice is numbered from 1 to 6

As both the dice rolled together order does not matter

Total possible outcomes are:

= { ( 1,1 ), (1,2) , (1,3),(1,4), (1,5), 1,6), (2,2), (2,3),(2,4),(2,5), (2,6), (3,3),(3,4), (3,5) ,(3,6), (4,4), (4,5), (4,6), (5,5), (5,6), (6,6) }

Total number of outcomes = 21

Dice shows sum of numbers to 7 are

= {(1,6), (2,5), (3,4), }

Number of favourable outcomes = 3

Probability of the thrown dice sum shows number 7

= (Number of favourable outcomes)/ (Total number of outcomes)

= 3 /21

= 1 / 7

Therefore, probability of the two six sided dice thrown together and show sum of numbers to 7 is equal to (1/7).

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Answer:

  (a)  A(x) = (12 -2x)√(3x -9)

Step-by-step explanation:

You want a formula for the area (a(x)) of an isosceles triangle with congruent sides of length x and perimeter 12. You also want its maximum value, and a graph and the maximum value of z = 2a(3x+3)+1.

Heron's formula for the area of a triangle with side lengths a, b, c is ...

  A = √(s(s -a)(s -b)(s -c)) . . . . . . where s = (a+b+c)/2, the semiperimeter

Given a perimeter of 12, and two sides x, this becomes ...

  A(x) = √(6(6 -x)(6 -x)(6 -(12-2x))) = √(6(6 -x)²(2x -6))

  A(x) = 2(6 -x)√(3(x -3)) . . . . . . factor out perfect squares

  A(x) = (12 -2x)√(3x -9) . . . . . . domain: 3 ≤ x ≤ 6

The domain is such that the radical and the area are non-negative.

The derivative of the area function is ...

  \(A'(x)=-2\sqrt{3x-9}+\dfrac{3(6-x)}{\sqrt{3x-9}}=\dfrac{-2(3x-9)+3(6-x)}{\sqrt{3x-9}}\\\\A'(x)=\dfrac{-9x+36}{\sqrt{3x-9}}\)

The derivative is zero at the maximum, so ...

  -9x +36 = 0   ⇒   x = 4 . . . . . . . an equilateral triangle

The maximum area is ...

  A(4) = (12 -2·4)√(3·4 -9) = 4√3

The maximum area is 4√3.

Since the maximum of A(x) is 4√3 at x=4, the maximum of 2A(3x+3) +1 will be ...

  2(4√3) +1 = 8√3 +1 . . . . . . . where 3x+3 = 4  ⇒  x = 1/3

The maximum of 2A(3x+3)+1 is 8√3 +1 at x = 1/3.

The function ...

  z = 2A(3x+3) +1 = 2A(3(x+1)) +1

Compare this to ...

  z = p·A(q(x -r)) +s

which is vertically expanded by p, horizontally compressed by q, then translated right r and up s.

We see that the parent function A(x) is vertically expanded by a factor of 2, compressed horizontally by a factor of 3, then translated left 1 and up 1.

Applying these transformations to the original A(x) domain and range, we find the domain is ...

  1/3[3, 6] -1 = [0, 1] . . . . . domain of z

And the range is ...

  2[0, 4√3] +1 = [1, 8√3 +1] . . . . . range of z

The "d" format specifier is used to denote a signed decimal integer in various programming languages and formatting systems.

When used in format strings or printf-style functions, the "d" specifier indicates that the corresponding argument should be formatted as a signed decimal integer. It allows for the representation of both positive and negative whole numbers, including zero.

For example, in C programming, the printf function can be used with the "%d" format specifier to display a signed decimal integer value. Similarly, in other languages such as Python, the "{:d}" format specifier can be used with the format() function or string interpolation to represent a signed decimal integer.

Using the "d" specifier ensures that the output is formatted as a base-10 representation of a signed integer, taking into account the sign of the number.

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Answer:

x=8

Step-by-step explanation:

4+4=x

4+4=8

x=8

The potential at the center of the square due to the four equal charges is (8k * q) / l.

To find the potential at the center of the square due to the four charges, we can calculate the electric potential at that point due to each charge individually and then sum them up.

Given:

Four equal charges, q, placed at the corners of a square of side length l.

The center of the square is at the center of the coordinate system.

The electric potential, V, at a point due to a point charge q is given by the formula:

V = k * q / r

Where:

k is the electrostatic constant (k = 9 * 10^9 Nm^2/C^2)

q is the magnitude of the charge

r is the distance from the charge to the point

Since the charges are placed at the corners of a square, the distance from each charge to the center of the square is l/2. Thus, the potential at the center due to each charge is:

V = k * q / (l/2) = 2k * q / l

Since all four charges are equal, the total potential at the center of the square is the sum of the potentials due to each charge:

V_total = 2k * q / l + 2k * q / l + 2k * q / l + 2k * q / l

V_total = (8k * q) / l

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The potential at the center of the square is the sum of the potentials due to each charge, which can be calculated using the formula V = k * q / r. Since the charges are placed at the corners of the square of side l, the distance from the center of the square to each charge is sqrt(2) * l/2. Therefore, the potential at the center is (4 * sqrt(2) * k * q) / l.

The potential at the center of the square can be found by considering the contributions from each of the four charges. Since the charges are equal and placed at the corners of the square, the electric field at the center will be zero. Therefore, the potential at the center of the square is simply the sum of the potentials due to each charge.

The potential due to a single charge can be calculated using the formula:

V = k * q / r

where V is the potential, k is the electrostatic constant (approximately 9 x 10^9 Nm^2/C^2), q is the charge, and r is the distance.

Since the charges are placed at the corners of the square of side l, the distance from the center of the square to each charge is sqrt(2) * l/2. Plugging in these values, we get:

V = 4 * (k * q / (sqrt(2) * l/2))

V = (4 * sqrt(2) * k * q) / l

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Corinne do 4 pages homework in one hour.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

Corinne take 3 hours to do 12 pages of homework.

Since, We have;

Corinne take 3 hours to do 12 pages of homework.

Hence, In 1 hour, Number of pages = 12 / 3

                                                       = 4

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The number of columns in the first matrix must equal the number of rows in the second matrix in order to multiply matrices with different dimensions.

    3. Determine the dot product of the corresponding row in matrix A          and the corresponding column in matrix B for each element in matrix C.

    4: The final response is matrix C, which is the union of the 2x3 matrix A and the 3x4 matrix B.

     Therefore, the result is a 2x4 matrix, which is produced by taking the dot product of the rows and columns of matrix A and matrix B.

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a computer randomly selects 800 names from a list of all registered voters. Then option C  is correct  that is Simple random sampling

A simple random sample in statistics, is a subset of individuals chosen from a larger set. Each individual is chosen randomly and entirely by chance, such that each individual has the same probability for the entire larger set.

the complete question is

Identify the sampling method as simple random​ sampling, systematic​ sampling, convenience​ sampling, or stratified sampling. A computer randomly selects 800 names from a list of all registered voters. Those selected are surveyed to predict who will win the election for Mayor.

Choose the correct sampling technique below.

A. Systematic sampling

B. Convenience sampling

C. Simple random sampling

D. Stratified sampling

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Deposit of $1400 will be double in 14.2 years.

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period.

Given,

Deposited Principal Amount P = $1400

Rate of interest r = 5% = 0.05

Amount A = double the deposit = 2× $1400 = $2800

Let the number of years = n

Amount A = P(1 + r)ⁿ

$2800 = $1400(1 + 0.05)ⁿ

(1 + 0.05)ⁿ = 2

Taking log on both side

n log(1.05) = log2

n =  log2 / log(1.05)

n = 0.3010/0.0212

n = 14.2

Hence, It will take 14.2 years to double the deposit of $1400.

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So the slope of the scenario is $28 per hour, which indicates that the expense of the tour increases by $28 for every extra hour spent on it.

The slope of a line indicates its steepness. Slope is computed mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation occurs when the equation of a line is stated in the form y = mx + b. The slope of the line is given by m. And b is the value of b in the y-intercept point (0, b). For example, the slope of the equation y = 3x - 7 is 3, while the y-intercept is (0, 7).

Here,

In this situation, the slope represents the rate of change in the cost of the tour with respect to the time spent on the tour. The slope of the situation can be calculated as the change in cost divided by the change in time.

Since the one-time fee is a fixed cost, it does not change with respect to the time spent on the tour. Therefore, the slope can be calculated as the rate of change in the cost due to the hourly fee of $28.

The slope can be represented as:

slope = Δcost/Δtime = $28/hour

So, the slope of the situation is $28 per hour, which means that for every additional hour spent on the tour, the cost of the tour increases by $28.

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A z-statistic reports how many standard deviations an observed value is from the expected value, where the expected value is calculated using the population mean and standard deviation.

To calculate the z-statistic, use the following formula:

Where:

x = the observed value

μ = the population mean

σ = the population standard deviation

n = the sample size

The z-statistic tells us how many standard deviations an observed value is from the expected value, which is the population mean. A positive z-score indicates that the observed value is above the expected value, while a negative z-score indicates that the observed value is below the expected value. A z-score of 0 indicates that the observed value is equal to the expected value. By calculating the z-statistic, we can determine how unusual or significant an observed value is relative to the population.

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Complete Question:

a z-statistic reports how many sds an observed value is from the expected value, where the expected value is calculated using the___.

Answer:

3 x \(r^{2}\)

Step-by-step explanation:

If the alternative hypothesis is that the proportion of items in population 1 is larger than the proportion of items in population 2, then the null hypothesis should be that there is no significant difference in the proportion of items between population 1 and population 2.

Based on the information provided, the null hypothesis should be:

The null hypothesis is that the proportion of items in population 1 is less than or equal to the proportion of items in population 2.

This is denoted as H₀: P₁ ≤ P₂. The alternative hypothesis, as you mentioned, is that the proportion of items in population 1 is larger than the proportion of items in population 2, which is represented as H₁: P₁ > P₂.

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Answer:

3/20

Step-by-step explanation:

-

Answer:

0.15

Step-by-step explanation:

Charge q is 1 unit of distance away from the source charge S. Charge p is two times further away. The force exerted between S and q is _____ the force exerted between S and p

a. 1/2

b. 2 times

c. 1/4

d. 4 times

Answer:

4 times

Step-by-step explanation:

Given the following :

Distance between q and S (r) = 1 unit

Distance between P and S (r) = 2 × 1 unit = 2

According to coliumbs law:

F = Ke(q1q2) /r^2

Where F = electrostatic force, Ke = coloumbs constant

q1,q2 = charges, r = distance between two charges

For q and S :

Fsq = Ke(q1q2) / 1^2

Fsq = Ke(q1q2) - - - - - equation 1

For P and S :

Fsp = Ke(q1q2) / 2^2

Fsp = Ke(q1q2) / 4 - - - - - equation 2

Dibiding equation 1 by equation 2

Fsq/Fsp = Ke(q1q2) / Ke(q1q2)/4

Fsq / Fsp = Ke(q1q2) × 4 / Ke(q1q2)

Fsq / Fsp = 4 / 1

Using cross multiplication

Therefore, Fsq = 4 × Fsp

Answer:

Step-by-step explanation:

Givens

V = 75716

pi = 3.14

r = ?

Formula

V =  (4/3) pi * r^3

Solution

75716 =  (4/3) * 3.14 * r^3              Multiply both sides by 3/4

75716 * 3/4 = 3.14 * r^3

56787 = 3.14 r^3                           Divide by 3.14

56787 / 3.14 = 3.14 * r^3/3.14

18085 = r^3

∛18985 = ∛ r^3

r = 26.25

Answer:

28.26

Step-by-step explanation:

A = area of a sector

π = 3.14

r = 9

θ = 40

A=πr²*θ/360=3.14*81*40/360=28.26

Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

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Answer:

I got 8

Step-by-step explanation:

The value of the equation A = (0.2 ) x 40 is A = 8

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be A

Now , the value of A = 0.2 x 40

On simplifying the equation , we get

The value of 0.2 = 1/5

Now , substituting the value of 0.2 in the equation , we get

The value of A = ( 1/5 ) x 40

The value of A = 40/5

The value of A = 8

Therefore , the value of A is 8

The equation can also be solved as

The value of A = 0.2 x 40

The value of A = ( 2 / 10 ) x 40

The equation can be simplified as

The value of A = 80/10

The value of A = 8

Therefore , the value of A is 8

Hence , The value of the equation A = (0.2 ) x 40 is A = 8

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Answer: −4x + 5.2

Step-by-step explanation: Add 3.2 and 2. Then reorder 5.2 and −4x.

Answer:

yeah

Step-by-step explanation:

yeah

Answer:

7,200

Step-by-step explanation:

180,000 divided by 100= 1,800=1%

1,800 x 4 = 7,200 = 4%

The degree of polynomial is 3

From the question, we have the following parameters that can be used in our computation:

zeros equal in x=1 with multiplicity =2 x= 0 with the multiplicity =1

The degree of a polynomial is the sum of the multiplicities

Using the above as a guide, we have the following:

Degree = 2 + 1

Evaluate

Degree = 3

Hence, the degree is 3

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Answer:

$3828 approx

Step-by-step explanation:

Given data

Principal=$2316

Rate= 3%

Time= 17 years

The compound interest formula is

A=P(1+r)^t

substitute

A=2316(1+0.03)^17

A=2316(1.03)^17

A=2316*1.652847

A=$3827.99

Hence the account balance after 17 years is $3828 approx

By means of Euclidean geometry and algebra, the line segment PQ has a length of 2 units.

In this problem we find the case of a geometric system formed by a line segment PR with a point Q on the line between P and R. Thus, a line segment PQ is inside the line segment described above.

According to the statement, the lengths of the line segments PR and QR are known and the length of line segment PQ can be known by Euclidean geometry and algebra:

PR = PQ + QR

PQ = PR - QR

If we know that PR = 10 and QR = 8, then the line segment PQ is calculated below:

PQ = 10 - 8

PQ = 2

In accordance with algebra and Euclidean trigonometry, the length of line segment PQ is 2.

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The height of the altitude of the given equilateral triangle is: 5√3 inches

We know that the sides of an equilateral triangle are equal and as such since we are given one side as 10 inches, then all the three sides will measure 10 inches.

Now, the altitude can be gotten by getting half the length of one side and using Pythagoras theorem to get the altitude.

Thus, if the altitude is denoted by h, then we have that:

h = √(10² - 5²)

h = √75

h = 5√3 inches

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Answer:

500

Step-by-step explanation:

The probability is 1/6.

So, find 1/6 of 3,000.

1/6 * 3,000 = 3,000/6 = 500

Answer:

x>-5 x ≤10

Step-by-step explanation:

-35/7=-5

7x/7=x

3x/3=x

30/3=10

Answer: -5 < x _< 10

Step-by-step explanation:

The area of a circle is given by:

And the area of the triangle is:

Therefore, the total area is: