Is mode a measure of center of center or a measure of variation

Answer:

it looks like c

Step-by-step explanation:

its not quite 50 but its extreemly close so its got to be c

\(12 {}^{2} = 9 {}^{2} + 8 {}^{2} - 2(9)(8)(cosx)\)

\(144 = 81 + 64 - 2(72)(cosx)\)

\(144 = 145 - 144(cosx)\)

\( - 144(cosx) = 144 - 145\)

\((cosx) = \frac{ - 1}{ - 144} \)

\(arccos( \frac{1}{144} ) = > a = 89.6\)

Let \(\(a\)\) and \(\(b\)\) be integers such that \(\(ab = 4\)\). We want to prove that \(\((a - b)^3 - 9(a - b) = 0\).\)

Starting with the left side of the equation, we have:

\(\((a - b)^3 - 9(a - b)\)\)

Using the identity \(\((x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3\)\), we can expand the cube of the binomial \((a - b)\):

\(\(a^3 - 3a^2b + 3ab^2 - b^3 - 9(a - b)\)\)

Rearranging the terms, we have:

\(\(a^3 - b^3 - 3a^2b + 3ab^2 - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\(a^3 - b^3 - 3a^2(4) + 3a(4^2) - 9a + 9b\)\)

Simplifying further, we get:

\(\(a^3 - b^3 - 12a^2 + 48a - 9a + 9b\)\)

Now, notice that \(\(a^3 - b^3\)\) can be factored as \(\((a - b)(a^2 + ab + b^2)\):\)

\(\((a - b)(a^2 + ab + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Since \(\(ab = 4\)\), we can substitute \(\(4\)\) for \(\(ab\)\) in the equation:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 48a - 9a + 9b\)\)

Simplifying further, we get:

\(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\)

Now, we can observe that \(\(a^2 + 4 + b^2\)\) is always greater than or equal to \(\(0\)\) since it involves the sum of squares, which is non-negative.

Therefore, \(\((a - b)(a^2 + 4 + b^2) - 12a^2 + 39a + 9b\)\) will be equal to \(\(0\)\) if and only if \(\(a - b = 0\)\) since the expression \(\((a - b)(a^2 + 4 + b^2)\)\) will be equal to \(\(0\)\) only when \(\(a - b = 0\).\)

Hence, we have proved that if \(\(ab = 4\)\), then \(\((a - b)^3 - 9(a - b) = 0\).\)

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Answer:

  6.4

Step-by-step explanation:

The hypotenuse of a right triangle can be found from the other two sides by making use of the Pythagorean theorem. It tells you the square of the hypotenuse is the sum of the squares of the other two sides:

  c² = 4² +5²

  c² = 16 +25 = 41

  c = √41 ≈ 6.4

The missing side length is about 6.4 units.

The probability of waiting between 10 and 15 minutes at the Maryland Department of Motor Vehicles (DMV), given an exponential distribution with an expectation of 10 minutes.

The median waiting time, which represents the 50th percentile of the waiting time distribution, can be found by solving the equation involving the CDF of the exponential distribution. In this case, the median waiting time is approximately 6.9315 minutes.

The exponential distribution is often used to model the time between events that occur at a constant rate independently of past occurrences.

The parameter of the exponential distribution is the expectation or mean, which is given as 10 minutes in this case.

The probability of waiting between 10 and 15 minutes can be calculated by subtracting the probability of waiting less than 10 minutes from the probability of waiting less than 15 minutes.

This can be done using the CDF of the exponential distribution. Plugging in the appropriate values, the probability is approximately 0.0916, or 9.16%.

The median waiting time represents the time at which 50% of the waiting times are less than or equal to the median. In the exponential distribution.

The median can be calculated by solving the equation 1 - e^(-λt) = 0.5, where λ is the rate parameter of the distribution and t is the median waiting time.

In this case, the rate parameter is 1/10, as the expectation is 10 minutes. Solving the equation gives us t ≈ 6.9315 minutes, which is the median waiting time at the Maryland DMV.

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Answer:

x+2

hope this helps ;)

and cute pfp

Answer:

Step-by-step explanation:

x-1, because 3 fits the criteria, x>=1

Answer:

4.5

Step-by-step explanation:

(-1,2) (1, -2)

√(x2 - x1)² + (y2 - y1)²

√[1 - (-1)]² + (-2 - 2)²

√(2)² + (-4)²

√(4) + (16)

√20

= 4.5

Divide price by quantity:

3.00 / 12 = $0.25 per can.

Answer:

x²+24x+144

Step-by-step explanation:

x*x = x²

12 x 12 = 144

2(x*12) = 24x

hence the answer is x²+24x+144

Answer: =432000

Step-by-step explanation: Hope this help :D

Answer:

3.14 is the simplified version (approximate) to π

Answer:

2.25, or 2 hours and 15 minutes.

The penguin would take 2 hours and 1/4 of an hour (or 15 minutes) to walk 3/4 mile.

To find the time it would take the Galapagos penguin to walk 3/4 mile, we can set up a proportion using the given information.

The proportion can be set up as follows:

(1/3 mile walked) / (1 hour) = (3/4 mile walked) / (x hours)

Now, cross-multiply to solve for 'x':

(1/3) * x = (3/4)

Next, we can simplify the equation by multiplying both sides by 3 (to eliminate the fraction on the left side):

x = (3/4) * (3)

x = 9/4

Now, we can convert the result to a mixed number:

x = 2 + 1/4

In conclusion, using the proportion, we found that the penguin would take 2 hours and 15 minutes to walk 3/4 mile at a rate of 1/3 mile per hour.

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Organise the information in a table.

If two rows of a 3×3 matrix A are the same, then detA = 0.

True, consider a 3 × 3 matrix A with two identical rows.

The determinant of a matrix is a scalar value that encodes various properties of the matrix.

One property of the determinant is that it changes sign if two rows (or two columns) of the matrix are interchanged.

Another property is that if two rows (or two columns) of the matrix are the same, then the determinant is zero.

Without loss of generality, assume that the first and second rows of A are the same.

Interchange the first and third rows of A using an elementary row operation without changing the value of the determinant, since this operation changes the sign of the determinant.

Then, we obtain a matrix B of the form:

[ a11 a12 a13 ]

[ a11 a12 a13 ]

[ a31 a32 a33 ]

Now, we can expand the determinant of B along the first column to get:

det(B) = a11 × det(B11) - a31 × det(B31)

B11 and B31 are the 2x2 matrices obtained by deleting the first row and the first column, and the third row and the first column of B, respectively.

Since the first and second rows of B are identical, we have det(B11) = 0. Hence, we obtain:

det(B) = a11 × det(B11) - a31 × det(B31) = -a31 × det(B31)

Now, we can expand the determinant of B31 along its first column to get:

det(B31) = a12 × a33 - a32 × a13

Substituting this into the previous expression, we obtain:

det(B) = -a31 × det(B31) = -a31 × (a12 × a33 - a32 × a13)

This shows that the determinant of A is zero, since det(A) = det(B) by elementary row operations.

If two rows of a 3 × 3 matrix A are the same, then detA = 0.

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Given

Procedure

Now for y

The answer would be x = 2.75 and y = 1.25

The radius of the circle is 21 mm

Remember that for a circle of radius R, the circumference is:

C = 2*pi*R

where pi = 3.14

Here the circumference of the circle is 131.88 mm

Replacing that value in the formula above, we will get the equation:

131.88mm = 2*3.14*R

Solving that for R we get:

R = 131.88mm/(2*3.14) = 21mm

That is the radius.

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The probability that event will not occur is 0.68 (1-0.32). The odds for event are 32:68 or simplified to 8:17 (divide both sides by 4). The odds against event are 68:32 or simplified to 17:8 (divide both sides by 4).

Given that the probability of the event occurring is 0.32, we can find the probability of the event not occurring by subtracting this value from 1:

Probability (Event Not Occurring) = 1 - Probability (Event Occurring) = 1 - 0.32 = 0.68

So, the probability that the event will not occur is 0.68.

Now, let's find the odds for the event. Odds for an event is calculated as:

Odds For = Probability (Event Occurring) / Probability (Event Not Occurring) = 0.32 / 0.68 ≈ 0.47

So, the odds for the event are approximately 0.47 to 1.

Lastly, let's calculate the odds against the event:

Odds Against = Probability (Event Not Occurring) / Probability (Event Occurring) = 0.68 / 0.32 ≈ 2.13

Therefore, the odds against the event are approximately 2.13 to 1.

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a) The parametric equations for simulating the motion of the softballs are x(t) = v₀ * cos(θ) * t and y(t) = h₀ + v₀ * sin(θ) * t - (1/2) * g * t²

b) Yes, the softballs will collide since their paths intersect.

c) Mary's softball hits the ground first.

d) To find the horizontal distance traveled by each softball when it hits the ground, substitute the time values obtained in part (c) into the respective x(t) equations.

a) The parametric equations for simulating the motion of the softballs are x(t) = v₀ * cos(θ) * t and y(t) = h₀ + v₀ * sin(θ) * t - (1/2) * g * t². For Mary's softball, v₀ = 45 ft/sec, θ = 44°, and h₀ = 7 ft. For Kelly's softball, v₀ = 41 ft/sec, θ = 39°, and h₀ = 6.5 ft. Substitute these values into the equations to obtain the parametric equations for each softball's motion.

b) The softballs will collide because their paths intersect. To determine this, we need to solve the system of equations x(t) for Mary's softball and x(t) for Kelly's softball, and find the time t at which their x-coordinates are equal.

c) Mary's softball hits the ground first. To find the time at which it hits the ground, we solve the equation y(t) = 0 for Mary's softball. Substitute the known values into the equation y(t) for Mary's softball, and solve for t.

d) To find the horizontal distance traveled by each softball when it hits the ground, substitute the time values obtained in part (c) into the respective x(t) equations. Calculate the x-coordinate at the corresponding time t for Mary's and Kelly's softballs to determine how far each softball travels horizontally before hitting the ground.

In summary, the parametric equations for simulating the motion of the softballs are obtained using the given initial velocities, angles of elevation, and release heights. The softballs will collide since their paths intersect. Mary's softball hits the ground first, and the time at which it hits the ground can be determined by solving the equation y(t) = 0. To find the horizontal distance traveled by each softball when it hits the ground, substitute the obtained time values into the respective x(t) equations.

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Answer:165degrees

Step-by-step explanation

Use formula N-2 × 180 N is the number of sides

24-2=22

22x180=3960 total

for each angle divide total by 24=165 degrees

Lerchs-Grossman algorithm is a pit optimization software that helps in the determination of the most profitable final pit outline. The section of a copper porphyry ore body given has a cut-off grade of 0.45% Cu. Each block has dimensions of 16m x 16m x 16m (HxLxW).

The cost of mining a block of waste is $50, and the value of a block of ore is approximated to be $100 x (grade expressed in %). Firstly, we have to calculate the net present value (NPV) for all the blocks that are above the cut-off grade. NPV is calculated using the formula given below:

NPV = ((grade*100)*100)-50

Here, the cost of mining a block of waste is $50 and the value of a block of ore is approximated to be $100 x (grade expressed in %).

1. Firstly, the net present value (NPV) of each block above the cutoff grade is calculated.2. The blocks are then sorted in descending order of their NPVs.

3. Next, the algorithm calculates the limits of the pit at a sequence of levels, starting with the block of highest NPV.

4. It is assumed that the pit will extend downwards through the blocks from the highest NPV downwards.

5. If the pit reaches the edge of the ore body before reaching a certain level, it is truncated and the lower level is tried.

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Answer:

yes it is

Step-by-step explanation:

to have a right traingle two sides cannot be equal and the first added and squared cannot be more than the last side squared

Answer:

Step-by-step explanation:

?

Answer:

la respuesta es 1.5

Step-by-step explanation:

18÷12=1.5

The equivalent expression to the complex number (3 + 4i) + (3-5i) is option C: 6 - i.

What is complex number?

A real number and an imaginary number are effectively combined to create a complex number. The complex number is written as a+ib, where a and ib are real and imaginary numbers, respectively.

The complex number expression is -

(3 + 4i) + (3 - 5i)

= 3 + 4i + 3 - 5i

= 3 + 3 + 4i - 5i

= 6 - i

Therefore, the value for the expression is 6 - i.

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S1: ∠YLF ≅ ∠FRY (Given)

S2: ∠RFY ≅ ∠LFY (Given)

S3: FY ≅ FY (Transitive property)

S4: ΔFRY ≅ ΔFLY (AAS theorem)

The AAS congruence theorem states that if two triangles have two pairs of corresponding congruent angles, and a pair of corresponding non-included side that are congruent, then both triangles area congruent.

To prove that ΔFRY ≅ ΔFLY, the proof that shows they are congruent by the AAS congruence theorem is:

S1: ∠YLF ≅ ∠FRY (Given)

S2: ∠RFY ≅ ∠LFY (Given)

S3: FY ≅ FY (Transitive property)

S4: ΔFRY ≅ ΔFLY (AAS theorem)

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The beta of the portfolio, considering $1 with a beta of 3% and $2 with a beta of 7% and a weight of 0.1 (w1), is 6.6%.


The beta of a portfolio measures its sensitivity to overall market movements. To calculate the beta of a portfolio, we need the individual asset weights and betas of each asset. Given that $1 has a beta of 3% and $2 has a beta of 7%, with a weight of 0.1 (w1), we can determine the beta of the portfolio.

To calculate the beta of the portfolio, we use the following formula:

β(portfolio) = (w1 * β1) + (w2 * β2) + ...

In this case, the portfolio contains two assets, so the formula becomes:

β(portfolio) = (w1 * β1) + (w2 * β2)

Substituting the given values:

β(portfolio) = (0.1 * 3%) + (0.9 * 7%)

β(portfolio) = 0.3% + 6.3%

β(portfolio) = 6.6%

Therefore, the beta of the portfolio is 6.6%.

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y+1=6/11(x+4) is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given two points are  (7, 5) and (−4, −1)

m=-1-5/-4-7

=-6/-11

=6/11

The point slope intercept form is y- y₁=m(x-x₁) through (-4,-1)

y-(-1)=6/11(x-(-4))

y+1=6/11(x+4)

Hence, y+1=6/11(x+4) is the equation in point-slope form of the line that passes through the points (7, 5) and (−4, −1).

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The measures are given as follows:

1. Length of 36 cm.

2. Height of 1.44 cm.

The measures are obtained applying the proportions in the context of this problem.

The ratio between the length and the width is given as follows:

Length/Width = 180/75

Length/Width = 2.4

Length = 2.4 Width.

For a width of 15 cm, the length is given as follows:

15 x 2.4 = 36 cm.

The ratio between the length and the height is given as follows:

Length/Height = 180/20

Length/Height= 9

Length = 9Height

Height = Length/9

Hence the height if the length is of 13 cm is given as follows:

13/9 = 1.44 cm.

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We have that the ratio for the length is 10/6 = 5/3.

Then we have that:

Then,

The ratio of the lengths is 5/3 : 1

The ratio of the areas is 25/9 : 1

Answer:

C

Step-by-step explanation:

from some other question so thank this guy

Frika

The scale is balanced so both sides need to weigh the same amount.

On the left side you have:

6 squares, 3 circles and 2 triangles

On the right side you have:

3 squares, 2 circles and 5 triangles

Sunday equal amounts of each from both sides you would have:

3 squares and 1 circle in the left and 3 triangles in the right.

So we know the 3 squares and 1 circle = 3 triangles:

3 squares x 2 grams = 6 grams

1 circle x 3 grams = 3 grams

6 + 3 = 9 grams

9 grams / 3 triangles = 3 grams per triangle.,