6nsquared - 5nsquared + 7nsquared simplify the expression

Answer:

1 acre foot = 43560 ft³

Step-by-step explanation:

1 square mile = 640 acres.

5280 feet = 1 mile

5280 x 5280 ft² = 640 acres.

1 acre = 43560 ft².

1 acre foot = 43560 x 1 ft³ = 43560 ft³

1 acre foot = 43560 ft³

To solve this problem, let us first calculate the probability of designing one shoe out of all the combinations.

Probability of designing one shoe = (probability of choosing 1 color for the base) * (probability of choosing 1 color for the accent) * (probability of choosing 1 font for the embroidery)

We know that probability is:

Probability = number of chosen event / number of total events

Therefore:

Probability of designing one shoe = (1 / 4) * (1 / 6) * (1 / 2)

Probability of designing one shoe = 1 / 48

This means that either Ray or Lilli has this probability of designing a specific shoe. Since we are asked for the probability that they will both design this specific shoe, so we multiply:

Probability they will design the same shoe = (1 / 48) * (1 / 48)

Probability they will design the same shoe = 1 / 2304 = 4.34 * 10^-4

The probability is around 0.043% that they will design the same shoe.

A continuous random variable can assume any value within one or more intervals and result from measurements, providing an uncountable range of possibilities. Continuous random variables are commonly used in many fields, including reliability engineering and standardized testing, to assess continuous data.

A continuous random variable is a type of random variable that can assume any value within one or more intervals. Unlike discrete random variables, which take on countable values, continuous random variables result from measurements rather than counts. For instance, the temperature of a day measured by a thermometer or the height of students measured by a ruler are examples of continuous random variables. The values are uncountable as they lie on a continuum, like the speed of an automobile or the duration of a telephone call.

Two main characteristics of a discrete probability distribution function include the fact that each probability must be between zero and one, inclusive, and the sum of the probabilities should equal one. These rules do not apply to continuous random variables, which instead use probability density functions to describe their distributions.

Continuous random variables play significant roles in numerous applications such as assessing baseball batting averages, calculating IQ scores, and evaluating SAT scores. In the field of reliability engineering, a variety of continuous random variables are essential for analyzing the life expectancy of components.

divide

42/96 = 0.4375

0.4375*100 = 43.75 percent

 round the answer as needed.

Answer:

The missing coordinate is 5

Step-by-step explanation:

Answer:

3181 yards.

Step-by-step explanation:

All the given information can be used to draw a simple diagram. The diagram shows a triangle which is formed by the ships. There are two angles given and one side is given. Therefore, the sine rule must be used to solve the question. The sine rule can be written as:

sin V / v = sin G / g.

It can be observed that the angle V is unknown, however, it can be calculated very easily. Simply use the law of triangle in which all the 3 angles sum up to 180 degrees. So V = 180 degrees - 44 degrees - 36 degrees = 100 degrees. So plugging in v = 4510 yards, V = 100 degrees, G = 44 degrees, and g = x yards into the sine rule gives:

sin 100 / 4510 = sin 44 / x.

Cross multiplying gives:

x*sin 100 = 4510*sin 44

Making x the subject gives:

x = (4510*sin 44)/sin 100.

x = 3181 yards (to the nearest yard).

Therefore, Norman and Voyager are 3181 yards apart from each other!!!

The required distance between the Norman and the Voyager is 3181 yards.

Given that,
A ship at sea, the Gladstone, spots two other ships, the Norman and the Voyager, and measures the angle between them to be 44°. The distance between the Gladstone and the Norman is 4510 yards. The Norman measures an angle of 36° between the Gladstone and the Voyager. To the nearest yard, what is the distance between the Norman and the Voyager is to be determined.

These are the equation which contains trigonometric operators such as sin, cos.. etc.. In algebraic operation.

Here,
The measure of the angle between Gladstone and the norman,
= 180 - 44 + 36
= 100°

sin(100) / 4510 = sin(44) / x.

x = 3181.12

x ≈ 3181 yards

Thus, the required distance between the Norman and the Voyager is 3181 yards.

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The standard form of the equation for the line passing through (-5, -1) and (10, -7) is y = x - 17.

The standard form of the equation for the line passing through the points (-5, -1) and (10, -7) can be found using the point-slope form given, which is y + 7 = (x - 10).

First, let's convert this equation into slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Subtracting 7 from both sides of the equation, we get y = x - 17.

This is the standard form of the equation for the line passing through (-5, -1) and (10, -7).

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515x + 285y = 11,080

x + y = 30

Answer:

The missing term is x=32.

Step-by-step explanation:

Given :  The median for the given set of six ordered data values is 26.5.

To find : What is the missing value?

Solution :

The data set is 7 12 21 ?41 50

let the missing term or 4th term be x.

We know, The median of an even number is sum of nth term by 2 and nth+1 term by 2.

So, Applying median formula for even terms is

Term, [tex](\frac{n}{2},\frac{n}{2}+1)[/tex]

[tex](\frac{6}{2},\frac{6}{2}+1)=3^{rd},4^{th}[/tex]

The median is sum of 3rd and 4th term.

[tex]26.5=\frac{21+x}{2}[/tex]

[tex]53=21+x[/tex]

[tex]53-21=x[/tex]

[tex]32=x[/tex]

Therefore, The missing term is x=32.

If the median for the given set of six ordered data values is 26.5 then the missing value is 32.

The ordered set of data values is:

7, 12, 21,x, 41, 50

Given that the median is 26.5, it represents the middle value of the data set.

Since the set has six values, the median should be the average of the two middle values.

Let's assume the missing value is 'x':

7, 12, 21, x, 41, 50

We can see that 'x' should be the fourth value to maintain the ascending order.

Now, we need to find the value of 'x' that makes the median equal to 26.5.

To calculate 'x', we can set up the equation:

(21 + x) / 2 = 26.5

Multiply both sides by 2:

21 + x = 53

Subtract 21 from both sides:

x = 32

Therefore, the missing value in the set is 32.

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The probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice will be 5/12.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

The total number of probability is given as,

Total event = 6 x 6

Total event = 36

The samples are given as,

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

Then the probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice will be given as,

P = (4/36) + (11/36)

P = 15/36

P = 5/12

The probability of getting either a sum of 5 or at least one 5 in the roll of a pair of dice will be 5/12.

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The rarest form of dichromatism is tritanopia. This condition affects the perception of blue and yellow colors and is less common than protanopia and deuteranopia which affect red and green perception respectively.

The rarest form of dichromatism is tritanopia. The term dichromatism refers to an abnormality in color vision where an individual can only perceive two of the three primary colors. This question is related to the broader topic of color vision deficiencies, a study within biology. Among the options listed, protanopia and deuteranopia tend to be the most common color vision deficiencies, both affecting the perception of red and green respectively. Tritanopia is a condition that impacts the ability to perceive blue and yellow and is the least common form, while 'Fruitopia' is not related to this topic as it's a brand of fruit drinks.

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A vector can be defined as an element of a vector space, which represents an object that has both magnitude and direction.

Assuming that; [tex]\left \{ {{x=rcos \theta} \atop {y=rsin \theta}} \right.[/tex]

For the channel:

The vector representing the flow from North to South is given by:

[tex]15 cos (\frac{3\pi}{2} ), \; 15 sin (\frac{3\pi}{2} )\\\\15(0),\; 15(-1)[/tex]

Vector = 0, -15

For the sailboat:

The vector representing the sailboat is given by:

[tex]40 cos (30 ), \; 40 sin (30)\\\\30(\frac{\sqrt{3} }{2} ),\; 30(\frac{1 }{2} )\\\\15\sqrt{3} ,\;15[/tex]

Vector = [tex]15\sqrt{3} ,\;15[/tex]

For the strong wind:

The vector representing the strong wind blowing towards northwest is given by:

[tex]30 cos (\frac{3\pi}{4} ), \; 30 sin (\frac{3\pi}{4} )\\\\30(\frac{-\sqrt{2} }{2} ),\; 30(\frac{\sqrt{2} }{2} )\\\\-15\sqrt{2},\;15\sqrt{2}[/tex]

Vector = [tex]-15\sqrt{2},\;15\sqrt{2}[/tex]

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Due to the lack of numerical details, a precise ratio of men to all members at the swim club cannot be determined. The ratio would be based on the exact number of men verses total members. Ratios offer a method to compare quantities.

Unfortunately, without more information, it's impossible to definitively say what the precise ratio of men to all members at the swim club is. To determine the correct ratio, we would need to know the total number of members at the club, and the number of those members who are men. A ratio is a way to compare quantities or numbers, and in this case, the quantity of men compared to the quantity of all members.

For example, if there were 20 members total in the club, and 10 of those members were men, the ratio would be 1:2 (choice C), because for every one man, there are two total members. However, if there were 4 members and 3 of them were men, then the ratio would be 3:4 (choice B). Without the specific numbers, we cannot determine the correct answer from choices A, B, C, or D.

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volume = l x w x h

51 x 44 x 8 = 17952 cubic feet

1 cubic foot = 0.0283168 cubic meters

17952 x 0.0283168 = 508.343 cubic meters

1 cubic meter = 1,000,000 cubic centimeters

508.343 x 1000000 = 508,343,000 cubic centimeters

Final answer:

To show that z = (xy)/(x+y) given that 3^x = 4^y = 12^z, logarithms and the properties of exponents are used to simplify and solve for z.

Explanation:

The problem given is to show that if 3^x = 4^y = 12^z, then z = (xy)/(x+y). To solve this, we can use logarithms or equate the expressions to a common variable. Since 12 = 3 × 4, it means that 12^z = (3^z)(4^z).

Remember that the original equations given were 3^x = 12^z and 4^y = 12^z.

Substituting z into these equations we have 3^x = 3^z × 4^z and 4^y = 3^z × 4^z.

Taking logarithms, we find

[tex]log(3^x) = log(3^z) + log(4^z) and log(4^y) = log(3^z) + log(4^z).[/tex]

Applying the power rule of logarithms, the equations simplify to

[tex]x log(3) = z log(3) + z log(4)[/tex]and  [tex]y log(4) = z log(3) + z log(4).[/tex]

Dividing these equations by log(3) and log(4) respectively gives

[tex]x = z + z(log(4)/log(3))[/tex] and [tex]y = z + z(log(3)/log(4)).[/tex]

Adding these equations, we get

[tex]x + y = 2z + z[(log(4)/log(3)) + (log(3)/log(4))],[/tex]

which simplifies to x + y = 2z because [tex](log(4)/log(3)) + (log(3)/log(4)) = 1.[/tex]Finally, solving for z gives z = (xy)/(x+y) as desired.

Answer:

five ordered pairs are (-2,1) (-1,3) (0,5) (1, 7) (2, 9)

y intercept is (0,5)

x intercept is (-2.5, 0)

Step-by-step explanation:

y=2x+5

To get 5 ordered pairs , plug in some random number for x and find out y

x           y= 2x+5

-2            2(-2) + 5= 1

-1             2(-1) + 5= 3

0             2(0) + 5= 5

1             2(1) + 5= 7

2             2(2) + 5= 9

five ordered pairs are (-2,1) (-1,3) (0,5) (1, 7) (2, 9)

When x=0 , the value of y = 5

So y intercept is (0,5)

To find x intercept we plug in 0 for y

y=2x+5

0 = 2x +5

subtract 5 from both sides

-5 = 2x

divide by 2 on both sides

x= -5/2

so x intercept is (-2.5, 0)

The probability of having at most three defects in a four-hour period is approximately 0.8572.

The Poisson probability distribution is used to model the number of events that occur in a fixed interval of time or space, given the average rate at which the events occur. In this problem, the rate of errors is given as one error every two hours. We need to find the probability of having at most three defects in a four-hour period.

To solve this problem, we can use the Poisson probability formula, which is:

P(x; λ) = (e^(-λ) * λ^x) / x!

where P(x; λ) is the probability of having exactly x events occur in the given interval, λ is the average rate of events, e is the base of the natural logarithm, and x! is the factorial of x.

First, we need to calculate the average rate of events in a four-hour period. Since the rate is given as one error every two hours, we can calculate the rate for a four-hour period as follows:

Average rate = (4 hours) / (2 hours/error) = 2 errors

Now, we can plug this average rate (λ = 2) into the Poisson probability formula for x = 0, 1, 2, and 3 to find the probabilities of having at most three defects:

P(0; 2) = [tex](e^{(-2)} * 2^0)[/tex] / 0! ≈ 0.1353

P(1; 2) = ([tex]e^{(-2)} * 2^1[/tex]) / 1! ≈ 0.2707

P(2; 2) = [tex](e^{(-2)} * 2^2)[/tex] / 2! ≈ 0.2707

P(3; 2) = [tex](e^{(-2)} * 2^3)[/tex] / 3! ≈ 0.1805

To find the probability of at most three defects, we sum up these individual probabilities:

P(at most 3 defects) = P(0; 2) + P(1; 2) + P(2; 2) + P(3; 2) ≈ 0.8572

So, the probability of having at most three defects in a four-hour period is approximately 0.8572.

Answer:

18 boxes of wrenches and 22 boxes of hammers.

Step-by-step explanation: