What is the ordered pair for y=3x-3

(a) The recursive formula for An is: An = (1.015)An-1 - 100.

(b) The explicit formula for An in summation notation is: An = 4000(1.015)^n - 100[1 + (1.015) + (1.015)^2 + ... + (1.015)^(n-1)].

(a) This formula says that to find the balance for month n, we take the balance for month n-1, multiply it by 1.015 (to account for the interest rate), and subtract 100 (to account for the withdrawal). This formula is consistent with the results for n=1,2,3 on the previous page.

(b) The explicit formula for An in summation notation is: An = 4000(1.015)^n - 100[1 + (1.015) + (1.015)^2 + ... + (1.015)^(n-1)].

This formula says that to find the balance for month n, we take the starting balance of 4000 multiplied by the interest rate raised to the power of n, and then subtract the sum of 100 multiplied by the geometric series (1 + r + r^2 + ... + r^(n-1)), where r = 1.015. This formula is consistent with the results for n=1,2,3 on the previous page.

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Based on the given data, The shape's whole surface area is about 252 mm².

Based on the image, the shape appears to be a set of rectangles with different lengths and widths.

To find the area of this shape, we can break it down into smaller rectangles and add up their areas.

Starting from the bottom, we can see that the first rectangle has a length of 6 mm and a width of 4 mm. Its area is:

Area1

= 6 mm × 4 mm

= 24 mm²

Moving up to the second rectangle, we see that it has a length of 6 mm and a width of 3 mm. Its area is:

Area2

= 6 mm × 3 mm

= 18 mm²

The third rectangle has a length of 6 mm and a width of 5 mm. Its area is:

Area3

= 6 mm × 5 mm

= 30 mm²

The fourth rectangle has a length of 6 mm and a width of 3 mm. Its area is:

Area4

= 6 mm × 3 mm

= 18 mm²

The fifth rectangle has a length of 6 mm and a width of 15 mm. Its area is:

Area5

= 6 mm × 15 mm

= 90 mm²

The sixth rectangle has a length of 3 mm and a width of 9 mm. Its area is:

Area6

= 3 mm × 9 mm

= 27 mm²

Finally, the seventh rectangle has a length of 5 mm and a width of 9 mm. Its area is:

Area7

= 5 mm × 9 mm

= 45 mm²

To find the total area of the shape, we can add up the areas of all seven rectangles:

Total Area

= Area1 + Area2 + Area3 + Area4 + Area5 + Area6 + Area7

= 24 mm² + 18 mm² + 30 mm² + 18 mm² + 90 mm² + 27 mm² + 45 mm²

= 252 mm²

Therefore, the total area of the shape is approximately 252 mm².

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Answer: 46.0 ft

Step-by-step explanation:

[tex]\text{sin} \ 24^o=\dfrac{x}{105}[/tex]

[tex]x=105 \ \text{sin 24}^o[/tex]

So, the distance above the ground is [tex]\text{105 sin} \ 24^o+3.25\thickapprox \boxed{46.0 \ \text{ft}}[/tex]

Answer:

10

Step-by-step explanation:

Based on the given conditions, formulate: 40x16 divided by 64

Cross out the common factor: 40/4

Cross out common factor: 10

Get the result

Answer: 10

we have

13x+6y=−30------------- > 6y=-30-13x--------------- > y=(-30-13x)/6

x−2y=−4-- > 2y=x+4-------- > y=(x+4)/2

Using a graphing tool---------- > see attached figure

the solution of the system is the point (-2.625,0688)

the best estimate pair for the solution to the system is (−2.5, 0.75)

Note that the solution of the system of equations will be (-6, -2). (Option A)

A system of equations is a collection of two or more equations with a shared set of unknown variables. The goal is to find the values of the variables that satisfy all the equations simultaneously.

Note that System of equations is represented by two straight lines on a graph.

And solution of the system of equations is the point of intersection of these lines, because that is the point where the values from both functions satisfy all the equations simultaneously.

From the graph attached, two straight lines represent the system of equations.

And the point of intersection of these lines is the solution.

Therefore, solution of the system of equations will be (-6, -2). (Option A)

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Full Question:

Although part of your question is missing, you might be referring to this full question:

What is the solution to the system of equations?
A (-6,2-)

B (-2, 6)

C (6,2)

D (-2,-6)​? See attached image.

30 percent chance

There are 30 possible numbers that a player can get on their uniform. Out of these, there are 9 single-digit numbers (1, 2, 3, 4, 5, 6, 7, 8, and 9) and 21 double-digit numbers (10, 11, 12, ..., 29, 30).

If no two players can have the same number, then the probability that the first player will get a single-digit number is simply the number of single-digit numbers divided by the total number of possible numbers:

P(single-digit number) = 9/30 = 0.3

So the player is correct that there is a 30% chance that she will get a single-digit number on her uniform.

An interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.

For each calculation, the smallest interval in which the result, using true instead of rounded values, must lie is as follows:

(a) 1.1062+0.947 = 2.0532 ≤ true result ≤ 2.053

(b) 23.46 - 12.753 = 10.707 ≤ true result ≤ 10.708

(c) (2.747) (6.83) = 18.6181 ≤ true result ≤ 18.6182

(d) 8.473/0.064 = 132.3906 ≤ true result ≤ 132.3907

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Answer: The given equation 2x + 5y = 10 can be rewritten in slope-intercept form (y = mx + b) by solving for y:

2x + 5y = 10

5y = -2x + 10

y = (-2/5)x + 2

where the slope is -2/5.

Since we want to find the equation of a line parallel to this one, the slope of the new line will also be -2/5. We can use the point-slope form of the equation of a line to find the equation of the new line, using the point (0,-3):

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the given point.

Substituting m = -2/5, x1 = 0, and y1 = -3, we get:

y - (-3) = (-2/5)(x - 0)

y + 3 = (-2/5)x

y = (-2/5)x - 3

Therefore, the equation of the line parallel to 2x + 5y = 10 which passes through (0,-3) is y = (-2/5)x - 3.

Step-by-step explanation:

Answer:

2x + 5y = - 15

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

2x + 5y = 10 ( subtract 2x from both sides )

5y = - 2x + 10 ( divide through by 5 )

y = - [tex]\frac{2}{5}[/tex] x + 2 ← in slope- intercept form

with slope m = - [tex]\frac{2}{5}[/tex]

• Parallel lines have equal slopes , then

y = - [tex]\frac{2}{5}[/tex] x + c

the line crosses the y- axis at (0, - 3 ) ⇒ c = - 3

y = - [tex]\frac{2}{5}[/tex] x - 3 ← equation of parallel line in slope- intercept form

multiply through by 5 to clear the fraction

5y = - 2x - 15 ( add 2x to both sides )

2x + 5y = - 15 ← in standard form

The slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.

An equation is an expression that states the equality of two things. It typically consists of an equal sign (=) and two expressions on either side of the equal sign that represent the same thing. Equations are used to describe relationships between different variables and can be used to solve mathematical problems. They can also be used to show the relationships between different quantities in physics and chemistry.

a)The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 6, and the run is 2, so the slope is 3.

b) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 3, and the run is -7, so the slope is -3/7.

c) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 4, and the run is 6, so the slope is 2/3.

Finding slope in tables and graphs is a common mathematical skill that is used to identify the rate of change of a linear equation. This is determined by finding the change in the dependent variable (the y-axis) divided by the change in the independent variable (the x-axis). This is what is referred to as the slope of the equation. To find the slope in tables and graphs, you must look at the differences between the points on the x-axis and y-axis, and divide the change in the y-axis by the change in the x-axis. This will give you the slope of the equation. Finding the slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.

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Consequently, the area of triangle $AMN$ is equal to $A = \frac{1}{2}bh = \frac{1}{2}(4)(2) = 4$ cm2.

The area of triangle $AMN$ in square $ABCD$ can be calculated using the formula for area of a triangle, $A = \frac{1}{2}bh$, where $b$ is the length of the base and $h$ is the height of the triangle.

Since side $BC$ has a length of 4 cm, we can determine that $N$ is located 2 cm away from point $B$ and 2 cm away from point $C$.

Similarly, we can conclude that $M$ is located 2 cm away from point $C$ and 2 cm away from point $D$.

Therefore, the base of triangle $AMN$ is equal to 4 cm, and the height of triangle $AMN$ is equal to 2 cm.

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The slopes are,

1) 7/6

2)7/2

3) -1

4) -2

5) 10/9

What is slope?

Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined. The difference between the line's y and x coordinate changes is known as the slope of the line.Any two distinct places along the line can be used to determine the slope of any line.

1) The given points , [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (6,8)[/tex] then,

=> slope  = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{8-1}{6-0} = \frac{7}{6}[/tex]

2) The given points [tex](x_1,y_1) =(-1,10)[/tex] and [tex](x_2,y_2) = (-5,-4)[/tex] then,

=> Slope = [tex]\frac{-4-10}{-5+1} = \frac{-14}{-4}=\frac{7}{2}[/tex]

3)  The given points [tex](x_1,y_1) =(-10,2)[/tex] and [tex](x_2,y_2) = (-3,-5)[/tex] then,

=> slope = [tex]\frac{-5-2}{-3+10} = \frac{-7}{7}=-1[/tex]

4)  The given points [tex](x_1,y_1) =(-3,-4)[/tex] and [tex](x_2,y_2) = (-1,-8)[/tex] then,

=> slope = [tex]\frac{-8+4}{-1+3} = \frac{-4}{2}=-2[/tex]

5)The given points [tex](x_1,y_1) =(0,1)[/tex] and [tex](x_2,y_2) = (-9,-9)[/tex] then,

=> slope = [tex]\frac{-9-1}{-9+0} = \frac{-10}{-9}=\frac{10}{9}[/tex]

Hence the slopes are,

1) 7/6

2)7/2

3) -1

4) -2

5) 10/9

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A person pays $1 to play a certain game by rolling a single die once. if a 1 or 2 comes up, the person wins nothing. if, however, the player rolls a 3, 4, 5, or 6 he or she wins the difference between the number rolled and $1, this means that the game is not fair, based on the expected value

We can see that the expected value of the game can be found by multiplying each payout by its probability of occurring and then summing up the results:Expected value = (0.2)($1) + (0.2)($1) + (0.2)($2) + (0.2)($3) + (0.2)($4) + (0.2)($0) + (0.2)($0)Expected value = $0.40 Since the expected value of the game is positive, it means that, over the long run, players are expected to make money on average. This means that the game is not fair.

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Answer:

The answer to 1 + 1 is 2.

Very complicated problem, please mark brainliest!

Answer:

1+1 = 2

Or, 1=2-1

1=1

we know value of one is one

so,

1+1=11

Answer:

Point-Slope Form: y - 1 = -1/2(x - 4) or Standard Form: y = -1/2x + 3

Step-by-step explanation:

For a line to be perpendicular, you take the negative inverse of the slope of 2x - y = 4. To do this, rearrange the y to one side and you get y = 2x - 4. The slope of the line is 2. So, taking the negative inverse would be -1/m (with m being slope of the the equation given in the problem. This would give you -1/2.

Using point slope formula, y - y1 = m(x - x1), you can plug in the point given, (4,1) and the slope you found to get y - 1 = -1/2(x - 4). For standard form, isolating the y gets you y = -1/2x + 3.

You can check your answer by using Desmos by putting in the line 2x - y = 4, the point (4,1), and the equation you got as your answer. You will see that the equation is perpendicular to 2x - y = 4 and passes through point (4,1). Your equation of the line is y - 1 = -1/2(x - 4) or y = -1/2x + 3

The probability that an 18-year-old man selected at random is between 70 and 72 inches tall is approximately 0.0793 and the probability that the mean height of a sample of eight 18-year-old men is between 70 and 72 inches is approximately 0.9057 and the probability in part (b) is much higher because the standard deviation is smaller for the x distribution.

What do you mean by normally distributed data?

In statistics, a normal distribution is a probability distribution of a continuous random variable. It is also known as a Gaussian distribution, named after the mathematician Carl Friedrich Gauss. The normal distribution is a symmetric, bell-shaped curve that is defined by its mean and standard deviation.

Data that is normally distributed follows the pattern of the normal distribution curve. In a normal distribution, the majority of the data is clustered around the mean, with progressively fewer data points further away from the mean. The mean, median, and mode are all the same in a perfectly normal distribution.

Calculating the given probabilities :
(a) The probability that an 18-year-old man selected at random is between 70 and 72 inches tall can be found by standardizing the values and using the standard normal distribution table. First, we find the z-scores for 70 and 72 inches:

[tex]z-1 = (70 - 71) / 5 = -0.2[/tex]

[tex]z-2 = (72 - 71) / 5 = 0.2[/tex]

Then, we use the table to find the area between these two z-scores:

[tex]P(-0.2 < Z < 0.2) = 0.0793[/tex]

So the probability that an 18-year-old man selected at random is between 70 and 72 inches tall is approximately 0.0793.

(b) The mean height of a sample of eight 18-year-old men can be considered a random variable with a normal distribution. The mean of this distribution will still be 71 inches, but the standard deviation will be smaller, equal to the population standard deviation divided by the square root of the sample size:

[tex]\sigma_x = \sigma / \sqrt{n} = 5 / \sqrt{8} \approx 1.7678[/tex]

To find the probability that the sample mean height is between 70 and 72 inches, we standardize the values using the sample standard deviation:

[tex]z_1 = (70 - 71) / (5 / \sqrt{8}) \approx -1.7889[/tex]

[tex]z_2 = (72 - 71) / (5 / \sqrt{8}) \approx 1.7889[/tex]

Then, we use the standard normal distribution table to find the area between these two z-scores:

[tex]P(-1.7889 < Z < 1.7889) \approx 0.9057[/tex]

So the probability that the mean height of a sample of eight 18-year-old men is between 70 and 72 inches is approximately 0.9057.

(c) The probability in part (b) is much higher because the standard deviation is smaller for the x distribution. When we take a sample of eight individuals, the variability in their heights is reduced compared to the variability in the population as a whole. This reduction in variability results in a narrower distribution of sample means, with less probability in the tails and more probability around the mean. As a result, it becomes more likely that the sample mean falls within a given interval, such as between 70 and 72 inches.

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By using  Bayes' theorem in probability.

a) The probability that isaac would not become a hurricane but remain a tropical storm when it reached the gulf of mexico is 0.31.

b) P(H|c) = 0.4493

c) It can be observed that the likelihood of a tropical storm developing into a hurricane decreases slightly when it passes over Cuba. This can be inferred from the fact that the conditional probability of a hurricane forming given that the storm has passed over Cuba (P(H|c) = 0.4493) is lower than the initial probability of 0.69.

a) The probability that Isaac would not become a hurricane but remain a tropical storm when it reached the Gulf of Mexico is:

P(not hurricane) = 1 - P(hurricane) = 1 - 0.69 = 0.31

So the probability is 0.31 (to 2 decimals).

b) We need to use Bayes' theorem to calculate the probabilities:

P(c|H) = P(H|c) * P(c) / P(H)

P(c|T) = P(T|c) * P(c) / P(T)

where c denotes passing over Cuba, H denotes becoming a hurricane, and T denotes remaining a tropical storm.

From the problem, we have:

P(H) = 0.69

P(T) = 1 - P(H) = 0.31

P(c|H) = 0.08

P(c|T) = 0.20

To calculate P(c), we need to use the law of total probability:

P(c) = P(c|H) * P(H) + P(c|T) * P(T)

= 0.08 * 0.69 + 0.20 * 0.31

= 0.1228

Now we can calculate P(c|H) and P(c|T):

P(c|H) = 0.08 * 0.69 / 0.1228

= 0.4493 (to 2 decimals)

P(c|T) = 0.20 * 0.31 / 0.1228

= 0.5065 (to 2 decimals)

To calculate P(H|c), we use Bayes' theorem again:

P(H|c) = P(c|H) * P(H) / P(c)

= 0.08 * 0.69 / 0.1228

= 0.4493 (to 4 decimals)

c) Passing over a landmass such as Cuba can alter the probability of becoming a hurricane because it can either enhance or weaken the storm. In this case, we can see that the probability of becoming a hurricane is actually slightly lower when a tropical storm passes over Cuba, as P(H|c) = 0.4493 is lower than the initial probability of 0.69. However, it is important to note that this is just one example and the effect of passing over a landmass can vary depending on many factors.

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The missing amounts for Walco Corporation and Gunther Enterprises assuming  all changes in stockholders equity are due to changes in retained earnings are
(a) Walco Corporation Total Stockholders' Equity =  $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues =  $135,100

A balance sheet is a financial statement that reports a company's assets, liabilities, and stockholder equity on a specific date. Assets are resources a company owns that have monetary value, liabilities are obligations that must be paid in the future, and stockholder equity is the difference between a company's assets and liabilities. To calculate the missing amounts, you need to subtract the beginning of year figures from the end of year figures.

a) Total liabilities + Total stockholders' equity = Total assets

Total liabilities + $54,000 = $100,000

Total liabilities = $46,000

(b) Total assets = Total liabilities + Total stockholders' equity

Total assets = $128,000 + $54,000

Total assets = $182,000

(c) Changes during year in retained earnings = Total revenues - Total expenses - Dividends

Changes during year in retained earnings = $219,000 - $167,000 - $4,900

Changes during year in retained earnings = $47,100

The missing values for Gunther Enterprises:

(d) Total liabilities + Total stockholders' equity = Total assets

$67,500 + $(e) = $159,000

$(e) = $91,500

(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends

Changes during year in retained earnings = $(f) - $79,000 - $4,900

Changes during year in retained earnings = $(f) - $83,900

Using the balance sheet equation, we can find the missing values:

(d) Total liabilities = Total assets - Total stockholders' equity

Total liabilities = $159,000 - $67,500

Total liabilities = $91,500

(e) Total stockholders' equity = Total assets - Total liabilities

Total stockholders' equity = $190,000 - $50,000

Total stockholders' equity = $140,000

(f) Changes during year in retained earnings = Total revenues - Total expenses - Dividends

Changes during year in retained earnings = $219,000 - $79,000 - $4,900

Changes during year in retained earnings = $135,100

Therefore, the missing amounts are:

(a) Walco Corporation Total Stockholders' Equity =  $54,000
(b) Walco Corporation Total Assets = $182,000
(c) Walco Corporation Dividends = $47,100
(d) Gunther Enterprises Total Liabilities = $140,000
(e) Gunther Enterprises Total Stockholders' Equity = $91,500
(f) Gunther Enterprises Total Revenues =  $135,100

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To make the table of 7, using the table of 4 and 3, we add the value of both table consecutively.

We have to make the table of 7, using table of 4 and 3.

As we know the table of 3 is:

3  6  9  12  15  18  21  24  27  30

As we know the table of 4 is:

4  8  12  16  20  24  28  32  36  40

To from the table of 7 using the table of 4 and 3 we add the consecutive value of both table respectively.

3 + 4    6 + 8    9 + 12    12 + 16    15 + 20    18 + 24    21 + 28    24 + 32      27 + 36    30+40

Now simplify

7    14    21    28    35    42    49    56    63    70

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The complete question is:

Math 4th 11-4: Help bunty to make the table of 7, using table of 4 and 3.

Answer:

Step-by-step explanation:

i think you have to times it

The distribution is skewed to the right.

If the median is to the left of the center of the box and the right whisker is substantially longer than the left whisker in a box plot, then the distribution is skewed to the right.

This means that the majority of the data is clustered on the left side of the box plot and there are some extreme values on the right side that are causing the right whisker to be longer.

The median being to the left of the center of the box indicates that the data is not symmetric and is pulled to the left by the majority of the values.

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The triangle LMN, with vertices L(6, −8), M(4, −4), and N(−12, 2), dilated with respect to the origin by a scale factor of 1/2, results in triangle L'M'N', with vertices L'(3, -4), M'(2, -2), and N'(-6, 1)

To dilate a triangle with respect to the origin, we need to multiply the coordinates of each vertex by the scale factor. In this case, the scale factor is 1/2, so we multiply each coordinate by 1/2.

The coordinates of L' are obtained by multiplying the coordinates of L by 1/2:

L'((1/2)6, (1/2)(-8)) = (3, -4)

The coordinates of M' are obtained by multiplying the coordinates of M by 1/2:

M'((1/2)4, (1/2)(-4)) = (2, -2)

The coordinates of N' are obtained by multiplying the coordinates of N by scale factor 1/2:

N'((1/2)×(-12), (1/2)×2) = (-6, 1)

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The given question is incomplete, the complete question is:

Triangle LMN with vertices L(6, −8), M(4, −4), and N(−12, 2) is dilated with respect to origin by a scale factor of 2 to obtain triangle L′M′N′. What are the new coordinates of  L′M′N′ ?

Answer:

(2, 0) and (-1, 0)

Step-by-step explanation:

[tex]4x^2 - 4x - 8 = 0 \text{ // Divide by 4} \\x^2 - x - 2 = 0\\\\x_{1, 2} = \frac{-(-1) \pm \sqrt{(-1)^2 - 4 \times 1 \times (-2)}}{2\times1}\\\\x_{1, 2} = \frac{1 \pm \sqrt{1 + 8}}2\\\\x_{1, 2} = \frac{1 \pm \sqrt9}2\\\\x_{1, 2} = \frac{1 \pm 3}2\\\\x_1 = \frac{1 + 3}2 = \frac42 = 2\\\\x_2 = \frac{1 - 3}2 = \frac{-2}2 = -1[/tex]

Therefore, the zeroes are (2, 0) and (-1, 0).

An assignment of probabilities to events in a sample space must obey all of the following: They must obey the addition rule for disjoint events, They must sum to 1 when adding over all events in the sample space, and The probability of any event must be a number between 0 and 1, inclusive. Hence, the correct option is All of the above.

Probability is the branch of mathematics that deals with the likelihood of a random event occurring. Probability is concerned with quantifying the probability of different results in a certain event.

The possibility that a specific event will occur is calculated using probability. Probability is calculated using several methods in mathematics, including axioms, probability spaces, events, random variables, and expectation values.

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Answer:

operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.

Answer:

operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.

Step-by-step explanation:

Random sampling 50 batteries throughout the day and testing to see if they would provide most valid results.

A sample is described as a smaller, more manageable representation of a larger group. A smaller population with characteristics of a larger one. A sample is used in statistical analysis when the population size is too large to include all participants or observations in the test.

The sample may be biased if it is taken from the first 25 batteries made each day or the last 25 batteries made each day.

The first and last battery made each day could not be an accurate representation of the total quality of the batteries produced that day if the battery manufacturing process is not consistent thought the day.

Although the battery quality can change during the day, sampling the first 50 batteries produced each day may also add bias into the sample.

The ideal course of action is to randomly select 50 batteries throughout the day, since this helps to ensure that the sample is reflective of the general calibre of batteries manufactured that day.

A more accurate image of the quality of the batteries manufactured can be obtained using this method, which is also more likely to capture any variations in battery quality over the day.

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The measure of ∠J in ΔJKL is approximately 57.5 degrees.

The measure of ∠J in ΔJKL can be found using the trigonometric function tangent, which is defined as the ratio of the opposite side to the adjacent side.

The straight line that "just touches" the plane curve at a given point is called the tangent line in geometry. It was defined by Leibniz as the line that passes through two infinitely close points on the curve.

tan(∠J) = JK/KL

tan(∠J) = 7.3/4.7

∠J = arctan(7.3/4.7)

∠J = 57.5 degrees (rounded to the nearest tenth of a degree)

Therefore, the measure of ∠J in ΔJKL is approximately 57.5 degrees.

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The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.

We have,

To find the work required to pump all the water out of the rectangular swimming pool, we can use the concept of work as the force multiplied by the distance.

First, let's calculate the weight of the water in the pool.

The weight of an object is given by the formula:

Weight = mass x gravitational acceleration

Since the density of water is given as 1 lb/ft³, we need to find the volume of water in the pool.

The volume of the pool is given by the formula:

Volume = length x width x depth

Volume = 50 ft x 30 ft x 6 ft = 9000 ft³

Now, let's calculate the weight of the water:

Weight = density x volume x gravitational acceleration

Weight = 1 lb/ft³ x 9000 ft³ x 32.2 ft/s² ≈ 290,400 lb

To pump all the water out over the top, we need to raise it to the height of the pool, which is 8 ft.

The work required to pump the water out is given by the formula:

Work = weight x height

Work = 290,400 lb x 8 ft = 2,323,200 ft-lb

Therefore,

The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.

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Answer:

-21

Step-by-step explanation:

y^2 + 8y - 9                       y = -6

(-6)² + 8(-6) - 9

36 - 48 - 9

-21

So, the answer is -21

Answer:y=\frac{7}{12}-i\frac{\sqrt{167}}{12},\:y=\frac{7}{12}+i\frac{\sqrt{167}}{12}

Step-by-step explanation:y=\frac{7}{12}-i\frac{\sqrt{167}}{12},\:y=\frac{7}{12}+i\frac{\sqrt{167}}{12}

Therefore, Person A is approximately 95.17 miles away from the building.

To find out how far person A is from the building, we'll need to use trigonometry. The diagram below shows the situation.

Given that Person A's angle of elevation to the building is 35 degrees, we'll let angle BAC be 35 degrees.

Similarly, since Person B's angle of elevation is 77 degrees, we'll let angle ABC be 77 degrees. We'll also let AB be x, the distance from Person A to the building, and BC be 8 miles, the distance from Person B to the building.

First, we'll use the tangent function to find the height of the building. In triangle ABC, tan(77) = height/8. Solving for the height, we get:

height = 8tan(77) ≈ 61.23 miles.

Next, we'll use the tangent function again to find x. In triangle ABC, tan(35) = height/x + 8. Solving for x, we get:

x = (height)/(tan(35)) - 8
≈ 103.17 miles - 8
≈ 95.17 miles.
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