Determine whether the planes are parallel, perpendicular, or neither. If neither, find the angle between them. x + 4 y − 3 z = 1 , − 3 x + 6 y + 7 z = 0

In the following question, the Total cost to production 50 barstools: $1,200 Total cost to produce 51 barstools: $1,228.91 "Total cost to produce 52 barstools: $1,258.44" Total cost to produce 53 barstools: $1,288.59 Therefore, the approximate total cost of producing 53 barstools is $559.15.

The cost function for producing $x$ items of a certain brand of barstool is given by C(x)=0.01x3-0.6x2+13x+200.

(a) C(x)=0.03x3- 0.12x2+13

(b) MC(50)=-82 dollars per barstool.

It approximately represents the cost of producing the 50th barstool.

(c) The exact cost of producing the 51st barstool is C51=C50+MC(50)=$28.91 dollars.

(d) Using C(50) and MC (50), the total cost of producing 53 barstools is approximately C50+(53-50) MC(50)=$229.82.

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Answer:

148.5 π

Step-by-step explanation:

Cone = 1/3 * base * height

1/3 * 22 * (9/2)^2 π = 148.5 π

The probability of drawing either a queen or a diamond is 15/52

To determine the probability of drawing either a queen or a diamond, we have to find the sum of the probabilities of drawing a queen and drawing a diamond, then subtract the probability of drawing both a queen and a diamond. This is because the probability of drawing both a queen and a diamond has been added twice when we added the individual probabilities.

Thus, we have:P(queen or diamond) = P(queen) + P(diamond) - P(queen and diamond)

The probability of drawing a queen is 4/52, since there are four queens in a deck of 52 cards. The probability of drawing a diamond is 13/52, since there are 13 diamonds in a deck of 52 cards.

There are two ways to draw a card that is both a queen and a diamond, namely the queen of diamonds and the diamond queen. Thus, the probability of drawing both a queen and a diamond is 2/52. Therefore, P(queen or diamond) = 4/52 + 13/52 - 2/52 = 15/52 = 15/4 = 3.75 As a reduced fraction, this is 15/52.

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The width of the automobile parking space is 52.8 meters.

First, we want to convert the duration of the second one base from centimeters to meters

3760 cm = 37.6 m

Subsequent, we're suitable to use the system for the vicinity of a trapezoid

A = ( b1 b2) h/ 2

In which b1 and b2 are the lengths of the two bases, h is the height( or range) of the trapezoid, and A is the area.

Substituting the given values, we have

= (73.437.6) h/ 2

= 111h/ 2

Multiplying both angles through 2 and dividing by 111, we get

h = 52.8

Hence, the width of the automobile parking space is 52.8 meters.

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400 is the total number of toy cards in his collection. This will be the total number of toy cards in his collection if Feng keeps 324 of the toy cars on his wall which is 81% of his entire collection.

A fraction is a mathematical value that illustrates the components of a whole. In general, the whole can be any particular thing or value, and the fraction might be a portion of any quantity out of it. The top and bottom numbers of a fraction are explained by the fundamentals of fractions. The bottom number reflects the entire number of components, while the top number represents the number of chosen or coloured portions of the whole.

Based on the given conditions, formulate: 324/81%

Convert decimal to fraction: 324/81/100

Divide a fraction by multiplying its reciprocal 324 * 100 / 81

Reduce the expression to the lowest term: 4*100

Calculate the product or quotient: 400

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Therefore, the net result of the transaction is a loss of $21.36. The answer is A) $21.36.

Selling price refers to the price at which a product or service is sold to customers or clients. It is the amount of money that a buyer pays to the seller in exchange for the product or service. The selling price is usually higher than the cost of producing or acquiring the product or service, and the difference between the selling price and the cost is the profit earned by the seller. In some cases, the selling price may also include additional charges such as taxes, shipping fees, or handling fees.

by the question.

To calculate the net result of the transaction, we need to determine how many shares were purchased with the $3,200 investment.

$3,200 divided by $11.95/sh = approximately 267.36 shares (rounded to the nearest hundredth)

Therefore, the total cost of purchasing 267 shares at $11.95/sh is:

267 shares x $11.95/sh = $3,195.65

The total revenue from selling 267 shares at $11.87/sh is:

267 shares x $11.87/sh = $3,174.29

To determine the net result of the transaction, we subtract the total revenue from the total cost:

$3,174.29 - $3,195.65 = -$21.36

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Angela's score is in the 87th percentile, which means that 87% of the scores were at or below her score.

To calculate the percentage of scores above her score, we subtract 87% from 100%. Therefore, the percentage of scores above Angela's score is 13%.

In summary, Angela's score is at or below 87% of the scores, and 13% of the scores are above her score. The percentile score indicates the percentage of scores that fall below a particular score. Therefore, Angela performed better than 87% of the test takers who took the aptitude test in accounting.

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Answer:

Step-by-step explanation:

I think a calculator is the only way to solve this question:

[tex]\sqrt{7} +\sqrt{3} = 2.96\\\\\sqrt{6} +\sqrt{4} = 2.54\\\\\sqrt{8} +\sqrt{2} =3.07[/tex]

So (c) is the greatest.

The probability that it the marble taken out of the box is not blue is [tex]\frac{112}{131}[/tex].

Probability is a branch of math that studies the chance or likelihood of an event occurring.
There are [tex]75[/tex] red marbles, [tx]37[/tex] white marbles, and [tex]19[/tex] blue marbles.

If a marble is randomly selected from the box, we have to find the probability that it is not blue.

Then the total number of marbles = [tex]75 + 37 + 19 = 131.[/tex]

The probability that a marble is not blue:-

[tex]P[/tex](Not blue) = [tex]P[/tex](Red or White)

[tex]P[/tex](Red or White) = [tex]\frac{(75 + 37)}{131}[/tex]

[tex]P[/tex](Red or White) = [tex]\frac{112}{ 131}[/tex]

[tex]P[/tex](Not blue) = [tex]1 - P[/tex](Blue)

[tex]P[/tex](Not blue) = [tex]1 - \frac{19}{131}[/tex]

[tex]P[/tex](Not blue) = [tex]\frac{112}{ 131}[/tex]

Therefore, the probability that a marble selected from the box is not blue is [tex]\frac{112}{131}[/tex].

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The probability that a 65-year-old man will survive to reach the age of 70 is 88.4%, and also the probability man to survive till his 75th birthday is approx.59.952%.

The probability of a 65-year-old man reaching the age of 70 is the probability of surviving from age 65 to age 70, which is given as

p(70)/p(65) ⇒ 0.657/0.742 ≈ 0.88544 or 88.544%.

The probability of a man who just turned 70 dying within the next 5 years is 0.176.

Therefore, the probability of surviving for the next 5 years after turning 70 is

⇒ 1 - 0.176 ⇒ 0.824.

Thus, the probability of a man surviving till his 75th birthday is the probability of surviving from age 70 to age 75, which is given as

p(75)/p(70) ⇒ 0.657/0.903 × 0.824

≈ 0.59952 or 59.952%.

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Maria's amount of land first exceeds Lucia's amount of land after 3 months.

To solve this problem, we need to find out when Maria's total amount of land first exceeds Lucia's total amount of land. Let's start by writing out the formulas for the amount of land each woman has after n months

Lucia's land after n months = 11 + 5n

Maria's land after n months = 6 × 1.4^n

Now we want to find the month, n, when Maria's amount of land first exceeds Lucia's amount of land. So we need to solve the following inequality

6 × 1.4^n > 11 + 5n

We can solve this inequality by using a trial-and-error approach or by using a graphing calculator. Here's one way to solve it using trial-and-error

Let's start by plugging in n = 1 and see if Maria's land is greater than Lucia's land:

6 × 1.4^1 = 8.4

11 + 5 × 1 = 16

Since 8.4 < 16, we know that Maria's land is not greater than Lucia's land after 1 month.

Now let's try n = 2

6 × 1.4^2 = 11.76

11 + 5 × 2 = 21

Since 11.76 < 21, we know that Maria's land is still not greater than Lucia's land after 2 months.

Let's keep trying larger values of n until we find the first month when Maria's land is greater than Lucia's land:

n = 3

6 × 1.4^3 = 16.384

11 + 5 × 3 = 26

Since 16.384 > 26, we know that Maria's land is greater than Lucia's land after 3 months.

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The given question is incomplete, the complete question is:

Lucia and Maria are business women who decided to invest their money by buying farmland in Brazil. They started their investments at the same time, and each month they buy more land. Lucia bought 11 hectares of land in the first month, and each month afterwards she buys 5 additional hectares. Maria bought 6 hectares of land in the first month, and each month afterward her total number of hectares increases by a factor of 1.4. In which month will Maria's amount of land first exceed Lucia's amount of land?

The  cd = ab · (an integer), and so ab | cd by definition of divisibility.

The question wants us to prove the following statement using the definition of divisibility. For all integers a, b, c, and d, if aſc and bld, then ab|cd.Definition of divisibility: Let a and b be integers. We say that b divides a or b is a divisor of a if there exists an integer k such that a = bk.

If b divides a, then we write b | a.Let a, b, c, and d be any integers such that alc and b | d. Then by definition of divisibility, c = ar and d = bs for some integers r and s. Then cd equals the product of ab and a number that can be written in terms of r and s as follows:cd = ab · rs, which is an integer because products of integers are integers.

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Yes, the distribution of heights for all adults is approximately normal because normal distribution has a bell-shaped curve. The bell curve indicates that the majority of the data points are located around the mean, with fewer data points on either side. Furthermore, normal distribution has certain characteristics that are relevant to this question.

The average height of men is 69.2 inches, while the average height of women is 63.7 inches. Therefore, we can assume that the mean height for both genders would be approximately 66.45 inches, assuming the distribution is equal (i.e., half male, half female).

If we plot the data of both males and females together, the plot will likely resemble a bell curve as per the properties of normal distribution. Since most adults would fall within the average height range, the distribution of heights for all adults is considered approximately normal. Therefore, we can conclude that the distribution of heights for all adults is approximately normal.

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The number of claims filed by the policyholders has a poisson distribution. Therefore, the variance of the number of claims filed will be about 2.5.

We need to use the Poisson Distribution for solving the question, which is as follows:

P(x) = (λˣ/x!) × [tex]e^(-lambda)[/tex]

where is the mean value of distribution and x is the number of events we want to calculate.

If a random variable follows a Poisson distribution, its variance is equal to its mean.

So, the mean will be λ.

Let the probability of filing four claims be p1.

Then, probability of filing two claims will be ⁵p₁

We know the sum of probabilities of different events of Poisson distribution will always be equal to 1.

So,

p₁ + ⁵p₁ = 1

p₁ = 1/6

The mean number of claims is λ, which is given by:

Now, the variance of the Poisson distribution is also λ.

So, the variance of the number of claims filed is 2.5.

Hence, the answer is variance of the number of claims filed is 2.5.

The mean number of claims is λ, which is given by:

λ = ⁴p₁ + 2⁵p₁ = 2.5

Now, the variance of the Poisson distribution is also λ.

So, the variance of the number of claims filed is 2.5.

Hence, the answer is variance of the number of claims filed is 2.5.

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Answer:

6 29 25

Step-by-step explanation:

those are the prime numbers on the 2023 feb calendar

There will be a population of 2,097,152 rabbits after 5 years.

A form of growth known as exponential growth occurs when a quantity's rate of expansion is proportionate to its present value. In other words, a quantity expands more quickly the greater it is. A prime example of exponential expansion is the rabbit population, which doubles in size every three months.

Given that, population of rabbits is doubling every 3 months.

That is,

5 years = 5 x 12 = 60 months

Number of doublings = 60 / 3 = 20

For every doubling, the population will be twice as large.

Thus,

P = 2 x 2²⁰ = 2 x 1,048,576 = 2,097,152 rabbits

Therefore, there will be approximately 2,097,152 rabbits after 5 years.

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Answer:

[tex] \frac{3}{2} {x}^{8} [/tex]

Step-by-step explanation:

[tex] \frac{9 {x}^{16} }{6 {( {x}^{2} )}^{3}{x}^{2} } = \frac{9 {x}^{16} }{6 {x}^{6} {x}^{2} } = \frac{9 {x}^{16} }{6 {x}^{8} } = \frac{3}{2} {x}^{8} [/tex]

a. The probability of guessing a wrong answer is 4/5

Since there are three guesses, the probability of the first 2 guesses being wrong and the 3rd being correct can be calculated using the multiplication rule as follows: P(2 wrong and 1 correct) = (4/5)^2 * 1/5 = 0.128.

b. The complete list of possibilities for 2 wrong and 1 correct is: WWC, WCW, CWW.

The probability of each can be calculated using the multiplication rule as follows: P(WWC) = (4/5)^2 * 1/5 = 0.128, P(WCW) = (4/5) * (1/5) * (4/5) = 0.128, and P(CWW) = 1/5 * (4/5)^2 = 0.128.

c. The probability of getting exactly one correct answer when 3 guesses are made is the sum of the probabilities of the three possible outcomes of 2 wrong and 1 correct, which is 0.128 + 0.128 + 0.128 = 0.384.

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Making r the subject of formula in this equation A = V²/r gives r = V²/A.

In Mathematics and Science, the centripetal acceleration of a physical object (body) can be calculated by using the following mathematical expression:

A = V²/r

Where:

In this exercise, you are required to make radius (r) the subject of formula. Therefore, by making radius (r) the subject of formula, we have the following:

Radius, r = V²/A

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Therefore, the slope of the line passing through the points (0,5) and (2,0) is -5/2.

In mathematics, slope refers to the measure of steepness of a line. It is the ratio of the change in y (vertical change) over the change in x (horizontal change) between any two points on the line. The slope of a line is represented by the letter "m" and can be calculated using the slope formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Here,

To find the slope of a line, we use the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line.

Using the given coordinates, we have:

x1 = 0, y1 = 5

x2 = 2, y2 = 0

slope = (0 - 5) / (2 - 0)

slope = -5/2

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Answer:

a = 3

Step-by-step explanation:

since the parabola passes through (7, 27 ) then te coordinates of the point make the equation true.

substitute x = 7 and y = 27 into the equation and solve for a

27 = a(7 + 2)(7 - 6) = a(9)(1) = 9a ( divide both sides by 9 )

3 = a

Answer:

its 126 and 54 hope this helps

Answer:

83.6%

Step-by-step explanation:

Let's say the original price is x

x decreased by 12% means 88% of x is left.

0.88x decreased by 5% means 95% of 0.88x is left.

This means the answer is: 0.88x * 0.95 = 0.836

The percent of the total decrease is 83.6%

Hope this helps :)

Have a great day!

To check whether the given lines are parallel, perpendicular, skew or neither, we will find their direction vectors. If the direction vectors are parallel, then the lines are parallel. If the direction vectors are perpendicular, then the lines are perpendicular. If the direction vectors are neither parallel nor perpendicular, then the lines are skew. If the direction vectors of one line is parallel to the vector joining two points of the other line, then the lines are neither parallel nor perpendicular.

Line 1:x=t−3, y=3t+8, z=5−2tThis line can be written as(r_1): r= a_1+ t u_1where r_1 is the position vector of any point on the line. a_1 = i(-3) + j(8) + k(5) = -3i + 8j + 5k is the point of intersection of the line with the coordinate axis. And u_1 is the direction vector of the line.u_1 = i + 3j - 2k

Line 2: x=2s−1, y=s−1, z=s−4This line can be written as(r_2): r= a_2+ s u_2where r_2 is the position vector of any point on the line. a_2 = i(-1) + j(-1) + k(-4) = -i - j - 4k is the point of intersection of the line with the coordinate axis. And u_2 is the direction vector of the line.u_2 = 2i + j + k Now we will find the direction vectors of the two lines and then check their properties. The direction vectors of the lines areu_1 = i + 3j - 2ku_2 = 2i + j + kSince the direction vectors are not parallel, we need to check whether they are perpendicular or not.u_1.u_2 = (i + 3j - 2k).(2i + j + k) = 2 + 3 - 2 = 3Since u_1.u_2 is not equal to zero, the two lines are neither parallel nor perpendicular to each other. Therefore, the lines are skew lines.

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The sugar concentration would be approximately 62.5%.

To find the concentration of sugar in the solution, we need to use the formula:

In this case, the solute is sugar and the solvent is water. We are given that the mass of sugar is 50 grams and the mass of water is 30 grams. However, we need to convert the mass of water to volume since we need the volume of the entire solution to calculate the concentration.

We can assume that the density of water is 1 g/mL, so the volume of water is 30 mL. The total volume of the solution is therefore 50 mL + 30 mL = 80 mL.

Now we can use the formula to find the concentration of sugar:

So the concentration of sugar in the solution is approximately 0.625 grams per milliliter.

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Answer:

75% correct

Step-by-step explanation:

Answer: 1/3

Step-by-step explanation:

The probability of selecting a chocolate cream pie can be found by dividing the number of chocolate cream pies by the total number of pies:

Probability of selecting a chocolate cream pie = Number of chocolate cream pies / Total number of pies

Probability of selecting a chocolate cream pie = 4 / 12

Simplifying this fraction by dividing the numerator and denominator by 4 gives:

Probability of selecting a chocolate cream pie = 1/3

Therefore, the probability of selecting a chocolate cream pie from Annie's Pie Shop is 1/3.

Therefore, the measure of the manila angle is 110 degrees.

The term "degree" can have several different meanings depending on the context. Here are a few possibilities:

Academic degree: This refers to the title or certificate awarded to a student upon the completion of a course of study at a college, university, or other educational institution. Examples of academic degrees include bachelor's degrees, master's degrees, and Doctoral degrees.

by the question.

Assuming that the pink, blue, and manila arcs are all part of the same circle, the sum of their measures must be 360 degrees.

Let's denote the measure of the manila arc as x degrees. Then we can set up an equation to solve for x:

200 degrees (pink arc) + 50 degrees (blue arc) + x degrees (manila arc) = 360 degrees

Simplifying the equation, we can solve for x:

x = 360 degrees - 200 degrees - 50 degrees

x = 110 degrees

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