match the following. 1. a length equal to the height in a square 2. any rhombus can be created by rotating this shape around the midpoint of its base 3. found by dividing 360 by the number of sides of a regular polygon 4. height of a parallelogram 5. each angle in a rectangle 6. a special type of trapezoid 7. perpendicular distance from the center of a regular polygon to its side 8. a special type of regular polygon
Altitude
base
apothem
parallelogram
isosceles triangle
right angle central angle

a. The mean of X is 1.7549 and the standard deviation is 0.3536.

b. To calculate the proportion of washing machines that will last for more than 15 years, we need to use the standard normal distribution table. The z-score for 15 years is (15-14)/0.3536 = 2.822. Using the table, we find that the proportion of washing machines that will last for more than 15 years is 0.9968.

c. To calculate the proportion of washing machines that will last for less than 10 years, we need to use the standard normal distribution table. The z-score for 10 years is (10-14)/0.3536 = -2.822. Using the table, we find that the proportion of washing machines that will last for less than 10 years is 0.0032.

d. To calculate the 90th percentile of the life of the washing machines, we need to use the standard normal distribution table. The z-score for the 90th percentile is 1.28. Using the table, we find that the 90th percentile is 17 years.

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Step-by-step explanation:

9+8=17

for ratio 9: 9/17 * 450=R238.24

for ratio 8: 8/17* 450= R211.17

Answer:

6/11 = 0.54

Step-by-step explanation:

Answer: Yes you are correct

Step-by-step explanation:

I inserted in an image below to help you with the rule.

The 1st point  is (6,1) . This becomes (1,-6).

The 2nd point is (-5,-6). This becomes (-6, 5)

The customers of Rhythm Time, an online music service, downloaded 397,970 songs last year.

Rhythm Time, an online music service, had 278,579 songs downloaded this year by its customers. That figure is 30% less than last year. Last year

We can begin by assuming that the total number of songs downloaded last year was x. According to the problem statement, 278,579 songs were downloaded this year, which is 30% less than last year. We can write it as an equation:x - 0.30x = 278,579 Simplifying, we get:0.70x = 278,579 Dividing both sides by 0.70, we get:x = 397,970Therefore, last year, Rhythm Time's customers downloaded 397,970 songs.

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Answer: y is equal to 8

Step-by-step explanation:

by substituting the x for its vale of three we can add the two values to get 8 or y=8

Answer:

39.77 -> 39 or 40, depending on rounding

Step-by-step explanation:

Since 2002-1992 is 10. T would equal 10. At that point, it would be a gesture of plugging in 10 whereever you see a "t" and solve for both

Answer:

i think 16 im not sure

Step-by-step explanation:

The probability that a randomly selected quartz timepiece will have a replacement time less than 13.3 years is approximately 0.015 with a mean of 17 years and a standard deviation of 1.7 years.

To find the probability that a randomly selected quartz timepiece will have a replacement time of less than 13.3 years, we need to use the standard normal distribution formula which is as follows:

[tex]Z =\frac{X -μ }{σ}[/tex]

Where Z is the standard score

X is the variable value

μ is the mean

σ is the standard deviation

Given that the mean (μ) of the replacement times for the quartz timepieces is 17 years, the standard deviation (σ) is 1.7 years, and the variable value (X) we are looking for is 13.3 years.

Substitute the values into the standard normal distribution formula to get:

[tex]Z = \frac{13.3-17}{1.7} = -2.17[/tex]

Looking at the standard normal distribution table, we can find the probability of the standard score Z = -2.17 to be 0.015.

Therefore, the probability that a randomly selected quartz timepiece will have a replacement time less than 13.3 years is approximately 0.015.

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The probability that a continuous random variable is equal to a single number zero because the area under a continuous probability density function (pdf) between any two points, even two extremely close points, is never equal to zero.

In other words, since the continuous random variable is infinite and continuous, the probability that it is equal to a single value is almost zero.

Steps in Hypothesis Testing:State the null and alternative hypotheses.Calculate the test statistic.

Determine the critical value or p-value.Calculate the p-value, if necessary.Make a decision and interpret the results.

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The given square with a side length of one unit is known to contain five points. One must prove that at least two of these points are within square root 2/2 units of each other.

According to the Pigeonhole principle, "if n items are put into m containers, with n > m, then at least one container must contain more than one item."In this context, the square is the container, and the points inside it are the objects. If more than four points are picked, the theorem is true, and two points are nearer to each other than the square root of 2/2 units.

Let's place four points on the square's four corners. The distance between any two of these points is the square root of two units since the square's side length is 1.

Let's add another point to the mix. That point is either inside the square or outside it. Without loss of generality, let us assume that the point is inside the square. It must then be within the perimeter outlined by joining the square's corners to the point that was not a corner already.

The perimeter of the square described above is a square with a side length of square root 2 units.

Since we have five points in the square, at least two of them must be in the same smaller square, due to the pigeonhole principle. Without loss of generality, let's assume that two of the points are in the upper-left square. As a result, any points within this square are within the square root 2 units of any of the other four points. Hence, at least two points of the five selected are within the square root of 2/2 units of each other.

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Let n be a positive integer. We can use the properties of modular arithmetic to calculate this remainder. Let's start with a = (32n + 4)-1 mod 9. We can rewrite this as a = 9 - (32n + 4)-1 because 9 = 0 mod 9.

We can use Fermat's Little Theorem to calculate (32n + 4)-1. This theorem states that (32n + 4)-1 mod 9 = (32n + 4)8 mod 9.

Using the identity (a + b)n mod m = ((a mod m) + (b mod m))n mod m, we can simplify the equation to (32n mod 9 + 4 mod 9)8 mod 9.

32n mod 9 = 0, so (32n mod 9 + 4 mod 9)8 mod 9 = 48 mod 9 = 1.

Finally, a = 9 - 1 = 8 mod 9, so the remainder when a is divided by 9 is 8.

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The number of minutes needed to complete a job, m, varies inversely with the number of workers, w.

Three workers can complete a job in 30 minutes.

To find, out how many minutes would it take 6 workers to complete the job.

The formula used for inverse variation is, m1w1 = m2w2

Where, m1 = 30,

w1 = 3,

m2 = ?

and w2 = 6

Substitute the given values in the above formula, 30 × 3 = m2 × 6

Simplify the above expression,90 = 6m2

Divide both sides by 6,90 / 6 = m2m2 = 15

Hence, it will take 15 minutes for 6 workers to complete the job.

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Therefore, when the equation  x = 72 - 3x, the value of 2 - 3x is -52.

An equation is a mathematical statement that shows the equality of two expressions. It typically contains one or more variables, which are symbols that can represent any number or value. The expressions on both sides of the equal sign are called the left-hand side (LHS) and the right-hand side (RHS) of the equation. Equations are used to describe relationships between quantities or to solve problems. They can be represented in various forms, including linear equations, quadratic equations, exponential equations, and trigonometric equations. Equations can be solved by performing operations on both sides of the equation to isolate the variable or variables.

Here,

When we are given that x = 72 - 3x, we can solve for x by first adding 3x to both sides of the equation:

x + 3x = 72

Combining like terms, we get:

4x = 72

Dividing both sides by 4, we get:

x = 18

Now that we know x = 18, we can substitute this value into the expression 2 - 3x:

2 - 3x = 2 - 3(18)

2 - 3x = 2 - 54

2 - 3x = -52

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The volume of the solid is 2160ft^3

Volume of Cuboid is the multiplication of length breath and height.

We know that, Volume of Cuboid = l×b×h

put the given values from figure,

= 12×10×15

=1800ft^3

Volume of top = Area of triangle × length

= 1/2 × 4× 12× 15

=360ft^3

Total volume= 1800 + 360

= 2160ft^3

Therefore, the volume of the solid is 2160ft^3

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Cuboid: According to the question the volume of the solid is [tex]2160ft^3[/tex].

A cuboid is a three-dimensional geometric shape which is composed of six rectangular faces. It has 12 edges and 8 vertices. It is also referred to as a rectangular prism. The three dimensions of a cuboid are its length, width, and height. The cuboid is a versatile shape that can be used in many different ways and can be seen in everyday objects such as boxes, desks, and bookshelves. It is also a common shape for mathematically-based problems such as calculating the volume of a cuboid.

We know that, Volume of Cuboid = l×b×h
put the given values from figure,
= 12×10×15
=[tex]1800ft^3[/tex]
Volume of top = Area of triangle × length
= 1/2 × 4× 12× 15
=[tex]360ft^3[/tex]
Total volume= 1800 + 360
= [tex]2160ft^3[/tex]
Therefore, the volume of the solid is [tex]2160ft^3[/tex]

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By the congruence postulate, we have shown that the quadrilateral is  ΔAED ≅ ΔCED.

Let's start by showing that AD = CD. Since AB = AD and BC = CD, we can rewrite AB + BC as AD + CD. This means that AD = AB + BC - CD. But we know that AB = AD, so we can substitute AD for AB to get AD + BC = 2AD + CD. Simplifying this equation, we get AD = CD.

Next, we can show that AE = CE. Since AC is a diagonal of the kite, we know that AC bisects angle BAD and angle BCD. This means that angle BAC = angle DAC and angle BDC = angle CDC. Since AD = CD, we know that triangle ACD is isosceles, so angle ACD = angle CAD.

Using these angle equalities, we can conclude that angle CAE = angle CDE. Since AC ⊥ BD, we know that angle CAD = angle CDE, so we can conclude that triangle ACE is isosceles, which means that AE = CE.

Finally, we need to show that angle AED = angle CED. Since AD = CD and AE = CE, we know that triangles AED and CED have two pairs of congruent sides. Additionally, we know that AC is a common side of the triangles.

Since AC is perpendicular to BD, we know that angle ACD and angle BDC are complementary angles.

This means that angle ACD = 90 - angle BDC and angle CAD = 90 - angle BAC. Using these angle equalities, we can conclude that angle AED = angle CED.

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We have that, if they put 40 chips in a hat, each one with the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10, and each number is put on four chips. Four tokens are drawn from the hat at random and without replacement, the value of q/p, q,p as probabilities, will be given by 360, therefore, the correct option is (D) 360

The probability that all four tokens have the same number (p) is equal to the total number of possible outcomes that meet that criterion divided by the total number of possible outcomes.

In this case, there are 10 possible numbers that could come up (1-10). Therefore, there are 10 possible outcomes for the four slips of paper that have the same number. Each outcome has the same probability of 1/10, so p = (1/10)^4 = 1/10000.

The probability that two of the slips have a number a and the other two have a number b (q) is equal to the total number of possible outcomes meeting that criterion divided by the total number of possible outcomes.

In this case, there are 10 possible numbers that could be drawn (1-10) and 2 ways to choose 2 different numbers out of 10, so there are 20 possible outcomes for two of the slips bearing a number and the other two bearing a number b. Each outcome has the same probability of 1/20, so q = (1/20)^4 = 1/3200000.

The ratio of q to p is q/p = 3200000/10000 = 360. Therefore, the value of q/p is 360.

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The coordinates of point C are: C = (2 + (3/2) * √(13), 2 + (3/2) *√ ((13))

How to find coordinates of point?

To find the coordinates of point C, we can use the midpoint formula, which gives the coordinates of the midpoint of a line segment. We know that point C is 3/4 of the way from point A to point B, so it is closer to B than to A. Therefore, we can find the coordinates of C by finding the midpoint of the line segment AB and then moving 3/4 of the distance from the midpoint to B.

The midpoint of AB can be found by averaging the x-coordinates and the y-coordinates of A and B, respectively:

Midpoint M = ((-4 + 8)/2 , (-2 + 6)/2) = (2, 2)

Now, we need to find the distance from M to B and move 3/4 of that distance in the direction of B. We can use the distance formula to find the distance between two points:

distance MB = √((8 - 2)² + (6 - 2)²) = √(36 + 16) = √(52)

So, the distance from M to C is 3/4 of √(52), which is:

distance MC = (3/4) * √(52) = (3/4) * 2 * √(13) = (3/2) * √(13)

To move in the direction of B, we need to add the x-component and y-component of the distance MC to the x-coordinate and y-coordinate of M, respectively:

x-coordinate of C = 2 + (3/2) * √(13)

y-coordinate of C = 2 + (3/2) * √(13)

Therefore, the coordinates of point C are:

C = (2 + (3/2) * √(13), 2 + (3/2) * √(13))

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Answer:

the maximum height is 2 meters

The experimental likelihood that probability the incoming train will be fully occupied is 0.56, or 56%.

It's simple to calculate the likelihood of a simple event occurring by adding the probabilities together. Your overall odds to win something, for instance, are 10% + 25% = 35% if your chances of winning $10 or $20, respectively, are 10% and 25%, respectively.

In this instance, 14 of the 25 arriving trains were completely full.

The following train's likelihood of being full is determined by the proportion of full trains to all other trains.

14/25 are in favor of the upcoming train being fully loaded.

The likelihood that the following train will have every seat taken is 0.56, or 56%.

It either happens or it doesn't, according to the four significant rules of probability. The chance of an event occurring when the probability of it not occurring is put together is always 1. The same principles apply to empirical probability.

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Answer:

1 minute = 1/6

2 minutes = 1/3

3 minutes =1/2

Step-by-step explanation:

one can eat a bag in 15 minutes so in 1 minute this cat can eat 1/15 of a bag

the other cat can eat a bag in 10 minutes so in 1 minute the cat can eat 1/10 of the bag

to find how much they can eat in 1 minute, add 1/10 and 1/15 which gives you 1/6. to find 2 and 3 minutes just multiply by 1/6 by 2 or 3

c. The mean of the random variable X is calculated as:

mean(X) = (-5)(1/4) + (0)(1/2) + (5)(1/4) = 0

The variance of X is calculated as:

var(X) = (-5 - 0)^2(1/4) + (0 - 0)^2(1/2) + (5 - 0)^2(1/4) = 25/2

d. The mean of the random variable X is calculated as:

mean(X) = (-5)(.01) + (0)(.98) + (5)(.01) = 0

The variance of X is calculated as:

var(X) = (-5 - 0)^2(.01) + (0 - 0)^2(.98) + (5 - 0)^2(.01) = 50.25

e. The mean of the random variable X is calculated as:

mean(X) = (-50)(.0001) + (0)(.9998) + (50)(.0001) = 0

The variance of X is calculated as:

var(X) = (-50 - 0)^2(.0001) + (0 - 0)^2(.9998) + (50 - 0)^2(.0001) = 500

g. The mean of the random variable X is calculated as:

mean(X) = (0)(1/2) + (2)(1/2) = 1

The variance of X is calculated as:

var(X) = (0 - 1)^2(1/2) + (2 - 1)^2(1/2) = 1

h. The mean of the random variable X is calculated as:

mean(X) = (.01)(.01) + (1.01)(.99) = 1

The variance of X is calculated as:

var(X) = (.01 - 1)^2(.01) + (1.01 - 1)^2(.99) = .098

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According to the solving  the annual rate of depreciation is approximately 4.77%.

Annual percentage rate (APR) is the word used to define the annual interest that is generated by a payment that is due to investors or assessed to borrowers. The annual percentage rate, or APR, is a gauge of how much it actually costs to borrow cash over the duration of a loan or the income from an investment.

V = V0 * e[tex]^(^-^r^t^)[/tex]

where:

V0 is the initial value of the asset (in this case, $35,000)

V is the current value of the asset (in this case, $26,796.88)

r is the annual rate of depreciation (what we want to find)

t is the time elapsed (in years)

We know that the time elapsed is 2021 - 2014 = 7 years.

26,796.88 = 35,000 * e[tex]^(^-^7^r^)[/tex]

Dividing both sides by 35,000, we get:

0.766195 = e[tex]^(^-^7^r^)[/tex]

ln(0.766195) = -7r

Solving for "r", we get:

r = -ln(0.766195) / 7

r ≈ 0.0477

the annual rate of depreciation is approximately 4.77%.

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120 is 30 percent of 400

the HCF of x, 2y, 3y, 4z, x², 3z, and 5, where x, y, z are

distinct prime numbers is 1.

To find the highest common factor (HCF) of the given numbers, we need to find the common factors of each pair of numbers and then find the highest common factor of all the resulting common factors.

First, let's find the prime factors of the given numbers:

x = a prime number (distinct from y and z)

2y = 2 × y

3y = 3 × y

4z = 2² × z

3z = 3 × z

x² = a prime number squared (distinct from y and z)

5 = a prime number

Next, we can pair up the numbers and find their common factors:

Common factors of x and 2y: 1, 2, y

Common factors of 3y and 4z: 1, 2, 3, y, z, 6

Common factors of x² and 3z: 1, 3, x, z, xz

Common factors of 5 and 2: 1

Finally, we find the highest common factor of all the resulting common factors:

The highest common factor of x, 2y, 3y, 4z, x², 3z, and 5 is 1, since it is the only factor that is common to all the pairs.

Therefore, the HCF of x, 2y, 3y, 4z, x², 3z, and 5 is 1.

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The factοred fοrm οf a pοlynοmial is

1. 30b³- 54b² = 6b²(5b−9)

2. 3y⁵ - 48y³ = 3y³(y  −4)(y + 4)

3. x³ + 8 = (x + 2) (x² – 2x + 2²)

4. y³ - 64 = (y - 4) (y² – 4y + 4²)

5.  8c³ + 343(2c + 7)(4c² − 14c + 49)

The factοred fοrm οf a pοlynοmial is represented as a³ + b³ = (a + b) (a² – ab + b²). All equatiοns are cοmpοsed οf pοlynοmials. Earlier we've οnly shοwn yοu hοw tο sοlve equatiοns cοntaining pοlynοmials οf the first degree, but it is οf cοurse pοssible tο sοlve equatiοns οf a higher degree.

One way tο sοlve a pοlynοmial equatiοn is tο use the zerο-prοduct prοperty. If yοu remember frοm earlier chapters the prοperty οf zerο tells us that the prοduct οf any real number and zerο is zerο.

We will use the formula

a³ + b³ = (a + b) (a² – ab + b²)

And

a³ - b³ = (a - b) (a² – ab + b²)

1. [tex]30b^3-\ 54b^2[/tex]

⇒ 6b²(5b−9)

2. 3y⁵ - 48y³

⇒ 3y³(  y² - 16y)

⇒ 3y³(  y² - 4 + 4 - 16y)

⇒ 3y³(y  −4)(y + 4)

3. x³ + 8

⇒ x³ + 2³

Using a³ + b³ = (a + b) (a² – ab + b²)

⇒ x³ + 2³

⇒ (x + 2) (x² – 2x + 2²)

4. y³ - 64

⇒ y³ -  4³

Using a³ - b³ = (a - b) (a² – ab + b²)

⇒ y³ -  4³

⇒ (y - 4) (y² – 4y + 4²)

5. 8c³ + 343

Using a³ + b³ = (a + b) (a² – ab + b²)

2c + 7

(2c + 7)(4c² − 14c + 49)

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The suggest that the method is effective.

Assuming different groups of couples use a particular method of gender selection and each couple gives birth to one baby, the probability of a girl is 0.5, and the groups consist of 17 couples, then:

a. The mean is μ= 8.5, and the standard deviation is σ= 3.5.

b. The values separating results that are significantly low or significantly high are 8.5 girls or fewer are significantly low, and 11.5 girls or greater are significantly high.

c. The result of 15 girls is significantly high, because 15 girls is greater than 11.5 girls. This would suggest that the method is effective.

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Answer:

The volume of a solid hemisphere with radius r is given by the formula:

V = (2/3)πr^3

In this case, the radius of the hemisphere is 2 cm. Substituting this value into the formula, we get:

V = (2/3)π(2 cm)^3

V = (2/3)π(8 cm^3)

V = (16/3)π cm^3

Therefore, the volume of the solid hemisphere is (16/3)π cubic centimeters.

Answer:

(16/3)π cm³ ≈ 16.76 cm³ (nearest hundredth)

Step-by-step explanation:

The volume of a solid hemisphere is given by the formula:

[tex]\boxed{V = \dfrac{2}{3}\pi r^3}[/tex]

where r is the radius of the hemisphere.

Substitute the given radius, r = 2 cm, into the formula, and solve for V:

[tex]\begin{aligned}\implies V &= \dfrac{2}{3}\pi(2)^3\\\\&= \dfrac{2}{3}\pi \cdot 8\\\\&= \dfrac{16}{3}\pi\; \sf cm^3\end{aligned}[/tex]

Therefore, the volume of the solid hemisphere of radius 2 cm is (16/3)π cm³ or approximately 16.76 cm³ (nearest hundredth).

The number of individuals who are homozygous dominant (VV) is 160 individuals, and the number of individuals who are heterozygous (Vv) is 320 individuals.

The population of Drosophila has 1000 individuals, 360 of which display the recessive phenotype. Homozygous dominant and heterozygous for this trait in Drosophila would be expected to be found in how many individuals?

In Drosophila, the dominant allele for normal-length wings is denoted as 'V' and the recessive allele for vestigial wings is denoted as 'v.'To determine the number of individuals who are homozygous dominant or heterozygous for this trait, we'll first determine the number of individuals who are homozygous recessive:

Homozygous recessive individuals in the population = number of individuals displaying the recessive phenotype = 360

This indicate that there are 360 individuals with the genotype vv (homozygous recessive), which will be used to determine the remaining genotypes via the Punnett square. To get the number of individuals who are heterozygous (Vv), we first need to identify the number of individuals with the dominant V allele (VV and Vv). The sum of these two genotypes equals the total number of individuals minus the homozygous recessive individuals, as follows:

Total number of individuals - homozygous recessive individuals = (VV + Vv) individuals+ (vv) individuals = 1000 individuals

Hence, VV + Vv = 1000 - 360 = 640 individuals.Now that we know VV + Vv = 640, we can use the expected genotypic ratio of 1:2:1 to calculate the number of homozygous dominant (VV) and heterozygous (Vv) individuals.1:2:1 represents the expected genotypic ratio in the progeny derived from a cross involving two heterozygotes of the same gene. The first "1" represents the proportion of dominant homozygotes, the second class, or class "2", the heterozygotes, and the second "1" the recessive homozygotes.

Therefore, homozygous dominant (VV) and heterozygous (Vv) individuals in the population would be expected in the following ratio:VV:Vv:vv = 1:2:1. Therefore, the number of individuals who are homozygous dominant (VV) is 1/4 of the total individuals (VV + Vv + vv):

Number of individuals who are homozygous dominant (VV) = 1/4 (VV + Vv + vv)= 1/4 (640) = 160 individuals

And the number of individuals who are heterozygous (Vv) is 2/4 of the total individuals (VV + Vv + vv):

Number of individuals who are heterozygous (Vv) = 2/4 (VV + Vv + vv)= 2/4 (640) = 320 individuals

Therefore, the number of individuals who are homozygous dominant (VV) is 160 individuals, and the number of individuals who are heterozygous (Vv) is 320 individuals.

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Parachutist's rate during free fall is 40 meters per second and will fall approximately 490 meters during 10 seconds of free fall.

First, we need to convert 132 feet per second to meters per second. We know that 1 meter is equal to 3.3 feet, so we can use the following conversion factor:

[tex]$\frac{3meter}{3.3 feet}[/tex]

To convert feet per second to meters per second, we can multiply by the conversion factor:

[tex]132 (\frac{1}{3.3} ) = 40 meters/second[/tex]

Therefore, the parachutist's rate during free fall is 40 meters per second.

Next, we can use the following formula to find the distance the parachutist falls during 10 seconds of free fall:

distance =[tex]\frac{1}{2}[/tex] * acceleration * time²

where acceleration due to gravity is approximately 9.8 meters/second^2.

Substituting the given values, we get:

distance = [tex]\frac{1}{2}[/tex] * 9.8 meters/second² * (10 seconds)²

distance = 490 meters

Therefore, the parachutist will fall approximately 490 meters during 10 seconds of free fall.

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