4. A stone nudged off the Royal Gorge Bridge near Cañon City, Colorado, falls 1053 feet before hitting water. Because its speed increases as it falls, the distance it travels each second increases. During the first second, it drops 16 feet. During the next second, it drops an additional 48 feet. During the third second, it drops another 80 feet. The distances traveled each second form an arithmetic sequence:
16, 48, 80, ...
Part I: How far does the stone fall during the 5th second? Find and use the explicit formula.
a. What is the first term of the sequence? _____
b. What is d, the common difference? _____
c. Write the explicit formula in function notation. Use f(n) = f(1) + (n – 1)d, where f(1) represents the first term. _______________
d. Use the explicit formula to find the distance the stone travels in the 5th second.

a. Mean=5 Median=5 Mode= 1

b. Range=9 Variance=10.16 Standard Deviation=3.19 Coefficient of variation=54.83%

c.  Z score 1.34.  no other z-scores as there is no more data set given

d.  skewed to the left

HTML is a markup language. It is used to structure and present content on the web. Therefore, answering the question formatted with HTML is not necessary. Nonetheless, the following are the solutions to the problem provided below.a. Compute the mean, median, and mode:Mean: (9+5+1+10+4) / 5 = 5.8Median: Arrange the numbers in order: 1, 4, 5, 9, 10. Then the median is the middle value. Hence, median = 5.Mode: The mode is the number that appears most frequently in the set of data. Therefore, the mode of the set of data is 1.b. Competo the range, variance, standard deviation, and coefficient of variation:The range is the difference between the largest and smallest numbers in the set of data. Range = 10 - 1 = 9.Variance: s² = [(9-5.8)² + (5-5.8)² + (1-5.8)² + (10-5.8)² + (4-5.8)²] / 5 = 10.16.Standard deviation: s = √(10.16) = 3.19Coefficient of variation: CV = (3.19 / 5.8) × 100% = 54.83%c. Compute the Z-scores. Are there any others?The formula for Z-score is given by: Z = (x - μ) / s where x = raw score, μ = mean, and s = standard deviation.Z-scores for the set of data are:z₁ = (1 - 5.8) / 3.19 = -1.5z₂ = (4 - 5.8) / 3.19 = -0.56z₃ = (5 - 5.8) / 3.19 = -0.25z₄ = (9 - 5.8) / 3.19 = 1.00z₅ = (10 - 5.8) / 3.19 = 1.34There are no other z-scores as there is no more data set given.d. Describe the shape of the data setThe data set is skewed to the left because the tail is longer in the left direction. It can be observed from the Z-scores, mean, and median, as the mean is less than the median.

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The steps to construct a parallel line to point C consists of drawing an arc from point C to intersect AB at points D and E and with the same radius, placing the compass at D to draw an arc intersecting the previous one at F. Join C and F to complete the construction of the parallel line to AB.

Please find attached the example drawing of the line CF parallel to AB created with MS Word

Parallel lines are lines that maintain the same distance from each other and do not meet.

A more detailed steps to construct a line parallel to AB passing through point C using only a straightedge and a compass includes;

The line that passes through C and G is parallel to AB

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Answer:

a) 7/9 * 2

Because 7*2/9 = 1.555556, which is less than 2.

All the other options' products are greater than 2.

Please mark as brainliest!

DONT FORGET!!

The factored forms of the equations and the intercepts would be:

g(x) = x² - 4x - 21:

h(x) = x² + 8x + 12:

For g(x) = x² - 4x - 21:

To find the factored form, we need to factor the quadratic expression:

g(x) = (x - 7)(x + 3)

To find the x-intercepts, we set g(x) = 0 and solve for x:

(x - 7)(x + 3) = 0

x = 7 or x = -3

To find the y-intercept, we set x = 0 and evaluate g(x):

g(0) = (0 - 7)(0 + 3) = -21

Therefore, the y-intercept of g(x) is (0,-21).

For h(x) = x² + 8x + 12:

h(x) = (x + 2)(x + 6)

To find the x-intercepts, we set h(x) = 0 and solve for x:

(x + 2)(x + 6) = 0

x = -2 or x = -6

To find the y-intercept, we set x = 0 and evaluate h(x):

h(0) = (0 + 2)(0 + 6) = 12

Therefore, the y-intercept of h(x) is (0,12).

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According to the given information, 0.97306, 0.02669, and 0.000005.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

a. The probability that a golfer does not score a hole in one on the sixth hole is [tex]$1 - \frac{1}{3,709}$[/tex]. Since there are 156 golfers, the probability that none of them score a hole in one is

[tex]$$\left(1 - \frac{1}{3,709}\right)^{156} \approx 0.97306$$[/tex]

The probability that no one gets a hole in one on the sixth hole is 0.97306

b. The probability that exactly one golfer gets a hole in one on the sixth hole is

[tex]$${156 \choose 1} \cdot \frac{1}{3,709} \cdot \left(1 - \frac{1}{3,709}\right)^{155} \approx 0.02669$$[/tex]

The probability that exactly one golfer gets a hole in one on the sixth hole is 0.02669

c. The probability that four golfers score a hole in one on the sixth hole is

[tex]$${156 \choose 4} \cdot \left(\frac{1}{3,709}\right)^4 \cdot \left(1 - \frac{1}{3,709}\right)^{156-4} \approx 0.000005$$[/tex]

The probability that four golfers score a hole in one on the sixth hole is 0.000005

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Therefοre , the sοlutiοn οf the given prοblem οf percentage cοmes οut tο be  a)k ≈ 0.0279,b)y = 0.593a  and  c)t ≈ 78.5 .

In statistics, a percentage is a figure οr an integer that is expressed as a fractiοn οf 100. Additiοnally, the wοrds "pct.," "pct," but alsο "pc" are rarely used. The "%" symbοl, hοwever, is cοmmοnly used tο denοte it. There are nο dimensiοns; the percentage tοtal is flat.

Percentages are really just numbers because the numeratοr is 100. Tο indicate that a number is a percentage, either the percent character (%) οr the text "percent" must appear befοre it.

Here,

a) We can apply the exponential decline equation:

=> [tex]y = ae^{(-kt)} (-kt)[/tex]

[tex]0.9a = ae^{(-5k)} (-5k)[/tex]

Using a to divide both sides:

[tex]0.9 = e^{(-5k)} (-5k)[/tex]

Using both sides' natural logarithms:

ln(0.9) = -5k

calculating k:

[tex]k = -ln(0.9)/5[/tex]

k ≈ 0.0279

Consequently, the decline formula's value of k is roughly 0.0279.

b)

[tex]y = ae^{(-kt)} (-kt)[/tex]

[tex]y = an e^{(-0.0279*10)[/tex]

[tex]y = 0.593a[/tex]

As a result, after 10 years, only about 59.3% of the initial DDT is still present.

c)

[tex]0.25a = ae^{(-0.0279t) (-0.0279t)[/tex]

Using a to divide both sides:

[tex]0.25 = e^{(-0.0279t) (-0.0279t)[/tex]

Using both sides' natural logarithms:

ln(0.25) = -0.0279t

calculating t:

t = -ln(0.25)/0.0279

t ≈ 78.5

Therefore, roughly 78.5 years after the ban in 1972, or in the year 2050, the concentration of DDT will drop below 25%.

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Answer:

y=-1/4x+1

Step-by-step explanation:

The cost of 10.0 gallons of gasoline priced at 1.449 per gallon is 14.49.

The cost of 10.0 gallons of gasoline priced at 1.449 per gallon can be determined using the formula Cost = Quantity * Price. To calculate the cost, first multiply 10.0 (the quantity) by 1.449 (the price). This gives the value 14.49, which is the cost of 10.0 gallons of gasoline priced at 1.449 per gallon.

To explain this further, when calculating the cost of an item, we need to take into account both the quantity and the price of that item. The quantity is the amount of the item that we will be purchasing, and the price is the amount that we will be paying for that item. In the case of gasoline, 10.0 gallons is the quantity, and 1.449 is the price per gallon.

To calculate the cost, we need to multiply the quantity by the price. This gives us the cost of the item. In this case, multiplying 10.0 (the quantity) by 1.449 (the price) gives us 14.49, which is the cost of 10.0 gallons of gasoline priced at 1.449 per gallon.

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The side which clοses tο the acute angle will be the adjacent side tο the acute angle and the lοngest side is the Hypοtenuse.

What are Sides οf a right-angled triangle?  

In a right-angled triangle, there are three sides. One side is called the hypοtenuse and the οther twο sides are adjacent tο the right angle and are called the legs οf the triangle.

In a right triangle, the side οppοsite the right angle is always the lοngest side and is called the hypοtenuse. The twο οther sides are called the legs οf the triangle, and οne οf the legs is adjacent tο each οf the acute angles.

Tο determine which side is adjacent tο a specific acute angle, yοu need tο identify which οf the twο legs is clοsest tο that angle. The side clοsest tο the angle is the adjacent side.

Fοr example, if yοu have a right triangle with acute angles A and B, and leg AB is adjacent tο angle A, then leg BC is adjacent tο angle B.

Alternatively, yοu can use the trigοnοmetric functiοns sine, cοsine, and tangent tο determine the relatiοnship between the sides οf a right triangle and its angles.

The side which clοses tο the acute angle will be the adjacent side tο the acute angle and the lοngest side is the Hypοtenuse.

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The missing value that completes the frequency table is 100

A frequency table is just a two-column "t-chart" or table that lists all of the potential outcomes and their corresponding frequencies as seen in a sample.

How to solve:

From the graph given,

The battery life(hours) from x = 15  to x= 20 has a frequency of 130

The battery life(hours) from x= 28 to x= 30 has a frequency of 100

It can be inferred that from the battery life of the different models, the missing value is 100 and when you crosscheck the data, you would find this is correct and accurate.

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The two values of b that make the system inconsistent are b = -4.79 (negative) and b = 4.79 (positive). This is found by setting the discriminant of the quadratic equation in x to be negative.

We can solve this problem by substituting y = 4x + b into the first equation:

x² + (4x + b)² = 25

Expanding the square and simplifying, we get:

x² + 16x² + 8bx + b² - 25 = 0

Combining like terms, we get a quadratic equation in x:

17x² + 8bx + (b² - 25) = 0

For the system to be inconsistent, this quadratic equation must have no real solutions (i.e., the discriminant must be negative). Therefore, we need:

(8b)² - 4(17)(b² - 25) < 0

Simplifying and solving for b, we get:

64b² - 4(17b² - 425) < 0

98b² < 1700

b² < 1700/98

b < ±sqrt(1700/98)

b < ±4.79

Therefore, the two values of b that make the system inconsistent are:

b = -4.79 (negative)

b = 4.79 (positive)

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The total grade for these 37 students is less than 2590.0 is 0.8745.

The distribution of students' grades is not approximately normal(b) If n = 37 students are selected at random, the distribution of the sample mean grade is approximately normal = with a mean of 68 and a standard deviation of 3.2152(c) The probability that the sample mean grade for these 37 students is less than 70.0 is 0.3909 If n = 37 students are selected at random, the distribution of the sample total grade is approximately normal = with a mean of 2516 and a standard deviation of 70.4583 The probability that the total grade for these 37 students is less than 2590.0 is 0.8745 The answer to the question is as follows: The distribution of students' grades is not approximately normal If n = 37 students are selected at random, the distribution of the sample mean grade is approximately normal = with a mean of 68 and a standard deviation of 3.2152.

The probability that the sample mean grade for these 37 students is less than 70.0 is 0.3909(d) If n = 37 students are selected at random, the distribution of the sample total grade is approximately normal = with a mean of 2516 and a standard deviation of 70.4583.

The probability that the total grade for these 37 students is less than 2590.0 is 0.8745. What is unimodal? Unimodal is a term that describes a distribution that has only one mode. A mode is a value that appears most frequently in a dataset, and in a unimodal distribution, there is only one such value.

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Width of the mat is 0.75 m

Answer:Triangle problemGiven a right triangle, perimeter = 198 cm Hypotenuse = 85 cmLet the other sides of the triangle be a and b respectively.To find the value of a and bSolutionWe know that, in a right triangle with sides a and b, and hypotenuse c Pythagoras Theorem can be usedc² = a² + b²Formula for perimeter of a triangle is P = a + b + cFrom the given values, we can substitute the values for P and c.198 = a + b + 85 198 - 85 = a + b 113 = a + bTo get the values of a and b, we need one more equation We can use Pythagoras theorem since it is a right triangle85² = a² + b²7225 = a² + b²a² = 7225 - b²b² = 7225 - a²Substitute b² into the previous equation113 = a + b7225 = a² + (7225 - a²)7225 = 2a²a² = 7225 / 2a = √(7225 / 2) = √(36125 / 8) = 75.59 cmNow that we have found the value of a, we can find b using the Pythagoras Theorem85² = 75.59² + b²b² = 85² - 75.59²b = √(85² - 75.59²) = 49.79 cm Therefore, a = 75.59 cm, b = 49.79 cmWidth of rubber matA square swimming pool has an area of 289 m²The area of the pool can be expressed as (side)²Therefore, side = √289 = 17 mLet the width of the rubber mat be w. Since it is uniform, it will be the same on all sides. Area of the pool and mat = (side + 2w)² - side² = 289From the above equation, we can solve for w:4w(side) + 4w² = 0+ 4w² + 4w(side) - 289 = 04(w + side/2)² - 289 = 0(w + side/2)² = 289 / 4w + side/2 = ±17/2 w + side/2 = 8.5 or w + side/2 = -8.5side/2 can never be negative, therefore we can consider only w + side/2 = 8.5 w = 8.5 - side/2w = 8.5 - 17/2 = 0.75m Width of the mat is 0.75 m

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The volume of the entire figure composed of a rectangular prism and pyramid is 2816 ft³

The volume of a figure is the amount of space the three dimensional object occupies.

The volume of the rectangular prism = length * width * height = 16ft * 16ft * 5 ft = 1280 ft³

The volume of the rectangular pyramid = (1/3) * length * width * height = 16ft * 16ft * 18 ft = 1536 ft³

The volume of the entire figure = volume of the rectangular prism + volume of the rectangular pyramid

The volume of the entire figure = 1280 ft³ + 1536 ft³ = 2816 ft³

The volume of the entire figure is 2816 ft³

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Therefore , the solution of the given problem of  arithmetic mean  comes out to be a2 = 1 is the following word in the sequence after a1.

The average values of a list, also known as the organization's values, are calculated by adding up all of the list's values. These average values are then adjusted by the proportion of list components in the largest density. similar growth patterns can be seen in math. The average of the actual numbers 5, 7, and 9 is 4, and the result of adding three to the number 21 (there are currently several three-digit numbers) is seven.

Here,

Each term in an arithmetic sequence is created by adding a constant difference (d) to the word before it. In order to determine the following term in the series where a1 = 5 and d = -4, we can use the following formula:

=> a = a1 +  (n-1)*d

where an is the sequence's nth word.

Inputting a1 = 5 and d = -4 results in:

=> a2 = a1 + (2-1)*d = 5 + (-4) = 1

As a result, a2 = 1 is the following word in the sequence after a1.

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As a result, the answer tο the fοllοwing questiοn, sum οf all sides οf a hexagοn = 720 where the value οf b = 136.

In geοmetry, a hexagοn is a six-sided pοlygοn οr hexagοn that fοrms the cube's shape. Internal angles οf a simple hexagοn add up tο 720°. A hexagοn is a clοsed twο-dimensiοnal pοlygοn with six sides. A hexagοn has six cοrners οn each side. Hexa represents six and gοna represents an angle. Hexagοnal shapes are fοund in sοccer balls, hοneycοmbs, flοοr tiles, and pencil surfaces. A hexagοn is a six-sided pοlygοn in geοmetry. A regular hexagοn is οne that has all οf its sides and angles the same length.

Sum οf all sides οf a hexagοn = (n - 2) × 180°

= (6 - 2) × 180°

= 720°

Frοm the given hexagοn, sum οf all angles

110 + 116 +(180 - 68) + (180 - 70) + 2bx = 720

b = 136

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As a result, 10 individuals purchased οnly Annapurna Pοst, 22 peοple variable and the tοtal number οf persοns whο participated in the pοll was: n = x + b + 34 = 10 + 22 + 34 = 66

A variable is anything that may be altered in the cοntext οf a mathematical nοtiοn οr experiment. Variables are frequently denοted by a single symbοl. The letters x, y, and z are οften used as generic variables symbοls. Variables are qualities with a wide range οf values that may be investigated. Size, age, mοney, where yοu were bοrn, academic pοsitiοn, and kind οf hοusing are just a few examples. Variables may be classified intο twο majοr grοups using bοth numerical and categοrical apprοaches.

k = 100 (100 peοple bοught Kantipur) (100 peοple bοught Kantipur)

a + x = 56 (56 individuals did nοt buy Kantipur) (56 peοple did nοt buy Kantipur)

b = 22 (22 individuals bοught Kantipur alοne) (22 peοple bοught Kantipur οnly)

x + b = n minus (k + a - b) = n minus (100 + (56 - x) - 22) = n minus 34 (With the knοwledge that a + x + b + k - n = 0), such as the elοquence οf the elοquence οf the elοquence οf the elοquence οf the e

n = x + b + 34

a + x = 56 x - an x + 22 = n - k - (a - 22)

x + 22 = x + 22 + a - 100 - a + 22 + 34

x = 10

As a result, 10 individuals purchased οnly Annapurna Pοst, 22 peοple purchased bοth Kantipur and Annapurna Pοst, and the tοtal number οf persοns whο participated in the pοll was:

n = x + b + 34 = 10 + 22 + 34 = 66

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Answer: 312

Step-by-step explanation:

Estimate: One way to estimate the quotient of 2,496 ÷ 8 is to round 2,496 to the nearest multiple of 8, which is 2,496 rounded to 2,496. Then, we can divide 2,496 by 8, which gives an estimated quotient of 312.

The former bedroom is 8 feet by 8 feet in dimensions.

In mathematics, a dimension is the length or width of an area, region, or space in one direction. It merely involves taking an object's length, width, and height into account.

Assume that the side length of the former bedroom is x.

Hence, the former bedroom had a square footage of x² feet.

The dimensions of the new bedroom are (x+3) and (x+2), respectively, as compared to the old bedroom, which is 3 feet wider and 2 feet deeper.

The new bedroom is (x+3)(x+2) square feet in size.

Since we are aware that the additional area is 46 square feet, we can construct the following equation:

(x+3)(x+2) - x² = 46

Expanding the left side of the equation:

x² + 5x + 6 - x² = 46

Simplifying:

5x + 6 = 46

Subtracting 6 from both sides:

5x = 40

Dividing both sides by 5:

x = 8

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To find f(-6), we need to substitute -6 for x in the expression for f(x):

f(x) = 2x^2 + 5x - x/3

f(-6) = 2(-6)^2 + 5(-6) - (-6)/3

f(-6) = 2(36) - 30 + 2

f(-6) = 72 - 30 + 2

f(-6) = 44

Therefore, f(-6) = 44.

The probability of a collision between two galaxies depends on a variety of factors, such as the size, mass, and relative velocities of the galaxies.

The probability of a collision between two galaxies depends on a variety of factors, such as the size, mass, and relative velocities of the galaxies. If the galaxies are in a spiral elipse, then the tangential velocity of the galaxies may be different, and this could affect the probability of a collision. However, without knowing more information about the galaxies, it is impossible to accurately calculate the probability of a collision.

If the galaxies are in a spiral elipse, then it is important to consider the tangential velocity of the galaxies, as this could affect the probability of a collision. Additionally, the relative angular momentum of the galaxies, their proximity to one another, and their respective trajectories also play a role. Without knowing more information about the galaxies, such as their exact positions, velocities, and masses, it is impossible to accurately calculate the probability of a collision.

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Answer:

4

Step-by-step explanation:

10x+2-2x=

10x-2x=2

8x=2

divide both sides by 8

x=2/8

x=4

Using trigonometric ratios the value for line segment DC is obtained as 30.5 units.

Triangle side length ratios are known as trigonometric ratios. In trigonometry, these ratios show how the ratio of a right triangle's sides to each angle. Sine, cosine, and tangent ratios are the three fundamental trigonometric ratios. In triangle ABD, the values given are -

∠BDA = 90°,

∠A = 54° and

AB = 20 units

According to the sum property of a triangle.

∠BDA + ∠A + ∠ABD = 180°

Substitute the values into the equation -

90° + 54° + ∠ABD = 180°

144° + ∠ABD = 180°

∠ABD = 180° - 144°

∠ABD = 36°

Now according to trigonometric ratios -

cos θ = Base / Hypotenuse

In triangle ABD -cos 36° = BD / AB

Substitute the values into the equation -

cos 36° = BD / 20BD

= cos 36° × 20BD

= 0.80901 × 20BD

= 16.18

≈ 16.2

Now in triangle BDC, the values given are -

∠BDC = 90°, ∠C = 28° and BD = 16.2

Now according to trigonometric ratios -tan θ = Perpendicular / Base

In triangle BDC -tan 28° = BD / DC

Substitute the values into the equation -

tan 28° = 16.2 / DC

DC = 16.2 / tan 28°

DC = 16.2 / 0.53170

DC = 30.46 ≈ 30.5 units

Therefore, the value for DC is obtained as 30.5 units.

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a)  A(5) = 10 * e^(-0.05*5)

b)  7.776

To solve the given problem, the initial amount of chlorine should be assumed as 'P0' and the exponential function should be written in the form of y = P_0 * e^(kt) where P_0 is the initial amount of chlorine and k is the rate of change. Therefore, for the given problem, the exponential function can be given by: y = P_0 * e^(-0.05t) where P_0 is the initial amount of chlorine and t is the number of hours. This equation will give the amount of chlorine remaining after t hours. The formula for exponential decay is given by:A(t) = A₀ * e^(-kt) Where A(t) is the amount after time t, A₀ is the initial amount, k is the rate of decay, and t is the time elapsed. To calculate the remaining amount of chlorine after a certain number of hours, we'll utilize the formula above .Let's start with the given information: An exponential function that gives the amount of chlorine remaining after t hours is to be found. P₀ = the initial amount of chlorine, which is 10.We can also figure out the rate of decay from the given information. The amount of chlorine is reduced by 5% per hour, which means the rate of decay is 0.05. We need to put a negative sign in front of the rate of decay to indicate that it is decreasing. Let's use the formula to find the amount of chlorine remaining after 5 hours. Then, substitute A₀ = 10, k = -0.05, and t = 5 into the equation above to obtain A(5) = 10 * e^(-0.05*5) = 7.776.So, the amount of chlorine remaining after 5 hours is 7.776.

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Answer:

Answer:19.54 square feet.

The amount of feet the circumference of the outer circle is greater than the circumference of the inner circle is 18.86 feet.

Circumference is the measure of distance around a circle.

To calculate the how many feet the circumference of the outer circle is greater than the circumference of the inner circle, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the difference in circumference between the outer and the inner is 18.86

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0.571

Given data: The accompanying table shows the numbers of male and female students in a certain region who received​ bachelor's degrees in a certain field in a recent year. A student is selected at random. Find the probability of each event listed in parts​ (a) through​ (c) below.Table:Males FemalesTotalsFreshman 12 25 37Sophomore 14 18 32Junior 17 14 31Senior 9 12 21Totals 52 69 121a) A freshman is selected at random.b) A senior male is selected at random.c) A female is selected at random.a) For part a, we have to find the probability of selecting a freshman at random. The total number of students is 121. And the number of freshmen is 37. The probability of selecting a freshman at random is:37/121 = 0.306b) For part b, we have to find the probability of selecting a senior male at random. The total number of seniors is 21. And the number of senior males is 9. The probability of selecting a senior male at random is:9/121 = 0.074c) For part c, we have to find the probability of selecting a female at random. The total number of females is 69. And the total number of students is 121. The probability of selecting a female at random is:69/121 = 0.571Therefore, the probability of each event is:a) 0.306b) 0.074c) 0.571

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The mark price of the shoes is Php 1250.

Mark price (MP) refers to the original or listed price of a product or service before any discounts, promotions or markdowns are applied. It is the price that a retailer sets for a product with the intention of making a profit.

Since Sarah bought the shoes at a sale of 20%, she paid only 80% of the mark price. This can be expressed as:

80% of MP = Php 1000

0.8MP = Php 1000

To find MP, we need to divide both sides by 0.8:

MP = Php 1000 / 0.8

MP = Php 1250

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Answer:

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