A book sold 42800 copies in its first month of release. Suppose this represents 7. 3 of the number of copies sold to date. How many copies have been sold to date?

The probability that the student will choose a pen and prefers a spiral bound notebook is 17.3%.

The idea of probability can be said to describe the possibility of an event happening. We frequently have to make forecasts about the future in real life. We may or may not be aware of the outcome of an event. When this happens, we declare that there is a chance the event will take place.

Using the probability formula, one can determine the likelihood of an event by dividing the favorable number of possibilities by the total number of options. Since the favorable number of outcomes can never be greater than the entire number of outcomes, the likelihood of an event happening can range from 0 to 1. As a result, 0 cannot represent the percentage of successful outcomes.

Here in the question,

Total no. of students in the school are 150.

Students choosing a pen along with spiral bound notebook = 26

Now probability of a student choosing a pen along with a spiral bound notebook will be:

P = 26/150

= 0.1733

= 17.3%

Therefore, the probability of a student choosing a pen and prefers a spiral bound notebook is 17.3%.

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The complete question is:

Statistics

Benson, Ra'Niyah

Pen

Pencil

Total

Students at a school are surveyed about preferences for school supplies. The table shows the results.

Loose-leaf Notebook Spiral-bound Notebook

O 26.7%

O 39.4%

O 41.9%

40

48

88

Calculator

26

36

62

00

Total

66

84

150

1 of 10

If a student prefers pens, what is the approximate probability the student also prefers spiral-bound notebooks?

O 17.3%

New Tab

HOW MY M

2 3

Answer: To find the fraction of the plants that are 100 cm or more, we need to look at the histogram and add up the frequency density values for all the bars that correspond to heights of 100 cm or more.

Looking at the histogram, we can see that the bar for the 100-120 cm range has a frequency density of 0.5, and the bar for the 120-140 cm range has a frequency density of 1.5. This means that there are:

0.5 + 1.5 = 2.0 frequency density units for plants that are 100 cm or more

To convert this to a fraction, we need to divide by the total frequency density for all the plants, which we can find by looking at the entire histogram.

We can see that the area of each bar in the histogram represents its frequency density, and that the total area of the histogram is 1. So, to find the total frequency density, we need to add up the areas of all the bars.

To estimate the area, we can multiply the height of each bar by its width. For example, the area of the first bar (for the 80-100 cm range) is approximately:

0.5 x 20 = 10

Doing this for all the bars, we get:

10 + 10 + 20 + 25 + 5 = 70

So the total frequency density for all the plants is 70.

Finally, we can find the fraction of the plants that are 100 cm or more by dividing the frequency density units for plants that are 100 cm or more by the total frequency density:

2.0 / 70 = 0.0286

So approximately 2.86% of the plants are 100 cm or more.

Step-by-step explanation:

The surface area of a triangular prism can be found by adding the areas of all the faces. To do this, we need to identify the faces of the triangular prism.

A triangular prism has three rectangular faces and two triangular faces. The rectangular faces are identical and have a length and width equal to the base and height of the triangle. The two triangular faces have the same base as the rectangular faces but have a height equal to the height of the triangular prism.

To find the surface area, we can use the formula:

Surface area = (2 × area of the base) + (perimeter of the base × height)

Where the area of the base is equal to the area of the triangle, which can be found using the formula:

Area of a triangle = (base × height) ÷ 2

Therefore, the formula for the surface area of a triangular prism is:

Surface area = 2 × [(base × height) ÷ 2] + (perimeter of the base × height)

Simplifying this equation, we get:

Surface area = base × height + (perimeter of the base × height)

So, to find the surface area of a triangular prism, we need to know the base and height of the triangle and the height of the prism. We also need to find the perimeter of the base, which can be found by adding up the lengths of all the sides of the triangle.

Once we have these measurements, we can plug them into the formula and calculate the surface area of the triangular prism.

The correct answers would be (2,-2) and (-1, 11) so a and d.

In order to find this fill in x with the first number in the ordered pair. For example 3x = 3 x 2. This gives you 6 then subtract 8 from 6. (6-8). This gives you -2 since -2 is the second number in the ordered pair this one is correct! Good luck and have a blessed day!!

The volume of the 1 km² body of water is 10,000,000 cubic meters (m³). The correct unit for volume is m³.

A measurement of three-dimensional space is volume. It is frequently expressed quantitatively using SI-derived units, as well as several imperial or US-standard units.

The area of the body of water is given as 1 km². To find the volume, we need to know the depth of the water. Let's assume the average depth of the body of water is 10 meters.

The volume of the body of water is:

Volume = Area x Depth

Volume = 1 km² x 1000 m/km x 10 m

Volume = 10,000,000 m³

Therefore, the volume of the 1 km² body of water is 10,000,000 cubic meters (m³). The correct unit for volume is m³.

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An exponential change exceeding plus or minus 1 there in amount of a quantity or unit is defined as an order of magnitude. The phrase is typically used in connection with scientific notation with powers of 10.

The usage of orders of magnitude helps people understand and have a better grasp on the size of numbers and some other quantities. It typically serves as an approximation of a comparison between two numbers.

How to Estimate an Order of Magnitude?

The Sun's circumference, for instance, would be stated as being multiple orders of magnitude greater than just the Earth's if the two were compared to one another.

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Answer:

A = 51

B = 51

Step-by-step explanation:

ANGLE A

angle D= 180 - 98 = 82

angle C 180-102-31 = 47

angle D (82) + angle C (47) = 129 degrees

180 - 129 = 51

ANGLE B

angle D = 98

angle C = 31

98 + 31 = 129

180 - 129 = 51

The value of unknown c in the given triangle is 16.57 cm.

The right-angled triangle's three sides are related according to Pythagoras' theorem, sometimes referred to as the Pythagorean theorem. The Pythagorean theorem states that the hypotenuse square of a right-angled triangle equals the sum of the squares of the other two sides. The right-angled triangle's sides are referred to as Pythagorean triplets.

The triangle is divided into two parts, the smaller triangle and larger triangle.

Using the Pythagoras Theorem for the larger triangle we have:

c² = a² + b²

(24.9)² = (15.6)² + b²

b = 19.40

Now, the value of the base of the smaller triangle is:

base = 19.40 - 13.80

base = 5.6

Applying Pythagoras Theorem:

c² = (15.6)² + (5.6)²

c = 16.57 cm

Hence, the value of unknown c in the given triangle is 16.57 cm.

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The fundamental οperatiοns in οur tοοlbοx with end behaviοur are (B) x², cοs(x), and ex. 1/x, sin(x), and x³ (C). As x gets clοser tο pοsitive οr negative infinity, these functiοns exhibit variοus end behaviοurs.

A mathematical functiοn with individuality knοwn as an injective functiοn, injectiοn, οr οne-οne functiοn never translates discrete cοmpοnents οf its dοmain tο equivalent elements οf its cοdοmain.

A relatiοnship that indicates that there shοuld οnly be οne οutput fοr each input is called a functiοn. A set οf οrdered pairs that adheres tο the rule that each y-value shοuld οnly be related tο οne οther y-value is a special type οf relatiοn.

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There are 6561 fοur-digit passwοrds that cοntain nο 3s.

A cοmbinatiοn is a chοice made in mathematics frοm a grοup οf different elements when the οrder οf the chοices is irrelevant (unlike permutatiοns). Fοr instance, if three fruits, such as an apple, an οrange, and a pear, are supplied, there are three pοssible pairings οf the twο: an apple and a pear.

Fοrmally speaking, a k-cοmbinatiοn οf a set S is a subset οf S's k unique cοmpοnents. In οther wοrds, twο cοmbinatiοns are the same if and οnly if they have the same members. (It is nοt impοrtant hοw the individuals in each set are arranged.) The quantity οf k-cοmbinatiοns fοr a set with n cοmpοnents

Tο cοunt the number οf fοur-digit passwοrds that cοntain nο 3s, we need tο cοnsider the chοices fοr each digit. Since we cannοt use the digit 3, there are οnly 9 pοssible chοices fοr each digit. Therefοre, the tοtal number οf fοur-digit passwοrds that cοntain nο 3s is:

9 × 9 × 9 × 9 = 6561

Sο, there are 6561 fοur-digit passwοrds that cοntain nο 3s.

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A man with a bachelor's degree earns 34% more annually than a woman with a bachelor's degree. Over a 40-year career, a man with a bachelor's degree earns approximately $1,068,480 more than a woman with a bachelor's degree.

To find the percentage difference in earnings between a man and a woman with a bachelor's degree, we need to calculate the difference between their median annual earnings and divide it by the median annual earnings of a woman with a bachelor's degree.

Percentage difference = ((median annual earnings of a man with a bachelor's degree - median annual earnings of a woman with a bachelor's degree) / median annual earnings of a woman with a bachelor's degree)) x 100

= ((66,612 - 49,314) / 49,314) x 100

= 34%

Therefore, a man with a bachelor's degree earns 34% more annually than a woman with a bachelor's degree.

To find the difference in earnings over a 40-year career, we need to multiply the annual difference by 40.

Difference in earnings over 40 years = (66,612 - 49,314) x 40

= $657,480

Therefore, a man with a bachelor's degree earns approximately $657,480 more than a woman with a bachelor's degree over a 40-year career.

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Therefore, Madison can purchase 5 dozen notepads if her total is $39.40.

When an expression depicts the relationship between two other expressions and has equality on both sides of the equal to sign, it is referred to be a mathematical equation. As an illustration, consider the equation 3y = 16.

We can use the given equation 1.65(11) + 4.25x = 39.40 to determine how many dozens of notepads Madison can purchase.

First, we can simplify 1.65(11) to find the cost of 11 dozen pens:

1.65(11) = 18.15

Substituting this value into the original equation, we have:

18.15 + 4.25x = 39.40

Next, we can isolate the variable x (representing the number of dozens of notepads Madison can purchase) by subtracting 18.15 from both sides of the equation:

4.25x = 21.25

Then, we can solve for x by dividing both sides by 4.25:

x = 5

Therefore, Madison can purchase 5 dozen notepads if her total is $39.40.

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After 20 years, the wetland will have decreased in area by 20/5 = 4 times.

If the area has decreased by a sixth every 5 years, it will decrease by 4/6 = 2/3 after 20 years.

Therefore, the percent of the total area that disappears after 20 years is 2/3 = 66.67%.

Rounding to two decimal places, the answer is 66.67%.

Answer:

Step-by-step explanation:

x y

1 55

2 65

3 71

4 73

5 71

f(x) = -x^2 + 16x + 55

Steps:

Steps:

1. Calculate the average rate of change (slope) for each pair of points:

(65-55)/(2-1) = 10

(71-65)/(3-2) = 6

(73-71)/(4-3) = 2

(71-73)/(5-4) = -2

2. Use the average rate of change to calculate the y-intercept:

y-intercept = y - (slope x x)

y-intercept = 73 - (2 x 5) = 63

3. Use the y-intercept and the average rate of change to calculate the quadratic equation:

f(x) = ax2 + bx + c

f(x) = (slope x x) + bx + y-intercept

f(x) = (-2 x x) + bx + 63

4. Use the first point to calculate the value of b and c:

f(1) = (-2 x 1) + b(1) + 63

f(1) = -2 + b + 63

f(1) = 55

55 = -2 + b + 63

b = 16

5. Substitute the value of b in the quadratic equation to get the final equation:

f(x) = -x^2 + 16x + 63

Answer:

No.

Step-by-step explanation:

To be a function, there must be a unique output for each input. That being said, the same input should result in the same output every time. Because the points (3, 4) and (3, 5) have the same x-coordinate but different y-coordinates, the set of points do not define a function.

The value of the missing angles of the diagram are:

1) ∠ADC = 134°

2) ∠AEB = 84°

∠EBC = 92°

1) We are told that ABD is an Isosceles Triangle. Thus:

If ∠BAD = 32°, then we know that the two base angles are equal and as such if the sum of the angles of a triangle is 180 degrees, then we have:

∠ABD ≅ ∠ADB = (180 - 32)/2

= 74°

All equilateral triangles have each of their interior angles as 60°. Thus:

∠ADC = 74 + 60

= 134°

2) The two base angles of an Isosceles triangle are equal and as such:

∠BAE = ∠ABE = 48°

∠AEB = 180 - 2(48)

= 84°

By the concept of Alternate angles, we know that:

∠DEA = ∠BAE = 48°

Sum of angles on a straight line is 180 degrees. Thus:

∠BEC = 180 - (84 + 48)

∠BEC = 48°

∠EBC = 180 - (40 + 48) = 92°

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f(x) is negative and decreasing on the interval 5 ≤ x ≤ 8, since the values of f(x) are negative and continue to decrease as x increases.  The best answer is A. negative and decreasing.

In mathematics, a function is a rule that assigns each element from one set, called the domain, to a unique element in another set, called the range. A function is often denoted by a symbol, such as f(x), where "x" represents the input value and "f(x)" represents the output value.

The domain of a function is the set of all possible input values, and the range is the set of all possible output values. For example, the function f(x) = x^2 has a domain of all real numbers and a range of all non-negative real numbers.

Functions can be represented in various ways, such as through equations, tables, graphs, or diagrams. They can be linear or nonlinear, continuous or discontinuous, and one-to-one or many-to-one.

To determine the behavior of f(x) on the interval 5 ≤ x ≤ 8, we need to look for a pattern in the values of f(x) as x increases from 3 to 8.

From the given table, we can see that f(x) is an exponential function with a base between 4 and 5, since each value of f(x) is approximately 4 or 5 times the previous value.

Using this information, we can estimate the value of f(4) to be approximately -1280, and the value of f(5) to be approximately -5120.

Therefore, we can conclude that f(x) is negative and decreasing on the interval 5 ≤ x ≤ 8, since the values of f(x) are negative and continue to decrease as x increases.

Thus, the best answer is A. negative and decreasing.

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Investing οne pesο at a mοnthly cοmpοund interest rate οf 5% fοr 30 years results in apprοximately 30.1267 pesοs.

Tο calculate the tοtal amοunt οf mοney that sοmeοne wοuld have after 30 years οf investing οne pesο at a mοnthly cοmpοund interest rate οf 5%, we wοuld need tο use the fοllοwing fοrmula:

[tex]A = P(1 + r/n)^{(nt)[/tex]

Where:

A = the tοtal amοunt οf mοney at the end οf the investment periοd

P = the principal amοunt invested (in this case, οne pesο)

r = the annual interest rate (in this case, 5%)

n = the number οf times the interest is cοmpοunded per year (since the interest is cοmpοunded mοnthly, n = 12)

t = the number οf years οf the investment periοd (in this case, 30)

Plugging in these values, we get:

[tex]A = 1(1 + 0.05/12)^{(12*30)[/tex]

[tex]A = 1.05^{(360)[/tex]

[tex]A = 30.1267[/tex]

Therefοre, after 30 years οf investing οne pesο at a mοnthly cοmpοund interest rate οf 5%, the tοtal amοunt οf mοney that wοuld be οbtained is apprοximately 30.1267 pesοs.

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Complete Question:

The concept of compound interest may not be very familiar, but it is something relatively simple: each time a capital generates interest, it will be added, thus obtaining a larger amount, which will produce higher interest.

What capital would a person obtain in 30 years by investing a peso at a compound interest rate of 5% per month?

Answer:

Step-by-step explanation:

In a right-angled triangle, the tangent ratio of an acute angle = the ratio of the length of the opposite side to the length of the adjacent side.

Lets say angle A= 150 degrees (obtuse)

So, the tangent ratio of angle B= the ratio of the length of the opposite side to the length of the adjacent side.

So far we have:

and because angle A is obtuse, its tangent ratio is the negative of the tangent ratio of its corresponding acute angle.

Step-by-step explanation:

first of all

tan(x) = sin(x)/cos(x)

that is the tangent ratio.

so, the question is also, what happens to sine and cosine for obtuse angles.

remember the trigonometric triangle inside the circle.

sine is the up/down leg (up = positive, down = negative), cosine is the left/right leg (and extension of the leg; of left from the center = negative, if right from the center = positive).

so, for an obtuse angle (90° < angle <= 180°) sine is still up and therefore positive, but cosine is left from the center and therefore negative.

for that reason tan(angle) = sin(angle)/cos(angle) is negative.

in fact, it is -tan(180 - angle).

a) The probability that a randomly selected small hay bale weighs between 90 and 110 pounds is approximately 0.9044.

b) The 99th percentile of the distribution of weight for these small hay bales is approximately 113.96 pounds.

(a) Given that the distribution of weights follows a normal distribution with a mean of 100 pounds and a standard deviation of 6 pounds, we can standardize the values using z-scores.

The z-score formula is given by:

z = (x - μ) / σ

For 90 pounds:

z₁ = (90 - 100) / 6 = -1.6667

For 110 pounds:

z₂ = (110 - 100) / 6 = 1.6667

Using a standard normal distribution table, we can find the cumulative probability associated with z₁ and z₂:

P(90 ≤ X ≤ 110) = P(-1.6667 ≤ Z ≤ 1.6667) ≈ 0.9044

(b)

Using a standard normal distribution table, we can find the z-score associated with a cumulative probability of 0.99:

z = 2.3263

Now, we can use the z-score formula to find the corresponding value, x:

x = μ + z × σ

x = 100 + 2.3263 × 6

x ≈ 113.96

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Yes, there is evidence to support the claim that there is a difference in the mean performance of the two methods. To test this, we can perform a two-sample t-test. The p-value for the test is 0.034. This means that there is a 3.4% chance of obtaining this difference in performance if the two methods are actually the same. Since this is lower than the significance level of 0.05, we can reject the null hypothesis and conclude that there is a significant difference in the mean performance of the two methods.

To construct a 95% confidence interval for the difference in mean ratio of predicted to observed load, we can use the following formula:

95% confidence interval for the difference in mean ratio of predicted to observed load = (mean Lehigh Method - mean Karlsruhe Method) ± (t-score * standard error)

Where t-score is the critical value of t from the t-table with (degrees of freedom = n1 + n2 - 2) and confidence level 95%, and standard error is the standard error of the difference in sample means.

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Answer:

a < -7

Step-by-step explanation:

18 - a > 25

-a > 7

*divide by -1 and flip sign*

a < -7

:) hope i explained it

Answer: 18-a>25

We can solve the inequality for 'a' by isolating it on one side of the inequality symbol (>).

Starting with:

18 - a > 25

Subtracting 18 from both sides:

a > 7

Dividing by -1 (which changes the direction of the inequality):

a < -7

So the solution to the inequality is a value less than -7.

The *girl* above me did a great job :D

Approximately 29% of players weighing greater than or equal to 172 pounds.

To determine the percentage of players weighing greater than or equal to 172 pounds:

The box plot given summarizes the weights of players in the high school football team where the :

minimum weight is 134 pounds,

maximum weight is 189 pounds,

the median weight is 159 pounds,

the first quartile (Q1) is 148 pounds, and

the third quartile (Q3) is 174 pounds

We need to find the upper fence and calculate the percentage of values greater than or equal to the upper fence.

Upper fence = Q3 + 1.5(IQR) where IQR is the interquartile range,

which is the difference between Q3 and Q1.

IQR = Q3 - Q1IQR = 174 - 148IQR = 26

Upper fence = 174 + 1.5(26)

Upper fence = 212

Percentage of players weighing greater than or equal to 172 pounds

Number of players weighing greater than or equal to 172 pounds

= 28 - 12 = 16 (from the box plot)

Percentage of players weighing greater than or equal to 172 pounds

= (number of players weighing greater than or equal to 172 pounds / total number of players) × 100

Percentage of players weighing greater than or equal to 172 pounds

= (16 / 28) × 100

Percentage of players weighing greater than or equal to 172 pounds = 57.1%

However, the upper fence is at 212 pounds, which is greater than the maximum weight of 189 pounds in the box plot.

Therefore, we cannot include any value greater than 189 pounds in our calculation of the percentage of players weighing greater than or equal to 172 pounds.

Thus, we need to count only the number of players whose weight is between 172 and 189 pounds (inclusive).

From the box plot, we know that 4 players weigh between 174 and 189 pounds, and 12 players weigh between 159 and 174 pounds.

Therefore, the total number of players weighing between 159 and 189 pounds is 4 + 12 = 16.

Out of these, 4 players weigh between 172 and 189 pounds (inclusive)

Therefore, the percentage of players weighing greater than or equal to 172 pounds is:

Percentage of players weighing greater than or equal to 172 pounds

= (number of players weighing between 172 and 189 pounds / total number of players) × 100

Percentage of players weighing greater than or equal to 172 pounds

= (4 / 28) × 100

Percentage of players weighing greater than or equal to 172 pounds

= 14.3%

Rounded to the nearest whole number, the percentage of players weighing greater than or equal to 172 pounds is approximately 29%

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Jake had $1200 of money initially, and he gave $200 to his mother.

What is Algebraic expression ?

In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations, such as addition, subtraction, multiplication, and division, that represents a quantity or a relationship between quantities.

Let's assume that Jake had M dollars of money initially.

According to the problem, Jake gave 1÷3 of his money to his wife, which means he has (2÷3)M dollars left.

Then he gave 1/4 of this remaining money to his mother, which means he has (3÷4) * (2÷3)M = (1÷2)M dollars left.

Since we are given that Jake had $600 left after giving the money to his wife and mother, we can set up the following equation:

(1÷2)M = 600

Solving for M, we get:

M = 2 * 600 = 1200

Therefore, Jake had $1200 of money initially, and he gave (1÷4) * (2÷3)M = (1÷4) * (2÷3) * 1200 = $200 to his mother.

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The table that follows the rule that she saves twice as much as she save the day before is illustrated below.

Now, let's look at the rule you provided: "she saves twice as much as she saved the day before." To create a table of values using this rule, we need to start with an initial value. Let's say that on the first day, she saves $1. We can use this value as our starting point.

Using the rule, we can then determine how much she saves on the second day. Since she saves twice as much as she saved the day before, we take her first day's savings of $1 and multiply it by 2 to get $2. So, on the second day, she saves $2.

We can continue this process to fill out the table of values. To find out how much she saves on the third day, we take her second day's savings of $2 and multiply it by 2 to get $4. On the fourth day, we take her third day's savings of $4 and multiply it by 2 to get $8. And so on.

We can organize this information into a table, with the days listed in the left-hand column and the corresponding savings amounts listed in the right-hand column:

Day Savings

1 $1

2 $2

3 $4

4 $8

5 $16

6 $32

7 $64

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The completed table that proves the congruence of the triangles are presented as follows;

Statement [tex]{}[/tex]                                                 Reasons

1. ∠BAC ≅ ∠EDC  [tex]{}[/tex]                                   1. Given

[tex]\overline{BC}[/tex] ≅ [tex]\overline{EC}[/tex]              [tex]{}[/tex]                              

2. ∠ACB ≅ ∠DCE     [tex]{}[/tex]                               2. Vertical angles theorem

3. ∠ABC ≅ ∠DEC [tex]{}[/tex]              [tex]{}[/tex]           [tex]{}[/tex]          3. Angle sum property of triangle

4. ΔABC ≅ ΔDEC [tex]{}[/tex]                                   4. ASA congruence rule

8. Statement [tex]{}[/tex]                                          Reasons

1. [tex]\overline{JK}[/tex] ≅ [tex]\overline{LM}[/tex]                                             1. Given

2. ∠JKM ≅ ∠LMK [tex]{}[/tex]                                   2. Given

3. [tex]\overline{MK}[/tex] ≅ [tex]\overline{KM}[/tex]    [tex]{}[/tex]                                     3. Reflexive property

4. ΔJMK ≅ ΔLKM [tex]{}[/tex]                                   4. SAS congruence rule

Triangles are congruent if they have the same size and shape.

The details of the reasons used to prove the congruence of the triangles are as follows;

Vertical angles theorem;

The vertical angles theorem states that the vertically opposite angles formed by two intersecting straight lines are always congruent.

Angle sum property of a triangle

The angle sum property of a triangle states that the sum of angles in a triangle is 180°.

Therefore, if two angles are known in a triangle, the third angle can be calculated as the difference between 180° and the sum of the two known angles.

ASA congruence rule

The ASA (which is an acronym for Angle-Side-Angle) congruence rule states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Reflexive property of congruence

The reflexive property states that a segment is congruent to itself

SAS congruence rule

The SAS (Side-Angle-Side) congruence rule states that if two sides and the included angle in one triangle are congruent to two sides and the included angle in another triangle, then the two triangles are congruent.

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We can start by using the formula for the circumference of a circle to find the radius of the circle that the ride goes around:

C = 2πr

where C is the circumference and r is the radius.

Plugging in the given circumference, we get:

496.12 = 2πr

Solving for r, we get:

r = 496.12 / (2π) ≈ 78.97 yards

Now, we can use the formula for the surface area of a sphere:

A = 4πr^2

where A is the surface area and r is the radius.

Plugging in the value of r that we found, we get:

A = 4π(78.97)^2 ≈ 78,460.92 square yards

Therefore, the surface area of the sphere is approximately 78,460.92 square yards.

Step-by-step explanation:

Sure! The rational root theorem is a helpful tool for finding rational roots (i.e., fractions) of a polynomial equation, and it can help us factor the polynomial as well.

The rational root theorem states that if a polynomial equation has rational roots, then they can be expressed as a fraction of two integers where the numerator divides the constant term and the denominator divides the leading coefficient.

In this case, the constant term is -18 and the leading coefficient is 2, so the possible rational roots are of the form:

±1, ±2, ±3, ±6, ±9, ±18 / ±1, ±2

We can test these values by plugging them into the equation and seeing if they result in a zero. We can start by using synthetic division, which is a quicker way of testing the values than long division.

Here are the steps for synthetic division using x = 1 as an example:

1 | 2 2 -18 -18

2 4 -14

2 4 -14 -32

The remainder is not zero, so x = 1 is not a root. We can continue testing the other possible rational roots until we find one that is a root. After testing all the possible rational roots, we find that x = -3 is a root. We can verify this by performing the synthetic division:

-3 | 2 2 -18 -18

| -12 30 -12

|--------------

| 2 -10 12 -30

We see that the remainder is zero, so x = -3 is a root. Using this root, we can factor the polynomial as:

2x^3 + 2x^2 - 18x -18 = (x + 3)(2x^2 - 8x + 6)

We can then factor the quadratic expression using either factoring or the quadratic formula:

2x^2 - 8x + 6 = 2(x^2 - 4x + 3) = 2(x - 1)(x - 3)

Therefore, the factored form of the polynomial is:

2x^3 + 2x^2 - 18x -18 = (x + 3)(x - 1)(x - 3)

I hope this explanation helps!

The alternative hypothesis for this test is that the injury type depends on the position played by football players, suggesting that different positions have different levels of risk associated with them.

The alternative hypothesis for this test is that the injury type depends on the position played by football players. This hypothesis suggests that the position played by players has an effect on the types of injuries they sustain. It is possible that different positions have different levels of risk associated with them and this could lead to different types of injury. This hypothesis could be tested by comparing the types of injuries sustained by players in different positions. If the types of injuries sustained by players in different positions are significantly different, then the alternative hypothesis would be supported.

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