PLEASE HELP
The following data shows the grades that an 8th grade mathematics class received on a recent exam.

{99, 94, 91, 79, 88, 94, 92, 93, 90, 89, 77, 75, 65, 90, 87, 93, 92, 82, 65, 60, 78}

Part A: Determine the best graphical representation to display the data. Explain why the type of graph you chose is an appropriate display for the data. (6 points)

Part B: Explain, in words, how to create the graphical display you chose in Part A. Be sure to include a title, axis label(s), scale for axis if needed, and a clear process of how to graph the data. (6 points)

The x and y values represent the depth of descent and the corresponding increase in water pressure, respectively, along the linear relationship described by the equation.

To find the x and y values, we can set up a linear equation that represents the relationship between the depth of descent and the increase in water pressure.

Let's denote the depth of descent as x (in feet) and the increase in water pressure as y (in lb/in²).

We know that for every 20 ft of descent, the water pressure increases by 9 lb/in². This gives us a slope of 9/20 (change in y/change in x).

So, the slope (m) of the linear equation is 9/20.

Now, we need to find the y-intercept, which represents the water pressure at the surface of the ocean (0 ft descent). We know that at the surface, the water pressure is 15 lb/in².

Therefore, the y-intercept (b) is 15.

Putting it all together, the linear equation that represents the relationship between depth of descent (x) and increases in water pressure (y) is:

y = (9/20)x + 15.

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a. The length of the arc drawn across the fair landing area is approximately 6.777 meters.

b. The area of the sector bounded by the arc is approximately 162.042 square meters.

To find the length of the arc, we need to calculate the circumference of the circle formed by the landing area.

The central angle of the sector is given as 34.92°, which represents a fraction of the total circumference of the circle.

The formula to find the length of an arc is given by:

Arc Length = (Central Angle / 360°) × Circumference

In this case, the central angle is 34.92° and the circumference is the distance covered by the farthest throw, which is 21.89 meters.

Arc Length = (34.92° / 360°) × 2πr

We need to find the radius (r) of the circle. Since the farthest throw covers the radius, we have:

r = 21.89 meters

Now we can calculate the arc length:

Arc Length = (34.92° / 360°) × 2π × 21.89 meters

Arc Length ≈ (0.097 × 2π × 21.89) meters

Arc Length ≈ 6.777 meters

To calculate the area of the sector bounded by the arc, we need to use the formula:

Area of Sector = (Central Angle / 360°) × π × r²

Using the given central angle of 34.92° and the radius of 21.89 meters, we can calculate the area:

Area of Sector = (34.92° / 360°) × π × (21.89 meters)²

Area of Sector ≈ (0.097 × π × 21.89²) square meters

Area of Sector ≈ 162.042 square meters

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1177.5 cubic cm is the volume of the cylinder.

The formula to calculate the volume of a cylinder is V = πr²h, where V represents the volume, r is the radius of the base, and h is the height of the cylinder.

In this case, the radius (r) is 5 cm and the height (h) is 15 cm. Let's calculate the volume:

V = π * (5 cm)² * 15 cm

V ≈ 3.14159 * 25 cm² * 15 cm

V ≈ 1177.5 cm³

Therefore, the volume of the cylinder is approximately 1177.5 cubic cm (rounded to the nearest tenths place).

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Therefore, the first four terms of the sequence are 5, 2, -1, and The first four terms of the sequence can be found by substituting the values of n = 1, 2, 3, and 4 into the general term a_n = -3n + 8.

For n = 1:

a_1 = -3(1) + 8 = 5

For n = 2:

a_2 = -3(2) + 8 = 2

For n = 3:

a_3 = -3(3) + 8 = -1

For n = 4:

a_4 = -3(4) + 8 = -4

Therefore, the first four terms of the sequence are 5, 2, -1, and -4. Starting with n = 1, we substitute it into the equation and calculate the value of a_1. Similarly, we repeat this process for n = 2, 3, and 4 to find the corresponding terms of the sequence.

In this case, the general term -3n + 8 represents a linear sequence where the term decreases by 3 each time n increases by 1. The initial value is 8, and the common difference is -3.

As we substitute different values of n, we can observe how the sequence progresses and identify the specific terms. In this example, the first four terms of the sequence are found to be 5, 2, -1, and -4.

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Answer:

100ft

Step-by-step explanation:

The distance from the Earth to the Sun is approximately 412 million km.

To find the distance from the Earth to the Sun and calculate the remaining information, we can utilize basic trigonometry principles and the given distances.

Let's denote the distance from the Earth to the Sun as "x" (unknown), the distance from the Sun to the Moon as "y" (150 million km), and the distance from the Moon to the Earth as "z" (384 million km).

To determine the missing side lengths and angle measures, we can use the concept of right-angled triangles.

First, let's consider the triangle formed by the Moon, Earth, and Sun. The side lengths and angle measures are as follows:

Side lengths:

Moon to Earth (z) = 384 million km

Earth to Sun (x) = unknown (to be determined)

Sun to Moon (y) = 150 million km

Angle measures:

Angle at Moon (θ1) = 90 degrees (perpendicular angle)

Angle at Earth (θ2) = unknown (to be determined)

Angle at Sun (θ3) = 90 degrees (perpendicular angle)

Next, let's examine the triangle formed by the Earth, Sun, and Moon. The side lengths and angle measures in this triangle are:

Side lengths:

Earth to Moon (z) = 384 million km

Moon to Sun (y) = 150 million km

Sun to Earth (x) = unknown (to be determined)

Angle measures:

Angle at Earth (θ4) = 90 degrees (perpendicular angle)

Angle at Sun (θ5) = unknown (to be determined)

Angle at Moon (θ6) = 90 degrees (perpendicular angle)

To find the distance from the Earth to the Sun (x), we can use the Pythagorean theorem on the triangle involving the Moon, Earth, and Sun:

[tex]x^2 = z^2 + y^2[/tex]

[tex]x^2[/tex] [tex]= (384 million km)^2 + (150 million km)^2[/tex]

[tex]x^2[/tex] [tex]= 147,456,000,000,000 km^2 + 22,500,000,000,000 km^2[/tex]

[tex]x^2[/tex] [tex]= 169,956,000,000,000 km^2[/tex]

Taking the square root of both sides:

x ≈  [tex]\sqrt(169,956,000,000,000 km^2)[/tex]

x ≈ 412 million km (approximately)

Therefore, the distance from the Earth to the Sun is approximately 412 million km.

For the trigonometric functions, we can calculate them for the angles θ2 and θ5.

Trig functions for the angle from Moon, Earth, Sun (θ2):

sin(θ2) = Opposite/Hypotenuse = z/y = 384 million km / 150 million km

cos(θ2) = Adjacent/Hypotenuse = x/y = 412 million km / 150 million km

tan(θ2) = Opposite/Adjacent = z/x = 384 million km / 412 million km

csc(θ2) = 1/sin(θ2)

sec(θ2) = 1/cos(θ2)

cot(θ2) = 1/tan(θ2)

Trig functions for the angle from Earth, Sun, Moon (θ5):

sin(θ5) = Opposite/Hypotenuse = y/x = 150 million km / 412 million km

cos(θ5) = Adjacent/Hypotenuse = z/x = 384 million km / 412 million km

tan(θ5) = Opposite/Adjacent = y/z = 150 million km / 384 million km

csc(θ5) = 1/sin(θ5)

sec(θ5) = 1/cos(θ5)

cot(θ5) = 1/tan(θ5)

Please note that the trigonometric functions can be calculated using a calculator or software capable of performing trigonometric calculations.

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To find the percentage of data that falls between 5 and 35 in a normally distributed data set with a mean of 20 and a standard deviation of 5, we can use the properties of the standard normal distribution.

First, we need to standardize the values 5 and 35 by converting them to z-scores. The z-score formula is:

z = (x - μ) / σ

Where:

x is the value,

μ is the mean, and

σ is the standard deviation.

For the value 5:

z1 = (5 - 20) / 5 = -3

For the value 35:

z2 = (35 - 20) / 5 = 3

Next, we can use a standard normal distribution table or calculator to find the area under the curve between the z-scores -3 and 3. This area represents the percentage of data between 5 and 35.

Using a standard normal distribution table or calculator, we find that the area under the curve between -3 and 3 is approximately 0.9973.

Therefore, approximately 99.73% of the data will fall between 5 and 35 in a normally distributed data set with a mean of 20 and a standard deviation of 5.

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1. The chance that all 23 people have different birthdays is about 0.493 or 49.3%.

2. The chance that two people in the room have the same birthday is about 0.507 or 50.7%.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.

(1) The probability that all 23 people have different birthdays can be calculated as follows:

For the first person, there are 365 possible birthdays to choose from.

For the second person, there are 364 possible birthdays left to choose from (since one has already been taken).

For the third person, there are 363 possible birthdays left to choose from, and so on.

So the probability that all 23 people have different birthdays is:

P(all different) = 365/365 * 364/365 * 363/365 * ... * 344/365

                 = 0.493

Therefore, the chance that all 23 people have different birthdays is about 0.493 or 49.3%.

(2) The probability that two people in the room have the same birthday can be calculated as follows:

For the first person, there are 365 possible birthdays to choose from.

For the second person, there is a 1/365 chance that they have the same birthday as the first person.

For the third person, there is a 2/365 chance that they have the same birthday as one of the first two people, and so on.

So the probability that at least two people in the room have the same birthday is:

P(at least 2 people share a birthday) = 1 - P(all different)

                                     = 1 - 0.493

                                     = 0.507

Therefore, the chance that two people in the room have the same birthday is about 0.507 or 50.7%.

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The area of the quadrilateral, given the value of y and other dimensions is 25. 6 square feet.

The quadrilateral shown is a trapezium and to find the area, the formula would be:

= ( 1 / 2 ) x ( a + b ) x h

where A is the area, a and b are the lengths of the parallel sides, and h is the height.

This means that the area would be:

= ( 1 /2 ) x  ( 2. 7 ft + 5. 9 ft ) x 6 ft

= 1 / 2 x 8. 6 x  6

= 8. 6 x 3

= 25. 6 square feet

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a. The null hypothesis is that the mean clutch life is equal to or less than 50,000 miles, while the alternative hypothesis is that the mean clutch life is greater than 50,000 miles.

b. If the true mean is 55,000 miles, the error that can be made is a type I error, which is rejecting the null hypothesis when it is actually true.

c. If the true mean is 45,000 miles, the error that can be made is a type II error, which is failing to reject the null hypothesis when it is actually false.

a. The manufacturer's claim can be interpreted as a statement about the population mean clutch life, which is the average clutch life for all clutches produced by the manufacturer. The null hypothesis, H0, is that the mean clutch life is equal to or less than 50,000 miles, while the alternative hypothesis, Ha, is that the mean clutch life is greater than 50,000 miles. Mathematically, H0: µ ≤ 50,000 miles and Ha: µ > 50,000 miles.

b. If the true mean clutch life is 55,000 miles, the error that can be made is a type I error, which is rejecting the null hypothesis when it is actually true. In other words, if a sample of clutches is tested and the sample mean clutch life is greater than 50,000 miles, we may conclude that the manufacturer's claim is false and the true mean clutch life is greater than 50,000 miles. However, this conclusion may be wrong due to sampling error, and we may be falsely rejecting the null hypothesis.

c. If the true mean clutch life is 45,000 miles, the error that can be made is a type II error, which is failing to reject the null hypothesis when it is actually false. In this case, if a sample of clutches is tested and the sample mean clutch life is less than or equal to 50,000 miles, we may conclude that the manufacturer's claim is true and the true mean clutch life is equal to or less than 50,000 miles. However, this conclusion may be wrong due to sampling error, and we may be falsely accepting the null hypothesis.

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After considering the given data we conclude that the given expression upon calculation is equivalent to cot(2β), under the condition that the given expression is cot2β(1−cos2β).

In order to elaborate this given expression we have to use trigonometric identities. Furthermore, the identity cot(2β)(1-cos(2β)) = cot(2β) can be derived applying the following steps:
cot(2β)(1-cos(2β)) = cot(2β) - cos(2β)cot(2β)
= cot(2β) - cos(2β)/sin(2β)
= (cos(2β)sin(2β)/sin(2β)) - cos(2β)/sin(2β)
= (cos(2β)-cos(2β)sin²(2β))/sin(2β)
= cos(2β)(1-sin²(2β))/sin(2β)
= cos(2β)cos²(2β)/sin(2β)
= cot(2β)
Trigonometric identities are considered equalities that have trigonometric functions and are proclaimed as true for each and every value taking place in variables for which both sides of the equality are defined.
These identities are really helpful  in the event expressions involving trigonometric functions need to be simplified.
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The linear approximation of sin(9x) at x = 0 is A + Bt, where A = sin(0) = 0 and B = f'(0) = 9 that  is  sin(9x) ≈ 0 + 9x = 9x

The linear approximation of a function at a point is given by its first-order Taylor polynomial, which can be expressed as f(a) + f'(a)(x-a). In this case, we have a = 0 and f(x) = sin(9x), so we need to find f'(x) and evaluate it at x = 0.

Taking the derivative of sin(9x) with respect to x, we get:

f'(x) = 9cos(9x)

Evaluating this at x = 0, we get:

f'(0) = 9cos(0) = 9

So the linear approximation of sin(9x) at x = 0 is given by:

sin(9x) ≈ 0 + 9x = 9x

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Answer:

1260 is the answer

Step-by-step explanation:

you solve for the area of the rectangle and multiply it by 3 because there are three sides so 17x20=340x3=1020 then, you solve for the area of a triangle which is 1/2 x base x height so, 1/2 x 16 x 15 = 120 then you multiply that by 2 since there are 2 triangles so 120 x 120=240 finally, you add 1020+240 = 1260

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \stackrel{ doubled }{28900}\\ P=\textit{initial amount}\dotfill &14450\\ r=rate\to 2.7\%\to \frac{2.7}{100}\dotfill &0.027\\ t=years \end{cases} \\\\\\ 28900 = 14450(1 + 0.027)^{t} \implies \cfrac{28900}{14450}=(1.027)^t\implies 2=1.027^t \\\\\\ \log(2)=\log(1.027^t)\implies \log(2)=t\log(1.027) \\\\\\ \cfrac{\log(2)}{\log(1.027)}=t\implies 26.02\approx t[/tex]

The hypothesis referred to in this statement is likely the null hypothesis in a regression analysis, which assumes that the slope coefficient (b1) of the regression line is equal to zero, indicating that there is no relationship between the independent variable and the dependent variable. If the hypothesis is rejected, it means that there is sufficient evidence to suggest that the slope coefficient is not zero and there is a significant relationship between the independent and dependent variables.

In this context, the sample regression coefficient b1 represents the change in the predicted value of the dependent variable for a unit change in the independent variable. In other words, it indicates the slope of the regression line and how much the dependent variable changes for a unit change in the independent variable. If b1 is positive, it means that the dependent variable increases as the independent variable increases, and if b1 is negative, it means that the dependent variable decreases as the independent variable increases. The magnitude of b1 indicates the strength of the relationship between the variables, with larger values indicating a stronger relationship.

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Answer:

Step-by-step explanation:

To find the number of tickets Kenji hoped to sell each week, we can set up an equation based on the information given.

Let's assume Kenji's goal was to sell x tickets each week.

According to the problem, Kenji sold a total of 115 tickets after 8 weeks but was still 21 tickets short of his goal. This means he sold 115 - 21 = 94 tickets towards his goal.

The equation to find the number of tickets Kenji hoped to sell each week can be written as:

8x = 94

Here, 8 represents the number of weeks and x represents the number of tickets Kenji hoped to sell each week.

To solve the equation for x, we divide both sides by 8:

x = 94/8

Simplifying:

x = 11.75

Therefore, Kenji hoped to sell approximately 11.75 tickets each week to reach his goal. Since it is not possible to sell a fraction of a ticket, we can conclude that Kenji aimed to sell 11 tickets per week.

Statistics report that the average successful quitter is able to stop smoking after multiple attempts, usually between 8 to 10 times.  everyone's journey to quitting smoking is unique and may take more or fewer attempts to achieve success.

According to statistics, the average successful quitter is able to stop smoking after attempting to quit 6 to 30 times. This number varies due to individual factors and the methods used for quitting. Remember, persistence is key, and it is never too late to quit smoking for a healthier lifestyle.

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The equation of the line that passes through the point (6,8) and is perpendicular to a line is y = (-2/3)x + 12.

Given the equation, y= 3/2x + 5. Compare it with the general equation of the line,

y =  m₁   x + c₁

y= (3/2) x + 5

Therefore, the slope of the given line is m₁=(3/2).

Since it is needed to find the line that is perpendicular to y= 3/2x + 5, therefore, the slope of the two lines can be written as,

(Slope of line 1) × (Slope of line 2) = -1

m₁ × m₂ = -1

(3/2) × m₂ = -1

m₂ = -2/3

Now, the equation of the given line can be written as,

y = m₂x + c₂

y = (-2/3)x + c₂

Substitute the given coordinate in the above equation to get the value of y-intercept(c),

8 = (-2/3)6 + c₂

8 = -4 + c₂

c₂ = 8 + 4

c₂ = 12

Hence, the equation is y = (-2/3)x + 12.

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The complete question is:

What is an equation of the line that passes through the point (6, 8) and is perpendicular to a line with equation y=3/2x 5.

Martina used 16 pounds of type A coffee in her blend.

What is algebra?

Algebra is a branch of mathematics that deals with mathematical operations and symbols used to represent numbers and quantities in equations and formulas. It involves the study of variables, expressions, equations, and functions.

Let's assume that Martina used x pounds of type A coffee in her blend. Since the blend used four times as many pounds of type B coffee as type A, the amount of type B coffee used would be 4x pounds.

The total cost of the blend is given as the sum of the cost of type A and type B coffee, so we can write:

Cost = Cost of type A + Cost of type B

= x* + 4x*

Simplifying the expression, we get:

Cost = ( + 4) x

We are given that the total cost of the blend is , so we can write:

( + 4) x =

Solving for x, we get:

x = / ( + 4)

Substituting the given values, we get:

x = / ( + 4)

= / ( + 4)

= / ( + 4)

Therefore, Martina used 16 pounds of type A coffee in her blend.

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Answer: To solve this problem, we will use the formula d = a2 - a1, where d is the common difference and a1 and a2 are two consecutive terms in the sequence.

Step 1: Identify two consecutive terms in the sequence.

In this case, the two consecutive terms are 13 and 18.

Step 2: Substitute the two consecutive terms into the formula d = a2 - a1.

d = 18 - 13

Step 3: Simplify the equation to calculate the common difference.

d = 5

Therefore, the common difference of the arithmetic sequence 13, 18, 23, 28,... is 5.

Step-by-step explanation:

The exact values of the trigonometric functions are (a) cos(19π/6) = √3/2,

(b) cos(-7π/6) = -√3/2, (c) cos(-11π/6) = -√3/2

To find the exact values of the trigonometric functions at the given angles, we can use the unit circle and the periodicity and symmetry properties of the functions.

(a) cos(19π/6):

First, we note that 19π/6 is equivalent to 18π/6 + π/6, which is equivalent to 3π + π/6. Since cosine has period 2π, we can reduce 3π to π and write:

cos(19π/6) = cos(3π + π/6) = cos(π/6) = √3/2

(b) cos(-7π/6):

We can use the symmetry property of cosine to write:

cos(-7π/6) = cos(π - 7π/6) = -cos(π/6) = -√3/2

(c) cos(-11π/6):

We can again use the symmetry property of cosine to write:

cos(-11π/6) = cos(π - 11π/6) = -cos(π/6) = -√3/2

Therefore, the exact values of the trigonometric functions are:

(a) cos(19π/6) = √3/2

(b) cos(-7π/6) = -√3/2

(c) cos(-11π/6) = -√3/2

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The area of the cone that gets sprayed, from using the radius obtained from the formula for the lateral surface area is about 186.22 in²

The lateral surface area of a cone is the area covered by the curved surface of the cone.

The lateral surface area of the cone = 65·π square inches

The distance of the can from the canvas = 12 inches

The distance of the can from the canvas is the height, h, of the cone

The formula for finding the lateral surface area of a cone, A, can be presented as follows;

A = π·r·√(h² + r²)

Therefore, we get;

A = π·r·√(12² + r²) = 65·π

r·√(12² + r²) = 65

r²·(12² + r²) = 65²

12·r² + (r²)² = 65²

(r²)² + 12·r² - 65² = 0

r² = -6 ± √(4261)

r = √(-6 ± √(4261))

r ≈ 7.699, and r ≈ √(-71.28) (An imaginary number)

The area of the part of the canvas that gets sprayed with paint therefore is; A = π × (7.699 in)² ≈ 186.22 in²

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The value of x that makes the denominators equal to zero are x = -3 and x = 3.

To find the value(s) of the variable that undefine the expression, we need to identify when the denominators are equal to zero. The given expression is:
((x^2 - 8x + 12)/(x^2 - 9)) / ((x - 6)/(x + 3))
Step 1: Identify the denominators in the expression:
Denominator 1: (x^2 - 9)
Denominator 2: (x + 3)
Step 2: Set each denominator equal to zero and solve for x:
Denominator 1: (x^2 - 9) = 0
x^2 = 9
x = ±3
Denominator 2: (x + 3) = 0
x = -3
Step 3: List the value(s) of x that undefine the expression:
The value of x that makes the denominators equal to zero are x = -3 and x = 3. Thus, these are the values that undefine the given expression.

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To look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

For a regular polygon with n sides, the sum of its interior angles is given by ((n - 2) × 180) degrees. In the case of a round table seating 6 people, the table can be considered as a hexagon, which has 6 sides. Using the formula, we can calculate the sum of the interior angles:

((6 - 2) × 180) / 6 = (4 × 180) / 6 = 720 / 6 = 120 degrees

Since the table forms a complete circle, the sum of the interior angles is divided equally among the guests. Therefore, each guest sits at an angle of 120 degrees. To look from the guest to their left to the guest to their right, you need to rotate by the angle between adjacent guests, which is half of the angle they sit at:

120 / 2 = 60 degrees

Thus, to look from the guest to their left to the guest to their right at a round table seating 6 people, you need to rotate by 60 degrees.

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The lowest common denominator Skyla could use to rewrite the fractions is 280.

We have,

Value is the relative what merit or important of something it can referred to an intangible concept such as a person principle or a tangible object such as rare coin. Will you very widely across culture society individual it can even very within the same individual overtime. Value is often used to describe the worth of something in terms of its usefulness beauty. Will you can also refer to the moral or ethical standard of a person or group.

To get this value, she would need to find the least common multiple of the denominators, which are 17, 20, 56, 8, and 15. To do this, she would list out the prime factors of each denominator and then multiply the highest number of each prime factor together.

17: 1 x 17

20: 2 x 10

56: 2 x 2 x 7

8: 2 x 2 x 2

15: 3 x 5

The highest number of each prime factor is 17, 10, 7, 2, and 5, so the least common multiple of the denominators is 17 x 10 x 7 x 2 x 5, which equals 280. This would be the lowest common denominator she could use to rewrite the fractions.

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complete question:

Skyla is trying to order the fractions below. Her first step is to rewrite each fraction with a common denominator. What is the lowest common denominator she could use? 17 20 56 8 15​

The numbers that would be considered rational are -0.3/2, 0.7 and 3/2. The correct option is B.

We are given that;

The four options

Now,

A rational number is a number that can be written as a fraction of two integers. For example, 3/2 and 0.7 are rational numbers because they can be written as 3/2 and 7/10 respectively. However, √2 and pi are not rational numbers because they cannot be written as fractions of integers. They are irrational numbers because their decimal expansions are non-terminating and non-repeating. You can write your answer as:

Therefore, by the given fraction the answer will be -0.3/2, 0.7 and 3/2.

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After 3 years, Ana's account balance would be approximately $1221.96, assuming a constant withdrawal rate of $200 per year.

Ana opened a bank account with an initial balance of $1000 and an annual interest rate of 0.02, compounded continuously. The function P(t) models the balance of the account in dollars at time t.
The function P models the balance of Ana's account, given the information provided.

1. Ana opens a bank account with $1000. This is the initial amount in the account.
2. The account earns interest compounded continuously at an annual rate of r = 0.02.
3. Money can be withdrawn, but no additions can be made.

Since money can be withdrawn from the account at regular intervals and no additions can be made, we can assume that the withdrawals are made at a constant rate. Let's call this rate "w" (in dollars per year). Therefore, the function P(t) can be modeled as:
The function P models the balance of the account, in dollars, at time t. Since the interest is compounded continuously, we will use the continuous compound interest formula:
P(t) = P₀ * e^(rt)

Where:
- P(t) is the balance at time t
- P₀ is the initial balance ($1000)
- e is the base of the natural logarithm (approximately 2.71828)
- r is the annual interest rate (0.02)
- t is the time in years

We get: P(t) = 1000*e^(0.02t) - wt

where e is the mathematical constant, approximately equal to 2.71828. The first term represents the balance of the account with continuous compounding, while the second term represents the withdrawals made from the account over time.

To calculate the balance of the account at a specific time t, we can substitute that value into the function P(t). For example, if we want to find the balance of the account after 3 years and assume that the withdrawal rate is $200 per year, we can write:

P(3) = 1000*e^(0.02*3) - 200*3
P(3) = 1000*e^(0.06) - 600
P(3) ≈ $1221.96
This function P(t) represents the balance of Ana's account, in dollars, at any given time t in years, considering continuous compounding and the possibility of withdrawals.

Therefore, after 3 years, Ana's account balance would be approximately $1221.96, assuming a constant withdrawal rate of $200 per year.

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The probability that the spinner lands on 4​ under the condition that he rolls a 1 is 2/27,

Given that the spinner with 9 equally spaced regions numbered 1 to 9​ and a standard number cube is rolled,

So, the probability of spinning a 4 is = 4/9

The probability of rolling a 1 is = 1/6

The probability of both happening is = 1/6 x 4/9 = 4 / 54 = 2/27

Hence the probability that the spinner lands on 4​ under the condition that he rolls a 1 is 2/27,

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Answer:

Step-by-step explanation:

here is the solution i hope u enjoy with math

[tex]9 {}^{5} \div 9 {}^{3} \\ = 9 {}^{5 - 3}(applying \: the \: law \: \frac{a {}^{m} }{a {}^{n} } \: = a {}^{m - n)} \\ = 9 {}^{2} [/tex]

9^2 is the answer

Hope it helps you

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[tex]\bold{Thank ~you~:)}[/tex]