1
2
Arionna claims that since there are 3 feet in a yard, there are 9 cubic feet in a cubic yard. Which statement about her claim is
true?
Arionna is correct because there are 3 feet across the length of a cubic yard and 3 feet across the depth of a cubic yard.
3x3-9
Arionna is correct because there are 3 feet in a yard and there are 3 dimensions in a cubic yard length, depth, and height
3x3-9
Arionna is incorrect. There are only 3 cubic feet in a cubic yard because there are 3 feet in a yard, and the proportion wil
remain constant
Arionna is incorrect. There are 27 cubic feet in a cubic yard because a cubic yard is a prism with dimensions 3ft, 3x3ft
A prism with those dimensions will take 27 cubes to fill it if each cube is a unit cube of 1 ft
Helppppp

Part 1

The equation is \(y=a(x+8)(x-72)\).

Using the point \((62, -490)\) to solve for \(a\),

\(-490=a(62+8)(62-72) \implies a=\frac{7}{10}\\\\\therefore \boxed{y=\frac{7}{10}(x+8)(x-72)}\)

Part 2

When \(x=-8\), \(y=0\).

When \(x=2\), \(y=-490\).

So, the average rate of change is \(\frac{-490-0}{2-(-8)}=\boxed{-49}\)

Answer:

1/21

Step-by-step explanation:

first round 2/7

second round 1/6

2/7×1/6=1/21

The rectangle measures 2" by 3" and it is scaled up (increased) with a scale factor of 3.

This means that the sides of the rectangle were increased by a factor of 3.

Therefore, the sides of the image will be:

2 * 3 = 6 inches

and

3 * 3 = 9 inches

The dimensions of the image is 6 inches by 9 inches

The area of a rectangle is given as:

A = L * W

where L = length

W = width

Therefore, the area of the image is:

A = 6 * 9 = 54 square inches

Answer: It would cost $47.3 to fill the same tank in 2010

Step-by-step explanation:

In 1970

Total cost to fill the tank = $6

Cost per capacity of tank = $0.36

Capacity of tank = Total cost / Cost per capacity of tank

Capacity = 6/0.36

Capacity = 16.6

Therefore

In 2010

Cost per capacity of tank = $2.84

And we now know it capacity = 16.6

Total cost to fill the tank = 2.84 * 16.6

Total cost = $47.3

Hope this helps have a awesome day ❤️✨

Answer:

14/15

Step-by-step explanation:

You are adding fractions, so you need a common denominator.

The least common denominator (LCD) for 3 and 5 is 3 × 5 = 15.

Both denominators must become 15.

3/5 + 1/3 =

= 3/5 × 3/3 + 1/3 × 5/5

= 9/15 + 5/15

= 14/15

Answer: 14/15

Answer: C

Step-by-step explanation:

The column on an accounting worksheet that may not balance at the end of an accounting period is the Adjustments column.

The Adjustments column on an accounting worksheet includes all the adjusting entries that are needed to update the accounts before the financial statements are prepared. These adjustments can include accruals, deferrals, depreciation, and other adjustments that need to be made to the accounts to accurately reflect the financial position of the company.

Since the Adjustments column is used to record these adjusting entries, it is possible that this column may not balance at the end of the accounting period, as the adjustments may not perfectly offset each other. However, this is not a problem, as the purpose of the worksheet is to help prepare the financial statements, not to balance each individual column.

Therefore, the correct answer is option D, the Adjustments column.

Answer:

C. The Income Statement

Step-by-step explanation:

The Income Statement column on an accounting worksheet may not balance at the end of an accounting period.

An accounting worksheet is a tool used by accountants to help organize and summarize financial information and to prepare financial statements. The worksheet is typically a multi-column form that includes columns for the unadjusted trial balance, adjustments, adjusted trial balance, income statement, and balance sheet.

The Adjustments column is used to record adjusting entries and to update the account balances to reflect accruals, deferrals, and other accounting adjustments. The Adjusted Trial Balance column is the result of the adjustments made in the Adjustments column and should include all the account balances that will be used to prepare the financial statements.

Given statement solution is :-  The Vector Calculations and Addition results are as follows:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 7, -11, 0, 0 >

And 4 + 20 = 24.

To find the sum of 4 + 20, we simply add the two numbers together:

4 + 20 = 24

As for the given vectors, let's perform the requested calculations:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 4 + (-4), -2 + (-32) > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 7 - (-8), -3 - (-30) > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 5 + 2, -11 + 0, 0 + 0, 0 + 0 > = < 7, -11, 0, 0 >

Therefore, the Vector Calculations and Addition results are as follows:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 7, -11, 0, 0 >

And 4 + 20 = 24.

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The value of x⁵ in the expansion of (2x + 3) (x - 2)⁶ is 48.

Given,

The expression: (2x + 3) (x - 2)⁶

We have to find the value of x⁵ in the expansion .

(x - 2)⁶ = ∑(n = 6 and n = 0) (⁶ₙ) xⁿ

First calculate the coefficients of x⁴ and x⁵

Calculate the coefficient of x⁴ in (x - 2)⁶  (⁶₄) = 6! / 4!2! = 720/48 = 15

Calculate the coefficient of x⁵ in (x - 2)⁶ (⁶₅) = 6! / 5!1! = 720/120 = 6

Now,

2 x 15 + 3 x 6 = 30 + 18 = 48

That is,

The value of x⁵ in the expansion of (2x + 3) (x - 2)⁶ is 48.

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The perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

Let's call the length of AB x and the length of BC y.

First, we can use the fact that CD is the height of the triangle to find the area of triangle ABC:

Area of triangle ABC = 1/2 * CD * AB

Substituting the given values, we have:

1/2 * 12 * x = 6x

So the area of triangle ABC is 6x square centimeters.

We can also use the fact that angle BCD is 30 degrees to set up a trigonometric equation involving x and y:

tan(30) = x/y

Simplifying, we get:

y = x/tan(30) = x/(1/√(3)) = √(3) * x

Now we can use the formula for the area of a triangle in terms of its sides:

Area of triangle ABC = 1/2 * AB * BC * sin(B)

where B is the angle between sides AB and BC. In this case, we know that angle BCD is 30 degrees, so angle BCA is 60 degrees, and angle ABC is 90 degrees. Therefore, we have:

Area of triangle ABC = 1/2 * x * √3 * x * sin(60)

Simplifying, we get:

Area of triangle ABC = 1/4 * √3 * x²

Since we already found that the area of triangle ABC is 6x square centimeters, we can set these two expressions equal to each other and solve for x:

6x = 1/4 * √(3) * x²

Multiplying both sides by 4/√3, we get:

24/√(3) * x = x²

Simplifying, we get:

x² - 24/√(3) * x = 0

Using the quadratic formula, we get:

x = (24/√(3) ± √((24/√(3))² - 410)) / 2*1

Simplifying, we get:

x = 16√(3) / 3 or x = 8 √(3) / 3

Since we are looking for the perimeter of triangle ABC, we need to find y as well. Using the equation we derived earlier, we have:

y = √(3) * x

Therefore, we have two possible triangles:

Triangle ABC1: AB = 16 √(3) / 3, BC = 16, and AC = 8 √7 / 3

Triangle ABC2: AB = 8 √3 / 3, BC = 8, and AC = 4 √7 / 3

The perimeter of each triangle is the sum of its side lengths. Therefore:

Perimeter of triangle ABC1 = 16 √3/ 3 + 16 + 8 √7 / 3 ≈ 27.98 cm

Perimeter of triangle ABC2 = 8 √3 / 3 + 8 + 4 √7 / 3 ≈ 14.66 cm

hence, the perimeter of triangle ABC could be either approximately 27.98 cm or approximately 14.66 cm, depending on the length of AB.

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(b) The probability that the call is not for medical assistance = 0.37

(c) The probability that two successive calls will both be for medical assistance = 0.3969

(d) The probability that the first is for medical assistance and the second is not for medical assistance = 0.2331

(e) The probability that exactly one of the next two calls is going to be for medical assistance = 0.4662

The probability of an event is the proportion of favourable outcomes to all other possible outcomes. The symbol x can be used to denote how many successful outcomes there were in an experiment with 'n' outcomes. The formula below can be used to determine a given event's probability:

Probability (Event) = Positive Results/Total Results

                                 = x/n

Given P (call for medical assistance) = 0.63

This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.63 or 63%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:

P (Not Medical Assistance) = 1 - P (Medical Assistance)

                                            = 1 - 0.63

                                            = 0.37

Now, assuming that successive calls are independent of one another, the probability that two successive calls will both be for medical assistance will be:

P (2 calls for medical assistance)

= 0.63 × 0.63

= 0.3969

The probability that the first is for medical assistance and the second is not for medical assistance will be:

P (1st for medical assistance × 2nd for not medical assistance)

= 0.63 × 0.37

= 0.2331

The probability that exactly one of the next two calls is going to be for medical assistance will be:

P (Exactly 1 call for medical assistance)

= (0.63×0.37) + (0.63×0.37)

= 0.2331 + 0.2331

= 0.4662

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image has the answers

The second coordinate of the given first coordinate is determined as;

f(0) = 1 and (1) = 0.7.

The second coordinate of the given first coordinate is calculated by applying the following method as follows;

The given function;

F(x) = 0.7ˣ

The value of f(0) is calculated as;

f (0) = 0.7⁰  = 1

The value of f(1) is calculated as;.

f (1) = 0.7¹ = 0.7

Thus, the second coordinate of the given first coordinate is determined by applying the appropriate substitute of the function as shown above.

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Answer: cos A=4/5

Step-by-step explanation:

soh, cah, toa

Adjacent A is 32, hypotenuse is 40

32/40 simplifies to 4/5

The x-intercepts of the graph of f(x) are x = 3/2 and x = 1,the Vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point, The vertex is at (5/4, 3/8). This is the minimum point of the graph.

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

2x^2 - 5x + 3 = 0

To factor this quadratic equation, we look for two numbers that multiply to give 3 (the coefficient of the constant term) and add up to -5 (the coefficient of the linear term). These numbers are -3 and -1.

2x^2 - 3x - 2x + 3 = 0

x(2x - 3) - 1(2x - 3) = 0

(2x - 3)(x - 1) = 0

Setting each factor equal to zero, we get:

2x - 3 = 0   -->   x = 3/2

x - 1 = 0   -->   x = 1

Therefore, the x-intercepts of the graph of f(x) are x = 3/2 and x = 1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or a minimum, we look at the coefficient of the x^2 term, which is positive (2 in this case). A positive coefficient indicates that the parabola opens upwards, so the vertex will be a minimum.

To find the coordinates of the vertex, we can use the formula x = -b/2a. In the equation f(x) = 2x^2 - 5x + 3, the coefficient of the x term is -5, and the coefficient of the x^2 term is 2.

x = -(-5) / (2*2) = 5/4

Substituting this value of x back into the equation, we can find the y-coordinate:

f(5/4) = 2(5/4)^2 - 5(5/4) + 3 = 25/8 - 25/4 + 3 = 3/8

Therefore, the vertex of the graph of f(x) is (5/4, 3/8), and it is a minimum point.

Part C: To graph f(x), we can use the information obtained in Part A and Part B.

- The x-intercepts are x = 3/2 and x = 1. These are the points where the graph intersects the x-axis.

- The vertex is at (5/4, 3/8). This is the minimum point of the graph.

We can plot these points on a coordinate plane and draw a smooth curve passing through the x-intercepts and the vertex. Since the coefficient of the x^2 term is positive, the parabola opens upwards, and the graph will be concave up.

Additionally, we can consider the symmetry of the graph. Since the coefficient of the linear term is -5, the line of symmetry is given by x = -(-5) / (2*2) = 5/4, which is the x-coordinate of the vertex. The graph will be symmetric with respect to this line.

By connecting the plotted points and sketching the curve smoothly, we can accurately graph the function f(x).

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The area of the poster in inches is,

⇒ A = 4 inches²

We have to given that;

A rectangular poster is 50 centimeters long and 25 centimeters wide.

Here, 1 centimeter is approximately 0.4 inches

Hence, Lenght = 50 cm

Lenght = 50 x 0.4

            = 2 inches

Width = 25 cm

          = 25 x 0.4

           = 1 inches

Thus, The area of the poster in inches is,

⇒ A = 1 x 4

⇒ A = 4 inches²

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Answer:

x = 4

Step-by-step explanation:

(5-x) / (3/4x) = 1/3

multiply  both sides by 3/4 x

5-x  = 3/12 x    add 'x' to both sides of the equation

5 = 15/12 x       multiply both sides by 12/15

4 = x

Given that  F = <7xy, 2y²> is a vector field in the plane, and C the path y = 8x² joining (0,0) to (1,8) in the plane.the line integral ∫F.dr = 355¹/₃ units

Line integrals are integrals evaluated along a curve. It is given by I = ∫F.dr

where dr = dxi + dyj

Given that F = <7xy, 2y²> is a vector field in the plane, and C the path y = 8x² joining (0,0) to (1,8) in the plane.

So, we need to find the line integral ∫F.dr

Since

So, ∫F.dr = ∫[(7xy)i + (2y²)j.(dxi + dyj)] = ∫(7xydx + 2y²dy)

We integrate y from 0 to 8 and x from 0 to 1 and susbstitute y = 8x² into the equation. So, we have

∫F.dr = ∫(7xydx + ∫2y²dy)

= ∫(7x(8x²)dx + ∫2y²dy)

= ∫56x³dx + ∫2y²dy

= 56∫₀¹x³dx + 2∫₀⁸y²dy

= 56[x⁴/4]₀¹ + 2[y³/3]₀⁸

= 56[1⁴/4 - 0⁴/4] + 2[8³/3 - 0³/3]

= 56[1/4 - 0] + 2[512/3 - 0]

= 56[1/4} + 2[512/3]

= 14 + 1024/3

= (42 + 1024)/3

= 1066/3

= 355¹/₃ units

So, given that  F = <7xy, 2y²> is a vector field in the plane, and C the path y = 8x² joining (0,0) to (1,8) in the plane.the line integral ∫F.dr = 355¹/₃ units

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The volume of the solid of revolution formed by revolving the region bounded by f(x) = -3x² + 8 and g(x) = 3x² + 2 about the x-axis is 16π cubic units.

To find the volume of the solid of revolution formed by revolving the region bounded by the curves f(x) = -3x² + 8 and g(x) = 3x² + 2 about the x-axis, we can use the method of cylindrical shells and integrate.

First, let's find the points of intersection between the two curves by setting them equal to each other:

-3x² + 8 = 3x² + 2

Rearranging the equation, we get:

6x² = 6

x² = 1

x = ±1

So, the curves intersect at x = -1 and x = 1.

To calculate the volume, we'll integrate along the x-axis from x = -1 to x = 1. The volume of each cylindrical shell can be determined by multiplying the circumference (2πy) by the height (dx), where y represents the distance from the axis of revolution to the curve at a given x-value.

The radius of the cylindrical shell, y, can be obtained by subtracting the lower curve (f(x)) from the upper curve (g(x)). Therefore, y = (3x² + 2) - (-3x² + 8) = 6x² - 6.

The integral to compute the volume of the solid can be expressed as:

V = ∫[from -1 to 1] 2π(6x² - 6) dx

V = 2π ∫[from -1 to 1] (6x² - 6) dx

Simplifying and evaluating the integral, we get:

V = 2π [2x³ - 6x] [from -1 to 1]

V = 2π [(2(1)³ - 6(1)) - (2(-1)³ - 6(-1))]

V = 2π [2 - 6 - (-2 + 6)]

V = 2π [8]

V = 16π

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Answer:

To determine the amount of engine oil needed, we need to find 5% of 3.8 gallons:

0.05 x 3.8 = 0.19

So, 0.19 gallons of engine oil should be added to the jerry can.

The number that has a 4 in the hundred places.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

A 4 with a value ten times less than the 4 in the number 123,469.

First, the value of the 4 in the number 123,469 can be found by separating each digit as:

123,469 = 100,000 + 20,000 + 3,000 + 400 + 60 + 9

Then the value of the 4 is 400.

Now we want a number that has a 4 with a value then times less than 400. Then we have

400/10 = 40

Then we want a number that has a 4 in the hundred places.

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The classification of the expressions as equivalent to 7^2m / 49^m is given as follows:

The equivalent expression are obtained applying exponent properties.

At the numerator, the expression is of:

7^2m.

Applying the square, the expression will be equivalent to:

49^m.

The denominator is given as follows:

49^m.

49 is equivalent to 7², hence the denominator can be written as follows:

7^2m.

Then the expression can be written as follows:

7^2m/7^2m

For the quotient of two terms with the same base and different expressions, we keep the base and subtract the exponents, hence:

7^2m/7^2m = 7^(2m - 2m)

Which is the equivalent expression.

The options are given by the image shown at the end of the answer.

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The transformations that map the strip pattern onto itself is a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°. Option A is the correct option.

Here, we have,

the conditions for mapping the strip transformation pattern onto itself:

The strip pattern can be mapped onto itself in two different ways.

The first way is to translate the strip pattern horizontally and then rotate it by 180° degrees.

The second way is to reflect the strip pattern across a vertical line.

Hence, the transformations that map the strip pattern onto itself can be achieved through a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°.

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complete question:

Which transformations map the strip pattern onto itself?

a horizontal translation, a reflection across a vertical line, a reflection across a horizontal line, a glide reflection, and a 180°

a horizontal translation only

a horizontal translation, a reflection across a horizontal line, and a glide reflection only

a horizontal translation and a 180° rotation only

Answer:

A

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

5 times 4 is 20 divided by 2 is 10 hope this helps

Answer:

126

Step-by-step explanation:

There are 126 different ways he can wear the outfit.

The definition of the combination is "An arrangement of objects where the order of the objects is irrelevant." Combining these two words indicates "Selection of things," where the order of the items is irrelevant.

Given:

Number of pairs of shoes= 7

Pants= 3 pairs

Shirts= 6

So, different outfits can he​ wear

= 7 x 3 x 6

= 21 x 6

= 126

Hence, there 126 different ways he can wear the outfit.

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Answer:

Option A

Step-by-step explanation:

Given function is,

f(x) = x² + 3x + 5

We have to find the value of f(a + h) so we will substitute (a + h) in place of x, and simplify the expression.

f(a + h) = (a + h)² + 3(a + h) + 5

           = a² + 2ah + h² + 3(a + h) + 5 [(a + b)² = a² + 2ab + b²]

           = a² + 2ah + h² + 3a + 3h + 5

Therefore, Option A will be the answer.

the data classification (categorical or quantitative) and type of data (Nominal or Ordinal or Continuous or Discrete)

A. Height of sunflowers in a field.

1.Quantitative

2.Continuous

B. Jersey color of all the NCAA football teams.

1.Categorical

2.Nominal

A. Height of sunflowers in a field.

1.Quantitative

2.Continuous

B. Jersey color of all the NCAA football teams.

1.Categorical

2.Nominal

Data classification is a process of organizing data into categories based on their characteristics, attributes, or features. There are two main types of data classification:

Categorical Data: Data that can be divided into categories or classes. For example, color, gender, and type of cuisine are all examples of categorical data. Categorical data can be further classified into two types:

a. Nominal Data: Data that does not have an inherent order or ranking. For example, hair color, eye color, and favorite movie are all examples of nominal data.

b. Ordinal Data: Data that has a natural order or ranking. For example, education level (high school, college, postgraduate), star rating (1 star, 2 stars, 3 stars), and satisfaction level (very unsatisfied, unsatisfied, neutral, satisfied, very satisfied) are all examples of ordinal data.

Quantitative Data: Data that can be measured and expressed as a number. For example, height, weight, and time are all examples of quantitative data. Quantitative data can be further classified into two types:

a. Continuous Data: Data that can take on any value within a specified range. For example, height, weight, and temperature are all examples of continuous data.

b. Discrete Data: Data that can only take on specific values. For example, number of children in a family, number of pets, and number of rooms in a house are all examples of discrete data

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Answer:

I don't know yet haheuehehheejejejej