Reflection across y = x

Answer:

3/4 a pint

Step-by-step explanation:

1/4 + 2/4 = 3/4

Answer:

60

Step-by-step explanation:

Let x = the number

x - 10%x = 54

x - 0.1x = 54

0.9x = 54

x = 54 / 0.9 = 60

Answer:

Ans: 36

Step-by-step explanation:

just separate it into three rectangles and use the formula

A=l*b

and at last add all of them

Answer:

$0.15

Step-by-step explanation:

1/4 of a can = 0.25 cans

4 ÷ 0.25 = 16

if 0.25 cans is 1/16 of 4, then the price of 0.25 cans would be 1/16 of $2.40

2.40 ÷ 16 = $0.15

Using line tangent, the approximation for f(2.1) is 3.95

Given,

The point (a, f(a)) is on the line tangent to the graph of y = f(x) at x = a, which has a slope of f'(a).

The equation be like;

y - f(a) / (x - a) = f'(a)

y = f'(a) (x - a) + f(a)

Using the provided data and a = 2, we can determine that the tangent line to the graph of y = f(x) at x = 2 has equation

y = f'(2) (x - 2) + f(2)

y = -1/2 (x - 2) + 4

To compute a "approximation of f(2.1) using the line tangent to the graph of f at x = 2," one must substitute x = 2.1 for f in the equation for the tangent line (2.1). You get 2.1 when you plug this in.

y = -1/2 (x - 2) + 4

y = -1/2 (2.1 - 2) + 4

y = -1/2 x 0.1 + 4

y = 3.95

That is,

The approximation for f(2.1) using line tangent is 3.95

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Answer:403.2

Step-by-step explanation:multiply whole numbers  multiply  19.6 times 27  which = 158.4

Principal steps in the design phase are Design Strategy, System Architecture, User Interface, Database and File Specification and Program Design, The Major deliverables are System Specification.

- Phases are broad groupings of tasks.

- Steps are tasks (work to be performed).

- Techniques are ways to carry out tasks.

- Deliverables are the understanding (or materials) produced during task accomplishment.

- Each phase is itself composed of a series of steps, which rely upon techniques that produce deliverables (specific documents and files that provide understanding about the project).

Principal steps in the Design Phase:

Design Strategy

- Determining proper approach for acquiring

System architecture

- Describing basic hardware, software, and networking

User interface

- Developing system's overall structure, navigation, inputs, outputs, and screens

Database and file specifications

- Specifying data storage structures

Program Design

- Plans and outlines for each program to be written

So,

Principal steps in the Design phase are Design Strategy, System Architecture, User Interface, Database and File Specification and Program Design, The Major deliverables are System Specification.

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According to fraction, another way to express 8 feet is written as 2 ²/₃ yards.

In math the term fraction refers the numerical values that are a part of the whole.

As we have given that a clothesline rope is 8 feet long.

Now, we have to find another way to express 8 feet.

The process of converting a foot measurement to a yard measurement, here we have to divide the length by the conversion ratio.

As we all know that one yard is equal to 3 feet, therefore, here you can use this simple formula to convert:

=> feet ÷ 3 = 1 yard

As the given feet measurement is 8 feet.

Then the equivalent yard measurement is written as,

=> 8/3 feet = yards

After the simplification, that is convert it into mixed fraction form, then we get the resulting yards as 2 ²/₃ yards.

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Answer:

The amount of metal recovered at the eight pass is approximately 4.27 kg

Step-by-step explanation:

The mass of metal recovered formed the following geometric sequence;

32 kg, 24 kg, 18 kg, 13.5 kg

∴ The first term, a = 32 kg

The common ratio in the geometric sequence is found as follows;

r = a·r/a = 24 kg/(32 kg) = 0.75

r = a·r²/a·r = 18 kg/(24 kg) = 0.75

r = a·r³/a·r² = 13.5 kg/(18 kg) = 0.75

The mass of the metal recovered in the eight pass will be the 8th term of the geometric series given as follows;

nth term = a·rⁿ⁻¹

a = 32, r = 0.75, n = 8

∴ 8th term = 32·(0.75)⁸⁻¹ = 32·0.75⁷ = 2187/512 ≈ 4.27

The amount of metal recovered at the eight pass ≈ 4.27 kg.

The eight term of the geometric sequence is 4.27.

A geometric sequence is in the form:

aₙ = ar⁽ⁿ⁻¹⁾

where aₙ is the nth term, a is the first term and r is the common difference.

Given that a = 32, r = 24/32 = 0.75

The eight term is a₈ = 32(0.75)⁸⁻¹ = 4.27

The eight term of the geometric sequence is 4.27.

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Answer:

(x+a)²-7=x²+10x+b

simplifying,we get

x²+2ax+a²-7=x²+10x+b

the coefficient of x on both sides should be equal

therefore

2a=10

a=10/2=5

also for b

a²-7=b

5²-7=25-7=b

b=18

a=5

Answer:

12/25 and 12/24

Step-by-step explanation:

Answer:

12 over 25 and 11 over 24

Step-by-step explanation:

12 yellow marble out of 25 then you take one away because a marble wasn't put back into the bag so 11 over 24

According one-way ANOVA, the test is false.

We learn about one-way ANOVA

"One-Way ANOVA, also known as "analysis of variance," examines the refers to two or more independent groups to see if there is statistical support for the notion that the related population means are statistically substantially different."

According to the given information, it is inappropriate to compare two means at a time using multiple independent two sample​ t-tests. It will create multiple testing problem and error.

So using one way ANOVA test when comparing three or more populations refers to within a set of quantitative data that is categorized according to one​ factor/treatment and compare two means at a time using multiple independent two sample​ t-tests is false.

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Answer:

x = -4

Step-by-step explanation:

hope this helps you

The ordered pair that lies on the inverse of the function is (25, 0)

From the question, we have the following parameters that can be used in our computation:

g(x)=−(x−3)^3−2.

Set x = 0

So, we have the following representation

g(0) =−(0−3)^3−2.

Evaluate the expression

This gives

g(0) = 25.

So, the ordered pair of teh inverse is (25, 0)

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Answer: -3,4

Step-by-step explanation:

The projected ending cash balance for theTmonth is -$260. Therefore, the correct option is OB. ($260).

Initial cash balance: $1,200

Projected revenue: $2,350

Gas: $100

Equipment maintenance fees: $290

Truck payment: $400

Payroll: $2,900

Insurance: $120

Total expenses: $100 + $290 + $400 + $2,900 + $120 = $3,810

Projected ending cash balance: Initial cash balance + Projected revenue - Total expenses

= $1,200 + $2,350 - $3,810

= $1,200 + $2,350 - $3,810

= $3,550 - $3,810

= -$260

Based on the calculations, the projected ending cash balance for the month is -$260. Therefore, the correct option is OB. ($260).

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Answer: 16/20, or reduced, 4/5

Step-by-step explanation:

Cos = adjacent / hypotenuse

Cos = 16/20

The explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

The given sequence is -4, 16, -64, 256,...

If we observe the sequence it is a geometric sequence

aₙ=a.rⁿ⁻¹

a is the first term and r is the common ratio

From the sequence the first term is -4 and common ratio is -4

aₙ=(-4).(-4)ⁿ⁻¹

Plug in the value n as 8

a₈=(-4).(-4)⁷

The value of minus four power seven is minus sixteen thousand three hundred eighty four

a₈=(-4)(-16384)

When four is multiplied with sixteen thousand three hundred eighty four we get sixty five thousand five hundred thirty six

a₈= 65536

Hence, the explicit formula for the sequence is aₙ=(-4).(-4)ⁿ⁻¹ and the 8th term is 65536

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Among the given options, the equation that does NOT represent a line perpendicular to the line 8x-4y=1 is option D: y = -1/2x.

To determine if a line is perpendicular to another line, we need to compare their slopes.

Two lines are perpendicular if and only if the product of their slopes is -1.

The given line, 8x-4y=1, can be rewritten in slope-intercept form as y = 2x - 1.

The slope of this line is 2.

Let's analyze each option:

A. x + 2y = 7: This equation can be rewritten as y = -1/2x + 7/2.

The slope of this line is -1/2.

The product of the slopes (-1/2 * 2) is -1, indicating that this line is perpendicular to the given line.

B. 4x - 8y = 1: Dividing by 4 and rearranging the equation, we have y = 1/2x - 1/8.

The slope of this line is 1/2.

The product of the slopes (1/2 * 2) is 1, which means this line is not perpendicular to the given line.

C. y - 4 = -1/2(x + 8): Simplifying the equation, we get y = -1/2x - 6.

The slope of this line is -1/2.

The product of the slopes (-1/2 * 2) is -1, indicating that this line is perpendicular to the given line.

D. y = -1/2x: The slope of this line is -1/2.

However, the product of the slopes (-1/2 * 2) is not -1, indicating that this line is not perpendicular to the given line.

Therefore, the equation that does NOT represent a line perpendicular to the line 8x-4y=1 is option D: y = -1/2x.

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To find the derivative of the following function f(x) = 9x² - 4x + 73 by using the limit definition, the following steps need to be followed:Step 1: Start with the limit definition of derivative:lim h→0 f(x+h) - f(x) / h

Step 2: Substitute the function f(x) with the given function f(x) = 9x² - 4x + 73.f(x) = 9x² - 4x + 73f(x+h) = 9(x+h)² - 4(x+h) + 73Step 3: Expand the function f(x+h).f(x+h) = 9(x² + 2xh + h²) - 4x - 4h + 73Step 4: Substitute f(x+h) and f(x) in the limit definition of derivative.lim h→0 9(x² + 2xh + h²) - 4x - 4h + 73 - (9x² - 4x + 73) / h

Step 5: Simplify the above equation by removing the like terms and cancelling out the opposite terms.lim h→0 18xh + 9h² - 4h / h Step 6: Cancel out h from numerator and denominator of the above equation and simplify the remaining expression. lim h→0 18x + 9h - 4 = 18x - 4Step 7: Write the final answer which is the derivative of the given function. f'(x) = 18x - 4Therefore, the derivative of the function f(x) = 9x² - 4x + 73 by using the limit definition is f'(x) = 18x - 4.

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Answer:

Step-by-step explanation:

diagonal  = 32 cm

Area of square = \(\dfrac{d^{2}}{2}\)

                        \(=\dfrac{32*32}{2}\\\\=512 \ cm^{2}\)

Diagonal separate the square into two equal triangles.

Area of upper triangle that is shaded black = area of lower triangle = 512/2

= 256 cm²

Isosceles triangle:

a = 6 cm  ; b = 6 cm c = 8cm

\(s = \dfrac{a+b+c}{2}\\\\=\dfrac{6+6+8}{2}\\\\=\dfrac{20}{2}\\\\=10\\\\s-a = 10 - 6 = 4 \ cm\\\\s-b = 10-6 = 4 \ cm\\\\c - c = 10 - 8 = 2 \ cm\\\\Area = \sqrt{s*(s-a)(s-b)(s-c)}\\\\=\sqrt{10*4*4*2}\\\\=\sqrt{2 * 2 * 4 * 4 * 5}\\\\=4*2\sqrt{5}\\\\=8\sqrt{5}\\\\=8*2.24\\\\=17.92 \ cm^{2}\)

Area of black shade paper = 256 + 17.92 =  273.92 cm²

Area of white shade paper = 256 cm²

Area of the isosceles triangle = s(s-a)(s-b)(s-c)

Confidence interval refers to a statistical measure that helps quantify the amount of uncertainty present in a sample's estimate of a population parameter.

This measure expresses the degree of confidence in the estimated interval that can be calculated from a given set of data. In this scenario, the task is to build a 95% confidence interval for the regression line's slope. The regression analysis output has already been given. According to the output given, the estimated regression model is:y = 25,000 + 9,000 x, where x represents the number of miles the car has been driven and y represents the car's selling price.

The formula to calculate the 95% confidence interval for the slope is:Slope ± t · SE, where Slope is the point estimate for the slope, t represents the critical t-value for a given level of confidence and degrees of freedom, and SE represents the standard error of the estimate. The value of t can be calculated using the degrees of freedom and a t-table. Here, the number of pairs in the sample size is 20, and the model uses two parameters.

Therefore, the degrees of freedom would be 20 - 2 = 18.The critical t-value for a 95% confidence interval and 18 degrees of freedom is 2.101. Using the formula given above, we can calculate the 95% confidence interval for the slope as follows:Slope ± t · SE= 9000 ± (2.101)(700) ≈ 9000 ± 1,467.7 = [7,532.3, 10,467.7]Therefore, the 95% confidence interval for the slope is [7,532.3, 10,467.7]. This means that we are 95% confident that the true value of the slope for this model falls within the interval [7,532.3, 10,467.7].

It implies that the price of the car increases by $7,532.3 to $10,467.7 for each mile driven by the car. In conclusion, a 95% confidence interval has been calculated for the regression line's slope, which indicates that the actual slope of the model lies between the range [7,532.3, 10,467.7].

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Step-by-step explanation:

the general slope-intercept form is

y = ax + b

a is the slope, b is the y-intercept.

we need to transform x + 2y = 6, so that we end up with y being all alone on one side, and the rest on the other side.

x + 2y = 6

2y = -x + 6

y = -x/2 + 6

9) We have: 23,15% × 35 = 8,1025 kg

There are 8,1025 kilograms of cashew nuts were there in the mixed nuts

10) We have:

Answer:

For a day VFR flight in a Piper Archer, you would need a fuel reserve of approximately 5 gallons.

Step-by-step explanation:

The amount of fuel reserve that must be carried on a day VFR (Visual Flight Rules) flight, the FAA requires a minimum fuel reserve of 30 minutes at cruising speed for day VFR flights. To calculate the gallons needed for a Piper Archer, follow these steps:

1. Determine the fuel consumption rate of the Piper Archer at cruising speed, which is typically around 10 gallons per hour (GPH).
2. Divide the required fuel reserve minutes (30) by the minutes in an hour (60): 30 / 60 = 0.5 hours.
3. Multiply the fuel consumption rate (10 GPH) by the required fuel reserve time in hours (0.5 hours): 10 * 0.5 = 5 gallons.

Therefore, for a day VFR flight in a Piper Archer, you would need a fuel reserve of approximately 5 gallons.

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Answer:

100 degrees

Step-by-step explanation:

You can tell by just looking at the picture :)

The arc length is D) 3.14 meters.

What is arc length?

In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.

It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.

The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.

                                      \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

Here the give circle Radius PR = 3m and θ=60°.

Now using arc length formula then,

=> Arc length \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

=> \(A_L=\frac{60}{360} \times2\times3.14\times3\)

=> \(A_L=\frac{1}{6}\times2\times3.14\times3\)

=> \(A_L\) = 3.14 m.

Hence the arc length is D) 3.14 meters.

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Answer:

y=-4

x=-12

Step-by-step explanation:

Set up the system

Then you have to cancel out a variable

Then you solve for the remaining variable

Then plug in to find other variable

I'm sorry if that's confusing:/

The probability that the book is non-fiction, round to 2 decimal place = 1.72

Based on the given conditions,

A shelf holds 19 different books

8 are fiction and rest non-fiction.

If a shelf holds19 books on her bookshelf and it has 8 fiction books, the number of non-fiction books .

A shelf has will be 19-8 = 11 non- fiction books.

Probability = Expected outcome of event/total outcome.

Our anticipated result will be 11, as we're looking for the expression that captures the likelihood that the book she chooses will be non-fiction (the total non fiction she selected)

The total outcome will be the total number of books

That is, 19.

Probability that she elects non fiction book = 19/11

= 1.72

Therefore,

The probability that the book is non-fiction, round to 2 decimal place = 1.72

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