Connor's family took a road trip to Niagara Falls. Connor slept through the last 15% of the trip. If Connor fell asleep after they had travel 663 miles what was the total length of the trip.

Answer:

Step-by-step explanation:

Common difference is the difference between two consecutive terms:

Or you can use the slope of the line as common difference, which is 8.

Step-by-step explanation:

\(we \: want \: to \: find \: commen \: differe \: nce \\ so \: put \: n= 1 \: and \: n = 2 \\ then \: calculate \: its \: difference \\ then \\ f(n) = 8n + 2 \\ f(1) = 8 \times 1 + 2 = 8 + 2 = 10 \\ f(2) = 8 \times 2 + 2 = 16 + 2 = 18 \\ f(2) - f(1) = 18 - 10 = 8 \\ 8is \: the \: commen \: difference \\ thank \: you\)

Answer:

  none

Step-by-step explanation:

We assume you intend positive rational bases.

\(663_b\) is divisible by 3, so cannot be prime.

Answer:

50 inches.

Step-by-step explanation:

Answer:

cosA ≈ 0.55

Step-by-step explanation:

cosA = \(\frac{adjacent}{hypotenuse}\) = \(\frac{AC}{AB}\) = \(\frac{6}{11}\) ≈ 0.55 ( to the nearest hundredth )

The transpose of A⁻¹ is the inverse of the transpose of A⁻¹, which implies that if A⁻¹ is orthogonal, then A is orthogonal. Therefore, we have shown that the matrix A is orthogonal if and only if its transpose A⁻¹ is orthogonal.

To find the orthogonal projection of vector w into the plane spanned by vectors u and v, we need to calculate the projection vector proj_w(uv).

First, we calculate the normal vector n of the plane. The normal vector is obtained by taking the cross product of vectors u and v:

n = u x v

= (1, 0, -1) x (4, 3, -2)

The cross product can be calculated as follows:

n = ((0)(-2) - (-1)(3), (-1)(4) - (1)(-2), (1)(3) - (0)(4))

= (-3, -6, 3)

Next, we normalize the normal vector n to obtain the unit normal vector n:

n = n / ||n||

= (-3, -6, 3) / √(9 + 36 + 9)

= (-3, -6, 3) / √54

= (-1/√6, -2/√6, 1/√6)

Now, we can calculate the projection of vector w onto the plane using the formula:

proj_w(uv) = w - ((w · n) / (n · n)) * n

The dot product of w and n is given by:

w · n = (2)(-1/√6) + (3)(-2/√6) + (-2)(1/√6)

= -2/√6 - 6/√6 - 2/√6

= -10/√6

The dot product of n and n is:

n · n = (-1/√6)(-1/√6) + (-2/√6)(-2/√6) + (1/√6)(1/√6)

= 1/6 + 4/6 + 1/6

= 6/6

= 1

Substituting these values into the projection formula, we have:

proj_w(uv) = (2, 3, -2) - ((-10/√6) / 1) * (-1/√6, -2/√6, 1/√6)

= (2, 3, -2) + (10/√6)(-1/√6, -2/√6, 1/√6)

= (2, 3, -2) + (-10/6, -20/6, 10/6)

= (2, 3, -2) + (-5/3, -10/3, 5/3)

= (2 - 5/3, 3 - 10/3, -2 + 5/3)

= (1/3, 1/3, -1/3)

Therefore, the orthogonal projection of vector w into the plane spanned by vectors u and v is (1/3, 1/3, -1/3).

Now, let's prove the statement that the matrix A is orthogonal if and only if its transpose A⁻¹ is orthogonal.

To prove this, we need to show two conditions:

If A is orthogonal, then A⁻¹ is orthogonal:

If A is orthogonal, it means that A · A⁻¹ = I, where I is the identity matrix.

Taking the transpose of both sides, we have (A · A⁻¹)ᵀ = Iᵀ, which simplifies to (A⁻¹)ᵀ · Aᵀ = I.

This shows that the transpose of A⁻¹ is the inverse of the transpose of A, which implies that if A is orthogonal, then A⁻¹ is orthogonal.

If A⁻¹ is orthogonal, then A is orthogonal:

If A⁻¹ is orthogonal, it means that (A⁻¹) · (A⁻¹)ᵀ = I, where I is the identity matrix.

Taking the transpose of both sides, we have ((A⁻¹) · (A⁻¹)ᵀ)ᵀ = Iᵀ, which simplifies to ((A⁻¹)ᵀ) · (A⁻¹) = I.

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The three types of consulting services that audit firms are now prohibited from providing to clients that are public companies are:

1. Bookkeeping services: Audit firms are prohibited from providing bookkeeping services to their audit clients. Bookkeeping involves the recording, organizing, and maintaining of financial transactions.

By prohibiting audit firms from providing bookkeeping services, it helps to ensure independence and objectivity in the audit process. This separation reduces the risk of potential conflicts of interest that could compromise the integrity of the audit.

2. Legal services: Audit firms are also prohibited from providing legal services to their audit clients. Legal services include activities such as drafting legal documents, providing legal advice, and representing clients in legal proceedings.

The prohibition on providing legal services aims to maintain independence and prevent any potential conflicts of interest that could arise if the audit firm were to also provide legal advice or services to the audited company.

3. Financial information systems design and implementation: Audit firms are further prohibited from designing and implementing financial information systems for their audit clients.

This involves the development and implementation of computerized systems that record and process financial data. The prohibition on providing financial information systems design and implementation services helps to avoid any potential bias or lack of objectivity in the audit process,

as the audit firm should remain independent and not be involved in the design and implementation of the systems they are auditing.

By prohibiting audit firms from providing these consulting services, it helps to ensure that the audit process is conducted objectively and independently, without any conflicts of interest.

This enhances the credibility and reliability of financial statements and promotes transparency and trust in the financial markets.

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Answer:

9.17cm (3s.f.)

Step-by-step explanation:

Using Pythagoras Theorem,

5² = 2² + (Height of Triangle)²

Height of Triangle = 4.5826cm (5s.f.)

Area = ½ × 4 × 4.5826

= 9.1652cm (5s.f.)

= 9.17cm (3s.f.)

Answer:

the answer would be it costs $30 for 20 bags of rice

Step-by-step explanation:

divide $3 by 2 to get $1.50 and then multiply $1.50 by 20 to get $30

Answer:

30 dollars

Step-by-step explanation:

2 x 10 equals 20, so multiply 10 by 3 and you get 30.

Answer:

.767

Step-by-step explanation:

0. ones, tens, hundreds, thousands

Answer:

perpendicular :)))))))))))))

Answer:

the rise and run would be 2/1 so the transformation would be 2

Step-by-step explanation:

the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.

Given the system of equations:

1) y = 6x - 11

2) -2x - 3y = -7

Step 1: Solve equation (1) for y.

  y = 6x - 11

Step 2: Substitute the value of y from equation (1) into equation (2).

  -2x - 3(6x - 11) = -7

Step 3: Simplify and solve for x.

  -2x - 18x + 33 = -7

  -20x + 33 = -7

  -20x = -7 - 33

  -20x = -40

  x = (-40)/(-20)

  x = 2

Step 4: Substitute the value of x into equation (1) to find y.

  y = 6(2) - 11

  y = 12 - 11

  y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.

To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.

Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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Hence, in answering the stated question, we may say that We can travel slope intercept down 3 units and right 1 unit to acquire another point on the line because the slope is -3.

The intersection point in mathematics is the point on the y-axis where the slope of the line intersects. a point on a line or curve where the y-axis intersects. The equation for the straight line is Y = mx+c, where m represents the slope and c represents the y-intercept. The intercept form of the equation emphasises the line's slope (m) and y-intercept (b). The slope of an equation with the intercept form (y=mx+b) is m, and the y-intercept is b. Several equations can be reformulated to seem to be slope intercepts. When y=x is represented as y=1x+0, the slope and y-intercept are both set to 1.

We must solve for y in order to find the slope-intercept form of the equation:

6x + 2y = 4

2y = -6x + 4

y = -3x + 2

As a result, the slope is -3 and the y-intercept is 2.

To graph the line, first plot the y-intercept at the point (0, 2). The slope can then be used to find another point on the line. We can travel down 3 units and right 1 unit to acquire another point on the line because the slope is -3.

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The value of a Chi-Square goodness-of-fit test at a 5% significance level is 13.45

We need to perform a Chi-Square goodness-of-fit test at a 5% significance level.

First we need to calculate the expected count

expected value = ∑(x)/n

= (40 + 33 + 35 + 32 + 60)/5

= 200/5

= 40

Now we need tocalculate the test statistic value

Observed  expected  O - E    (O - E)^t/E       %

40                40             0            0                   0

33                40             -7          1.225          9.11

35                40             -5          0.625         4.65

32                40             -8         1.6                11.90

60                40             20        10                 74.35

Chi square test is 13.45

Therefore, the value of test statistics is 13.45.

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9514 1404 393

Answer:

  ₹663

Step-by-step explanation:

The ratio of the tax to the total is ...

  13%/(100%+13%) = VAT/5763

  VAT = 5763(0.13/1.13) = 663

The value added tax is ₹663.

The components of the vector when A = 3.00 and θ₃ = -30.0° are (2.60, -1.50).

The question requires us to find the components of vectors in two different cases.

We are given the magnitude and angle of each vector with respect to the positive or negative x-axis.Let us start with the first vector.

Given,A = 6.00θ₂

= 120°

We can find the components using the following equations:

x = Acosθ

y = Asinθ

Substituting the values, we get:

x = 6.00cos120°

y = 6.00sin120°

Now, let us simplify these expressions.

x = -3.00

y = 5.20

Therefore, the components of the vector when

A = 6.00 and

θ₂ = 120° are (-3.00, 5.20).

Let us move on to the second vector. Given,

A = 3.00θ₃

= -30.0°

We can find the components using the following equations:

x = Acosθ

y = Asinθ

Substituting the values, we get:

x = 3.00cos(-30.0°)

y = 3.00sin(-30.0°)

Now, let us simplify these expressions.

x = 2.60y

= -1.50

Therefore, the components of the vector when

A = 3.00 and

θ₃ = -30.0° are (2.60, -1.50).

Given,

A = 6.00,

θ₂ = 120°,

A = 3.00,

θ₃ = -30.0°

We use the equations: x = Acosθ

y = Asinθ

For the first vector, we get:

x = 6.00cos120°

y = 6.00sin120°

Simplifying these expressions, we get:

x = -3.00

y = 5.20

Therefore, the components of the vector when

A = 6.00 and

θ₂ = 120° are (-3.00, 5.20).

For the second vector, we get:

x = 3.00cos(-30.0°)

y = 3.00sin(-30.0°)

Simplifying these expressions, we get:

x = 2.60

y = -1.50

Therefore, the components of the vector when A = 3.00 and θ₃ = -30.0° are (2.60, -1.50).

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Answer:

$20.84

Step-by-step explanation:

div 1 = $0.50

div 2 = $0.50

div 3 = $0.50 x 1.05 = $0.525

div 4 = $0.525 x 1.05 = $0.55125

years 5 and beyond we need to use the growing perpetuity formula:

stock price = [div 4 x (1 + g)] / (r - g) = ($0.55125 x 1.1) / (12% - 10%) = $30.32

now to determine the current value of the stocks we must calculate the present value of the future dividends and stock price:

stock price = $0.50/1.12 + $0.50/1.12² + $0.525/1.12³ + $0.55125/1.12⁴ + $30.32/1.12⁴ = $0.45 + $0.40 + $0.37 + $0.35 + $19.27 = $20.84

Etta needs to add the source of the information to better arrange these notes.

A note is a place where information about a specific item is recorded for later reference. The main goals of taking notes are to promote active learning and create study materials for tests. You should be able to organise material into an understandable format that will aid in your learning process by developing note-taking skills.

As a result, it is clear from the question that Etta is making notes for the purpose of creating a webpage about healthy eating. Once her notes have been organised with the relevant facts and information, Etta will need to cite her sources.

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Answer:

the answer is 42

Step-by-step explanation:

12-6+(14-8)^2

12-6(6)^2

12-6+36

=42

Answer:

$6.83

Step-by-step explanation:

37 x 59 = 2183

Because it is dollars you need to divide it by 100:

$21.83 - 15 = 6.83

Answer:

540 miles an hour or 2,851,200 Feet an hour

Step-by-step explanation:

Answer:

.... The answer is (3.8)^12

Answer:

Option A

Step-by-step explanation:

x : y = 1 : 3

This can be also written as

\( \frac{x}{y} = \frac{1}{3} \)

Multiplying y on both the sides

\( = > \frac{x}{y} \times y = \frac{1}{3} \times y\)

\( = > x = \frac{1}{3} \times y\)

Hence , x is one-third of y

Answer:

A and B

x is \(\frac{1}{3}\) of y

AND

y is \(\frac{3}{4}\) of (x+y)

Step-by-step explanation:

x:y is 1:3

=>  y is bigger than x

=>  y is 3x bigger than x

=>  y = 3 lots of x

=>  \(y =\) \(3x\)

=>  \(\frac{y}{3}\) \(= x\)

=>  \(\frac{1}{3} y\) \(= x\)

So x is \(\frac{1}{3}\) of y

y is \(\frac{3}{4}\) of (x+y)

If x = 1 and y = 3 (substitute in values)

=>  3 is \(\frac{3}{4}\) of (4)

=>  3 is \(\frac{3}{4}\)(4)

=>  3 is (\(\frac{3}{4}\)x4)

=>  3 = 3

Therefore, y is \(\frac{3}{4}\) of (x+y) is true

So the answers are:

x is \(\frac{1}{3}\) of y

AND

y is \(\frac{3}{4}\) of (x+y)

Answer: B

Step-by-step explanation:

The area of a circle is pi*radius^2. But only a diameter is given, so in order to find the radius, you must divide the diameter by 2:

3.6/2 = 1.8

Now, you can plug the radius, 1.8, into the equation pi*radius^2 (\(\pi r^{2}\)):

\(\pi (1.8)^2 = \pi(3.24)\) = about 10.18

Lastly, you must divide the area 10.18 by 2 because you are looking for only half the area.

10.18/2 = 5.09

The area of the shaded region is 5.09 square cm if the radius of the circle is 1.8 cm, option (B) is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the centre of a circle)

We have:

The diameter of the circle = 3.6 cm

The radius of the circle = 3.6/2 = 1.8 cm

Area of shaded region = (180/360)π(1.8)²

Area of the shaded region = 5.089 ≈ 5.09 square cm

Thus, the area of the shaded region is 5.09 square cm if the radius of the circle is 1.8 cm, option (B) is correct.

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The volume of a pyramid is 60 inches.

Given that,

A pyramid's volume varies in tandem with both its base area and height. When a pyramid's base is square inches and its height is inches, its volume is cubic inches.

V1 = 35 cubic inches

A1 = 15 square inches

h1 = 7 inches

A2 = 36 inches

h2 = 5 inches

To find  : What is V2

The following formula is used to determine a pyramid's volume:

V = (Base Area × Height)/3

V2 = (36 square inches multiplied by 5)/3

V2 = 60 cubic inches

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If two angles are complementary, then the

sum of their measures is 90 degrees.

We can find the m<B by taking 90 minus the measure of <A.

So here, we have 90 - 15 which is 75.

So m<A is 75 degrees.

Using the table the linear function that relates y to x is y = 2x/3 + 5

The term linear function refers to functions that represents a straight line in a coordinate plane. Linear functions have variables have do not exponents

The equation of linear function is usually of the form y = mx + c.

c is the y intercept and the value of y when x = 0

Studying the table we start from when x = 0 and y = 5 to solve

hence c =5

using x = -3 and y =- 3

y = mx + c

3 = -3m + 5

3 - 5 = 3m

-2 = 3m

m = -2/3

Therefore the required equation is y = -2x/3 + 5

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