5+2x+7+2x Simplify the expression .

The graph of the inequality y ≥ (1/2)x - 1 and x - y > 1 is attached. Shannon's graph is correct.

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Inequalities are used for the non equal comparison of numbers and variables.

Given the inequalities:

y ≥ (1/2)x - 1     (1)

and

x - y > 1     (2)

The graph of the inequality is attached. Shannon's graph is correct.

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Answer: 11 weeks

Step-by-step explanation:

G(t) = 25 + 14t

A(t) = 80 + 9t

set G equal to A and find t

25 + 14t = 80 + 9t

5t = 55

t = 11

The given function is: `y = f(x) = 6x + 5/3x - 2`, the horizontal and vertical asymptotes of the function y = f(x) are 2 & 2/3 respectively.

Horizontal Asymptotes:

To find horizontal asymptotes, let's consider `x` is going to infinity and negative infinity.

Limit of f(x) as `x` approaches `infinity`:

We have to divide the numerator and denominator by the highest degree term of the denominator.

Here the highest degree term of the denominator is `x` so, dividing by `x`, we get:`

y = f(x)

  = 6x/x + 5/x ÷ 3x/x - 2/x

On simplifying the above expression we get,

y = f(x)

  = 6 + 5/x ÷ 3 - 2/x

As x goes to infinity, 5/x and 2/x tend to zero.

So, we get:

y = f(x)

  = 6/3

   = 2

Therefore, the horizontal asymptote is y = 2.

Limit of f(x) as `x` approaches negative `infinity`:

We have to divide the numerator and denominator by the highest degree term of the denominator.

Here the highest degree term of the denominator is `x` so, dividing by `x`, we get:

y = f(x)

  = 6x/x + 5/x ÷ 3x/x - 2/x

On simplifying the above expression we get,

y = f(x)

   = 6 + 5/x ÷ 3 - 2/x

As x goes to negative infinity, 5/x and 2/x tend to zero.

So, we get:

y = f(x)

  = 6/3

   = 2

Therefore, the horizontal asymptote is y = 2.

Vertical Asymptotes:

Vertical asymptotes occur at the values of `x` that make the denominator zero.

So, 3x - 2 = 0

x = 2/3.

So, x = 2/3 is the vertical asymptote of the given function.

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Answer:

\( \boxed{ \bold{ \sf{Price \: of \: the \: article = \: Rs \: 6678.3}}}\)

\( \boxed{ \bold{ \sf{Vat \: amount = \: \: Rs \: 768.3}}}\)

Step-by-step explanation:

Given,

Marked Price ( MP ) = Rs 6000

Vat percent = 13 %

Discount percent = 15%

▪️Finding the discount amount

Discount amount = Discount % of MP

= 15 % of 6000

= Rs 900

▪️Finding the selling price

Selling price ( SP )= Marked price - Discount amount

= Rs 6000 - Rs 900

= Rs 5910

▪️Finding the vat amount

Vat amount = Vat % of SP

= 13 % of 5910

= Rs 768.3

▪️Finding SP with VAT

SP with vat = SP + vat amount

= Rs 5910 + Rs 768.3

= Rs 6678.3

Hope I helped!

Best regards!

Answer:

1 hours = 60 min

60 x 9/10 = 54 min

3 divided by 54 = 1/18

so she walks 1/18 miles per hour.

Im not sure though. It might be 3 divided by 9/10 = 3 1/3. I’m not that confident in my answer. But it is definitely one of them, either 1/18 or 3 1/3.

Mandy's home computer system is expected to be worth $1,576.11.

Mandy's home computer system is expected to depreciate at a rate of 10% per year. After 1 year, the value of the computer system will be 90% of its original value.

After 2 years, it will be worth 90% of that value, or 0.9 × 0.9 = 0.81 times the original value. Continuing in this way, we can write the value of the computer system after n years as \(0.9^n\) times its original value. Thus, after 9 years, the computer system will be worth \(0.9^n\) times its original value:

Value after 9 years = 4995 × \(0.9^n\)

Using a calculator, we find that the value is approximately $1,576.11 when rounded to the nearest hundredth. Therefore, after 9 years, Mandy's home computer system is expected to be worth $1,576.11.

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Answer:

$72

Step-by-step explanation:

100 - 10% = 90

90 - 20% = 72

Answer:

74.4

Step-by-step explanation:

Answer:

he will pay 55.16

Answer:

5

Step-by-step explanation:

Answer:

11 x 2

Step-by-step explanation:

By BODMAS rule,

B - Brackets

O - Orders

D - Division

M - Multiplication

A - Addition

S - Substraction

Consider DMAS alone.

Here, there is no division.

So,

Multiplication ( x ) should be the first step.

By using isometric dot paper in the picture we can see sketch the triangular prism.

Given that,

A triangular prism with height 4 units, with two sides of the base that are 3 units long and 4 units long

We have to use isometric dot paper to sketch a triangular prism.

We know that,

Mark the corner of the solid.

Draw 4 units down, 4 units to the left, and 3 units to the right.

Then draw a triangle for the top of the solid.

Draw segments 4 units down from each vertex for the vertical edges.

Connect the appropriate vertices using a dashed line for the hidden edge.

Therefore, by using isometric dot paper in the picture we can see sketch the triangular prism.

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The value of x in 1 + (1/x+2) - (2x/x*x-4) = 0 are x = -2 and x = 3

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

1+(1/x+2)-(2x/x*x-4)=0

Rewrite as

1 + (1/x+2) - (2x/x*x-4) = 0

Rewrite the equation properly

So, we have

1 + (1/x+2) - (2x/x²- 4) = 0

Factorize the expression

So, we have

1 + (1/x+2) - (2x/(x- 2)(x + 2)) = 0

Multiply through the equation by x + 2

So, we have the following representation

x + 2 + 1 - 2x/(x- 2) = 0

Evaluate the like terms

So, we have the following representation

x + 3 - 2x/(x- 2) = 0

Multiply through the equation by x - 2

So, we have the following representation

x² - 2x + 3x - 6 - 2x = 0

So, we have

x² - x - 6 = 0

Factorize the equation

So, we have

x²  + 2x - 3x - 6 = 0

This gives

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

So, we have

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

Evaluate

x = -2 and x = 3

Hence, the solution for x is x = -2 and x = 3

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The resulting set of orthogonal unit vectors \(\(\{\vec{v}_{1}, \vec{v}_{2}, \vec{v}_{3}, \vec{v}_{4}\}\)\) forms an orthogonal basis for the subspace\(\(W\) of \(\mathbb{R}^{5}\).\)

To find an orthogonal basis of \(W\), we will use the Gram-Schmidt process to orthogonalize the given vectors \(\(\vec{u}_{1}\), \(\vec{u}_{2}\), \(\vec{u}_{3}\), and \(\vec{u}_{4}\).\)

1. Start by setting the first vector\(\(\vec{v}_{1} = \vec{u}_{1}\).\)

2. Orthogonalize the second vector \(\(\vec{u}_{2}\)\) with respect to \(\(\vec{v}_{1}\).\)Subtract the projection of \(\(\vec{u}_{2}\)\) onto \(\(\vec{v}_{1}\)\) from \\((\vec{u}_{2}\)\) to obtain an orthogonal vector \(\(\vec{v}_{2}\)\). Normalize \(\(\vec{v}_{2}\)\) to obtain an orthogonal unit vector.

3. Orthogonalize the third vector \(\(\vec{u}_{3}\)\) with respect to \(\(\vec{v}_{1}\) and \(\vec{v}_{2}\).\) Subtract the projections of\(\(\vec{u}_{3}\)\)onto \(\(\vec{v}_{1}\)\)and \(\(\vec{v}_{2}\)\) from \((\vec{u}_{3}\)\)to obtain an orthogonal vector \(\(\vec{v}_{3}\)\). Normalize \(\(\vec{v}_{3}\)\) to obtain an orthogonal unit vector.

4. Orthogonalize the fourth vector \(\(\vec{u}_{4}\)\) with respect to \(\(\vec{v}_{1}\), \\)\((\vec{v}_{2}\), and \(\vec{v}_{3}\).\) Subtract the projections of\(\(\vec{u}_{4}\) onto \(\vec{v}_{1}\), \\) \((\vec{v}_{2}\), and \(\vec{v}_{3}\) from \(\vec{u}_{4}\)\) to obtain an orthogonal vector \(\(\vec{v}_{4}\).\) Normalize \(\(\vec{v}_{4}\)\) to obtain an orthogonal unit vector.

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Find an orthogonal basis of the subspace \(\( W \) of \( \mathbb{R}^{5} \)\)spanned by \(\[ \left\\)\({\vec{u}_{1}=(1,1,1,0,1), \vec{u}_{2}=(1,0,0,-1,1), \vec{u}_{3}=(3,1,1,-2,3), \vec{u}_{4}=(0,2,1,1,-1)\righ\)

Answer:

-11, -6, 0, 3, 9, 10

Step-by-step explanation:

I don't really know how to explain but that is correct

Answer: -11,| -6 |, 0, | 3 |, 9, 10

Step-by-step explanation:

The pair of statements can be written in symbolic form as follows:

P: You activate your cell phone before October 9.

Q: You receive 100 free minutes.

Statement 1: If P, then Q.

Statement 2: If not Q, then not P.

To determine if the statements are equivalent, we need to check if Statement 1 implies Statement 2 and if Statement 2 implies Statement 1.

If P, then Q: This means that if you activate your cell phone before October 9 (P), then you receive 100 free minutes (Q).

If not Q, then not P: This means that if you do not receive 100 free minutes (not Q), then you do not activate your cell phone before October 9 (not P).

The statements are indeed equivalent because they express the same logical relationship. If you activate your cell phone before October 9, you will receive 100 free minutes. Conversely, if you do not receive 100 free minutes, it means that you did not activate your cell phone before October 9.

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Algebra was made to solve mathematical problems that involve unknown quantities.

Two or more expressions with an Equal sign is called as Equation.

Algebra was developed to solve mathematical problems that involve unknown quantities.

It provides a way to represent and manipulate mathematical equations using symbols and rules, making it easier to solve complex problems and answer questions about relationships between variables.

The earliest known algebraic text is the "Al-jabr wa'l muqabalah" by the Persian mathematician Al-Khwarizmi, which was written in the 9th century.

Hence, Algebra was made to solve mathematical problems that involve unknown quantities.

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The equation for slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

You can eliminate answer choices B, C, and D, because the y-intercept doesn't fit. The y-intercept is where the line crosses the y-axis. There's no way it could be 6 or -1/4.

So now it's between A and D. In the image, the line is going down so we know the slope is negative, and slope is rise/run. It goes down about 1 and to the right about 4.

Meaning A is the only option that makes sense.

Answer:

(x, y) =(-1, - 1)

Step-by-step explanation:

-Substitute the value of x

-solve the equation

-Substitute the value of y

-check the possible solution

-check solution

-simplify

Answer:

A.)

Lower Value = 295

Upper Value = 485

B.)

Lower Value = 200

Upper Value = 580

C.)

Lower Value = 105

Upper Value = 675

Step-by-step explanation:

Given that mean (M) = 390

Standard deviation (σ) = 95

Lower Value = mean value - number of standard deviations specified

Upper Value = mean value + number of standard deviations specified

a. Μ ± 1σ of the observations lie between what two values?

Lower Value = 390 - 1(95) = 295

Upper Value = 390 + 1(95) = 485

b. Μ ± 2σ of the observations lie between what two values?

Lower Value = 390 - 2(95) = 200

Upper Value = 390 + 2(95) = 580

c. Μ ± 3σ of the observations lie between what two values?

Lower Value = 390 - 3(95) = 105

Upper Value = 390 + 3(95) = 675

Answer:

perimeter is 20 cm

the probability that the system will fail is approximately 0.421096 or 42.11%.

To find the probability that the system will fail, we need to consider the components working in series. In this case, for the system to fail, at least one of the components must fail.

The probability of the system failing is equal to 1 minus the probability of all three components working together. Let's calculate it step by step:

1. Find the probability of all three components working together:

  P(all components working) = (1 - p1) * (1 - p2) * (1 - p3)

                            = (1 - 0.09) * (1 - 0.11) * (1 - 0.28)

                            = 0.91 * 0.89 * 0.72

                            ≈ 0.578904

2. Calculate the probability of the system failing:

  P(system failing) = 1 - P(all components working)

                    = 1 - 0.578904

                    ≈ 0.421096

Therefore, the probability that the system will fail is approximately 0.421096 or 42.11%.

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Answer:

20w

Step-by-step explanation:

If you have 20 bottles, and each contains w ounces, we can use the following example to solve.

If there were 4oz per bottle,

20 * 4 = 80

80oz

We have w oz per bottle,

20 * w = ?

20w

The probability mass function for N is \(P(N = n) = (\frac{1}{2})^n\), and the mean  E[N], is 0. This means that the expected value for the index of the first bid better than the initial bid, in this scenario, is 0.

What is the probability mass function?

The probability mass function (PMF) is a function that describes the probability distribution of a discrete random variable. In the case of N, the index of the first bid better than the initial bid, the PMF can be derived as follows:

\(P(N = n) = (\frac{1}{2})^n\).

To determine the probability mass function (PMF) for N and the mean E[N], let's analyze the problem step by step.

Given:

To find the PMF of N, we need to calculate the probability that N takes on a specific value n, where n is a positive integer.

Let's consider the event that N = n. This event occurs if\(X_{1} \leq X_{0}, X_{2} \leq X_{0},...,X_{(n-1)} \leq X_{0},X_{n} \leq X_{0}.\)

Since \(X_{0} ,X_{1}, X_{2} ,X_{3},...\)are identically distributed random variables, we can calculate the probability of each individual event using the properties of the continuous distribution. The probability that\(X_{k} > X_{0}\) for any specific k is given by:

\(P(X_{k} > X_{0})=\frac{1}{2}\) (assuming a symmetric continuous distribution)

Now, let's consider the event that \(X_{1} \leq X_{0}, X_{2} \leq X_{0},...,X_{(n-1)} \leq X_{0}.\)Since these events are independent,  their probabilities:

\(P(X_{1} \leq X_{0}, X_{2} \leq X_{0},...,X_{(n-1)} \leq X_{0},X_{n} \leq X_{0})=[P(X_{1} \leq X_{0}]^{n-1}\)

Finally, the PMF of N is given by:

P(N = n) =\(P(X_{1} \leq X_{0}, X_{2} \leq X_{0},...,X_{(n-1)} \leq X_{0},X_{n} \leq X_{0})*P(X_{n} > X_{0})\\\\=[P(X_{1} \leq X_{0})]^{n-1}*P(X_{n} > X_{0})\\\\=(\frac{1}{2})^{n-1}*\frac{1}{2}\\\\=(\frac{1}{2})^n\)

So, the probability mass function (PMF) for N is\(P(N = n) = (\frac{1}{2})^n.\)

To calculate the mean E[N], we can use the formula for the expected value of a geometric distribution:

E[N] = ∑(n * P(N = n))

Since\(P(N = n) = (\frac{1}{2})^n.\), we have:

E[N] = ∑(\(n * (\frac{1}{2})^n\))

To calculate the sum, we can use the formula for the sum of an infinite geometric series:

E[N] = ∑(\(n * (\frac{1}{2})^n\))

= ∑(\(n * {x}^n\)) (where x = 1/2)

\(\frac{d}{dx}\sum(x^n) = \sum(n * x^{n-1})\)

Now, multiply both sides by x:

\(x\frac{d}{dx}\sum{x}^n = \sum(n * {x}^{n})\)

Substituting x = \(\frac{1}{2}\):

\(\frac{1}{2}*\frac{d}{dx}\sum(\frac{1}{2})^n = \sum(n * (\frac{1}{2})^{n})\)

The sum on the left side is a geometric series that converges to \(\frac{1}{1-x}\). So, we have:

\(\frac{1}{2}*\frac{d}{dx}(\frac{1}{1-\frac{1}{2}})=E[N]\\\)

Simplifying:

\(\frac{1}{2}*\frac{d}{dx}(\frac{1}{\frac{1}{2}})=E[N]\\\\\frac{1}{2}*\frac{d}{dx}(2)=E[N]\\\\\frac{1}{2}*0=E[N]\\\)

E[N] = 0

Therefore, the mean of N, E[N], is equal to 0.

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Answer:

90

Step-by-step explanation:

X/10-4=5

add 4 to both sides

X/10=9

mulitiple 10 to both sides

X=90

check

(90)/10-4=5

9-4=5

Answer:

90

Step-by-step explanation:

By completing the square, the equation in standard form is (x - 2)² + (y + 4)² = 4².

In Mathematics and Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

From the information provided below, we have the following equation of a circle:

x² - 4x + y² + 8y = -4

x² - 4x + (-4/2)² + y² + 8y + (8/2)² = -4 + (-4/2)² + (8/2)²

x² - 4x + 4 + y² + 8y + 16 = -4 + 4 + 16

(x - 2)² + (y + 4)² = 16

(x - 2)² + (y + 4)² = 4²

Therefore, the center (h, k) is (2, -4) and the radius is equal to 4 units.

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Complete Question:

Complete the square to rewrite the following equation in standard form. x² - 4x + y² + 8y = -4.

95% confidence that the population means lies between $110.25 ($120 - $9.75) and $129.75 ($120 + $9.75).

To estimate the population mean, we can use the sample mean as an unbiased estimate. Therefore, the estimated population mean is also $120. However, to calculate the margin of error for this estimate, we can use the formula:
The margin of error = (z-score) x (standard deviation / square root of sample size)
Since the population is assumed to be normal, we can use the z-distribution. For a 95% confidence level, the z-score is 1.96. Substituting the given values, we get:
Margin of error = 1.96 x (25 / √64) = 9.75
Therefore, we can say with 95% confidence that the population mean lies between $110.25 ($120 - $9.75) and $129.75 ($120 + $9.75).
It's important to note that this is only an estimate and the true population mean could still be outside of this range. However, with a 95% confidence level, we can be fairly certain that our estimate is accurate within this range.

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The integral of g(x) is g(x) = -(1/2)sin(x³/2) + (1/2).

To find g(x), we use the following steps:

Therefore, the integral of g(x) is g(x) = -(1/2)sin(x³/2) + (1/2).

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