The sum of three consecutive integers is -27. Find the value of the middle of the
three.

Given

Mike took a taxi from home to Airport. The taxi driver charged $6 as initial fees and $3 per mile and the total fare is $24.

Required

we need to find total number of miles he covered on this ride.

Explanation

Let total number of miles he travelled be x

Then total fare =6+3x

i.e

So total number of miles covered is 6 miles.

Ben Collins plans to buy a house for $184,000, and if the real estate in his area is expected to increase in value by 3 percent each year, its approximate value will be around $208,943.95 six years from now.

To calculate the approximate value of the house six years from now, we can use the formula for compound interest: \(\(A = P(1 + r/n)^{nt}\), where \(A\)\) is the future value, \(\(P\\)) is the principal amount, \(\(r\)\) is the annual interest rate (expressed as a decimal), \(\(n\)\) is the number of times that interest is compounded per year, and \(\(t\)\) is the number of years.

In this case, the principal amount is $184,000, the annual interest rate is 3 percent (or 0.03 as a decimal), the compounding is done annually \((so \(n = 1\))\), and the time period is 6 years. Plugging these values into the formula, we get:

\(\(A = 184,000(1 + 0.03/1)^{(1)(6)}\)\)

Simplifying the equation, we have:

\(\(A = 184,000(1.03)^6\)\)

Evaluating this expression, we find:

\(\(A \approx 208,943.95\)\)

Therefore, the approximate value of the house six years from now would be around $208,943.95, assuming a 3 percent annual increase in real estate value.

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Answer: M=2n-2

2n-2=0

2n-2+2=0+2

2n=2

Divide both side by 2

n=1

Step-by-step explanation:

Answer:

-15

Step-by-step explanation:

set it up

f(40)=-2x+10

40=-2x+10

subtract ten

30=-2x

divide by -2 to isolate the x

-15=x

Answer:

f(x) = -2x + 10

If f(x)= 40

By using equation,

or, 40=-2x+10

or, 40-10=-2x

or, 30=-2x

or, 30/-2=x

Therefore x=-15

Period of the functions: The period of the function f(t) = (7 cos t)² is given by 2π/b where b is the period of cos t.The period of the function f(t) = cos (2φt²/m) is given by T = √(4πm/φ). The period of the function f(t) = (7 cos t)² is given by 2π/b where b is the period of cos t.

We know that cos (t) is periodic and has a period of 2π.∴ b = 2π∴ The period of the function f(t) =

(7 cos t)² = 2π/b = 2π/2π = 1.

The period of the function f(t) = cos (2φt²/m) is given by T = √(4πm/φ) Hence, the period of the function f(t) =

cos (2φt²/m) is √(4πm/φ).

The function f(t) = (7 cos t)² is a trigonometric function and it is periodic. The period of the function is given by 2π/b where b is the period of cos t. As cos (t) is periodic and has a period of 2π, the period of the function f(t) = (7 cos t)² is 2π/2π = 1. Hence, the period of the function f(t) = (7 cos t)² is 1.The function f(t) = cos (2φt²/m) is also a trigonometric function and is periodic. The period of this function is given by T = √(4πm/φ). Therefore, the period of the function f(t) = cos (2φt²/m) is √(4πm/φ).

The period of the function f(t) = (7 cos t)² is 1, and the period of the function f(t) = cos (2φt²/m) is √(4πm/φ).

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The \((3,-3)\)is a solution of the inequality \(y\leq -5x + 3\).

We can test whether\((3,-3)\)is a solution of the inequality \(y \leq -5x + 3\) by substituting the values of x and y into the inequality and seeing if the inequality is true or false.

Substituting \(x=3\) and \(y=-3\) into the inequality, we get:

\(-3 \leq -5(3) + 3\)

Simplifying the right side of the inequality, we get:

\(-3 \leq -15 + 3\\-3 \leq -12\)

Since \(-3\) is indeed less than or equal to \(-12\), the inequality is true when \(x=3\) and \(y=-3\).

Therefore, \((3,-3)\) is a solution of the inequality \(y \leq -5x + 3\).

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The 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).

Let the random variable & parameters be;

x1 : Number of successes from group 1

x2 : Number of successes from group 2

p1: Proportion of successes in group 1

p2: Proportion of successes in group 2

n1 : number of trial in group 1

n2: number of trial in group 2

We are given;

x1 = 260

n1 =985

x2 = 194

n2 = 842

Thus;

p1 = 260/985

p1 =0.2640

p2 = 194/842

p2 = 0.2304

Constructing a (1 - α)100% confidence interval for proportion from the formula;

(p₁ - p₂) - z√[((p₁(1 - p₁)/n₁) + p₂(1 - p₂)/n₂)]

plugging in z = 2.576 and the values of p₁, p₂, n₁ and n₂, we have the confidence interval as;

(-0.0184631, 0.0855743)

Therefore the 99% confidence interval for the decrease in the defective rate after the reconfiguration is (-0.018, 0.086).

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For two equations to have no solution, they must have the same slope or same variable term.

Let's simplify the equation on the left side.

The slope of the equation on the left side is 4.

As mentioned above, for two equations to have no solution, they must have the same slope, hence, the slope on the right side of the equation must be 4 too.

Hence, the missing number in the equation is 4.

Answer:

x=-3.75

Step-by-step explanation:

17 = -13-8x

30=-8x

x=-3.75

Answer:

Step-by-step explanation:

17=-13-8x

Step 1: add 13 to both sides

30=-8x

Step 2: divide by -8

-3.75=x

The slope would be Zero.

on a graph the line would be horizontal.

Horizontal lines are zero and vertical ones are undefined.

So, the gradient vector field of f is (∇f) = (cos(5y/z), -5x sin(5y/z)/z, 5xy sin(5y/z)/z^2).

To find the gradient vector field of the function f(x, y, z) = x cos(5y/z), we need to calculate the partial derivatives with respect to each variable and combine them into a vector.

The gradient vector is defined as:

∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)

Taking the partial derivatives of f(x, y, z) with respect to each variable:

∂f/∂x = cos(5y/z)

∂f/∂y = -5x sin(5y/z)/z

∂f/∂z = 5xy sin(5y/z)/z^2

Putting these partial derivatives together, we have:

∇f = (cos(5y/z), -5x sin(5y/z)/z, 5xy sin(5y/z)/z^2)

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Answer:

14-

Step-by-step explanation:

Answer: yes, this is a fuction

Step-by-step explanation:

hope this helps

Answer: 7

Step-by-step explanation:

7

Answer:

..

Step-by-step explanation:

Because teachers dont understand the pain we go through so they continue to push us to the point where we give up..

The test statistic for this sample is z = (0.254 - 0.203) / (p_hat * (1 - p_hat) * (1/n1 + 1/n2))

Based on the given information, we can set up the hypotheses as follows:

Null hypothesis: p1 - p2 = 0
Alternative hypothesis: p1 - p2 > 0

where p1 represents the proportion of successes in the first population and p2 represents the proportion of successes in the second population.

Since the sample sizes are large (n1 and n2 are not given, but we can assume they are large enough for the normal approximation to hold), we can use the normal distribution to approximate the sampling distribution of the difference in sample proportions.

The test statistic for this sample can be calculated as follows:

z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))

where p_hat = (x1 + x2) / (n1 + n2), x1 and x2 are the number of successes in the two samples respectively.

Plugging in the given values, we get:

p_hat = (0.254n1 + 0.203n2) / (n1 + n2)
z = (0.254 - 0.203) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))

Since the significance level is not given, we cannot determine the critical value for the test. However, we can use the test statistic to calculate the p-value for the test, which is the probability of observing a difference in sample proportions as extreme as the one we observed (or more extreme) under the null hypothesis.

Once we have the p-value, we can compare it to the significance level to make a decision about whether to reject or fail to reject the null hypothesis.

Note: It is important to mention that using the normal approximation without the continuity correction may not always be accurate, especially when the sample sizes are small or the proportion of successes is close to 0 or 1. In such cases, it is recommended to use other methods (such as exact tests or simulation) that do not rely on the normal approximation.

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The midpoint formula and the normal vector of the plane can be used to determine the equation of the plane that contains all points equidistant from the points (1,0,-2) and (3,4,0).

Given by: The midpoint of the two points is:

M = [(1 + 3)/2, (0 + 4)/2, (-2 + 0)/2] = (2, 2, -1) (2, 2, -1)

The following vector runs between the two points:

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

The cross product of two non-parallel plane vectors yields the normal vector to the plane. The midpoint M to a point on the plane is one such vector, while the other is the vector V. Consider the point P = (2, 2, -1) + t(2, 4, 2) as an illustration, where t is a scalar.

The normal vector is then provided by:

N = V x (P - M) = (2, 4, 2) x (2t, 4t, 2t -1), which equals (12t, -8t, 4t + 2)

The point-normal form, which makes use of the normal vector N and the point M, can be used to determine the equation for the plane:

(x - 2) * 12t = (y - 2) * -8t = (z + 1) * 4t + 2

The final equation of the plane is obtained by multiplying both sides of the equation by t and setting t 0.

12(x - 2) = -8(y - 2) = 4(z + 1) + 2

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The mathematical expression y(x,t) = Asin(kx)sin(wt) provides a way to describe the behavior of a standing wave in terms of its amplitude, frequency, and location along the string.

At time t=0,

the standing wave can be mathematically expressed as

y(x,0) = Asin(kx)sin(w*0) = Asin(kx)sin(0) = 0.

This means that the displacement of the string is zero at time t=0.

However, it is important to note that this does not mean that the string is not moving at all. Rather, it means that the string is in a state of equilibrium at time t=0, with the maximum transverse displacement being A.

As time progresses, the standing wave will oscillate between the maximum positive and negative transverse displacement values, creating a pattern of nodes (points of zero displacements) and antinodes (points of maximum displacement).

The wave number k and angular frequency w are both constants that are dependent on the physical properties of the string and the conditions under which the wave is being produced.

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If the dot indicates the center of the circle, the equation that must be true is

The diameter of the semicircle is shown by line segment bearing the dot at the center.

By drawing a line from each end of the diameter to any location on the semicircle, the inscribed angle is created anywhere you perform this is a 90-degree angle will result.

This mean that angle B = angle A = 90 degrees

hence there addition is 180 degrees

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The five-number summary of the data include the following:

In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set, the five-number summary for the given data set include the following:

Minimum (Min) = 36.

First quartile (Q₁) = 38.

Median (Med) = 44.

Third quartile (Q₃) = 50.

Maximum (Max) = 60.

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Answer: 7^3/7^6= 1/343

Step-by-step explanation: We move 7^-6 to a denominator because we cannot have a negative exponent in the numerator.

So it would be 7^3/7^6

Which then would be 7*7*7/7*7*7*7*7*7

Which would equal 343/117649

Simplify and you get 1/343

The data source in this case is an advertisement, which is a form of secondary data.

Secondary data is information collected by someone other than the user. In this case, the television ad is promoting a specific car brand as being "considered to be the best" and suggesting that "now is the best time to replace your car". This information is not based on a sample or experimental data, but rather on the claims made by the car brand itself in their advertisement.

The data source in this case is secondary data, specifically an advertisement. This means that the information provided should be critically evaluated and further research should be conducted to verify its accuracy and reliability.

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The measure of angle A is 112 degrees. Hence, option d is correct.

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.

Similarly, since the angle of the cut is 36 degrees, the angle opposite it (angle BCD) is also 36 degrees. Since angles BCD and BDC add up to 90 degrees (because triangle BCD is a right triangle), angle BDC measures 54 degrees (90 - 36 = 54).

Now, we can find angle BDA by subtracting angle ADB and angle BDC from 180 degrees:

angle BDA = 180 - angle ADB - angle BDC

= 180 - 58 - 54

= 68

Finally, we can find angle A by subtracting angle BDA from 180 degrees:

angle A = 180 - angle BDA

= 180 - 68

= 112

Therefore, the measure of angle A is 112 degrees. Hence, option d is correct.

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Complete question:

The population grows each year by 20%.

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.

y = a(1+r)ˣ,

where a is the initial population and r is the rate in decimals and x is the time period.

Given:

The equation g(t ) = 15,000(1.02\()^{t}\)models the population of a small town over time in years, t.

The initial population is 15000.

Compared with the growth function from the definition,

r = 0.2 = 20%

Therefore, the growth percentage is 20%.

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The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

We have,
Vermont had 65.3% of respondents who said yes to exercising for at least 30 minutes a day, 3 days a week.

To find the sample proportion, you can convert the percentage to a decimal by dividing the percentage by 100.

Step 1:

Convert the percentage to a decimal.
65.3 / 100 = 0.653

Thus,
The value of the sample proportion of people from Vermont who exercised for at least 30 minutes a day, 3 days a week is 0.653.

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Answer:

no because she would get the same total if she added it before or after

Step-by-step explanation:

To solve the linear program graphically, we need to plot the feasible region determined by the given constraints and then identify the corner points of this region.

We can then evaluate the objective function at each corner point to find the maximum value. Let's start by graphing the feasible region: The constraint 0 ≤ x₁ ≤ 7 represents a horizontal line segment on the x₁-axis, ranging from x₁ = 0 to x₁ = 7. The constraint 0 ≤ x₂ ≤ 6 represents a vertical line segment on the x₂-axis, ranging from x₂ = 0 to x₂ = 6. Plotting these two constraints on a graph, we get a rectangular feasible region with vertices at (0, 0), (7, 0), (7, 6), and (0, 6). Next, we evaluate the objective function 3x₁ + 7x₂ at each corner point: At (0, 0): 3(0) + 7(0) = 0

At (7, 0): 3(7) + 7(0) = 21.  At (7, 6): 3(7) + 7(6) = 63. At (0, 6): 3(0) + 7(6) = 42. From these calculations, we find that the maximum value of the objective function occurs at the corner point (7, 6) and is equal to 63.

Therefore, the maximum value of the objective function 3x₁ + 7x₂, subject to the given constraints, is 63.

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The scale factor that was used to create triangle J’K’L’ is 1/3

From the graph, we have the following highlights:

KL = 3

K'L' = 1

The scale factor (k) from JKL to J'K'L is calculated as:

Scale factor = K'L'/KL

This gives

k = 1/3

Hence, the scale factor that was used to create triangle J’K’L’ is 1/3

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Answer:

2 1/7 kg

Step-by-step explanation:

Multiply 5/7 kg by 3, obtaining 15/7 kg, or 2 1/7 kg