Write the following phrase as an algebraic expression and simplify if possible. Let x represent the unknown number
Six-sevenths of a number, increased by six

Answer:

4

Step-by-step explanation:

(a²-b)/ 6

=(5²-1)/ 6

=(25-1)/6

=24/6

=4

======================================================

Explanation:

Let's label the sides of the triangle a, b, and c.

Furthermore, let's have 'a' & b represent known sides and  \(b \ge a\) be the case. For a triangle to be possible, the missing side c must have these restrictions placed on it:

b-a < c < b+a

This inequality is valid because of a modification to the Triangle Inequality Theorem. I'll leave the proof to the reader.

-------

In this case we have a = 3 and b = 8 which lead to...

b-a < c < b+a

8-3 < x < 8+3

5 < x < 11

The third side is between 5 and 11, excluding both endpoints. We cannot have x = 5. Furthermore, we cannot have x = 11 either. If x were either of those endpoints, then we'd form a straight line rather than a triangle.

Having x be an integer leads to the roster set notation {6,7,8,9,10} to represent all possible values of x. For instance, we could have a triangle with side lengths 3, 8, and 6. I recommend getting slips of paper of these lengths to try it out yourself. Or you can use software such as GeoGebra to see why this works.

Answer: \(y=\frac{4}{x}\)

Step-by-step explanation:

To find the inverse function, you want to replace y with x and x with y, and then solve.

\(y=\frac{4}{x}\)           [replace y with x and x with y]

\(x=\frac{4}{y}\)           [multiply bith sides by y]

\(xy=4\)          [divide both sides by x]

\(y=\frac{4}{x}\)

Now, we know the inverse is \(y=\frac{4}{x}\).

Answer:

The answer to the question provided is 72.

We need to determine a few characteristics of the following linear equation:

The first step we need to take is to isolate the "y" variable on the left side.

Now we need to analyze this function and provide the necessary characteristics.

First is the Domain. The Domain of a function is the group of all numbers that can be used as an input (x), in this case the Domain is the whole Real group.

Second is the Range, which is the group of numbers that can be the output of the function (y), for this case we also have the whole Real group as Range.

Then we need to find the "Zero". Which is the value at which the function crosses the x-axis, to calculate it we must make "y=0" and solve for x.

The zero is equal to 12.

The slope of the function is the number multiplying "x", in this case it is -1/2.

The slope is negative, decrescent.

To find the value of f(8), we need to replace x by 8 and solve for y.

The value of f(8) = 2.

To determine the value of x where f(x) is equal to 5, we need to replace f(x) by 5 and solve for x.

The value of x for which f(x) is equal to 5, is 2.

Now we need to graph the equation, for that we have to use two of the points we found before, we will use (8, 2) and (2,5). We need to mark these points at the coordinate plane and draw a line between them:

To reach a 99% confidence level, a lot of effort will be needed. A 1% chance of wrong acceptance is acceptable to the superior because confidence levels and this risk go hand in hand.

Your sample size and variability will determine how precise your statistics are.

Tighter confidence intervals with smaller error margins are produced by greater sample sizes or lower variability. Wider confidence intervals and greater error margins are produced by smaller sample sizes or increased variability.

The interval width depends on the degree of confidence. That interval won't be as narrow if you desire a higher degree of confidence. At 95% or higher confidence, a narrow interval is preferred.

A 99% CI is going to be wider than a 95% CI from the same sample. Given that the wider interval would have a higher possibility of having the genuine population value, this makes sense.

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Trapezoid 1 is similar to trapezoid 2 because trapezoid 1 can be mapped onto trapezoid 2 by a series of transformations.

In Mathematics and Geometry, two geometric figures such as trapezoids are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.

This ultimately implies that, the lengths of the pairs of corresponding sides or corresponding side lengths are proportional to one another when two (2) geometric figures are similar;

Scale factor = √10/√2 = 5/2.5 = 7/3.5

Scale factor = 2.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

95 is not a term here as the next verse should be 98 as it is a 94 term in this pattern

95 will not be a term in the sequence 1, 5, 9, 13, 17, ....., as the value of n for the nth term is not integer.

An ordered group of numbers with a shared difference between each succeeding word is known as an arithmetic sequence.

The given sequence of numbers is,

1, 5, 9, 13, 17, .....

The first term of the given sequence a₁ =1,

From the given sequence, the common difference pair of two consecutive terms d = 4,

Let nth term of the sequence aₙ= 95,

By arithmetic sequence formula,

aₙ = a₁ + (n-1).d

Substitute the value of aₙ and d,

95 = 1 + (n-1).4

94 = (n-1). 4

(n-1) = 23.5

n = 24.5

The value of n can't be decimal, so 95 can't be a term of the given sequence.

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The virtual condition for the .376² MMC pin with a perpendicularity tolerance of .008² diameter at MMC is approximately .001131.

To determine the virtual condition for a .376² MMC (Maximum Material Condition) pin with a perpendicularity tolerance of .008² diameter at MMC, we need to calculate the tolerance zone.

The perpendicularity tolerance specifies the allowable deviation of the pin from a perfect perpendicular orientation. The tolerance zone is defined as a cylindrical volume around the pin, with a diameter equal to the perpendicularity tolerance.

In this case, the perpendicularity tolerance is given as .008² diameter at MMC. Since the diameter at MMC is .376², we can calculate the tolerance zone as follows:

Tolerance zone = .008² * .376²

Simplifying the calculation:

Tolerance zone = .008 * (.376 * .376)

Tolerance zone = .008 * .141376

Tolerance zone = .001131

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Answer:

x = 30°

Step-by-step explanation:

4x + 2x = 180°  because they are supplemental angles

6x = 180°

divide both sides of the equation by 6:

x = 30°

Answer:

2 hours and 24 minutes.

This can be done by finding the CPI or another price index for the same period. Once you have the GDP deflator, you can use the formula above to calculate the real GDP.

If you only know the nominal GDP, you cannot determine the real GDP. In order to determine the real GDP, you need to take into account inflation. This is done by adjusting the nominal GDP for inflation using a price index, such as the Consumer Price Index (CPI).The formula for calculating real GDP is:Real GDP = Nominal GDP / GDP DeflatorThe GDP deflator is a measure of inflation that takes into account changes in the prices of all goods and services produced in an economy. It is calculated by dividing nominal GDP by real GDP and multiplying by 100. This gives us a ratio of the current price level to the base year price level.

The base year price level is assigned a value of 100.Using this formula, we can see that if we know the nominal GDP and the GDP deflator, we can calculate the real GDP. For example, if the nominal GDP is $10 trillion and the GDP deflator is 120, the real GDP would be:Real GDP = $10 trillion / 1.2 = $8.33 trillionTherefore, in order to determine the real GDP if you only know the nominal GDP, you need to obtain the GDP deflator.

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Answer:

n = 113°

Step-by-step explanation:

⭐What is an isosceles triangle?

⭐What is the exterior angles theorem?

In this case, n is the exterior angle, because it is outside of the triangle.

The 46° is opposite of n.

Thus, we need to find the left base angle, because it is opposite of n, and use the exterior angles theorem to find n.

Knowing that the triangle is an isosceles triangle, we can make an equation to find the base angles.

The internal angles of a triangle sum to 180°. Let the base angles = x.

\(46 + x + x = 180\)

\(46 + 2x = 180\)

\(2x = 134\)

Solving for one base angle:

\(x = 67\)

∴ The left base angle is 67°

Now, apply the exterior angles theorem knowing the two angles opposite of n.

\(n = 46 + 67\)

\(n = 113\)

∴ n = 113°

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To calculate the concentrations of all species present in a 0.72 M NH3 solution (Kb=1.8×10−5), we can use the principles of the equilibrium expression for the dissociation of NH3 in water.

NH3 (ammonia) is a weak base that reacts with water to form NH4+ (ammonium) and OH- (hydroxide) ions. The equilibrium expression for this reaction can be written as:

NH3 + H2O ⇌ NH4+ + OH-

Since the initial concentration of NH3 is 0.72 M, we can assume that x mol/L of NH3 will dissociate to form x mol/L of NH4+ and OH-. Therefore, the concentrations of NH4+ and OH- will also be x mol/L.

To calculate the value of x, we can use the Kb expression, which relates the equilibrium constant to the concentrations of the species. In this case, Kb = [NH4+][OH-]/[NH3]. Substituting the known values, we have:

1.8×10−5 = x * x / (0.72 - x)

Solving this equation will give us the value of x, which represents the concentration of NH4+ and OH-. Finally, we can express the concentrations of NH3, NH4+, and OH- using two significant figures, separated by commas, based on the calculated value of x.

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The statement "If the conclusion of an argument is a tautology, then the counterexample set of that argument must be inconsistent" is true.

Let's understand why?

Explanation:

An argument with a tautology conclusion is an argument that arrives at a conclusion that is always true, regardless of the truth values of the premises. In other words, it is impossible for the premises to be true while the conclusion is false.

This means that any attempt to find a counterexample that disproves the conclusion will always fail, as there is no possible scenario in which the conclusion is false.

The counterexample set of an argument is the set of all possible scenarios in which the premises are true but the conclusion is false. If the conclusion is a tautology, then there is no possible scenario in which the conclusion is false, and thus the counterexample set is empty. An empty counterexample set is equivalent to an inconsistent counterexample set, as it means that there is no consistent scenario in which the conclusion is false.

Therefore, if the conclusion of an argument is a tautology, then the counterexample set of that argument must be inconsistent.

Hence, the statement is true.

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Answer:

1)

Domain: 0, 2, 5, 8

Range: -1, -7, -3, 1

2)

Domain: 10, -6, -2, 0

Range: 1, 3, 5, 9

Step-by-step explanation:

A Domain is the x-value

A Range is the y-value

Given, A = [-1 3; 2 -3; -1 3], b = [12; 9; 9], the least-squares solution of Ax=b is x = [1.4; 0.6].

To find the least-squares solution of A*x=b

(a) Construct the normal equations for x.

For a given matrix A with dimensions m x n and a column vector b with dimensions m x 1, the normal equations are as follows: AᵀAx = Aᵀb Where Aᵀ is the transpose of matrix A.

Now, let us construct normal equations for the given problem.

A = [-1 3; 2 -3; -1 3], b = [12; 9; 9]Normal equation is, AᵀAx = AᵀbSince, A is of dimension 3x2, AT will be of dimension 2x3.

Therefore, the normal equation will be of dimension 2x2.x = (ATA)−1ATb ⇒ x = inv(ATA)ATb

Let's calculate AT and ATA.AT = [-1 2 -1; 3 -3 3]ATA = [6 -12; -12 27](b) Solve for x.Substituting AT, ATA, and b in the equation we get,x = inv(ATA)ATb ⇒ x = inv([6 -12; -12 27]) * [-1; 3; -1; 3; -1; 3]⇒ x = [1.4; 0.6]

Therefore, the least-squares solution of Ax=b is x = [1.4; 0.6].

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Removing the electric car from the data set will reduce the standard deviation as the extreme value of 112 mpg is taken out, resulting in a decrease in the spread of the data. The interquartile range (IQR) will also be affected as the extreme outlier is taken out, will decrease the spread of the data in the boxplot.

The electric car with a rating equivalent to 112 miles per gallon is an extreme outlier, which means it is very far from the rest of the data. Therefore, removing this outlier from the data set will decrease the variability and, consequently, decrease the standard deviation. The extreme outlier with the rating equivalent to 112 miles per gallon is outside of the whiskers of the boxplot, which means it is beyond the range of the middle 50% of the data. Therefore, removing this outlier from the data set will decrease the spread of the data in the boxplot and, consequently, decrease the IQR.

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Answer:

guy above me is right

Step-by-step explanation:

Answer:

A. One Solution

Step-by-step explanation:

To determine if a system of equations has no solutions, infinitely many solutions, or exactly one solution, we can solve the system by any method, such as elimination or substitution.

In this case, we can solve the system by elimination. Multiplying the first equation by -2 and adding it to the second equation, we get:

0x + 4y = -3

This equation tells us that y must be equal to -3/4, but we still need to check if this value of y satisfies the original equations. Substituting -3/4 for y in the first equation, we get:

2x + (-3/4) = 7

Solving this equation for x, we get x = 5/4. Substituting this value of x and -3/4 for y in the second equation, we get:

-2(5/4) + 2(-3/4) = -5

which simplifies to:

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

This equation is true, so the solution of the system is x = 5/4 and y = -3/4. Since the system has a unique solution, the answer is (A) One Solution.

Answer:

(x,y)=(-2,-1)

Step-by-step explanation:

4x - y = -7: 8x-2y=-14

8x-2y=-14

-8x + 4y = 12

add these two:

2y=-2

y=-1

plug in the y:

-8x-4=12

-8x=16

x=-2

The measurement of altitude BE is 4 unit.

As the average level of the sea's surface, sea level is used to measure altitude. A high altitude is defined as being significantly higher than sea level, such as Mount Everest. It is referred to as having a low altitude when something is closer to the ground, like a plane coming in to land.

As ABCD is rectangle

AD = BC = 12

ΔABC = ΔBCD

BE = FD

5² = 3²+BE²

AE = 3

BE = √(5²-3²)

BE = 4

Thus, The measurement of altitude BE is 4 unit.

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Answer:

9.54 cm

Step-by-step explanation:

In triangle ABD, AD is the hypotenuse (longest side)

We know that according to Pythagoras theorem,

a^2+b^2=c^2

In the figure, c (10cm) and a (5cm) is given. So,

(5)^2 + b^2 = 100

25+b^2 = 100

b^2 = 75

So b is √75 = 8.66

Therefore BD is 8.66 cm

Now even BDC is a triangle

In it, the hypotenuse is missing but we know the value of other sides

so, in Pythagorean theorem,

a=4 (CD)

b=8.66 (BD)

c=x

Therefore,

(4)^2 + (8.66)^2 = x^2

16+74.99= x^2

x^2 = 90.99

x= 9.54 cm

Hope this helps!

Answer:

Option A - Neither. Lines intersect but are not perpendicular. One Solution.

Option B - Lines are equivalent. Infinitely many solutions

Option C - Lines are perpendicular. Only one solution

Option D - Lines are parallel. No solution

Step-by-step explanation:

The slope equation is known as;

y = mx + c

Where m is slope and c is intercept.

Now, two lines are parallel if their slopes are equal.

Looking at the options;

Option D with y = 12x + 6 and y = 12x - 7 have the same slope of 12.

Thus,the lines are parrallel, no solution.

Two lines are perpendicular if the product of their slopes is -1. Option C is the one that falls into this category because -2/5 × 5/2 = - 1. Thus, lines here are perpendicular and have one solution.

Two lines are said to intersect but not perpendicular if they have different slopes but their products are not -1.

Option A falls into this category because - 9 ≠ 3/2 and their product is not -1.

Two lines are said to be equivalent with infinitely many solutions when their slopes and y-intercept are equal.

Option B falls into this category.

The first 3 consecutive odd numbers are 1,3,5. x and x + 2 are consecutive odd numbers if x is an odd number.

Consecutive numbers are those that always appear in the same order, from smallest to largest.

For instance:

The numbers 1, 2, 3, 4, 5, 6, and so on are consecutive.

consecutive odd numbers:

Let's call the odd number "x." The subsequent term becomes "x + 4" and the next consecutive odd number becomes "x + 2."

Numbers that begin with 1, 3, 5, 7, or 9 are considered odd. 1, 3, 5, 7, 9, 11, 13, 15, and so on are examples of consecutive odd numbers.

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The probability that a single randomly selected value from a population with a normal distribution, where the mean (μ) is 189.2 and the standard deviation (σ) is 83.2, falls between 195.2 and 214.1 is approximately 0.1632.

To find the probability, we can standardize the values using the z-score formula: z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.

For 195.2:

z1 = (195.2 - 189.2) / 83.2 = 0.0721

For 214.1:

z2 = (214.1 - 189.2) / 83.2 = 0.2983

Using a standard normal distribution table or a calculator, we can find the area under the curve between these z-scores, which represents the probability:

P(195.2 < x < 214.1) = P(0.0721 < z < 0.2983) ≈ 0.1632

Therefore, the probability that a single randomly selected value falls between 195.2 and 214.1 is approximately 0.1632.

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