Which of the following shows the correct first step to solve x^2-18x=-45

A x^2 - 18x + 18= -45 + 18
B. x^2 - 18x + 9 = -45 + 18
C. x^2 -18x + 81 = -45
D. X^2 -18 + 81 = -45 + 81

By increasing the irrigation efficiency from 69% to 81%, 607.14 inches of water could be saved.

To find out how much water could be saved by increasing the irrigation efficiency, follow these steps:
Calculate the total amount of water needed for the 83 acres of grapes with the current irrigation efficiency:
  Total water needed (net) = 83 acres * 34 inches/acre = 2822 inches.

Calculate the actual amount of water used with 69% irrigation efficiency:
  Actual water used = 2822 inches / 0.69 = 4089.86 inches
Calculate the new amount of water used if the irrigation efficiency is increased to 81%:
  New water used = 2822 inches / 0.81 = 3482.72 inches.

Determine the amount of water saved by comparing the actual water used with the new water used:
  Water saved = 4089.86 inches - 3482.72 inches = 607.14 inches.

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Bill signed up for a mobile phone contract with at&t. bill pays a fixed monthly charge for the phone service plus a per-minute charge for use of the phone. this is an example of Two part pricing

here, we have,

Two-Part Pricing (also known as Two-Part Tariff) = A form of pricing in which consumers are charged both an entry fee (fixed price) and a usage fee (price per unit). An example of two-tiered pricing is a phone plan that charges a fixed monthly fee and a fee per minute of phone usage.

Two-part pricing (TPT) is a form of price discrimination in which the price of a product or service consists of two parts: a flat fee and a unit fee. Generally, such pricing techniques only occur in partially or completely monopolistic markets. It is designed to help businesses capture more consumer surplus than they would in a non-discriminatory pricing environment. Split fees can also exist in a competitive market if consumers are not sure of the ultimate demand.

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complete question:

Bill signed up for a mobile phone contract with at&t. bill pays a fixed monthly charge for the phone service plus a per-minute charge for use of the phone. this is an example of _______

The meaning of 0 < a < 1  is that if the scale factor is between 0 and 1 (exclusive of 0 and 1), then the graph will be conpressed

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

0 < a < 1

The above inequality in this context is used in function transformation

In this case, we have

If 0 < a < 1, then the graph will be compressed

This means that if the scale factor is between 0 and 1 (exclusive of 0 and 1), then the graph will be conpressed

Where the variable a represents the scale factor

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The domain of a linear transformation is the set of all possible input vectors that can be operated on by the transformation, and in this case, T is defined for input vectors with three components (x1, x2, x3), indicating that the domain of T is R3, the three-dimensional real coordinate space.

The domain of T is R3.

Given that A is an m x n matrix, where m > n, and Ax = 0 does not have a non-trivial solution, we can determine the number of pivot columns in matrix A.
Understand the conditions
Since Ax = 0 does not have a non-trivial solution, it means that the only solution is the trivial solution (x = 0).

This implies that the columns of A are linearly independent.
Determine the number of pivot columns
Since the columns of A are linearly independent, the number of pivot columns in A will be equal to the number of columns in A.

Since A has more rows than columns, it cannot have full column rank (i.e., n pivot columns), and therefore it has at most n-1 pivot columns.

If Ax=0 does not have a non-trivial solution, then the null space of A is trivial, meaning that the only solution to Ax=0 is the zero vector.

By the rank-nullity theorem, we know that the dimension of the null space of A is n minus the rank of A.

Since the null space is trivial, its dimension is zero, which means that the rank of A is n.

Therefore, A has exactly n pivot columns, which is the maximum possible given that m>n.

These n pivot columns correspond to linearly independent columns of A, and their existence ensures that Ax=0 has only the trivial solution.

Matrix A has n pivot columns.

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Answer: 5/16

Step-by-step explanation:

If 1/8 of a fence is built in 2/5 of an hour, the question is how much of the fence will be completed in an hour.

To be able to solve this, we need to figure out what to multiply 2/5 of an hour by to make it become 1 hour so that we can do the same to 1/8.

To do this, we can divide 2/5 by 1. 1/(2/5) = 2.5. This means 2/5 x 2.5 = 1. If we have to multiply 2/5 x 2.5 to make 1 hour, then we have to multiply 1/8 x 2.5 to find the amount of fence done in one hour.

(1/8) x 2.5 = 0.3125. 0.3125% of the fence will be completed in 1 hour, or 5/16 of the fence.

The coordinates of the points represent the vertices of a rectangle. The perimeter of rectangle WXYZ is 36 units.

To find the perimeter of the rectangle, we need to add up the length of all four sides. We can use the distance formula to find the length of each side:

WX = 8 - 3 = 5

WY = 7 - 3 = 4

YZ = 8 - 3 = 5

XZ = 7 - 3 = 4

Adding up the length of all four sides, we get:

WX + WY + YZ + XZ = 5 + 4 + 5 + 4 = 18

However, we need to remember to count each side twice since the perimeter goes all the way around the rectangle. Therefore, the perimeter is:

2 × (WX + WY + YZ + XZ) = 2 × 18 = 36

So the perimeter of rectangle WXYZ is 36 units.

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Thus, the volume of the frustum of the right circular cone with height 25, lower base radius 29 and top radius 11 is approximately 10,677.54 cubic units.

The frustum of a right circular cone is a three-dimensional shape that is formed by cutting off the top of a cone with a plane parallel to the base.

To find the volume of the frustum, we need to use the formula for the volume of a frustum, which is given by:

V = (1/3)πh(R^2 + r^2 + Rr)

where V is the volume of the frustum, h is the height of the frustum, R is the radius of the lower base, and r is the radius of the top base.

In this case, the height of the frustum is 25, the radius of the lower base is 29, and the radius of the top base is 11. So, we can substitute these values into the formula and simplify:

V = (1/3)π(25)(29^2 + 11^2 + 29*11)
V = (1/3)π(25)(841 + 121 + 319)
V = (1/3)π(25)(1281)
V = (1/3)(25π)(1281)
V = 10,677.54

Therefore, the volume of the frustum of the right circular cone with height 25, lower base radius 29 and top radius 11 is approximately 10,677.54 cubic units.

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The correlation between age and physical fitness, and the relationship between the number of hours spent studying and stress levels.

A negative correlation between two variables is observed when an increase in the value of one variable results in a decrease in the value of the other variable.

In other words, as one variable goes up, the other variable tends to go down. There are several associations between two variables that are likely to have a negative correlation.
One of the most common examples of negative correlation is the relationship between the price of a product and its demand.

When the price of a product increases, the demand for it tends to decrease.

This is because people are less likely to buy the product if it is too expensive.

Similarly, the correlation between age and physical fitness is also likely to be negative.

As a person grows older, their physical fitness tends to decline.
Another example of negative correlation is the relationship between the number of hours a person spends studying and their stress levels.

As the number of hours a person spends studying increases, their stress levels tend to decrease.

Conversely, as the number of hours a person spends studying decreases, their stress levels tend to increase.
In conclusion, there are many associations between two variables that are likely to have a negative correlation.

These include the relationship between the price of a product and its demand, the correlation between age and physical fitness, and the relationship between the number of hours spent studying and stress levels.

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The probability of rolling a 1 with this loaded die is 1/9.

Let's first assign probabilities to the possible outcomes of rolling the die:

There are 3 even numbers (2, 4, and 6) and 3 odd numbers (1, 3, and 5) on a standard six-sided die.

Since rolling an even number is twice as likely as rolling an odd number, we can assign probabilities as follows:
P(2) = P(4) = P(6) = 2x
P(1) = P(3) = P(5) = x
Now, we need to remember that the total probability of all outcomes must add up to 1:
P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = x + 2x + x + 2x + x + 2x = 9x
Since the total probability is 1, we can write the equation:
9x = 1.

Now, we can solve for x:
x = 1/9
Since we want the probability of rolling a 1, we just use the value of x:
P(1) = x = 1/9.

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Answer: 40%

Step-by-step explanation:

Possibilities that both Tyrone and Alisha are correct, depending on the specific expression they are trying to simplify.

In order to determine who is correct between Tyrone and Alisha, we must first look at the expression that they are trying to simplify.

Depending on the expression, different methods may be more appropriate. Without the expression provided, it is difficult to say definitively who is correct.
However,

If we assume that the expression is in the form of a fraction with variables raised to different powers, then both Tyrone and Alisha could potentially be correct.
Raising the numerator and denominator to the third power is a valid method of simplifying expressions that involve fractional exponents.

This is because raising a fraction to a power is equivalent to raising both the numerator and denominator to that power.

By doing this, we can eliminate the fractional exponents and potentially combine like terms.
On the other hand, applying the quotient of powers is another valid method of simplifying expressions with exponents.

This involves dividing the powers of the same base when they are being divided. For example, if we have ([tex]a^3[/tex])/([tex]a^2[/tex]), we can simplify this to a(3-2) = a.
It is important to remember that there may be multiple ways to simplify an expression and it is up to the individual to choose the method that they are most comfortable with.

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In a 2x3 ANOVA, you would have a total of 5 marginal means.

ANOVA, or Analysis of Variance, is a statistical technique used to analyze the differences among group means in a sample.

In a 2x3 ANOVA, there are two independent variables, one with 2 levels and the other with 3 levels.

The marginal means are the average scores for each level of an independent variable, collapsing across the other independent variable.

For a 2x3 ANOVA, you will have 2 marginal means for the first independent variable (2 levels) and 3 marginal means for the second independent variable (3 levels).

To calculate the total number of marginal means, simply add the marginal means for each independent variable:

2 (marginal means for the first independent variable) + 3 (marginal means for the second independent variable) = 5 marginal means in total.

So, the correct answer is (b) 5 marginal means.

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No, it is not possible for a quadrilateral to have only 2 right angles. A quadrilateral is a polygon with four sides and four angles, and the sum of the interior angles of a quadrilateral is always 360 degrees.

If a quadrilateral has two right angles, that means the other two angles must add up to 180 degrees in order to make the total sum of the angles equal to 360 degrees. However, the only way for two angles to add up to 180 degrees is if they are both straight angles, which means they are equal to 180 degrees each. This would result in a total sum of 360 + 180 + 180 = 720 degrees, which is twice the sum of the interior angles of a quadrilateral. Therefore, it is not possible for a quadrilateral to have only 2 right angles. A quadrilateral can have at most one pair of opposite right angles, which would make it a rectangle.

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Answer:

To solve this equation by factoring, we can first try to factor out a common factor of 2:

2x^3 - 5x^2 + 40x - 100 = 0

2(x^3 - (5/2)x^2 + 20x - 50) = 0

Next, we can use the rational root theorem to find possible rational roots of the polynomial x^3 - (5/2)x^2 + 20x - 50. The rational root theorem states that any rational root of a polynomial with integer coefficients must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The constant term of our polynomial is -50, which has factors of ±1, ±2, ±5, ±10, ±25, and ±50. The leading coefficient is 1, which has factors of ±1. So, the possible rational roots are:

±1, ±2, ±5, ±10, ±25, and ±50

We can try plugging in each of these values and see if any of them make the polynomial equal to 0. After some trial and error, we find that x = 5 is a root:

x^3 - (5/2)x^2 + 20x - 50 = 0

(5)^3 - (5/2)(5)^2 + 20(5) - 50 = 0

125 - (5/2)25 + 100 - 50 = 0

125 - 62.5 + 50 = 0

112.5 ≠ 0

Since x = 5 is a root, we can factor the polynomial as:

2(x - 5)(x^2 + 5x + 10) = 0

Using the quadratic formula, we can find the roots of the quadratic factor:

x = (-5 ± sqrt(5^2 - 4(1)(10))) / 2(1)

x = (-5 ± sqrt(-15)) / 2

x = (-5 ± i sqrt(15)) / 2

So, the solutions to the equation 2x^3 - 5x^2 + 40x - 100 = 0 are:

x = 5, (-5 + i sqrt(15)) / 2, (-5 - i sqrt(15)) / 2

The calculated incidence rate may not be a true reflection of the number of Listeria infections that occur in the United States every year because it only includes reported cases and may underestimate the true number of cases due to underreporting and asymptomatic infections.

The calculated incidence rate of Listeria infections may not be a true reflection of the actual number of cases occurring in the United States every year for several reasons:
Underreporting:

Not all cases of Listeria infections are reported to health authorities. Some individuals may have mild symptoms and do not seek medical attention, leading to an underestimation of the actual incidence rate.
Misdiagnosis:

Listeria infections can present with symptoms similar to other illnesses, and without proper testing, they may be misdiagnosed.

This can result in an inaccurate incidence rate.
Surveillance limitations: The quality and coverage of public health surveillance systems can impact the accuracy of the incidence rate. Incomplete or inconsistent reporting from healthcare providers or laboratories may contribute to a less accurate representation of the true number of cases.
Population data inaccuracies:

The incidence rate is calculated using population data, which may not always be up-to-date or accurate. Any errors in the population data can affect the calculated incidence rate.
In conclusion, the calculated incidence rate of Listeria infections may not accurately represent the true number of cases in the United States due to factors such as underreporting, misdiagnosis, surveillance limitations, and population data inaccuracies.

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The statement is generally true.

In materials science, the close-packing of atoms in crystal structures can affect the mechanical properties of the material, such as its ductility and ability to undergo plastic deformation.

In general, structures with closely packed planes (i.e., structures with a higher atomic packing factor) are more likely to undergo plastic deformation because the closely packed planes allow for more slip planes for atoms to move along without disrupting the overall crystal structure.

This means that when a force is applied to the material, the planes can slide more easily past one another, leading to plastic deformation.

In contrast, structures that are not closely packed (i.e., structures with a lower atomic packing factor) have fewer slip planes and are less likely to undergo plastic deformation. Instead, they may experience brittle fracture or other types of failure when subjected to stress.

However, it is important to note that the relationship between atomic packing and plastic deformation is complex and depends on a variety of factors, including the type of crystal structure, the presence of defects or impurities in the material, and the conditions under which the material is being deformed.

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The value of function of f(2) is  6.416. So, the correct answer is C).

We need to find f(2) given f'(x) = cos(x²) and f(3) = 7. We can begin by using the fundamental theorem of calculus

f(x) = ∫cos(t²) dt

Now, we can substitute x² for t²

f(x) = ∫cos(x²) dx

Taking the derivative of both sides, we get

f'(x) = cos(x²)

So we know that f'(2) = cos(2²) = cos(4).

Using the mean value theorem, we can find a value c between 2 and 3 such that

f(3) - f(2) = f'(c) * (3 - 2)

Substituting the given values, we get

7 - f(2) = cos(c²)

We don't know the exact value of c, but we do know that it is between 2 and 3, so we can say

-1 ≤ cos(c²) ≤ 1

Therefore

-1 ≤ 7 - f(2) ≤ 1

Subtracting 7 from all sides, we get

-8 ≤ -f(2) ≤ -6

Multiplying by -1 and flipping the inequality signs, we get

6 ≤ f(2) ≤ 8

So the only answer choice within this range is C. 6.416. Therefore, the answer is C. 6.416.

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Based on available data, the mean number of social ties for a cell phone user is estimated to be around 500.

One way to estimate the mean number of social ties for a cell phone user is to look at data from large-scale studies. For example, a study by Pew Research Center in 2019 found that the average American adult has around 500 social ties. This includes family members, friends, and acquaintances. Since cell phone usage is ubiquitous in the United States, it is reasonable to assume that the mean number of social ties for a cell phone user would be similar to the overall average for adults. Of course, this is just an estimate and there may be individual differences in the number of social ties depending on factors like age, gender, and social context. However, looking at large-scale studies can provide a useful starting point for estimating means in the absence of individual-level data.

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Answer: The circumference of the unicycle wheel is given by:

C = 2πr = 2 x 3.14 x 6 = 37.68 inches

In one revolution, the unicycle travels the distance equal to the circumference of the wheel. Therefore, in 6 revolutions, the unicycle will travel:

6 x 37.68 = 226.08 inches

Rounding to the nearest hundredth of an inch, we get:

226.08 ≈ 226.1 inches.

Therefore, the unicycle will travel approximately 226.1 inches in 6 revolutions.

The area of Circle A is approximately 201.06 in².

The area of a circle is given by the formula:

Area = π * r²

Let's start by calculating the radius of each circle:

Circle A: r = 8 in.

Circle B: r = 4 in. + 8 in. = 12 in.

Circle C: r = 2 in. + 12 in. = 14 in.

Circle D: r = 14 in. - 3 in. = 11 in.

Now we can use the formula for the area of a circle to calculate the area of each circle:

Circle A: Area = π * (8 in.)^2 ≈ 201.06 sq. in.

Circle B: Area = π * (12 in.)^2 ≈ 452.39 sq. in.

Circle C: Area = π * (14 in.)^2 ≈ 615.75 sq. in.

Circle D: Area = π * (11 in.)^2 ≈ 380.13 sq. in.

To find out how many times greater the area of Circle D is than the area of Circle A, we can divide the area of Circle D by the area of Circle A:

Area ratio = Area(D) / Area(A)

Area ratio = (π * (11 in.)^2) / (π * (8 in.)^2)

Area ratio = (11 in.)^2 / (8 in.)^2

Area ratio ≈ 1.92 (about 2 times)

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Answer: A. 1400000

Step-by-step explanation:

Their hourly wage in 9 more years is $23.60 per hour.

To find the hourly wage in 9 more years, we can use the formula for exponential growth:

A = [tex]P * (1 + r)^t[/tex]

Where:

To find the annual growth rate, we can use the formula:

r = [tex](A/P)^(^1^/^t^)[/tex] - 1

Substituting the given values, we get:

r = [tex](\$16.09 / \$6.90)^(^1^/^1^1^)[/tex] - 1

r = 0.0883 or 8.83%

Now we can use this growth rate to find the hourly wage in 9 more years:

A = $6.90 * [tex](1 + 0.0883)^9[/tex]

A = $23.60 (rounded to the nearest cent)

Therefore, the hourly wage of the automobile plant workers in 9 more years, if their wages continue to grow exponentially at the same rate, would be $23.60 per hour.

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The slope intercept form of the given equation is y=-2/5 x-5.

The given equation is 6x+15y=-75.

The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept.

The standard form of the slope intercept form is y=mx+c.

Here, 6x+15y=-75

3(2x+5y)=-75

2x+5y=-25

5y=-25-2x

y=-2/5 x-5

Therefore, the slope intercept form of the given equation is y=-2/5 x-5.

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The best estimate for the total number of games played in 4 years would be 80 games

To estimate the total number of games played in 4 years, we need to determine the average number of games played per season and then multiply it by 4.

Given that a team plays between 18 and 22 games per season, we can take the average of these two values:

Average number of games per season = (18 + 22) / 2 = 40 / 2 = 20

Total number of games played in 4 years = Average number of games per season * Number of seasons

Total number of games played in 4 years = 20 games/season * 4 seasons = 80 games

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The semiannual interest payments in the years between 2021 and 2028, as they have already been recorded through the straight-line method.

Here are the journal entries to record the purchase of the bonds by Wang Communications on January 1, 2021, interest revenue on June 30, 2021, and interest revenue on December 31, 2028:

Record the investment in bonds on January 1, 2021:

Debit: Investment in Bonds $166,000,000

Credit: Cash $166,000,000

Record interest revenue on June 30, 2021:

Debit: Cash $8,300,000 (166,000,000 x 10% x 6/12)

Credit: Interest Revenue $8,300,000

Record interest revenue on December 31, 2028:

Debit: Cash $8,300,000 (166,000,000 x 10% x 6/12)

Credit: Interest Revenue $8,300,000

Note: No entries are needed for the semiannual interest payments in the years between 2021 and 2028, as they have already been recorded through the straight-line method.

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The value of the function f(x) at x = 1.477.

f(1.477) = 32.857

The value of the function g(x) at x = 20.

g(20) = 1.729

We have,

Two functions:

f(x) = b^x

g(x) = log_b(x)

Now,

From the table,

f(0.699) = b^0.699 = 5

Taking the logarithm of both sides with base b.

log_b(5) = 0.699

b = 5^(1/0.699)

b = 8.343

Now, we can find the value of f(1.477).

f(1.477) = b^1.477 = 8.343^1.477 = 32.857

Similarly, we can find the value of g(20).

g(20) = log_b(20) = log_8.343(20) = 1.729

Thus,

The value of the function f(x) at x = 1.477.

f(1.477) = 32.857

The value of the function g(x) at x = 20.

g(20) = 1.729

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θ lies in the fourth quadrant where cos θ is negative and sin θ is also negative. θ lies in the fourth quadrant.

If sin θ < 0 and sec θ < 0, we can use the following rules to determine the quadrant in which θ lies:

In quadrant I, all trigonometric functions are positive.

In quadrant II, sin θ and csc θ are positive.

In quadrant III, tan θ and cot θ are positive.

In quadrant IV, cos θ and sec θ are positive.

Since sin θ < 0, we know that θ lies in either the third or fourth quadrant. Similarly, since sec θ < 0, we know that cos θ, which is the reciprocal of sec θ, is negative. This means that θ lies in the fourth quadrant where cos θ is negative and sin θ is also negative.

Therefore, θ lies in the fourth quadrant.

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