What value of a satisfies the equation -3 (4x - 5) = 2 (1 - 5x)?

The correct representations of the inequality –3(2x – 5) < 5(2 – x) are:

-6x - 5 < 10 - x

-6x + 15 < 10 - 5x

Therefore, the first and second options are the correct representations.

For the number line, we first need to solve the inequality for x:

-3(2x - 5) < 5(2 - x)

-6x + 15 < 10 - 5x

-x < -5

x > 5

Using this solution, we can plot the open circle at 5 and the bold line pointing to the right on a number line from -3 to 3 in increments of 1. This matches the first option provided. The second option represents a number line with an open circle at -5 and a bold line pointing to the left, which does not correctly represent the solution to the inequality.

Answer:

x = 4

y = 2

Step-by-step explanation:

{y = x - 2,

{5x + 4y = 28;

Replace y in the second equation with the 1st equation's value:

5x + 4(x - 2) = 28

5x + 4x - 8 = 28

9x = 28 + 8

9x = 36 / : 9

x = 4

y = 4 - 2 = 2

The missing entries are (a) $686, (b) $635, (c) $1035, (d) $1010, (e) $938.88 and (f) $447.37.

A debit card is one that a person owns, and when they use it to make a purchase, the money is instantly withdrawn from or added to their account.

A table listing Gino's debit card purchases is provided.

He has made a $778.19 starting deposit.

The disparity between the old balance and the payment will be the new balance in the account.

He spent $92.19 on the bat.

a = $778.19 - 92.19 = $686

He bought gas for $51.00.

b = $686 - $51 = $635

He deposited $400.

c = $635 + $400 = $1035

He paid $25 for gas.

d = $1035 - $25 = $1010

Dinner at Spooner's on the shore cost him $71.12.

e = $1010 - $71.12 = $938.88

He spent $491.51 on books for the entire term.

f = $938.88 - $491.51 = $447.37

The missing records are thus discovered.

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The solutions for y are:

We can simplify the expression sqrt(160) by factoring 160 into its prime factors:

160 = 2^5 * 5

Taking the square root of each factor, we get:

sqrt(160) = sqrt(2^5 * 5) = sqrt(2^4 * 2 * 5) = 2^2 * sqrt(2 * 5) = 4 * sqrt(10)

Therefore, we can simplify the expression for y as follows:

y = (7 +- sqrt(160))/10 = (7 +- 4sqrt(10))/10

So the solutions for y are:

y = (7 + 4sqrt(10))/10

y = (7 - 4sqrt(10))/10

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The given statement, points that minimize a nonlinear function are inherently less accurately determined than points for which a nonlinear function has a zero value is FALSE.

In mathematics, a nonlinear function is a function that is not linear, i.e. a function whose graph is not a straight line. Simplest non-linear functions are quadratic function, exponential function and logarithmic functions. Nonlinear functions do not follow the superposition principle, which is fundamental to linear systems, which states that if the input is scaled by any factor, then the output will also be scaled by that factor.

Points that minimize a nonlinear function are inherently less accurately determined than points for which a nonlinear function has a zero value. The above statement is false because the points that minimize a nonlinear function can be determined more accurately than the points where the nonlinear function has zero value.

Also, there is no such rule that the points that minimize a nonlinear function are less accurate than points for which a nonlinear function has a zero value.

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According the given question the slοpe is 3/4.

Calculated using the slοpe οf a line fοrmula, the ratiο οf "vertical change" tο "hοrizοntal change" between twο different lοcatiοns οn a line is determined. The difference between the line's y and x cοοrdinate changes is knοwn as the slοpe οf the line.Any twο distinct places alοng the line can be used tο determine the slοpe οf any line.

Here the accοrding to the table , let us take any twο coordinates are,

[tex](x_1,y_1)=(4,6) , (x_2,y_2)=(8,3)[/tex]

Nοw using slope formula then,

=> Slοpe m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> Slοpe m = [tex]\frac{6-3}{8-4}=\frac{3}{4}[/tex]

Hence the slοpe οf the linear function is 3/4.

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Answer:

381.7 cubic inches.

A container size of at least 66.03 ounces will ensure that overflow occurs only 0.5% of the time.

To make sure overflow occurs only 0.5% of the time, we would have to find the container of size "c" such that the amount of distilled water dispensed by the machine does not exceed c with a probability of 0.995 (or 1-0.005).

Let X be the amount of distilled water dispensed by the machine. Then X ~ N(64, 0.78^2).

We want to find c such that P(X ≤ c) = 0.995.

We can standardize X to a standard normal distribution:

Z = (X - μ) / σ

Z = (c - 64) / 0.78

Then we can find the value of Z such that P(Z ≤ z) = 0.995, where z is the z-score associated with the 0.995 percentile of the standard normal distribution.

Using a standard normal distribution table or a calculator, we can find that z ≈ 2.576.

Therefore, 2.576 = (c - 64) / 0.78. Solving for c, we get:

c = 64 + 2.576 * 0.78 ≈ 66.03

So a container size of at least 66.03 ounces will ensure that overflow occurs only 0.5% of the time.

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Even if the sample is representative and the survey questions are well-crafted, there is a possibility that the findings will differ from those of the actual population due to sampling error.

Sampling bias: The survey sample may not be representative of the community, resulting in an imbalance between the representation of some groups in the sample. As a result, there may be inaccuracies in the findings because the sample may not fairly represent the population's diversity. There are a number of factors why survey results might not be a reliable indicator of what the population will actually do. The following claims may help to clarify this:

Non-response bias: A biassed sample may result if some members of the sample decide not to take part in the poll. If the non-response rate is high among specific groups, such as minority groups or low-income households, this may be a particular issue.

Social preference bias: Respondents may be influenced to provide answers that make them appear more desirable.Instead of being fully honest, I'll be polite. As a result, socially acceptable behaviour may be overreported while socially unacceptable behaviour may be underreported.

topic wording: How a topic is worded can have an impact on the responses it receives. It's possible that ambiguous or deceptive questions don't accurately represent the respondent's true viewpoint.

Response options: How respondents react to a survey can also be influenced by the response options that are offered. Respondents might feel under pressure to select a response that doesn't accurately represent their opinions, for instance, if the choices are few or don't include a "neutral" option.

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The answer of the given question based on expression is  the value of p that satisfies the given condition is -2.

The binomial theorem is a fundamental concept in algebra that provides a formula for expanding expressions of the form (a + b)ⁿ, where n is a non-negative integer and a and b are real numbers. The formula is as follows:

(a + b)ⁿ = C(n, 0)aⁿ b⁰ + C(n, 1)a⁽ⁿ⁻¹⁾ b¹ + ... + C(n, r)a⁽ⁿ⁻r⁾ b^r + ... + C(n, n)a⁰bⁿ

The binomial theorem states that the nth power of a binomial can be expanded as the sum of the products of each term in the binomial raised to a power and the corresponding binomial coefficient. The binomial coefficient represents the number of ways of choosing r objects from a set of n objects, and is often denoted by "n choose r" or written as a combination symbol, (nCr).

We can use the binomial theorem to expand the given expression as:

(2-3px) (4x⁴ + 5x₃ - x) = 8x⁴ + 10x³ - 2x - 12px⁵ - 15px⁴ + 3px²

To find the coefficient of x⁴ in this expansion, we need to look at the terms that contain x⁴. There are two such terms: 8x⁴ and -15px⁴. Therefore, the coefficient of x⁴ is 8 - 15p.

We are given that this coefficient is 38, so we can set up the equation:

8 - 15p = 38

Solving for p, we get:

-15p = 30

p = -2

Therefore, the value of p that satisfies the given condition is -2.

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No, a non-complex equation cannot have two horizontal asymptotes. A horizontal asymptote is a line that a function approaches as the input variable increases or decreases without bounds.

Since a non-complex equation represents a single function, it cannot have more than one horizontal asymptote. A non-complex equation cannot have two vertical asymptotes. A vertical asymptote is a vertical line that a function approaches as the input variable approaches a certain value. Again, since a non-complex equation represents a single function, it cannot have more than one vertical asymptote. If a complex number is used as the input variable in an equation, the equation can pass through a vertical asymptote since the notion of "approaching" a point does not apply to complex numbers. However, the concept of a horizontal asymptote does not apply to complex numbers since there is no notion of "increasing" or "decreasing" in the complex plane.

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Answer:

The solution to the system of equations is (-1/2, 3).

Step-by-step explanation:

To solve this system of equations using substitution method, we first need to solve one of the equations for one of the variables in terms of the other variable. Let's solve the first equation for y:

-2x + y = 4

y = 2x + 4

Now we can substitute 2x + 4 for y in the second equation:

-2x + 2y = 7

-2x + 2(2x + 4) = 7

Simplifying the equation:

-2x + 4x + 8 = 7

2x = -1

x = -1/2

Now we can use this value of x to find the value of y:

y = 2x + 4

y = 2(-1/2) + 4

y = 3

Answer:

10%

Step-by-step explanation:

Percent proportion:

$28 - 100%

$8,40 - x%

Cross-multiply to find x:

[tex]x = \frac{8.40 \times 100\%}{28} = \frac{840}{84} = 10 \: \%[/tex]

Answer  30%

Step-by-step explanation:

To find what percentage $8.40 is of $28, we can use the following proportion:

part/whole = percent/100

Let x be the percentage we are trying to find, then we can write:

8.40/28 = x/100

To solve for x, we can cross-multiply:

28x = 8.40 * 100

Dividing both sides by 28, we get:

x = (8.40 * 100) / 28 = 30

Therefore, $8.40 is 30% of $28.

The calculated surface area of the figure is 152 square feet

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

The triangular prism

The surface  area is calculated as

SA = hp + 2B

Where

h = height

p = perimeter of base

B = base area

From the figure, we have

B = 1/2 * 6 * 4 = 12

p = 5 + 5 + 6 = 16

h = 8

So, we have

SA = 8 * 16 + 2 * 12

Evaluate

SA = 152

Hence, the surface area is 152 square feet

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Answer:

the total answer is 41.89 ft square

Step-by-step explanation:

i dont have it separately sorry

cos² u / sin² u = cos² u / (1 - cos² u) is the simplified expression for (csc u cot u) / sec u in terms of cos u. We can calculate it in the following manner.

We can simplify the expression (csc u cot u) / sec u using trigonometric identities.

Recall that:

csc u = 1 / sin u

cot u = cos u / sin u

sec u = 1 / cos u

Therefore, we have:

(csc u cot u) / sec u

= (1/sin u * cos u / sin u) / (1 / cos u) (substituting the identities)

= (cos u / (sin u)²) * cos u (simplifying the fractions)

= cos² u / sin² u (simplifying further)

Recall that:

sin² u + cos² u = 1

Therefore, we can substitute sin² u by 1 - cos² u:

cos² u / sin² u = cos² u / (1 - cos² u)

This is the simplified expression for (csc u cot u) / sec u in terms of cos u.

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f(x) = 12x and  [tex]g(x)= \sqrt{x-12}[/tex] both include domain values of [12, ∞), and both functions increase over the interval (12, ∞).

The set containing all input values is known as a function's domain while a function's range is the collection of all possible output values.

Function f(x) is defined by: f(x) = 12x.

Function g(x) is defined by: [tex]g(x)= \sqrt{x-12}[/tex]

Therefore, the correct option is (d) Both f(x) and g(x) include domain values of [12, ∞), and both functions increase over the interval (12, ∞).

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a) Ratio analysis is a financial analysis tool that helps to evaluate the financial performance and health of a business by comparing different financial figures

b) There are three categories of ratios in ratio analysis: liquidity ratios, profitability ratios, and solvency ratios.

c) Ratio analysis is important because it helps to provide a quick snapshot of a company's financial health and performance.

Ratio analysis is a financial analysis tool that helps to evaluate the financial performance and health of a business by comparing different financial figures. It involves calculating and interpreting various ratios that provide insight into the financial position, profitability, and liquidity of a company.

There are three categories of ratios in ratio analysis

Liquidity ratios: These ratios help to determine a company's ability to meet its short-term financial obligations. Examples include the current ratio and the quick ratio.

Profitability ratios: These ratios help to evaluate a company's ability to generate profit in relation to its revenue, assets, and equity. Examples include the gross profit margin, net profit margin, and return on assets.

Solvency ratios: These ratios help to assess a company's ability to meet its long-term financial obligations. Examples include the debt-to-equity ratio and the interest coverage ratio.

Ratio analysis is important because it helps to provide a quick snapshot of a company's financial health and performance. It is useful for investors, lenders, and other stakeholders in making informed decisions about investing in or lending to a company.

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The graph which shows a system of linear-equations with one unique solution at (0,5) is option-B which shows lines, intersecting at (0,5).

What is system of linear equations?

The collection of two or more linear equations is called as system of linear equations. The linear equations have the degree of variable as one. Though a single linear equation can have infinite number of solutions, but a pair of linear equation can be classified as consistent or inconsistent. The equations which are consistent have either one solution or infinte solutions. The intersecting pair of consistent equations have unique solution whereas the coinciding pair of consistent equations have infinite number of solutions. The equations which are inconsistent are the parallel lines which do not have any solution.

Here the system must have one unique solution as (0,5)

a)graph as parallel lines: which means they are inconsistent & do not have any solution.

b)The graph shows lines intersecting at (0,5): which means the system is consistent with unique solution (0,5)

c)The graph shows lines intersecting at (1,6): which means the system is consistent with unique solution (1,6)

d)graph shows two lines which appear as one: means the lines are coinciding with infinite solutions.

So the answer is option-B

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Answer:

$134 per month

Step-by- step explanation:

Simply divide 536 by 4, and you get 134.

Answer:

I think the answer is

1760

In terms of using specific terms in your answer, you should incorporate any keywords or phrases from the student's question that are relevant to your response.

For example, in response to the question "a restaurant wants to know if its customers like its new menu. in surveys 100 randomly selected customers over one week. what is the population in this study?" you might write:"

In this study, the population refers to the entire group of customers who might potentially like or dislike the restaurant's new menu.

While the study only surveyed 100 randomly selected customers over one week, the population could include all customers who visited the restaurant during that time period or even a larger group of potential customers who have not yet visited the restaurant."

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the values that represent the probability of the team not winning.

b) 0.25

d) 25%

e) 3/4

f) 1/4

These values represent the probability of the team not winning, which is the complement of the probability of winning (75%).

b) 0.25 is the decimal representation of the probability of not winning, which is 1-0.75.      

d) 25% is the percentage representation of the probability of not winning, which is also 100%-75%.

e) 3/4 is the fraction representation of the probability of winning, so 1-3/4 gives the probability of not winning.

f) 1/4 is the fraction representation of the probability of not winning, which is the complement of the probability of winning (3/4).

These are the options that represent the probability of the team not winning.

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A sportscaster predicted that the local high school baseball team has a 75% chance of winning tonight. Select all of the values that represent the probability of the team not winning.

a)0.75 b)25% c)0.25d) 75%e)3/4f)1/4

a=b, The curve approaches the line y=a as x approaches infinity or negative infinity.

since the y-intercept is the point where the curve intersects the y-axis, i.e., x=0.

Since we have (0, a) as our y-intercept, then a=b, where a and b are constants.

The y-intercept, as indicated in the question, is (0, a) meaning that for the function f(x), when x=0, then f(x) = a.

The horizontal asymptote of a function is a horizontal line that the graph approaches as x approaches infinity or

negative infinity.

If the horizontal asymptote is y=b, it means that the value of y approaches b as x approaches infinity or negative infinity.

Therefore, since a=b, the curve approaches the line y=a as x approaches infinity or negative infinity.

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Answer:  42

Step-by-step explanation:

  6x7=42 ft

The probability that the shipment came from company X, given one ineffective vial was found, is 0.4 or 40%.

To find the probability ,we will use the Bayes' theorem.

Determine the prior probabilities.

P(X) = Probability that the shipment is from company X = 1/5

P(Y) = Probability that the shipment is from other companies = 1 - 1/5 = 4/5

Determine the likelihood probabilities.

P(I|X) = Probability of finding an ineffective vial given the shipment is from company X = 8%

P(I|Y) = Probability of finding an ineffective vial given the shipment is from other companies = 3%

Determine the probability of finding an ineffective vial.

P(I) = P(I|X) × P(X) + P(I|Y) × P(Y) = (8% × 1/5) + (3% × 4/5)

     = 0.08 × 0.2 + 0.03 × 0.8 = 0.016 + 0.024

     = 0.04

Use Bayes' theorem to find the probability that the shipment is from company X given an ineffective vial.

P(X|I) = (P(I|X) × P(X)) / P(I)

        = (0.08 × 0.2) / 0.04 = 0.016 / 0.04

        = 0.4

The probability that the shipment came from company X, given one ineffective vial was found, is 0.4 or 40%.

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The solution to the equation is 3[tex]z^{2}[/tex] - [tex]z^{3}[/tex] = 5z + 1 and it has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers can be described by the four fundamental operations, sometimes known as "arithmetic operations." Operations like quotient, product, sum, and difference come before operations like division, multiplication, addition, and subtraction in mathematics.

We are given an equation as:

[tex]\frac{z+1}{z-1}[/tex] - [tex]\frac{z}{3}[/tex] = [tex]\frac{2}{z-1}[/tex]

Now, we will simplify the equation first.

⇒ [tex]\frac{z+1}{z-1}[/tex] - [tex]\frac{z}{3}[/tex] = [tex]\frac{2}{z-1}[/tex]

⇒ [tex]\frac{3(z+1) - z(z-1)}{3 (z-1)}[/tex] = [tex]\frac{2}{z-1}[/tex]

Now, on cross multiplying we get,

⇒[3 (z + 1) - z (z - 1)] * (z - 1)  = 2 (3z - 1)

⇒[3z + 3 - [tex]z^{2}[/tex] - z] * (z - 1)  = 6z - 2

⇒3[tex]z^{2}[/tex] + 3z - [tex]z^{3}[/tex] - [tex]z^{2}[/tex] - 3z - 3 + [tex]z^{2}[/tex] + z = 6z - 2

⇒3[tex]z^{2}[/tex] - [tex]z^{3}[/tex] - 3 + z = 6z - 2

⇒3[tex]z^{2}[/tex] - [tex]z^{3}[/tex] = 5z + 1

Hence, the required solution has been obtained.

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Account I.

$822.12

$17.88