8 -3 (1 point) Consider the matrix 2 k For the matrix to have 0 as an eigenvalue, k must be - 4 4 (1 point) Consider the matrix 5 k For the matrix to have 0 as an eigenvalue, k must be [1

The sine function that will model the situation is:

h(t) = 1 * sin(2π/28 * t) + 10, where h(t) represents the water level in feet and t represents the number of days.

To model the water level in the pond using a sine function, we need to consider the period, amplitude, and vertical shift.

Given that the cycle repeats every 28 days, the period of the sine function is 28 days. This means that the function will complete one full cycle every 28 days.

The water level varies between the average level of 10 feet and a maximum level of 12 feet. The difference between these two levels is 2 feet, which represents the amplitude of the sine function.

The sine function is symmetric around the average level, so the vertical shift or the mean value of the function is 10 feet.

Putting all the pieces together, we can write the sine function that models the situation as:

h(t) = 1 * sin(2π/28 * t) + 10

The sine function h(t) = 1 * sin(2π/28 * t) + 10 accurately models the water level in the pond, where h(t) represents the water level in feet and t represents the number of days. This function has a period of 28 days, an amplitude of 2 feet, and a vertical shift of 10 feet. It captures the cyclical nature of the water level, oscillating between the maximum, minimum, and average levels over the course of the 28-day cycle.

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Putting all the given values in the formula, we get:n = [1.96² x 0.21 x 0.79] / 0.03²On solving, we get,n = 2734.84 ≈ 2735Therefore, 2735 public accountants should be contacted to update the study with a margin of error of 3% and a 95% level of confidence. Answer: 2735.

Given Information :A study conducted several years ago reported that 21% of public accountants changed companies within 3 years.

The American Institute of CPAs would like to update the study.

They would like to estimate the population proportion of public accountants who changed companies within 3 years with a margin of error of 3% and a 95% level of confidence.

Required:a. To update this study, how many public accountants should be contacted? Solution: Given that: the percentage of public accountants changed companies within 3 years is 21%.The level of confidence is 95%.

The margin of error is 3%.We have to find out the sample size.To find the sample size we use the formula :n = [Z² x p x q ] / E²

Where, Z = Standard normal deviation corresponding to a 95% confidence level is 1.96.p = proportion = 21/100 = 0.21q = 1-p = 1-0.21 = 0.79E = margin of error = 3/100 = 0.03

Putting all the given values in the formula, we get:n = [1.96² x 0.21 x 0.79] / 0.03²On solving, we get,n = 2734.84 ≈ 2735Therefore, 2735 public accountants should be contacted to update the study with a margin of error of 3% and a 95% level of confidence. Answer: 2735.

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\(\\ \rm\longmapsto (a-b)\sqrt{a-b}\)

\(\\ \rm\longmapsto (a-b)(a-b)^{\frac{1}{2}}\)

\(\\ \rm\longmapsto (a-b)^{1+\dfrac{1}{2}}\)

\(\\ \rm\longmapsto (a-b)^{\dfrac{3}{2}}\)

Answer:

\(\dashrightarrow \: { \tt{(a - b) \sqrt{a - b} }} \\ \\ \dashrightarrow \: { \tt{ {(a - b)}^{1} {(a - b)}^{ \frac{1}{2} } }}\)

• from law of indices:

\({ \boxed{ \rm{ ({x}^{n} )( {x}^{m} ) = {x}^{(n + m)} }}}\)

therefore:

\(\dashrightarrow \: { \tt{ {(a - b)}^{(1 + \frac{1}{2} )} }} \\ \\ \dashrightarrow \: { \tt{ {(a - b)}^{ \frac{3}{2} } }}\)

Answer:

y = 4x - 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 4 , then

y = 4x + c ← is the partial equation

To find c substitute (3, 10) into the partial equation

10 = 12 + c ⇒ c = 10 - 12 = - 2

y = 4x - 2 ← equation of line

Therefore, since there are more moles of HC₂H₃O₂ (0.0833 mol) than NaHCO₃ (0.0595 mol), NaHCO₃ is the limiting reagent.

Division is a mathematical operation used to find the number of times one quantity is contained within another quantity of the same kind. It is the inverse operation of multiplication. In division, the quantity being divided is called the dividend, the number by which it is divided is called the divisor, and the result is called the quotient. Division is denoted by the symbol "÷" or "/", and it is commonly used in arithmetic and algebra to solve problems involving ratios, fractions, and percentages.

Here,

a. To determine which is the limiting reagent, we need to calculate the moles of each reactant and compare them to the stoichiometric ratio in the balanced chemical equation.

First, we need to convert the mass of each reactant to moles:

moles of HC₂H₃O₂ = 5.00 g / molar mass of HC₂H₃O₂

moles of NaHCO₃ = 5.00 g / molar mass of NaHCO₃

Using the molar masses of each compound, we get:

moles of HC₂H₃O₂ = 5.00 g / 60.05 g/mol = 0.0833 mol

moles of NaHCO₃ = 5.00 g / 84.01 g/mol = 0.0595 mol

The stoichiometric ratio of the balanced equation tells us that the ratio of moles of HC₂H₃O₂ to NaHCO₃ is 1:1.

b. To find the theoretical yield, we need to use the balanced chemical equation and the amount of limiting reagent (in moles) to calculate the moles of the product formed, and then convert that to grams using the molar mass of the product. The balanced equation tells us that 1 mole of NaHCO₃ produces 1 mole of CO₂.

moles of CO₂ = moles of NaHCO₃ = 0.0595 mol

mass of CO₂ = moles of CO₂ x molar mass of CO₂

mass of CO₂= 0.0595 mol x 44.01 g/mol = 2.62 g

Therefore, the theoretical yield of CO₂ is 2.62 g.

c. If the percent yield is 68.7%, we can use this percentage to calculate the actual yield. Percent yield is calculated as follows:

percent yield = (actual yield / theoretical yield) x 100

Rearranging this equation, we get:

actual yield = (percent yield / 100) x theoretical yield

actual yield = (68.7 / 100) x 2.62 g

actual yield = 1.80 g

Therefore, the actual yield of CO₂ is 1.80 g.

d. To find a mass of each reactant where neither is the limiting reagent, we can use the stoichiometric ratio of the balanced chemical equation to calculate the maximum amount of product that can be formed from each reactant.

Let's assume we have x grams of HC₂H₃O₂ and y grams of NaHCO₃. The moles of each reactant are:

moles of HC₂H₃O₂ = x / molar mass of HC₂H₃O₂

moles of NaHCO₃ = y / molar mass of NaHCO₃

If neither reactant is limiting, they will react completely according to the stoichiometric ratio of the balanced equation. That is, 1 mole of HC₂H₃O₂ reacts with 1 mole of NaHCO₃ to produce 1 mole of CO₂.

So, to find the maximum amount of CO₂ that can be produced from each reactant, we can calculate the moles of CO₂ produced from 1 mole of each reactant and then convert that to grams using the molar mass of CO₂:

Maximum yield of CO₂ from HC₂H₃O₂:

moles of CO₂ = moles of HC

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The given expression :

The total number of pounds of cheese Kala bought is 1.75.

Bar graph (bar chart) is a graph that represents the categorical data using rectangular bars.

The bar graph shows the comparison between discrete categories.

Given

Kala bought two types of cheese at a deli.

She bought 0.50 pound of American cheese and 1.25 pounds of Swiss cheese.

The bar diagram and equation below represent Kala’s purchase, where p represents the total number of pounds of cheese she bought.

A bar diagram. The top bar contains p.

The bottom bars contain 0.50 and 1.25.

p = 0.50 + 1.25

The total number of pounds of cheese Kala bought is;

= 0.50 + 1.25

= 1.75

Hence, the total number of pounds of cheese Kala bought is 1.75.

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The sum of 18.420 and 28.49, rounded to the correct number of significant figures, is 46.91.

To add the numbers 18.420 and 28.49, we align the decimal points and perform the addition. After adding the numbers, we obtain a sum of 46.910. However, we need to round the answer to the correct number of significant figures.

The rule for determining the number of significant figures in addition is to retain the same number of decimal places as the number with the fewest decimal places being added. In this case, 18.420 has three decimal places, while 28.49 has two decimal places. Therefore, we round the sum to two decimal places: 46.910 rounded to two decimal places is 46.91.

Thus, the sum of 18.420 and 28.49, rounded to the correct number of significant figures, is 46.91.

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Answer:

8/10 or 16/20

Step-by-step explanation:

hope it helps

Answer:

Step-by-step explanation:

\(a_1=35\\d=8\\\\a_n=a_1+d(n-1)\\\\a_n=35+8(n-1)\\a_n=35+8n-8\\a_n=8n+27\)

The answer is low using correlation.

What is correlation?

The terms "co" and "relation" are combined to form the word "correlation." Correlation is the relationship between any set of data when taken as a whole because the term "co" signifies together.

The correlation coefficient, which in statistics is a number between -1 and +1, measures the linear dependency of the collection of data.

It cannot capture nonlinear correlations between two variables and only assesses the magnitude and direction of the linear link between the two variables.

The difference between dependent and independent variables is not possible.

In the question, it is given that there is a high positive correlation between x and y, which means for every increase in x there is a corresponding increase in y

So if x is having low score, than y is also having low score

Hence the answer is low.

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Binding constraints directly influence the optimal solution in a linear Programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution.

binding constraints and positive slack in the context of linear programming. In a linear programming problem, we aim to find the optimal solution for an objective function, given a set of constraints. The terms "binding constraints" and "positive slack" are related to these constraints.

1. Binding constraints: These are constraints that directly impact the optimal solution of the problem. In other words, they "bind" the feasible region (the area where all the constraints are satisfied) and affect the maximum or minimum value of the objective function. Binding constraints are active constraints, as they influence the final solution.

2. Positive slack: Slack is the difference between the left-hand side and right-hand side of a constraint when the constraint is satisfied. If this difference is positive, it means that there is some "extra" or "unused" resource in that constraint. Positive slack indicates that the constraint is non-binding, meaning it does not directly impact the optimal solution. It shows that there is some room for the constraint to be further tightened without affecting the final outcome.

In summary, binding constraints directly influence the optimal solution in a linear programming problem, whereas constraints with positive slack are non-binding and do not directly impact the solution. Knowing the difference between these terms can help you better understand and analyze linear programming problems.

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Answer:

The square root of 20.25 is 4.5!

Step-by-step explanation:

The value of number is,

⇒ 4.5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The number is,

⇒ √20.25

Now, We can simplify as;

⇒ √20.25

Hence, The square root of 20.25;

⇒ 4.5

Thus, The value of number is,

⇒ 4.5

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Answer:

\(6c-8\)

Step-by-step explanation:

We have:

\(-(2c+8)+8c=\)

\(-2c-8+8c=\\\)

\(6c - 8\)

Using the inscribed angle theorems, the measure of the indicated angles are:

1. m∠BOA = 26°

2. m∠BDA = 13°

3. m∠BCA = 13°

Based on the inscribed angle theorem, the following relationships are established:

Given:

Intercepted arc BA = 26°

1. ∠BOA is central angle

Thus:

m∠BOA = 26° (inscribed angle theorems)

2. ∠BDA is inscribed angle.

m∠BDA = 1/2(30) = 13° (inscribed angle theorems)

3. m∠BCA = m∠BDA = 13° (inscribed angle theorems)

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Answer:

-289 degrees

Step-by-step explanation:

You are looking for what is called  Coterminal Angles.

To find a coterminal angle between 0 and 360 you add or subtract 360.

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9514 1404 393

Answer:

  12 quarters

  20 dimes

Step-by-step explanation:

If all were dimes the value would be $3.20. It is $1.80 more than that. Each replacement of a dime with a quarter adds $0.15 to the value, so there must be $1.80/$0.15 = 12 such replacements.

There are 12 quarters and 20 dimes.

_____

Let q represent the number of quarters.

  0.25q +0.10(32 -q) = 5.00 . . . . . total value

  0.15q +3.20 = 5.00 . . . . . . . . . simplify

  q = (5.00 -3.20)/0.15 . . . . . . subtract 3.20 and divide by 0.15

  q = 12

Answer:

First number is -2.5

Second number 5

Step-by-step explanation:

Four times the first number minus three times the second number is 2.

To represent this statement, 4x -3y =2

Two times the first number increased by three times the second is 10.

To represent thsi statement, 2x+ 3y = 10

4x - 3y = 2

2x + 3y =10

4x - 2x = 2x

2x = -5

x= -2.5

The first number is -2.5

By using Substitution

2x + 3y = 10

2(-2.5) + 3y = 10

-5 + 3y = 10

3y = 10 +5

3y =15

y = 5

The second number is 5

....To check my answer

-5 + 15 = 10

Answer: Cups

Step-by-step explanation: Only your car drinks that much

Answer:

v = b

hope this helps

You can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:

For x = 2:

slope = -1 / (3 - 2(2))

slope = -1 / (3 - 4)

slope = -1 / (-1)

slope = 1

To find the slope of the secant line PQ, we need two points on the line: P(x, 4) and Q(3 - x, 3).

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 - y1) / (x2 - x1)

In this case, the coordinates of P are (x, 4) and the coordinates of Q are (3 - x, 3). Plugging these values into the slope formula, we have:

slope = (3 - 4) / (3 - x - x)

slope = -1 / (3 - 2x)

To find the slope of the secant line for different values of x, we substitute those values into the expression for the slope.

For example, if x = 1, the slope of the secant line PQ is:

slope = -1 / (3 - 2(1))

slope = -1 / (3 - 2)

slope = -1 / 1

slope = -1

Similarly, you can find the slope of the secant line PQ for other values of x by substituting them into the expression for the slope:

For x = 2:

slope = -1 / (3 - 2(2))

slope = -1 / (3 - 4)

slope = -1 / (-1)

slope = 1

And so on, you can calculate the slope of the secant line for different values of x.

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The expression for modelling the pattern is n² + 2

Charlie can observe 38 guppy fish in month 6.

Given,

Number of guppy fish in Charlie's fish tank for the first time = 3

Number of guppy fish after one month = 6

Number of guppy fish in the following month = 11

The increasing pattern of guppy fish in the tank:

First month = 6 - 3 = 3

Second month = 11 - 6 = 5

So, we get that the number of guppy fish is increasing by odd numbers.

That is, 3, 6, 11, ........

Now, we have to find an expression for this pattern.

First term is 3.

That is, first term² + 2 = 1² + 2 = 3

Let n be the number of term.

n = 3

So, third term be:

3² + 2 = 9 + 2 = 11

So the expression for modelling the pattern is n² + 2

Now, we have to find the number of guppy fish in month 6.

That is,

n = 6

So,

n² + 2

6² + 2 = 36 + 2 = 38

That is, Charlie can observe 38 guppy fish in month 6.

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Stem-and-leaf plots contain original data values where histograms do not. Therefore, option B is the correct answer.

The "stem" values are listed down, and the "leaf" values go right (or left) from the stem values.

The "stem" is used to group the scores and each "leaf" shows the individual scores within each group.

The advantage of a stem leaf diagram is it gives a concise representation of data. The advantage of a frequency histogram is, that it is visually strong. Histograms are usually preferable to stem and leaf diagrams in large data sets. The disadvantage of a stem leaf diagram is not visual.

Therefore, option B is the correct answer.

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Considering that the points are part of the same linear function, the missing x-value is given by:

a. 1.1.

A linear function is modeled by:

y = mx + b

In which:

Given two points, the slope is given by change in y divided by change in x. In this problem, we are given points (6, 10.2) and (1.5, 3.45), hence the slope is:

m = (10.2 - 3.45)/(6 - 1.5) = 1.5.

Hence:

y = 1.5x + b.

When x = 6, y = 10.2, hence we use it to find b as follows:

10.2 = 1.5(6) + b

9 + b = 10.2

b = 1.2.

Hence the function is:

y = 1.5x + 1.2.

The value of x when y = 2.85 is given by:

y = 1.5x + 1.2.

2.85 = 1.5x + 1.2.

1.5x = 1.65.

x = 1.65/1.5

x = 1.1.

Hence option A is correct.

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Answer:

  C. Dilation by 1/2, rotation 180°

Step-by-step explanation:

You want the sequence of transformations that moves ∆ABC to ∆DEF.

We note that the coordinates of corresponding points are ...

Comparing these, we find that D = (-1/2)·A.

The scale factor of -1/2 is equivalent to a dilation by a factor of 1/2 and reflection across the origin. Reflection across the origin is equivalent to a rotation of 180°.

The sequence of transformations that moves ∆ABC to ∆DEF is ...

  C.  A dilation by a factor of 1/2 centered at the origin, followed by a 180° clockwise rotation about the origin.

__

Additional comment

The direction of rotation is irrelevant when the rotation angle is 180°. When the center of dilation is unspecified, it is assumed to be the origin.

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The unit cost of apples is found to be $5.5 per pound. So the cost of 7.9 pounds of apple will be 43.45.

Here we have to calculate the value of a pound of apple from the given data, and then should multiply the unit value to find the cost of the given weight.

Weight of apple that was purchased = 3.3 lbs.

Cost of 3.3 lbs. of apples = 18.15

Cost of a pound of apple = Cost of apples purchased/ weight of apples purchased

= 18.15/3.3 = 5.5.

So each pound of apple will cost $5.50.

Weight of apple to be purchased = 7.9 lbs.

Cost of the apples = Weight of apples × unit price

                               = 7.9 × 5.50 = 43.45.

So the cost of 7.9 pounds  of apple will be $43.45.

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The values of yn for the given flow rates Q can be calculated using the Manning's equation for a trapezoidal channel with the given parameters n, S, b, and z.

The Manning's equation relates flow rate (Q) in a channel to its parameters: n (Manning's roughness coefficient), S (channel slope), b (bottom width), and z (side slope). The equation is given by Q = (1.49/n) * (b/z) * (A * R^(2/3)) * S^(1/2), where A is the cross-sectional area and R is the hydraulic radius.

To find yn (depth of flow), we rearrange the Manning's equation as A = (Q * n * z) / (1.49 * (b/z) * R^(2/3) * S^(1/2)). We then substitute the given values of n, S, b, and z, and calculate the values of A for each flow rate Q using the equation. Finally, we solve for yn by dividing A by the bottom width b.

Performing these calculations for each given flow rate Q (1070, 1369, 1624, 1829, 2171, and 2331), we can determine the corresponding values of yn for each flow rate using the Manning's equation and the provided parameters.

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Answer: A

Step-by-step explanation: A function means that your x can only have one y but your y can have multiple x's.

Answer:

The first one is the first picture.

The second answer is zero.

I don't know how 2 do the 3rd sry

Step-by-step explanation: