For the function y = xi + 7 at (4, 1), find the following. (Give exact answers. Do not round.) x 19 (a) the slope of the tangent line (b) the instantaneous rate of change of the function

To find the mean salary for the 50 employees of the new company, we need to combine the salaries of all the workers from both companies and divide by the total number of employees. So, the mean salary for the 50 employees of the merged company is $90 per week.

The mean salary for the 20 workers in Company A is $93 per week, and for the 30 workers in Company B, it's $88 per week. To find the mean salary for the 50 employees of the merged company, you'll need to calculate the total combined salary for all workers and divide it by the total number of employees.

finding the total salary of the 20 workers in company A. We know that the mean salary is $93 per week, so we can multiply that by the number of workers to get the total salary:

Total salary in company A = 20 x $93 = $1860

Next, we'll do the same thing for company B. The mean salary is $88 per week, and there are 30 workers:

Total salary in company B = 30 x $88 = $2640

Now we can add the two total salaries together to get the total salary for all 50 employees:

Total salary for all 50 employees = $1860 + $2640 = $4500

Finally, we can divide the total salary by the total number of employees (50) to find the mean salary for the new company:

Mean salary for the new company = $4500 / 50 = $90 per week

Therefore, the mean salary for the 50 employees of the new company is $90 per week.

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The solutions to the quadratic equation -2p² - 5p + 1 = 7p² + p are p₁ = (-1 + √2) / 3 and p₂ = (-1 - √2) / 3. To solve the quadratic equation -2p² - 5p + 1 = 7p² + p, we can rearrange the equation to bring all the terms to one side, creating a standard quadratic form: 0 = 7p² + p + 2p² + 5p - 1.

Combining like terms, we get 0 = 9p² + 6p - 1.

Now, we can apply the quadratic formula, which states that for an equation in the form ax² + bx + c = 0, the solutions for x are given by x = (-b ± √(b² - 4ac)) / (2a).

For our equation, a = 9, b = 6, and c = -1. Plugging these values into the quadratic formula, we have:

p = (-6 ± √(6² - 4[tex]\times[/tex] 9 [tex]\times[/tex] -1)) / (2 [tex]\times[/tex] 9)

Simplifying further:

p = (-6 ± √(36 + 36)) / 18

p = (-6 ± √72) / 18

Since the value under the square root (√72) can be simplified as √(36 [tex]\times[/tex] 2) = 6√2, we have:

p = (-6 ± 6√2) / 18

Now, we can simplify and express the two solutions:

p₁ = (-6 + 6√2) / 18

p₂ = (-6 - 6√2) / 18

To further simplify, we can divide both the numerator and denominator by 6:

p₁ = (-1 + √2) / 3

p₂ = (-1 - √2) / 3

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The system of linear equations is not necessarily inconsistent just because its 3x5 augmented matrix has a non-pivot column in the fifth position.

It is possible that the system has infinitely many solutions. However, it is also possible that the system has no solutions. The key factor that determines whether the system is consistent or not is whether the corresponding coefficient matrix has full row rank (i.e., has three pivot rows).

If the coefficient matrix has full row rank, then the system is consistent, regardless of the structure of the augmented matrix. If the coefficient matrix does not have full row rank, then the system is inconsistent.

If the system is consistent, we can use row operations to reduce the augmented matrix to row echelon form or reduced row echelon form, and then use back substitution to find the solutions.

If the system is inconsistent, we can use row operations to derive a contradiction (e.g., a row of the form [0 0 ... 0 b], where b is a nonzero constant), which means that the system has no solutions.

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Answer:

Thus, the number is equal to x =16 the Answer 16 Basically

Answer:

write a story illustrate the saying that a lazy man goes to bed hungry

Answer:  [tex]\frac{-3}{10}[/tex]

Given:

   (b + d) - a

Substitute known values:

   ([tex]\frac{3}{5}[/tex] + - [tex]\frac{1}{5}[/tex]) - [tex]\frac{7}{10}[/tex]

Addition and subtraction becomes subtraction:

   ([tex]\frac{3}{5}[/tex] - [tex]\frac{1}{5}[/tex]) - [tex]\frac{7}{10}[/tex]

Subtract:

   [tex]\frac{2}{5}[/tex] - [tex]\frac{7}{10}[/tex]

Common denominators:

   [tex]\frac{4}{10}[/tex] - [tex]\frac{7}{10}[/tex]

Subtract:

   [tex]\frac{-3}{10}[/tex]

The kilograms of apple she sell at the farmer's market is A = 2.175 kg

Given data ,

To find the weight of apples sold by the farmer, we can subtract the weight of pears from the total weight

Given that 3/4 of the weight is pears, we can calculate the weight of pears by multiplying the total weight by 3/4:

Weight of pears = (3/4) x 8.7 kilograms = 6.525 kilograms

Since the total weight is 8.7 kilograms, we can subtract the weight of pears to find the weight of apples

On simplifying the equation , we get

Weight of apples = Total weight - Weight of pears

A = 8.7 kilograms - 6.525 kilograms = 2.175 kilograms

Hence , the farmer sold approximately 2.175 kilograms of apples at the farmer's market

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The quadratic function for the graph in this problem is given as follows:

y = 2(x + 1)(x - 2).

The roots for the quadratic function in this problem are given as follows:

Hence the linear factors of the function are given as follows:

Considering the factor theorem, the function is given by the product of it's linear factors and the leading coefficient a, hence:

y = a(x + 1)(x - 2)

When x = 0, y = -4, hence the leading coefficient a is obtained as follows:

-2a = -4

2a = 4

a = 2.

Hence the function is:

y = 2(x + 1)(x - 2).

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The measure of arc BC in a circle where the two chords, chord AD and chord AC are equal in measure, is 146°. Therefore, the correct option is option C.

The measure of arc made by parallel chord in a circle are equal in measure.

arc BC=8x-46°                

arc AD=5x+26°                

arc BC=arc AD

8x-46°=5x+26°

x=24°

arc BC=8x-46°

arc BC=8(24°)-46°

arc BC=192°-46°

arc BC=146°

Therefore, the correct option is option C.

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Your question is incomplete but most probably your full question was,  

Check the picture below.

[tex]\tan(23^o )=\cfrac{\stackrel{opposite}{h}}{\underset{adjacent}{35}} \implies 35\tan(23^o)=h \implies 15\approx h\\[/tex]

Make sure your calculator is in Degree mode.

P(X < 2) ≈ 0.1338 and P(X ≥ 2) ≈ 0.8662.

To find the probability P(X < 2), we need to calculate the probability of having fewer than 2 successes in 9 independent trials. This includes the cases where X is 0 or 1.

To find the probabilities P(X < 2) and P(X ≥ 2) in this scenario, we'll use the binomial distribution formula.

The binomial distribution formula is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

P(X = k) is the probability of getting exactly k successes,

n is the number of trials,

k is the number of successes,

p is the probability of success in a single trial, and

C(n, k) is the number of combinations of n items taken k at a time.

Given that n = 9 and p = 2/5, we can calculate the probabilities as follows:

P(X < 2):

P(X < 2) = P(X = 0) + P(X = 1)

P(X = 0):

P(X = 0) = C(9, 0) * (2/5)^0 * (1 - 2/5)^(9 - 0)

Using the combination formula C(9, 0) = 1:

P(X = 0) = 1 * 1 * (3/5)^9

P(X = 1):

P(X = 1) = C(9, 1) * (2/5)^1 * (1 - 2/5)^(9 - 1)

Using the combination formula C(9, 1) = 9:

P(X = 1) = 9 * (2/5) * (3/5)^8

Now we can calculate P(X < 2) by adding P(X = 0) and P(X = 1).

P(X ≥ 2):

P(X ≥ 2) = 1 - P(X < 2)

After calculating P(X < 2), we can subtract it from 1 to find P(X ≥ 2).

Let's perform the calculations:

P(X = 0) = 1 * 1 * (3/5)^9 = 0.01917808 (rounded to 8 decimal places)

P(X = 1) = 9 * (2/5) * (3/5)^8 = 0.11462304 (rounded to 8 decimal places)

P(X < 2) = 0.01917808 + 0.11462304 = 0.13380112 (rounded to 8 decimal places)

P(X ≥ 2) = 1 - P(X < 2) = 1 - 0.13380112 = 0.86619888 (rounded to 8 decimal places)

Therefore, P(X < 2) ≈ 0.1338 and P(X ≥ 2) ≈ 0.8662.

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The exact length of the polar curve described by r=4e^(-theta) on the interval 7/6pi ≤ theta ≤ 5pi is approximately 36.60 units.

To find the length of the polar curve, we can use the formula: L = ∫(a to b) sqrt[r^2 + (dr/d theta)^2] d theta. Applying this formula to the given polar curve, we get L = ∫(7/6pi to 5pi) sqrt[(4e^(-theta))^2 + (-4e^(-theta))^2] d theta. Simplifying this expression, we get L = 8∫(7/6pi to 5pi) e^(-theta) dtheta. Evaluating this integral, we get L = 8[e^(-7/6pi) - e^(-5pi)] ≈ 36.60 units.

Therefore, the exact length of the polar curve described by r=4e^(-theta) on the interval 7/6pi ≤ theta ≤ 5pi is approximately 36.60 units. This formula can be used to find the length of any polar curve, given its equation and the interval in which it is being evaluated. It is important to note that the formula for the length of a polar curve is derived using calculus, specifically the arc length formula. The arc length formula is used to find the length of a curve in the Cartesian coordinate system, while the formula for the length of a polar curve is used to find the length of a curve in the polar coordinate system.

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The simplified expression using a piecewise function:

f(x) = { x + 18, if x ≥ -18

{-x - 18, if x < -18

To simplify the expression |x - (-18)| without using the absolute value symbol, we need to consider two cases: when the expression inside the absolute value is positive (or equal to zero) and when it is negative.

When x - (-18) ≥ 0:

x - (-18) = x + 18, so in this case, the expression simplifies to x + 18.

When x - (-18) < 0:

Negate expression: -(x + 18) = -x - 18.

Now, we need to write the simplified expression using a piecewise function:

f(x) = { x + 18, if x ≥ -18

{-x - 18, if x < -18

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The t-value such that the area in the right tail is 0.15 with 13 degrees of freedom is approximately 1.350.

To find the t-value such that the area in the right tail is 0.15 with 13 degrees of freedom, we can use a t-table or a calculator with a t-distribution function.

Using a t-table:

Look for the row that corresponds to 13 degrees of freedom.

Look for the column that contains the area 0.15.

The intersection of the row and column is the t-value we are looking for.

Using a calculator:

Use the t-distribution function with 13 degrees of freedom.

Set the upper limit of integration to a large number, such as 100, to calculate the area in the right tail.

Find the t-value such that the area to the right of it is 0.15.

Using either method, we find that the t-value such that the area in the right tail is 0.15 with 13 degrees of freedom is approximately 1.350.

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The percentage of data that falls within three standard deviations of the mean is 99.7%.

The percentage of data that falls within three standard deviations of the mean is determined as follows;

one standard deviation below the mean = 34%

one standard deviation above the mean = 34%

So one standard deviation of the mean = 34% + 34% = 68%

Based on this information, we can conclude the following for a  normal distribution:

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The complete question is below:

For a normal distribution (shown in the diagram), what percentage of data falls within three standard deviations of the mean?

According to the model, an additional 10 minutes waiting in line would cause a customer to lower his or her rating by 1.

To determine the additional minutes waiting in line that would cause a customer to lower their rating by 1, we set s = 4 (since 5 - 1 = 4) in the equation and solve for m:

Given: s = -0.10m + 5

where:

s = the numerical rating given by the customer

m = the number of minutes the customer spent waiting in line.

So, 4 = -0.10m + 5

-0.10m = -1

m = 10

Therefore, based on the model, an additional 10 minutes waiting in line would cause a customer to lower their rating by 1.

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So, at 0 K, the value of the partition function is equal to the number of energy states plus one, which is 1.

The partition function (Z) is a concept used in statistical mechanics to describe the distribution of particles among different energy states. It is a sum of exponential terms, each corresponding to a different energy state. At absolute zero temperature (0 K), all particles are in their lowest energy state, and there is only one possible state with zero energy.

The partition function at 0 K is given by:

Z = Σ exp(-Ei/kT)

where Ei represents the energy of the ith state, k is the Boltzmann constant, and T is the temperature.

Since all particles are in the lowest energy state (E = 0), the term exp(-Ei/kT) becomes exp(0) = 1. Therefore, the partition function simplifies to:

Z = Σ (for i = 0 to N) 1 = N + 1

where N represents the total number of energy states.

At 0 Kelvin (absolute zero), the value of the partition function should be 1.

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The curve given by the equation y = x(t^2/t^2 + t + 9) dt on the interval [0,∞) is concave downward on the interval [3, ∞).

To find where the curve is concave downward, we need to take the second derivative of the function and check where it is negative. Taking the second derivative of the given function with respect to x, we get:

y'' = 2t^2(t^2 + 18)/[(t^2 + t + 9)^3]

To find where y'' is negative, we need to solve the inequality 2t^2(t^2 + 18)/[(t^2 + t + 9)^3] < 0. Factoring the numerator, we get:

2t^2(t^2 + 18) = 2t^2(t+√18)(t-√18)

This is negative when t is between -√18 and 0, and also when t is between 0 and √18. However, we need to consider the interval [0,∞) only, which means we should take the solution from the interval [0, √18]. Therefore, the curve is concave downward on the interval [3, ∞).

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Rosa has a certain amount of dough, and each medium loaf of bread requires a fraction of a pound. To determine how many medium loaves of bread Rosa can make, we divide the total amount of dough by the fraction of a pound needed for one loaf. So the answer is 5.

Explanation: If we let "x" represent the total amount of dough that Rosa has in pounds, and "y" represent the fraction of a pound needed for one medium loaf of bread, we can set up a simple equation to solve for the number of loaves, "n":

x / y = n

Given that Rosa has a certain amount of dough, we need to determine the value of "y" (the fraction of a pound needed for one loaf) in order to calculate "n" (the number of loaves). Since the exact fraction is not provided in the question, we would need additional information to solve for "y" and compute the exact number of medium loaves Rosa can make.

For example, if it is given that Rosa uses 1/4 pound of dough for one medium loaf, we can substitute this value into the equation:

x / (1/4) = n

Simplifying the equation, we would multiply both sides by 1/4:

4x = n

(15/4)/(3/4) = 5

So, Rosa would be able to make 4 times the amount of dough in medium loaves of bread, which is 5.

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Complete Question: Rosa has 3 3/4 pounds of dough. She uses 3/4 of a pound for one medium loaf of bread. How many medium loaves of bread could be made from Rosa's dough?

The algorithm that involves getting the next unsorted number and doing comparisons to determine its position within a sorted sublist is called the Insertion Sort algorithm.

The Insertion Sort algorithm works by maintaining a sorted sublist and repeatedly inserting the next unsorted element into the correct position within the sorted sublist.

Starting with the second element, it compares the element with the previous elements in the sorted sublist and shifts them to the right if they are greater, until finding the correct position to insert the element.

This process is repeated until all elements are sorted. Insertion Sort has a time complexity of O(n^2) in the worst case, making it efficient for small lists or partially sorted data.

Its main advantage is that it performs well for nearly sorted or small input sizes. The key idea of this algorithm is the comparison-based approach to find the correct position for each unsorted element within the sorted sublist.

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The box plot that represents the data is the third option.

A box plot is a graph that is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers.

The first whisker represents the minimum number and the end of the second whisker represents the maximum number. On the box, the first line to the left represents the lower quartile. The next line on the box represents the median. The third line on the box represents the upper quartile.

The numbers arranged in ascending order : 64, 68, 68, 74, 76, 82, 84, 86, 90, 90, 92,  94,

The minimum number is 64 and the maximum number is 94.

First quartile = 1/4(n + 1)

1/4 x (12 + 1) = 3.25 number = 71

Third quartile =  3/4(n + 1)

3/4 x (12 + 1) = 9.75 number = 90

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To solve the given initial-value problem, we can separate the variables and integrate both sides. The final answer is Therefore, the solution to the initial-value problem is y = [tex]\frac{-1}{(-14t - 1)}[/tex], where y(0) = 1.

Given: y' = [tex]-(14)y^2\\[/tex]

Initial condition: y(0) = 1

Separating variables:

[tex]\frac{Dy}{y^2 }[/tex]= -14 dt

Integrating both sides:

∫([tex]\frac{1}{y^2}[/tex]) dy = ∫-14 dt

Integrating the left side:

[tex]\frac{-1}{y}[/tex]= -14t + C1

Solving for y:

y = [tex]\frac{-1}{-14t + C1}[/tex]

Using the initial condition y(0) = 1:

1 = [tex]\frac{-1}{C1}[/tex]

C1 = -1

Substituting the value of C1 back into the solution:

y = [tex]\frac{-1}{(-14t - 1)}[/tex]

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The statement is a suggestion or guideline for how to assign subjective probabilities.

Subjective probabilities are probabilities that are based on personal beliefs or judgments rather than on empirical evidence. Experience and intuition can be used to make informed guesses about the likelihood of an event occurring.

Available data can also be used to inform subjective probabilities, such as historical data or expert opinions. However, subjective probabilities may not always be reliable as they can be influenced by personal biases or limited information.

Therefore, it is important to use critical thinking and consider multiple sources of information when assigning subjective probabilities.

Additionally, subjective probabilities may be useful in situations where empirical data is not available or difficult to obtain, but they should be used with caution and always be subject to reassessment as new information becomes available.

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Thus, a one-way ANOVA test is robust if the data meets the above requirements. It is a powerful statistical tool that can help analyze differences between means of multiple groups.

A one-way ANOVA is a statistical test used to analyze the differences between means of two or more groups. There are certain requirements that need to be met before performing a one-way ANOVA.

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To perform a one-way ANOVA, the observations need to be independent, the data should be normally distributed, and the variances should be equal. However, the test is robust to deviations from these assumptions, particularly if the group sizes are equal.

To perform a one-way ANOVA (Analysis of Variance), there are several requirements you should meet:

The one-way ANOVA is considered robust to deviations from normality and homogeneity of variance, especially when the group sizes are equal. However, if smokes are very unequal or if there are extreme outliers, it might not be as robust.

If these assumptions are not met, a non-parametric alternative like the Kruskal-Wallis test might be a better choice.

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The variation in assembly times within each assembly method the treatment sum of squares is 2, and the degrees of freedom (df2) for the error sum of squares is 12.

To determine the degrees of freedom (df1) for the treatment sum of squares, we need to consider the number of groups (assembly methods) being compared.

In this case, there are three different ways of assembling the part. Since there are three groups, the degrees of freedom for the treatment sum of squares is calculated as:

df1 = number of groups - 1

= 3 - 1

= 2

To calculate the degrees of freedom (df2) for the error sum of squares, we need to consider the total number of observations and the number of groups.

In this case, there are 5 people assigned to each assembly method, and there are 3 assembly methods in total. so the total number of observations is 5 * 3 = 15.

df2 = total number of observations - number of groups

= 15 - 3

= 12

Therefore, the degrees of freedom (df1) for the treatment sum of squares is 2, and the degrees of freedom (df2) for the error sum of squares is 12.

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The experimental probability of rolling a 5 is 4/36, which simplifies to 1/9, or approximately 0.11.

We have,

The experimental probability of an event happening is the ratio of the number of times the event occurred to the total number of trials.

In this case,

The event is rolling a 5 and the total number of trials is the sum of the frequencies, which is 8 + 3 + 9 + 6 + 4 + 6 = 36.

The frequency of rolling a 5 is 4.

Therefore,

The experimental probability of rolling a 5 is 4/36, which simplifies to 1/9, or approximately 0.11.

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Answer:

6

Step-by-step explanation:

£5 - £1.45 = £3.55

£3.55 ÷ 0.53p = 6.698

since you cant have .6 of a pencil, the maximum number of pencils Rio can buy is 6

Answer:

6

Step-by-step explanation:

call £5 500p.

£1.45 =145p

500 - 145 = 355.

355/53 = 6.7

so the maximum number of pencils he can buy is 6.

you can check this by inputting those numbers.

£1.45 + 6 X £0.53

= £1.45 + £(3.18)

=£4.63

Rio still has 37p left. not enough for another pencil

Answer:

$200

Step-by-step explanation:

To find the original price of an item that costs $217 with an 8.5% sales tax, you would first divide the total cost by 1 plus the tax rate (as the tax is calculated as a percentage of the original price plus tax). This would give you the price without the sales tax. So, $217 divided by 1.085 equals approximately $200. The original price before the sales tax was added would be $200.

The answer is option D, which is 1 and 8.To find the values of x where f has a removable discontinuity, we need to check if there are any values of x that make the denominator of f(x) equal to zero.

If this occurs, the function will have a vertical asymptote at that point, and if the limit of the function as x approaches that point exists, then the function has a removable discontinuity at that point.

In this case, we can see that the denominator of f(x) is (2x-1)(4x+8), which equals zero at x=1/2 and x=-2. However, we need to check if these values of x result in a removable discontinuity. At x=1/2, the function f(x) is undefined, and the limit as x approaches 1/2 is -1/3. Therefore, f(x) has a removable discontinuity at x=1/2. At x=-2, the function f(x) is also undefined, but the limit as x approaches -2 does not exist. Therefore, f(x) does not have a removable discontinuity at x=-2. Thus, the answer is option D, which includes the value 1 where f has a removable discontinuity, and the value 8 where f does not have a removable discontinuity.

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