Find the quotient and remainder for

Answer:

x= -7

Step-by-step explanation:

the labeled angles are alternate-interior angles which are congruent

we can solve for 'x' by creating this equation:

x+139 = 132

x = -7

For the given cost function, C(x) = 54√x * x^2 * 274625, let's find the cost, average cost, and marginal cost at the production level of 1450.

1. Cost at the production level 1450:
C(1450) = 54√1450 * 1450^2 * 274625
C(1450) ≈ 328,034,242,150

2. Average cost at the production level 1450:
Average Cost (AC) = C(x) / x
AC(1450) = 328,034,242,150 / 1450
AC(1450) ≈ 226,237,751

3. Marginal cost at the production level 1450:
To find the marginal cost (MC), we first need to find the derivative of the cost function C(x) with respect to x.

Given the complexity of the function, I suggest using a symbolic calculator or a software tool like Wolfram Alpha to find the derivative. Once you have the derivative, plug in x = 1450 to get the marginal cost.

4. Production level that minimizes average cost:
To find the production level that minimizes the average cost, set the derivative of the average cost function (with respect to x) to 0 and solve for x. The resulting x-value will give you the production level that minimizes the average cost.

5. Minimal average cost:
Once you have the production level that minimizes the average cost, plug that value back into the average cost function to find the minimal average cost. Please note that the given cost function appears to be incorrect or incomplete, so these calculations may not be accurate. Make sure to double-check the original cost function before proceeding with these steps.

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The equation of a vertical asymptote to the graph of y = sec(6x - π) is x = π/6. Hence, option a is correct.

The function y = sec(6x - π) has vertical asymptotes at the values of x where the denominator of sec(6x - π) becomes zero. The reciprocal of sec(θ) is cos(θ). Because the cosine function has the values π/2, 3π/2, 5π/2, we will insert such an input that we get 0 in denominator.

6x - π = π/2

Solving for x,

6x = π/2 + π

6x = 3π/2

x = (3π/2) / 6

x = π/6

Therefore, the equation of a vertical asymptote to the graph of y = sec(6x - π) is x = π/6.

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The comparison of the lengths of the sides based on the angles are given

by sine rule.

The lengths of the sides from greatest to least are;

Reasons:

The given parameters are;

∠A = 78°, ∠B = 56°, ∠C = 46°

By sine rule, we have;

\(\displaystyle \frac{AC}{sin(56^{\circ})} = \frac{AB}{sin(46^{\circ})} = \frac{BC}{sin(78^{\circ})}\)

Given that, sin(46°) ≈ 0.719, sin(56°) ≈ 0.829, sin(78°) ≈ 0.978, we have;

sin(78°) > sin(56°) > sin(46°)

Therefore, applying equal proportions of similar ratios, we have;

BC > AC > AB

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BC > AC > AB

hope this helps >:3

Answer:

Solution given:

3(5x+8)

distribute

15x+8*3

15x+24 is a required answer.

Answer:

15x + 24

Step-by-step explanation:

Apply the Distributive Property of Multiplication.  Multiply each of the two terms inside parentheses by 3:

3(5x + 8) = 15x + 24

Answer:

The X and Y intercepts to the equation -3x - 7y = 84 is

x-intercept (s): (−28,0)

y-intercept (s): (0,−12)

Step-by-step explanation:

To find the x-intercept(s), substitute in 0 for y and solve for x

−3x−7⋅0=84

Solve the equation.

x=−28

x-intercept(s) in point form.

x-intercept (s): (−28,0)

To find the y-intercept(s), substitute in 0 for x and solve for y .

−3⋅0−7y=84

Solve the equation.

y=−12

y-intercept(s) in point form.

y-intercept (s): (0,−12)

Hope this helps.

Answer:

1. 5.2 units.

2. 66.63

( Diagonal = √45^2 + 45^2 = √2025+2025 = √4050 = 63.63. )

Step-by-step explanation:

A perpendicular bisector is a line that cuts a line segment connecting two points exactly in half at a 90 degree angle. To find the perpendicular bisector of two points, all you need to do is find their midpoint and negative reciprocal, and plug these answers into the equation for a line in slope-intercept form.

any more help just ask :)

Answer:

\(5(x - 2) = x + 1 \\ 5x - 10 = x + 1 \\ 5x - x = 1 0+ 1 \\ 4x = 11 \\ x = \frac{11}{4} \)

Answer:

2.5 scoops of flour

Step-by-step explanation:

We know

A recipe calls for 2 3/4 cups of flour

2 3/4 = 11/4

Stephanie has 1/4 cup

How many scoops of flour would Stephanie need?

11/4 - 1/4 = 10/4 = 5/2 = 2.5 scoops of flour

So, Stephanie needs 2.5 scoops of flour.

A Type I error is the incorrect rejection of a true null hypothesis. A Type II error is the failure to reject a false null hypothesis. The level of significance (alpha) determines the trade-off between these two types of errors.

The p-value is used to help determine whether or not the null hypothesis is statistically significant, which is used to make decisions based on sample data. If the p-value is less than or equal to the alpha level, it is considered significant, and the null hypothesis is rejected.

If the p-value is greater than the alpha level, it is not significant, and the null hypothesis is not rejected. Large p-values indicate that there is insufficient evidence to reject the null hypothesis. An alpha level is the probability of making a Type I error, which is the likelihood of rejecting the null hypothesis when it is true. The level of alpha is determined by the researcher and is usually set at 0.05 or 0.01.

For a result to be statistically significant, it means that it is unlikely that the result occurred due to chance. The significance level (alpha level) must be lower than the p-value to consider the result significant.

A 95% confidence interval corresponds to a two-sided hypothesis test at an alpha level of 0.05. A 90% confidence interval corresponds to a one-sided hypothesis test at an alpha level of 0.1.A Type I error is the incorrect rejection of a true null hypothesis. A Type II error is the failure to reject a false null hypothesis. The level of significance (alpha) determines the trade-off between these two types of errors.

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Marcia made a more concentration of salt because she dissolved more salt in a lesser volume of water.

The concentration of each solution is calculated as follows;

Concentration = mass/volume

Concentration =  1 /3 = 0.33 kg/L

Concentration = 0.908/3.318 = 0.27 kg/L

Thus, Marcia made a more concentration of salt because she dissolved more salt in a lesser volume of water.

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Marcia made a more concentrated salt solution because the concentration is 0.33 kg/L which is more than the concentration of 0.27 kg/L.

It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.

We have:

For A science experiment, Marcia dissolved 1.0 kilograms of salt in 3.0 liters of water, for a different experiment Bobby dissolved 2.0 pounds of salt and 7.0 pints of water.

For Marcia, the concentration:

The ratio of mass to volume = 1/3 = 0.33 kg/L

For Bobby, the concentration:

The ratio of mass to volume = 2/7 pounds/pint = (2/2.205)/(7/2.11)

= 0.907/3.317 = 0.27 kg/L

Thus, Marcia made a more concentrated salt solution because the concentration is 0.33 kg/L which is more than the concentration of 0.27 kg/L.

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Consider the following nonlinear system: x˙1=x12⋅cos(kπx2)+sin(πx2)ux˙2=(x1+a1+αx2)(x2+a2+βx1)+x12u. Find out the equilibrium points of the system in terms of the variables. There are four equilibrium points of the system in terms of the variables and those are:(0,0), (0.4755,-1.0833), (-0.4755,1.0833), (-0.9755,-1.0223).

Given k=10, a1=5, a2=5, α=1, and β=1.

So, the general linearization of any equilibrium point x∗, u∗ is:Δx1˙=0Δx2˙=−1.025x1Δu=1.0101x1+x2Here, the equilibrium points are as follows: Case 1: (0,0)For this case, the linearized system is:Δx1˙=0Δx2˙=0Δu=0

Here, the A matrix is:At this point, the eigenvalues of the system are given by λ1=0 and λ2=0. So, the system is neutrally stable.

This system is also controllable, output controllable, and observable.Case 2: (0.4755,-1.0833)For this case, the linearized system is:Δx1˙=0Δx2˙=1.1101Δu=0Here, the A matrix is:At this point, the eigenvalues of the system are given by λ1=0 and λ2=-1.0459. So, the system is unstable.

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given: the ages of the employee

to find: median of the ages.

explanation:

median: it is the number in group of ascending or descending numbers

so here first we will find the middle number

for that we are going to cancel one bigger and one smaller number one by one

for example in the given table the first number we have is 22 which is the smallest number and 65 which is the biggest number so we cancel that

now the next smaller and bigger numbers are 23 and 63 respectively that would get cancelled in the similar manner we move on so next we cancel 29 and 62

so after cancelling the numbers in similar manner the number with which we are left is 45

so that means that is the middle term or middle number of the table so that makes it a median

final answer: the median of the ages in this stem and leaf plot is 45.

The basic unit of mass of the ball in the metric system is the gram.

The base units of length (distance), capacity (volume), and weight (mass) in the metric system are the meter, liter, and gram, respectively. We utilize units that are derived from metric units to measure smaller or greater quantities.

Mass is a physical body's total amount of matter. Inertia, or the body's resistance to acceleration when a net force is applied, is also measured by this term. The strength of an object's gravitational pull to other bodies is also influenced by its mass.

Therefore, the basic unit of mass of the ball in the metric system is the gram.

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The amount of rain the city received in July is r = 2.5 inches

Given data ,

City received 3/4 inch of rain on July 31

Now , it represents 3/10 of the total amount of rain this to received in July

So , the equation is represented as A

Now , the value of A is

( 3/10 )r = 3/4

Multiply by 10 on both sides , we get

3r = 30/4

Divide by 3 on both sides , we get

r = 30/12

r = 2.5 inches

Hence , the city received 2.5 inches of rain

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Answer:

y = -x - 1

Step-by-step explanation:

-2y=-x+2

y—x-1

Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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Answer:

Interest = Principal x rate x time

Principal = 5000     rate = 4.5%                      t= 10 years

Amount =P(1 + r/n)nt

Amount = 5000(1 +.045/10)10

          A = 5000( 1 + .0045) 10

          A = 5000( 1.0045) 10    

Total Amount money in 2020 = Php. 50,225

The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

According to the statement

we have to find that the number of ways are there to select the applicants who will be hired.

So, For this purpose, we know that the

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Here we use the combination.

And from the given information:

20 applicants from a pool of 90 applications will be hired.

And according to this the combination becomes:

\(C_{20} ^{90}\)

then solve it

\(C_{20} ^{90} = \frac{90!}{20! (70!)}\)

\(C_{20} ^{90} = \frac{90*89*88*87*86*85*84*83*82!}{20*19*18*17*16*15*14!}\)

Then after solve it

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82!}{19*14!}\)

Now open another factorial

\(C_{20} ^{90} = \frac{89*11*87*43*14*83*82*81*80*79*78*77*76*75*74*73*72*71}{19*14*13*12*11*10*9*8*7*6*5*4*3*2*1}\)

Now solve this then

\(C_{20} ^{90} = {89*11*87*43*83*82*79*15*74*73*71}\).

So, The ways are the \(C_{20} ^{90}\) which are we  there to select the applicants who will be hired with the help of combination.

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Answer:  8832 divided by 42 =  210 R 10

Answer and explanation:

A function is given f(x)= y where x is independent variable and y is dependent variable. Y is a function of x therefore y takes up a value because x has a certain value, y is dependent on x values.

Therefore if government office y is a function of minister's name x then a government office would hold a particular value, example be named after the minister's name because it is dependent on the minister's name x

Answer:

D.) You can show your name printed on the team roster.Step-by-step explanation:

By showing your name printed on the team roster we can informally prove to your friend that you are a member of the baseball team.

So by showing your name printed on the team roster we can informally prove to your friend that you are a member of the baseball team.

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The solutions to the equation are x= -9 and x = 6

From the information given, we have that;

|x2 + 9x| = 6x + 54

To solve the quadratic equation, collect the like terms, we have;

x² + 9x - 6x = 54

subtract the terms

x² + 3x = 54

Put in standard form

x² + 3x - 54 = 0

Find the pair factors of -54 that add up to give 3 and substitute the values

x² + 9x - 6x - 54 = 0

group in pairs

(x² + 9x) - (6x - 54) = 0

factorize the expressions

x(x + 9) - 6(x + 9) = 0

Then, we have;

x- 6 = 0

x = 6

x + 9 = 0

x = -9

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Locating the smallest pie slice at 12 o'clock decreases the effectiveness of pie charts because it distorts the visual perception of relative proportions and makes accurate comparisons between slices more challenging.

Pie charts are graphical representations used to display data as a circular "pie" divided into slices, with each slice representing a category or proportion of a whole. The effectiveness of a pie chart lies in its ability to accurately convey the relative sizes of the different categories.

By locating the smallest pie slice at 12 o'clock, we introduce a visual distortion that can mislead viewers. When the smallest slice is at the top, it appears larger than it actually is due to the psychological effect of gravity and our tendency to perceive objects at the top as larger. This can lead to incorrect interpretations of the data and misrepresentation of the proportions.

To ensure the effectiveness of pie charts, it is generally recommended to order the slices based on their size, with the largest slice starting at 12 o'clock and proceeding clockwise in decreasing order. This allows viewers to easily compare the sizes of the slices and accurately understand the proportions they represent.

Therefore, locating the smallest pie slice at 12 o'clock decreases the effectiveness of pie charts by distorting the perception of relative proportions and making accurate comparisons more challenging.

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There are 3 fourths in 3/4.When you divide 3 by 4, you get 0.75, which is equivalent to three fourths.

1. To find how many fourths are in a given fraction, you need to divide the numerator by the denominator.
2. In this case, the numerator is 3 and the denominator is 4. So, you divide 3 by 4.
3. Dividing 3 by 4 gives you 0.75, which is equivalent to three fourths.

To find how many fourths are in 3/4, you divide the numerator (3) by the denominator (4).

This can be done by converting the fraction to a decimal.

When you divide 3 by 4, you get 0.75, which is equivalent to three fourths.

Another way to see this is by understanding that the fraction 3/4 means you have 3 parts out of 4 equal parts.

So, you have three fourths. In fraction form, this is written as 3/4.

Therefore, the answer is that there are 3 fourths in 3/4.

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