Find the critical point of the given function and then determine whether it is a local maximum, local minimum, or saddle point. (Order your answers from smallest to largest xx, then from smallest to largest yy.)f(x,y)=(x−y)(xy−9)

Answer:

n=20

Sum of age of men = 50n

when 2 left,

(50n-55-63)/n-2=50-1

50n-55-63=49n-98

50n-55=49n-35

50n-49n=-35+55

n=20

The result of each trigonometric functions are:

a) sin X = 7√149 / 149

b) sin Z = 10√149 / 149

c) cos X = 10√149 / 149

d) cos Z = 7√149 / 149

In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse, and the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Using this trigonometric functions, we can calculate sin X, sin Z, cos X, and cos Z as follows

sin X = YZ / XZ = 7 / √149

cos X = XY / XZ = 10 / √149

sin Z = XY / XZ = 10 / √149

cos Z = YZ / XZ = 7 / √149

To simplify these fractions, we can rationalize the denominator by multiplying the numerator and denominator by √149:

sin X = 7√149 / 149

cos X = 10√149 / 149

sin Z = 10√149 / 149

cos Z = 7√149 / 149

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The given question is incomplete, the complete question is:

Find sin X, sin Z, cos X, and cos Z. Write each answer as a simplified fraction.

Given that the graph is falling downward, it can be seen that the graph is negative.

Before the tank's water level starts to drop, there are 120 gallons there.

Finding the slope of the graph will give us the amount of water that was lost every minute.

Slope is equal to a climb or a run.

increase = water in gallons

run equals time in minutes.

Slope equals y2 - y1 / x2 - x1

Two points will be chosen from the graph.

( 30, 80) and (60, 40) (60, 40)

Let x1=30, y1=80, x2=60, and y2=40.

Slope = 40 - 80 / 60 - 30

Slope = -40 / 30

Slope = -4/3

The result in the negative represents a loss in gallons of water per minute.

According to the line of best fit, a gallon of water was lost every minute or so.

The graph indicates that the tank will be empty in around 60 minutes.

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Answer:

To determine which test Elena got a higher ratio of correctly spelled words to total words, we need to calculate the ratio of correctly spelled words to total words for each test and compare them.

For last week's test, the ratio of correctly spelled words to total words is:

16/20 = 0.8

For this week's test, the ratio of correctly spelled words to total words is:

13/15 ≈ 0.867

Since 0.867 is greater than 0.8, Elena got a higher ratio of correctly spelled words to total words on this week's test. Therefore, the new studying method appears to be working better for Elena. However, it is important to note that a single comparison is not sufficient to draw a definitive conclusion about the effectiveness of the studying method, and it would be beneficial for Elena to continue tracking her performance over a longer period of time.

Answer:

11 weeks

Step-by-step explanation:

42 + 15 * x = 207

42 + 15x = 207

15x = 207 - 42

15x = 165

x = 11

Hope this helps <3

Answer:

7/12 pizzas have been eaten

Step-by-step explanation:

3 + 4= 7

7/12

7-12=5

5 pizzas left

Answer:

(3480 - 600)/2 = 1440cm

Step-by-step explanation:

So the correct answer is option A) m=5, LO=14, NO-12 for the indicated variables and measures for the figure below.

A triangle is a closed two-dimensional geometric figure with three straight sides and three angles. It is one of the basic shapes in geometry and can be classified based on the length of its sides and the measures of its angles. The sum of the interior angles of a triangle is always 180 degrees, and the length of each side is less than the sum of the lengths of the other two sides. Triangles have many properties and are used in various mathematical and real-world applications, including trigonometry, geometry, and engineering.

Here,

Since all the angles are equal, we can set up the following proportion:

LO/NO = 7/2

Multiplying both sides by NO, we get:

LO = (7/2)NO

We can also use the fact that the angles are equal to set up an equation involving m:

m + (1/2)LO + (1/2)NO = 180

Substituting LO = (7/2)NO, we get:

m + (7/4)NO = 180

Now we can substitute the given values for LO and NO:

m + (7/4)(14) = 180

m + 49 = 180

m = 131

Therefore, the answer is: m = 131, LO = 49, NO = 14

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In mathematics, a logarithm is a mathematical operation that determines how many times a given number (known as the base) must be multiplied by itself to produce another given number.

Logarithms are used to simplify complex calculations involving exponents and to convert between exponential and logarithmic expressions.

The logarithm of a number x to a given base b is represented as logb(x). For example, log10(100) = 2 because 10 multiplied by itself twice equals 100.

Logarithms have a wide range of applications in various fields, including mathematics, physics, engineering, finance, and computer science. They are particularly useful in scientific calculations involving large numbers, where working with exponents can become cumbersome. Logarithms are also used in the study of exponential growth and decay, as well as in the analysis of data sets with a wide range of values.

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Answer: To plot and connect the points, you can use a graphing software or a graphing calculator. Once the points are plotted, you can determine if the graph is linear or exponential by looking at the slope of the line. If the slope is increasing or decreasing exponentially, the graph is exponential. If the slope is constant, the graph is linear.

Step-by-step explanation:

They would each need to sell 5 bicycles to make the same amount of money and if they both sell 5 bicycles, they would each make $500.

What do you mean by finding the break-even point ?

The key concept used here is the idea of finding the break-even point between two scenarios. In this case, the break-even point is the number of bicycles that Jim and Tom each need to sell in order to make the same amount of money. This is found by setting their total earnings equal to each other and solving for the number of bicycles. Once the break-even point is found, the total earnings for that number of bicycles can be calculated by plugging it back into the original equations. This concept is commonly used in business and finance to determine the minimum level of sales needed to cover costs and make a profit.

Calculating the number of bicycle and money :

To make the same amount of money, Jim and Tom would have to each sell the same number of bicycles, let's call it "b".

So Jim would make a total of:

250 + 50b dollars

Tom would make a total of:

400 + 20b dollars

To find the value of "b" where they both make the same amount of money, we can set the two expressions equal to each other and solve for "b":

250 + 50b = 400 + 20b

30b = 150

b = 5

Therefore, they would each need to sell 5 bicycles to make the same amount of money.

To find out how much they would make, we can substitute "b=5" into either of the expressions above:

Jim:

250 + 50(5) = $500

Tom:

400 + 20(5) = $500

Therefore, if they both sell 5 bicycles, they would each make $500.

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[tex]x=\textit{Liters of solution at 20\%}\\\\ ~~~~~~ 20\%~of~x\implies \cfrac{20}{100}(x)\implies 0.2 (x) \\\\\\ y=\textit{Liters of solution at 50\%}\\\\ ~~~~~~ 50\%~of~y\implies \cfrac{50}{100}(y)\implies 0.5 (y) \\\\\\ \textit{600 Liters of solution at 21\%}\\\\ ~~~~~~ 21\%~of~600\implies \cfrac{21}{100}(600)\implies 126 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{array}{lcccl} &\stackrel{Liters}{quantity}&\stackrel{\textit{\% of Liters that is}}{\textit{acid only}}&\stackrel{\textit{Liters of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&x&0.2&0.2x\\ \textit{2nd Sol'n}&y&0.5&0.5y\\ \cline{2-4}&\\ mixture&600&0.21&126 \end{array}~\hfill \begin{cases} x + y = 600\\\\ 0.2x+0.5y=126 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{x+y=600}\implies x=600-y \\\\\\ \stackrel{\textit{substituting on the 2nd equation}}{0.2(600-y)+0.5y=126}\implies 120-0.2y+0.5y=126 \\\\\\ 120+0.3y=126\implies 0.3y=6\implies y=\cfrac{6}{0.3}\implies \boxed{y=20} \\\\\\ \stackrel{\textit{since we know that}}{x=600-y}\implies \boxed{x=580}[/tex]

Probability that X = 5:Since, Joe selects only 4 bags of lettuce. X can't be 5.P(X=5) = 0Hence, the probability that X = 0 is 0.3164 and the probability that X = 5 is 0.

The given problem can be solved using the concept of binomial distribution.

In the given question, there are 48 bags of lettuce out of which 12 bags are contaminated with listeria.

Joe selects 4 bags of lettuce. X is the random variable which represents the number of contaminated bags of lettuce selected by Joe. X can take values from 0 to 4. (as Joe selects only 4 bags).

Part A)Number of ways to select 4 bags of lettuce out of 48:This can be solved using the concept of combinations. The formula to calculate the number of combinations is[tex]:nCr = n! / r!(n-r)![/tex]Here, n = 48 and r = 4.

Number of ways = 48C4 = 194,580

Part B)Probability that X = 0:This can be calculated using the formula for the binomial distribution :

[tex]P(X = r) = nCr * p^r * q^(n-r)[/tex]

Here, p = probability of selecting contaminated bag = 12/48 = 0.25q = probability of selecting non-contaminated bag = 1-0.25 = 0.75Also, n = 4 and r = [tex]0P(X=0) = 4C0 * 0.25^0 * 0.75^4= 0.3164[/tex]

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Answer:

y = 3x - 3

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 )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (3, 6 ) and (x₂, y₂ ) = (- 1, - 6 )

m = [tex]\frac{-6-6}{-1-3}[/tex] = [tex]\frac{-12}{-4}[/tex] = 3 , then

y = 3x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (3, 6 )

6 = 3(3) + c = 9 + c ( subtract 9 from both sides )

- 3 = c

y = 3x - 3 ← equation of line

Answer:

Option B

Step-by-step explanation:

Using Proportionality, we get

Let x be the quantity of water in bathtub. Y be time it be removed.

By formula, x2/y2= k = x1/y1

x/y = 5/1(x1=5, y1= 1)[Given]

5x2= 35.5

35.5 = 5y2

=> y = 35.5/5 = 7.1 minutes

The expression represents the difference of 7 and twice the product of a and b is 7 - 2ab

Let's break down the given problem step by step. First, we need to find the product of a and b, which is done by multiplying the two variables together using the multiplication symbol (*). Then, we need to multiply this result by 2, which is done by placing the entire product inside parentheses and then multiplying it by 2 using the multiplication symbol again.

Once we have found twice the product of a and b, we need to subtract it from 7. This can be done using the subtraction symbol (-), which we place between 7 and the expression we just found.

Putting it all together, the expression we get is:

7 - 2ab

where a and b are the two variables we were given.

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The solutions for the systems of inequalities are:

a) (0, -100), (0, -150), (0, -1000)

b)  (0, 50), (0, 55) , (0, 1,204).

When we have a system of inequalities, a solution is a point that solves both ienqualities at the same time.

The first one is:

y ≤ x - 8

y < -3x - 9

Here y must be smaller than x, then we can define x like x = 0, and really small values for y, like y = -100, replacing that we will get:

-100  ≤ 0 - 8 = -8

-100 < - 3*0 - 9 = -9

Both of these are true, so (0, -100) is a solution, and trivially, (0, -150) and (0, -1000) are other two solutions.

For the second system:

y > 5x + 1

y > 3

Let's do the same thing, x = 0 and y gets really large values, like y = 50

50 > 5*0 + 1 = 1  this is true.

50 > 3   this is true.

so (0, 50) is a solution, and also are (0, 55) and (0, 1,204).

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When performing a hypothesis test based on a 95% confidence level, the chances of making a type II error are 5%.

The process of hypothesis testing is used to determine whether or not a given statistical hypothesis is valid. The objective of this method is to determine whether the null hypothesis can be accepted or rejected based on the sample data obtained.

Hypothesis testing can be used to evaluate two hypotheses. The null hypothesis is the one that must be accepted or rejected, while the alternative hypothesis is the one that must be supported. In other words, hypothesis testing is a way of determining whether the null hypothesis is reasonable or not.

The Type II error is defined as the error that occurs when the null hypothesis is not rejected even though it is incorrect. In hypothesis testing, this type of error is referred to as a beta error or a false-negative error. The chances of making a Type II error depend on several factors, including the sample size, the level of significance, and the power of the test. When the level of significance is lowered to 0.05, the chances of making a Type II error are 5%.

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When a point is rotated, it must be rotated around a point.

See attachment for the image of the rotation about point K

We should note the following:

In order to construct triangles, you will need a protractor, a pair of compasses and a ruler. To draw the triangle, three properties must be taken into account: length, angle and shape

The given parameters are:

ΔEFG

The angle of rotation is

∅ = 180⁰

The above angle of rotation means that:

The translated triangle will be 180 degrees from ΔEFG about point K.

It also means that:

ΔEFG and ΔE'F'G' will be equidistant from point K

See attached image for ΔE'F'G'

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Answer:

The perimeter is the sum of the lengths of all the sides of a polygon. Thus, the perimeter of this quadrilateral is:

(10a-6) + (7a+4) + (7a+4) + (10a-6)

Simplifying the expression:

= 34a - 4

Therefore, the perimeter of the quadrilateral is 34a - 4.

When a double cone is sliced at the apex by a plane perpendicular to the base of the cone, the resulting conic section is a parabola.

Option B is the correct answer.

We have,

A parabola is a type of conic sect ion that can be defined as the locus of points equidistant from a fixed point (the focus) and a fixed line (the directrix).

In the case of slicing a double cone at the apex, the resulting conic section will have the characteristic shape of a parabola.

The slicing plane intersects both sides of the double cone, creating a curved shape that opens upward or downward, depending on the orientation of the cone.

The vertex of the parabola corresponds to the point of intersection of the slicing plane with the double cone.

Therefore,

When a double cone is sliced at the apex by a plane perpendicular to the base, a parabola is formed.

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The complete question:

Which degenerate conic is formed when a double cone is sliced at the apex by a plane perpendicular to the base of the cone?

A. Circle

B. Parabola

C. Ellipse

D. Hyperbola

We can simplify the expressiοn tο  [tex]52x^3y,[/tex] nοt [tex]52x^2y[/tex].

Yοu must substitute a number fοr each variable and perfοrm arithmetic οperatiοns tο evaluate an algebraic expressiοn. Because 6 + 6 = 12, the variable x in the preceding example is equal tο 6. We can evaluate the expressiοn after replacing the variables with their values if we knοw their values.

We can use expοnent prοperties tο simplify the expressiοn [tex]13x[/tex]• [tex]4x^2y[/tex]:

[tex]13x[/tex]•[tex]4x^2y = 13[/tex] • [tex]x^1[/tex]• 4 • [tex]x^2[/tex]•[tex]y^1[/tex]

[tex]= 52[/tex]• [tex]x^3[/tex]•[tex]y^1[/tex]

As a result, we can simplify the expressiοn tο [tex]52x^3y[/tex] rather than[tex]52x^2y.[/tex]

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It would take the two painters together eight hours to paint the house

Step-by-step explanation: Given that, One painter can paint the entire house in twelve hours. The second painter takes eight hours to paint a similarly-sized house. To find, How long would it take the two painters together to paint the house? Suppose one painter takes x hours to paint the house.

Therefore, the other painter will take x-4 hours to paint the same house. According to the question, [tex]1/x+1/(x-4)=1/12+1/8[/tex] Multiply by LCM, [tex]8(x-4)=12x+12(x-4)8x-32=6x+484x=80x=20[/tex]Therefore, the first painter will take 20 hours to paint the house. The second painter will take 16 hours (20-4). Together they will take, [tex]1/20+1/16=0.1+0.0625=0.1625[/tex] Thus, they will take 6.1538 hours which can be rounded to 4.8 hours.

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Answer: To convert the given equation, √y = (6/p)x - (2/q), into the linear form y = mx + c, we can use the following steps:

Square both sides of the equation to eliminate the square root:

√y = (6/p)x - (2/q)

√y^2 = (6/p)x - (2/q)^2

Simplifying the right-hand side, we get:

y = (36/p^2)x - (4/q) + 4/q^2

Rearrange the equation to the form y = mx + c:

y = (36/p^2)x + (4/q^2 - 4/q)

So the linear form of the given non-linear equation is y = (36/p^2)x + (4/q^2 - 4/q).

Step-by-step explanation:

Using  the substitution method, the solution of the system of equations -4x + y = 3 and 5x - 2y = -9 is (x, y) = (1, 7)

We can solve this system of equations using the substitution method by solving for one variable in terms of the other in one equation, and then substituting that expression into the other equation. Here's how:

-4x + y = 3 (Equation 1)

5x - 2y = -9 (Equation 2)

Solving Equation 1 for y, we get:

y = 4x + 3

Now, we substitute this expression for y into Equation 2 and solve for x:

5x - 2(4x + 3) = -9

5x - 8x - 6 = -9

-3x = -3

x = 1

We have found the value of x to be 1. Now, we substitute this value back into Equation 1 to find the value of y:

-4(1) + y = 3

y = 7

Therefore, the solution to the system of equations is (x, y) = (1, 7)

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Answer:

Step-by-step explanation:

We can use the compound interest formula to solve this problem:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (which is given as $18,100)

P = Principal amount (the amount Tristan needs to invest)

r = Annual interest rate (6.2%)

n = Number of times interest is compounded per year (12)

t = Time in years (12)

Substituting the values in the formula:

18,100 = P(1 + 0.062/12)^(12*12)

Simplifying the right-hand side:

18,100 = P(1.00516666667)^144

Dividing both sides by (1.00516666667)^144:

P = 18,100 / (1.00516666667)^144

P = $8,167.75 (rounded to the nearest cent)

Therefore, Tristan needs to invest $8,167.75, to the nearest cent, for the value of the account to reach $18,100 in 12 years.

The option B is the correct option.

Suppose I'm trying to prove that 2 divides n2 - n for any natural number n. If the end/goal of my induction step is 2 divides p2 then my inductive hypothesis must have been 2 divides n2 - n for n = 0,1,...,p-1. The correct option is B.What is natural induction?The concept of natural induction is based on the notion of logical implication, in which the validity of the subsequent statement is demonstrated using the initial statement. Suppose, for example, you want to show that P(2) is valid. A hypothesis is a statement that is proven using induction; it is the statement that P(n) is valid for a natural number n.Suppose I'm trying to prove that 2 divides n2 - n for any natural number n. If the end/goal of my induction step is 2 divides p2 then my inductive hypothesis must have been 2 divides n2 - n for n = 0,1,...,p-1. Therefore, option B is the correct option.

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Answer:

9.5x + 8 = 65

Step-by-step explanation:

Let x = number of sandwiches.

The cost of x sandwiches is 9.5x.

The delivery fee is $8.

The total cost of an order is the price of the sandwiches, 9.5x plus the delivery fee, 8.

In this case, the total cost is $65.

9.5x + 8 = 65

Answer:

$65

Step-by-step explanation:

X=9.50 because you add the $8 delivery fee to equal 65 in total.

The required probability of drawing a blue marble on the next trial is also 11/50.

The probability of an event is a figure that represents how probable it is that the event will take place. In terms of percentage notation, it is stated as a number between 0 and 1, or between 0% and 100%. The higher the probability, the more probable it is that the event will take place.

Since the marbles are replaced after each draw, the probability of drawing a blue marble remains the same for each trial. Therefore, the experimental probability of drawing a blue marble on the next trial is also 11/50.

Expressed as a decimal, this is 0.22. Expressed as a percentage, it is 22%.

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The measure of angle G is 34° because the sum of the measures of the angles GFE and GF is 180° - 28° = 152° and the measure of angle GFE is 28°, so the measure of angle GF is 152° - 28° = 34°.

An angle is a shape formed when two lines or rays intersect. It is measured in degrees and is used in mathematics and geometry to describe the size and direction of a corner or turn. Angles measure the amount of turn between two lines, and can be described as either acute, obtuse, right, or reflex. Angles are also used to describe the orientation of objects in space, such as the position of the sun or the direction of a car relative to its surroundings.

The measure of angle GFE is 180° minus angle FEG, which is 180° - 28° = 152°. Since the sum of the measures of the angles of a triangle must equal 180°, the measure of angle GF is 180° - 152° = 28°. Therefore, the measure of angle G is 34° because the sum of the measures of the angles GFE and GF is 180° - 28° = 152° and the measure of angle GFE is 28°, so the measure of angle GF is 152° - 28° = 34°.

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The ∠E is 28°. Then what is the angle that is on the opposite side of ∠E It is ∠G.∠G would be 28°.

An angle is a shape formed when two lines or rays intersect. It is measured in degrees and is used in mathematics and geometry to describe the size and direction of a corner or turn. Angles measure the amount of turn between two lines, and can be described as either acute, obtuse, right, or reflex. Angles are also used to describe the orientation of objects in space, such as the position of the sun or the direction of a car relative to its surroundings.

198: line EF and line FG have same length of 6.

A triangle that has to be two sides of the equal length is the  called isosceles triangle.

So your triangle is an isosceles triangle!

An isosceles with the  triangle has two angles on facing each other are the same.

For example, the ∠E is 28°. Then what is the angle that is on the opposite to side of ∠E? It is ∠G.

∠G would be 28°.

So your answer is C. 28°.

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