find the local maximum and minimum values and saddle point(s) of the function. (enter your answers as a comma-separated list. if an answer does not exist, enter dne.)

NO. Your friend is incorrect because the solution to the system of equations on the graph is: (4, 3).

The solution to a system of linear equations is the coordinates of the point where the two lines of the linear equations intersect.

The x-coordinate and the y-coordinate of this point lie on each of the lines of the linear equations. This means that, both values of x and y are a solution to each of the linear equation given.

Therefore, the solution to a system of linear equations is usually represented as (x, y) and not just as a single value of x.

The system of linear equations that is graphed above shows that both lines intersect at (4, 3), that is, when x = 4, the value of y = 3.

However, your friend only stated the value of x = 4, as the solution to the system of linear equations that is represented on the graph.

Therefore, your friend is wrong.

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In 1820  different ways a group of four people can be selected from this group of 16.

In 35 ways four women can be chosen from the group of 7 women.

The probability that all women will be chosen to attend the conference is 1.92%.

The proportion of favourable outcomes to all possible outcomes of an event is known as the probability. The number of positive outcomes for an experiment with 'n' possible outcomes can be represented by the symbol x. The probability of an event can be determined using the following formula.

To find how many different ways can a group of four people be selected from this group of 16, we will implement the combination formula.

[tex]^n C_r=\frac{n !}{r ! (n-r) !}[/tex]

Where,

nCr = number of combinations

n = total number of objects in the set

r = number of choosing objects from the set

Here, n = 16 and r = 4, substituting the values we get

[tex]^{16} C_4=\frac{16 !}{4 ! (16-4) !}[/tex]

[tex]^{16} C_4 =[/tex] 1820

Hence, in 1820  different ways a group of four people can be selected from this group of 16.

To find how many ways can four women be chosen from the group of 7 women we will implement the combination formula.

Here, n = 7 women and r  = 4 women, substituting the values we get

[tex]^7 C_4=\frac{7 !}{4 ! (7-4) !}[/tex]

[tex]^7 C_4=[/tex] 35

Thus, in 35 ways four women can be chosen from the group of 7 women.

The probability that all women will be chosen to attend the conference is

[tex]\frac{^7 C_4}{^{16}C_4}[/tex] = 35/1820

       = 0.01923076

       = 1.92%

Thus, the probability that all women will be chosen to attend the conference is 1.92%.

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If a cave explorer is at an elevation of −32 feet and the explorer starts moving at a rate of −6 feet per minute. it will take, 9 in minutes for the explorer to reach an elevation deeper than −140 feet.

Elevation of feet =  −32 feet.

Feet per minute =  −6 feet per minute

Elevation deeper than  feet = −140 feet

Let x  represent the time for reach the desired height

Inequality

-32 - 6x = ≤ -140

Substract 32 from both side

12x ≤ 140 -32

12x  ≤ 108

Divide both side by 12x

x ≤ 108/12

x ≤ 9

Therefore we can conclude that the explorer will have to use 9 minutes to get to the elevation.

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Value of x is 28.5 and y is 14.

An angle is a figure in Euclidean geometry made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles created when two rays are in the plane where the rays are located. The intersection of two planes also creates angles. We refer to these as dihedral angles.

Given Data

a = 2x + 3y

b = 4x - y

c = 3x + 2y

∠b = 100° ( corresponding angle)

4x - y = 100

4x - 100 = y

∠a = ∠b ( alternate angle)

2x + 3y = 4x - y

Equating values of y

2x + 3(4x - 100) = 4x - 4x + 100

2x + 12x - 300 = 100

14x = 400

x = [tex]\frac{400}{14}[/tex]

x = 28.5

For the values of y,

4(28.5) -100

114 -100

14

Value of x is 28.5 and y is 14.

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1. First we find the product of 3 and 6. Product=addition

3+6=8

8 is the product of 3 and 6.

2. Now we find the difference between 8 and the square root of 36.

The square root of 36 is 6. (6x6=36)

8-6=2.

3. Now we must divide 36 by 2.

36/2=18.

ANSWER= 18

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these are a bit complicated, but i hope that helped!! the tricky part is breaking it up and trying to find which goes first.- || much love! <33

Dividing 36 by the difference between product of 3 and 6 and the square root of 36 gives 3.

The problem asks us to divide 36 by the difference between the product of 3 and 6 and the square root of 36.

First, we need to find the product of 3 and 6, which is 18.

Then, we need to find the square root of 36, which is 6.

So, the difference between the product of 3 and 6 and the square root of 36 is 18 - 6 = 12.

Therefore, we need to divide 36 by 12.

We can do this by performing long division, or by using the calculator.

The answer is 3.

Here is the long division solution:

36 / 12 = 3

Here is the calculator solution:

36 / 12 = 3

Therefore, the answer to the problem is 3.

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The answers to all the subparts are given below:

So, (A) Chebyshev's theorem is used:

So,

Therefore, the minimum proportion of commuters who are within two standard deviations of the mean is:

(B) Minimum percentage of commuters in the city has a commute time within 1.5 standard deviations of the​ mean:

Here, k = 1.5

Consequently, the shortest commute within two standard deviations of the mean is:

Within 1.5 standard deviations, commute times:

(C) Minimum percentage of commuters who have commute times between 6 minutes and 48.6 ​minutes:

So,

Therefore, the answer to all the subparts are given below:

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The correct question is given below:
The mean commute time to work for a resident of a certain city is 27.3 minutes. Assume that the standard deviation of the commute time is 7.1 minutes to complete parts​ (a) through​ (c).

​(a) What minimum percentage of commuters in the city has a commute time within 2 standard deviations of the​ mean?

nothing​% ​(Type an integer or a​ decimal.)

​(b) What minimum percentage of commuters in the city has a commute time within 1.5 standard deviations of the​ mean? What are the commute times within 1.5 standard deviations of the​ mean?

The minimum percentage of commuters in the city that has a commute time within 1.5 standard deviations of the mean is nothing​%. ​(Round to one decimal place as​ needed.)

The commute times within 1.5 standard deviations of the mean are between nothing and nothing.

​(Type an integer or a decimal. Use ascending​ order.)

​(c) What is the minimum percentage of commuters who have commute times between 6 minutes and 48.6 ​minutes?

nothing​% ​(Round to one decimal place as​ needed.)

Answer:

0.86

Step-by-step explanation:

Move the decimal point one place to the right

Answer: HL

Step-by-step explanation: the diagram compares the two sides, or legs, and the hypotenuse.

Answer:

Step-by-step explanation: $3.02

3 pounds difference

Answer: 9.73

Step-by-step explanation:

the five at the end indicates rounding up so the answer for the 2 decimal places is 9.73.

Answer:

9.73

Rule #1: If the last digit in 9.725 is less than 5, then remove the last digit.

Rule #2: If the last digit in 9.725 is 5 or more and the second to the last digit in 9.725 is less than 9, then remove the last digit and add 1 to the second to the last digit.

Rule #3: If the last digit in 9.725 is 5 or more and the second to the last digit in 9.725 is 9, and the third to the last digit is less than 9, then remove the last digit, make the second to last digit 0, and add 1 to the number to the third to the last digit.

Rule #4: If the last digit in 9.725 is 5 or more and the second to the last digit is 9, and the third to the last digit is 9, then add 1 to the number on the left side of the decimal point and make the right side of the decimal point 00.

When rounding 9.725 to two decimal places we use Rule #2. Therefore, the answer to "What is 9.725 rounded to 2 decimal places?" is:

The price of an adult ticket and a student ticket is $14 and $8, respectively.

Using algebraic expression and equation, we can express each statement and determine the price of each ticket.

Let x = the price of an adult ticket

y = the price of a student ticket

If on the first day of ticket sales, the school sold 3 student tickets and 1 adult ticket for a total of $38, then we can express this as:

3y + x = 38     (equation 1)

If the school took in $52 on the second day by selling 3 student tickets and 2 adult tickets, then we can express this as:

3y + 2x = 52     (equation 2)

3y + 2x = 52     (equation 2)

-(3y + x = 38)    (equation 1)

x = 14

Substitute the value of x in any of the two equations.

3y + x = 38     (equation 1)

3y + 14 = 38

3y = 38 - 14

3y = 24

y = 8

price of an adult ticket = $14

price of a student ticket = $8

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The output value of h( 2 ) in the function h( x ) = 4x + 4 is 12.

A function is a relationship that maps one input to one output, for a relation to qualify as a function, each of its x-value can only have one y-value.

Given the data in the question;

To solve for the output value of h( 2 ), replace all the occurrence of x with 2 in the function and simplify.

h( x ) = 4x + 4

h( 2 ) = 4( 2 ) + 4

Multiply 4 and 2

h( 2 ) = 8 + 4

Add 8 and 4

h( 2 ) = 12

Therefore, the output value is 12, this forms an ordered pair of (2,12) on the graph.

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Answer:

77/12

Step-by-step explanation:

3 3/4 + 2 2/3

15/4+8/3

45/12+32/12

77/12

For the first function, the coordinates of A are (0, 1).

The equation of circle B is (x -4)^2 + y^2 = 25

And the circle intercepts the x-axis at:

(9, 0) and (-1, 0)

We have the equation:

y = a^x

And we know that A is the y-intercept of that equation, remember that the y-intercept is the point such that x = 0, so the y-coordinate will e:

y = a^0 = 1

So the y-intercept (point A)  is the point (0, 1).

We start with the circle:

x^2 + y^2 = 25

And we apply a translation of 4 units to the right, so we write this as:

(x - 4)^2 + y^2  = 25

c) The circle intercepts the x-axis when y = 0, then:

(x - 4)^2 + 0^2 = 25

x - 4 = ±√25

x - 4 = ±5

x = 4 ± 5

Then the two points where the circle intercepts the x-axis are:

(9, 0) and (-1, 0)

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Applying mathematical operations with the remaining parts, you could have 1 more kit if you had A.1 more marker and 1 more die.

Using mathematical operations of divisions, subtractions, and additions, we can determine the number of kits made from the materials and the part required to make one additional kit.

For instance, 287 people marker can make 47 (287/6) kits with 5 remaining, which requires another 1 part to complete another kit.

143 6-sided die can also make 47 kits (143/3) with 2 parts, which require an additional 1 part to make another kit.

The above parts are unlike the teleporter marker, which had already made 48 kits with 5 of its part remaining.

Part                     Number in each kit    Number available   # of Kits Made

People marker                   6                            287                      47

6-sided die                         3                            143                      47

Teleporter marker             7                            341                      48

Thus, using mathematical operations, we can determine that to complete the number of kits to 48, the kit maker requires Option A.

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Answer:

g(x) = |x + 3|

g(x) is nonnegative on all real numbers.

g(x) is decreasing on x <= -3 and increasing on x >= -3.

As x tends to negative infinity, g(x) tends to positive infinity.

As x tends to positive infinity, g(x) tends to positive infinity.

Domain: all real numbers

Range: all nonnegative real numbers

Answer:

See picture

Step-by-step explanation:

The parameters are ΔUVW with side UW extended to X then m ∠UVW = (3x + 4)°, m ∠VWX = (8x -12)° and m ∠WUV = (x + 20)° then the value of x = 9°.

The given parameters exist;

ΔUVW with side UW extended to X

m ∠UVW = (3x + 4)°, m ∠VWX = (8x -12)° and m ∠WUV = (x + 20)°

We have that m ∠UVW + m ∠WUV + m ∠VWU = 180° (Sum of the interior angles of a triangle theorem)

Therefore, m ∠VWU = 180° - (m ∠UVW + m ∠WUV)

Also, we have that m ∠VWX and m ∠VWU exist supplementary angles, (The sum of angles on a straight line)

∴ m ∠VWX + m ∠VWU = 180° (Definition of supplementary angles)

m ∠VWU = 180° - m ∠VWX

∴ m ∠VWX = (m ∠UVW + m ∠WUV)

Substituting the values in the above equation, we get;

(8x -12)° = (3x + 4)° + (x + 20)°

simplifying the above equation, we get

8x - 3x - x = 4 + 20 + 12

4x = 36

x = 36/4 = 9

Therefore, the value of x = 9°.

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The digits at ones place are 8 and the hundredth place is 9.

The number which is left to the decimal is considered in one's places as proceeding with the numbers tens places and the hundredth place is obtained. Similarly on the right side moving towards the right gives tenth place and hundredth place.

18.09

(1) - It is in the Tens place

(8) - Ones place

(.) - Decimal point

(0) - Tenth place

(9) Hundredth place

Therefore, The digits at one place are 8 and the hundredth place is 9.

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The equation of the line that has a slope of -3 and passes through the point (5, -1) is 3x + y = 14.

What is slope ?

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

We know the slope point form,

y - y1 = m( x - x1 )

Where x1 and y1 atre the coordinates of the points and m is the slope.

Putting thew values from the question:

y - (-1) = -3 ( x - 5)

=> y  + 1 = -3x + 15

=> 3x + y = 14

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note that parallel lines have equal gradients.

give the line 2x+3y =5 write it in the form y=mx+c first so that you can be able to know its gradient. Mind you getting the gradient of the given line means finding the gradient of the new equation because they are equal as stated above.

[tex]2x + 3y = 5 \\ 3y =5 - 2x \\ \frac{3y}{3} = \frac{5}{3} - \frac{2x}{3} \\ y = \frac{5}{3} - \frac{2}{3} x[/tex]

FROM THE GIVEN EQUATION WE CAN NOW SEE THAT THE GRADIENT IS

[tex] - \frac{2}{3} [/tex]

Meaning the gradient of the new EQUATION sknce it is parallel to the given one will be

[tex]m = - \frac{2}{3} [/tex]

also.

given the points we can substitute to get the value of the unknown c.

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

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

Answer:

For example, 7 is a divisor of 84 because 84 ÷ 7 is an even division. However, that also means that 7 × (a number) = 84, so 7 is a factor of 84.

Answer:

x = 27

Step-by-step explanation:

AOB is a straight angle = 180°

the 3 angles on it therefore sum to 180° , that is

36 + 90 + 2x = 180

126 + 2x = 180 ( subtract 126 from both sides )

2x = 54 ( divide both sides by 2 )

x = 27

Answer:

3.26 time 102

Step-by-step explanation:

Because a square of 10 is 100

3.26 x 100 = 326

We know that the decimal move 2 spots to the right

So the answer is 3.26 x 102

Answer:

1/5

Step-by-step explanation:

Finding the unknown value in exponent form:

Prime factorize 125.

      125 = 5 * 5 * 5 = 5³

   [tex]\sf k^3 = \dfrac{1}{125}\\\\ k^3 = \left(\dfrac{1}{5}\right)^3[/tex]

As exponents are same, compare the bases,

 [tex]\sf k = \dfrac{1}{5}[/tex]

Answer:

x=1/5

Step-by-step explanation:

[tex]k^3=1/125\\[/tex]

[tex](k^3)^\frac{1}{3} =(\frac{1}{125} )^\frac{1}{3}[/tex]

 [tex]k^3^\frac{1}{3} =\frac{1}{125^\frac{1}{3}}[/tex]

[tex]k=\frac{1}{5}[/tex]

Hope this Helps :)

I just checked it for you. yes it can

[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"d" proportional to }t^2}{ {\Large \begin{array}{llll} d=kt^2 \end{array}}}\qquad \textit{we also know that} \begin{cases} d=80\\ t=4 \end{cases}\implies 80=k(4)^2 \\\\\\ \cfrac{80}{4^2}=k\implies 5=k\hspace{15em}\boxed{d=5t^2} \\\\\\ \textit{when t = 8, what is "d"?}\qquad d=5(8)^2\implies d=640~in[/tex]