Find the range, IQR, and MAD of the data set.
15, 22, 16, 13, 14, 20, 40, 44

While looking at the critical points of a function f(x) is a useful first step in finding its maxima and minima, it is not enough by itself to determine all of them.

The statement is partially correct. If a function f(x) is continuous on a closed interval, it is possible to find its absolute maxima and minima by looking at the points where f'(x) = 0, but this is not enough to guarantee that you have found all of them.

The reason why this is the case is because the condition f'(x) = 0 only identifies critical points, which are points where the function may have an extremum (either a maximum or a minimum). To determine whether a critical point is indeed a maximum or a minimum, you need to analyze the behavior of the function near the critical point.

One way to do this is by using the second derivative test, which states that if f(x) is twice differentiable and f''(x) > 0 at a critical point x, then f(x) has a local minimum at x. Similarly, if f''(x) < 0 at a critical point x, then f(x) has a local maximum at x.

You also need to use additional tools, such as the second derivative test, to verify whether the critical points are indeed extrema.

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Answer:

[tex]x=5[/tex]

Step-by-step explanation:

[tex]\cos 60^{\circ}=\frac{x}{10} \\ \\ \frac{1}{2}=\frac{x}{10} \\ \\ x=5[/tex]

Answer:

$1.80 per 4 mini muffins

Step-by-step explanation:

12 mini muffins = 5.40

divide by 3

4 mini muffins = 1.80

:]

The given expression is a fifth-degree polynomial.

An expression represents a polynomial when these following conditions are satisfied:

The exponents for this problem are given as follows:

5, 2 and 1.

Hence the function represents a polynomial, of the fifth degree, as the highest exponent is of 5.

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Answer:

Step-by-step explanation:

The percent yield formula is used to calculate the efficiency of a chemical reaction in producing a desired product. It is defined as the ratio of the actual yield of a product to its theoretical yield, expressed as a percentage.

The formula for percent yield is:

Percent Yield = (Actual Yield / Theoretical Yield) * 100%

where:

Actual Yield is the amount of product actually produced in the reaction.

Theoretical Yield is the maximum amount of product that could be produced in a reaction under ideal conditions, calculated from the stoichiometry of the reaction.

By using this formula, you can determine how well a reaction is performing and identify areas for improvement to increase the yield of the desired product.

Answer:

(a) x= 20 (b) x= 41

Step-by-step explanation:

(a)

180-54= 126

360-126-90= 144

7x+4= 144

7x= 140

x= 20

(b)

(n-2)(180)= (5-2)(180)

= 540

(2x-10)+3x+(4x+20)+(2x-5)+(2x+2)= 13x+7

13x+7= 540

13x= 533

x= 41

Answer:

The percentage increase can also be calculated using this method. Imagine you have a function that adds the number 1 to a number between 0 and 10, which we call T. Now the percentage of the function's answer will be the percentage increase from T.

[tex]f=1+t\\t=0-10\\d=f\frac{t}{100} = percentage- f- of- t[/tex]

With this method, we obtain the percentage increase of the f function.

Step-by-step explanation:

The inequality representing the number system in which only the whole numbers less than 5 are used is given as follows:

{x ∈ W| x < 5}.

The four inequality symbols, along with their meaning, are presented as follows:

The inequality representing numbers less than 5 is given as follows:

x < 5.

As the numbers are whole numbers, the inequality is defined as follows:

{x ∈ W| x < 5}.

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Answer:At low tide the water reaches the 1-foot mark. Assume that high tide occurs at 12 noon and at midnight, and that low tide occurs at 6 pm and 6 am.

Step-by-step explanation:

Answer:

12 inches

Step-by-step explanation:

21/3=7

84/7=12

12 inches

Answer: 10

Step-by-step explanation:

4x - 28 = 12

4x - 28 = 12 + 28

4x = 40

4x/4 = 40/4

x = 10

The value of the fraction is A = 20 / 9

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fraction be represented as A

Now , the first fraction is p = 5/6

Let the second fraction be q = 3/8

Now , the equation is A = p/q

On simplifying , we get

A = ( 5/6 ) / ( 3/8 )

A = ( 5/6 ) x ( 8/3 )

On further simplification , we get

The fraction A = ( 20 / 9 )

Hence , the fraction is A = 20/9

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Answer:

11/x because split is the same as divide so she split 11 pieces with x people

Step-by-step explanation:

The integral of 1/(1-x^2) is arctan(x).

An integral is a mathematical operation that calculates the area under a curve by breaking it into infinitely small segments and summing them up.

To solve this integral, we use the substitution method with u=1-x^2:

∫1/(1-x2)dx =∫du/u (substitute u=1-x2)
= ln|u| + C (integrate with respect to u)
= ln|1-x2| + C (substitute back in the original expression)
= ln|1-x2| + C (substitute back in the original expression)
= arctan(x) + C (use the identity ln|1-x2| = arctan(x))

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Answer:

Two ways.

(1) 4 notebooks,3 pencils, have change $12;

(2)3 notebooks, 5 pencils, have no change.

Step-by-step explanation:

set student buy x notebooks and y pencils,

x≥3,y≥3,

60x+36y≤360

if x=3, 180+36y≤360

         36y≤180

             y≤5

and y≥3, so y={3,4,5}

(1)when y=3, 60x≤360-36x3=252, x≤4.2,so x=4,

and change=360-36x3-60x4=12

(2)when y=4, 60x≤360-36x4=216, x≤3.6,so x=3,

and change=360-36x4-60x3=36, since student have to spend as much as possible of his money, $36 can buy a pencil, so this is not accepted.

(3)when y=5, 60x≤360-36x5=180, x≤3, so x=3,

and change =360-36x5-60x3=0

The student has two ways to spend his money on notebooks and pens. In one option, she can buy 4 notebooks and 3 pens and in the other option she can buy 3 notebooks and 5 pens.

To find the student's possibilities to buy pens and notebooks we must take into account his total budget of $360. Additionally, the values of the notebooks and pens that are: $60 and $36 respectively.

We must multiply the value of the notebooks by the number of notebooks that we believe the student can buy, this would be a range between 3 and 4 notebooks. Additionally, once we decide the number of notebooks we can divide the remaining money in the value of the pens to find the number of pens that the student can buy. According to the above:

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Answer: 60%

Step-by-step explanation:

2,400/4,000 x 100/1

0.6 x 100 = 60%

[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{8})\hspace{10em} \stackrel{slope}{m} ~=~ 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{8}=\stackrel{m}{ 1}(x-\stackrel{x_1}{5})\implies {\Large \begin{array}{llll} y=x+3 \end{array}}[/tex]

Step-by-step explanation:

Looks like this was scaled by 5 because

2 x 5 = 10

4 x 5 = 20

5 x 5 = 25

CAB ..

CA is 5

HJ is 25

AB is 2

JG is 10

CAB = HJG

Answer:

You check a solution to an equation by replacing the variable in the equation with the value of the solution

Step-by-step explanation:

Answer:

m = 73/13

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

(0, 0), (13, 73)

We see the y increase by 73 and the x increase by 13, so the slope is

m = 73/13

The amount of KES that one would have to get for R150 is given as 1053.54 KES

​The KES tells us of the Kenyan currency. That is the Kenyan shillings. The R is the name that is used to refer to the Rands

Hence we would have to convert rands to KES

1 south African Rand is given as 7.0236

then 150 rand would be = ?

Hence the amount you would get of KES is: 7.0236 * 150

= 1053.54 KES

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The weight of Alicia's camera is 8/5 kg. We can record this value in the table.

A fraction is a number that represents a part of a whole. It is expressed as a ratio of two numbers, where the top number is called the numerator and the bottom number is called the denominator.

We need to record the weight of Alicia's camera in the table. We know that the weight of her lunch is greater than the weight of her camera, and we know that the weight of her lunch is 2 kg. Therefore, the weight of her camera must be less than 2 kg.

We are also given that the weight of her camera is 1\dfrac35 kg. To convert this mixed number to an improper fraction, we can multiply the whole number (1) by the denominator of the fraction (5) and add the numerator (3), and then put the result over the denominator:

[tex]1\dfrac35 = \dfrac{1\times5+3}{5} = \dfrac{8}{5}[/tex]

Therefore, The weight of Alicia's camera is 8/5 kg. We can record this value in the table.

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No, The point (30, 61) does not lie on the given line y  = 2x - 1.

The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.

Given that,

The line,

y = 2x -1

To check if the point (30, 61) is on the line y = 2x - 1, we need to substitute x = 30 and y = 61 into the equation and see if the equation holds true.

So, we have:

y = 2x - 1

61 = 2(30) - 1

61 = 60 - 1

61 = 59

Since 61 is not equal to 59, the point (30, 61) is not on the line y = 2x - 1.

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The value of x is 0.85 of the equation.

Two or more expressions with an Equal sign is called as Equation.

Let the given equation be 4x+2=5.4

We need to find the value of x

Substitute 2 from both sides

4x=5.4-2

4x=3.4

Divide both sides by 4

x=0.85

Hence, the value of x is 0.85 of the equation.

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The fact that both rays are equal in the case at hand is not given, hence the incorrect statement will be (A) AB = AC.

By selecting a curve that is perpendicular to the wavefronts of the actual light and points in the direction of energy flow, one can create an idealized geometrical model of light or other electromagnetic radiation known as a ray in the field of optics.

By segmenting the actual light field into discrete rays that can be computationally propagated across the system using ray tracing techniques, rays are used to mimic the propagation of light through an optical system.

As a result, even extremely complicated optical systems can be mathematically or computationally investigated.

For as long as light waves travel through and around objects whose dimensions are significantly larger than the light's wavelength, approximate solutions to Maxwell's equations are appropriate for use in ray tracing.

So, in the given situation it is nowhere given that both rays are equal, and hence the wrong statement will be AB = AC.

Therefore, the fact that both rays are equal in the case at hand is not given, hence the incorrect statement will be (A) AB = AC.

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The graph of given inequalities is plotted on the number line is attached below.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequalities are x≥6 and 15.5>x.

The solution set of the inequality x≥6 is

{6, 7, 8, 9, 10, 11, 12, 13, 14,......}

Interval Notation: [6,∞)

x<15.5

Interval Notation: (−∞, 15.5)

Therefore, the solution set of the inequality x≥6 is {6, 7, 8, 9, 10, 11, 12, 13, 14,......}.

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The equivalent of the expression -2w-9+5w+3 is 3(w-2)

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value(s) for the variable(s). Examples is 2x+ 6y is equivalent to 2(x+3y)

The expression -2w-9+5w+3 can be factorized;

collect like terms

-2w-9+5w+3 = -2w+5w-9+3

= 3w-6

= 3( w-2)

therefore the equivalent of the expression -2w-9+5w+3 is 3(w-2)

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The surface area of a square pyramid net can be found by adding the areas of the base and the four triangular faces.

First, find the area of the base by multiplying the length and width of the square base.

Area of base = length × width

Next, find the area of one of the triangular faces by using the formula:

Area of triangle = 0.5 × base × height

Since there are four triangular faces in a square pyramid, multiply the area of one triangle by four to find the total area of the triangular faces.

Area of triangular faces = 4 × (0.5 × base × height)

Finally, add the area of the base and the area of the triangular faces to find the total surface area of the square pyramid net.

Surface area = Area of base + Area of triangular faces

= (length × width) + (4 × (0.5 × base × height))

= (length × width) + (2 × base × height)

So, the surface area of a square pyramid net is the sum of the area of the base and the area of the four triangular faces.

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The conversion of 73 Kilogram (kg) pounds (lbs) is 160.9358 lbs

The standard metric conversion of a unit weight from one S.I. unit to another follows a standard approach that is universally acceptable and timeless. For the conversion of 1 kilogram to pounds, 1 kg is equivalent to  2.2046 lbs.

To convert 73 kilograms to pounds, multiply 73 kilograms by 2.2046 lbs. Mathematically;

[tex]=73 \ kg \times \dfrac{2.2046 \ lbs}{1 \ kg}[/tex]

Cancel the common units

[tex]=73 \times \dfrac{2.2046 \ lbs}{1}[/tex]

= 160.9358 lbs

Therefore, we can conclude that the conversion of 73 kilograms (kg) to metric pounds (lbs) is 160.9358 lbs.

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Answer:

The probability that two independent events will both occur can be calculated by multiplying the probabilities of the individual events. If event A has probability p(A) and event B has probability p(B), then the probability that both events A and B occur is given by:

p(A and B) = p(A) * p(B)

This relationship holds because the occurrence of event A does not affect the occurrence of event B, and vice versa. Hence, the two events are considered to be independent.

For example, if event A has a probability of 0.6 of occurring and event B has a probability of 0.7 of occurring, then the probability that both events will occur is 0.6 * 0.7 = 0.42.