How do you find the maximum value of a parabola using calculus?

A linear function is a type of function that can be expressed in the form of a linear equation with one or more variables.

The equation is written as y = mx + b, where m is the slope and b is the y-intercept. The slope is the rate at which the line rises or falls and the y-intercept is the point where the line crosses the y-axis. The slope and y-intercept of a linear function are constants, meaning that the line does not curve or change direction. This is why it is called a linear function.

When calculating linear functions, the equation is used to identify the slope and the y-intercept. The slope and y-intercept are then used to plot the points on a graph. A linear equation has the form y = mx + b, where m is the slope and b is the y-intercept. The slope indicates the rate of change of the function and the y-intercept indicates the point where the line crosses the y-axis. To find the slope of a linear function, the equation is solved for m, which is the rise over run. To find the y-intercept, the equation is solved for b, which is the y-value when x = 0. Once the slope and y-intercept are determined, the points can be plotted on a graph and the linear equation can be written.

In summary, a linear function is a type of function that can be expressed in the form of a linear equation. The equation of the linear function is used to identify the slope and y-intercept, which are then used to plot the points on a graph. Linear functions can be used to model many real-world situations and to solve for x and y values for any given point.

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Answer:

A cuboid is a 3-dimensional shape with six rectangular faces, four of which are the sides or lateral faces, and the other two are the base and the top. To solve the problem, we can first find the perimeter of the base of the cuboid by dividing the lateral surface area by the height. In this case, the perimeter of the base is 26 cm.

To find the dimensions of the base, we can set up an equation using the given information. Let x be one of the sides of the base, and let y be the other side. Since one of the sides is 3 cm smaller than the other, we can write the equation as:

x + x - 3 + x + x - 3 = 26 cm

We can simplify the equation by combining like terms:

4x - 6 = 26 cm

Next, we can solve the equation by adding 6 to both sides and then dividing by 4:

4x = 32 cm

x = 8 cm

Therefore, the dimensions of the base of the cuboid are 8 cm x 11 cm (since one side is 3 cm smaller than the other). The perimeter of the base is 26 cm, and the height of the cuboid is 10 cm.

Step-by-step explanation:

The range is 4.

The range is 4 because y=y can only take on 4 at any point.

Answer:

Step-by-step explanation: 44/59 = 0.74576271186 so that means the answer is around 74.5% or 74.6%

The median of the first 50 whole numbers is 24.5.

The midway value in a given set of figures or data is referred to as the median. To get the average value for a given group of integers, three distinct metrics are employed in mathematics.

Non-negative numbers, which can be expressed without fractions, are known as whole numbers.

The first fifty whole numbers are 0,1,2,3,4,5................49

The number of terms in the data, n=50.

Let [tex]n^{th}[/tex] term be denoted by [tex]t_{n}[/tex]

As the number of terms is even, thus the median will be [tex]\frac{t_{\frac{n}{2} } +t_{\frac{n}{2} }+1}{2}[/tex]

Substitute n with 50.

Median = [tex]\frac{t_{\frac{50}{2} } +t_{\frac{50}{2} }+1}{2}= t_{25}+t_{26} /2[/tex]

The 25th term of the sequence is 24.

The 26th term of the sequence is 25.

Thus, median = 24+25/2 = 49/2 = 24.5

Complete question: What is the median of the first 50 whole numbers?

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3,7,11,15 is an example of sequence since we can see a pattern is previous and next term.

Arithmetic sequence

Geometric sequence

Harmonic sequence

Fibonnaci numbers.

In contrast to a set, the same items might appear more than once in a sequence at various points, and unlike a set, the order is important. A sequence can be described formally as a function from natural numbers (the positions of the sequence's elements) to the items at each of those positions.

A sequence is a list of elements that has been arranged in a certain way. For instance, the sequence 3, 7, 11, 15,... is a sequence because it follows a pattern where each term is created by adding 4 to the term before it.

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SSS congruence of triangles is proved when all three sides of considered two triangles are congruent(that is, of equal measures).

If two considered triangles have corresponding side pairs congruent(for all three sides), then both the triangles are congruent. This proof of congruence is triangle is done by SSS congruence of triangles (Side Side Side congruence)

Since it is given that the sides CB and FE are congruent, and since it is given that sides AB and DE are congruent too.

Thus, for SSS congruence of both considered triangles, we need the third side pair of the given triangles to be congruent too.

Thus, we need the line segment DF congruent to the line segment AC.

We can write it symbolically as:

[tex]$\overline{D F} \cong \overline{A C}$[/tex] (remember that order doesn't matter here. This can be written as [tex]$\overline{A C} \cong \overline{D F}$[/tex] .)

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WX is a segment bisector

WX is a perpendicular bisector

W is the midpoint of a segment in the diagram

Answer:

497

Step-by-step explanation:

a(87) = -19+(87-1)6

a(87)=-19+(86)6

a(87)=-19+516

a(87)=497

I used the arithmetic formula which is an=a1+(n-1)d.....

The minimum and maximum heights accepted for NASA astronauts are 62 inches and 75 inches, respectively. These values can be represented by the following equation: 62 <= height <= 75

This equation can be read as "the height must be greater than or equal to 62 inches and less than or equal to 75 inches."

Alternatively, you can represent the minimum and maximum heights using the following inequality:

62 < height < 75

This inequality can be read as "the height must be greater than 62 inches and less than 75 inches."

Either of these equations can be used to represent the minimum and maximum heights accepted for NASA astronauts.

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From the proof below, we have been able to prove that IK bisects ∠HIJ by CPCT postulate

Congruent angles are defined as angles that have equal measure.

Now, we are given that;

IK bisects ∠HKJ

HK ≅ JK

Thus, since IK bisects ∠HKJ, then it means that by definition of angle bisector that;

∠HKI = ∠JKI

Now, we are also told that HK ≅ JK.

Now, by reflexive property of congruence, we can say that IK is congruent to itself.

Thus, we now have 2 congruent sides and an include angle and as such both triangles are congruent by SAS Congruency postulate.

Thus, we can conclude that ∠HIK = ∠JIK by CPCT which states that Corresponding parts of Congruent Triangles are congruent.

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In substitution method we have to put the the value of one variable from one equation to the other equation. Then we solve the equation and can find the value of variable x and y.

In the given question we have to explain how we can solve for x and y using substitution.

In the Substitution method we find the value of one variable in term of other variable from the one equation then we put the value of that variable in other equation. After putting the value of that variable in other equation, equation converts into the similar variable. Then after solving we can easily find the value of one variable. After finding the value of one variable we put the value of that variable in first equation. By this we can find the value of both variable.

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No , cousin is not correct because when 5,953 is rounded  to the nearet hundred the value should be 6000 .

Given :

What is rounding to the nearest hundred ?

Rounding a number to the nearest hundred means to write down the multiple of 100 that is nearest to the number .

so here given number = 5,953

so here the number 53 is greater than 50 .

We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

so the number after rounded = 6000

so his cousin is incorrect .

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The number of servings that can be made from 3 / 4 cups, the number of cups of flour needed for 10 servings is 1/4 cups.

Given :

First the number of servings that can be made per cup :

= Number of servings / Number of cups

= 30 / 3/4

= 30 * 4 / 3

= 120 / 3

= 40 servings

To get 10 servings therefore, you would need:

= Number of servings needed / Number of servings per cup

= 10 / 40

= 1/4 cups

Hence the flour will be needed  is 1/4 cup is needed.

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Answer:

(b) mean=95, standard deviation=7.2.

Step-by-step explanation:

To find the new mean and standard deviation, we first need to apply the transformation to the original mean and standard deviation.

The new mean is given by: x*=65+0.6x

Substituting in the original mean of 50, we get: x*=65+0.6(50) = 95

The new standard deviation is given by: s*=0.6s

Substituting in the original standard deviation of 12, we get: s*=0.6(12) = 7.2

Therefore, the new mean and standard deviation are (b) mean=95, standard deviation=7.2.

The volume of a cone is given by the formula:

V = (1/3) * π * r² * h

Where V is the volume, r is the radius, and h is the height.

In this case, we know the radius (4.96) and the volume (102), so we can use the formula to solve for the height.

Substituting the known values into the formula, we get:

102 = (1/3) * π * (4.96)² * h

Dividing both sides by (1/3) * π * (4.96)², we get:

h = 102 / [(1/3) * π * (4.96)²]

Substituting in the value for π, we get:

h = 102 / [(1/3) * 3.14 * (4.96)²]

Which simplifies to:

h = 102 / [(1/3) * 3.14 * 24.1952]

Which simplifies to:

h = 102 / (0.7853 * 24.1952)

Which simplifies to:

h = 102 / 19.1268

Which is approximately 5.33.

Therefore, the estimated height of the cone is approximately 5.33.

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Answer:

Step-by-step explanation:

The volume of a clone = 1/3 × π × r^2 × h

Volume, v = 102
Radius r = 4.96
r^2 = 4.96^2 = 24.6016  
Approximately = 24.6

π = 3.142
v = 1/3  x π x r^2 x h

Cross multiply

3v = π x r^2 x h

h = (3 x 102) / 24.6 x 3.142

h = 3.959 cm

I hope this was helpful

Answer:

Step-by-step explanation:

(a)  If the n's are placed first, 36 ways are there to choose positions for them. If the e's are placed second, 35 ways are there to choose positions for them. If the s's are placed third, 3 ways are there to choose positions for them. If the t is placed fourth, 1 way is there to choose a position for it.

(b)  If the e's are placed first, 126 ways are there to choose positions for them. If the t is placed second, 5 ways are there to choose a position for it. If the s's are placed third, 6 ways are there to choose positions for them. If the n's are placed fourth, 1 way is there to choose position for it.

(c) Part (b) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 36*35*3*1=3780. Part (a) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 126*5*6*1 =3780.

What is permutation of rearranging letters?

A permutation is a (possible) rearrangement of objects. For example, there are 6 permutation of rearranging letters a, b, c: abc, acb, bac, bca, cab, cba. a b c , a c b , b a c , b c a , c a b , c b a .

The total number of ways to reorder the letters in the word "tennessee" is calculated by considering the different ways the letters can be placed first, second, third, and fourth. The number of ways to place the n's first is 9!/(7!2!), the number of ways to place the e's second is 7!/(4!3!), the number of ways to place the s's third is 3!/2!1!, and the number of ways to place the t fourth is 1. When these values are multiplied together, the total number of ways to reorder the letters is 36*35*3*1=3780.

Again placing the letters into positions in a different order. The number of ways to place the e's first is 9!/(4!*5!), the number of ways to place the t second is 5!/(4!*1!), the number of ways to place the s's third is 4!/(2!*2!) and the number of ways to place the n's fourth is 2!/(2!*0!). When these values are multiplied together, the total number of ways to reorder the letters is 126*5*6*1 =3780.

Therefore, the total number of ways to reorder the letters in the word "tennessee" is 3780 in both orders.

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a) 36, 35, 3, 1 ways; b) 126, 5, 6, 1 ways; c) total number of ways to reorder the letters in the word tennessee is 3780 for both a) and b).

(a)  If the n's are placed first, 36 ways are there to choose positions for them. If the e's are placed second, 35 ways are there to choose positions for them. If the s's are placed third, 3 ways are there to choose positions for them. If the t is placed fourth, 1 way is there to choose a position for it.

(b)  If the e's are placed first, 126 ways are there to choose positions for them. If the t is placed second, 5 ways are there to choose a position for it. If the s's are placed third, 6 ways are there to choose positions for them. If the n's are placed fourth, 1 way is there to choose position for it.

(c) Part (b) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 36*35*3*1=3780. Part (a) is used to find the total number of ways to reorder the letters in the word tennessee, the result is 126*5*6*1 =3780.

What is permutation of rearranging letters?

A permutation is a (possible) rearrangement of objects. For example, there are 6 permutation of rearranging letters a, b, c: abc, acb, bac, bca, cab, cba. a b c , a c b , b a c , b c a , c a b , c b a .

The total number of ways to reorder the letters in the word "tennessee" is calculated by considering the different ways the letters can be placed first, second, third, and fourth. The number of ways to place the n's first is 9!/(7!2!), the number of ways to place the e's second is 7!/(4!3!), the number of ways to place the s's third is 3!/2!1!, and the number of ways to place the t fourth is 1. When these values are multiplied together, the total number of ways to reorder the letters is 36*35*3*1=3780.

Again placing the letters into positions in a different order. The number of ways to place the e's first is 9!/(4!*5!), the number of ways to place the t second is 5!/(4!*1!), the number of ways to place the s's third is 4!/(2!*2!) and the number of ways to place the n's fourth is 2!/(2!*0!). When these values are multiplied together, the total number of ways to reorder the letters is 126*5*6*1 =3780.

Therefore, the total number of ways to reorder the letters in the word "tennessee" is 3780 in both orders.

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The property scale factor make the similar shapes similar one.

The term shape in math refers the outline or the boundary of an object.

Here we need to find the property that makes the similar shape similar.

As per the definition of shape we have identified that the shape has the following property, they are listed as,

=> Length

=> Breadth

=> height.

All these are collectively called scaling factor,

Based on these values we have take the two similar shapes such as similar triangles, similar rectangles, similar square, are the shapes whose dimensions are in equal or common ratio but the size or length of their sides vary.

Therefore the common ratio is called the scale factor.

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Girls of 25  says Yes, 10 boys say No. 30 total Students say No, 45 girls total, with a total of 60 Students

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

An expression that uses numbers, variables, or both is a mathematical expression. The equal symbol is never used in expressions. Here are a few phrases as examples. A mathematical statement stating the equality of two expressions is known as an equation.

Given,

5 boys tell yes and total boys and girls tell yes is 30 by simplifying

no of girls tell yes =30 - 5= 25

no of girls tell no =20

overall total boys tell no = 15-5=10

The no of boys tell no =10

So total no of boys and girls tell no = 20+10=30

total no of girls tell yes and no =60-15=45

The complete question is  : You ask 60 of your classmates if they have any siblings. Complete the​ two-way frequency table to show the results of the survey.

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The velocity of Rosie when running is 2 meters per second

From the question, we have the following parameters that can be used in our computation:

Time = 1/3 of 78 seconds

Distance covered = 52 meters

The velocity can be calculated using the following equation

Velocity = Distance covered/Time

Substitute the known values in the above equation, so, we have the following representation

Velocity = 52/(1/3 * 78)

Evaluate the quotient

Velocity = 2

Hence, the velocity is 2 meters per second

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Answer:

9

Step-by-step explanation:

add all the numbers: 6+12+10+8=36

then divide by the amount of numbers there are: 36/4=9

A number is said to be prime if the integers smaller than its square root cannot divide it, as numbers higher than its square root cannot possibly do so.

A mathematical concept known as a square root is a factor of a number that, when multiplied by itself, equals the original value. For instance, 3 and -3 are the square roots of 9. Starting in the second millennium BC, the Babylonians created effective methods for approximating square roots.

here ,

In other words, if we encounter a number when counting from 2 to sqrt(N), and that number is a factor of N .

then indicates that the number has more than two factors and is thus not a prime number.

Otherwise, if we are unable to locate any factors for N, it is likely that N only has two factors, one and itself, making it a prime number.

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The average degree of variability in the dataset is represented by the standard deviation. It reveals the average deviation of each statistic from the mean.

Empirical principle

If your frequency distribution follows a normal distribution, the standard deviation and mean combined might help you determine where the majority of the values are located.

The 68-95-99.7 rule, often known as the empirical rule, reveals your values to you:

Thus, the standard deviation is a less trustworthy indicator of variability for non-normal distributions and should be combined with other metrics like range or interquartile range.

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The associative property looks like a + (b + c) = (a + b) + c.

According to the associative property, if 3 numbers are added or multiplied then the grouping of numbers does not change the final result.

The associative property is applicable in addition as well as in multiplication.

According to the associative property in addition - when 3 numbers, say a, b, and c are being added then their sum will not change even if the grouping of numbers is changed. It can be presented as:

(a + b) + c = a + (b + c)

According to the associative property in multiplication - when 3 numbers, say a, b, and c are being multiplied then their product will not change even if the grouping of numbers is changed. It can be presented as:

(a × b) × c = a × (b × c)

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A set X is a subset of set Y (Written as X ⊆ Y) if every element of X is an element of set Y.

A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.  

A set has many types, such as;

Empty Set or Null set: It has no element present in it.Example: A = {} is a null set.

Finite Set: It has a limited number of elements.Example: A = {1,2,3,4}

Infinite Set: It has an infinite number of elements.Example: A = {x: x is the set of all whole numbers}

Equal Set: Two sets which have the same members.Example: A = {1,2,5} and B={2,5,1}: Set A = Set B

Subsets: A set ‘A’ is said to be a subset of B if each element of A is also an element of B.Example: A={1,2}, B={1,2,3,4}, then A ⊆ B

Universal Set: A set which consists of all elements of other sets present in a Venn diagram.Example: A={1,2}, B={2,3}, The universal set here will be, U = {1, 2,3}

A set X is a subset of set Y (Written as X ⊆ Y) if every element of X is an element of set Y.

Example : − Let, X = { 1, 2, 3, 4, 5, 6 } and Y = { 1, 2 }. Here set Y is a subset of set X as all the elements of set Y is in set X. Hence, we can write Y ⊆ X.

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Only one three digits number 111 would satisfy this condition.

Let the three digits be x, y and z. Since the sum of the digits is equal to the product of the digits, we can write x + y + z = xyz

Simplifying the equation, we get x + y + z - xyz = 0

This is a quadratic equation in the form ax2 + bx + c = 0 where a = 1, b = 1 and c = -xyz

To solve this equation, we use the quadratic formula: x = [-b ± √(b2 - 4ac)]/2a

In this case, x = [-1 ± √(1 - (-4 * 1 * (-xyz))]/2

Since xyz must be a positive integer, the only solution is when the square root of 1 - (-4 * -xyz) is 0

This means xyz must be 1, so x + y + z = 1 + y + z = 3

Since x, y and z are all distinct digits, the only possible solution is when x = 1, y = 1 and z = 1, giving the solution 111.

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The fractions equivalent to 3/5 are 6/10, 9/15, 12/20, etc.

Now, According to the question:

Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number. This is the reason why these fractions get reduced to the same number when they are simplified.

Let us understand the two ways in which we can make equivalent fractions:

Hence, the equivalent fractions for 3/5 are:

(3/5) × (2/2) = (3 × 2) / (5 × 2) = 6/10

(3/5) × (3/3) = (3 × 3) / (5× 3) = 9/15

(3/5) × (4/4) = (3 × 4) / (5 × 4) = 12/20

Thus, 6/10, 9/15, 12/20 are equal to 3/5,

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Answer:

63 with 3 left over

Step-by-step explanation:

381/6=63.5

63x6=378

378+3=381

The value of the function (f o g )(11) is -1

Applying composite function formula,

(f o g )(x) = f [g (x)]

Here ,f(x) = [tex]\sqrt{x} - 3[/tex]

g (x ) = x - 7

(f o g )(x)  =f [x - 7 ]

                =[tex]\sqrt{x-7} -3[/tex]   --(1)

Substitute x = 11 in the given function in (1)

 [tex](f o g )(11) =\sqrt{11-7} -3\\(f o g )(11) =\sqrt{4} - 3\\(f o g )(11) = 2 -3 = -1[/tex]

The value of the function (f o g )(11) is -1

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Answer:c

Step-by-step explanation:

Answer: C) 5 years

Step-by-step explanation:

Formula for the simple interest is: I = P * r * t, where: I = $500, P = $2,500, r = 0.04 and t stays for the number of the years. 500 = 2,500 * 0.04 * t; 500 = 100 * t; t = 500 : 100; t = 5.