The result of adding the numbers in the given data set

489
527
758

To calculate the average (mean) value of a function, you need to find the area under the curve of the function, divide it by the interval over which the function is defined, and then find the value of the function at the midpoint of the interval.

In this case, the function is 3t³ - t² and we need to find an interval to calculate the average (mean) value. A common interval used for this calculation is from 0 to 1.

The area under the curve of the function from 0 to 1 can be found by integrating the function from 0 to 1. However, to keep it simple, we can also use the definite integral of the function from 0 to 1, which is:

∫ (3t³ - t²) dt = 3t⁴/4 - t³/3 | from 0 to 1

= (3/4) - (1/3) = 1/4

So, the average (mean) value of the function 3t³ - t² over the interval 0 to 1 is: 1/4 ÷ 1 = 1/4

And the value of the function at the midpoint of the interval, which is 0.5, is: 3(0.5) ³ - (0.5) ² = 3/8 - 1/4 = -1/32

So, the average (mean) value of the function 3t³ - t² over the interval 0 to 1 is -1/32.

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The slope of the linear equation perpendicular to:

x - 6y = 24

is a = -6.

A general line can be written in the slope-intercept form as:

y = a*x + b

Where a is the slope and b is the y-intercept.

Particularly, two lines are perpendicular if the product between their slopes is equal to -1.

Here we want to find a line perpendicular to:

x - 6y = 24

First, we need to find the slope of this line.

x - 6y = 24

-6y = -x + 24

y = (-1/6)*-x - 24/6

y = (1/6)*x - 3

The slope is 1/6, then if the slope of the perpendicular line is a, the slope must be a solution of:

a*(1/6) = -1

a = -6

The slope of the perpendicular line is -6.

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Answer:

5 km / 15 km/h = 0.3333 hours

Step-by-step explanation:

This is calculated by dividing the distance he has to travel (5 km) by his average speed (15 km/h) and then converting the result to minutes.

0.3333 hours x 60 minutes/hour = 20 minutes

Answer:

a = 15 , b = [tex]\frac{2}{9}[/tex]

Step-by-step explanation:

the equation of proportion is

y = kx ← k is the constant of proportion

to find k substitute x = 0.7, y = 2.1 , values from the table into the equation

2.1 = 0.7k ( divide both sides by 0.7 )

3 = k

y = 3x ← equation of proportionality

then using x = 5

a = 3 × 5 = 15

using y = [tex]\frac{2}{3}[/tex]

[tex]\frac{2}{3}[/tex] = 3b ( multiply both sides by 3 to clear the fraction )

2 = 9b ( divide both sides by 9 )

[tex]\frac{2}{9}[/tex] = b

The value of x and y in right angle triangle is  16√2 and 16

What is a Right Angle Triangle ?

A right triangle is a triangle having one right angle or two perpendicular sides. It is also referred to as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle. The relationship between the sides and various angles of the right triangle serves as the basis for trigonometry.

The Pythagorean theorem, often known as Pythagoras' theorem, in Euclidean geometry relates the three sides of a right triangle. This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

In the triangle 2 angles are 90° and 45° respectively.

The third angle is  = 180°+90°-45°=45°

The triangle is issosceles triangle

So the side which is not x is 16.

Now by using Pythagoras Theorem

x = √16^2+16^2 = 16√2

The value of x is 16√2

The value of y is y^2 + 16^2 = 16√2^2

y^2 = 512 - 256

y^2 = 256

y = 16

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For you to make 5 pecan pies, it would be necessary to buy 1.9 pounds of pecans.

Based on the information displayed on the label 1 cup of pecans is equal to 99 grams.

We know 1 pecan pie requires  1 3/4 cups or 1.75 cups (3/4 = 0.75)

1.75 x 5 = 8.75 cups in total

Now, let's calculate this in grams:

8.75 x 99 = 866.22 grams

Finally, let's calculate the pounds

1 pound = 453

 x           = 866.22

x = 866.22 / 453 = 1.9

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The answer is pint of milk

A mixture refers to the mix that is derived as a result of mixing two or more items or substances in a certain ratio or proportion.

Given here: 1 tablespoon of grape juice is mixed into the milk and 1 tablespoon of this mixture is mixed with grape juice.

Thus the milk is more contaminated as the latter mixture contains some amount of grape juice and as a result the grape juice mixture is not contaminated to the extent of the pint of milk.

Hence, The answer is pint of milk

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Answer:

D

Step-by-step explanation:

26+169=0

The hourly pay that was charged for the repairs to Victor's car was $ 57.14

To find the hourly wage, find the total labor wages that were charged as a cost to Victor's repairs. This cost would be:

= 272 - 6 - 28. 50 - 20 .00 - 15. 00 - 2. 50

= $ 200

The total hourly wage charged was $ 200 for 3 . 5 hours of work.

This means that the hourly pay charged was :

= Total labor wages / Number of hours

= 200 / 3 . 5

= $ 57.14

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A normal distribution with a mean of 0 and a standard deviation of 1 is called a standard normal distribution.

Tables of the standard normal distribution are frequently used to show different regions of the normal distribution. A standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

Tables of the standard normal distribution are frequently used to show different regions of the normal distribution.The standard deviation reveals the degree of data skewedness. It gauges how far away from the mean each observed value is. Approximately 95% of values in any distribution will be within two standard deviations of the mean.

A sigma value, typically represented by the Greek letter or lower case s, is a measure of how far a sample or point of data is from its mean. It is given in standard deviations.

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Answer and explanation: The equation for the slope-intercept form is y=mx+b. M represents the slope and b is y-intercept/when x= 0.

We have to arrange the given equation into the form y=mx+b.

3x+2y=-14, We want to somehow isolate y.

2y=-14-3x, We can move all the terms that don't have y to the right

y=(-14-3x)/2, We can get rid of the 2 by dividing by 2 on both sides

y=-7-(3/2)x, We can distribute the division by 2 to both terms on the right

y=-(3/2)x-7, We can now just rearrange the terms

The equation is now in the form y=mx+b as -3/2 is m and -7 is b. Your answer to the first question is A.

For part B, we can use the equation for part A. We know m or the slope is -3/2 so our answer is also A.

Expressions → Type of factoring

3x³ + 15x² + 2x + 10 → Grouping

x³ + 27 → Sum of cubes

2x² + 6x → Greatest common factor

x² - 25 → Difference of squares

x² + 6x + 8 → Unfoil

x³ - 1 → Difference of cubes

'Factor' is a term used to express a number as a product of any two numbers. Factorization is a method of finding factors for any mathematical object, be it a number, a polynomial or any algebraic expression. Thus, factorization of an algebraic expression refers to finding out the factors of the given algebraic expression.

Given expressions

Using grouping method

= (3x³ + 15x²) + (2x + 10)

= 3x²(x + 5) + 2(x + 5)

Factoring out common term

= (x+5)(3x² + 2)

It can be written as

= x³ + 3³

Which is sum of cubes

it can be written as

= 2x.x + 2x.3

GCF (greatest common factor) = 2x

= 2x (x + 3)

It can be written as

= x² - 5²

which is difference of squares

= x² + 4x + 2x + 8

= x(x + 4) + 2(x + 4)

= (x + 4) (x + 2)

Which is unfoil.

it can be written as

= x³ - 1³

which is difference of cubes.

Hence, the factoring of expressions 3x³ + 15x² + 2x + 10, x³ + 27,  2x² + 6x, x² - 25, x² + 6x + 8, x³ - 1 refers to grouping, sum of cubes, greatest common factor, difference of squares, unfoil and difference of cubes respectively.

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Answer:

[tex]k = 2[/tex]

Step-by-step explanation:

[tex]\textrm{P(blue \;bead)} = \dfrac{\textrm{Number of blue beads}}{\textrm{Total number of beads}}\\\\\textrm {Number of blue beads } = k\\\\\textrm{Total number of beads } = k + 4\\\\[/tex]

[tex]\textrm{P(blue \;bead)} = \dfrac{k}{k+4}\\\\[/tex]

[tex]\textrm{We are given this probability as } \dfrac{1}{3}\\\\\textrm{So,}\\\\\dfrac{k}{k+4} = \dfrac{1}{3}\\\\[/tex]

Cross-Multiplying this equation we get
[tex]k\cdot 3 = 1 \cdot (k + 4)\\\\\longrightarrow 3k = k + 4\\\\3k - k = 4\\\\2k = 4\\\\k = 2\\\\[/tex]

The amount of pints of punch that Jason served is; 52 pints

Algebraic word problems are defined as the questions that require translating sentences to equations, then solving those equations. and a single variable.

We are given that;

Amount of punch made = 8 gallons

Amount of punch left after serving = 12 pints

Now, conversion of pints to gallon is;

1 pint = 0.125 gallons

Thus;

12 pints = 1.5 gallons

Thus;

Amount of pints served = 8 - 1.5 gallons

= 6.5 gallons

Converting to pints gives 52 pints

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This is false, hence, the portion of the graph which does not contain (0, 0) is shaded.

Given the inequalities :

y ≥ 2x + 1

y ≤ 2x - 2

From y ≥ 2x + 1 ;

Since the inequality sign is ≥, a solid line is used to draw the straight line graph of  y ≥ 2x + 1

From :

y = mx + c

Where, m = slope ; c = intercept

Hence, a straight line graph with ;

Intercept, c = 1 (where the line crosses the y-intercept)

Slope, m = 2

Consider a point, which isn't on the line ;

Take point (0,0) and use it to test the inequality :

0 ≥ 2(0) + 1

0 ≥ 0 + 1

0 ≥ 1

Since this is untrue, the area of the graph that does not contain (0, 0) is shaded.

From : y ≤ 2x - 2

Since the inequality sign is ≤, a solid line is used to draw the straight line graph of  y ≤ 2x - 2

Graph the line y ≤ 2x - 2, with ;

Intercept, c = - 2

Slope = 2

Consider a point, which isn't on the line ;

Take point (0,0) and use it to test the inequality y ≤ 2x - 2:

0 ≤ 2(0) - 2

0 ≤ 0 - 2

0 ≤ - 2

This is untrue, hence the area of the graph that doesn't include (0, 0) is shaded.

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Let f be a function defined on all of that satisfies the additive condition is,

f(x) = [tex]kx[/tex] for every x∈ R.

It is given that:

f: R → R is a continuous function such that:

[tex]f(x+y)[/tex] = [tex]f(x) + f(y)[/tex]    ∀  x , y ∈ R  (Equation-1)

Now, let us assume f(1)=k

Also,

f(0) = 0( Since, f(0)=f(0+0)

That is,

f(0)=f(0)+f(0)

By using property (1)

Also,

f(0)=2f(0)

That is,

2f(0)-f(0)=0

That is,

f(0)=0  )

Also,

f(2)=f(1+1)

That is,

f(2)=f(1)+f(1)         ( By using property (1) )

i.e.

f(2)=2f(1)

That is,

f(2)=2k

Similarly for any m ∈ N

f(m)=f(1+1+1+...+1)

That is,

f(m)=f(1)+f(1)+f(1)+ ....... +f(1) (m times)

That is,

f(m)=mf(1)

That is,

f(m) = [tex]mk[/tex]

Now,

f(1) = [tex]f(\frac{1}{n} +\frac{1}{n} +......\frac{1}{n} )[/tex]

f(1) = [tex]f(\frac{1}{n} )+f(\frac{1}{n} )+......f(\frac{1}{n} )[/tex]

f(1) = n [tex]f(\frac{1}{n} )[/tex]

f(1) = k

[tex]f(\frac{1}{n} )[/tex] = k * [tex]\frac{1}{n}[/tex]

Also,

when x∈ Q

[tex]x = \frac{p}{q}[/tex]

Then,

[tex]f(\frac{p}{q})[/tex] = [tex]f(\frac{1}{q} )+ f(\frac{1}{q} )+ .....f(\frac{1}{q} )[/tex]

[tex]f(\frac{p}{q})[/tex] = p * [tex]f(\frac{1}{q} )[/tex]

[tex]f(\frac{p}{q})[/tex] = [tex]p\frac{k}{q}[/tex]

[tex]f(\frac{p}{q})[/tex] = [tex]k\frac{p}{q}[/tex]

So,

[tex]f(x) = kx[/tex] for all x belongs to Q

Now, as we know that:

Q is dense in R.

So Э x∈ Q' such that Э a seq < [tex]x_{n}[/tex] >  belonging to Q such that:

< [tex]x_{n}[/tex] > ⇒[tex]x[/tex]

Now, we know that: Q'=R

This means that:

Э α ∈ R

such that Э sequence [tex]a_{n}[/tex] such that:

[tex]a_{n}[/tex] belongs to Q,

[tex]a_{n}[/tex] ⇒ [tex]\alpha[/tex]

[tex]f(a_{n} )= ka_{n}[/tex]

( since [tex]a_{n}[/tex] belongs to Q )

Let f is continuous at x=α

This means that:

[tex]f(a_{n} )[/tex] ⇒ [tex]f(\alpha )[/tex]

k [tex]a_{n}[/tex] ⇒ [tex]f(\alpha )[/tex]

k [tex]a_{n}[/tex] ⇒ k [tex]\alpha[/tex]

This means that:

[tex]f(\alpha )[/tex] = k [tex]\alpha[/tex]

This means that:

f(x) = [tex]kx[/tex] for every x∈ R

Therefore,

Let f be a function defined on all of that satisfies the additive condition is,  f(x) = [tex]kx[/tex] for every x∈ R.

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Answer:33

Step-by-step explanation:

49-16=33

Using Pythagoras theorem, the altitude a is √33.

The Pythagorean theorem, a cornerstone of Euclidean geometry, connects the side lengths of a right triangle via the straightforward formula a² + b² = c². Ancient scholars and architects from Babylon, Egypt, China, and India were aware of the connection.

While Pythagoras lived and wrote between 569 and 475 BCE, the work that bears his name first appeared on clay Babylonian tablets around 1800 BCE. Early Chinese scholars were also aware of the Pythagorean theorem, and it was mentioned in ancient Indian sacred texts that dealt with the construction of altars.

To solve a,

We can see a right triangle forming by those 3 squares

Lets take theirs sides as the base, altitude and hypotenuse

Hypotenuse = 7

Base = 4

Altitude = to find

Using Pythagoras theorem

[tex]a^2 + b^2 = c^2[/tex]

[tex]\Rightarrow a = \sqrt{c^2 - b^2 }[/tex]

[tex]\Rightarrow a = \sqrt{7^2 - 4^2 }[/tex]

[tex]\Rightarrow a = \sqrt{49 - 16 }[/tex]

[tex]\Rightarrow a = \sqrt{33 }[/tex]

Thus, Using Pythagoras theorem, the altitude a is √33.

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You need to know the direction of the line and at least one point on it in order to parametrize a line. x is  5 + 4.0t ,y is  0 + 4.0t

x = 5 + 4.0t

y = 0 + 4.0t

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On solving the provided question we can say that the Measure of complementary angles   ∠ZY is 40 degrees.

When the sum of the measurements of two angles is 90 degrees, they are said to be complimentary.For instance, the angles of 30 and 60 degrees are supplementary. A supplementary angle is two angles combined to make a 180 degree angle, while a supplemental angle is two angles combined to make a 90 degree angle. Two angles are referred to as complimentary if their total is 90 degrees. Alternatively said, a right angle is created by the complementary angles (90 degrees).

Since ∠ZS and ∠ZY are complementary,

∠ZY+∠ZS=45                                                                                       We also have another relation which says

∠ZS=2∠ZY -30

Substituting 2. in 1. gives

∠ZY+2∠ZY -30=90

3∠ZY=120

∠ZY=40

Hence the measure of angle is 40 degrees.

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The likelihood that the basketball player will convert at least six of his or her eight free throw tries is 0.32.

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics refers to the study of events subject to probability.

The ratio of all potential cases to the number of cases that are favorable to an event determines its likelihood when there is no reason for us to believe that any one of these circumstances will happen more frequently than any other, making them all equally likely.

The likelihood that an event will occur is quantified by probability. The probability of an event is the relative frequency throughout time of that event. Probabilities are all numbers between 0 and 1, inclusive—that is, any numbers between 0 and 1.

Therefore, the correct answer is option d) 0.32.

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The company Sea Esta can elect a president, vice-president, secretary and treasurer in 495 different ways.

What is Combination in Mathematics?

In mathematics, a combination is a way of selecting a certain number of items from a larger set of items, without regard to the order in which the items are selected. It is a way to count the number of distinct subsets of a given size from a larger set.

The formula for combination is:

(n!) / (r! * (n-r)!)

The company Sea Esta has 12 members on its board of directors, and they need to elect a president, vice-president, secretary, and treasurer. The number of ways to elect these four positions is determined by using the formula of combination, which is:

Where n is the total number of options (in this case, the number of board members) and r is the number of positions to be filled (in this case, 4).

So, the number of ways to elect a president, vice-president, secretary, and treasurer is:

(12!) / (4! * (12-4)!) = (1211109) / (4321) = 495

Therefore, the company Sea Esta can elect a president, vice-president, secretary and treasurer in 495 different ways.

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Answer:

Text are too tiny for me to see sorry

Answer:

2.5

Step-by-step explanation:

P=29

w+w=4+4=8(rule of perimeter is 2w+2L)

29-8=21

21-16=5(L+L=8+8=16)

5 will be over 2 since it's for the 2 sides so 5÷2=2.5

your welcome

Part (a)

[tex]\lim_{h \to 0} \frac{(h-1)^5+1}{h} \\ \\ =\lim_{h \to 0} \frac{5(h-1)^4}{1} \\ \\ =\boxed{5}[/tex]

Part (b)

[tex]y+1=5(x+1) \\ \\ y+1=5x+5 \\ \\ \boxed{y=5x+4}[/tex]

Answer:

Using the substitution method, we know that the values of A is 19,200.

The substitution method is typically used in mathematics to solve an equation system.

In this approach, you solve the equation for one variable first, then you enter its value into the other equation.

So, we know that:

I = 240

W = I / 3

A = I * W

A = ?

Now, keep substituting the values to get A as follows:

I = 240

W = 240/3

W = 80

A = I * W

A = 240 * 80

A = 19,200

Therefore, using the substitution method, we know that the values of A is 19,200.

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The quadratic equation are y= 5x-3/2+x^2, y= x^2+5x-2 and y= x-1/x.

it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.

Here,

A. y= 5x-3/2+x^2

It has a degree is 2, So quadratic equation.

B. y= x^2+5x-2

It has a degree is 2, So quadratic equation.

C. y=-x+2

It has a degree is 1, So it's not quadratic equation.

Hence the value of k is 0.33.

D. y= x-1/x

y = x² -1/x

It has a degree is 1, So it's not quadratic equation.

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The percentage of  concentration of sugar in water will be 166.67%.

Concentration is the ability to focus on a single task or activity for an extended period of time. It requires both mental and physical effort, and involves staying attentive and motivated. Concentration helps us achieve our desired outcomes and complete tasks more efficiently. It also improves our ability to retain information, allowing us to better understand and remember what we have learned. Practicing concentration can lead to improved mental health, increased productivity, and better problem solving skills.

50/30 = x/100

30x = 100 × 50

30x = 5000

x = 166.67 %

Thus, The percentage of  concentration of sugar in water will be 166.67%.

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Answer:

x <= 1.

Step-by-step explanation:

Let x be the number of jeans Jordan can purchase.

We know that the total cost of the leather jacket, hat and jeans is $45 + $10 + $35x = $45 + $10 + $35x.

We also know that the total cost cannot exceed the amount of money Jordan has, which is $90.

So we can write the inequality: $45 + $10 + $35x <= $90

Solving for x, we get: $35x <= $35

x <= 1

So the number of jeans Jordan can purchase is x <= 1.

Answer:

4 * 24 - 9 = 87 cookies left.

Step-by-step explanation:

Answer: 48.6 minutes

Step-by-step explanation:

First find the total square feet:

9 x 9 = 81

Next, divide this by the increments give:

81 / 75 = 1.08

Now, the increments were each 45 minutes, so multiply this by the product:

45 x 1.08 = 48.6