find the gradient vector field of f. f(x, y, z) = 6 x2 + y2 + z2

For the sample provided, The formula for standard deviation is slightly different than the population standard deviation. The answer is

[tex]\sqrt \frac{\sum (x-\bar x)^2}{n-1}[/tex] .

Sampling is the process of choosing a portion of a statistical population to estimate attributes of the entire population in statistics, quality control, and survey methods. Statisticians try to get samples that are typical of the population under consideration.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

sample size = n

sample standard deviation (s) = [tex]\sqrt \frac{\sum (x-\bar x)^2}{n-1}[/tex]

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The values of the input functions when put into the function are;

f(3) = 5

f(3²) = 9

f(-2) = 8/3

f(6) = 7

We are given the function to be represented as;

f(x) = ²/₃x + 3

Now, we are told that the input value of x are;

X = (3, 3², -2, 6)

Thus;

for f(3), we plug in the value of 3 into the function for x to get;

f(3) = ²/₃(3) + 3

f(3) = 2 + 3

f(3) = 5

for f(3²), we plug in the value of 3² into the function for x to get;

f(3²) = f(9) = ²/₃(9) + 3

f(3²) = 9

for f(-2), we plug in the value of -2 into the function for x to get;

f(-2) = ²/₃(-2) + 3

f(-2) = 8/3

for f(6), we plug in the value of -2 into the function for x to get;

f(6) = ²/₃(6) + 3

f(6) = 7

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The height of the pyramid BC is equal to 14 units if The base of a solid oblique pyramid is an equilateral triangle with a base edge length of 14 units

We have a right angled triangle BAC

Using the trigonometric formula

The tangent here = 45°

The opposite side, h (this is the side that is facing the angle)

The adjacent = 14°

This is due to the fact AD=DC=AC

When we put the values into the formula:

Tan 45= 1

When we cross multiply,

14*1 = h

Therefore the height of the pyramid BC is 14 units.

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The function Y = -3 is a linear function.This means that the graph of the function will be a straight line.

This is because the equation has only one variable (Y) and the change in Y is directly proportional to the change in the independent variable, in this case X.

To prove that the function is linear, we can use the formula y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is 0, as the line is horizontal, and the y-intercept is -3. Thus, we can calculate the equation as follows:

y = 0x + (-3)

y = -3

Therefore, we can conclude that the function Y = -3 is a linear function.

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Answer: 0

Step-by-step explanation:

slope = Δy/Δx

slope = (17-17)/(3-8) = 0

The average temperature on Saturday was 62.6 °F, then the actual temperature will be equal to 17 °C.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the given information in the question,

The temperature on Saturday was 62.6 F

Then, the actual temperature will be,

C = 5/9(F -32)

C = 5/9(62.6 - 32)

C = 5/9(30.6)

= 17 °C

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Answer:

Ok So From What You Said I Calculated This:

1:00-2:00

cars=c, trucks=t

answer=a

c x 3 = a

a÷3=t

Step-by-step explanation:

Answer:Ok So From What You Said I Calculated This:

1:00-2:00

cars=c, trucks=t

answer=a

c x 3 = a

a÷3=t

Step-by-step explanation: I rlly hope this helps please mark brainliest thanks for the points! please tell meif im wrong have a good day night!! :)

A summary table of the given data set is given below.

You can compare typical study methodologies, conclusions, limits, etc. using a summary table. You can arrange the entries in any way you find convenient; for example, you might arrange your research according to timeliness or group entries with comparable study aims, models, or outcomes.

Only code:

d=read.csv(file.choose(),header = T) ### data file is selected after this command run

dataframe=as.data.frame(d) ### a) creating data frame

last_15=tail(data frame,15) # b) last 15 observation

last_15

str(d)

par(mfrow=c(2,2)) ## c) Plots

plot(d[,5],d[,2])

plot(d[,5],d[,3])

plot(d[,5],d[,4])

model=lm(d$sales~d$TV,data = d) # d) linear model

summary(model) ## summary of model

plot(model,color="red") ## plot model

code and output:

d=read.csv(file.choose(),header = T) ### data file is selected after this command run

dataframe=as.data.frame(d) ### a) creating data frame

last_15=tail(data frame,15) # b) last 15 observation

last_15

X                  TV       radio       newspaper       sales

186       205.0           45.1                 19.6             22.6

187       139.5             2.1                  26.6             10.3

188       191.1              28.7                18.2             17.3

189       286.0            13.9                3.7             15.9

190       18.7               12.1                 23.4             6.7

191       39.5               41.1                 5.8             10.8

192       75.5              10.8               6.0             9.9

193       17.2               4.1                 31.6             5.9

194       166.8            42.0              3.6             19.6

195       149.7            35.6              6.0             17.3

196       38.2              3.7                13.8             7.6

197       94.2              4.9               8.1             9.7

198       177.0            9.3               6.4             12.8

199       283.6           42.0            66.2             25.5

200       232.1           8.6               8.7            13.4

str(d)

'data. frame': 200 obs. of 5 variables:

X: int 1 2 3 4 5 6 7 8 9 10 ...

TV : num 230.1 44.5 17.2 151.5 180.8 ...

radio: num 37.8 39.3 45.9 41.3 10.8 48.9 32.8 19.6 2.1 2.6 ...

newspaper: num 69.2 45.1 69.3 58.5 58.4 75 23.5 11.6 1 21.2 ...

sales: num 22.1 10.4 9.3 18.5 12.9 7.2 11.8 13.2 4.8 10.6 ...

par(mfrow=c(2,2)) ## c) Plots

plot(d[,5],d[,2])

plot(d[,5],d[,3])

plot(d[,5],d[,4])

model=lm(d$sales~d$TV,data = d) # d) linear model

summary(model) ## summary of model

Call:

lm(formula = d$sales ~ d$TV, data = d)

Residuals:

Min 1Q Median 3Q Max

-8.3860 -1.9545 -0.1913 2.0671 7.2124

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 7.032594 0.457843 15.36 <2e-16 ***

d$TV 0.047537 0.002691 17.67 <2e-16 ***

---

Sign in. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 3.259 on 198 degrees of freedom

Multiple R-squared: 0.6119, Adjusted R-squared: 0.6099

F-statistic: 312.1 on 1 and 198 DF, p-value: < 2.2e-16

plot(model,color="red") ## plot model

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You can tell if a graph is positive or negative infinity by looking at the slope of the graph. Positive infinity means the slope is increasing without bound, while negative infinity means the slope is decreasing without bound.

In order to determine if a graph is positive or negative infinity, you need to look at the slope of the graph. Slope is a measure of the steepness of a line and is calculated by looking at the change in y-values divided by the change in x-values. If the slope of the graph is increasing without bound, this means that the graph is approaching positive infinity. On the other hand, if the slope of the graph is decreasing without bound, the graph is approaching negative infinity. This means that the y-values are getting closer and closer to negative infinity as the x-values get larger. You can also look at the graph itself to get an idea of the direction of the graph. If the graph is increasing without bound, the graph is approaching positive infinity, while if the graph is decreasing without bound, it is approaching negative infinity.

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Yes, both the rates i.e. 24 laps in 6 minutes and 72 laps in 18 minutes are equivalent.

The unit rates for equivalent rates are the same. Similar to equivalent ratios, equivalent rates can be calculated by multiplying or dividing the numerator and denominator by the same amount.

When two expressions can be reduced to a single-third expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. When values are replaced for the variable and both expressions yield the same result, you may also tell if the two expressions are equal.

To determine whether the rates are equivalent, we need to compare the number of laps completed per unit of time. In the first case, the rate is 24 laps in 6 minutes, which is equal to 4 laps per minute. In the second case, the rate is 72 laps in 18 minutes, which is also equal to 4 laps per minute. Since both rates are equal to 4 laps per minute, the rates are equivalent.

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The rates of 24 laps in 6 minutes and 72 laps in 18 minutes are equal, therefore yes.

Equivalent rates have the same unit rates. Equivalent rates can also be determined by multiplying or dividing the numerator and denominator by the same number, just like equivalent ratios.

Two expressions are considered to be equivalent if one of them can be written in the same way as the other or if they can both be condensed to a single-third expression. You may also tell if two expressions are equivalent if, when the values for the variable are changed, both expressions provide the same outcome.

In order to determine whether the rates are similar, we must compare the number of laps completed per unit of time. The pace in the first scenario is 4 laps per minute, or 24 laps done in 6 minutes. When 72 laps are completed in 18 minutes, the rate is similarly 4 laps per minute. Due to the fact that they both equal 4 laps per minute, their rates are equal.

Answer:

135 degree or 33/14 radian

Step-by-step explanation:

It is given that the arc HK= 33cm and the radius of the circle is 14cm

We can think of the angle subtended by arc HK as x

we know,

[tex] arc = \: radius \: \times angle(in \: radian)[/tex]

or

[tex]angle =\frac{arc}{radius} [/tex]

So,in the question above the arc HK= 33cm and the radius is 14cm

So, angle x is equal to,

[tex]x = \frac{33}{14} [/tex]

Thus,

the angle is,

[tex]angle \: = \frac{33}{14} radians[/tex]

and if u want to know the degree value we know,

[tex]1radian \: = \: \frac{180}{\pi} degree \:[/tex]

so,

[tex] \frac{33}{14} radian \: = \frac{33}{14} \times \frac{180}{\pi} degree[/tex]

[tex]which \: is \: = 135 \: degree[/tex]

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It’s discriminant is zero, so it has one real solution statement is true for  x²-2x +1=0.

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The given quadratic equation is x²+1=2x

This can also be written as x²-2x +1=0

a=1, b=-2 and c=1

The expression b² − 4ac is called the discriminant, and can be used to determine whether the solutions are real, repeated, or complex.

(-2)² − 4(1)(1)=4-4

b² − 4ac= 0

A discriminant of zero indicates that the quadratic has a repeated real number solution.

It’s discriminant is zero, so it has one real solution.

Hence, It’s discriminant is zero, so it has one real solution statement is true for  x²-2x +1=0.

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Linear equations are one-degree equations, it is formulated as: ax + by + c = 0.

A linear equation has the following standard form: ax + by + c = 0.

Here, variables x and y and constants a, b, and c are used.

Also, a ≠ 0, and b ≠ 0.

For linear equations, the slope-intercept formula is: y=mx+b

Where m stands for the line's slope and b represents the y-intercept.

The three types of linear equations are point-slope, slope-intercept, and standard form.

When an algebraic equation is graphed, it always produces a straight line since each term has an exponent of 1 or 0. This type of equation is known as a linear equation.

Steps are -

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the symbol for inequality with that for equality.

Step 3: In the xy plane, graph the boundary line from step 2. You are creating the boundary line that would divide or cut the xy-plane into two sections in this stage.

Step 4: Shading one side or area of the boundary line is the final step.

Step 5: Use this optional step to check or confirm that you have shaded the boundary line's side appropriately.

So, the region of the coordinate plane where the inequality is satisfied is shown by a linear inequality.

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The required mean of the values 20 and 40 is 30.

The total of all numbers multiplied by the total number of values yields the mean (also known as the arithmetic mean, which varies from the scaling factor) of a dataset.

The term "average" is frequently used to describe this central trend measurement.

So, we have the values:

20, 40

Mean formula: Sum of terms / Number of terms

Obtain mean using the formula as follows:

Mean: Sum of terms / Number of terms

Mean: 60/2

Mean: 30

Therefore, the required mean of the values 20 and 40 is 30.

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The ordered pair that is a solution to both equations is the solution of such a system graph.

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Answer:

10. Some of the class 4 children Amar, Bindu, Charisma, Danny are friends with some of the class 5 children Amar Diana Ekta Raghu Prem. The following table tells us which 2 children are friends with each other.

11. A

12. 20 cm - 2(4cm) = 12

2(6cm length) + 2(4cm width) = 20 cm

12 + 8 = 20 cm

area = length * width

area = 6 * 4

area = 24 cm²

Step-by-step explanation:

The multiple inverse of 16 is 0.0625.

1/N or N-1 is used to denote a number's multiplicative inverse, such as the number N. It also goes by the name reciprocal.

Inverse refers to something that is the opposite. The acquired reciprocal of a number is such that its value equals identity 1 when multiplied by the original number. In other terms, it is a technique for producing identity 1 by diluting a number by itself, as in N/N = 1.

Inverse of x = 1/x  or  x⁻¹.

It is also called as the reciprocal of a number and 1 is called the multiplicative identity.

Let the multiple inverse of 16 is x, then

16 * x = 1

⇒ x = 1/16

⇒ x = 0.0625

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the 4 parallel line rules are Alternate angles are equal. ...Co-interior angles add to 180° ...Vertically opposite angles are equal. ...Angles on a line add to 180°

What are the 4 parallel line rules?

Working with angles in parallel lines

Corresponding angles are equal. A line cutting across two parallel lines creates four pairs of equal corresponding angles, as in the diagram below: ...

Alternate angles are equal. ...

Co-interior angles add to 180° ...

Vertically opposite angles are equal. ...

Angles on a line add to 180°

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Answer:

n = 6

Step-by-step explanation:

-15 + n = -9

Add 15 to both sides

n = 6

So, the answer is 6

We can find sample mean by:

Sample Mean = Sum of terms [tex]\div[/tex] Number of Terms

We can find range by:

Range = Highest Value (H) - Lowest Value (L)

Sample mean:

Sample mean represents the measure of the center of the data. Any population's mean is estimated using the sample mean.

An average value found in a sample is termed the sample mean. the sample mean so calculated is used to find the variance and thereby the standard deviation.

Sample Mean = Sum of terms [tex]\div[/tex] Number of Terms

[tex]& =\frac{\sum x i}{n} \\& =\frac{\left(x_1+x_2+x_3+\ldots+x_n\right)}{n}[/tex]

Range:

The range formula determines the difference between the highest and the lowest values in a given set of numbers.

In distribution, the large range means higher variability whereas the small range means low variability.

The range formula includes the other aspects of statistics such as mean, median, and mode. Hence, the formula to calculate the range is:

R = Highest Value (H) - Lowest Value (L)

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How do you find the sample mean and range?

Answer:

they are called whole numbers

Step-by-step explanation:

The leading coefficient and the constant term must both be divisible by the fraction's denominator in order to factor using the rational root theorem.

In plants, a stem's primary role is to aid in the transfer of water and minerals from the roots to the leaves and other sections of the plant. Additionally, it supports the buds, leaves, flowers, fruits, and branches of plants.

The rational root theorem, also known as the rational root test, is an algebraic principle that states that for a polynomial equation with one variable and integer coefficients to have a solution (root) that is a rational number, both the leading coefficient and the constant term must be divisible by the fraction's denominator.

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Answer:

Mohammed ibn-Musa al-Khowarizmi

Answer:

53/8, 6 17/25, 6.71, 6.713

Step-by-step explanation:

6.713, 6.71, 53/8, 6 17/25

53/8 = 6.625

6 17/25 = 167/25 = 6.68

So, the order from least to greatest is: 53/8, 6 17/25, 6.71, 6.713

The concept of zero as a number and not merely a symbol for separation was developed by ancient Indian mathematicians as early as the 7th century CE, where it was used to represent the null set, or void in mathematics. However, the invention of zero as a number is attributed to Indian mathematician Brahmagupta in 628 CE.

The concept of zero as a number was developed by ancient Indian mathematicians in the 7th century CE. It was used to represent the null set, or void in mathematics. This concept was further developed by Indian mathematician Brahmagupta in 628 CE. He is credited with the invention of zero as a number and not merely a symbol for separation. Brahmagupta used zero to represent both positive and negative numbers, and developed rules for calculations with zero. This allowed mathematicians to develop the operations of arithmetic and algebra. Today, zero is an integral part of mathematics, and is used in many fields such as calculus and analysis. The invention of zero as a number is credited to Brahmagupta, and it is one of the most influential contributions to mathematics

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The confidence interval of p+/-E is 0.555+/-0.444

A confidence interval is often represented as the estimated value plus and minus the margin of error.

Let the mid-point of the interval be 'p'

Therefore,'

[tex]p=\frac{0.111+0.999}{2} =0.555[/tex]

Now,

The error term 'E' is the distance between 'p' and the end of the interval.

[tex]E=\frac{0.999-0.111}{2} =0.444[/tex]

So finally we get, the answer as

p+/-E = 0.555+/-0.444

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Answer:

the answers it's 3x+4 siuuuuuuuuuuuuuyyyyy

The expression can be evaluated using the property of zeros as 0.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

The given equation is x³ - 3x + 1 = 0.

Its zeros are given as x₁, x₂ and x₃.

As per the properties of zeros of a cubic equation, the  following expressions can  be written as,

x₁x₂x₃ = Constant term ÷ Coefficient of x³

⇒ x₁x₂x₃ = 1.

And,  x₁x₂ + x₂x₃ + x₁x₃ =  Coefficient of x² ÷  Coefficient of x³

⇒ x₁x₂ + x₂x₃ + x₁x₃ = 0.

Now, the given expression 1/x₁ + 1/ x₂ + 1/x₃ can be evaluated as below,

(x₁x₂ + x₂x₃ + x₁x₃)/x₁x₂x₃  = 0/1

⇒ 0

Hence, the given expression can be evaluated as 0.

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 The rational root theorem, also known as the rational zero theorem or the rational root test, holds that a single-variable polynomial with integer coefficients has rational roots if and only if constant term and leading coefficients are both divisible by the root's numerator and denominator, respectively.

    A theorem that is applied to polynomial roots is known as the rational root theorem or the rational zero test. The values of the variable that bring the polynomial to zero are known as the roots. Since the number of exact roots for a particular polynomial is always equal to the degree of the polynomial, we can determine this information from the polynomial's degree.

     For a linear polynomial, there is only one root, for instance. The number of zero roots in a cubic polynomial is three, whereas the number of  zero roots in a quadratic polynomial is two.

   f(x)=aₙxⁿ+aₙ₋₁xⁿ⁻¹+aₙ₋₂xⁿ⁻²+a₂x²+a₁x+a₀  where the coefficients aₙ to a₀ are all integers.

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A theorem that is applied to polynomial roots is known as the rational root theorem or the rational zero test. The values of the variable that bring the polynomial to zero are known as the roots. Since the number of exact roots for a particular polynomial is always equal to the degree of the polynomial, we can determine this information from the polynomial's degree.

f(x)=aₙxⁿ+aₙ₋₁xⁿ⁻¹+aₙ₋₂xⁿ⁻²+a₂x²+a₁x+a₀  where the coefficients aₙ to a₀ are all integers.