Let f(x)= -4x-1 and g(x)= x^2 +3. Find (f o g)(-6).

12/√3 is  the direction of the vector v .

What does a basic math vector mean?

A thing with both magnitude and direction is called a vector.

                               A vector can be visualized geometrically as a directed line segment, where the direction is indicated by an arrow and the length of the segment equals the magnitude of the vector.

Normalize (make length 1) the vector v = <1, 1, -1>.

||v|| = √(1^2 + 1^2 + (-1)^2) = √3.  

So, the unit vector u is given by u = v/||v|| = <1, 1, -1>/√3.  

To find the rate of change of the potential in the direction of the vector v, you should calculate the   ∇f(6, 6, 5) and multiply by u.

=<df/dx, df/dy, df/dz>*u

= <4x-3y+yz, -3x+xz, xy> {at (6, 6, 5)} * u

= <36, 12, 36> · <1, 1, -1>/√3

= 12/√3.

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The complete question is -

Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 2x2 − 3xy + xyz (a) Find the rate of change of the potential at P(6, 6, 5) in the direction of the vector v = i + j − k.

The end behavior of the functions is obtained considering the limits of the functions as the input variable x goes to infinity.

For limits when x goes to infinity, only the term with the highest exponent of each of the numerator and of the denominator is considered, hence the functions are written as follows:

Applying the exponent properties, the equivalent expressions are given as the base x elevated to the subtraction of the exponents 2 and 3, hence:

Which is how the functions behave as x goes to infinity.

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The f(x) = -ax²+18 function equation for his parabolic path. x=√8  is he reached, to the nearest tenth of a foot.

A function is an equation that has just one answer for y for every possible value of x. When utilizing a function, each input of a certain type receives exactly one output.

f(x) = -ax² + 18

f(2)= -a(2)²+18 = 12

-4a = 12-18

-4a = -6

  a = -6/-4

  a = 3/2

f(x) = (-3/2) x² + 12

f(0) = (-3/2) x² + 12

(3/2) x² = 12

x² = 8

x = √8

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Answer:

B. Sammy

Step-by-step explanation:

Kara, Sammy, Liz and Mark each took many samples from the same population of students. But the number of students in the Sammy's sample  is largest, hence their mean will have lest variation.

Check the picture below.  Let's recall is an isosceles, so it has twin sides and is a right-triangle.

[tex]x^2+(\sqrt{6x+16})^2\implies \sqrt{x^2+6x+16}\qquad \impliedby hypotenuse \\\\[-0.35em] ~\dotfill\\\\ x~~ = ~~\sqrt{6x+16}\implies \stackrel{\textit{squaring both sides}}{x^2=6x+16}\implies x^2-6x-16=0 \\\\\\ (x-8)(x+2)=0\implies x= \begin{cases} 8 ~~ \textit{\LARGE \checkmark}\\\\ -2 ~~ \bigotimes \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\underset{\textit{length of each side}}{\stackrel{\sqrt{(8)^2 + 6(8) + 16}}{{\Large \begin{array}{llll} 8\sqrt{2} \end{array}}}\hspace{5em}\stackrel{x}{\text{\Large 8}}\hspace{5em}\stackrel{\sqrt{6(8) - 16}}{\text{\Large 8}}}[/tex]

now, let's notice, the negative value is a legitimate value, however for this case is invalid since the lengths of the triangle can't be negative.

Answer:

Step-by-step explanation:

SORRY CANT HELP YOU I AM ONLY IN 4 GRADE SO SORRY

Micro Middle store sold the least number of video game consoles.

The two dimensions of a matrix are represented by rows and columns. The row index and the column index are the two subscripts that each element is specified by.

The rows and columns in a matrix stand in for the two dimensions. The row index and the column index serve as two subscripts that each define an element. A 2D matrix is expanded into a multidimensional array, which uses additional subscripts for indexing.

The total no. of consoles sold by each store is:

Game Go = 53+21+48 = 122

Better Buy = 65+34+70 = 169

Micro Middle = 18+11+15 = 44

The least number of consoles were sold by Micro Middle(44).

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The linear equation each graph is y = (1/5)x +3, y = 2x,  y = -3x+5 and y = (1/3)x +5 respectively

The equation of a line is of the form y = mx+c

Where m is the slope and c is the y-intercept

Graph 1

c = 3

m = 1/5 = 0.2

y = mx+c

Thus, the linear equation is y = (1/5)x + 3 or y = 0.2x + 3

Graph 2

c = 0

m = 2/1 = 2

y = mx+c

Thus, the linear equation is y = 2x+0 or y = 2x

Graph 3

c = 5

m = -3/1 = -3

y = mx+c

Thus, the linear equation is y = -3x+5

Graph 4

c = 5

m = 1/3 = 1/3

y = mx+c

Thus, the linear equation is y = (1/3)x+5 or y = 0.33x+5

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The measure of the reference angle for the angle A = -319° is 41°

What is Reference Angle?

Every angle is measured from the positive part of the x-axis to its terminal line (the line that determines the end of the angle) traveling counterclockwise. For angles in the first quadrant, i.e., angles less than or equal to 90 degrees, the reference angle is equal to the original angle.

The reference angle is always positive

0° to 90°: reference angle = angle

90° to 180°: reference angle = 180° - angle

180° to 270°: reference angle = angle - 180°

270° to 360°: reference angle = 360° - angle

Given data ,

Let the reference angle be = R

Let the angle be represented as A

Now , the value of A is = -319°

And , The reference angle is always positive

So , the value of A = 319°

So , the angle lies in the first quadrant

Now , the reference angle is calculated by

R = 360° - A

Now , the value of the reference angle R = 360° - 319°

The value of R = 41°

Therefore,  the value of R = 41°

Hence , The measure of the reference angle for the angle A = -319° is 41°

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m = -[tex]\frac{17}{7}[/tex]

1. Combine like terms

-2m - 4m - 17 = 1m

-6m - 17 = 1m

2. Multiply by 1

-6m - 17 = 1m

-6m - 17 = m

3. Add 17 to both sides

-6m - 17 = m

-6m - 17 + 17 = m + 17

4. Simplify

Add the numbers:

-6m - 17 + 17 = m + 17

-6m = m + 17

5. Subtract m from both sides

-6m = m  + 17

-6m - m = m + 17 - m

6. Simplify

Combine like terms:

-6m - m = m + 17 - m

-7m = m + 17 - m

Combine like terms:

-7m = m + 17 - m

-7m = 17

7. Divide both sides by the same factor

-7m = 17

[tex]\frac{-7m}{-7}[/tex] = [tex]\frac{17}{-7}[/tex]

8. Simplify

Cancel terms that are in both the numerator and denominator:

[tex]\frac{-7m}{-7}[/tex] = [tex]\frac{17}{-7}[/tex]

m = [tex]\frac{17}{-7}[/tex]

Divide the numbers:

m = -[tex]\frac{17}{7}[/tex]

m = -[tex]\frac{17}{7}[/tex]

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Assuming that Susan types at a constant rate, the situation can be represented as a linear equation as:

n = 0.4t, where n represents the number of pages that Susan can type and t represents time in minutes in which Susan would type.

Number of pages Susan can type in 10 minutes = 4

The number of pages that Susan can type in 1 minute

= 4/10 = 0.4

Therefore, the number of pages that Susan can type in t minutes

= 0.4 × t = 0.4t

Hence, this can be represented in the form of a linear equation as

n = 0.4t

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The 99 percent confidence interval for the true mean length of the bolt is CI = (2.8712, 3.1288)

Confidence Interval is used to tell us the degree of certainty or uncertainty that is existent in a sampling method.

The general formula for confidence interval is;

CI = x' ± z(s/√n)

where;

x' is sample mean

z is z-score at confidence level

s is sample standard deviation

n is sample size

We are given;

sample size; n = 36

Sample mean; x' = 3 inches

standard deviation; s = 0.3 inches

confidence level = 99%

z at 99% CL = 2.576

Thus;

CI = 3 ± 2.576(0.3/√36)

CI = 3 ± 0.1288

CI = (2.8712, 3.1288)

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a) The probability that random guessing will lead to a passing score is of: 0%.

b) The probability that random guessing will lead to a perfect score is of: 3.35 x 10^-18.

c) The first version of the test is safer against examinees guessing to achieve a passing score.

The mass probability formula, giving the probability of x successes, is presented as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

For item a, considering that for 50 questions, all are guessed among five answer, the values of these parameters are given as follows:

n = 50, p = 1/5 = 0.2.

The probability of passing is given as follows:

P(X ≥ 35).

Using a binomial distribution calculator, with the given parameters, we have that:

P(X ≥ 35) = 0%.

For item b, the parameters are given as follows:

n = 25, p = 1/4 = 0.2.

Hence the probability of a perfect score is given as follows:

P(X = 25) = 0.2^25 = 3.35 x 10^-18.

For item c, we have that the first version is safer against examinees guessing to achieve a passing score, as:

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This data collection may be characterized as numerical and univariate.

If the collection of all potential values for a numerical univariate data is finite or countably infinite, the data is discrete. Usually, discrete univariate data are used in counting (such as the number of books read by a person). If the range of all potential values is a set of numbers, then a numerical univariate data is continuous.

Categorical variables represent different sorts of data that may be categorized. Race, sex, age group, and educational level are some examples of categorical variables.

Data types that may be kept and recognized based on the names or labels assigned to them are referred to as categorical data. Numerical data refers to the data that is in the form of numbers, and not in any language or descriptive form. Also known as qualitative data as it qualifies data before classifying it.

Over here we have the data for the average time spent reading per day for students in an 8th grade class.

Average Time is a numerical data

Bivariate data deals with two variables

univariate data, which is one variable data

we have numerical data and one variables so its

Numerical and univariate

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Answer:

904.32 cm³

Step-by-step explanation:

Assuming 12cm is the diameter.

The given solid is a sphere, we must find the volume.

Given radius:

[tex]6[/tex]6

Use the equation [tex]v=\frac{4}{3} \pi r^3[/tex] to find the volume of the sphere.

[tex]\frac{4}{3} \times\pi\times6^3[/tex]

≈ 904.77868

Rounding, 904.32 cm³

What is parallelogram side theorem?

The parallelogram side theorem simply means that the opposite sides of a parallelogram are equal and also parallel to each other.

Proof: We have AD || BC [Opposite sides of parallelogram ABCD]

∠BAC= ∠ACD …(i) [Alternate angles with transversal AC]

Now, AB || CD [Opposite sides of parallelogram ABCD]

∠DAC = ∠ACB …(ii) [Alternate angles with transversal AC]

In ΔABC and ΔACD, we have

∠1 = ∠3 [From (i)]

∠2 = ∠4 [From (ii)]

and AC = CA [Common]

∴ ΔABC≅ ΔCDA [By ASA Congruence]

Hence Proved.

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ΔABC≅ ΔCDA By ASA Congruence, therefore m∠ BAC ≅ m∠ DCA, hence proved using parallelogram side theorem.

What is parallelogram side theorem?

The parallelogram side theorem simply means that the opposite sides of a parallelogram are equal and also parallel to each other.

Proof: We have AD || BC [Opposite sides of parallelogram ABCD]

∠BAC= ∠ACD …(i) [Alternate angles with transversal AC]

Now, AB || CD [Opposite sides of parallelogram ABCD]

∠DAC = ∠ACB …(ii) [Alternate angles with transversal AC]

In ΔABC and ΔACD, we have

∠1 = ∠3 [From (i)]

∠2 = ∠4 [From (ii)]

and AC = CA [Common]

∴ ΔABC≅ ΔCDA [By ASA Congruence]

Hence Proved.

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The required percentage is 95%  data lies between the given data.

What is percentage?

Let X be the lengths of screws.

X~ Normal (μ = 5.5, σ = 0.1)

P[5.3 < X < 5.7]

= P[(5.3-5.5)/0.1 < (X-μ)/σ < (5.7-5.5)/0.1]

= P[-2 < Z < 2] Z is a standard normal variable.

= 2*P[Z < 2] - 1

= 2*0.97725 - 1, from standard normal table.

= 0.9545

P[5.3 < X < 5.7] = 0.95

Hence, the required percentage is 95%  data lies between the given data.

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The cost of each drink is $5.5

The cost of each candy is $5

Using the elimination method, you may either add or subtract the equations to produce an equation in one variable. To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.

According to the given information

Let number of drinks = x

Let number of candies = y

Christian bought 8 drinks and 10 candies and it costed $94

So the equation becomes

8x + 10 y = $94

Other guy bought 9 drinks and 6 candies and it costed $79.50

So the equation becomes

9x + 6y = $79.50

By applying elimination method

9x + 6y = $79.50

Dividing by 2

3x + 2y = $26.5

multiplying the above equation by 5

15x + 10y =  $132.5

8x + 10 y = $94

Subtract the following equation

7x = 38.5

x = 5.5

substituting the value of x in above one equation we get

y = 5

So the cost of each drink is $5.5

the cost of each candy is $5

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Answer:

D = the price of each drink

C = The price of each candy

One drink costs d. So 8 drinks cost 8d. Same thing with candies except a different variable. One candy costs c. Therefore 10 candies cost 10c. So the first equation here would be :

8d + 10c = 94

Same thing with the second equation but with different numbers :

9d + 6c = 79.50

If you're also looking for a solution to this answer. You use a process called the elimination method.

Let me know if you have any questions ! <3

Answer:

m = -4

b =1

y = -4x+1

Step-by-step explanation:

We want to find the slope and y intercept

Given the two points ( -1,5) and ( 1,-3), we can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( -3 -5)/( 1 - -1)

   = -8/( 1+1)

   = -8/2

   = -4

The y intercept is where it crosses the y axis

It crosses at 1

The slope intercept form of the line is

y = mx+b

y = -4x+1

Using fractions and mathematical operations, the number of students in the class are 53, the number of juniors are 21 and 16 seniors did not attend the field trip

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.

A)

From the information given, 3/5 of the students are seniors

However, we know that he has 32 seniors currently

Let's use the concept of percentage here

3/5 = 0.6. Expressing this in percentage = 60%

This we can say 60% of the students are seniors

60/100 = 32/ x

x = total number of students

x = 32 / 0.6

x = 160/3 = 53 students

We have 53 students in the class

B) The number of juniors in the class are

53 - 32 = 21

C) The number of seniors that did not go will be

3/5 * 40 =  24

40 - 24 =  16

16 seniors did not go

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Answer:

let width=x

length = x + 2ft

Area = 82ft^2

Area= length×width

=(x+2)x

=x^2 +2x=82

x^2+2x-82=0

Use Quadratic Equation to get x.

x = -10.1(reject, length cannot be minus value or 8.11)

x = 8.11

width = 8.11ft

length = 10.11ft

Answer:

please download the attached file and let me know if you need any further information about addmition in roots international and if so how to make food with clay

Step-by-step explanation:

ok inshallah and a have of safe Earth’s warm and and

[tex]85(94 + 611) < 64(85 - 54)[/tex]

it same like before the end

Answer: 2/5 days

Step-by-step explanation:

4 / 5 = 2d

4 / 10 = d

2 / 5 = d

The graph that shows a dilation among the given graphs is; Graph F.

Dilation in graphs simply means each side is multiplied by the same

scale factor. What this means is that the ratio of each dilated side to their respective old sides before dilation must be the same scale factor.

We can see that the pre-dilated image has 2 units along the y - axis and 4 units across the x-axis. After dilation, it now has 4 units along the y - axis and 8 units across the x-axis. This means the scale factor in both axis are; 4/2 = 2 and 8/4 = 2. They are both the same scale factors and as such this graph shows a dilation.

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Answer:

The answer is A

Step-by-step explanation:

took the test.

Answer:

By Pythagorean theorem: [tex]ET=\sqrt{113}[/tex]

By distance formula: [tex]ET=\sqrt{113}[/tex]

Step-by-step explanation:

The given rectangle has vertices R(-3,-4), E(-3, 4), C(4,4), and T(4-4).

The points have been plotted on the coordinate plane as shown in the attachment.

A. Using the Pythagoras Theorem;

[tex]ET^2=EC^2+CT^2[/tex]

We substitute the side lengths to obtain:

[tex]ET^2=EC+CT^2[/tex]

[tex]ET^2=49+64[/tex]

[tex]ET^2=113[/tex]

Take positive square root to obtain:

[tex]ET=\sqrt{113}[/tex]

B. The distance formula is given by:

[tex]d=\sqrt{(x_{2}-x_{1)^2+(y_{2}- y_{1} )[/tex]

The endpoints of ET are at E(-3,4) and T(4,-4).

Using the distance formula;

[tex]ET=\sqrt{4--3)^2+(-4-4)^2}[/tex]

[tex]ET=\sqrt{(7)^2} +(-8)^2[/tex]

[tex]ET=\sqrt{49+64}[/tex]

[tex]ET=\sqrt{113}[/tex]

The automobile needs 26.5 gallons of gas to reach 890 miles.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, An automobile uses 17 gallons of fuel to go 570 mi.

∴ The automobile requires (17/570) gallons of gas to reach 1 mile.

∴ To reach 890 miles the automobile needs (17/570)×890.

= 26.5 gallons of gas.

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the regular daily charge is "x", oddly enough that's the 100%.

so the new charge is 17% up, that means the new charge is 100% + 17% = 117%, and we know that's $135, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 135& 117 \end{array} \implies \cfrac{x}{135}~~=~~\cfrac{100}{117} \\\\\\ 117x=13500\implies x=\cfrac{13500}{117}\implies x=\cfrac{1500}{13}\implies x=115\frac{5}{13}[/tex]

The reason why looking back is important in mathematical answers is that; Option D: Looking back allows a student to check that the answer is correct and makes sense in context of the problem.

We know that in mathematics, every problem has steps to solve it whether algebra, proportion, trigonometry, calculus, congruency, angles, logarithms, e,t,c

Now, since we know that every Maths problem has steps to solve them, then we can say that, in some instances, we definitely have to look back to be sure that the answer actually makes sense when we consider the solution being required.

Now, if we have to look back to check that the answer is actually correct and properly portrays the solution being demanded, then we can say that the appropriate option for looking back her is option D.

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