Graph: y > 6

Is (-2,7) a solution? yes or no
Is ( 2,6) a solution? yes or no

Answer:

a) [tex]A(x)=360x-2x^2[/tex]

b) [tex]90m[/tex]

c) [tex]16200m^2[/tex]

Step-by-step explanation:

This is related to a differential topic called optimisation.

We here have two sides of the field that are equal to [tex]x[/tex], and another unknown (that we will call [tex]y[/tex]). Maya has 360m of fencing, so we will say that [tex]2x+y=360[/tex], and this means that [tex]y=360-2x[/tex].

Our first task is to find a function for the area of the field. We know that the area of a field is length × width. We know we have a length of [tex]y[/tex] which is [tex]360-2x[/tex] and a width of [tex]x[/tex], therefore:

[tex]A(x)=x(360-2x)=360x-2x^2[/tex]

To find the maximum value of [tex]x[/tex], we must first differentiate the function:

[tex]A'(x)=360-4x[/tex]

We must then set the equation equal to 0 and solve for [tex]x[/tex], where the line/curve would be stationary.

[tex]360-4x=0[/tex]

[tex]4x=360[/tex]

[tex]x=90[/tex]

Finally, to find the maximum area, we would substitute this value of [tex]x[/tex] back into the original equation:

[tex]A(x)=360x-2x^2\\\\A(90)=360(90)-2(90)^2\\\\A(90)=16200[/tex]

For the following:

(a) To find a function A(x) that gives the area of the field in terms of x, use the information given about the fencing and the shape of the field.

Let the length of the other two sides (perpendicular to the side with length x) be y (in meters).

The perimeter of the rectangle is given by the sum of all four sides:

Perimeter = 2x + 2y

According to the problem, the perimeter is 360 meters, set up an equation:

2x + 2y = 360

Now, solve this equation for y in terms of x:

2y = 360 - 2x

y = (360 - 2x) / 2

y = 180 - x

The area A(x) of the rectangle is given by the product of its length (x) and width (y):

A(x) = x × y

A(x) = x × (180 - x)

(b) To find the side length x that gives the maximum area for the field, maximize the function A(x) from part (a). To do that, take the derivative of A(x) with respect to x, set it equal to zero, and solve for x:

A(x) = x × (180 - x)

dA/dx = (180 - x) - x

dA/dx = 180 - 2x

Now, set dA/dx = 0 and solve for x:

180 - 2x = 0

2x = 180

x = 90

So, the side length x that gives the maximum area is 90 meters.

(c) Now there is the value of x, find the maximum area by substituting x = 90 into the area function A(x) from part (a):

A(x) = x × (180 - x)

A(90) = 90 × (180 - 90)

A(90) = 90 × 90

A(90) = 8100

The maximum area that the field can have is 8100 square meters.

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Answer:

good job

Step-by-step explanation:

The t-statistic for this hypothesis test is 2.019 and the appropriate conclusion is that we fail to reject the null hypothesis.

To find the p-value, we can use the t-distribution calculator and enter in the degrees of freedom (df = 59), the t-statistic (t = 2.019), and the significance level (alpha = 0.01). The resulting p-value is 0.055, which is greater than the significance level of 0.01. Therefore, we are unable to reject the null hypothesis.

The formula for the t-statistic can be used to calculate the t-statistic for this hypothesis test:

t = (1151 - 1120) / (112 / √60)

t = 2.019

Therefore, the t-statistic for this hypothesis test is 2.019 and the appropriate conclusion is that we fail to reject the null hypothesis.

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The kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1 mT is 0.07623125 eV.

In the given question, the charge on an electron is 1.60218 x 10^(-19) C and its mass is 9.10939 x 10^(-31) kg.

We have to find the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1 mT.

E = 0.18 kV/m

B = 1.1 mT

mass m = 9.10939*10^(-31) kg

Then force on a moving charge in electric and magnetic field = Lorentz force

F = qE+ q*VB

So,

F = qE+ q*VB = 0

E = V*B

Find V , so

V = E/B

V = 0.18*10^3 /( 1.1*10^-3)

V =163637 m/s

so KE = 1/2*m*v^2

Then put values..

KE = 0.5*9.11*10^(-31)*163637^(2)

KE = 1.2197*10^(-20) J

in eV = 1.2197*10^-20 / ( 1.6*10^-19 )

eV = 0.07623125 eV

Hence, the kinetic energy of an electron that passes undeviated through perpendicular electric and magnetic fields if E=0.18 kV m and B=1.1 mT is 0.07623125 eV.

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The correct answer would be C, 6.36246 × 1019

Pseudocode doesn't depend on the syntax and subtitles of a particular programming language, so his readers will be able to understand it as long as they know at least one language.

In computer science, pseudocode is a undeniable language description of the stairs in an set of rules or any other system. Pseudocode frequently makes use of structural conventions of a regular programming language, however is supposed for human studying as opposed to gadget studying. Pseudocode is known via way of means of the programmers of all types. it allows the programmer to pay attention most effective at the set of rules a part of the code development. It can't be compiled into an executable program.

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Complete question:

Ryland is creating an article about commonly used compression algorithms for an online educational site.

He's debating whether to express each algorithm in natural language, flow charts, pseudocode, or C++, a general-purpose programming language.

Which of these is a good argument for expressing the algorithm in pseudocode?

The campers will be 40 miles from their car after 12 hours.

Given :

A group of hikers park their car at a trail head and hike into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, d, from the car on the day of their hike after h hours .

We can pick two points on the line graphed and substitute the coordinates into this formula to find the slope:

slope m = y2 - y1 / x2 - x1

Choosing the points (0,4) and (2,10), we get:

m = 4 - 10 / 0 - 2

= -6 / -2

= 6 / 2

= 3

We can substitute the point (0,4) and the slope into y = mx + b and solve for "b":

4 = 3 * 0 + b

b = 4

Then, the equation of this line is:

y = 3x + 4

Since the distance in miles is represented on the y-axis and the time in hours is represented on the x-axis. we can rewrite the equation as:

d = 3h + 4

if h = 12

d = 3 * 12 + 4

= 36 + 4

= 40 miles

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Full question :

A group of hikers park their car at a trail head and hike into the forest to a campsite. The next morning, they head out on a hike from their campsite walking at a steady rate. The graph shows their distance in miles, d, from the car on the day of their hike after h hours.How many miles will the campers be from their car after 12 hours?

Answer:

[tex]92.05^{\circ}[/tex]

Step-by-step explanation:

By the exterior angle theorem, the answer is [tex]m\angle Y+m\angle Z=92.05^{\circ}[/tex].

Answer:

A

Step-by-step explanation:

exterior angle = sum of the other two angles

63.25 + 28.8

92.05°

The point that the line estimate best fits is the point x = 6 with a residual of 0.18

We are given a table which displays the point and then their residual values are also added from the graph to get;

The table is as follows:

x      y       Residual      Absolute Residual value

1      10       0.4                         0.4

2      8        -1.125                    1.125

2.5   9.5      0.625                   0.625

4       8        -0.25                       0.25

5     8        0.2                             0.2

6    7.5       0.18                          0.18

7.2     7        0.19                          0.19

8.5     6       -0.25                        0.25

The residual value is negative if the point on the scatter plot lies below the regression line and it is positive if the point on the scatter plot lies above the regression line.

Formula for the residual value is;

Residual value = Actual y-value(i.e. on scatter plot) - Observed y-value

Now, the residual value is farthest from the line if the absolute value of the residual value is highest.

Hence, the highest absolute residual value is: 1.125

The point that it best fits is the lowest absolute value which is 0.18

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Answer: 10

Step-by-step explanation: As I said in your previous question, we can make this an addition problem, to make it easy, and make more sense. S0, it would be 5+5, which is our answer; 10. I hoped this helped

The required inverse function of the given function is given as f⁻¹(x) = [9 - 8y] / [1 + y], the domain of the inverse function is all real numbers except -1, and the range of the inverse function is all real numbers.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

here,
f(x) = -x + 9 / [8 + 9x]
Now,
y = f(x)
y = -x + 9 / [8 + 9x]
x = 9 - 8y / [1 + y]
Now,
x ⇄ y
y = 9 - 8x / 1 + x
Now y = f⁻¹[x]
f⁻¹(x) = [9 - 8y] / [1 + y],

Thus, the required inverse function is f⁻¹(x) = [9 - 8y] / [1 + y], the domain of the inverse function is all real numbers except -1, and its range is all real numbers.

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Answer:

for g(-2)

we wil take -1/4 x -1

so g(-2) = - 1/2

for g(1)

we will take (x+1)²

so g(1) = (1+1)² = 4

for g(2)

we will take (x+1)²

so g(2)= ,(2+1)² = 9

A. y = 3x-1; slope is 3 and y-intercept is -1

B. -x+3 = y; slope is -1 and y-intercept is 3

C. x-3 = y; slope is 1 and y-intercept is -3

D. y = 1-3x; slope is -3 and y-intercept is 1

In math, slope interceptor form is the method of writing an equation for a line in the form y = mx + b.

Slope-Intercept form

The slope - intercept form equation with slope m and y intercept c is given by, y = mx+c

Option A:

y = 3x-1

slope m = 3

y-intercept c = -1

Option B:

-x+3 = y

slope m = -1

y-intercept c = 3

Option C:

x-3 = y

slope m = 1

y-intercept c = -3

Option D:

y = 1-3x

slope m = -3

y-intercept c = 1

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Answer:

61.9%

Step-by-step explanation:

percent = part/whole × 100%

part = 86

whole = 139

percent = 86/139 × 100%

percent = 61.9%

Answer:

The percent is:

61.87%

Step-by-step explanation:

86 / 139 = 0.6187

0.6187 * 100 = 61.87%

Lets turn 3.85% into a decimal first. Multiply 0.0385 with 410,000 which gives you 15785. Add that to 410,000 which gives you 425785. Multiply 3.85 by 425785. Repeat that process 5 times until you get the amount of interest earned after 5 years.

Answer:

25

Step-by-step explanation:

Answer: correct answer is A

Step-by-step explanation:The numbers of sets which cannot represent the lengths of the sides of a triangle are 8, 9, 11.We have to determineWhich set of numbers cannot represent the lengths of the sides of a triangle?According to the questionThe length of sides which can not form a triangle is determined in the following steps given below.

Answer:

The correct answer is A.

Step-by-step explanation:

You have to look at the triangle inequality theorem where a + b ≥ c. Any two sides of a triangle must be greater than or equal to the third, in this case, 1 ft + 3 ft only = 4. Therefore A does not represent the length of 3 sides of a triangle.

Hope this helps, Have an amazing day!

As per the limit theorem, the CDF of the standardized variable tends to a limiting value.

The term limit theorem states that the average of a large number of id and the random variables converges to the expected value.

Here we have given that let u1,..., un be independent uniform random variables on [0, 1], and let u(n) be the maximum. find the CDF of u(n) and a standardized u(n).

And we need to prove that the  the cdf of the standardized variable tends to a limiting value.

Let us consider the density function of a uniform random variable on [0,1] is f(x)=1 and the cdf is F(x)=x for x∈[0,1], so for U(n), the density function is

fₙ(x) = nxⁿ⁻¹

Whereas the CDF is written as,

fₙ(x) = xⁿ

When we equate both then we get

fₙ(x) = nx²ⁿ⁻¹

Therefore, the given statement is proved.

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Therefore, the value of the scalar k for which the two vectors are orthogonal is k =1/5.

In physics and mathematics, the term "vector" is used to refer, informally, to certain quantities that cannot be described by a single number or to certain constituents of vector spaces.

Here,

When the dot product of two vectors is zero, those two vectors are said to be orthogonal.

Dot product:

Let's assume we have the two vectors a and b.

a = (1,2) (1,2)

b = (2,3) (2,3)

Their dot item is:

a.b = (1,2). (1,2).

(2,3) = 1*2 + 2*3 = 8

Regarding this issue:

u = (2,3) (2,3)

(k + 1, k - 1) = v

So

u.v = (2,3). (2,3).

(k + 1, k - 1) = 2k + 1, 3k - 1, or 2k + 2, 3k - 3, or 5k - 1

The vectors must be orthogonal for the dot product to equal 0.

So:

=> 5k -1 =0

=> 5k =1

=> k =1/5

Therefore , the value of the scalar k for which the two vectors are orthogonal is k =1/5.

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Answer:

D) 540

Step-by-step explanation:

he sum of the interior angles of a polygon can be found using the formula (n - 2) * 180 degrees, where n is the number of sides in the polygon. In this case, we are given that the polygon has 5 sides, so we can plug this into the formula to find the sum of its interior angles:

(5 - 2) * 180 degrees = 3 * 180 degrees = 540 degrees

Therefore, the sum of the interior angles of a regular polygon with 5 sides is 540 degrees.

Answer:

(a) To find the range of the function f(x), we need to consider all possible values of x in the range -7 ≤ x ≤ 7 and x ≠ -5. For each value of x, we can evaluate the function to find the corresponding value of f(x). Then, we can find the minimum and maximum values of f(x) in this range to determine the range of the function.

For example, if x = -7, then the function will return a value of 2 - 12/(-7) + 5 = 2 + 2 + 5 = 9. If x = 7, then the function will return a value of 2 - 12/7 + 5 = 2 - 1 + 5 = 6.

We can see that the minimum value of the function is 6, which is achieved when x = 7, and the maximum value of the function is 9, which is achieved when x = -7. Therefore, the range of the function is {6, 9}.

(b) To find the inverse of the function f(x), we need to switch the x and y values in the function definition to obtain a new function g(y) such that g(f(x)) = x for all values of x in the domain of the original function.

In this case, the inverse of the function f(x) is given by g(y) = (2 - y + 5)/(-12). This inverse function is defined for all values of y in the range {6, 9}, which is the range of the original function.

To find the value of f^-1(0), we can plug in 0 for y in the inverse function g(y) to obtain g(0) = (2 - 0 + 5)/(-12) = -1/12. Therefore, f^-1(0) = -1/12.

The probability states that- (r+w+b+g)min =21,

Probability refers to possibility.

A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.

Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

According to our question-

r−3=4w,r−2=3b,r−1=2g

r=4w+3,r=3b+2,r=2g+1

rmin=11⇒w min=2⇒bmin​=3⇒g min =5

Hence,  (r+w+b+g)min =21,

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Answer: it should be 12.8 percent

Step-by-step explanation:

Answer:

y = 2 (This equation is in slope intercept form.)

Step-by-step explanation:

y = 0x + b

2 = 0(13) + b

2 = 0 + b

b = 2

y = 2

Answer:

Step-by-step explanation:

You want the graphs of the given lines, and the centroid of the triangle they form.

It works well to start by plotting the y-intercept of each equation, then using the slope to identify the "rise" and "run" to another point on the line. Then the line can be drawn through the points.

The graph shows you the points of intersection of the lines are ...

  (-4, 2), (4, 8), (0, -4) . . . . . . . . . the last is the y-intercepts of y1 and y3

The centroid coordinates are the average of the vertex coordinates, their sum divided by 3.

  centroid = ((-4, 2) +(4, 8) +(0, -4))/3 = (-4+4+0, 2+8-4)/3 = (0, 6)/3

  centroid = (0, 2)

__

Additional comment

The slope of each line is the x-coefficient in the equation. That slope is the ratio of "rise" (change in y) to "run" (change in x) for the line. It is often convenient to draw a graph by finding points on the line counting the grid squares for rise and run.

Answer:

Step-by-step explanation:

let the distance be x miles

the difference in time taken  between two towns = 7 minutes

   44 - x = 49

x = 49 - 44

      x = 5 miles

Therefore , the distance between two towns is 5 miles .

0.9(315 000) * 30(0.0375)

= 283 500 * 1.125

= 318 937.5   (total amount of 30 year mortgage)

= 318 937.5 / 360

= $885.94   (monthly payment)

315 00 * 0.1 = 31 500   (amount of down)

315 000 - 31 500 = 283 500 (balance without interest)

283 500 * 30(0.0375) = 318 937.5  (balance with interest)

318 937.5 / 30(12) = 885.94

Therefore, the monthly payment will be $885.94

The numbers of each beads that Sharon will need to make all of the key chains is given as follows:

The amounts for each bead are obtained applying the proportions built from the image given at the end of the answer.

From the images, for a single key chain, the amounts needed are given as follows:

Hence, for each 4 green beads, 3 red beads are needed. For 20 green beads, the number of red beads needed is given as follows:

3/4 x 20 = 60/4 = 15 red beads.

For each 4 green beads, 6 blue bears are needed. For 20 green beads, the number of blue beads needed is given as follows:

6/4 x 20 = 120/4 = 30 blue beads.

The image is given at the end of the answer.

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