A number is rounded off to the nearest thousand. The rounded number is less than the original
number. Which of these can be the original number?
a) 4832
b) 5789
c) 6315
d) 7956

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.

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

Answer:

in the picture

Step-by-step explanation:

in the picture

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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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:

[tex]61.8^{\circ}[/tex]

Step-by-step explanation:

Vertical angles are congruent

Answer:

61.8

Step-by-step explanation:

The measure of angle C is 61.8 degrees.

Vertical angles are a pair of nonadjacent angles formed by two intersecting lines. They are called "vertical" because they are opposite each other and share the same vertex (the point at which the two lines intersect). Because vertical angles share the same vertex, they are always congruent, which means that they have the same measure.

In this case, angles C and E are a pair of vertical angles, so they are congruent. Since the measure of angle E is 61.8 degrees, the measure of angle C must also be 61.8 degrees. Therefore, the answer is 61.8 degrees.

Pentagons ABCDE and FGHIl are similar. The ratio of each side of pentagon ABCDE to its corresponding side of pentagon FGHIJ is 4:1. the length of FG is  x + 1.

Generally, A distance may be measured in terms of its length. A quantity that has the dimension distance in the International System of Units is referred to as length. In the vast majority of measuring systems, a length base unit is selected, and it is from this unit that all other units are derived.

The meter serves as the fundamental measuring device for length in accordance with the International System of Units.

Since the ratio of the sides of the two pentagons is 4:1, the length of FG is 1/4 of the length of AB.

Therefore, the length of FG is

(1/4)(4x + 4) = x + 1.

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Complete Question not found

Image not found

Answer:

its 1/4

Step-by-step explanation:

Step 1: Calculate the ratio of the side lengths for the original image to the corresponding side lengths of the transformed image using side FG and its corresponding side in

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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At any given time there are N people on an elevator, N being a discrete random variable with mean E(N)=n, then E(Y1) = w

Let W be the total weight of all people in the elevator at a given time and N be the number of people in the elevator at a given time.

E(W) = E[E(W|N)]

Since N and Y are independent, we can also write with mean:

E(W|N) = E[E(W|N,Y)]

Since the weight of each person is independent of the others, we can write:

E(W|N,Y) = E[E(W|N,Y1)]

Since Y is a continuous random variable and the weights of each person are independent, we can further write:

E(W|N,Y1) = E(Y1) = w

Therefore, we can conclude that:

E(W) = E[E(W|N)] = E[E(W|N,Y)] = E[E(W|N,Y1)] = E(Y1) = w

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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

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!

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

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?

After 26 years Judy purchased the home for $109,000.

What is function?

A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, and the set Y is known as the function's codomain.

A function is a relationship between a set of inputs and a set of potential outputs, where each input is related to exactly one output.

Given:

Judy purchased a home in 1956.

The function represents y, the value of the home x years since 1956.

f(x) = 11,500(1.09)^x

Let Judy purchased the home for $109,000.

We have to find the the number of years when Judy purchased the home for $109,000.

Plug f(x) = 109,000 in the above equation.

109,000 = 11,500(1.09)^x

218/23 = (1.09)^x

Taking log on both sides,

ln(218/23) = ln(1.09)^x

ln(218/23) = x ln(1.09)

             x = ln(218/23)/ln(1.09)

             x = 26.097

⇒           x ≈ 26

Hence, after 26 years Judy purchased the home for $109,000.

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Answer:

25

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.

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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The correct answer would be C, 6.36246 × 1019

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:

[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 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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Answer:

good job

Step-by-step explanation:

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 .

For the number of calls greater than 140, the plan [1] is more economical than plan [2].

Given is that a telephone company offers two billing plans for local calls. Plan 1 charges ​$25 per month for unlimited calls and Plan 2 charges ​$18 per month plus ​$0.05 per call.

For the part [1] -

25 < 18 + 0.05x

25 < 18 + 0.05x

25 - 18 < 0.05x

7 < 0.05x

x > (7/0.05)

x > 140

For part [2] -

For the number of calls greater than 140, the plan [1] is more economical than plan [2].

Therefore, for the number of calls greater than 140, the plan [1] is more economical than plan [2].

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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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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:

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.