The length of a rectangle is 22 centimeters and the width is
4 centimeters. A similar rectangle has a width of 6 centimeters. Write and solve a proportion to
find the perimeter of the second rectangle?
(10 Points)

The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

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Answer:

The area under a curve between two points can be found by doing a definite integral between the two points. To find the area under the curve y = f(x) between x = a and x = b, integrate y = f(x) between the limits of a and b. Areas under the x-axis will come out negative and areas above the x-axis will be positive.

Step-by-step explanation:

The last option which says  the roots of the auxiliary equation are √6 and -√6 is the correct one.

Auxiliary equation is the equation of characteristic polynomial which is calculated by substituting the right member of a standard differential equation by zero.

The roots of the equation is helpful in determining the nature of the general solution of the given differential equation.

We have the differential equation given in the question,

d²y / dx²  - 6y = 0

Now we can replace d²y / dx² as y''.

y'' - 6y = 0, where y'' is the second derivative of y.

Now we have to find the roots of the auxiliary equation.

Let c = y', then c² = y''

c² - 6 = 0

c² = 6

c = +√6 and -√6

So the roots of the equation are √6 and -√6.

Hence the roots of the auxiliary equation of the differential equation given are +√6 and -√6.

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Answer:

-235+84i

Step-by-step explanation:

I hope this is what you were looking for.

Answer:

Step-by-step explanation:

Tuesday

Answer: Tuesday

Step-by-step explanation:

Second after Monday is Wednesday and then immediately is Thursday and second after Thursday is Saturday after which three days is Tuesday.

Answer:

d = √[(-2 - 3)2 + (1 - 1)2] = √25 = 5 units

Joel be not able to make a right triangle with his fence because the given dimensions are not satisfying for Pythagoras theorem.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Dimensions of triangle he has to use for fencing are

15 feet, 8 feet, and 20 feet.

For making it a right triangle it must satisfy the "Pythagoras theorem" which states that

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

H²=B²+P²

20²=15²+18²

400=225+64

400≠289

No, it will not be able to make a right triangle.

Hence, Joel will be not able to make a right triangle with his fence because the given dimensions are not satisfying for pythagoras theorem.

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The complete question is given below:

Joel wants to fence off a triangular portion of his yard for his chickens. The three pieces of fencing he has to use are 15 feet, 8 feet, and 20 feet long.

1. Will he be able to make a right triangle out of his fence? Why or why not?

The perimeter of flag (rectangle) is 2 (L + W). From given information, length (L) is twice as width (W). From this, you can rewrite the equation as:

Perimeter = 2 ( 2W + W ) = 120. To make it simpler, rewrite as 2 (3W) = 120 ---> 6W = 120.

After calculating/solving for W, you will get W = 20.

Let's go back and plug this value into perimeter equation 2 ( 2W + W) =120 to find out the length and width.

The Width is 20 and length is twice that which it gives 40.

Since the unit is in inches, Length = 40 in, and Width = 20 in.

Plug these two measurements into the equation 2 (L + W) = 120 to see if it comes out to be true.

2 (40 + 20) = 120 2 (60) = 120 120 = 120 It works. Finally, Length = 40 in and Width = 20 in.

I hope my work isn't too long. Good luck to you,

Answer:

x=1.6

Step-by-step explanation:

first follow PEMDAS

so you multiply -2 into the parentheses

-8x and +10

so now it is

5x+3x=-8x+10

add 5x +3x

get 8x

then we have

8x=-8x+10

add -8 to the other side

get 16x

so now 16x=10

divide 16 by 10

get x=1.6

Answer:

3280

Step-by-step explanation:

52×63=3276

Round 3276 to 3280

Hope this helps! :)

Answer:

0.169

Step-by-step explanation:

This is a question on binomial distribution where we only have two outcomes: success or failure

Binomial distribution formula:

P(X= x) = n!/[x!(n-x)!] p^x × q^(n-x)

n is the number of questions in the quiz n = 6

Probability of guessing a correct number = probability of success = p

We told each question has 4 options in which one is correct.

The probability of guessing a correct answer = p= 1/4

p = 0.25

q = 1-p = 1-0.25

q = 0.75

Probability that Richard will answer at least half the questions correctly = P(X≥3)

P(X≥3) = P(X=3) +P(X=4) +P(X=5) +P(X=6)

See attachment for details

P(X≥3) = 0.01318 + 0.0330 + 0.0044 + 0.0002

P(X≥3) = 0.1694

The probability that Richard will answer at least half the questions correctly = 0.169

a. The critical points of f are x = π/2, x = 2π/3, and x = 4π/3.

b. f is increasing on the intervals (0, π/2) and (2π/3, 2π).

  f is decreasing on the interval (π/2, 2π/3) and (4π/3, 2π).

c. f assumes a local maximum at x = π/2 and x = 4π/3.

  f assumes a local minimum at x = 2π/3.

a. The critical points of f occur where the derivative f'(x) equals zero or is undefined.

Note that the derivative is defined for all values of x in the given interval:

0 ≤ x ≤ 2π

Therefore, we need to find the values of x where f'(x) = 0:

  f'(x) = (8 sin x - 8)(2 cos x + 1) = 0

Setting each factor equal to zero gives us:

  8 sin x - 8 = 0   ==>   sin x - 1 = 0 ==>  sin x = 1

                                                                      x = π/2 + 2πk,

                                                                      where k is an integer.

  2 cos x + 1 = 0   ==>   cos x = -1/2  

                                            x = 2π/3 + 2πk or x = 4π/3 + 2πk,

                                            where k is an integer.

  Therefore, the critical points of f are x = π/2, 2π/3, and 4π/3.

b. To determine where f is increasing or decreasing, we can examine the sign of the derivative f'(x) within different intervals. The intervals can be defined by the critical points we found in part (a):

Interval (0 ≤ x < π/2):

In this interval, sin x and cos x are positive. Thus, both factors in f'(x) are positive, resulting in f'(x) > 0.

Therefore, f is increasing on this interval.

Interval (π/2 < x < 2π/3):

In this interval, sin x is positive, but cos x is negative. Thus, the first factor in f'(x) is positive, while the second factor is negative, resulting in f'(x) < 0.

Therefore, f is decreasing on this interval.

Interval (2π/3 < x < 4π/3):

In this interval, sin x and cos x are negative. Both factors in f'(x) are negative, resulting in f'(x) > 0.

Therefore, f is increasing on this interval.

Interval (4π/3 < x ≤ 2π):

In this interval, sin x is negative, but cos x is positive. The first factor in f'(x) is negative, while the second factor is positive, resulting in f'(x) < 0.

Therefore, f is decreasing on this interval.

c. To find the points where f assumes local maximum or minimum values, we need to consider the critical points we found in part (a) and check the behavior of the function around these points.

  At x = π/2: Since f'(x) changes from positive to negative as we move from the left side of π/2 to the right side, this implies that f has a local maximum at x = π/2.

  At x = 2π/3: Since f'(x) changes from negative to positive as we move from the left side of 2π/3 to the right side, this implies that f has a local minimum at x = 2π/3.

  At x = 4π/3: Since f'(x) changes from positive to negative as we move from the left side of 4π/3 to the right side, this implies that f has a local maximum at x = 4π/3.

Therefore, the function f has local maximum values at x = π/2 and 4π/3, and a local minimum value at x = 2π/3.

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Work Shown:

Plug x = 4.3 into the equation given

ŷ = 2.6 − 3.1x

ŷ = 2.6 − 3.1(4.3)

ŷ = 2.6 − 13.33

ŷ = -10.73

Note: The symbol ŷ is read as "y hat". It's used to estimate the y value when it comes to regression equations.

The interval notation for the solution set is (-∞, -4] and the number line is on the image at the end.

Here we want to find the solution set of the inequality below:

x ≤ -4

First let's do the interval notation. This will be the set that contains all the numbers from negative infinity to -4 (with -4 included, so  we need to have a closed set at that end)

This is written as:

(-∞, -4]

The use of the symbols [ ] means that the element belongs to the set.

Now to the number line, we will have a closed circle at x = -4 (because it is a solution) and a line that goes to the left of it. You can see an example in the graph at the end.

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Answer:

3a-b/(x-b)=1/(x+1)Doing criss cross multiplication

3a(x+1)-b(x+1)=x-b

3ax+3a-bx-b=x-b

3ax-bx-x=b-3a-b

x(3a-b-1)=-3a

x=3a/(3a-b-1)

Answer:

x = 15

Step-by-step explanation:

since the sides are bisected, the inner line is parallel to the largest side.

8x+9 + 5x-24 = 180

The solution to the system of equations shown above is: A. More than 1 solution.

In order to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;

3y - 3x = -9   ......equation 1.

4y - 4x=-12 ......equation 2.

Based on the graph shown in the image attached above, we can logically deduce that the solution to this system of equations is the point of intersection of the lines on the graph representing each of them, which is given by multiple ordered pairs and as such, it has more than one solution or infinitely many solutions because the lines coincide.

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A set of data that could be represented by the box-and-whisker plot include the following: D.

The median of the set of data is equal to 10.

In Mathematics and Statistics, a box-and-whisker plot is a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the data set (2, 2, 7, 10, 10, 11, 13, 15, 17, 20, 20, 24, 26, 27, 27, 28), the five-number summary for the given data set include the following:

Minimum (Min) = 2.

First quartile (Q₁) = 16.

Median (Med) = 10.

Third quartile (Q₃) = 25.5.

Maximum (Max) = 28.

In conclusion, we can logically deduce that the median of the data set is 10 and it has no outlier.

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Answer:

2(6x+78)

Unless it's the exact number. You hadn't specified what x is.

Answer:

The answer is 61.

Step-by-step explanation:

7(9)-2

63-2

61

Answer:61

7*(9)-2

63-2

61

Hope it's useful

Answer:

The ordered pair (15, 12) means that 15 pounds of beans cost $12.

Step-by-step explanation:

We know that the x-axis is the pounds of beans and the costs are the y-axis.

The result is that x = 8 is the smallest positive number such that f(x) surpasses g(x).

An integer is a whole number that may be positive, minus, or zero and is not a percentage. Integer examples include: -5, 1, 5, 8, 97, as well as 3,043. The following figures are examples of non-integer numbers: -1.43, 1 3/4, 3.14,.09, and 5,643.1.

To find the smallest positive integer x for which f(x) exceeds g(x)

we need to set the two functions equal to each other and solve for x:

f(x) = g(x)

-x² + 5x = -10x + 10

Simplifying the equation, we get:

x² + 15x - 10 = 0

Using the quadratic formula, we can solve for x:

x = (-15 ± sqrt(15² - 4(1)(-10))) / (2(1))

x = (-15 ± sqrt(265)) / 2

The two possible solutions are approximately -0.372 and -14.628. Since we are looking for the smallest positive integer solution, we take the ceiling of the positive solution to get x = 8.

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Answer:

-7

Step-by-step explanation:

Answer:

An acute angle

Step-by-step explanation:

An acute angle is smaller than an obtuse ad right angle.

hope this helps and hope it was right 'cause I really don't know what you meant. :)

According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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Answer:

(x+4)(x+11)

Step-by-step explanation:

x^2+15x+44 is known as a simple quadratic. It is considered "simple" because x^2 is not greater than 1.

To solve quadratics, you need to factorise them (put them into brackets). You can do this by seeing what 2 numbers multiply to give 44, and add to give 15. I have attached a photograph of me breaking down the number 44 into its multiplying factors, and identifying which factors have the sum of 15.

You can see that I have got the numbers 4 and 11.

I now need to put these numbers into 2 sets of brackets. Remember, the two sets of brackets need to multiply to give x^2+15x+44 when calculated using the grid method.

The two brackets that I have got are (x+4)(x+11), and it doesn't matter which way around you write it.

7.81 lb of 21% aluminium and 33.19 lb of 42% aluminium must be use to make 41 lb of a third alloy containing 38% aluminium.

Given:

one alloy containing 21 % aluminum and another containing 42% aluminum.

41 pounds of a third alloy containing 38 % aluminum.

Let x represents the quantity containing of alloy 21% aluminium

Let y represents the quantity containing 42% of alloy aluminium.

From the question;

x + y = 41 ----------------------------(1)

21%x + 42%y = 38% (41)

⇒0.21x + 0.42y = 15.58 ------------------------------------(2)

We can now solve equation (1) and (2) using the substitution method

From equation (1);

x = 41 - y

Substitute into the equation equation and solve for y

0.21(41 - y) + 0.42y = 15.58

8.61 - 0.21y + 0.42y = 15.58

8.61 + 0.21y = 15.58

0.21y =6.97

Divide both-side by 0.21

y= 33.19

Substitute the value of y into x = 41 - y to deermine the x -value.

x = 41 - 33.19

x = 7.81

x=7.81 and y = 33.19

Hence, 7.81 lb of 21% aluminium and 33.19 lb of 42% aluminium must be use to make 41 lb of a third alloy containing 38% aluminium.