Help with problem 21- there is more to this problem.

(A∩B)∪(A∩C) using roster method is as follows:

(A∩B)∪(A∩C)  = {a, e, f}

Sets are an organized collection of objects that can be represented in set-builder form or roster form.

Therefore,

The universal sets is as follows:

U = {a, b, c, d, e, f, g, h}

The subsets are as follows:

A = {c, e, f}

B = {a, e, f}

C = {a, b, d, g, h}

Therefore, let's find (A∩B)∪(A∩C) using roster method.

The roster method is defined as a way to show the elements of a set by listing the elements inside of brackets.

Hence,

(A∩B) = {e, f}

(A∩C) = {a}

Finally,

(A∩B)∪(A∩C) = {a, e, f}

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Answer:

The slope is \( - \frac{2}{9} \).

Step-by-step explanation:

☆Remember:

\(m = \frac{y_2 - y_1}{x_2 - x_1} \)

-

☆All we need to do is plug in!

\(m = \frac{3 - 1}{ - 2 - 7} = \frac{2}{ - 9} = - \frac{2}{9} \)

Answer:

\(\Large \boxed{12.9}\)

Step-by-step explanation:

BC = B’C’

BC = 2

The perimeter of a triangle is the sum of all its sides.

\(\sf \Rightarrow 5.1+5.8+2 \\\\\\ \Rightarrow 12.9\)

The perimeter of the triangle is 12.9.

Answer:

12.9 is the perimeter

Step-by-step explanation:

BC is 2 since B’C’ is equal to BC.

Add all sides to get perimeter.

5.1+5.8+2=12.9

You’re welcome.

- bananamilkshake43

If the size of matrix "M" is 9×10, and a scalar "c" is multiplied by matrix, then the size of "cM"  will be 9×10.

We know that when a scalar is multiplied to a matrix, each element of the matrix gets multiplied by that scalar.

In this case, the scalar "c" is multiplied with the Matrix "M";

So if a scalar "c" is multiplied by a matrix "M" of size 9×10, then the resulting matrix "cM" will also have the same number of rows and columns as the original matrix "M".

Therefore, the size of "cM" will also be 9×10.

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Using proportions, we can get the value of the unknown variables as:

1. m = 4/3

2. b = 16/5

3. x = 40/9

4. x = 20

5. x = 11/3

6. k = 28/3

A part, piece, or number that is measured in comparison to a total is referred to as a proportion in general.

According to the definition of proportion, two ratios are in proportion when they are equal. It is an equation or a statement that shows that two ratios or fractions are equal.

Here in the question,

We have:

2/6 = m/4

Cross multiplying the values,

m = 2× 4/6

m = 4/3

Now,

4/5 = b/4

b = 4×4/5

=16/5

8/9 = x/5

x = 8×5/9

=40/9

10/x = 2/4

x = 10×4/2

x = 20

(x-2)/5 = 2/6

⇒ 6(x-2) = 2×5

⇒ 6x -12 = 10

⇒ 6x = 22

⇒ x = 22/6

⇒ x =11/3

6/5 = 10/(k-1)

⇒ 6(k-1) = 10 × 5

⇒ 6k - 6 = 50

⇒ 6k = 56

⇒ k = 56/6

⇒ k = 28/3

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The function that would have the greatest value at x = 16 include the following: B. y = x² - 17x + 182.

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

In this exercise, we would determine the corresponding output value for this function of y based on the x-value (x = 16) in simplified form as follows;

\(y = 10^{16}\)

y = 10,000,000,000,000,000.

y = x² - 17x + 182

y = 16² - 17(16) + 182

y = 256 - 272 + 182

y = 166.

\(y = 1.17^x\\\\y = 1.17^{16}\)

y = 12.330304108137675851908392069373.

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Answer:

Step-by-step explanation:

Answering a comes from simplification, and answering b and c are done all in one step: completing the square on the quadratic that results from a.

(a)  If Martina has 240 m of fencing and is only utilizing one side for the length and 2 sides for the width, the perimeter formula is

240 = x + 2w where x is a length and w is the width. Solving this for w in terms of x:

240 - x = 2w so

\(w=120-.5x\) The area for a rectangle is L * W, so our area using the lengths we have is

A(x) = x(120 - .5x) and we simplify:

A(x) = 120x - .5x²  That's the answer to a.

Now for b and c, we will complete the square on this to get the vertex.

Begin by factoring out the -.5:

\(A(x)=-.5(x^2-240x)\) Now we take half the linear term, square it and add it both inside the parenthesis and outside the parenthesis. Our linear term is 240. Half of 240 is 120, and 120 squared is 14400:

\(A(x)=-.5(x^2-240x+14400)+7200\) (The 7200 comes from multiplying the 14400 times the -.5; -.5 times 14400 is -7200 so to balance things out, we have to add 7200).

The perfect square binomial that results from this is

A(x) = -.5(x - 120)² + 7200. From this we determine that our vertex is

(120, 7200). The 120 is the value of x, the length we are asked to find in b; the 7200 is the max area we are asked to find in c.

The required solutions are,,
(a) area = 240x - 2x²
(b) the side adjacent to the rivers gives the maximum length of the field.
(c) the maximum area could be 6400-meter square.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
length of the field is x,
The perimeter of the field, = 240
x + x + width = 240
width = 240 - 2x
now,
(a)
area of the field,
= length * width,

= x(240-2x)
= 240x - 2x²

Similarly,
(b) the side adjacent to the rivers gives the maximum area of the field.
(c) the maximum area could be 6400-meter square.

Thus, the required solutions are mentioned above.

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The limit of each function at the given point i n the question 10 to 14, is explained below.

A function may get close to two distinct limits. There are two scenarios: one in which the variable approaches its limit by values larger than the limit, and the other by values smaller than the limit. Although the right- and left-hand limits are present in this scenario, the limit is not defined.

When a variable approaches its limit from the right, the function's right-hand limit is the value that approaches.a

10). The limit of f(z) = Arg z as z approaches Zo = 1 does not exist. This is because the argument function is not continuous at the point z = 1, where there is a branch cut.

11). The limit of f(z) = \((1 - lm z)^{-1}\) as z approaches z0 = -8 does not exist. This is because the function approaches infinity as z approaches -8 from the left, and negative infinity as z approaches -8 from the right.

However, if we consider the limit of f(z) as z approaches z0 = -8 + i from both the left and the right, the limit exists and is equal to 0. This is because in the complex plane, the value of Im z cannot exceed 1, so as z approaches -8 + i, the denominator (1 - Im z) approaches 0, and the function approaches infinity. However, the numerator approaches a finite value of 1, which cancels out the denominator, and the overall limit is equal to 0.

12). The limit of f(z) = (z - 2) log(z - 2) as z approaches z0 = 2 is 0. This is because the term (z - 2) approaches 0 as z approaches 2, and log(z - 2) approaches 0 as well because log(z - 2) is continuous at z = 2. Therefore, the limit is equal to 0.

13). The limit of f(z) = -1/z as z approaches z0 = 0 does not exist. This is because as z approaches 0, the magnitude of 1/z approaches infinity, but the direction of approach depends on which quadrant the limit is approached from. Since the limit does not approach a unique value from all directions, the limit does not exist.

14). The limit of f(z) = 2 + \(2^{1/z}\) as z approaches infinity does not exist. This is because as z approaches infinity, the term  \(2^{1/z}\) approaches 1, and the limit approaches 2 + 1 = 3. However, if we approach infinity along the real axis, the limit of \(2^{1/z}\) approaches 1, but if we approach infinity along the imaginary axis, the limit of \(2^{1/z}\) approaches infinity. Therefore, the limit of f(z) does not exist.

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The binomial theorem states that: \((x + y)^n = \sum_{k=0}^n{n\choose k} x^{n-k}y^k\). So, the binomial expansion of (2x - 3y)⁵ is: \(32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\).

Now, let's use the Binomial Theorem to find the binomial expansion of (2x - 3y)⁵. We will have to find the coefficients for each term. So, let's get started. n = 5x = 2xy = -3[nCr = n! / (r! * (n-r)!)]

Term k = 0: \( {5 \choose 0} (2x)^5 (-3y)^0\) = 32x⁵

Term k = 1: \({5 \choose 1} (2x)^4 (-3y)^1\) = -240x⁴y

Term k = 2: \({5 \choose 2} (2x)^3 (-3y)^2\) = 720x³y²

Term k = 3: \({5 \choose 3} (2x)^2 (-3y)^3\) = -1080x²y³

Term k = 4: \({5 \choose 4} (2x)^1 (-3y)^4\) = 810xy⁴

Term k = 5: \({5 \choose 5} (2x)^0 (-3y)^5\) = -243y⁵

Now we can combine all of these terms to form the binomial expansion of (2x - 3y)⁵:\((2x - 3y)^5 = 32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\)

Therefore, the binomial expansion of (2x - 3y)⁵ is: \(32x^5 - 240x^4y + 720x^3y^2 - 1080x^2y^3 + 810xy^4 - 243y^5\).

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Answer: 2500

Step-by-step explanation: If you calculate out 5x6 that equals 30 and 5x5-5 equals 20, when you do 30+20 that equals 50 and 50 to the 2nd power is 50x50 and that would equal 2500

Answer: See Explanation

Step-by-step explanation:

Simple interest is calculated as:

= principal × rate × time.

The interest for a 2% interest rate loan of $3000 for 1 year will be:

= principal × rate × time.

= $3000 × 2% × 1

= $3000 × 2/100 × 1

= $3000 × 0.02 × 1

= $60

The interest for a 3% interest rate loan of $3500 for 1 year will be:

= principal × rate × time.

= $3500 × 3% × 1

= $3500 × 3/100 × 1

= $3500 × 0.03 × 1

= $105

Given:

Rate of sales tax = 7%

Marked price of an item = $19.94

To find:

The final cost of the item once tax is included.

Solution:

We have,

Rate of sales tax = 7%

Marked price of an item = $19.94

\(\text{Sales tax}=\dfrac{7}{100}\times 19.94\)

\(\text{Sales tax}=1.3958\)

Now, final cost of the item once tax is included is

\(\text{Final cost}=\text{Marked price}+\text{Sales tax}\)

\(\text{Final cost}=19.94+1.3958\)

\(\text{Final cost}=21.3358\)

Therefore, the final cost of the item once tax is included is $21.3358.

========================================================

Explanation:

Any rational number is of the form p/q, where p and q are integers and q is nonzero. So basically it's any fraction you can think of.

If a decimal terminates (ie stops) then it is a rational number.

For instance, 0.9 = 9/10 is rational

If a decimal repeats in some way, then it is rational

Eg: 0.0833333.... = 1/12

The dots after the 3 indicate the 3's go on forever.

So far, the facts mentioned allow us to rule out choices A and C. Choice B can be ruled out as well because any integer is always rational. We can easily prove it as such by writing the integer x as x/1.

A more concrete example could be writing the integer 7 as 7/1. So this shows 7 is rational and any integer is rational. Simply stick the integer over 1.

The only thing left at this point is choice D. Any non-repeating non-terminating decimal will be irrational. An example would be pi = 3.14159... which goes on forever without a pattern that repeats. Effectively the decimal digits of pi are more or less random. An irrational number is one that is not rational, and therefore cannot be written as a ratio of two integers.

Answer:

288

Step-by-step explanation:

you would do 180 devided by 3 then multiply that number by 5

Camila can have 300 different combinations to choose from.

A permutation is an arrangement of things where order matters, AB and BA are two different permutations.

The combination is a selection of things where order does not matter, AB and BA are the same combinations.

The statement, This afternoon, she can ice skate, make a snowman, or ski has \(^3C_1\) different things to choose from.

Similarly, all the options have \(^3C_1\times^4C_1\times^5C_1\times^5C_1\) different combinations.

= 3×4×5×5 different combinations.

= 300 different combinations.

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Answer:34.5

Step-by-step explanation:

5.25 x 6 + 3.

You multiple 5.25 however many hours it says and then you have the 3$ for the fee.

Answer:

Hope you can understand my handwriting though

Volume of the cylinder is 15197.60(to the nearest hundredth).

In mathematics, Cylinder is  the basic 3d shapes,  which has two parallel circular bases at a distance. The two circular bases are joined by a curved surface, at a fixed distance from the center which is called height of the cylinder.

Given that the radius of the cylinder  is 11yd.

and the height of the cylinder is 40yd.

Formula for the volume of cylinder  is π × r² × h where π=3.14, r= radius and h= height.

Putting the values we get,

Volume of the cylinder is = 3.14 × (11)² × 40 cubic yd.

                                          = 15197.6

Hence, Volume of the cylinder is 15197.60(to the nearest hundredth).

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a) The let-statements defining the variable for the number that yields the same profit are

b) The profit (function) equation for location A is 45x - 1,200 and for location B, 60x - 1,800.

c) The number of manicures and pedicures generating the same profit at each location is 40.

d) If only 40 manicures/pedicures will be performed at each of the two locations, the profit will be the same.

                                            Location A     Location B

Rent per month                        $1,200           $1,800

Charge for manicure/pedicure    $45               $60

Let price (p) at Location               45                  60

Let total revenue at Locations    45x                60x

Where x is the number of manicures/pedicures at each location

Profit at each location =          45x - 1,200       60x - 1,800

The number of manicures and pedicures that will make the same profit at each location is 60x - 1,800 = 45x - 1,200.

60x - 1,800 = 45x - 1,200

60x - 45x = 1,800 - 1,200

15x = 600

x = 40

Location A:

45x - 1,200

45(40) - 1,200

1,800 - 1,200 = 600

= $600

Location B:

60x - 1,800

60(40) - 1,800

2,400 - 1,800 = 600

= $600

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Answer:

Hello! The answer is A) B=3

Step-by-step explanation:

Hope I helped! Please mark brainiest if get chance.

(Ps: Are you an army?)

The length of the diameter of the sphere is 30 cm.

The surface area of a sphere is given by the formula:

\(A = 4\pi r^2\)

where A is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 900π cubic cm. Therefore:

\(A = 4\pi r^2 = 900\pi\)

Dividing both sides by 4π, we get:

\(r^2 = 225\)

Taking the square root of both sides, we get:

r = 15

The diameter of the sphere is twice the radius, so:

d = 2r = 30

Therefore, the length of the diameter of the sphere is 30 cm.

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Answer:

B).

Step-by-step explanation:

Add 8 to half the difference of 6 and 2 then subtract 1.

Answer:

I apologize but I haven't worked for an answer. but my mind is, what is the point of this question? everyone is familiar with the "when am I ever going to use this in life and why do I need to learn this?" but this is a whole new level of w t f.

Answer: (1/2)x + y + (3/2) = 0

Step-by-step explanation:

The equation of a line in point-slope form is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope of the line. In this case, the point is (3, -2) and the slope is 1/2, so the equation of the line is:

y - (-2) = (1/2)(x - 3)

Simplifying, we get:

y + 2 = (1/2)x - (3/2)

Finally, rearranging the terms, we get:

(1/2)x + y + (3/2) = 0

Therefore, the equation of the line in point-slap form is:

(1/2)x + y + (3/2) = 0

The required, general solution for x that satisfies the equation cos(x + 30) = -1 is x = (2n + 1)π - 30.

To find the general solution for the equation cos(x + 30) = -1, we can start by considering the general form of the cosine function. The cosine function has a period of 2π, meaning it repeats every 2π radians.

In this equation, we have cos(x + 30) = -1. Since the cosine function has a maximum value of 1 and a minimum value of -1, the only way for cos(x + 30) to equal -1 is if x + 30 is an odd multiple of π. We can write this as:

x + 30 = (2n + 1)π

Here, n is an integer representing the number of periods of the cosine function. To find the general solution, we can solve for x by subtracting 30 from both sides:

x = (2n + 1)π - 30

This equation gives us the general solution for x that satisfies the equation cos(x + 30) = -1. We can see that for each integer value of n, we have a different solution.

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Okay so you put -6 in where y is then solve and youll get your answer

-8x-7(-6)=-6

Answer:

\(y =\frac{x}{4}\)

Step-by-step explanation:

We are given several functions, and we want to figure out which one is linear.

A linear function has both of its variables (x and y) with a power of 1. Variables with other powers do not mean that the function is linear.

Let's go through the list.

Starting with \(y=\frac{3}{x} -7\), we can see that x is in the denominator. If this is the case, it means that the power of x is -1.

Even though y has a power of 1, this is NOT linear, because x has a power of -1.

Now, with y=√x-2, this is also not linear. This is because √x = \(x^\frac{1}{2}\), even though y has a power of 1.

For x² - 1 = y, we can clearly see that x has a power of 2, while y has a power of 1. This means that the function is not linear.

This leaves us with \(y = \frac{x}{4}\). x is in a fraction, however it is not in the denominator. This means that the power of x in this function is 1. We can also see that the power of y in this function is 1.

This means that \(y=\frac{x}{4}\) is linear.

Answer:

\(\large \boxed{\sf \ \ \ (-8,0) \ \text{ and } \ (4,0) \ \ \ }\)

Step-by-step explanation:

Hello,

from the expression of f(x) we can say that there are two zeroes, -8 with a multiplicity of 1 and 4 with a multiplicity of 1.

So the image of the parabolic lens crosses the x-axis at two points:

   (-8,0)

and

   (4,0)

For information, I attached the graph of the function.

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer: C

Step-by-step explanation:

For box and whiskers plot the box is where the majority of the data is.  the whiskers(the lines on both sides will tell you where the range of numbers lie)

The middle line in the box is the median number.

The question is worded oddly where they want least likely to be more than 30 which means which one will have less than 30. (Double negative question)

You want the majority of the data to be less than 30, which is subway.  C

-8x - 9 > -21

Move -9 to right side

-8x > -21 + 9

-8x > -12

x < -12/-8

x < 3/2

the answer to -8x - 9 > -21 is x < 3/2