Sets A, B, and C are subsets of the universal set U. These sets are defined as follows.
U= {f,g,h,p,q,r,x,y,z}
A={f,g,p,q}
B={g,h,q,x,y}
C={p.q.x.y.z}

Find (C ∪ B) ∩ A'.
Write your answer in roster form or as Ø.

The Taylor series up to the degree 4 terms is:

e^8 + (x - 8)e^8 + (x - 8)^2/2! e^8 + (x - 8)^3/3! e^8 + (x - 8)^4/4! e^8

The Taylor series of a function f(x) at point a is an infinite sum of terms that approximates the value of the function near point a. The general form of the Taylor series of f(x) at a is:

f(x) = f(a) + (x - a)f'(a) + (x - a)^2/2! f''(a) + (x - a)^3/3! f'''(a) + ...

Where,

In the case of e^x, the function is infinitely differentiable, so all its derivatives are equal to itself. Hence the Taylor series at a=8 is:

e^8 + (x-8)e^8 + (x-8)^2/2! e^8 + (x-8)^3/3! e^8 + (x-8)^4/4! e^8 + ....

by taking the degree 4 terms we can find the Taylor series of e^x at a = 8 up to the degree 4 terms, which is

e^8 + (x-8)e^8 + (x-8)^2/2! e^8 + (x-8)^3/3! e^8 + (x-8)^4/4! e^8

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The number of cups of milk that she will need would be = 20 cups.

A ratio is defined as the expression that shows the relationship between two numbers of the same unit.

The ratio used by Aunt Janelle to make hot chocolate is as follows;

The quantity of milk to cocoa = 5 cups : 2 cups respectively.

Therefore the cups of milk to 8 cups would be = X

That is, 5 cup of milk = 2 cups of cocoa

X cup of milk = 8 cups of cocoa

make X the subject of formula;

X = 5 × 8/2

X= 40/2

X = 20

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Answer:

Step-by-step explanation:

J:  y = 29 cm + (1 cm/mo)x

Z:  y = 12 cm + (2 cm/mo)x

29 cm + (1 cm/mo)x =  12 cm + (2 cm/mo)x

Solve for x to find how many months it will take for them to have the same length of hair:

29 cm - 12 cm = (2 cm/mo)x - (1 cm/mo)x

17 cm = (1 cm/mo)x

x = (17 cm) / (1 cm/mo) = 17 months

Plug this value for x (17 months) into the equations to find how long their hair will be:

J:  y = 29 cm + (1 cm/mo)(17 mo) = 46 cm

Z:  y = 12 cm + (2 cm/mo)(17 mo) = 46 cm

This shows that it will take 17 months for each girl's hair to be 46 cm long.

The cost of bag of popcorn is $7.5 and that of one drink is $5.

The formula for finding the general equation of a straight line is -

[y] = [m[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have Xochitl who went into a movie theatre and bought 6 bags of popcorn and 4 drinks, costing a total of $65, Alonso went into the same movie theatre and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50.

Assume that the cost of one popcorn bag is $[x] and one drink is $[y].

Then we can write -

6x + 4y = 65

6x + 4y = 659x + 8y = 107.5

Plot the graph of both equations and the points of intersection would be the solution set. Refer to the graph below. We get x = $7.5 and y = $5.

Therefore, the cost of bag of popcorn is $7.5 and that of one drink is $5.

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Answer:

$7.5 and 5

Step-by-step explanation:

i did this on my assignment

Answer: 32

Step-by-step explanation:

32+33+34 = 99

They are consecutive numbers.

In calculus, we can find the maximum and minimum value of any function or variable without on looking at the graph of the function.

Maxima will be the giant point on the curve within the given range and minima would be the minimum point on the curve. The combination of both is extrema.

Since 0 ≤ x^2 + y^2 ≤ 6, we have e^ (6*0) ≤ e^ (6(x^2 + y^2)) ≤ e^ (6*6) on D.

So, ∫∫ 1 dA ≤ ∫∫ e^ (6(x^2 + y^2)) dA ≤ ∫∫ e^36 dA

==> 6π ≤ ∫∫ e^ (6(x^2 + y^2)) dA ≤ 6π * e^36, since the area of D is 6π.

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Answer:

Rick read for 1 hour.

Step-by-step explanation:

Tina read 3 hours, Larry read twice as long that is 6 hours, Rita read one third of Larry's so 6 times one-third is 2 hours, half that for Rick's hours and you get 1 hour

Answer:

im sorry but i need the points

Answer:

a. 2/3 < 5/3

b. 2 1/2 > 9/4

c. 2/5 < 3/7

a. 5/3 > 1 1/3

b. 2 1/2 = 10/4

c. 3 5/6 < 21/4

Step-by-step explanation:

2/3 = 0.6667 (Rounded Answer)

5/3 = 1.6667 (Rounded Answer)

2 1/2 = 2.5

9/4 = 2.25

2/5 = 0.4

3/7 = 0.4286 (Rounded Answer)

5/3 = 1.6667 (Rounded Answer)

1 1/3 = 1.3334 (Rounded Answer)

2 1/2 = 2.5

10/4 = 2.5

3 5/6 = 3.8334  (Rounded Answer)

21/4 = 5.25

In this question, we use the theory of LCM (Least Common Multiple) for finding the numbers which are divisible by 2,5 and 10. As we know, in arithmetic, the LCM is the smallest or least positive integer that is divisible by both a and b. So, in this question we need to calculate the LCM of 2,5

step 1

Solution

LCM of 2,5,10 is 10

So, if a number is divisible by 10 then it will be divisible by 2,5,10

Like 60,100,120,450,600

step-by-step answer:

For example, let us take two positive integers 4 and 6. Multiples of 4 are: 4,8,12,16,20,24… Multiples of 6 are: 6,12,18,24…. The common multiples for 4 and 6 are 12,24,36,48…and so on.

2, 5 and 10 (LCM by Division Method).

LCM of 2, 5 and 10 = 2X5

                                 = 10

we get LCM of 2, 5 and 10 is 10.

So, if a number is divisible by 10

Then it will be divisible by 2,5,10.

Therefore, any number which is multiple of 10 or which is divisible by 10. We say it will be divisible by 2,5,10.

Like- 10, 20, 30, 40, 50, 60, 70, 80 etc.

Thus, 10, 20, 30, 40, 50 are 5 numbers which are divisible by 2,5 and 10.

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y=2x²+4x+4 and y=3x²+6x+9 are two instances for the provided standard form, y=ax²+bx+c.

In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A condition on a variable (or variables) such that two expressions in the variable (variables) have equal value is referred to as an equation. • The solution or root of the equation is the value of the variable for which the equation is fulfilled.

Here,

given standard form,

y=ax²+bx+c

examples of this,

y=2x²+4x+4

y=3x²+6x+9

The 2 examples for given standard form, y=ax²+bx+c is y=2x²+4x+4 and y=3x²+6x+9.

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The number of mandarins in the bag is 3 * 33 + 3 = 102 mandarins.

This is a Diophantine equation problem, which is a type of mathematical problem that looks for integers that satisfy a given equation.

We know that the number of mandarins in the bag is equal to 4n + 3, 5m + 2 and 6p + 3 and 7q + 3 for some integers n, m, p and q.

We also know that the number of mandarins in the bag is equal to 3r, where r is an integer.

From the information provided, we can set up the following equation:

4n + 3 = 5m + 2 = 6p + 3 = 7q + 3 = 3r

Now we can use the information that when he finally put them into 3 piles and he didn't have any left over, meaning that the number of mandarins in the bag is divisible by 3, we can see that the remaining number in each case is 3.

Thus the number of mandarins in the bag is 3 * (some integer) + 3.

We can then use the information that the number of mandarins in the bag was less than 100, meaning the possible value of r is less than 34.

Testing values of r starting from 1, we can see that r = 33 satisfies the equation and the number of mandarins in the bag is 3 * 33 + 3 = 102 mandarins

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Answer:

180.4 is 140.9% of 128.

Step-by-step explanation:

180.4 is what percent of 128 Rounded to the nearest tenth?

Answer:

[tex]8x-10[/tex]

Step-by-step explanation:

[tex]5x+3(x-4)+2[/tex]

Distribute:

[tex]=5x+(3)(x)+(3)(-4)+2\\=5x+3x+-12+2[/tex]

Combine Like Terms:

[tex]=5x+3x+-12+2\\=(5x+3x)+(-12+2)\\=8x+-10\\= 8x - 10[/tex]

Answer:

79 degrees

Step-by-step explanation:

there are 180 degrees in a triangle

if you deduct the sum of 15 and 86, which is 101, the third angle must measure 79 degrees

Answer:

x+9

Step-by-step explanation:

for example x is 18 , add 9 to it will become 18+9=27

Answer:

56 pages per hour

Step-by-step explanation:

Penny reads 14 pages in 1/4 of an hour.

An hour is 4 times more than 1/4 of an hour (you could think of it as 15 minutes compared to 60 minutes)

Multiply the amount penny reads in 1/4 of an hour (14 pages) by 4 to get the rate she reads in 1 hour.

14 x 4 = 56

Now add the rate of time (per hour) to get that she reads a total of 56 pages per hour.

Hope this helps!

86 ml of dirt will remain after 9 passes

An equation is an expression showing the relationship between numbers and variables.

Let y represent the amount of dirt on the floor after x passes, hence:

y = abˣ

During each pass, 17% of the dirt is removed, therefore b = 100% - 17% = 0.83

If the floor initially has 460.0 ml of dirt, then a = 460.

The equation becomes:

y = 460(0.83)ˣ

After 9 passes:

y = 460(0.83)⁹ = 86

86 ml of dirt will remain

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The area between the x-axis and y = x from x = 3 to x = 6 will be 13.50 square feet.

Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.

The function is given below.

y = x

Integrate the function under the limit from  x = 3 to x = 6 will be given as,

[tex]\begin{aligned} I &= \int^6_3 y dx\\\\ I &= \int^6_3x dx\\\\I &= \left [\dfrac{x^2}{2} \right ]^6_3 \\\\I &= \dfrac{6^2 - 3^2}{2} \end{aligned}[/tex]

Simplify the equation further, then we have

I = (36 - 9) / 2

I = 27 / 2

I = 13.50 square units

The area between the x-axis and y = x from x = 3 to x = 6 will be 13.50 square feet.

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Answer:

  x = -2 and 4

Step-by-step explanation:

You want a plot of the x-intercepts of H(x) = (x -1)² -9.

The x-intercepts are the points where the graph crosses the x-axis, the points where H(x) = 0. Solving, we get ...

  H(x) = (x -1)² -9

  9 = (x -1)² . . . . . . . . add 9

  ±3 = x -1 . . . . . take the square root

  ±3 +1 = x = {-2, 4} . . . . . add 1

The attached graph shows the coordinates of the x-intercept points on the x-axis. The coordinates of the vertex of the parabola are also shown.

By applying the required transformation, the coordinates of the translated point Q' are (-1, -11).

A translation is a type of transformation in geometry that moves every point of a figure in a fixed direction and by a fixed distance, without changing its size or shape. It is one of the basic geometric transformations along with rotation, reflection, and dilation.

Coordinates are a set of values that determine the position of a point in a certain space. In a two-dimensional space, coordinates are usually represented by an ordered pair of numbers (x, y), where x is the horizontal distance from a fixed point called the origin and y is the vertical distance from the origin. In a three-dimensional space, coordinates are represented by an ordered triple of numbers (x, y, z). Coordinates are often used to locate points in space, to describe the position of objects, and to plot graphs.

To find the coordinates of the translated point Q', we can use the rule that in a translation, the x-coordinate is decreased by the horizontal translation distance and the y-coordinate is decreased by the vertical translation distance.

Given that point Q has coordinates (5, -6) and is translated 6 units left and 5 units down, we can find the coordinates of the translated point Q' as follows:

x' = x - 6 (horizontal translation distance)

y' = y - 5 (vertical translation distance)

So the coordinates of the translated point Q' are:

x' = 5 - 6 = -1

y' = -6 - 5 = -11

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Answer:

92.5 cubic units

Choice A

Step-by-step explanation:

To approach this problem, separate out the composite solid figure into individual easily manageable components

At the bottom we have a rectangular prism which has a base length of 2a, a height of a and a width of c

Its volume = L X H X W = 2a·a·c= 2a²c

Plugging in values for a and c we get

Volume of rectangular prism

= 2 x (3.7)² x 2

= 54.76 cubic units

On top of this rectangular prism are two right-angled triangular prisms

The volume of a right-angled triangular prism =

Here height = b (confusing :)

base = a

width = c

So volume of each triangular prism
[tex]=\textrm{$\dfrac{1}{2} \times $ base x height x width}\\\\= \dfrac{1}{2} a \times b \times c\\\\ = \dfrac{1}{2} \times 3.7 \times 5.1 \times 2\\\\= 18.87[/tex]

Since there are 2 such prisms the volume of both

= 18.87 x 2 = 37.74 cubic units

Total volume of composite solid = 54.76 + 37.74 = 92.5 cubic units

Therefore , the solution of the given problem of area is largest map that may be utilized while still fitting on the page is 20/3 inches by 10 inches.

The term "area" refers to how much room a 2D structure or surface occupies. We use these units to measure surface in cm2 or m2. By dividing the length by the breadth of a form, you can determine its area.

Area = length times breadth and Perimeter = 2 (length + width)

Here,

Given: 2 feet by 3 feet is the size of the map.

8 by 10 inches is the size of a sheet of paper; in inches:

12 inches per foot

24 inches are equal to two feet, or two times twelve.

36 inches are equal to three feet, or three times twelve.

Scale factor is 24/36, or two-thirds.

Paper's longer side equals ten inches.

Using the scale, determine how long the shorter side is:

2/3 = x/10

the cross-multiply

3x = 2 × 10

3x = 20

x = (20 ÷ 3)

x=6.23 inches

The largest map that may be utilized while still fitting on the page is 20/3 inches by 10 inches.

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The set W1 could be a basis for R3 if it spans R3 and is linearly independent, but without the specific elements of W1, it's not possible to determine if it meets those criteria.

The specific elements that make up the set W1. However, I can tell you that to be a basis for R3, a set of vectors must meet two criteria:

So, depending on the specific elements of W1, it could be either A, B, or C.

If the set W1 doesn't span R3, it would be A.

If the set W1 is linearly dependent, it would be C.

If both conditions are met the set is a basis, so the answer would be B.

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The mathematical expression for the given algebraic expression is,

⇒ k / 5

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The algebraic expression is,

⇒ One-fifth of a number, k

Now, We can write the mathematical expression for the given algebraic expression is,

⇒ One-fifth of a number, k

⇒ 1/5 of k

⇒ 1/5 × k

⇒ k / 5

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The value of percent in 1 decimal point is, 52.7%.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

There 19 out of 36 in a class are girls.

Hence, The percentage of girls is,

⇒ 19 / 36 × 100 %

⇒ 1900/36 %

⇒ 52.7%

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Therefore , the solution of the given problem of expression comes out to be sixty-seven billion five hundred eighty million.

Each variable must be replaced with a number and arithmetic operations must be performed to check an algebraic equation. Given that 6 + 6 equals 12, the answer variable in the aforementioned case is comparable to 6. We can substitute the variables values with those we know in order to evaluate the expression.

Here,

6.758 1010 in scientific notation

The scientific notation is = 6.758e10.

Engineering notation: 67.58 109 billion; prefix: giga- (G)

6.758 x 1010 standard form

10 Order of Magnitude for scientific notation and conventional forms

=>67580000000  (real number) 

=>67,580,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000  

sixty-seven billion five hundred eighty million

word form.

Therefore , the solution of the given problem of expression comes out to be sixty-seven billion five hundred eighty million.

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On solving the provided question, we can say that quadratic equation x² - 5x+7=0 => x = 1 , -3

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

x² - 5x+7=0

x(x-1) +3(x-1)

(x-1)(x+3) = 0

x = 1 , -3

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The measure of ∠Q is equivalent to 21°.

Congruent triangles have both the same shape and the same size.

Given is that in △QRS, SQ ​≅ RS and m ∠R=21°.

Now, it is given that SQ ​≅ RS, this means that -

SQ = RS

Angles opposite to equal sides are equal.

∠R = ∠Q = 21°

Therefore, the measure of ∠Q is equivalent to 21°.

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