3/4 - 5/8 step by step

The intersection is the set of all elements in both sets, so the answer is {-2, 4, 8}.

The union is the set of all elements in at least one of the sets, so the answer is {-2, 0, 3, 4, 5, 6, 8}.

Answer:

8a-2ab

Step-by-step explanation:

5a-2b+2b+3a-2ab

Simplify 'a'

5a+3a=8a

Simplify 'b'

2b+2b=4b

8a-2ab

The graph of the linear equation can be seen in the image below.

Here we have the linear equation:

x - 2y = -2

To graph it, we need to find two points that belong to the line, and then we can graph these and connect them with a line.

If x = 0, we have:

0 - 2y = -2

y = -2/-2 = 1

if x = 1 then:

1 - 2y = -2

1 + 2 = 2y

3 = 2y

3/2 = y

Then we have the points (0, 1) and (1, 3/2), now just graph these points on a coordinate axis and then connect them with a line, we will get:

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Answer:

1022 minutes

Step-by-step explanation:

Let x be the number of minutes the executive used the phone

There is a base charge of $35 and only minutes greater than 900 min are charged at the rate of $0.40 per minute

So total bill A = 35 + 0.4(x-900)

We know the bill was $83.80

So we can rewrite the equation as

35 + 0.4(x-900) = 83.30

and solve for x

To make it easier for computational purposes

1)  Multiply both sides by 10

[tex]35\cdot \:10+0.4\left(x-900\right)\cdot \:10=83.8\cdot \:10[/tex]

2) Perform individual multiplication

[tex]350+4\left(x-900\right)=838[/tex]

3)  Subtract 350 from both sides

[tex]350+4\left(x-900\right)-350=838-350[/tex]

4)  Simplify

[tex]4\left(x-900\right)=488[/tex]

5) Divide both sides by 4

[tex]\frac{4\left(x-900\right)}{4}=\frac{488}{4}[/tex]

6) Simplify

[tex]x-900=122[/tex]

7) Add 900 to both sides to isolate x

[tex]x-900+900=122+900[/tex]

8) Simplify to obtain x

[tex]x=1022[/tex]

Answer: The executive used the phone for 1022 minutes that month

Answer:

  93 square units  (the figure is not a rhombus)

Step-by-step explanation:

You want the area of the figure whose vertex coordinates are A(0,-5), B(9,2), C(12,13), and D(2,7).

The formula for the area of a polygon based on its coordinates might be written ...

  [tex]\displaystyle A=\frac{1}{2}\left|\sum_{k=1}^n{x_k(y_{k+1}-y_{k-1})}\right|[/tex]

where coordinate indices wrap around from the end to the beginning.

Using this formula, we find the area to be ...

  A = 1/2|0(2-7) +9(13-(-5)) +12(7-2) +2(-5-13)|

  A = (1/2)|0 +162 +60 -36| = 1/2(186) = 93

The area of the figure is 93 square units.

The area of a rhombus could be calculated as half the product of the lengths of the diagonals. This is only true because the diagonals of a rhombus cross at right angles.

Here, the differences between diagonally opposite coordinates are ...

  AC = (12, 18) . . . . slope = 18/12 = 3/2

  BD = (-7, 5) . . . . slope = 5/-7 = -5/7

If the diagonals are perpendicular, their slopes have a product of -1. Here, the product is ...

  (3/2)(-5/7) = (-15/14) ≠ -1

The given figure is not a rhombus.

If we assume the diagonals are perpendicular, then the area would be ...

  A = 1/2√(12²+18²)√((-5)²+7²) = 1/2√34632 ≈ 93.048

Rounded to the nearest tenth, this area would be 93.0 square units.

The diagonals actually cross at an angle of about 88.152°, so the area is actually ...

  93.048·sin(88.152°) = 93 square units (exactly)

(Development of this formula is beyond the scope of this answer.)

If we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour,then we would need 38 number of cups.

Given that we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour.

We are required to find the number of cups that are needed.

Fraction is the combination of two numbers,one above the division sign and other one below the division sign. The number which is above the division sign is known as numerator and the number which is below the division sign is known as denominator.

Measuring cup=1/3

Number of cups needed in recipe=12+2/3=38/3

Number of cups needed=38/3/1/3

=38 cups

Hence if we have a 1/3 measuring cup and a recipe calls for 12 and 2/3 cups of flour,then we would need 38 number of cups.

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Answer:

207  2 hundreds seven ones

Step-by-step explanation:

Answer:

102.0625 square units

Step-by-step explanation:

First determine the length of each side using the distance formula  for two points. Then use Heron's formula to determine the area of a triangle given three sides

Distance Formula

The distance between two points is the length of the path connecting them

The distance between points (x₁, y₁) and (x₂, y₂) is given by the Pythagorean theorem:

[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

Let's compute the lengths of the sides FH, FG and HG

The three vertices are F(-2, 5)   G(7, -10) and H(-9, -6)  as indicated on the graph

So length FG between (-2,5) and (7,-10)

[tex]FG= \sqrt {(7 - (-2))^2 + (-10 - 5)^2}[/tex]

[tex]= \sqrt {(9)^2 + (-15)^2}[/tex]

[tex]= \sqrt {{81} + {225}}[/tex]

[tex]= \sqrt {306}[/tex]

FG [tex]= 17.492856[/tex]  (round to 17.5)

Length FH between(-2,5) and (-9, -6) is

[tex]FH = \sqrt {(-9 - (-2))^2 + (-6 - 5)^2}[/tex]

[tex]= \sqrt {(-7)^2 + (-11)^2}[/tex]

[tex]= \sqrt {{49} + {121}}[/tex]

[tex]= \sqrt {170}[/tex]

FH [tex]= 13.038405[/tex]  (can be rounded to 13.04

Length GH between (7, -10) and (-9, -6) is

[tex]GH = \sqrt {(-9 - 7)^2 + (-6 - (-10))^2}[/tex]

[tex]= \sqrt {(-16)^2 + (4)^2}[/tex]

[tex]= \sqrt {{256} + {16}}[/tex]

[tex]= \sqrt {272}[/tex]

GH [tex]= 16.492423[/tex]   (can be rounded to 16.5)

Determining the area of a triangle given 3 sides

Heron's formula allows us to find the area of a triangle given 3 sides If the sides are a, b and c the general form of Heron's formula is

[tex]Area = \sqrt {s(s-a)(s-b)(s-c)}[/tex]

where s is the semi-perimeter = [tex]\frac{a+b+c}{2}[/tex]

Substituting values we get

s = [tex]\frac{17.5+13.04+16.5}{2} = 23.52[/tex]

[tex]Area = \sqrt {23.52(23.52-17.5)(23.52-13.04)(23.52-16.5)}[/tex]

[tex]= \sqrt{23.52\cdot6.02\cdot10.48\cdot7.02}[/tex]

[tex]102.0625[/tex]  square units

Step-by-step explanation:

You want to know how the squeeze theorem applies to help you find the limit of f(x) is zero as x approaches zero.

The short of it is that you have ...

  f(x) = [messy finite function] × [function that cleanly approaches 0 at x=0]

The zero product rule tells you that the product of any finite value and 0 is zero, so the limit of this product is 0 at x=0.

The graph in the attachment shows the "function that cleanly approaches 0" in red. When multiplied by the "messy finite function", the result is the blue curve. You can see that the result is a function that has a limit of 0 at x=0.

Here, we'll decompose f(x) into two parts:

Messy finite function

The numerator sine function factor of f(x) gets increasingly messy as x approaches zero, due to the cosine term it contains. We can define ...

  [tex]g(x)=\sin(1+\cos(\pi x^{-3}))[/tex]

Because this is a sine function, its value is always in the range |g(x)| ≤ 1.

Function cleanly approaching zero

The remaining factors of f(x) need to be rearranged a bit to make a function that obviously approaches zero at x=0. We do that by factoring ∛x from the denominator and rearranging the leading fraction.

  [tex]h(x)=\dfrac{e\dfrac{-1}{13+x^{-2}}\sqrt{3x^4+5x^6}}{(x+x^{1/3})(3+\arctan\sqrt{7+x^{-8}})}\\\\=-e\dfrac{x^2}{13x^2+1}\cdot\dfrac{x^2\sqrt{3+5x^2}}{x^{1/3}(x^{2/3}+1)(3+\arctan{\sqrt{7+x^{-8}}})}\\\\h(x)=-e\dfrac{x^{11/3}\sqrt{3+5x^2}}{(13x^2+1)(x^{2/3}+1)(3+\arctan{\sqrt{7+x^{-8}}})}[/tex]

Recognizing that the arctangent term will approach π/2 as x→0, this can be (more or less) directly evaluated at x=0 to give ...

  [tex]h(0)=-e\dfrac{0\cdot\sqrt{3}}{1\cdot1\cdot(3+\dfrac{\pi}{2})}=0[/tex]

The sign of h(x) will be opposite the sign of x. The graph of h(x) is shown in red in the attachment.

As h(x) approaches zero, the product ...

  f(x) = g(x)·h(x)

approaches zero. This is the essence of the squeeze.

Starting from our description of g(x) above, we can multiply both sides of the inequality by the positive value |h(x)| to get ...

  |g(x)| ≤ 1 . . . . . . . . . . the range of the sine function

  |h(x)|·|g(x)| ≤ |h(x)|·1 . . . . . . multiply by |h(x)|

Simplifying, this is ...

  |f(x)| ≤ |h(x)| . . . . true for all x

So, the limit is ...

  [tex]\displaystyle \lim_{x\to0}|f(x)|\le\lim_{x\to 0}|h(x)|\\\\\lim_{x\to0}|f(x)|=0[/tex]

The attachment illustrates this nicely, showing that the oscillating f(x) has its amplitude limited by h(x), which approaches zero.

__

Additional comments

The limit of x^-8 is positive infinity as x approaches zero. This means the arctangent function argument is positive infinity as x approaches zero, so the function value is π/2. The sign of x is irrelevant.

We cannot tell if the fraction following "e" in this function is supposed to be an exponent. The two typeset versions of f(x) seem to show "e" as a multiplier, not the base of an exponential term. Even if an exponential term is what is intended, that term would approach 1 at x=0, so the conclusion here remains unchanged.

The equation to the tangent line to [tex]y = e^{(x^2)}[/tex] at point (1,0) is given by:

y = 2e(x - 1).

Supposing that we have a function f(x) at a point [tex](x_0, y_0)[/tex], the equation of the tangent line to this function is given by:

[tex]y - y_0 = f^{\prime}(x_0, y_0)(x - x_0)[/tex]

In which f' is the derivative.

In this problem, the function is:

[tex]f(x) = e^{(x^2)}[/tex]

Applying the chain rule, the derivative is:

[tex]f^{\prime}(x) = 2xe^{(x^2)}[/tex]

At x = 1, the derivative is:

[tex]f^{\prime}(1) = 2(1)e^{((1)^2)} = 2e[/tex]

Hence the tangent line at point (1,0) is given by:

y = 2e(x - 1).

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Answer:

230

Step-by-step explanation:

Answer:

To see if something is a function, just draw lines down the graph, if it touches the line twice, then that means it does not pass the vertical line test, meaning it is not a function
(By the line, I mean what you wrote on the paper,)
For example, a parabola is a function, because when you do the vertical line test, it only touches the line at one point, and not two,

Step-by-step explanation:

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

(I included a picture that should help explain better)

Answer:

a

Step-by-step explanation:

because the chart matches the scenario

The meaning of the terms and factors in the expression are

The expression is given as

180 + 15x

The above expression can be split as follows:

The meaning of the above terms and factors are

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There will be an outcome of 16380 times.

What is an outcome?

The football team will play 14 games

and each game can result in one of 2

Hence, the total possible number of outcomes for the season is [tex]2^{14}[/tex].

Now, let us explain

Let the result can be represented by an 'ordered set" i.e. 14- box.

|1|2|3|4|5|6|7|8|9|10|11|12|13|14|

Hence, the first box can be filled in 2 ways.

Similarly, all boxes.

Hence, the total number of cases will be,

2*2*2*2.... 14 times

=  [tex]2^{14}\\[/tex]

=16380 times.

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Answer:

y = 6x + 760

Step-by-step explanation:

In the problem you are given two pairs of numbers. These are both a pair of inputs and outputs, (x, y):

(390, 3100) also,

(490, 3700)

Write an equation by finding and filling in m and b in the following equation:

y = mx + b

To find m, which is the slope of the line, subtract y-y and put that on top. Then subtract x-x and put that on the bottom. See image.

Next, find b by use EITHER pair of numbers to find b.

I used (390, 3100).

see image.

m = 6 and b = 760

Fill these into

y= mx + b

y = 6x + 760

In case they ask, this means each calculator takes $6 to make and it costs $760 to set up your operation even before you have made any calculators.

Answer:

15

Step-by-step explanation:

[tex]3x-15=4x \\ \\ x-15=0 \\ \\ x=15[/tex]

The total volume of the tank is 300L.

The volume of a 3D figure is the space that it occupies.

Here, we are given that Yuki adds cleaning solution that is 7/900 of the tank's total volume.

Let the total volume of the tank be V

We know that the cleaning solution required to clean this tank is 2 1/3 L

Firstly, we need to convert this mixed fraction into an improper fraction, Thus, 2 1/3 = (2*3 + 1)/ 3

= 7/3 L

Thus, we can make the following equation,

(7/900)* V = 7/3

V = 7/3 (900/7)

V = 900/ 3

V = 300

Thus, the volume of the tank is 300L.

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Your question was incomplete. Check for full content here-

Yuki works at an aquarium. To clean a tank, she calculates 7/ 900 of the tank's total volume, and she adds that much cleaning solution to the tank. For a certain tank, this works out to be  2 1/3 L of cleaning solution. What is the total volume of the tank?

Answer:

300L

Step-by-step explanation:

Just did it on Khan academy.

Answer:

A

Step-by-step explanation:

Since the leading coefficient of the function is greater than 0, then it opens upward.

Answer:

5 studs (3^3)

(3^3) = 5

Step-by-step explanation:

1a) The total direct manufacturing cost incurred to make 14,000 units is $187,600.

1b) The total indirect manufacturing cost incurred to make 14,000 units is $74,200.

2a) The total manufacturing cost directly traceable to the Manufacturing Department is $187,600.

2b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department is $74,200.

3a) When the company sells 14,000 units, the total direct selling expense, which can be readily traced to individual sales representatives, is $18,200.

3b) When the company sells 14,000 units, the total indirect selling expense, which cannot be readily traced to individual sales representatives, is $14,000.

4a) The total manufacturing cost directly traceable to the Manufacturing Department per unit is $13.40.

4b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department per unit is $5.30.

3a. Sales commissions per unit is $1.30.

3a. The number of units sold is 14,000 units.

3a. Total sales commission is $18,200.

3a. Fixed portion of sales representatives’ compensation is $14,000.

3a. Total direct selling expense is $18,200.

3b. The total indirect selling expense is $14,000.

Relevant production range = 12,000 to 16,000 units

Production and sales units = 14,000 units

                                                  Average Cost

                                                       per Unit

Direct materials                                $ 7.30

Direct labor                                      $ 4.30

Variable manufacturing overhead  $ 1.80

Direct cost per unit                         $13.40

Fixed manufacturing overhead     $ 5.30

Total manufacturing cost per unit $18.70

Fixed selling expense                   $ 3.80    $53,200 ($3.80 x 14,000)

Fixed administrative expense      $ 2.80     $39,200 ($2.80 x 14,000)

Total fixed costs per unit               $6.60     $92,400 ($6.60 x 14,000)

Variable selling and admin:

Sales commissions                        $ 1.30

Variable administrative expense $ 0.80

Total variable selling and admin per unit = $2.10

1a) The total direct manufacturing cost incurred to make 14,000 units is $187,600 ($13.40 x 14,000).

1b) The total indirect manufacturing cost incurred to make 14,000 units is $74,200 ($5.30 x 14,000).

2a) The total manufacturing cost directly traceable to the Manufacturing Department is $187,600 ($13.40 x 14,000).

2b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department is $74,200 ($5.30 x 14,000).

3) Fixed selling expenses =  $53,200 ($3.80 x 14,000)

Advertising expenses = $39,200

Sales Compensation = $14,000 ($53,200 - $39,200)

Sales Commission = $18,200 ($1.30 x 14,000)

Total Salespersons' compensation = $32,200

a) When the company sells 14,000 units, the total direct selling expense, which can be readily traced to individual sales representatives, is $18,200.

b) When the company sells 14,000 units, the total indirect selling expense, which cannot be readily traced to individual sales representatives, is $14,000.

4a) The total manufacturing cost directly traceable to the Manufacturing Department per unit is $13.40.

4b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department per unit is $5.30.

3a. Sales commissions per unit is $1.30.

3a. The number of units sold is 14,000 units.

3a. Total sales commission is $18,200 (14,000 x $1.30)

3a. Fixed portion of sales representatives’ compensation is $14,000.

3a. Total direct selling expense is $18,200.

3b. The total indirect selling expense is $14,000.

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The possible perimeters are 140 feet, 148 feet and 160 feet.

In order to determine the width that would be used to determine the possible perimeters, the formula for the area would have to be rewritten.

A rectangle is a 2-dimensional quadrilateral with four right angles and two diagonals that bisect each other at right angles.

Area of a rectangle = length x width

Width = area / length

1200 / 40 = 30 feet

1200 / 50 = 24 feet

1200 / 60 = 20 feet

Perimeter of a rectangle = 2 x (length + width)

Perimeter when width is 30 feet : 2(40 + 30) = 140 feet

Perimeter when width is 24 feet : 2(24 + 50) = 148 feet

Perimeter when width is 20 feet : 2 (20 + 60) = 160 feet

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Answer:

Step-by-step explanation:

Find the area of the figure. (Sides meet at right angles.)

1 rettangle on a square

Area Rectangle

(2+2+5)*5=

9*5=

45in²

Area of the Square

5*5=

25in²

sum

45+25=

70in²

The line segment that is skew line to line segment BF is CD.

Skew line:

Skewed lines are two lines that are not parallel to one another, and neither do they intersect. Only dimensions greater than two-dimensional space can have skew lines. They must be non-coplanar, which means that they must exist on several planes. Two lines in two-dimensional space can either intersect or run parallel to one another. Therefore, skew lines are impossible in 2D space.

The line segment AB is perpendicular to the line segment BF which means it is not the skew line to line segment BF

The line segment CD is not parallel and not perpendicular to the given line segment BF which means it is a skew line to the given line segment BF.

Therefore, The line segment that is skew line to line segment BF is CD.

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Answer:

x-2-10123

y0.1 0.3 0.9 2.7 8.1 24.3

The cost of the car is $27,546

The sales tax is 7%

Jorge bought a ford mustang having a sales tax of $1,928.22

Therefore the cost of the car can be calculated as follows

1928.22÷ 7/100

= 1928.22/0.07

= 27,546

Hence the cost of the car is $27,546

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Answer:

4x + 27

Step-by-step explanation:

12x + 36 - 14 - 8x + 5 Combine like terms (36, -14, 5)

12x + 27 - 8x Combine like terms (12x, -8x)