Tony made 14 \text{ L}14 L14, start text, space, L, end text of lemonade for a party. His guests drank 9{,}500 \text{ mL}9,500 mL9, comma, 500, start text, space, m, L, end text of the lemonade.

How many milliliters of lemonade did Tony have left over?

By applying the law of cosine, the length of side CE is equal to 9.22 cm and the image of right-angled triangle BCE is shown in the image attached below.

In order to determine the length of side CE, we would apply the law of cosine because both side CE and side BC respectively represent the adjacent side and hypotenuse of right-angled triangle BCE.

cos(θ) = Adj/Hyp

Where:

Substituting the parameters into the formula, we have;

cos(θ) = CE/BC

cos(11.46) = CE/9.41

Cross-multiplying, we have:

CE = 9.41 × cos(11.46)

CE = 9.41 × 0.9801

CE = 9.22 cm.

By applying the law of cosine, the length of side CE is equal to 9.22 cm and the image of right-angled triangle BCE is shown in the image attached below.

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Answer:

30 yards for 24 vs 1 foot for 25 cents

so lets multiple the yards by 3 to see how many feet

90 feet = 30 yards

90 feet 24 dollars

now lets divide 90 by 24

3.75 so 3.75 per foot

so the second one is way better

Hope This Helps!!!

Answer:

150 feet at $.25 per foot ($.75 per yard) is the better buy.

Step-by-step explanation:

150 feet is equal to 50 yards. So 2 30-yard spools would be $48. $48 for 60 yards equals $.80 per yard. So 150 feet at $.25 per foot ($.75 per yard) is the better buy.

Answer:

0.0000432

Step-by-step explanation:

In scientific notation, 10 raised to a negative number means that the number is less than 1. If the exponent is -5, the decimal place needs to be moved to the left 5 places. This makes the number in standard form: 0.0000432.

The person that would cover the most tile is Bruce because 1/4 is bigger than 1/6.

Bruce has been said to have the need for 1/4 square foot of tiles

Felicia on the other hand would need

1/6 for 1 sq foot

12 for 2 square foot

18 for 3 square foot

Bruce is knwon to cover

[tex]\frac{1}{4} x[/tex]

For felicia one square foot is covered by 1/6th

Now we have to know the one that is larger.

1/4 is bigger than 1/6

Hence we can conclude that Bruce is going to cover a larger are than Felicia.

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Answer: The person who covered the most tiles is Bruce, because 1/4 is bigger than 1/9.

Step-by-step explanation:

Answer:

200 cupcakes

Step-by-step explanation:

12 cupcakes = 6%

12/x=6/100 6x=1200 x=200

so 200 cupcakes

hope this helps

The total number of cupcakes the bakery sells that day is 200.

The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.

Given that,

A bakery sold 12 vanilla cupcakes in a day, which is 6% of the total cupcakes.

Let's say the total cupcakes were x

Then,

6% of x = 12

6 × x/100 = 12

Divide both sides by 6

x/100 = 2

Multiply both sides by 100

x = 200

Hence "The total number of cupcakes the bakery sells that day is 200".

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When a relation is drawn on an xy-plane, another name for the set of all x values from its graph is a function.

It should be noted that a function simply means an expression or rule that defines a relationship between variables.

In this case, when a relation is drawn on an xy-plane, another name for the set of all x values from its graph is a function.

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Answer:

-3/4

Step-by-step explanation:

So you have the equation: [tex]y=\frac{4}{3}x-\frac{5}{3}[/tex]. For a perpendicular line, the only thing that matters is the slope. The slope of the perpendicular line can be defined as: [tex]\frac{a}{b} = > -\frac{b}{a}[/tex]. It's the reciprocal with the sign being the opposite. So if the sign of the original line was negative it's now positive, and if it's positive, it's not negative. The fraction is also flipped, even if it's an integer, it can be defined as a fraction e.g ([tex]6 = > -\frac{1}{6}[/tex] (sign also changed too))

So in this case the slope is 4/3x, since it's given in slope-intercept form: y=mx+b where m is the slope and b is the y-intercept. So we flip it to get 3/4 and change the sign to negative to get -3/4

Answer:

8*8*8*8*8

Step-by-step explanation:

Answer:

8 x 8 x 8 x 8 x 8

Step-by-step explanation:

8^5 is basically 8 times itself five times.

The final amount if $10 000 invested for 6 years at 4% compounded quarterly is $12,697

The formula for calculating the compound interest is given as:

A = P(1+r/n)^nt

Given the following parameters

A = 10000(1+0.04/4)^4(6)

A = 10000(1+0.01)^24

A = 10000(1.01)^24

A = 1.2697(10,000)

A = $12,697

Hence the final amount if $10 000 invested for 6 years at 4% compounded quarterly is $12,697

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The information given about the probability shows that the expected maintenance cost is $22950.

From the information given, the repair hours and the probability are given.

In this case, the maintenance cost will be:

= (8 × 0.05) + (10 × 0.12) + (12 × 0.15) + (14 × 0.32) + (15 × 0.22) + (17 × 0.14) × $1700

= 13.50 × $1700

= $22950

In conclusion, the correct option is D.

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Answer:

14/24 are ill so

58 percent

if you add 5 it does not get more complicated you just add 5 so 14/29

Hope This Helps!!!

Answer:

0/6

Step-by-step explanation:

There are 6 numbers on the die: 1, 2, 3, 4, 5, 6

As you can see there is no 7, so the possibility is 0/6.

Answer:

fvbafdbai

Step-by-step explanation:

gyhghg

Answer:

P = 4x+10

Step-by-step explanation:

So a parallelogram has 2 set of sides which are parallel and equal. So if you're given two adjacent sides, that means you're given a side from each set of sides, which are equal. This means the perimeter is simply: 2(x+3) + 2(x+2). This can be further simplified by distributing the 2 which gives you the equation: 2x+6+2x+4, which further simplifies to 4x+10.

Answer:

y = -4x + 25

Step-by-step explanation:

You are given the slope, but you can find the slope using 2 points.  Slope is the change in y over the change is x.  Your two y's are 1 and 9.  Your two x's are 6 and 4.

1-9/6-2  

1 - 9 = -8

6-4 = 2

-8/2 is -4.

We want an equation in the form y = mx +b.  We have the m (slope), we now just need the b.  We take either of the ordinal points (4,9) or (6, 1) to find b.  They will both work, but the question tells us to us (4,9).  4 is the x and 9 is the y.

y = mx + b

9 = (-4)(4) + b  a negative times a positive is a negative.

9 = -16 + b  Add 16 to both sides

25 = b

We know now m which is -4 and b which is 25.  We plug them into the model y = mx + b

y = -4x + 25

Answer:

I believe the answer is B, it makes the most sense

Step-by-step explanation:

Answer: (a * 50%)^3

Step-by-step explanation:

length = a

(a * 50%)^3

If a would've been the length and would've been decreased to 50%, the volume would be equal to that expression.

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

Reason:

Let's find the distance from A to B. This is equivalent to finding the length of segment AB. I'll use the distance formula.

[tex]A = (x_1,y_1) = (3,5) \text{ and } B = (x_2, y_2) = (7,6)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-7)^2 + (5-6)^2}\\\\d = \sqrt{(-4)^2 + (-1)^2}\\\\d = \sqrt{16 + 1}\\\\d = \sqrt{17}\\\\d \approx 4.1231\\\\[/tex]

Segment AB is exactly [tex]\sqrt{17}[/tex] units long, which is approximately 4.1231 units.

If you were to repeat similar steps for the other sides (BC, CD and AD) you should find that all four sides are the same length. Because of this fact, we have a rhombus.

-------------------------

Let's see if this rhombus is a square or not. We'll need to see if the adjacent sides are perpendicular. For that we'll need the slope.

Let's find the slope of AB.

[tex]A = (x_1,y_1) = (3,5) \text{ and } B = (x_2,y_2) = (7,6)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{6 - 5}{7 - 3}\\\\m = \frac{1}{4}\\\\[/tex]

Segment AB has a slope of 1/4.

Do the same for BC

[tex]B = (x_1,y_1) = (7,6) \text{ and } C = (x_2,y_2) = (6,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 6}{6 - 7}\\\\m = \frac{-4}{-1}\\\\m = 4\\\\[/tex]

Unfortunately the two slopes of 1/4 and 4 are not negative reciprocals of one another. One slope has to be negative while the other is positive, if we wanted perpendicular lines. Also recall that perpendicular slopes must multiply to -1.

We don't have perpendicular lines, so the interior angles are not 90 degrees each.

Therefore, this figure is not a rectangle and by extension it's not a square either.

The best description for this figure is a rhombus.

Answer:

  Rhombus

Step-by-step explanation:

The diagonals of a parallelogram bisect each other. That is, they have the same midpoint. If they are the same length, that parallelogram is a rectangle. If they cross at right angles, it is a rhombus. If it is a rectangle and rhombus, then it is a square.

The midpoints of AC and BD are ...

  (A+C)/2 and (B+D)/2

To determine if the midpoints are the same, we can skip the division by 2 and simply look at the sums:

  A +C = (3, 5) +(6, 2) = (9, 7)

  B +D = (7, 6) +(2, 1) = (9, 7)

The midpoints of the diagonals are the same, so the figure is at least a parallelogram.

The diagonal vectors will be the same length if the figure is a rectangle. They will be perpendicular if the figure is a rhombus. The vectors are ...

  AC = C -A = (6, 2) -(3, 5) = (3, -3)

  BD = D -B = (2, 1) -(7, 6) = (-5, -5)

The length of each of these is the root of the sum of squares of its components. These are obviously different lengths (3√2 vs 5√2).

The dot-product of these will be zero if they are perpendicular:

  AC·BD = x1·x2 +y1·y2 = (3)(-5) +(-3)(-5) = -15 +15 = 0

The diagonals are different length and mutual perpendicular bisectors, so the figure is a rhombus.

__

Additional comment

Looking at the dot-product is a simple way to check that the slopes are opposite reciprocals. The slope of a vector with components (x, y) is m = y/x.

The requirement that slopes be opposite reciprocals means ...

  y1/x1 = -1/(y2/x2) . . . . . . . . slope relationship

  (y1)(y2)/((x1)(x2)) = -1 . . . . . multiply by y2/x2

  y1·y2 = -x1·x2 . . . . . . . . . . multiply by (x1·x2)

  x1·x2 +y1·y2 = 0 . . . . . . . . add x1·x2

This shows the vector dot product being zero is equivalent to the slopes being opposite reciprocals. The vectors are perpendicular in this case.

Answer:

10 years

Step-by-step explanation:

the average or mean value is the sum of all data points divided by the number of data points.

x = the unknown age of the 5th student.

average = 9 = (5 + 7 + 8 + 15 + x)/5

45 = 5 + 7 + 8 + 15 + x = 35 + x

x = 45 - 35 = 10

the 5th student is 10 years old.

If the cost of equity is 12% , cost of debt 10%, tax rate 25%, 20 million market value of debt , 60 million market value of equity then the weighted average cost of capital is 10.875%

Given cost of equity is 12% , cost of debt 10%, tax rate 25%, 20 million market value of debt , 60 million market value of equity.

We know that weighted average cost of capital= cost of equity* weight of equity+ cost of debt* weight of debt.

Cost of debt (consider after tax)=10%(1-25%)

=10%*0.75

=0.075

Weight of equity=60/80

=0.75

Weight of debt=20/80

=0.25

Weighted average cost of capital=12%*0.75+0.075*0.25

=0.09+0.01875

=0.10875

=10.875%

Hence the weighted average cost of capital is 10.875%

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Answer:

Hello i am here to give the answer of the above question................................................................................................................................

Solution:Here

Given,

Volume of a cube is 27 so.

Length of a side of the cube =?

So I think the correct answer of this question is 3

Thank you......... ..................

Answer: -8

Step-by-step explanation:

[tex]g(-1)=2(-1)+5=3\\\\f(g(-1))=f(3)=1-3^{2}=\boxed{-8}[/tex]

Answer:

b.) f(g(-1)) = -8

Step-by-step explanation:

Given following:

Start solving from the right while doing these sums.

Answer:

y=886000(1.04)^t

t=1 year so answer is 886000*1.04 = 921440

Then g(x) is a translation of 3 units downwards of f(x). The correct option is B.

Here we have:

[tex]f(x) = \sqrt{x}[/tex]

first we want to evaluate it in x = 0, 1, 4, 9.

Doing that we get:

[tex]f(0) = \sqrt{0} = 0\\f(1) = \sqrt{1} = 1\\f(4) = \sqrt{4} = 2\\f(9) = \sqrt{9} = 3[/tex]

The other function is:

[tex]g(x) = \sqrt{x} -3[/tex]

Evaluating in the same values of x.

[tex]g(0) = \sqrt{0} -3 = -3\\g(1) = \sqrt{1} -3 = -2\\g(4) = \sqrt{4} -3 = -1\\g(9) = \sqrt{9} -3 = 0[/tex]

Then we can see that for all the values of x, g(x) is 3 units less than f(x).

Then g(x) is a translation of 3 units downwards of f(x). The correct option is B.

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It sounds like you're saying

[tex]z = \dfrac38 \left(\cos\left(\dfrac\pi8\right) + i \sin\left(\dfrac\pi8\right)\right)[/tex]

[tex]w = 2 \left(\cos\left(\dfrac\pi{16}\right) + i \sin\left(\dfrac\pi{16}\right)\right)[/tex]

The product [tex]zw[/tex] is obtained by multiplying the moduli and adding the arguments. In other words

[tex]z = |z| e^{i\arg(z)} \text{ and } w = |w| e^{i\arg(w)} \implies zw = |z||w| e^{i(\arg(z)+\arg(w))}[/tex]

where [tex]e^{it}=\cos(t)+i\sin(t)[/tex], so that

[tex]zw = \dfrac38\times2 \left(\cos\left(\dfrac\pi8+\dfrac\pi{16}\right) + i \sin\left(\dfrac\pi8 + \dfrac\pi{16}\right)\right) = \boxed{\dfrac34 \left(\cos\left(\dfrac{3\pi}{16}\right) + i \sin\left(\dfrac{3\pi}{16}\right)\right)}[/tex]

The swimsuits that can be produced with the new partner is  23,043.

The swimsuits that can be produced without the partner is  16,521.

The equation that relates total cost, operating cost and cost per swimsuit together is

Total cost = operating cost + (cost per swimsuit x number of swimsuits)

500,000 = 120,000 + ($23x s)

500,000 - 120,000 = 23s

380,000 = 23s

s = 380,000 / 23

s = 16,521

Number of swimsuits that can be produced with the new partner:

(500,000 + 150,000)  = 120,000 + ($23x s)

650,000 = 120,000 + 23s

650,000 - 120,000 = 23s

530,000 = 23s

s = 530,000 / 23

s = 23,043

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