You’re making 40 servings of English custard. Each serving is 250 ml. The following recipe yields 2 L.

Calculate how much of each ingredient you will need to make enough servings of the custard.

Milk 2 L

Vanilla essence 4 ml

Sugar 200 g

Egg yolks 20

[tex]4\pi[/tex]

Step-by-step explanation:

[tex]C = 2\pi r,\:\:\:\:r = 4[/tex]

The circumference of the circle of radius 4 is [tex]8\pi[/tex]. Since we are dealing with only half of the circle, the arc length is then half the circumference or [tex]4\pi[/tex].

(1) Recall that

sin(x - y) = sin(x) cos(y) - cos(x) sin(y)

sin²(x) + cos²(x) = 1

Given that α lies in the third quadrant, and β lies in the fourth quadrant, we expect to have

• sin(α) < 0 and cos(α) < 0

• sin(β) < 0 and cos(β) > 0

Solve for cos(α) and sin(β) :

cos(α) = -√(1 - sin²(α)) = -3/5

sin(β) = -√(1 - cos²(β)) = -5/13

Then

sin(α - β) = sin(α) cos(β) - cos(α) sin(β) =  (-4/5) (12/13) - (-3/5) (-5/13)

==>   sin(α - β) = -63/65

(2) In the second identity listed above, multiplying through both sides by 1/cos²(x) gives another identity,

sin²(x)/cos²(x) + cos²(x)/cos²(x) = 1/cos²(x)

==>   tan²(x) + 1 = sec²(x)

Rewrite the equation as

3 sec²(x) tan(x) = 4 tan(x)

3 (tan²(x) + 1) tan(x) = 4 tan(x)

3 tan³(x) + 3 tan(x) = 4 tan(x)

3 tan³(x) - tan(x) = 0

tan(x) (3 tan²(x) - 1) = 0

Solve for x :

tan(x) = 0   or   3 tan²(x) - 1 = 0

tan(x) = 0   or   tan²(x) = 1/3

tan(x) = 0   or   tan(x) = ±√(1/3)

x = arctan(0) + nπ   or   x = arctan(1/√3) + nπ   or   x = arctan(-1/√3) + nπ

x = nπ   or   x = π/6 + nπ   or   x = -π/6 + nπ

where n is any integer. In the interval [0, 2π), we get the solutions

x = 0, π/6, 5π/6, π, 7π/6, 11π/6

(3) You only need to rewrite the first term:

[tex]\dfrac{\sin(x)}{1-\cos(x)} \times \dfrac{1+\cos(x)}{1+\cos(x)} = \dfrac{\sin(x)(1+\cos(x))}{1-\cos^2(x)} = \dfrac{\sin(x)(1+\cos(x)}{\sin^2(x)} = \dfrac{1+\cos(x)}{\sin(x)}[/tex]

Then

[tex]\dfrac{\sin(x)}{1-\cos(x)}+\dfrac{1-\cos(x)}{\sin(x)} = \dfrac{1+\cos(x)+1-\cos(x)}{\sin(x)}=\dfrac2{\sin(x)}[/tex]

Answer:

-15 -3.45 -3.15 -3.0

Step-by-step explanation:

Step-by-step explanation:

2tan 30° / 1 + tan² 30° =

2(⅓√3) /1 + (⅓√3)² =

⅔√3 / 1+ ⅓ =

⅔√3 / 4/3 =

2/4 √3 =

½√3 = sin 60° (proven)

Answer:

By using a pair of compasses and a ruler you can draw all angles

Answer:

7.3 units

Step-by-step explanation:

Hi there!

We're given an angle and one leg of this right triangle and we must solve for the other leg. Given this circumstance, we can use the tangent ratio:

[tex]tan\theta=\frac{opposite}{adjacent}[/tex]

Plug in all values

[tex]tan39=\frac{x}{9}\\9*tan39=x\\7.3=x[/tex]

Therefore, the value of x when rounded to the nearest tenth is 7.3 units.

I hope this helps!

Answer:

Step-by-step explanation:

The number 5.071 written in english words is "five and seventy-one thousandths

Answer:

A. quotient of Powers

Step-by-step explanation:

hope it helps

Answer:

A. Quotient of powers

Step-by-step explanation:

Hope it helps

Answer:

HOPE IT HELPS PLZ MARK ME BRAINLIEST

Step-by-step explanation:

abc=1

⟹c=1/ab

1/(1+a+1/b)+1/(1+b+1/c)+1/(1+c+1/a)

=1/(1+a+1/b)+1/(1+b+ab)+1/(1+1/ab+1/a)

=b/(1+b+ab)+1/(1+b+ab)+ab/(1+b+ab)

=1+b+ab/(1+b+ab)

=1

Answer:

The ANSWER is 18*3= 54

Step-by-step explanation:

total angle inside pentagon = 540 degrees so 3(8x)+2(3x)=540 and that is 30x=540

Answer:

C = 144

Step-by-step explanation:

A 5 sided figure has the interior angle sum of 540 degrees

8x+8x+8x+3x+3x = 540

Combine like terms

30x= 540

30x/30 = 540/30

x = 18

<C = 8*18 = 144

9514 1404 393

Answer:

  10

Step-by-step explanation:

Put the values where the arguments are and do the arithmetic.

  g(h(-2)) = g(-2+4) = g(2) = 5(2)

  g(h(-2)) = 10

Answer:

Assuming you want better payment each week, any number of hours above 33.333 or 33 hours and 20 minutes per week

Step-by-step explanation:

There are several ways we could do this.  We could say we want to have Tim Hortons be the better employer on the first week, or after so many weeks by adjusting the hours.  I am going to assume we are saying we want it to be a better employer on the first week, so the profit will be the amount made every week plus the money made per hour times the number of hours.

Let's say number of hours is H

So Tim Hortons winds up as 200 + 5H for one week and  Mcdonalds will be 300 + 2H.

If you set the two expressions equal to each other you will find where they intersect, which means at that number of hours they will give the same amount of money while any amount before one of the companies will give more and after that many hours the other will.  Let's go ahead and solve.

200 + 5H = 300 + 2H

3H = 100

H = 100/3

So H is about 33.333.  let's check.

200 + 5(33.333) = 366.665 which rounds to 366.67 dollars

300 + 2(33.333) = 366.666 which also rounds to 366.67 dollars

So at 33.333 hours both give 366.67 dollars.  Let's look at a value below it, say 32.

200 + 5(32) = 360

300 + 2(32) = 364

So you can see here Tim Hortons  pays less.  Now we will try 34 as a value above 33.333

200 + 5(32) = 370

300 + 2(32) = 368

Here Mcdonalds pays less.  This was to show that values below 33.333 make Tim Hortonspay less and values above 33.333 make Mcdonalds pay less.  In other words any value above 33.333 hours will have Tim Hortons be the better employer.  And this is per week

I want to repeat, you can expand this to be multiple weeks and see which of the two becomes better in that epriod of time.  This was, I think, the simplest way to answer though.  

So the conditions where Tim Horton pays more isif you work more than 33.333 hours per week.  This will make them pay more every single week.  

Answer:

Positive

Step-by-step explanation:

This is an equation, with distribution in it. The number on the outside is positive, and the one inside is negative. Furthermore, since the number on the outside is larger than the one inside, the outcome will be positive.

Answer:

positive

Step-by-step explanation:

when both positive and negative will multiply then will  makes negatives. so negative is correct option.

Answer:

a speaker receive credibility is a combination of competence trustworthiness and caring

Answer:

[tex]x = \sqrt{-2} = 2i[/tex]

Step-by-step explanation:

[tex]5x^2-2=-12[/tex]

[tex]5x^2 =-10[/tex]

[tex]x^2 =-2[/tex]

[tex]x = \sqrt{-2} = 2i[/tex]

Answer:

[tex]x = 2.62[/tex] and [tex]x = 0.381[/tex]

Step-by-step explanation:

[tex]y = \sqrt x\\[/tex]

[tex]y = x - 1[/tex]

Required

y, when they are equal.

To do this, we set them to another

[tex]\sqrt{x} = x - 1[/tex]

Square both sides

[tex]x = (x - 1)^2[/tex]

Expand

[tex]x = x^2 - 2x + 1[/tex]

Collect like terms

[tex]x^2 -x-2x+1 = 0[/tex]

[tex]x^2 - 3x + 1 = 0[/tex]

Using quadratic formula

[tex]x = 2.62[/tex] and [tex]x = 0.381[/tex]

Answer:

hello again.. I think you have a problem about figures

Step-by-step explanation:

please be brave when you try to solve..try to draw new lines to get angle and then look at the overall of shape.. the photo helps you good bye

Step-by-step explanation:

0 is the ans my guy

dngjdjvkdkckgkdkgkskfkfkv

Answer:

root(250)

answer choice C

Step-by-step explanation:

explanation in the pic above.

Answer:

The percentage of people that could be expected to score the same as Matthew or higher on this scale is:

= 93.3%.

Step-by-step explanation:

a) Data and Calculations:

Mean score on the scale, μ = 50

Distribution's standard deviation, σ = 10

Matthew scores, x = 65

Calculating the Z-score:

Z-score = (x – μ) / σ

= (65-50)/10

= 1.5

The probability based on a Z-score of 1.5 is 0.93319

Therefore, the percentage of people that could be expected to score the same as Matthew or higher on this scale is 93.3%.

Answer:

I will answer in English.

We can prove that the angle APS is a triangle rectangle.

Remember that for a triangle rectangle of catheti A and B, and hypotenuse H, the Pythagorean's theorem says that:

A^2 + B^2 = H^2

In this case, we can assume that the hypotenuse is the longer side, AS, and the other two sides are the catheti.

Then we have:

H = 5x + 10

A = 3x + 6

B = 4x + 8

Now let's write the equation from the theorem, and let's see if its true.

A^2 + B^2 = H^2

( 3x + 6 )^2 + (4x + 8)^2 = (5x + 10)^2

So we can start with:

( 3x + 6 )^2 + (4x + 8)^2

And try to "transform" this into:

(5x + 10)^2

First, let's expand it:

((3x)^2 + 2*(3x)*6 + 6^2) + ( (4x)^2 + 2*(4x)*8 + 8^2)

9x^2 + 24x + 36 + 16x^2 + 64x + 64

25x^2 + 40x + 100

Now we can complete squares on the left side, by writing:

(5x)^2 + 2*10*(5x) + 10^2

(5x + 10)^2

Then we saw that the equation is true for every value of x, then we just prove that the triangle fulfills the theorem, thus, the triangle is a triangle rectangle.

Answer:

-18

Step-by-step explanation:

Answer: -18 is the difference

Step-by-step explanation:

Evaluate = -18

[tex]{\color{red}{\huge{\underbrace{\overbrace{\mathfrak{\:\:\:\:\:\:\:꧁"Answer"꧂\:\:\: }}}}}}[/tex]

[tex]\small\color{blak}{{\underline{\bold{ Find \:a X } } } }[/tex]

[tex]\small\color{black}{{\underline{\bold{173°=15z+10x-2 } } } } \\ = 173 = 25x - 2 \\ = - 25x = - 2 - 173 \\ = - 25x - 175 \\ = \small\color{blue}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: x=7\:\:\:\: }}}}[/tex]

[tex]\small\color{blak}{{\underline{\bold{ Find\:a\:m<QSR } } } }[/tex]

[tex]\small\color{blak}{{\underline{\bold{ 10(7)-2 } } } }\\=70-2\\=\small\color{red}{{{\boxed{\tt\red{} \:\:\:\:\:\:\:\:\:\: m<QSR=68°\:\:\:\: }}}}[/tex]

[tex]\Large\color{red}{{\underline{\mathfrak {{꧁"Carry\:on\: learning"꧂ }}}}}[/tex]

The measure of angle QSR is 68 degrees.

Substitution means putting numbers in place of letters to calculate the value of an expression.

According to the given question.

m ∠TSQ = 15x

m ∠TSR = 173 degrees

m ∠QSR = 10x -2

Since,

m ∠TSR = m ∠TSQ + ∠QSR

Substitute the value of m ∠TSR, m ∠TSQ and m ∠QSR in the above expression.

⇒ [tex]173 = 15x + 10x - 2[/tex]

⇒ [tex]173 = 25x - 2[/tex]

⇒ [tex]175 = 25x[/tex]

⇒ [tex]x = \frac{175}{25}[/tex]

⇒ [tex]x = 7[/tex]

Again, for finding the value of angle QSR substitute the value of x in 10x - 2.

Therefore,

m ∠QSR = 10(7) - 2

⇒ m ∠QSR = 70 - 2

⇒ m ∠QSR = 68 degrees

Hence, the measure of angle QSR is 68 degrees.

Fid out more information about substitution here:

brainly.com/question/27810586

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Answer:

B. the mean

Step-by-step explanation:

According to the Bar Chart shown, the number of DVDs sold at a local music store during one week are displayed.

Therefore, the measure(s) of central tendency that can be used to determine the average number of DVDs sold each day is the mean.

This is because the mean is the sum total of the number of DVDs sold, divided by the number, which gives the average.

Answer:

The Mean

Step-by-step explanation:

I took the test

Answer:

[tex]82\sqrt{21}\text{ or approximately 375.77 miles per hour}[/tex]

Step-by-step explanation:

Please refer to the diagram below. R is the radar station and x is the distance from the station to the plane.

We are given that the plane is flying horizontally at an altitude of two miles and at a speed of 410 mph. And we want to find the rate at which the distance from the plane to the station is increasing when it is five miles away from the station.

In other words, given da/dt = 410 and x = 5, find dx/dt.

From the Pythagorean Theorem:

[tex]a^2+4=x^2[/tex]

Implicitly differentiate both sides with respect to time t. Both a and x are functions of t. Hence:

[tex]\displaystyle 2a\frac{da}{dt}=2x\frac{dx}{dt}[/tex]

Simplify:

[tex]\displaystyle a\frac{da}{dt}=x\frac{dx}{dt}[/tex]

Find a when x = 5:

[tex]a=\sqrt{5^2-2^2}=\sqrt{21}[/tex]

Therefore, dx/dt when da/dt = 410, x = 5, and a = √(21) is:

[tex]\displaystyle \frac{dx}{dt}=\frac{(\sqrt{21})(410)}{5}=82\sqrt{21}\approx 375.77\text{ mph}[/tex]

The rate at which is distance from the plane to the radar station is increasing at a rate of approximately 375.77 miles per hour.

The measure of angle ∠AOB is 180°. The correct option from the following is (A).

A turn's angle is quantified using degrees or °. A full turn encompasses 360°. A protractor can be used to determine the size of an angle. The term "acute" refers to an angle smaller than 90°. Obtuse refers to an angle between 90° and 180°. Reflex is an angle larger than 180 degrees. Right angles have an angle of exactly 90 degrees.

A quadrilateral is an enclosed form created by uniting four points, any three of which cannot be collinear. A quadrilateral is a polygon that has four sides, four angles, and four vertices. Let us study more about quadrilaterals' shapes, their characteristics, and the various kinds of quadrilaterals, as well as some examples of quadrilaterals.

For the given quadrilateral, the sum of angles is:

∠A + ∠O + ∠B = ∠AOB

60° + 60° + 60° = 180°

Hence, the correct option is (A).

To learn more about Angle, here:

https://brainly.com/question/17039091

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She gets a 4% raise so her new pay is 100% + 4% of her previous pay.

104% = 1.04 as a decimal.

Divide her new pay by 1.04:

24,960 / 1.04 = 24,000

Her previous pay was $24,000

Answer:

mapping an area

Step-by-step explanation:

One situation and probably the most common is mapping an area. Graphs are great for dividing a geographical location into various sections and creating a model representation of the area. The graph itself allows for specific directions to be shared using the x and y coordinates on the graph. The same applies for finding the midpoint of a line segment. For example, this is useful if you were trying to find a place to meetup with a friend that is an equal distance from where you are and from where your friend is currently located. Therefore, allowing you to meetup at the midpoint.

Answer:

C

Step-by-step explanation:

Start by simplifying what you can in each radicalfor example, the

∛(xy⁵)= y∛(xy²)

and

∛(x⁷y¹⁷)=x²y⁵∛(xy²)

So know our equation looks like

y∛(xy²)*x²y⁵∛(xy²)

Now because what's inside the radical is the same we can combine them

y⁶x²∛(xy²)²

distribute the square

so

∛(xy²)²=  ∛(x²y⁴)= y∛(x²y)

and finally,

y⁶x²*y∛(x²y)= y⁷x²∛(x²y)

this is equal to option C