To make a chocolate sponge cake for 8 people you need:
300g flour
100g cocoa
400g sugar
350g butter
1 egg
a) How much of each ingredient do you need to make a cake for 10 people?
b) if you only had 60g of cocoa,how much of each ingredient would you now need?​

Answer: 2.2532

Step-by-step explanation:

From the table attached :

Expected probability = sum of p(x) * x ; wher P-X) is the probability of x

E(p(x), x) = (0*0) + (1 * 0.06) *(2*0.1) + (3 * 0.16) * (4 *0.16)+ (5*0.26) * (6 *0.08) + (7 * 0.13) + (8 * 0.05)

Pp(x) * x) = 2.2532

Therefore, the expected value of the distribution is 2.2532

Answer:

y + c ÷ m = x

Step-by-step explanation:

You start of with:

y = mx - c

We can get rid of the + c by putting it on the other side. When a number goes to the other side it does the opposite, so the - will become a +. It will end up as:

y + c = mx

We just need x on itself so we need to get ride of m. In this sum, mx means that they are multiplying together, we need to make that divide. So we take m on the other side and make it divide. This brings us to x on itself.

(y+c) ÷ m = x

Hope this helps.

x can be changed into the subject of the formula as x = (y + c) / m.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Subject of an equation is that variable we are going to find out.

The given equation is y = mx - c.

Here y is the subject.

We need to rewrite the equation to make x the subject.

y = mx - c

Adding c on both sides,

y + c = mx - c + c

y + c = mx

Dividing both sides by m, we get,

(y + c) / m = mx / m

(y + c) / m = x

Hence the given formula y = mx - c can be rewritten to make x the subject as x = (y + c) / m.

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Answer:

AAS

Step-by-step explanation:

As we can see, they tell us that both of the angles on the bottom are congruent. Since they share a side, that means that one side is congruent too. So it must be two angles and one side. It can't be ASA, because the congruent side is not in between the two congruent angles, so it must be AAS

Hey There!!

Your correct choice will be AAS Theorem.

Step-by-step explanation:

Because, two angles and any side of one triangle are congruent to two angles and any side of another triangle, then these triangles are congruent Thus, given a triangle ADB and CDB. ∠BAD = ∠BCD = 90°. (Angle), Then, BD = BD (The common side) As given AAS Theorem. Therefore, ∆ADB ≅ ∆CDB by the AAS theorem.

Hope This Explaining was not confusing . . .

By ☆Itsbrazts☆

Hey Mate !

Your Answer is given in the snip below !!

Please do mark me as brainliest !!!

(ANSWER=  (D)   [tex]\frac{1}{6}[/tex] )

Explanation

Answer:

You have a standard number cube.

What is the probability of rolling a number less than 3, and then rolling a prime number?

D. 1/6

Answer:

2 by 3

Step-by-step explanation:

please mark brainliest if it helped

Answer: probability of getting two 5s =0.04

probability of getting at least one 5 =0.36

probability of getting a total score greater than 5 =0.6

Step-by-step explanation:

Total outcomes on 1 spinner = 5

Then , total outcomes of spinning it 2 times=  [tex]5\times5 = 25[/tex]

Number of outcomes for getting two 5's = 1

Then, the probability of getting two 5s [tex]=\dfrac{\text{Favorable outcomes of getting two 5's }}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{1}{25}=0.04[/tex]

Number of outcomes for getting at least one 5 [ {(1,5),(2,5),(3,5),(4,5),(5,5), (5,1), (5,2), (5,3), (5,4)} ] =9

Then, the probability of getting at least one 5[tex]=\dfrac{\text{Favorable outcomes of getting at least one 5 }}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{9}{25}=0.36[/tex]

Number of outcomes for getting a total score of 5, [ {(1,4),(4,1),(2,3),(3,2)} ] =4

Then, the probability of getting a total score of 5,[tex]=\dfrac{\text{Favorable outcomes of getting a total score of 5 }}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{4}{25}[/tex]

Number of outcomes for getting a total score greater than 5 [ {(1,5),(5,1),(2,4),(4,2),(2,5), (5,2), (3,4),(4,3), (3,5), (5,3), (3,3), (4,5), (5,4), (4,4), (5,5)} ] =15

Then, the probability of getting a total score greater than 5,[tex]=\dfrac{\text{Favorable outcomes of getting a total score greater than 5 }}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{15}{25}=\dfrac{3}{5}=0.6[/tex]

Answer:

Step-by-step explanation:

From the expression xy = 4, y = 4/x

Substituting y = 4/x into the expression  y(x-4)(x+2) and expanding;

=  y(x-4)(x+2)

= 4/x(x-4)(x+2)

On expansion;

= (4-16/x)(x+2)

= 4x+4(2)-(16/x)x-(16/x)2

= 4x+8-16-32/x

= 4x-8-32/x

The equivalent expression is 4x - 8 - 32/x

Answer:

2

Step-by-step explanation:

substitute n=1 and n=3 in the given equation

1 st term is (1)^2-1-2 = 1 -1 -2 = -2

3rd term is (3)^2-3-2 = 9-3-2=4

sum of 1st and 3rd term is -2 + 4 = 2

Answer:

D

Step-by-step explanation:

Apply rule : [tex]-(-a)=+a[/tex]

Negative times negative is positive.

The expression turns into a sum of fractions.

Answer: is your  first option

Step-by-step explanation:

after going over all the available equations, your first option is the only one that had results that were much more reasonable than the others. hope it helps.

Answer:

answer is 1 answer is 4-5 = 1 is 3-6 answer is only 3

Answer:

A. Choosing the third person listed on every fifth page of the phone book is stratified sampling.

Step-by-step explanation:

Stratified sampling involves grouping the population into subgroups before sampling. It provides a more manageable and cheaper means of sampling data by placing the population into grouped strata. The only problem is that this sampling method cannot be used in a data population that cannot be stratified. In this question, the phone book is stratified into subgroups of every five pages, and the third person listed is chosen to represent the subgroup

Answer:

8.1

Step-by-step explanation:

Answer:

  £531.52

Step-by-step explanation:

We are given the profit in week 1 and information about week 2. We are asked for the difference between week 2 profit and week 1 profit.

__

In week 2, pizza is sold 4 ways. The diagram shows the numbers of pizzas sold each way. The table shows the profit made for each way the pizza was sold. We need to add up the profits from each of the sales to find the profit for week 2.

Then the total profit in week 2 is ...

  £1514.04 -175.42 +888.94 -5.68 = £2221.88

So, profit in week 2 exceeds profit in week 1 by ...

  £2221.88 -1690.36 = £531.52 . . . more profit in week 2

the answer is A,when X=0

Answer:

28>x

Step-by-step explanation:

7>x/4

remove the denominator by multiplying both sides by 4

4×7>x/4×4

28>x

Answer:

                [tex]8\frac23\ cm^2[/tex]

Step-by-step explanation:

sector of the circle if the angle at the center is 150° means  [tex]\frac{150^o}{360^o}[/tex] of full circle of given radius

area of a circle of given radius R is:  πR²

so area of given sector:

[tex]A=\dfrac{150^o}{360^o}\cdot \pi\cdot8^2=\dfrac5{12}\cdot3.1\cdot64=82,(6)=8\frac23\ cm^2[/tex]

The area of a sector of the circle if the angle at the center is 150° is 82.67 square centimeter.

A circle is a locus of a point whose distance always remains constant from a given specific point. The general equation is -

x² + y² = r²      (for circle centered at origin)

Given is a circle has a radius of 8 cm.

The area of the sector subtending the angle 150° at center is -

A = (150/360) x 3.1 x 8 x 8

A = 82.67 square centimeter.

Therefore, the area of a sector of the circle if the angle at the center is 150° is 82.67 square centimeter.

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Answer:

[tex]\boxed{-10000}[/tex]

Step-by-step explanation:

[tex]F(x)=\frac{1}{x}[/tex]

Let x = -10000

[tex]F(-10000)=\frac{1}{-10000}[/tex]

[tex]F(-10000)= -0.0001[/tex]

-0.0001 is closest to 0 when x value is -10000.

No other value can work from the other options, options B and C increase the value from 0. Option D would make the function undefined.

Answer:

1) A. y= (20 - 2x) /5

2) C. 141.3

3) True ( Your answers are here.)

Answer:

1. is A 2. is C 3. is I believe True

Step-by-step explanation:

1.

2x + 5y = 20

-2x          -2x

5y = 20 - 2x

/5          /5

Answer: y = 20 - 2x /5

2.

V = πr^2h

π=3.14  r=3  h=5

3.14*3^2*5

1.413*10^2 which = 141.3

3.

I am not completely sure but I think it is True

Hope this helps

Answer:

30°, 60° and 90°

Step-by-step explanation:

Given the expression Arccos (√3/2)=β, we can use the expression to calculate one of the acute angles in a right angled triangle.

Note that a right angled triangle is made up of two acute angles and a right angled (90°)

Let's get one of the acute angles first

If Arccos (√3/2)=β

β = cos^-1 √3/2

β = 30°

This shows that one of the acute angles is 30°

To get the third angle, we know that sum of angles in a triangle is 180° and since we already know two of the angles, i.e 90° and 30°, we can get the third angle.

90+30+x = 180

120+x = 180

x = 180-120

x = 60°

All the angle measurement for the right angled triangle are 30°, 60° and 90°

Answer:

[tex]\large \boxed{\sf \ \ \ 4 \ \ \ }[/tex]

Step-by-step explanation:

Hello, please find below my work.

[tex]x^2-4x-1=0 \ \ \text{add 1 to both parts of the equation}\\\\<=> x^2-4x-1+1=0+1=1\\\\<=> x^2-4x=1[/tex]

We know that for any a and x real numbers we can write

[tex](x-a)^2=x^2-2ax+a^2[/tex]

When we compare with the left part of the equation we can identify the term in x so that -4=-2a (multiply by -1) <=>4=2a (divide by 2) <=> a = 4/2 = 2

So we can write

[tex](x-2)^2=x^2-4x+2^2=x^2-4x+4[/tex]

So we have to add 4 to both sides of the equation to complete the square and it comes:

[tex]x^2-4x-1=0 \ \ \text{add 1 to both parts of the equation}\\\\<=> x^2-4x-1+1=0+1=1\\\\<=> x^2-4x=1 \ \boxed{\text{ add 4 to complete the square}} \\\\<=>x^2-4x\boxed{+4}=1+4=5\\\\<=>(x-2)^2=5 \ \text{ we take the root } \\ \\ <=>x-2=\pm \sqrt{5}\ \text{ we add 2 } \\ \\ <=> x = 2+\sqrt{5} \ \text{ or } \ x = 2-\sqrt{5}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

  two thirds, because the angles are complementary

Step-by-step explanation:

The cosine of an angle is equal to the sine of its complement.

  cos(23°) = 2/3 = sin(67°)

The cos23° = 2/3 = sin67° because the angles are complementary If the cos 23° = two thirds.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have given:

cos23° = 2/3

The above expression can be written as:

cos(90-67) = sin67°    (cos(90-θ) = sinθ)

Thus, the cos23° = 2/3 = sin67° because the angles are complementary If the cos 23° = two thirds.

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Answer:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Answer:

Two remote interior angles.

Answer:

2m  

4

−2m  

3

−26m  

2

−23m+20

Step-by-step explanation:

Answer:

subtract 3, because that'll allow the variables to be on one side and the constants on the other

Step-by-step explanation:

Answer:

12.8

Step-by-step explanation:

you have to use the law of sines to calculate it. the measure of angle c is 110 and you have to do

Sin(110)x=17sin(45)

and then it turns into 17sin(45)/sin(110)

then put it into desmos with it being in degrees mode

Answer:

a = 1, b = - 2

Step-by-step explanation:

The points that lie on the curve and straight line satisfy the corresponding equations.

Substitute the points into their corresponding equations, that is

(1, - 1 ) → - a = 1² + b = 1 + b ( multiply both sides by - 1 )

a = - 1 - b → (1)

(3, 3 ) → [tex]\frac{-3b}{2}[/tex] = [tex]\frac{3}{a}[/tex] ( cross- multiply )

- 3ab = 6 ( divide both sides by - 3 )

ab = - 2 → (2)

Substitute a = - 1 - b into (2)

(- 1 - b)b = - 2 , distribute left side

- b - b² = - 2 ( multiply through by - 1 )

b² + b = 2 ( subtract 2 from both sides )

b² + b - 2 = 0 ← in standard form

(b + 2)(b - 1) = 0 ← in factored form

Equate each factor to zero and solve for b

b + 2 = 0 ⇒ b = - 2

b - 1 = 0 ⇒ b = 1

Substitute these values into (1) for corresponding values of a

b = - 2 : a = - 1 - (- 2) = - 1 + 2 = 1

b = 1 : a = - 1 - 1 = - 2

Thus a = - 2, b = 1 or a = 1, b = - 2

Given that a > b then a = 1, b = - 2

Answer:

Option (A)

Step-by-step explanation:

By satisfying the equation of a function 'f' by each coordinates given in the options we can get the point which lies on the graph of f(x) = [tex]2\times (5)^x[/tex]

Option (A). (1, 10)

f(1) = [tex]2\times (5)^1[/tex]

10 = 10

True.

Therefore, point (1, 10) lies on the graph.

Option (B). (0, 10)

f(0) = [tex]2\times 5^0[/tex]

10 = 2

Not true.

Therefore, point (0, 10) doesn't lie on the graph.

Option (C). (10, 1)

f(10) = [tex]2\times 5^{10}[/tex]

1 = 19531250

Not true.

Therefore, point (10, 1) doesn't lie on the graph.

Option (D). (0, 0)

f(0) = [tex]2\times 5^0[/tex]

0 = 2

Not True.

Point (0, 0) doesn't lie on the graph.

Option (A) will be the answer.

Answer:

A=3244.8 dollars

Step-by-step explanation:

A=p(1+r)^t

A=3000(1+0.04)^2

A=3244.8 dollars