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

Answer:

0.9216 = 92.16% probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A hotel manager believes that 23% of the hotel rooms are booked.

This means that [tex]p = 0.23[/tex]

Sample of 610 rooms

This means that [tex]n = 610[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.23[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.23*0.77}{610}} = 0.017[/tex]

What is the probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%?

p-value of Z when X = 0.23 + 0.03 = 0.26 subtracted by the p-value of Z when X = 0.23 - 0.03 = 0.2. So

X = 0.26

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.26 - 0.23}{0.017}[/tex]

[tex]Z = 1.76[/tex]

[tex]Z = 1.76[/tex] has a p-value of 0.9608

X = 0.2

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.2 - 0.23}{0.017}[/tex]

[tex]Z = -1.76[/tex]

[tex]Z = -1.76[/tex] has a p-value of 0.0392

0.9608 - 0.0392 = 0.9216

0.9216 = 92.16% probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%

Answer:

78.5 (I think 90% sure)

Step-by-step explanation:

sum of both scores

75+82 = 157

average for a third test

157÷2=78.5

Answer:

Third one.

BO is not 7.8 cm

Step-by-step explanation:

Answer:

[tex]P(x < 3) = 25\%[/tex]

[tex]E(x) = 3[/tex]

Step-by-step explanation:

The given parameters can be represented as:

[tex]\begin{array}{ccccccc}x & {5} & {4} & {3} & {2} & {1}& {0} & P(x) & {25\%} & {30\%} & {20\%} & {15\%} & {5\%} & {5\%} \ \end{array}[/tex]

Solving (a): P(x < 3)

This is calculated as:

[tex]P(x < 3) = P(x = 0) + P(x = 1) + P(x =2)[/tex] ----- i.e. all probabilities less than 3

So, we have:

[tex]P(x < 3) = 5\% + 5\% + 15\%[/tex]

[tex]P(x < 3) = 25\%[/tex]

Solving (b): Expected number of events

This is calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

[tex]E(x) = 5 * 25\% + 4 * 30\% + 3 * 20\% + 2 * 15\% + 1 * 5\% + 0 * 5\%[/tex]

[tex]E(x) = 125\% + 120\% + 60\% + 30\% + 5\% + 0\%[/tex]

[tex]E(x) = 340\%[/tex]

Express as decimal

[tex]E(x) = 3.40[/tex]

Approximate to the nearest integer

[tex]E(x) = 3[/tex]

Answer:

Step-by-step explanation:

Even function has following property:

It is easy to show this works with the second choice only. All the others don't work:

This is not correct as x - 1 ≠ -x - 1 so as their squares, so g(x) ≠ g(-x)

The last two choices are not even similarly.

Answer:

B. g(x) = 2x2 + 1

Correct on edge

Answer:

3x+4

Step-by-step explanation:

When you factor 9x^2+24x+16, it factors to (3x+4)^2

Factoring 9x^2 - 16 factors to (3x+4)(3x-4)

Therefore the common factor is 3x+4

I hope this helps!

Step-by-step explanation:

[tex]\tan^2 \theta - 3\tan \theta + 2 = 0[/tex]

Let [tex]x = \tan \theta[/tex]

We can then write

[tex]x^2 -3x + 2 = 0\:\:\Rightarrow\:\:(x - 2)(x - 1) = 0[/tex]

or

[tex](\tan \theta - 2)(\tan \theta - 1) = 0[/tex]

The zeros occur when

[tex]\tan \theta = 2\:\:\:\text{or}\:\:\:\tan \theta = 1[/tex]

or when [tex]\theta = 63.4°[/tex] or [tex]\theta = 45°[/tex].

Answer:

<A ≈ 45 degrees

<B ≈ 57 degrees

<C ≈ 78 degrees

Step-by-step explanation:

Hi there!

1) Find <C with the law of cosines

Typically, we want to solve for the angle opposite the largest side first.

Law of cosines: [tex]cosC=\frac{a^2+b^2-c^2}{2(a)(b)}[/tex]

Plug in given values

[tex]cosC=\frac{5^2+6^2-7^2}{2(5)(6)}\\cosC=\frac{1}{5}\\C=cos^-^1(\frac{1}{5} )\\C=78[/tex]

Therefore, <C is approximately 78 degrees.

2) Find <B with the law of cosines

[tex]cosB=\frac{a^2+c^2-b^2}{2(a)(c)}[/tex]

Plug in given values

[tex]cosB=\frac{5^2+7^2-6^2}{2(5)(7)}\\cosB=\frac{19}{35}\\B=cos^-^1(\frac{19}{35})\\B=57[/tex]

Therefore, <B is approximately 57 degrees.

3) Find <A

The sum of the interior angles of a triangle is 180 degrees. To solve for <A, subtract <B and <C from 180:

180-57-78

= 45

Therefore, <A is 45 degrees.

I hope this helps!

Answer:

2√14 prob I'm not 100% sure

Answer:

a. If the area of the tiles is greater than or equal to the area of all the rooms.

b. 24

c. 360

Step-by-step explanation:

a. Explain how you would estimate whether Ted has enough tiles to cover all the kitchen floors in the entire apartment building?

Ted would have enough tiles if the  area of the tiles is greater than or equal to the area of all the rooms. Since we have 500 one meter square tiles, we have 500 m² of tiles.

Since the rooms are 6 m long and 4 m wide, the area of each room is 6 m × 4 m = 24 m². Since there are 15 rooms, the area of all the rooms is 15 × 24 m² = 360 m².

Since the area of the tiles = 500 m² is greater than the area of the rooms = 360 m², Ted would have enough tiles to cover all kitchen floors in the entire apartment building.

b. How many tiles, each measuring 1 square meter, are needed to cover one room floor?

Since the area of each room floor is 24 m² and the area of each tile is 1 m², so the number of  1 square meter tiles needed to cover each floor is n = area of floor/area of tile = 24 m²/1 m² = 24.

c. How many tiles are needed to cover all the floors in the entire building?

Since 24 tiles are needed to cover each floor and there are 15 rooms in the building, we would require 24 tiles/room × 15 rooms/building = 360 tiles.

So we require 360 tiles.

Answer:

a+3b

Step-by-step explanation:

3a+4b-2a-b

=3a-2a+4b-b

=a+3b

Answer:

17

Step-by-step explanation:

because they are both above 5 so add 1

Answer:

so this as a fraction is 3500/12000 which is equivalent to

0.29166666666 we multiply this by 100

29.166666666

so about 29.1% or the students are female and have served a mission

Hope This Helps!!!

Answer:

The general equation for a parabola is:

y = f(x) = a*x^2 + b*x + c

And the vertex of the parabola will be a point (h, k)

Now, let's find the values of h and k in terms of a, b, and c.

First, we have that the vertex will be either at a critical point of the function.

Remember that the critical points are the zeros of the first derivate of the function.

So the critical points are when:

f'(x) = 2*a*x + b = 0

let's solve that for x:

2*a*x = -b

x = -b/(2*a)

this will be the x-value of the vertex, then we have:

h = -b/(2*a)

Now to find the y-value of the vertex, we just evaluate the function in this:

k = f(h) = a*(-b/(2*a))^2 + b*(-b/(2*a)) + c

k =  -b/(4*a) - b^2/(2a) + c

So we just found the two components of the vertex in terms of the coefficients of the quadratic function.

Now an example, for:

f(x) = 2*x^2 + 3*x + 4

The values of the vertex are:

h = -b/(2*a) = -3/(2*2) = -3/4

k = -b/(4*a) - b^2/(2a) + c

=  -3/(4*2) - (3)^2/(2*2) + 4 = -3/8 - 9/4 + 4 = (-3 - 18 + 32)/8 = 11/8

Answer: -9x-1y-9/

Step-by-step explanation:

Answer: b

Step-by-step explanation:

I really dont like edge

Answer:

65 km/hr

Step-by-step explanation:

The average of numbers can be calculated by adding them up and dividing that by how many numbers there are.

Here, we have two numbers. Therefore, we first add them (55+75 = 130) and then divide by 2 because there are 2 numbers, so 130/2 = 65

20x-5

Answer:

Solution given;

perimeter=sum of all sides

=4x-1+9x-1+7x-3=20x-5

The perimeter of the line segments 4x - 1, 9x - 1, and 7x - 3 is 20x - 5.

To find the perimeter of the given line segments, you need to add up the lengths of all the line segments.

The lengths of the line segments are:

4x - 1,

9x - 1,

7x - 3.

To find the perimeter, add these lengths together:

Perimeter = (4x - 1) + (9x - 1) + (7x - 3)

= 4x + 9x + 7x - 1 - 1 - 3

= 20x - 5.

Therefore, the perimeter of the line segments 4x - 1, 9x - 1, and 7x - 3 is 20x - 5.

To learn more on Perimeter click:

https://brainly.com/question/7486523

#SPJ6

Answer:

= x^2 + 3 + √3x^2 - 1

Step-by-step explanation:

Remove parentheses: (a) = a

= x^2 + 3 + √x . 3x - 1

x . 3x = 3x^2

= x^2 + 3 + √3x^2 - 1

Answer:

The zeroes of f(x) = (x-7)(x+8) are 7 and -8.

Step-by-step explanation:

You have to figure out what makes each of the equal to zero.

Step 1 : Make the 2 equations both equal 0.

x-7 = 0

x+8 = 0

Step 2: Solve for x

x-7 = 0

x=7

x+8 = 0

x=-8

So 7 and -8 are both zeroes of this function.

Answer:

8.50 cm²

Step-by-step explanation:

The dimension of each square is given as 0.5cm by 0.5cm

The area of the a square is, a²

Where, a = side length

Area of each square = 0.5² = 0.25cm

The number of blue colored squares = 34

The total area of the blue colored squares is :

34 * 0.25 = 8.50cm²

Answer:

the answae is D THEN C THE. 1

Answer:

[tex]\frac{1}{12}[/tex] probability of getting a head on the coin and the number 2 on the die

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Independent events:

If two events, A and B are independent, the probability of both events happening is the multiplication of the probabilities of each event happening, that is:

[tex]P(A \cap B) = P(A)P(B)[/tex]

Probability of getting a head on the coin:

Head or tails, fair coin, so:

[tex]P(A) = \frac{1}{2}[/tex]

Probability of getting the number 2 on the die:

6 numbers, one of which is 2, so:

[tex]P(B) = \frac{1}{6}[/tex]

What is the probability of getting a head on the coin and the number 2 on the die?

[tex]P(A \cap B) = P(A)P(B) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}[/tex]

[tex]\frac{1}{12}[/tex] probability of getting a head on the coin and the number 2 on the die

Hello,

I have only found 113 solutions (i have num 15 given)

nb= 1         ::: 27*n +  98= 30*n + 56===> n= 1  4

nb= 2         ::: 28*n +  95= 30*n + 67===> n= 1  4

nb= 3         ::: 29*n +  65= 30*n + 17===> n= 4  8

nb= 4         ::: 29*n +  65= 30*n + 18===> n= 4  7

nb= 5         ::: 29*n +  65= 30*n + 47===> n= 1  8

nb= 6         ::: 29*n +  65= 30*n + 48===> n= 1  7

nb= 7         ::: 29*n +  74= 30*n + 16===> n= 5  8

nb= 8         ::: 29*n +  74= 30*n + 18===> n= 5  6

nb= 9         ::: 29*n +  74= 30*n + 56===> n= 1  8

nb= 10        ::: 29*n +  74= 30*n + 58===> n= 1  6

nb= 11        ::: 30*n +  16= 29*n + 74===> n= 5  8

nb= 12        ::: 30*n +  17= 29*n + 65===> n= 4  8

nb= 13        ::: 30*n +  18= 29*n + 65===> n= 4  7

nb= 14        ::: 30*n +  18= 29*n + 74===> n= 5  6

nb= 15        ::: 30*n +  47= 29*n + 65===> n= 1  8

nb= 16        ::: 30*n +  48= 29*n + 65===> n= 1  7

nb= 17        ::: 30*n +  56= 27*n + 98===> n= 1  4

nb= 18        ::: 30*n +  56= 29*n + 74===> n= 1  8

nb= 19        ::: 30*n +  58= 29*n + 74===> n= 1  6

nb= 20        ::: 30*n +  67= 28*n + 95===> n= 1  4

nb= 21        ::: 36*n +  97= 40*n + 25===> n= 1  8

nb= 22        ::: 38*n +  59= 40*n + 27===> n= 1  6

nb= 23        ::: 38*n +  65= 40*n + 27===> n= 1  9

nb= 24        ::: 38*n +  69= 40*n + 15===> n= 2  7

nb= 25        ::: 39*n +  78= 45*n + 6===> n= 1  2

nb= 26        ::: 39*n +  82= 40*n + 15===> n= 6  7

nb= 27        ::: 39*n +  82= 40*n + 17===> n= 6  5

nb= 28        ::: 39*n +  82= 40*n + 65===> n= 1  7

nb= 29        ::: 39*n +  82= 40*n + 67===> n= 1  5

nb= 30        ::: 40*n +  15= 38*n + 69===> n= 2  7

nb= 31        ::: 40*n +  15= 39*n + 82===> n= 6  7

nb= 32        ::: 40*n +  17= 39*n + 82===> n= 6  5

nb= 33        ::: 40*n +  25= 36*n + 97===> n= 1  8

nb= 34        ::: 40*n +  27= 38*n + 59===> n= 1  6

nb= 35        ::: 40*n +  27= 38*n + 65===> n= 1  9

nb= 36        ::: 40*n +  65= 39*n + 82===> n= 1  7

nb= 37        ::: 40*n +  67= 39*n + 82===> n= 1  5

nb= 38        ::: 46*n +  87= 50*n + 39===> n= 1  2

nb= 39        ::: 46*n +  87= 52*n + 9===> n= 1  3

nb= 40        ::: 47*n +  68= 50*n + 29===> n= 1  3

nb= 41        ::: 47*n +  83= 50*n + 26===> n= 1  9

nb= 42        ::: 47*n +  98= 51*n + 6===> n= 2  3

nb= 43        ::: 47*n +  98= 53*n + 2===> n= 1  6

nb= 44        ::: 48*n +  63= 50*n + 29===> n= 1  7

nb= 45        ::: 48*n +  73= 52*n + 9===> n= 1  6

nb= 46        ::: 49*n +  63= 51*n + 7===> n= 2  8

nb= 47        ::: 49*n +  72= 53*n + 8===> n= 1  6

nb= 48        ::: 49*n +  78= 52*n + 30===> n= 1  6

nb= 49        ::: 49*n +  87= 56*n + 3===> n= 1  2

nb= 50        ::: 50*n +  26= 47*n + 83===> n= 1  9

nb= 51        ::: 50*n +  29= 47*n + 68===> n= 1  3

nb= 52        ::: 50*n +  29= 48*n + 63===> n= 1  7

nb= 53        ::: 50*n +  39= 46*n + 87===> n= 1  2

nb= 54        ::: 52*n +  30= 49*n + 78===> n= 1  6

nb= 55        ::: 57*n +  92= 63*n + 8===> n= 1  4

nb= 56        ::: 58*n +  72= 60*n + 34===> n= 1  9

nb= 57        ::: 58*n +  73= 60*n + 49===> n= 1  2

nb= 58        ::: 58*n +  79= 60*n + 31===> n= 2  4

nb= 59        ::: 58*n +  97= 60*n + 13===> n= 4  2

nb= 60        ::: 59*n +  47= 62*n + 8===> n= 1  3

nb= 61        ::: 59*n +  71= 60*n + 23===> n= 4  8

nb= 62        ::: 59*n +  71= 60*n + 28===> n= 4  3

nb= 63        ::: 59*n +  71= 60*n + 43===> n= 2  8

nb= 64        ::: 59*n +  71= 60*n + 48===> n= 2  3

nb= 65        ::: 59*n +  74= 63*n + 2===> n= 1  8

nb= 66        ::: 59*n +  78= 61*n + 30===> n= 2  4

nb= 67        ::: 59*n +  84= 61*n + 30===> n= 2  7

nb= 68        ::: 59*n +  87= 61*n + 3===> n= 4  2

nb= 69        ::: 60*n +  13= 58*n + 97===> n= 4  2

nb= 70        ::: 60*n +  23= 59*n + 71===> n= 4  8

nb= 71        ::: 60*n +  28= 59*n + 71===> n= 4  3

nb= 72        ::: 60*n +  31= 58*n + 79===> n= 2  4

nb= 73        ::: 60*n +  34= 58*n + 72===> n= 1  9

nb= 74        ::: 60*n +  43= 59*n + 71===> n= 2  8

nb= 75        ::: 60*n +  48= 59*n + 71===> n= 2  3

nb= 76        ::: 60*n +  49= 58*n + 73===> n= 1  2

nb= 77        ::: 61*n +  30= 59*n + 78===> n= 2  4

nb= 78        ::: 61*n +  30= 59*n + 84===> n= 2  7

nb= 79        ::: 65*n +  89= 70*n + 24===> n= 1  3

nb= 80        ::: 68*n +  59= 72*n + 3===> n= 1  4

nb= 81        ::: 68*n +  91= 70*n + 45===> n= 2  3

nb= 82        ::: 69*n +  43= 70*n + 15===> n= 2  8

nb= 83        ::: 69*n +  43= 70*n + 18===> n= 2  5

nb= 84        ::: 69*n +  43= 70*n + 25===> n= 1  8

nb= 85        ::: 69*n +  43= 70*n + 28===> n= 1  5

nb= 86        ::: 69*n +  48= 72*n + 3===> n= 1  5

nb= 87        ::: 69*n +  52= 70*n + 14===> n= 3  8

nb= 88        ::: 69*n +  52= 70*n + 18===> n= 3  4

nb= 89        ::: 69*n +  52= 70*n + 34===> n= 1  8

nb= 90        ::: 69*n +  52= 70*n + 38===> n= 1  4

nb= 91        ::: 69*n +  54= 71*n + 8===> n= 2  3

nb= 92        ::: 69*n +  58= 73*n + 2===> n= 1  4

nb= 93        ::: 69*n +  82= 75*n + 4===> n= 1  3

nb= 94        ::: 69*n +  85= 74*n + 20===> n= 1  3

nb= 95        ::: 70*n +  14= 69*n + 52===> n= 3  8

nb= 96        ::: 70*n +  15= 69*n + 43===> n= 2  8

nb= 97        ::: 70*n +  18= 69*n + 43===> n= 2  5

nb= 98        ::: 70*n +  18= 69*n + 52===> n= 3  4

nb= 99        ::: 70*n +  24= 65*n + 89===> n= 1  3

nb= 100       ::: 70*n +  25= 69*n + 43===> n= 1  8

nb= 101       ::: 70*n +  28= 69*n + 43===> n= 1  5

nb= 102       ::: 70*n +  34= 69*n + 52===> n= 1  8

nb= 103       ::: 70*n +  38= 69*n + 52===> n= 1  4

nb= 104       ::: 70*n +  45= 68*n + 91===> n= 2  3

nb= 105       ::: 74*n +  20= 69*n + 85===> n= 1  3

nb= 106       ::: 76*n +  93= 80*n + 45===> n= 1  2

nb= 107       ::: 79*n +  45= 82*n + 6===> n= 1  3

nb= 108       ::: 79*n +  54= 83*n + 6===> n= 1  2

nb= 109       ::: 80*n +  45= 76*n + 93===> n= 1  2

nb= 110       ::: 87*n +  64= 90*n + 25===> n= 1  3

nb= 111       ::: 87*n +  65= 90*n + 23===> n= 1  4

nb= 112       ::: 90*n +  23= 87*n + 65===> n= 1  4

nb= 113       ::: 90*n +  25= 87*n + 64===> n= 1  3

9514 1404 393

Answer:

  x² +y² -6x -16y +48 = 0

Step-by-step explanation:

Given:

Find:

  general form equation for the circle

Solution;

The standard form equation for the circle is ...

  (x -h)² +(y -k)² = r² . . . . . circle with radius r centered at (h, k)

  (x -3)² +(y -8)² = 5²

Subtracting 25 and expanding this will give the general form.

  x² -6x +9 +y² -16y +64 -25 = 0

  x² +y² -6x -16y +48 = 0

_____

Additional comment

"General form" of an equation is usually the form f(x,y) = 0, where f(x, y) is written in "standard form," with terms in lexicographical order and decreasing degree.

Answer:

2

Step-by-step explanation:

8*8 is 64

Since it looks like the empty box is an exponent, and there are 2 8s being multiplied, the answer is 2

Answer:

D. 34

Step-by-step explanation:

Because this is a right triangle we can use sin, cos, tan.

Use cosine because the values of the adjacent side and hypotenuse are already given.

cos(θ) = 72/87

Because we are solving for the angle measure (and not the measure of the side) we need to use inverse cos.

cos⁻¹ = 72/87

put into a calculator and answer is approximatelyn34 degrees.

Answer:

128 for 4.99

64 for 2.99 times 2 is more than 4.99.

12 oz. for 0.99 is also more than 4.99.

Answer:

8

Step-by-step explanation: