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4/8 Marks

a)
Here are the ingredients needed to make 8 pancakes.
b)
250 ml milk
1 egg
140 g flour
5g butter
a) Simon makes 4 pancakes.
Work out how much milk he needs.
b)
Craig makes 12 pancakes.
Work out how much butter he needs.

Answer:

If you need to find how deep Lake Michigan is, it is 280 meters below the surface

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x ← is in slope- intercept form

with slope m = 1

Answer:

1

Step-by-step explanation:

Answer:

Organize

Step-by-step explanation:

To calculate the rate of return for the extra investment, we need more information such as the cash inflows from the extractor and the alternate equipment. Without this information, it is not possible to determine the rate of return.

To calculate the rate of return, we would need the cash inflows generated by both the existing extractor and the alternate equipment. Cash inflows could come from the sale of vegetable oil or any other revenue generated by using the equipment. Without these values, we cannot calculate the rate of return.

Additionally, the rate of return calculation would also require the initial investment, salvage value, and the time period considered. In this case, the initial cost and salvage value for the existing extractor are provided, but we still need the initial cost and salvage value for the alternate equipment.

Without the necessary data, it is not possible to determine the rate of return for the extra investment in the extractor replacement.

The calculation of the rate of return for the extra investment in the extractor replacement cannot be determined without knowing the cash inflows from both the existing extractor and the alternate equipment.

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The amount of commission made in the last week and in the year 2011 is $936 and $48,672, respectively.

The Stock Market Alexander is a stockbroker. It is given that he earns 13% commission each week. He sold $7,200 worth of stocks last week. We need to calculate the amount of commission he made in the last week.

Let the commission earned be represented by "C". The commission earned is the product of the rate of commission and the amount of stocks sold.

C = 13% of $7,200

C = 0.13*7200

C = $936

The commission made in the last week is $936. It is also given that he makes the same amount every week on an average. We need to calculate the commission earned in the whole year 2011.

We know that there are 52 weeks in a year. So, the total commission made in the year 2011 is the product of commission made in a week and the total number of weeks.

C = 52*936

C = $48,672

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Answer:

x = 3√7.

y = 12.

Step-by-step explanation:

The 2 triangles are similar so:

x/9 = 7/x

x^2 = 63

x = √63

   = 3√7.

By Pythagoras' theorem

y^2 = 9^2 + (3√7)^2

      =  81 + 63

      = 144

y = 12.

The probability that a randomly selected month's number of order is more than 150 is 0.13%

Given, shawn finds that the monthly number of take-out orders at a restaurant is normally distributed with mean 132 and standard deviation 6.

⇒ mean = 132

⇒ standard deviation = 6

Analysis:

Set the monthly number of take out order as x.

From the question, we know:

P(x > 150) = P(x-132/ > 150-132/6)

= P(x=132/6 > 3)

= 1 - P(x-132/6 ≤ 3)

≈ 1 - 0.9987 {standard normal distribution table}

≈ 0.0013

= 0.13%

Hence we get the probability as 0.13%.

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Pseudocode algorithms are used as prototypes of an actual program.

The required pseudocode algorithm is as follows:

1. Start

2. Input n

3. Odd = 1

4. For i in range(n):

    4.1 Print Odd     4.2 Odd = Odd + 2

The pseudocode that prints the first n odd numbers starting from 1 is as follows:

1. Start

2. Input n

3. Odd = 1

4. For i in range(n):

    4.1 Print Odd     4.2 Odd = Odd + 2

The above pseudocodes would print the first n odd numbers starting from 1, given that n is the input

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Answer:The last option is correct.

Step-by-step explanation:

Let S be and show is a sphere of radius R centered at the arigin. We will compare the flux that it does not depends on R. Parametic equation of sphare Y(4,0)= Rsind caso + Rsind sine j + R Cord F

and 014≤ 640 ≤ 2TT outward normal is

(r = 18) = √x² + y²+z2)

= F = ૪ 3

flux = [[Finds

. Rsing dodo = 83

(from put value of n

13 sind do do 23

2 TT, TT sing do do

R 11 R [["e. / sind dado (r= 171 = radius of ephare)

Π 2T ए [e" [" sind do do= ["- Casp" "do 0

[-(-1-1) do 2TT = 2x (2-0) 2 = do flux

flux = [[F·ñ-ds S = 4π

The flux is 411 and it depends on radius 'R'

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The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.

In this case, we are estimating the difference in population means between two groups - upperclassmen and underclassmen. The point estimate is calculated by subtracting the sample mean of the underclassmen from the sample mean of the upperclassmen, which gives us

0.76 - 0.60 = 0.16.
the point estimate of the difference in population mean exercised between underclassmen and upperclassmen is 0.16 hours, which was calculated by subtracting the sample mean of underclassmen from the sample mean of upperclassmen.
Point Estimate = (Sample Mean of Upperclassmen) - (Sample Mean of Underclassmen)
Point Estimate = (0.76) - (0.60)
Point Estimate = 0.16

Hence, the point estimate of 0.16 suggests that, on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours. This is a rough estimate of the difference between the two population means based on the provided sample data.

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Answer:

possibly 4 if not I'm sorry

Answer:

x=15
y=2

Step-by-step explanation:

the scale factor is 6:1

if you divide 12 by 6 you get 2
so y=2

if you multiply 6 by 2.5 you get 15
so x=15

The center of the dilation is a fixed point in the plane about which all the points are expanded or contracted, the center of the dilation is the only point that does not change. Hence in this case the center of the dilation is the point D.

Now, we notice that the dilation contracted in half the original figure.

Therefore, the dilation is: center D and scale factor 1/2

The principal investment required to get a total amount of $3,700.00 from compound interest at a rate of 3.5% per year compounded 365 times per year over 15 years is $2,287.26.

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Given Data

Rate = 3.5%

Final Amount = $3,700

Time = 15 Years

First, convert R as a percent to r as a decimal

r = R/100

r = 3.5/100

r = 0.035 per year,

Then, solve the equation for P

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

P = 3,700.00 / (1 + 0.035/365)(365)^(15)

P = 3,700.00 / (1 + 0.00010137)^(4745)

P = $2,287.26

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Answer: m=-39

Step-by-step explanation:

3m-27=2m-12

     -27        -27     Subtract 27 on both sides

3m=2m-39

-2m -2m                Subtract 2m on both sides

1m=-39

m=-39                    Simplify

Answer:

m = 15

Step-by-step explanation:

Step 1: Subtract 2m from both sides.

3m - 27 - 2m = 2m - 12 - 2m

m - 27 = - 12

Step 2: Add 27 to both sides.

m - 27 + 27 = - 12 + 27

m = 15

To prove the given statement using the Principle of Mathematical Induction, two conditions must be satisfied: (a) the statement is true for the natural number 1, and (b) if the statement is true for a natural number k, it is also true for the next natural number k + 1.

The Principle of Mathematical Induction is a method used to prove statements that depend on a variable n being a natural number. It consists of two steps: the base step and the inductive step.

The base step requires showing that the statement is true for the first natural number, in this case, n = 1. Evaluating the left-hand side (LHS) of the equation when n = 1 gives:

4 = 2(1)(1 + 1) = 2(2) = 4.

Since the LHS matches the right-hand side (RHS), the base step is satisfied.

The inductive step involves assuming that the statement is true for some arbitrary natural number k and then proving that it is also true for the next natural number k + 1. Assuming the statement is true for k, we have:

4 + 8 + 12 + ... + 4k = 2k(k + 1).

Now, we need to prove that the statement is true for k + 1. Adding 4(k + 1) to both sides of the equation yields:

4 + 8 + 12 + ... + 4k + 4(k + 1) = 2k(k + 1) + 4(k + 1).

Simplifying the right-hand side gives:

2k(k + 1) + 4(k + 1) = 2(k + 1)((k + 1) + 1).

Therefore, if the statement holds for k, it also holds for k + 1.

By satisfying both the base step (condition a) and the inductive step (condition b), the Principle of Mathematical Induction guarantees that the given statement is true for all natural numbers.

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Answer:

If r = 5, then:

(-5) - (-5) + (5) - (5) = 0

Always remember order of operations (PEMDAS)

Hope this helps :)

(1) The significant figure will be 710.

Hence the correct option is (b).

(2) (a) The modulus of A and B are,

| A | = √62

| B | = √30

(b) The value of A + B = 7 i - 2 j + 9 k

(c) The value of A - B = -3 i - 4 j + 5 k

(3) (a) a ⋅ (b × c) is meaningful and result is a scalar.

(b) a × (b ⋅ c) is not meaningful.

(c) a × (b × c) is meaningful and result is a vector.

(d) (a ⋅ b) × c is not meaningful.

(e) (a ⋅ b) × (c ⋅ d) is not meaningful.

(f) (a × b) ⋅ (c × d) is meaningful and result is a scalar.

The not meaningful is because to conduct cross product we need two vectors.

(4) Given lines are parallel because the cross product of the vectors along that lines is zero vector.

(1) Given the multiplication is,

20.6 × 5.5 × 6.27

That gives the result,

20.6 × 5.5 × 6.27 = 710.391

Here significant figure will be 710.

So the correct option is (b).

(2) Given the vectors are,

A = 2 i - 3 j + 7 k

B = 5 i + j + 2 k

(a) The modulus of A and B are,

| A | = √[2² + (-3)² + 7²] = √62

| B | = √[5² + 1² + 2²] = √30

(b) The value of A + B vector is,

A + B = [2 i - 3 j + 7 k] + [5 i + j + 2 k] = 7 i - 2 j + 9 k

(c) The value of A - B vector is,

A - B = [2 i - 3 j + 7 k] - [5 i + j + 2 k] = -3 i - 4 j + 5 k

(3) We know that the cross product gives vector result and dot product gives scalar result.

The statements are,

(a) a ⋅ (b × c) is meaningful and result is a scalar.

(b) a × (b ⋅ c) is not meaningful.

(c) a × (b × c) is meaningful and result is a vector.

(d) (a ⋅ b) × c is not meaningful.

(e) (a ⋅ b) × (c ⋅ d) is not meaningful.

(f) (a × b) ⋅ (c × d) is meaningful and result is a scalar.

The not meaningful is because to conduct cross product we need two vectors.

(4) Here for first line vector is,

A = [(-2) - (-4)] i + [0 - (-6)] j + [(-3) - 1] k = 2 i + 6 j - 4 k

for second line vector is,

B = [5 - 10] i + [3 - 18] j + [14 - 4] k = -5 i - 15 j + 10 k

So now the cross product is,

A × B = \(\left[\begin{array}{ccc}i&j&k\\2&6&-4\\-5&-15&10\end{array}\right]\) = 0 i + 0 j + 0 k

So the cross vector is a zero vector so the initial vectors are parallel to each other.

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The volume of the solid tetrahedron is \(\frac{1}{144}\) cubic units.

T's base is a triangle in the xy-plane (z= 0), with one edge being the line y=x, z= 0; the front side is a triangle in the vertical plane x= 1; the left side is a triangle in the xz-plane (y= 0); and the top is the plane xyz= 0 (this plane contains the three points (0,0,0), (1,1,0), (1,0,1).

The equation must be ax+by+cz+d=0 and must be satisfied by the three points as well as the edge (x=y, z=0).

T is thus described as 0≤z≤(xy), 0≤y≤x, 0≤x≤1.

for which it is suitable to used V=dzdydx.

\(\int\limits\int\ \int\limits{xyz} \, dV=\int\limits^1_0 \int\limits^x_0 \int\limits^{x-y}_0 {xyz} \, dxdydz\\ \\ =\int\limits^1_0 \int\limits^x_0[\frac{1}{2}xyz^2]\limits^{x-y}_0 dydx\\\\=\frac{1}{2}\int\limits^1_0 \int\limits^x_0(x^3y-2x^2y^2+xy^3)dydx\\\\=\frac{1}{2}\int\limits^1_0 [\frac{1}{2}x^3y^2-\frac{2}{3}x^2y^3+\frac{1}{4}xy^4]\limits^x_0dx\\\\=\frac{1}{2}\int\limits^1_0\frac{1}{12}x^5dx\\\\=\frac{1}{2}[\frac{1}{72}x^6]\limits^1_0\\\\=\frac{1}{144}\)

Thus, the volume of the solid tetrahedron is \(\frac{1}{144}\) cubic units.

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The quadratic example is ax² + b x + c = 0 where x stands for an unknown value and where a, b, and c stand for known numbers is known as a quadratic equation in algebra.

Quadratic equations are second-degree polynomial equations with at least one squared term. It is also referred to as quadratic equations.

The numerical coefficients a, b, and c are known, while the unknown variable x is. For example , x2 + 2x + 1. It also goes by the name quadratic equation as in: b x +c=0    

The terms a, b, and c are also referred to as quadratic coefficients.    

'Examples of Quadratics

x² –x – 9 = 0

5x² – 2x – 6 = 0
3x² + 4x + 8 = 0

-x² +6x + 12 = 0  (an example of non-quadratic equation is x³ − x² − 5 = 0)

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Answer:

The each price for pad of paper is 35

Step-by-step explanation:

If one notebook cost 42. Then for 5 notebook

5*42 =210

For pad of paper

350-210

= 140

140÷4

= 35.

Answer:

35(enjoy your day)

Step-by-step explanation:

Voluntary sampling is one type of sampling method that is not probability based this means that the survey's findings cannot be reliably extrapolated or generalized.

What is voluntary sampling?

A sample made up of people who freely decided to take part in the sample group is known as a voluntary sampling. Those who want to participate in a voluntary sampling typically do so because they are passionate about the topic of the survey. According to definitions, a sample with self-selected individuals is one that includes voluntary responses.

Researchers who wanted to be able to generalize their findings to the entire community would not choose volunteer sampling because it does not produce a representative sample.

A convenience sample is one that the researcher can use at their discretion, such as voluntary sampling.

However, because only those who have strong opinions about the poll will typically agree to participate, voluntary sampling can result in bias.

The survey's findings cannot be confidently extrapolated or generalized because of the possibility of bias.

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The number of times I would expect to roll a number that is not a 5 is 300 times.

A standard die has 6 faces. There are 5 numbers that are not 5 on a standard die. They are 1, 2, 3, 4, 6.

The number of times a 5 won't be rolled = (5/6) x 360

5 x 60 = 300 times

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The variance is the average squared deviation of each value from the mean. It calculates how far each value in a group is from the mean, and then it squares the result of each of those calculations. Finally, it averages the sum of the squares to produce a figure that represents how varied the data is from the mean.

The variance formula is as follows:

Var(X) = (Σ (Xi - μ)^2) / (n - 1)

Where, X is a random variable representing the group data, μ is the mean of the group data, Xi is each value in the group data, Σ is the sum of all Xi values, and n is the number of values in the group data.

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According to given information, the probability that a contract will last between 15 and 35 weeks is `0.905`.

To compute the probability that a contract will last between 15 and 35 weeks, we must utilize the standard deviation for the normal distribution.

To solve for the probability of a normal distribution, we use the formula `z = (x - μ) / σ`, where `x` is the value we are looking for, `μ` is the mean, and `σ` is the standard deviation.

We can compute the standard deviation using the variance, which is the square of the standard deviation, which is `σ^2`.

To begin, we first find the standard deviation.  `σ = sqrt(36) = 6`.

Next, we will calculate the `z-scores` for 15 and 35.

\(`z1 = (15 - 25) / 6 = -10 / 6 = -1.67`\)

and \(`z2 = (35 - 25) / 6 = 10 / 6 = 1.67`\).

Now we can use the `Z-table` to find the probabilities that correspond to `z1` and `z2`. We can see that the probability of `z1` is `0.0475` and the probability of `z2` is `0.9525`.

Finally, to obtain the probability that a contract will last between 15 and 35 weeks, we must subtract the probabilities corresponding to `z1` from `z2`.

\(`P(15 ≤ X ≤ 35) = P(Z ≤ 1.67) − P(Z ≤ −1.67) = 0.9525 − 0.0475 = 0.905`\).

Therefore, the probability that a contract will last between 15 and 35 weeks is `0.905`.

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Given:

From the above expression,

The answer would be 18.8

Answer:

A

Step-by-step explanation:

If you plug in (2, -2) to each one, you would get -2= 5/2(2)-7

5/2 = 2.5 and 2.5 x 2 = 5, 5-7 does in fact equal the Y which is -2

Answer:

i think its 3x-8 not sure