A shop sells apple juice in cartons of two sizes. A 500 ml carton costs $1.30.
a) Work out the cost of 250 ml of this apple juice. A 750 ml carton costs $1.86.
b) Work out the cost of 250 ml of this apple juice.
c) Which carton is better value for money?

Answer:

An equilateral triangle is formed.

Step-by-step explanation:

Since you construct two lines of 60° at points P and Q, the two ends of the line, you construct a triangle with two angles as 60°.

Hence, with the knowledge that the angle sum of a triangle is 180°, we can find that the remaining angle is [tex](180\textdegree - 60\textdegree - 60\textdegree)[/tex] = [tex]60\textdegree[/tex].

Therefore, a triangle with all angles at 60° is an equilateral triangle.

Hope this helped!

Answer:

a)  A simple random sample of 340 employees

b)  a) Cluster sample

Step-by-step explanation:

a) Remember, the sample size of most research work is a factor to consider in other to determine if the data collected represents the true percentage of the entire population.

Hence, a small random sample of 34 employees will not give more precise information than a larger sample of 340 employees because the larger sample contains more representation of the population.

b) A cluster sample is best used in this case because it involves dividing the population into several clusters or groups, then the researcher randomly selects a particular cluster or group in other collect research data for analysis.

Whereas in this case, the randomly selected clusters are the different (individual restaurant) franchise locations.

Answer:

y = 1/2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

3(2y - 3) - 6 = -12

Step 2: Solve for y

Answer:

Step-by-step explanation:

here you go mate

step 1

3(2y-3)-6=-12  equation

step 2

3(2y-3)-6=-12  simplify

(3)(2y)+(3)(-3)+-6=-12

step 3

(3)(2y)+(3)(-3)+-6=-12  distribute

6y+(-9)+(-6)=-12

step 4

(6y)+(-9+-6)=-12  combine the terms

6y-15=-12

step 5

6y-15(+15)=-12(+15) add +15 to both sides

6y=3

step 6

6y/6=3/6

answer

y=1/2

Let the daily rate of each associate, A = $700

And the daily rate of each partner, P = $1700

Let the total number of individuals involved in the case = NT

Total number of partners = NP

Total number of associates = NA

NP + NA = NT -------- (i)

From the question; NP - NA = 4 -------- (ii)

From (i), NA = NT - NP

Substitute in (ii) as: NP - (NT - NP) = 4

Therefore, 2NP - NT = 4.

And NP = 2 + (NT/2) --------- (iii)

Substitute for NP in (i) above: NT = NA + 2 + (NT/2)

Therefore, NT - (NT/2) - 2 = NA.

NA = (NT/2) - 2 ---------- (iv)

Finally, the total daily rate was $21200. This is a composite of the daily rate and numbers of both associates and partners.

Therefore, (A * NA) + (P * NP) = $21200 ---------- (v)

To find the individual number of associates and partners involved in this case, first substitute the values of NP and NA from (iii) and (iv) respectively into (v) such that the only variable in (v) is NT.

Solve for NT and then use the value to find NP and NA.

NT = 16

NP = 10

NA = 6

Notice that 10 - 6 = 4. Q.E.D

Hope this helps.

Answer:

p=a+4

Step-by-step explain:

Let a=the number of associates designated

let p=the number of partners designated

Write System of Equations:

700a+1700p=21200

Answer:

the sale price is 42

Step-by-step explanation:

120-65% = 42

Answer:

234

Step-by-step explanation:

48 x 3=144

30 x 3=90

144+90=234

Answer:

m < 1 = 72

Step-by-step explanation:

Since we know that line l and line m are parallel and that p is one of their transversals, it sets up a situation where we can identify which angles are congruent (equal) to one another according to their positions.

In this case, we can see that < 3 and < 1 are in the same matching corners created by the transversal. When angles are in the same matching corners they are called corresponding angles - and according to the Corresponding Angles Postulate, corresponding angles are congruent.

Therefore, m < 3 = m < 1, and since it's given that  m < 3 = 72, we know that m < 1 = 72 too.

Answer:

B: Divide by -2

Step-by-step explanation:

The only logical conclusion would be divide by -2, though that may not be the entire correct answer. Why?

Firstly, the sequence of 8, -4, 2, -1 only follows division by -2. Division by 2 would result in 8, 4, 2 and 1, multiplication by -2 would result in 8, -16, 32, -64, and multiplication by 2 would result in 8, 16, 32 and 64. Hence, the only logical conclusion would be division by -2.

However, this rule breaks down as we go into the fractions. -1 / -2 is 1/2, sure, but (1/2) / -2 should be - 1/4, and not 1/4. Hence, as we go into the fractions, the rule should have changed to division by 2 instead.

The only solution to unite the whole sequence would be to correct 1/4 to -1/4, and maybe OP should check whether that is the case.

Hope this helped!

Answer:

b. divided by -2

Step-by-step explanation:

Answer:9

Step-by-step explanation:

I think it’s 9 as the area of a parallelogram is A=bh. The height is 3 as well as the base so times them together equates to 9.

Answer:

it's B

Step-by-step explanation:

i got right on my assessment and because if you look closer when X is in the negative side the line is straight but when the line increases and the x is in the positive side it's curved

when x<0 the graph is linear and when x>0 then the graph is non- linear.

A linear function is one that, when plotted, forms a straight line. Therefore, non-linear functions are all non-linear functions. We can discern if a function is linear or non-linear from its input/output table or equation, but graphing may be the quickest way to do it.

Something that is linear is related to a line. A line is built using all of the linear equations. A non-linear equation is one that cannot be represented by a straight line. It has a variable slope value and resembles a graphed curve.

Given:

We have the graph

From the graph we can see that when x<0 then there linearity or proportionality between x and y.

and, when x>0 then the graph is not a line it is turned out in a curve, which is not linear.

Hence, when x<0 the graph is linear and when x>0 then the graph is non- linear.

Learn more about linear and non linearity in a graph here:

https://brainly.com/question/28393413

#SPJ6

Answer:

a) The slope of the function is 3.

c) The equation is represented by [tex]n(t) = 3\cdot t + 35[/tex].

d) The y-intercept of the function is 35.

Step-by-step explanation:

a) According to the statement, we must assume that number of pieces of mail that must be hand-sorted (dependent variable) is represented by a linear function in terms of time (independent variable). That is:

[tex]n(t) = m\cdot t + n_{o}[/tex] (1)

Where:

[tex]m[/tex] - Slope, measured in number of pieces per minute.

[tex]t[/tex] - Time, measured in minutes.

[tex]n_{o}[/tex] - Initial number of pieces of mail that must be hand-sorted (y-intercept), measured in pieces.

[tex]n[/tex] - Current number of pieces of mail that must be hand-sorted, measured in pieces.

From Geometry, we know that a line can be formed by know two distinct points. If we know that [tex]n(15\,min) = 80\,p[/tex] and [tex]n(45\,min) = 170\,p[/tex], then the following system of linear equations is formed:

[tex]15\cdot m + n_{o} = 80[/tex] (2)

[tex]45\cdot m + n_{o} = 170[/tex] (3)

The solution of the system of equations is:

[tex]m = 3[/tex] and [tex]n_{o} = 35[/tex]

The slope of the function is 3.

c) By (1) and using results from a) we conclude that the equation function is:

[tex]n(t) = 3\cdot t + 35[/tex] (4)

d) The y-intercept of the function is 35.

Answer:

1 hour and 15 minuets

Step-by-step explanation:

5 hours and he was hedging for 25% of that time.

25%=.25

5(0.25)

1.25

A quarter of an hour is 15 minutes.

So the final answer would be 1 hour and 15 minuets.

Answer:

8% sales tax

Step-by-step explanation:

$330 x .15 = $49.50

$330 - $49.50 = $280.50

$302.94 - $280.50 = $22.44

$22.44/$280.50 = .08 x 100 x 8%

Answer:

It’s either 1 or 2

Step-by-step explanation:

Answer:

Mp=QN

Step-by-step explanation:

Answer:

136

Step-by-step explanation:

20% * 680

Cheers! :)

Answer:

(a) Percentage of girls = 55[tex]\frac{5}{7}[/tex]

(b) Percentage of boys = 44[tex]\frac{2}{7}[/tex]

Step-by-step explanation:

To find percentage, we multiply the fraction out of the total by 100%.

Percentage of girls = [tex]\frac{780}{1400}[/tex] × 100%

                                = 55[tex]\frac{5}{7}[/tex]

Percentage of boys = [tex]\frac{1400-780}{1400}[/tex] × 100%

                                 = 44[tex]\frac{2}{7}[/tex]

Answer:

(-1,0) these two points have the same x-value

(x,y)

Step-by-step explanation:

Step-by-step explanation:

Line AP = Line AO - Line PO = sqrt2 - 1.

Answer:

15 litres

Step-by-step explanation:

Given

5 litres = 12 guests

Required

Determine the number of litres for 36 guests

Represent the required number of litres with L.

So, we have the following relationship:

[tex]5\ litres = 12\ guests[/tex]

[tex]L = 36\ guests[/tex]

Cross Multiply

[tex]L * 12\ guests = 5\ litres * 36\ guests[/tex]

[tex]L * 12= 5\ litres * 36[/tex]

[tex]12L = 180\ litres[/tex]

Solve for L

[tex]L = \frac{180\ litres}{12}[/tex]

[tex]L =15\ litres[/tex]

Hence, 15 litres are needed

Answer:

b=-0.0019a + 215

at 2500 ft, b=210.25 degrees F

Step-by-step explanation:

First find the slope. a=altitude, b = temperature

slope is b2-b1 / a2-a1

points are (8200, 199.42) and (4700, 206.07)

(206.07 - 199.42) / (4700-8200)

= 6.65/ -3500

= - 0.0019

we have b = -0.0019a + intercept

plug in a point to find intercept

199.42 = -0.0019*8200 + intercept

intercept = 199.42 + 15.58 = 215

b=-0.0019a + 215

at a=2500 ft, substitute into equation

b= -0.0019*2500 + 215

= -4.75 + 215

= 210.25 degrees F

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It looks like you're given

F'(x) = 3x² + 7

and

F (0) = 5

and you're asked to find F(b) for the values of b in the list {0, 0.1, 0.2, 0.5, 2.0}.

The first is done for you, F (0) = 5.

For the remaining b, you can solve for F(x) exactly by using the fundamental theorem of calculus:

[tex]F(x)=F(0)+\displaystyle\int_0^x F'(t)\,\mathrm dt[/tex]

[tex]F(x)=5+\displaystyle\int_0^x(3t^2+7)\,\mathrm dt[/tex]

[tex]F(x)=5+(t^3+7t)\bigg|_0^x[/tex]

[tex]F(x)=5+x^3+7x[/tex]

Then F (0.1) = 5.701, F (0.2) = 6.408, F (0.5) = 8.625, and F (2.0) = 27.

On the other hand, if you're expected to approximate F at the given b, you can use the linear approximation to F(x) around x = 0, which is

F(x) ≈ L(x) = F (0) + F' (0) (x - 0) = 5 + 7x

Then F (0) = 5, F (0.1) ≈ 5.7, F (0.2) ≈ 6.4, F (0.5) ≈ 8.5, and F (2.0) ≈ 19. Notice how the error gets larger the further away b gets from 0.

A better numerical method would be Euler's method. Given F'(x), we iteratively use the linear approximation at successive points to get closer approximations to the actual values of F(x).

Let y(x) = F(x). Starting with x₀ = 0 and y₀ = F(x₀) = 5, we have

x₁ = x₀ + 0.1 = 0.1

y₁ = y₀ + F'(x₀) (x₁ - x₀) = 5 + 7 (0.1 - 0)   →   F (0.1) ≈ 5.7

x₂ = x₁ + 0.1 = 0.2

y₂ = y₁ + F'(x₁) (x₂ - x₁) = 5.7 + 7.03 (0.2 - 0.1)   →   F (0.2) ≈ 6.403

x₃ = x₂ + 0.3 = 0.5

y₃ = y₂ + F'(x₂) (x₃ - x₂) = 6.403 + 7.12 (0.5 - 0.2)   →   F (0.5) ≈ 8.539

x₄ = x₃ + 1.5 = 2.0

y₄ = y₃ + F'(x₃) (x₄ - x₃) = 8.539 + 7.75 (2.0 - 0.5)   →   F (2.0) ≈ 20.164

Answer:

2x-5y=-3

Slope=  2.000 /0.800

​x-intercept=-3/2=-1.50000

y-intercept=3/5=0.60000

y=16-4x

Slope=-8.0000/2.0000=-4.000

x-intercept=16/4=4

y-intercept=6/1=16.00000

Step-by-step explanation: