Question 4
12 marks
4.1 a. In each case find the unit cost and then state which is the better buy.
4 marks
6kg of potatoes for $2.45 or
15 kg of potatoes for $5.9 or
10 kg of potatoes for $3.92?

Answer:

c=5/72

Step-by-step explanation:

5/9=14c-5/12

Switch sides

14c-5/12=5/9

Add 5/12 tp both sides

14c-5/12+5/12=5/9+5/12

Simplify;

14c-5/12+5/12

=14c

Simplify;

5/9+5/12

LCM of 9, 12;

36

The least common multiplier of a, b is the smallest positive number that is divisible by both a and b.

Prime factorization of 9;

3*3

Prime factorization of 12;

2*6

=2*2*3

=3*3*2*2

=36

5/9=5*4/9*4=20/36

5/12=5*3/12*3=15/36

=20/36+15/36

20+15/36

=35/36

14c=35/36

14c/14=35/36/14

14c/14=c

35/36*14

=35/504

=5/72

Answer c=5/72

Answer to the following question is as follows;

Value of C = 5 / 72

Step-by-step explanation:

Given:

[tex]\frac{5}{9} = 14c - \frac{5}{12}\\\\[/tex]

Find:

Value of C

Computation:

[tex]\frac{5}{9} = 14c - \frac{5}{12}\\\\[/tex]

By taking 5/12 to LHS Side

[tex]\frac{5}{9} + \frac{5}{12} = 14c\\\\[/tex]

By taking LCM;

[tex]\frac{(4)(5) + (3)(5)}{36} = 14c\\\\[/tex]

[tex]\frac{20 + 15}{36} = 14c\\\\[/tex]

[tex]\frac{35}{36} = 14c\\\\[/tex]

By transfer 14 to LHS side

[tex]\frac{35}{36 \times 14 } = c\\\\[/tex]

[tex]\frac{5}{36 \times 2 } = c\\\\[/tex]

[tex]\frac{5}{72} = c\\\\[/tex]

Value of C = 5 / 72

Learn more;

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Answer:

D. The same point

Step-by-step explanation:

An equilateral triangle can be defined as a type of triangle that has all of its sides being equal in length.

This ultimately implies that, an equilateral triangle comprises of three (3) congruent sides and as such creates three (3) congruent angles that measures 60° each. Also, the sum of the congruent angles of an equilateral is always equal to 180°.

Hence, in an equilateral triangle, the incenter, orthocenter, circumcenter, and centroid are the same point i.e all of the three (3) centers fall on the same point or spot.

Answer:

whats the question?

Step-by-step explanation:

Answer:

is this just to get free points cause you didint add your question?

Step-by-step explanation:

Answer:

[tex]f(x) = 3(x - 1)^2-3[/tex]

Step-by-step explanation:

Given

[tex]f(x) = 3x^2 - 6x + 6[/tex]

Required

Write as:

[tex]f(x) = a(x - h)^2 + k[/tex]

In [tex]f(x) = 3x^2 - 6x + 6[/tex], the coefficient of x is -6

Divide by 2: -3

Square: 9

Add 9 - 9 to the above equation

[tex]f(x) = 3x^2 - 6x +9-9+ 6[/tex]

Split to 2

[tex]f(x) = [3x^2 - 6x +9]-[9- 6][/tex]

[tex]f(x) = [3x^2 - 6x +9]-[3][/tex]

Factorize:

[tex]f(x) = [3x^2 - 3x -3x+9]-[3][/tex]

[tex]f(x) = [3x(x - 1) -3(x-1)]-[3][/tex]

[tex]f(x) = [(3x - 3)(x-1)]-[3][/tex]

Factorize 3x - 3

[tex]f(x) = [3(x - 1)(x-1)]-[3][/tex]

[tex]f(x) = 3(x - 1)^2-[3][/tex]

[tex]f(x) = 3(x - 1)^2-3[/tex]

Answer:

b = 1

JK = 3

Step-by-step explanation:

5b - 2 = 9b - 6

4b = 4

b = 1

JK = 3

Answer:

5.5×5.5=30.5

we rounded 30.25 in nearest tenth it becomes 30

Answer:

C.] 5.5

Step-by-step explanation:

It is mentioned that the number was multiplied by the number itself.

Let's take 'x' as the number. It was multiplied by itself and the product is 30. So the equation will be:

x × x = 30

[tex]x^{2}[/tex] = 30

x = [tex]\sqrt{30}[/tex]

x = 5.47 = 5.5 (to the nearest tenth)

Answer:

Step-by-step explanation:

Answer:

[tex]+\sqrt{55i}[/tex]

Step-by-step explanation:

Khan <3

Answer:

96:144

Step-by-step explanation:

Since there are 240 students and the known value is 96 students buying lunch, you simply subtract the two numbers.

240 - 96 = 144

There are 144 students bringing bag lunch.

The ratio is asking students purchasing  lunch to students bringing a bag lunch, which would be 96:144

The simplified answer is 2:3

To get this, divide 144 by 96

This, in turn, would give you in answer of 3/2 which can be inversed to get the right answer

Answer:

it's less than

Step-by-step explanation:

12/8 simplified is 3/2

11/6 cannot be further simplified

3/2<11/6

Answer:

scalene triangle

..... .

Answer:

Figure 0 = 5 tiles

Figure 1 = 5 + 7 = 12 tiles

So, the equation is:

y = 7x + 5

because, it adds 7 tiles in every new figure.

The equation is y = 7x +5.

Answer is y = 7x +5

Answer:

B

Step-by-step explanation:

2/5 is equal to 40 percent

Adnswer:

18m+42n in distributive property=6(3m+7n)

Step-by-step explanation:

Answer and Step-by-step explanation:

The answer to this expression would be 6(3m + 7n).

18m + 42n is the distributive version of the same expression.

To un-distribute, you would find the greatest common factor of both numbers, and pull it out of the expression.

18 and 42 have a greatest common factor of 6.

18 divided by 6 is 3.

42 divided by 6 is 7.

That leaves us with 6(3m + 7n).

#teamtrees #PAW (Plant And Water)

Answer:

C. 245.5

Step-by-step explanation:

(5.5) (3) + (12.5) (3) + (5.5) (3) + (12.5) (5.5) + (12.5) (5.5) + (3) (12.5)

= 245.5

Answer:

its 245.5

Step-by-step explanation:

Answer:

The Binomial model is inappropriate because the Trials are independent of each other

Step-by-step explanation:

Given data :

probability of a company started by a person  failing with 2 years = 0.3

14 start-ups ( 98 people ) are followed for 2 years

The probability that at least 42 of these 98 people will fail in 2 years

Reason why the Binomial model is inappropriate for finding the probability that at least 42 of these 98 people will fail

The Binomial model is inappropriate because the Trials are independent of each other

Answer:

there is no pic -_-

Step-by-step explanation:

Answer:36

Step-by-step explanation: 6 sided dice = 6 possible outcomes

6×6=36

The required number of outcomes is 36 after rolling all six dice. Option B is correct.

Jane has to roll a set of six standard dice and record the results of each
trial. She wonders how many different outcomes are possible after rolling all six dice. the total number of possible outcomes for each trial to be determined.

Probability can be defined as the ratio of favorable outcomes to the total number of events for a system of the certain events.

For 1 dice, sample space = { 1  2  3  4  5  6}
total possible outcome = 6
Now 6 dice roll at once and the total outcome = 6 * 6
                                                                                = 36
Meanwhile, Jane has a total of 36 outcomes.

Thus, the required number of outcomes is 36 after rolling all six dice. Option B is correct.

Learn more about probability here:

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Answer:

15. there are 11 cubes

16. there are 18 cubes

17. there are 6 cubes

18. the pencil case

19. the stapler

20. The Pencil Case is heavier than the wallet

21. The stapler is lighter than the wallet

Step-by-step explanation:

Okay so looking at the unit cubes you must count how much there are and see how much unit cubes the weight is equivalent to

15. there are 11 cubes

16. there are 18 cubes

17. there are 6 cubes

18. the pencil case

19. the stapler

20. The Pencil Case is heavier than the wallet

21. The stapler is lighter than the wallet

your work is correct!! Good job!!

Hope this helps!!

-Ketifa

Answer:

<8 corresponds with <3

Answer:

(a) [tex]A = 1500(1 - e^{-0.01t})[/tex]

(b) [tex]t = 0[/tex]

Step-by-step explanation:

Given

[tex]V= 300gal[/tex] --- Volume of tank

[tex]B = 5lb/gal[/tex] --- Brine solution

[tex]R_1 = 3gal/min[/tex]  --- Rate in, in gallon/min

[tex]R_2 = 6gal/min[/tex] --- Rate out, in gallon/min

Required

Determine A(t)

First, calculate the rate in (R in) and (R out) in lb/min

[tex]R_{in} = B * R_1[/tex]

[tex]R_{in} = 5lb/gal * 3gal/min[/tex]

[tex]R_{in} = 15lb/min[/tex]

R(out) is calculated by multiply the rate at which brine leaves the tank (lb/gal) * R2

So, we have:

[tex]R_{out} = \frac{A(t)}{300} lb/gal * 3gal/min[/tex]

[tex]R_{out} = \frac{3*A(t)}{300} lb/min[/tex]

[tex]R_{out} = \frac{A(t)}{100} lb/min[/tex]

The change in the amount of brin e in the tank at time t is given as:

[tex]A'(t) = R_{in} - R_{out}[/tex]

[tex]A'(t) = 15 - \frac{A(t)}{100}[/tex]

Rewrite:

[tex]\frac{dA}{dt} = 15 - \frac{A}{100}[/tex]

Multiply through by dt

[tex]dA = [15 - \frac{A}{100}]* dt[/tex]

Make dt stand alone

[tex]\frac{dA}{15 - \frac{A}{100}} = dt[/tex]

[tex]ln|15 - \frac{A}{100}| = -0.01t + ln\ c[/tex]

Express as exponents

[tex]15 - \frac{A}{100} = ce^{-\frac{t}{100}}[/tex]

Multiply through by 100

[tex]1500 - A = 100ce^{-\frac{t}{100}}[/tex]

[tex]A = 1500 - 100ce^{-\frac{t}{100}}[/tex]

[tex]A = 1500 - 100ce^{-0.01t}[/tex]

Apply initial conditions

[tex]A(0) = 0[/tex]

Substitute 0 for t in: [tex]A = 1500 - 100ce^{-0.01t}[/tex]

[tex]0 = 1500 - 100ce^{-0.01*0}[/tex]

[tex]0 = 1500 - 100ce^{0}[/tex]

[tex]0 = 1500 - 100c[/tex]

[tex]100c = 1500[/tex]

[tex]c = 15[/tex]

Substitute 15 for c in [tex]A = 1500 - 100ce^{-0.01t}[/tex]

[tex]A = 1500 - 100*15e^{-0.01t}[/tex]

[tex]A = 1500 - 1500e^{-0.01t}[/tex]

Factorize:

[tex]A = 1500(1 - e^{-0.01t})[/tex]

How long to empty the tank

Set A to 0

[tex]1500(1 - e^{-0.01t}) = 0[/tex]

Divide through by 1500

[tex]1 - e^{-0.01t} = 0[/tex]

Collect Like Terms

[tex]e^{-0.01t} = 1[/tex]

Take ln of both sides

[tex]ln\ (e^{-0.01t}) = ln\ 1[/tex]

[tex]-0.0t = 0[/tex]

[tex]t = 0[/tex]

She bought $27.40 worth of roast beef.

Answer:

angle 7

Step-by-step explanation:

Answer:

angle 7 angle forms a pair of alternate

exterior angles with angle 2.

Answer:

0.9692 = 96.92% probability of getting someone in the 22-29 age bracket or someone who agreed to respond.

Step-by-step explanation:

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

Find the probability of getting someone in the 22-29 age bracket or someone who agreed to respond.

357 people.

281 in the 22-29 age bracket + 65 in the 18-21 that agree to respond. So

[tex]p = \frac{281+65}{357} = 0.9692[/tex]

0.9692 = 96.92% probability of getting someone in the 22-29 age bracket or someone who agreed to respond.

Answer:

6 / 8 or 3 / 4

Step-by-step explanation:

Subtraction lol

Answer:

[tex]q=31.7\\p=28.4[/tex]

Doing all calculations with 3 significant figures.

Step-by-step explanation:

First, we'll obtain the value of 'q', this by realizing how the two angles together form a right triangle with inner angles of 30, 60, 90.

Furthermore, the opposite side of the angle of 30 is 'q' and its adjacent is given as 55. Hence, we can solve for 'q' using tangent as follows:

[tex]tan(30)=\frac{q}{55} =.577[/tex]

We solve for 'q':

[tex]q=.577*55=31.7[/tex]

Now to solve for 'p', we first will calculate what '55-p' is equal to.

First, we realize '55-p' corresponds to the adjacent side to the angle of 50 inside the small right triangle (the one with inner angles of 50, 40, 90) and q (which we now know is 31.7) correspond to the opposite side. Hence, we again use tangent as follows:

[tex]tan(50)=\frac{q}{55-p} =\frac{31.7}{55-p} =1.19[/tex]

We solve for 'p':

[tex]1.19(55-p)=31.7\\65.5-1.19p=31.7\\1.19p=33.8\\p=\frac{33.8}{1.19}=28.4[/tex]

Answer:

140

Step-by-step explanation:

30% of a number(x) is 105. To find the number(x) we must set up the equation below and solve for x:

0.3=105/x (multiply x)

0.3x=105 (divide by 0.3)

x=350

Solve for 40% of the number by multiplying 0.4 by the number:

350x.4=140

Answer: 104

Step-by-step explanation:

It is a full circle

Circle = 360

We have 126 and 26 so

360 - (126+26) = 208

Since the a's are opposite thet means they are equal ( I forgot the law name)

208 divided by 2

104

Answer:

5u-15=10 |+15

5u=25 |:5

u=5

The solution is 25

I hope it helps

have anice day