How can you tell the difference between a terminating decimal and a repeating decimal?

a. The lowest total number of cars is ( x = 3 ) Fiats and ( y = 7 ) Rolls Royces, totaling 10 cars.

b. the cheapest solution is to use 3 Fiats and 7 Rolls Royces, costing £240.

To solve this problem, we need to use a system of linear equations and optimization techniques.

Let's define ( x ) as the number of Fiats and ( y ) as the number of Rolls Royces.

The constraints are:

1. People constraint: [tex]\( 2x + 2y \geq 20 \)[/tex] (at least 20 people)

2. Sheep constraint: [tex]\( x + 4y \geq 32 \)[/tex] (at least 32 sheep)

3. Car constraint: [tex]\( x + y \leq 15 \)[/tex] (no more than 15 cars)

We also want to minimize the total number of cars, so the objective function is simply ( x + y ).

(a) To find the lowest total number of cars, we'll solve the system of equations:

[tex]\[\begin{cases}2x + 2y \geq 20 \\x + 4y \geq 32 \\x + y \leq 15\end{cases}\][/tex]

We solve these inequalities by  algebraically:

1. Solve the first two equations simultaneously:

 [tex]\[ \begin{cases} 2x + 2y = 20 \\ x + 4y = 32 \end{cases} \][/tex]

  Multiply the second equation by 2 to match coefficients with the first equation:

 [tex]\[ \begin{cases} 2x + 2y = 20 \\ 2x + 8y = 64 \end{cases} \][/tex]

Subtract the first equation from the second:

[tex]\[ \begin{aligned} (2x + 8y) - (2x + 2y) &= 64 - 20 \\ 6y &= 44 \\ y &= \frac{44}{6} \\ y &= 7.33 \end{aligned} \][/tex]

However, ( y ) must be a whole number, so we take ( y = 7).

Substitute ( y = 7 ) into the first equation:

  [tex]\[ \begin{aligned} 2x + 2(7) &= 20 \\ 2x + 14 &= 20 \\ 2x &= 6 \\ x &= 3 \end{aligned} \][/tex]

Therefore, the lowest total number of cars is ( x = 3 ) Fiats and ( y = 7 ) Rolls Royces, totaling 10 cars.

(b) To find the cheapest solution, we calculate the cost for each option:

Cost of Fiats: £10 x 3 = £30

Cost of Rolls Royces:  £30 x 7 = £210

Total cost:  £30 + £210 = £240

So, the cheapest solution is to use 3 Fiats and 7 Rolls Royces, costing £240.

Complete Question:

A farmer has to transport 20 people and 32 sheep to a market. He can use either Fiats (x) which take 2 people and 1 sheep, or Rolls Royces ( y) which take 2 people and 4 sheep. He must not use more than 15 cars altogether.

(a) What is the lowest total numbers of cars he could use?

(b) If it costs £10 to hire each Fiat and £30 for each Rolls Royce, what is the cheapest solution?

Answer:

5

Step-by-step explanation:

A little trick: the imaginary part ([tex]i[/tex]) in the coordinates of complex numbers act same as the y-coordinate in a rectangular plane.

So we want the distance between the coordinate points (4,2) and (7,-2).

How do we get the distance between 2 points? We use the distance formula.

Distance Formula = [tex]\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}[/tex]

Where [tex](x_1,y_1)=(4,2)[/tex]  and  [tex](x_2,y_2)=(7,-2)[/tex]

Let's solve for distance:

[tex]\sqrt{(-2-2)^2+(7-4)^2}\\ =\sqrt{(-4)^2+(3)^2} \\=\sqrt{16+9} \\=\sqrt{25} \\=5[/tex]

Hence, the length of the segment in the complex plane with endpoints at 4 + 2i and 7 – 2i is 5.

To describe the dimensions of the frame, we can represent the width as x inches and the length as (x+3) inches. The perimeter is less than 52 inches. We can solve an inequality using this information to find the possible values for the width.

To describe the dimensions of the picture frame, let's represent the width of the frame as x inches. According to the information given, the length of the frame is 3 inches greater than the width, so it can be represented as (x+3) inches. The perimeter of a rectangle is given by the formula: Perimeter = 2(width + length). Since the perimeter is less than 52 inches, we can form the following inequality: 2(x + (x+3)) < 52. Solving this inequality will give us the range of possible values for the width, and we can then determine the corresponding length of the frame.

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Answer:

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

Step-by-step explanation:

Given expression 1/4 divided by 5/7

For any division [tex]\frac{a}{b}[/tex]

'a' is the dividend and 'b' is the divisor

Denominator is the divisor

[tex]\frac{\frac{1}{4} }{\frac{5}{7}}[/tex]

Here, the denominator is 5/7

So the divisor is [tex]\frac{5}{7}[/tex]

The scale factor is 3.5 and the length of the banner is 84 inches. Then the correct option is A.

Dilation means the changing of the size of the object without changing the shape. The size of the object may be increased or decreased based on the scale factor.

A picture of a school’s mascot is 18 in. wide and 24 in. long.

It is enlarged proportionally to banner size.

If the width is enlarged to 63 in.

Then the scale factor will be

[tex]\rm S.F. = \dfrac{63}{18}\\\\S.F. = 3.5[/tex]

Then the length of the banner will be

[tex]\rm Banner \ length = S.F. \times 24\\\\Banner \ length = 3.5 \times 24\\\\Banner \ length = 84[/tex]

The length of the banner is 84 inches.

More about the dilation link is given below.

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Answer:

6

Step-by-step explanation:

If he sold half of 6 thats 3, then he bought 8 more that equals 11.

Hope that helps!

Answer:

Multiply the Rate by the Time

Step-by-step explanation:

Hiya! So you would multiply R(rate) by T(time) Then you would divide by I(interest) and you should get your answer for P(principle)

Ex 24= P x 0.04 x 3   0.04 x 3= 0.12   24 divided by 0.12 = 200 So 200= P

                  (4%)

Hope this helped you!

A square pyramid's height is three times the side of the base of a cube if they have the same base and volume, due to their differing volume formulas.

If a square pyramid and a cube have the same base and volume, the relationship between their heights can be determined using the formulas for their volumes. The volume of a cube is given by [tex]V = s^3,[/tex] where s is the length of a side of the cube's base. The volume of a square pyramid is [tex]V = (1/3) * b^2 * h,[/tex] where b is the length of the base side and h is the pyramid's height. Since both have the same volume, we can set these equations equal to each other and solve for h.

Setting the volumes equal: [tex]s^3 = (1/3) * s^2 * h,[/tex] simplifying to h = 3s. Thus, the height of the pyramid is three times the side of the base of the cube. This is because a cube's volume grows as a cube of its side length, while a pyramid's volume is one third of the base area times the height. Therefore, since they have the same volume, the height of the pyramid must be three times larger to compensate for the 1/3 factor in its volume formula.

Each term in the sequence is obtained by dividing the previous term by 2. Therefore, the rule for the pattern in the given sequence is to halve each term to obtain the next term.

The pattern in the given sequence is a halving pattern.

The rule for the pattern:

1. The first term in the sequence is 128.

2. Each subsequent term is obtained by dividing the previous term by 2.

Let's see how this rule applies to the given sequence:

128 / 2 = 64

64 / 2 = 32

32 / 2 = 16

Every term in the series is created by dividing the one before it by two. The rule for the pattern in the above sequence is to divide each phrase in half to produce the following term.

To know more about the series follow

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Answer:

Naomi earns $8 per hour.

Step-by-step explanation:

Naomi has earned$54 mowing lawns the past two days.

She worked 2.5 hours yesterday and 4.25 hours today.

Suppose she earns x dollars per hour and is paid the same amount every hour she works.

We get the equation;

[tex]2.5x+4.25x=54[/tex]

[tex]6.75x=54[/tex]

x = 8

Hence, she gets $8 per hour.