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dolphi86 [110]
3 years ago
8

Sara can complete 3/4 of a puzzle in 7/8 of an hour. How much a puzzle can she complete in an

Mathematics
1 answer:
8090 [49]3 years ago
7 0

Answer:

x = 6/7 of a puzzle

Step-by-step explanation:

Number of puzzle : time taken

= 3/4 : 7/8

How much a puzzle can she complete in an hour?

Let

x = number of puzzle to complete

Number of puzzle : time taken

= x : 1

Equate both ratios to solve for x

3/4 : 7/8 = x : 1

3/4 ÷ 7/8 = x / 1

3/4 × 8/7 = x / 1

24/28 = x / 1

Cross product

24 * 1 = 28 * x

24 = 28x

x = 24/28

= 6/7

x = 6/7 of a puzzle

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a company that manufactures bicycles has a fixed cost of $80,000. it costs $100 to produce each bicycle. the total cost for the
frez [133]

C(x) = 80000 + 100x is the total cost as function of number of cycles produced

C(90) = 89000 and it costs $ 89000 to produce 90 bicycles

<em><u>Solution:</u></em>

Given that, company that manufactures bicycles has a fixed cost of $80,000

Fixed cost = $ 80,000

Let x be the number of cycles produced

Let C(x) be the total cost as function of number of cycles produced

It costs $100 to produce each bicycle

Variable cost = 100 x number of cycles produced

variable cost = 100x

The total cost for the company is the sum of its fixed cost and variable costs

total cost = fixed cost + variable cost

C(x) = 80000 + 100x

Thus total cost as function of "x" is found

<em><u>Find and interpret C(90)</u></em>

Substitute x = 90 in C(x)

C(90) = 80000 + 100(90)

C(90) = 80000 + 9000

C(90) = 89000

Thus it costs $ 89000 to produce 90 bicycles

3 0
2 years ago
to find the perimeter of the rectangle you can see the formula P=21+2W. find the perimeter P of a rectangle whose length L is 10
Olin [163]

Answer:

rectangle, the distance around the outside of the rectangle is known as perimeter. A rectangle is 2-dimensional; however, perimeter is 1-dimensional and is measured in linear units such as feet or meter etc.

The perimeter of a rectangle is the total length of all the four sides.

Perimeter of rectangle = 2L + 2W.

Example 1: Rectangle has the length 13 cm and width 8 cm. solve for perimeter of rectangle.

Solution:

Given that:

Length (l) = 13 cm

Width (w) = 8 cm

Perimeter of the rectangle = 2(l + w) units

P = 2(13 + 8)

P = 2 (21)

P = 42

Thus, the perimeter of the rectangle is 42 cm.

Example 2: If a rectangle's length is 2x + 1 and its width is 2x – 1. If its area is 15 cm2, what are the rectangle's dimensions and what is its perimeter?

Solution:

We know that the dimensions of the rectangle in terms of x:

 l = 2x + 1

w = 2x – 1

Since the area of a rectangle is given by:

A = l * w

We can substitute the expressions for length and width into the equation for area in order to determine the value of x.

A = l * w

15 = (2x + 1) (2x -1)

15 = 4x2 – 1

16 = 4x2

x = ±2

 

 Note that the value of x must be positive and therefore in our case, the value of x is 2. And now we have:

l = 5 cm

w = 3 cm

Therefore, the dimensions are 5cm and 3cm.

Now, substituting these values in the formula for perimeter, we will get

P = 2l + 2w

P = 2(5)+2(3)

P = 10+6

P = 16 cm

Example 3: Find the area and the perimeter of a rectangle whose length is 24 m and width is 12m?

Solution:

Given that:

length = L = 24m

width = W = 12m

Area of a rectangle:

A = L × W

A = 24 × 12

A = 188 m2

Perimeter of a rectangle:

P = 2L + 2W

P = 2(24) + 2(12)

P = 48 + 24

P = 72 m

Example 4: Find the area and perimeter of a rectangle whose breadth is 4 cm and the height 3 cm.

Solution:

Area = b×h = 4×3 = 12 cm2.

Perimeter = 2(b) + 2(h) = 2(4) + 2(3) = 8 + 6 = 14.

Example 5: Calculate the perimeter of the rectangle whose length is 18cm and breadth 7cm

Solution:

Given that:

L = 18 cm

B = 7 cm

Perimeter of rectangle = 2(length + breadth)

P = 2 (L + B)

P = 2 (18 + 7)

P = 50 cm

Example 6: Find the perimeter of rectangle whose length is 6 inches and width is 4 inches.

Solution:

P = 2(L + B)

P = 2(6 + 4)

P = 20 in

Example 7: A boy walks 5 times around a park. If the size of the park is 100m by 50m, find the distance the boy has walked. If he walks 100m in 5 minutes, how long will it take for him in total?

Solution:

Given that:

Length = L = 100m

Width = W = 50m

Rounds = 5

Time per 100m = 5minutes.

Perimeter of the park:

P = 2 L + 2 W.

P = 2 × 100 + 2 × 50

P = 200 + 100

P = 300 m

Total distance walked = 5 × Perimeter of the park.

= 5 × 300

= 1500 meters

Total time taken = Total distance walked × time taken to walk 1m.

= 1500 × 5/100

= 75minutes or 1hr 15minutes

6 0
3 years ago
EASY POINTS
SVEN [57.7K]
I think the answer is B.78Degrees
8 0
2 years ago
Use the rules of exponents to simplify the expressions. Match the expression with its equivalent value.
Lelechka [254]

Answer:

1) \frac{(-2)^{-5}}{(-2)^{-10}}=-32

2) 2^{-1}.2^{-4} = \frac{1}{32}

3) (-\frac{1}{2} )^3.(-\frac{1}{2} )^2=-\frac{1}{32}

4) \frac{2}{2^{-4}} = 32

Step-by-step explanation:

1) \frac{(-2)^{-5}}{(-2)^{-10}}

Solving using exponent rule: a^{-m}=\frac{1}{a^m}

\frac{(-2)^{-5}}{(-2)^{-10}}\\=(-2)^{-5+10}\\=(-2)^{5}\\=-32

So, \frac{(-2)^{-5}}{(-2)^{-10}}=-32

2) 2^{-1}.2^{-4}

Using the exponent rule: a^m.a^n=a^{m+n}

We have:

2^{-1}.2^{-4}\\=2^{-1-4}\\=2^{-5}

We also know that: a^{-m}=\frac{1}{a^m}

Using this rule:

2^{-5}\\=\frac{1}{2^5}\\=\frac{1}{32}

So, 2^{-1}.2^{-4} = \frac{1}{32}

3) (-\frac{1}{2} )^3.(-\frac{1}{2} )^2

Solving:

(-\frac{1}{2} )^3.(-\frac{1}{2} )^2\\=(-\frac{1}{8} ).(\frac{1}{4} )\\=-\frac{1}{32}

So, (-\frac{1}{2} )^3.(-\frac{1}{2} )^2=-\frac{1}{32}

4) \frac{2}{2^{-4}}

We know that: a^{-m}=\frac{1}{a^m}

\frac{2}{2^{-4}}\\=2\times 2^4\\=2(16)\\=32

So, \frac{2}{2^{-4}} = 32

3 0
3 years ago
I really need help with this any1?
maxonik [38]

Answer:

2x-4 = -8

Step-by-step explanation:

5 x -22= -110

4 0
2 years ago
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