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1 year ago

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The cost of making a chair is $28 correct to the nearest dollar. Calculate the lower and upper bounds for the cost of making 450

chairs

1 answer:

Anna71 [15]1 year ago

3 0

Answer:

$12,375

$12820.50

Step-by-step explanation:

To obtain a rounded value of $28 (to nearest dollar) the lowest and highest possible value before rounding will be : 27.50 and 28.49

Hence,

Lower bound = $27.50

Upper bound = $28.49

Therefore. Cost of making 450 chairs ;

27.50 * 450 = $12,375 (lower bound)

28.49 * 450 $12820.50 (upper bound)

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which of the following is equivalent to 3 sqrt 32x^3y^6 / 3 sqrt 2x^9y^2 where x is greater than or equal to 0 and y is greater

Nutka1998 [239]

Answer:

$\frac{\sqrt[3]{16y^4}}{x^2}$

Step-by-step explanation:

The options are missing; However, I'll simplify the given expression.

Given

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$

Required

Write Equivalent Expression

To solve this expression, we'll make use of laws of indices throughout.

From laws of indices $\sqrt[n]{a} = a^{\frac{1}{n}}$

So,

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$ gives

$\frac{(32x^3y^6)^{\frac{1}{3}}}{(2x^9y^2)^\frac{1}{3}}$

Also from laws of indices

$(ab)^n = a^nb^n$

So, the above expression can be further simplified to

$\frac{(32^\frac{1}{3}x^{3*\frac{1}{3}}y^{6*\frac{1}{3}})}{(2^\frac{1}{3}x^{9*\frac{1}{3}}y^{2*\frac{1}{3}})}$

Multiply the exponents gives

$\frac{(32^\frac{1}{3}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

Substitute $2^5$ for 32

$\frac{(2^{5*\frac{1}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

$\frac{(2^{\frac{5}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$

From laws of indices

$\frac{a^m}{a^n} = a^{m-n}$

This law can be applied to the expression above;

$\frac{(2^{\frac{5}{3}}x*y^{2})}{(2^\frac{1}{3}x^{3}*y^{\frac{2}{3}})}$ becomes

$2^{\frac{5}{3}-\frac{1}{3}}x^{1-3}*y^{2-\frac{2}{3}}$

Solve exponents

$2^{\frac{5-1}{3}}*x^{-2}*y^{\frac{6-2}{3}}$

$2^{\frac{4}{3}}*x^{-2}*y^{\frac{4}{3}}$

From laws of indices,

$a^{-n} = \frac{1}{a^n}$ ; So,

$2^{\frac{4}{3}}*x^{-2}*y^{\frac{4}{3}}$ gives

$\frac{2^{\frac{4}{3}}*y^{\frac{4}{3}}}{x^2}$

The expression at the numerator can be combined to give

$\frac{(2y)^{\frac{4}{3}}}{x^2}$

Lastly, From laws of indices,

$a^{\frac{m}{n} = \sqrt[n]{a^m}$ ; So,

$\frac{(2y)^{\frac{4}{3}}}{x^2}$ becomes

$\frac{\sqrt[3]{(2y)}^{4}}{x^2}$

$\frac{\sqrt[3]{16y^4}}{x^2}$

Hence,

$\frac{\sqrt[3]{32x^3y^6}}{\sqrt[3]{2x^9y^2} }$ is equivalent to $\frac{\sqrt[3]{16y^4}}{x^2}$

8 0

2 years ago

a(0.3−y)+1.1+2.4x (y−1.2) =0 =−1.2(x−0.5) Consider the system of equations above, where aaa is a constant. For which value o

Veseljchak [2.6K]

Answer:

For a = 1.22 there is one solution where y = 1.3

Step-by-step explanation:

Hi there!

Let´s write the system of equations:

a(0.3 - y) + 1.1 +2.4x(y-1.2) = 0

-1.2(x-0.5) = 0

Let´s solve the second equation for x:

-1.2(x-0.5) = 0

x- 0.5 = 0

x = 0.5

Now let´s repalce x = 0.5 and y = 1.3 in the first equation and solve it for a:

a(0.3 - y) + 1.1 +2.4x(y-1.2) = 0

a(0.3 - 1.3) + 1.1 + 2.4(0.5)(1.3 -1.2) = 0

a(-1) + 1.1 + 1.2(0.1) = 0

-a + 1.22 = 0

-a = -1.22

a = 1.22

Let´s check the solution and solve the system of equations with a = 1.22. Let´s solve the first equation for y:

1.22(0.3 - y) + 1.1 +2.4(0.5)(y-1.2) = 0

0.366 - 1.22y + 1.1 + 1.2 y - 1.44 = 0

-0.02y +0.026 = 0

-0.02y = -0.026

y = -0.026 / -0.02

y = 1.3

Then, the answer is correct.

Have a nice day!

4 0

2 years ago

Find the point estimate of the proportion of people who wear hearing aids if, in a random sample of 493 people, 40 people had he

Anna71 [15]

Point estimate proportion is the average of lower and upper interval limit.

Point estimate proportion )p) = x/n
Where x = observations, n=sample size

Substituting;

p= 40/493 = 0.0811

8 0

2 years ago

Read 2 more answers

6 points Emily’s family needs to rent a moving truck to move their belongings to a different house. The rental cost for Trucks-A

Alexxx [7]

Answer/Step-by-step explanation:

Equation to represent the daily rental cost for each type of truck can be written as follows:

Daily rental cost for Trucks-A-Lot = 42 + 0.72m

Daily rental cost for Move-in-Truckers = 70 + 0.12m

Where, m = Emily's mileage

To determine the number of miles for which the truck cost the same amount, set both equations equal to each other and solve for m.

$42 + 0.72m = 70 + 0.12m$

Collect like terms

$0.72m - 0.12m = 70 - 42$

$0.6m = 28$

Divide both sides by 0.6

$\frac{0.6m}{0.6} = \frac{28}{0.6}$

$m = 46.7$

At approximately 47 miles, both trucks would cost the same amount.

Check:

Daily rental cost for Trucks-A-Lot = 42 + 0.72m

Plug in the value of x = 47

= 42 + 0.72(47) = $75.84 ≈ $76

Daily rental cost for Move-in-Truckers = 70 + 0.12m

Plug in the value of x = 47

= 70 + 0.12(47) = $75.64 ≈ $76

7 0

2 years ago

A bicycle wheel is 63 centimeters from top to bottom. When the wheel goes all the way around one time,the bicycle travels 198 ce

OlgaM077 [116]

Answer:

π = 198/63

Divide the distance traveled by the wheel to guess the value or estimate the value of π.

Step-by-step explanation:

Height of the wheel: Diameter of the circle

Perimeter of the circle = π*diameter of the circle

Divide the diameter of the circle by the perimeter of the circle.

π = 198/63

<em><u>Hope this helps.</u></em>

8 0

2 years ago