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mash [69]
3 years ago
7

thomas has 6.35 in dimes and quarters the number of dimes is three more than three times the number of quarters how many quarts

does he have
Mathematics
1 answer:
Feliz [49]3 years ago
6 0

Answer:

11 quarters

Step-by-step explanation:

If Thomas ignores the extra 3 dimes, he can arrange his coins in groups of 3 dimes and 1 quarter, each group valued at 55¢. It takes

... 6.05/0.55 = 11

groups to bring the total value to the $6.05 remaining after ignoring the extra dimes.

Thomas has 11 quarters and 36 dimes.

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If the dimensions of an equilateral triangle are trebled, how is the area affected?
Daniel [21]
Dimension of an equilateral
5 0
3 years ago
Custom Office makes a line of executive desks. It is estimated that the total cost for making x units of their Senior Executive
Ivan

Answer:

(a) The average cost function is \bar{C}(x)=95+\frac{230000}{x}

(b) The marginal average cost function is \bar{C}'(x)=-\frac{230000}{x^2}

(c) The average cost approaches to 95 if the production level is very high.

Step-by-step explanation:

(a) Suppose C(x) is a total cost function. Then the average cost function, denoted by \bar{C}(x), is

\frac{C(x)}{x}

We know that the total cost for making x units of their Senior Executive model is given by the function

C(x) = 95x + 230000

The average cost function is

\bar{C}(x)=\frac{C(x)}{x}=\frac{95x + 230000}{x} \\\bar{C}(x)=95+\frac{230000}{x}

(b) The derivative \bar{C}'(x) of the average cost function, called the marginal average cost function, measures the rate of change of the average cost function with respect to the number of units produced.

The marginal average cost function is

\bar{C}'(x)=\frac{d}{dx}\left(95+\frac{230000}{x}\right)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g\\\\\frac{d}{dx}\left(95\right)+\frac{d}{dx}\left(\frac{230000}{x}\right)\\\\\bar{C}'(x)=-\frac{230000}{x^2}

(c) The average cost approaches to 95 if the production level is very high.

\lim_{x \to \infty} (\bar{C}(x))=\lim_{x \to \infty} (95+\frac{230000}{x})\\\\\lim _{x\to a}\left[f\left(x\right)\pm g\left(x\right)\right]=\lim _{x\to a}f\left(x\right)\pm \lim _{x\to a}g\left(x\right)\\\\=\lim _{x\to \infty \:}\left(95\right)+\lim _{x\to \infty \:}\left(\frac{230000}{x}\right)\\\\\lim _{x\to a}c=c\\\lim _{x\to \infty \:}\left(95\right)=95\\\\\mathrm{Apply\:Infinity\:Property:}\:\lim _{x\to \infty }\left(\frac{c}{x^a}\right)=0\\\lim_{x \to \infty} (\frac{230000}{x} )=0

\lim_{x \to \infty} (\bar{C}(x))=\lim_{x \to \infty} (95+\frac{230000}{x})= 95

6 0
3 years ago
Help with some math homework? The area of a triangle is 110 square inches. the height of the triangle is 8 less than 3 times its
Alenkasestr [34]
A = h x b; where A = area of a triangle; h = height of the triangle; b = base of the riangle;
So, we have the equation : 110 = (3b - 8)b;
We solve the equation 3b^2 - 8b - 110 = 0;
The positiv solution  is b = 7.53 cm;
h = 3 x 7.53 - 8;
h = 14.59 cm;
3 0
3 years ago
write and equation of the line parallel to the line  2 x + 4 y = 20 2 x + 4 y = 20 and containing the point  ( −
MAXImum [283]

Answer:

Step-by-step explanation:

The equation of a straight line can be represented in the slope intercept form as

y = mx + c

Where

m represents the slope of the line

c represents the y intercept

The equation of the given line is

2x + 4y = 20

4y = - 2x + 20

Dividing through by 4, it becomes

y = - x/2 + 5

Comparing with the slope intercept form, slope = - 1/2

If two lines are parallel, it means that they have the same slope. Therefore, the slope of the line passing through (- 6, 3) is - 1/2

To determine the y intercept, we would substitute m = - 1/2, x = - 6 and y = 3 into y = mx + c. It becomes

3 = - 1/2 × - 6 + c

3 = 3 + c

c = 3 - 3 = 0

The equation becomes

y = - x/2

4 0
3 years ago
Suppose a man offered to work for 30 days at the following salary: one cent for the first day two cents for the second day four
Ivahew [28]
It would be to little because it would only be 30 cents
8 0
3 years ago
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