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3 years ago

A piggy bank contains dimes and nickels that are worth a total of $42.45. If there are 197 nickels, how

Mathematics

2 answers:

Sonja [21]3 years ago

6 0

Answer: 326 dimes

Step-by-step explanation:

q + 0.05(197) = 42.45

q + 9.85 = 42.45

q = 42.45 - 9.85

q = $32.6

32.6 / 0.10 = 326

zimovet [89]3 years ago

5 0

Answer:

326 dimes.

Step-by-step explanation:

total value = 197 * value of one nickel

total value = 197 * 0.05

total value = 9.85

Value of dimes = 42.45 - 9.85

Value of dimes = 32.60

1 dollar contains 10 dimes

32.60 dollars contain x dimes

1/32.60 = 10/x Cross multiply

x = 32.60 * 10

x = 326 Dimes

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A restaurant operator in Accra has found out that during the lockdown,if she sells a plate of her food for Ghc 20 each,she can s

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The demand equation illustrates the price of an item and how it relates to the demand of the item.

The slope of the demand function is -1/2
The equation of the demand function is: $R(x) = (300 - 10x) \times (20 + 5x)$
The price that maximizes her revenue is: Ghc 85

From the question, we have:

$Plates = 300$

$Price = 20$

The number of plates (x) decreases by 10, while the price (y) increases by 5. The table of value is:

$\begin{array}{cccccc}x & {300} & {290} & {280} & {270} & {260} \ \\ y & {20} & {25} & {30} & {35} & {40} \ \end{array}$

The slope (m) is calculated using:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

So, we have:

$m = \frac{25-20}{290-300}$

$m = \frac{5}{-10}$

$m = -\frac{1}{2}$

The equation of the demand is as follows:

The initial number of plates (300) decreases by 10 is represented as: (300 - 10x).

Similarly, the initial price (20) increases by 5 is represented as: (20 + 5x).

So, the demand equation is:

$R(x) = (300 - 10x) \times (20 + 5x)$

Open the brackets to calculate the maximum revenue

$R(x) =6000 + 1500x - 200x - 50x^2$

$R(x) =6000 + 1300x - 50x^2$

Equate to 0

$6000 + 1300x - 50x^2 =0$

Differentiate with respect to x

$1300 - 100x =0$

Collect like terms

$100x =1300$

Divide by 100

$x =13$

So, the price at maximum revenue is:

$Price= 20 + 5x$

$Price= 20 + 5 * 13$

$Price= 85$

In conclusion:

The slope of the demand function is -1/2
The equation of the demand function is: $R(x) = (300 - 10x) \times (20 + 5x)$
The price that maximizes her revenue is: Ghc 85

Read more about demand equations at:

brainly.com/question/21586143

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3 years ago

F(x) = 1/x g(x) = x - 4 Can you evaluate (gof)(0)? Explain why or why not.

s344n2d4d5 [400]

(gof)(0) cannot be evaluated

Solution:

Given that,

$f(x) = \frac{1}{x}\\\\g(x) = x - 4$

A composite function is denoted by (g o f) (x) = g (f(x)).

The notation g o f is read as “g of f”

Therefore, let us find whether (gof)(0) can be evaluated or not

To find (gof)(0):

(g o f) (x) = g (f(x))

Now substitute the given value of f(x)

$(g o f) (x) = g(\frac{1}{x})$

$\text{ Substitute } x = \frac{1}{x} \text{ in } g(x) = x - 4$

$(g o f) (x) = \frac{1}{x} - 4$

Now to find (gof)(0), substitute x = 0

$(g o f) (x) = \frac{1}{0} - 4$

Since 1 divided by 0 is undefined, because any number divided by 0 is undefined

(gof)(0) cannot be evaluated

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