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JulijaS [17]
3 years ago
15

At a particular restaurant, each pizza roll has 60 calories and each mini hotdog has 70 calories. A combination meal with pizza

rolls and mini hotdogs has a total of 21 pizza rolls and mini hotdogs altogether and contains 1380 calories. Determine the number of pizza rolls in the combination meal and the number of mini hotdogs in the combination meal.
Mathematics
1 answer:
PolarNik [594]3 years ago
4 0

Answer:

There are 9 pizza rolls and 12 mini hotdogs in the meal.

Step-by-step explanation:

We are given the following in the question.

Let x be the number of pizza rolls sold and y be the number of mini hotdogs in the combination meal.

Total number of items in combination meal = 21

Thus, we can write the equation:

x + y = 21

Calorie in a pizza roll = 60

Calorie in a mini hotdog = 70

Total calories = 1380

Thus, we can write the equation:

60x + 70y = 1380

Solving the two equations, we get,

60x + 70y - (60x+60y) = 1380 - 60(21) \\10y = 120\\\Rightarrow y = 12\\\Rightarrow x = 21-12 = 9

Thus, there are 9 pizza rolls and 12 mini hotdogs in the meal.

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A traffic engineer monitors the rate at which cars enter the main highway during the afternoon rush hour. From her data she esti
sertanlavr [38]

Answer:

On average, cars enter the highway during the first half hour of rush hour at a rate 97 per minute.

Step-by-step explanation:

Given that, the rate R(t) at which cars enter the highway is given the formula

R(t)= 100(1-0.0001t^2)

The average rate of car enter the highway during first half hour of rush hour is the average value of R(t) from t=0 to t=30.

\therefore \int_0^{30}  100(1-0.0001t^2)\ dt

=[100(t-0.0001\frac{t^3}{3})]_0^{30}

=100[(30-0.0001\frac{30^3}{3})-(0-0.0001\frac{0^3}{3})]

=2901

The average rate of car is =\frac{\textrm{The number of car}}{Time}

                                           =\frac{2910}{30}

                                          =97

On average, cars enter the highway during the first half hour of rush hour at a rate 97 per minute.

8 0
3 years ago
Find the difference. 4/9-1/3
Iteru [2.4K]
1/9

Find the common denominator, 1/3 can be multiplied to get to ninths. 1/3 is equivalent to 3/9, and so 4/9 minus 3/9 is 1/9.
7 0
3 years ago
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For the function y=3x2: (a) Find the average rate of change of y with respect to x over the interval [3,6]. (b) Find the instant
nirvana33 [79]

Answer:

The instantaneous rate of change of y with respect to x at the value x = 3 is 18.

Step-by-step explanation:

a) Geometrically speaking, the average rate of change of y with respect to x over the interval by definition of secant line:

r = \frac{y(b) -y(a)}{b-a} (1)

Where:

a, b - Lower and upper bounds of the interval.

y(a), y(b) - Function exaluated at lower and upper bounds of the interval.

If we know that y = 3\cdot x^{2}, a = 3 and b = 6, then the average rate of change of y with respect to x over the interval is:

r = \frac{3\cdot (6)^{2}-3\cdot (3)^{2}}{6-3}

r = 27

The average rate of change of y with respect to x over the interval [3,6] is 27.

b) The instantaneous rate of change can be determined by the following definition:

y' =  \lim_{h \to 0}\frac{y(x+h)-y(x)}{h} (2)

Where:

h - Change rate.

y(x), y(x+h) - Function evaluated at x and x+h.

If we know that x = 3 and y = 3\cdot x^{2}, then the instantaneous rate of change of y with respect to x is:

y' =  \lim_{h \to 0} \frac{3\cdot (x+h)^{2}-3\cdot x^{2}}{h}

y' =  3\cdot \lim_{h \to 0} \frac{(x+h)^{2}-x^{2}}{h}

y' = 3\cdot  \lim_{h \to 0} \frac{2\cdot h\cdot x +h^{2}}{h}

y' = 6\cdot  \lim_{h \to 0} x +3\cdot  \lim_{h \to 0} h

y' = 6\cdot x

y' = 6\cdot (3)

y' = 18

The instantaneous rate of change of y with respect to x at the value x = 3 is 18.

5 0
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Answer:

15860

Step-by-step explanation:

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