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lubasha [3.4K]
3 years ago
8

Liam's breakfast was an egg and cheese biscuit with a carton of milk. He spent a total of $5.65. Finn spent $7.65 on an egg and

cheese biscuit and two cartons of milk. How much was an egg and cheese biscuit?
Mathematics
1 answer:
ruslelena [56]3 years ago
7 0

Answer:

An egg and cheese biscuit was $3.65.

Step-by-step explanation:

Liam's breakfast was:

P = E + C + M

Where:

P: total price

E: egg

C: cheese biscuit

M: carton of milk  

P = E + C + M

5.65 = E + C + M   (1)

Now, Finn's breakfast was:

P = E + C + 2*M

7.65 = E + C + 2*M   (2)      

By subtracting equation (2) from (1) we have:

7.65 - 5.65 = 2M - M

M = 2

Hence, the price of a carton of milk is $2, so by entering this value into equation (1) we can find the price of an egg and cheese biscuit:

5.65 = E + C + M

5.65 - 2 = E + C

E + C = 3.65

Therefore, an egg and cheese biscuit was $3.65.

I hope it helps you!

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navik [9.2K]
Find the total cost of producing 5 widgets. Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x. The company also discovered that it costs $15.50 to produce 3 widgets, $23.50 to produce 7 widgets, and $56 to produce 12 widgets.
OK...so we have
a(7)^2 + b(7) + c = 23.50 → 49a + 7b + c = 23.50 (1)
a(3)^2 + b(3) + c = 15.50 → 9a + 3b + c = 15.50 subtracting the second equation from the first, we have
40a + 4b = 8 → 10a + b = 2 (2)
Also
a(12)^2 + b(12) + c = 56 → 144a + 12b + c = 56 and subtracting (1) from this gives us
95a + 5b = 32.50
And using(2) we have
95a + 5b = 32.50 (3)
10a + b = 2.00 multiplying the second equation by -5 and adding this to (3) ,we have
45a = 22.50 divide both sides by 45 and a = 1/2 and using (2) to find b, we have
10(1/2) + b = 2
5 + b = 2 b = -3
And we can use 9a + 3b + c = 15.50 to find "c"
9(1/2) + 3(-3) + c = 15.50
9/2 - 9 + c = 15.50
-4.5 + c = 15.50
c = 20
So our function is
c(x) = (1/2)x^2 - (3)x + 20
And the cost to produce 5 widgets is = $17.50
7 0
3 years ago
There are 4 people at a party. Consider the random variable X=’number of people having the same birthday ’ (match only month, N=
yulyashka [42]

Answer:

S = {0,2,3,4}

P(X=0) = 0.573 , P(X=2) = 0.401 , P(x=3) = 0.025, P(X=4) = 0.001

Mean = 0.879

Standard Deviation = 1.033

Step-by-step explanation:

Let the number of people having same birth month be = x

The number of ways of distributing the birthdays of the 4 men = (12*12*12*12)

The number of ways of distributing their birthdays = 12⁴

The sample space, S = { 0,2,3,4} (since 1 person cannot share birthday with himself)

P(X = 0) = \frac{12P4}{12^{4} }

P(X=0) = 0.573

P(X=2) = P(2 months are common) P(1 month is common, 1 month is not common)

P(X=2) = \frac{3C2 * 12P2}{12^{4} } + \frac{4C2 * 12P3}{12^{4} }

P(X=2) = 0.401

P(X=3) = \frac{4C3 * 12P2}{12^{4} }

P(x=3) = 0.025

P(X=4) = \frac{12}{12^{4} }

P(X=4) = 0.001

Mean, \mu = \sum xP(x)

\mu = (0*0.573) + (2*0.401) + (3*0.025) + (4*0.001)\\\mu = 0.879

Standard deviation, SD = \sqrt{\sum x^{2} P(x) - \mu^{2}}  \\SD =\sqrt{ [ (0^{2} * 0.573) + (2^{2}  * 0.401) + (3^{2} * 0.025) + (4^{2} * 0.001)] - 0.879^{2}}

SD = 1.033

4 0
3 years ago
Zach wants to build a slanted skateboard ramp. He knows he wants the ramp to form a 15 degrees angle with the ground and be 4 fe
Fynjy0 [20]

Answer: The ramp would be 15.5 feet long.

Step-by-step explanation: Please refer to the attached diagram for details.

Angle C shows the angle to be formed by the ramp from the ground, which is 15 degrees. Also, from the ground, it’s going to be four feet tall, which is line AB. The top of the ramp is point A, which makes line AC the entire length of the ramp. Since we have a reference angle (angle C) and two sides, the opposite and the hypotenuse, we shall apply the trigonometric ratio.

SinC = opposite/hypotenuse

Sin 15 = 4/b

By cross multiplication we now have

b = 4/Sin15

b = 4/0.2588

b = 15.4599

Approximately b = 15.5

Therefore the length of the ramp would be 15.5 feet

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