Type the missing number that makes these fractions equal 12/18 = ?/6

a quantity of ethanol is cooled from 47.9° C to 12.3°C and releases 3.12 KJ of heat. what is the mass of the ethanol sample?

victus00 [196]

Answer:

35.9 grams

Step-by-step explanation:

We use the formula:

$q=m*C_p*\Delta T$

Where

q is heat released

m is mass

C_p is the constant 2.44

ΔT is change in temperature

We put the info in the formula and solve for m (mass):

$q=m*C_p*\Delta T\\-3.12 = m*2.44(12.3-47.9)\\-3.12*10^3=m*(-86.864)\\m=35.9$

The mass of ethanol is 35.9 grams

8 0

4 years ago

The height and sides of a triangle are four consecutive integers. the height is the first integer, and the base is the third int

Maru [420]

Answer:

84 in²

Step-by-step explanation:

The side lengths of the triangle are 3 consecutive integers whose sum (the perimeter) is 42. The average of those integers, 42/3 = 14, is the middle of the three, so they are 13, 14, 15. We're told the perimeter is in inches, so all of these dimensions are inches.

These are the last three of 4 consecutive integers, so the first, the height of the triangle, is 12. The base of the triangle is the 3rd of the four integers, so is 14. Then the area is ...

A = (1/2)bh = (1/2)(14)(12) = 84 . . . . . square inches.

5 0

3 years ago

Find values of a, b, and c (if possible) such that the system of linear equations has a unique solution, no solution, and infini

Cerrena [4.2K]

Answer:

IMPOSSIBLE

Step-by-step explanation:

First we set the equation system:

$x+y+0z=0\\0x+4y+z=0\\4ax+by+cz=0$

Now we set the matrix in order to have a solution for the system:

$\left[\begin{array}{ccc}1&1&0\\0&4&1\\4a&b&c\end{array}\right]$

Now we are going to apply Gauss-Jordan to find the solution of the system in terms of a, b and c:

$-4aR_{1}+R_{3}\rightarrow R_{3}\\\\{\left[\begin{array}{ccc}1&1&0\\0&4&1\\0&(-4a+b)&c\end{array}\right]$

Next step:

$(4a-b)R_{2}+4R_{3} \rightarrow R_{3}\\\\{\left[\begin{array}{ccc}1&1&0\\0&4&1\\0&0&(4a-b+c)\end{array}\right]$

Next step:

$(4a-b+c)R_{2}-R_{3} \rightarrow R_{2}\\\\{\left[\begin{array}{ccc}1&1&0\\0&4(4a-b+c)&0\\0&0&(4a-b+c)\end{array}\right]$

Next step:

$4(4a-b+c)R_{1}-R_{2} \rightarrow R_{1}\\\\{\left[\begin{array}{ccc}4(4a-b+c)&0&0\\0&4(4a-b+c)&0\\0&0&(4a-b+c)\end{array}\right]$

With this solution, we have a new equation system:

$4(4a-b+c)=0\\4(4a-b+c)=0\\4a-b+c=0$

This system can be solved by Cramer's rule, by finding the matrix determinant:

$\left[\begin{array}{ccc}16&-4&4\\16&-4&4\\4&-1&1\end{array}\right]$

$\Delta s= (-64-64-64)-(-64-64-64)=0$

As the determinant is zero, we can say that the second system is imposible to solve.

4 0

3 years ago

Please help! Correct answer only!

Anastasy [175]

Answer:

" Expected Payoff " ⇒ $ 1.80 ; Type in 1.80

Step-by-step explanation:

Take the probability of winning into consideration;

$Total Number of Tickets - 500,\\Tickets 1 Person Can Enter - 1 Ticket,\\\\Probability of Winning - 1 / 500,\\Money Won - 900 Dollars,\\\\Proportionality - 1 / 500 = x / 900 - where, x = " Expected Payoff "\\1 / 500 = x / 900 - CrossMultiplication,\\\\500 * x = 900,\\x = 900 / 500,\\x = 1.80 Dollars Won!\\\\Conclusion ; x = 1.80 Dollars$

Solution ; " Expected Payoff " ⇒ $ 1.80

5 0

3 years ago

Use the disturbitive property to write an expression that is equivalant to 8(a+4)

Pachacha [2.7K]

Answer:

8a + 32

Step-by-step explanation:

To use the distributive property, multiply 8 x a and multiply 8 x 4

6 0

3 years ago