Answer:
a). x = 11
b). m∠DMC = 39°
c). m∠MAD = 66°
d). m∠ADM = 36°
e). m∠ADC = 18°
Step-by-step explanation:
a). In the figure attached,
m∠AMC = 3x + 6
and m∠DMC = 6x - 49
Since "in-center" of a triangle is a points where the bisectors of internal angles meet.
Therefore, MC is the angle bisector of angle AMD.
and m∠AMC ≅ m∠DMC
3x + 6 = 8x - 49
8x - 3x = 49 + 6
5x = 55
x = 11
b). m∠DMC = 8x - 49
= (8 × 11) - 49
= 88 - 49
= 39°
c). m∠MAD = 2(m∠DAC)
= 2(30)°
= 60°
d). Since, m∠AMD + m∠ADM + m∠MAD = 180°
2(39)° + m∠ADM + 66° = 180°
78° + m∠ADM + 66° = 180°
m∠ADM = 180° - 144°
= 36°
e). m∠ADC = 
= 
= 18°
<span>The answer is c. 1.5r + 2.5(5 – r) = 10.50. Let r be the number of raisins and p be the number of peanuts. Raisins cost $1.50 per pound: 1.5r. Peanuts cost $2.50 per pound: 2.5p. Jeremy spends $10.50: 1.50r + 2.50p = 10.50. Jeremy makes 5 pounds of trail mix: r + p = 5. So, we have the system of two equations: 1.5r + 2.5p = 10.50 and r + p = 5. Use the second equation to express p: p = 5 - r. Now, substitute p in the first equation: 1.5r + 2.5(5 - r) = 10.50. Therefore, the correct choice is c. 1.5r + 2.5(5 – r) = 10.50.</span>
Answer:
All in all, Jonathan's piggy bank contains 100 coins. Among these coins, only 50 are one-dollar coins. Therefore, the theoretical probability of picking one-dollar coin from the piggy bank is equal to 50/100 or 1/2.
Similarly, from the experiment, 20 coins were picked and among these there are 12 one-dollar coins. The answer to the second question is therefore 12/20 or 3/5.
Step-by-step explanation:
The answers are: 4.5 g and 56.25 g respectively.
Since the first type of measurement in this question is weight or mass, I'll suppose that the percentage concentration is % mass/mass. For that type of concentration measurement, just multiply the percentage by the total mass to get the mass of the wanted material.
So 150 g * 3% = 150 g * 0.03 = 4.5g
For the 8% solution with the same amount of dry substance, use the ratio of percentages, multiplied by the mass of the first solution to get the wanted amount of new solution:
3/8 * 150 g = 56.35 g
