Answer:
Each Jersey: $6.75
Each pair of socks: $7.47
Sales tax: $1.03
Step-by-step explanation:
$22.00 total.
$1.03 sales tax.
$6.75 jersey x2 = $13.50
$13.50 + $1.03 = $14.53 jerseys & sales tax.
$22.00 - $14.53 =7.47
703.55 minus the flask weight
-345.8 equals
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357.75
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density = 357.75 / 225 = 1.59 grams / milliliter
density = 1,590 grams / liter
If the track is 10km long, and X travels at 40 km/h, it will take 1 hour to do 4 laps. this means that car X will do one lap in 15 minutes. Y travels at 30 km/h, which means it will do 3 laps in 1 hour, meaning that car X will do 1 lap in 20 minutes.
X- 15, 30, 45, 60
Y-20, 40, 60
Therefore, after an hour, they will pass again.
Answer:
x= -2 and (x+3)=0, x= -3
Step-by-step explanation:
"The sum of a number" well we do not know what the number is right, so let's call the number x. So we know we have x and we are adding it to something because it says sum. What are we adding it to? "5 times its reciprocal". A reciprocal of a number is equal to 1/the number. So the reciprocal of x is just 1/x. But we want 5 times this so multiply by 5. So now we have x + 5(1/x). Now we need to set it equal to something to be able to solve it. The problem says the sum of a number and 5 times its reciprocal is -6, so x + 5(1/x) = -6. Now just use order of operations to solve for x. First multiply: x + 5/x =-6. Then the next stperfect is harder because we want to get x by itself but we have x + 5/x. A trick you can do here is multiply the whole equation by x. This cancels out the fraction for us: x(x + 5/x) = -6(x) becomes x^2 +5 = -6x. Now we have a quadratic equation, to solve this you have to Factor or use the quadratic formula. I'll try factoring: first we need all of the terms on one side: x^2 +5x +6 =0. Now we need factors of 6 that add or subtract to 5. There are a couple of options here we could use 6 and -1 or 2 and 3. 6 and -1 would not work because both signs in the equation are plus which means we need our factors to both be positive, also if you tried 6 and -1 and then foiled out the factors to check it, it would not work. So 2 and 3 have to be the factors so the equations equals (x+2)(x+3)=0. Now we set each factor equal to zero and solve for x: (x+2)=0, x= -2 and (x+3)=0, x= -3. Those are the two numbers that would work! Hope this helps!!
Answer:
Time,t that it will elapse before the concerntration of the dye in the tank reaches1% of its original value is 460.52 seconds
Step-by-step explanation:
Let Q(t) = amount of dye for all time,t.
Let Q'= rate in - rate out.
But Q/200 = concerntration of dye
Therefore rate out= Q/200 ×2.
Q'/Q = - 1/100
Dividing by Q gives
Ln/Q/ + c = -1/100t + c1
Integrating both sides with respect to t
Ln/Q/ = -1/100t + c2.
c1 and c1 are just another constants
Q= c3e^-t/100
Exponentiating both sides will cause the absolute values to get absorbed into the constants giving rise to a new constant c3
200= c3-0/100
c3= 200
2= 200e^-t/100
Ln1/100= - t/100
Ln0.01 = - t/ 100
Cross multiply
t= Ln0.01 × 100
t = 4.6052 ×100
t = 460.52seconds