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kvasek [131]
4 years ago
14

One student ate 3/20 of all candies and another 1.2 lb. The second student ate 3/5 of the candies and the remaining 0.3 lb. What

weight of candies did they each eat?
Mathematics
1 answer:
Roman55 [17]4 years ago
8 0
The students ate 6 lbs of candies.
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Evaluate the integral. (sec2(t) i t(t2 1)8 j t7 ln(t) k) dt
polet [3.4K]

If you're just integrating a vector-valued function, you just integrate each component:

\displaystyle\int(\sec^2t\,\hat\imath+t(t^2-1)^8\,\hat\jmath+t^7\ln t\,\hat k)\,\mathrm dt

=\displaystyle\left(\int\sec^2t\,\mathrm dt\right)\hat\imath+\left(\int t(t^2-1)^8\,\mathrm dt\right)\hat\jmath+\left(\int t^7\ln t\,\mathrm dt\right)\hat k

The first integral is trivial since (\tan t)'=\sec^2t.

The second can be done by substituting u=t^2-1:

u=t^2-1\implies\mathrm du=2t\,\mathrm dt\implies\displaystyle\frac12\int u^8\,\mathrm du=\frac1{18}(t^2-1)^9+C

The third can be found by integrating by parts:

u=\ln t\implies\mathrm du=\dfrac{\mathrm dt}t

\mathrm dv=t^7\,\mathrm dt\implies v=\dfrac18t^8

\displaystyle\int t^7\ln t\,\mathrm dt=\frac18t^8\ln t-\frac18\int t^7\,\mathrm dt=\frac18t^8\ln t-\frac1{64}t^8+C

8 0
4 years ago
Please help me with this problem. Serious people
rjkz [21]
A triangle is the anwser because it is made of many triangles

5 0
3 years ago
2x-y=4 and y=-2x+8.<br><br> Can anyone help me solve
Komok [63]

Answer:

The correct answer is x = 3 and y = 2.

Step-by-step explanation:

There are many ways to solve systems of equations like this, but I'm going to use substitution.  This means taking the value of y given by the second equation and plugging it into the first equation.  This is modeled below:

2x - y = 4

2x - (-2x+8) = 4

Now, we can simplify the left side of the equation.

2x + 2x - 8 = 4

4x - 8 = 4

We should add 8 to both sides as the next step.

4x = 12

Now we can divide by 4.

x = 3

To solve for y, we can substitute this value found for x back into either one of our original equations.

y = -2x + 8

y = (-2*3) + 8

y = -6 + 8

y = 2

Therefore, the correct answer is x = 3 and y = 2.

Hope this helps!

5 0
3 years ago
Read 2 more answers
The First Chicago Bank is reviewing its service charges and interest-paying policies on checking accounts. The daily balance of
mrs_skeptik [129]

Answer:

The percentage of the bank's customers carry daily balances between $700 and $1,000 is 65.7%.

The minimum daily balance on which it should be willing to pay interest is $1,198.

Step-by-step explanation:

We have a normal distribution with mean = $800 and standard deviation = $150.

a) We can calculate this value with the standard normal distribution, calculating the z-value for $700 and $1,000.

z_1=\frac{x-\mu}{\sigma} =\frac{700-800}{150}= \frac{-100}{150} =-0.67\\\\\\z_2=\frac{1,000-800}{150}=\frac{200}{150}=1.33\\\\\\P(700

The percentage of the bank's customers carry daily balances between $700 and $1,000 is 65.7%.

b) We must calculate from what amount only 6% of the accounts remain.

This is done by solving:

P(z>x)=0.06

This happens for a z-value of z=2.652.

This corresponds to a amount of $1,198.

x=\mu+z*\sigma=800+2.652*150=800+398=1,198

The minimum daily balance on which it should be willing to pay interest is $1,198.

8 0
4 years ago
Christopher bought a new watch at the store when they were having a 20\%20%20, percent off sale. If the regular price of the wat
ioda
You're having some formatting problems.   You may have to do without the special symbols.

<span>Christopher bought a new watch at the store when they were having a 20% off sale.

</span><span>If the regular price of the watch was $48, what did Chris have to pay after the discount was applied?

Let w represent the cost of the watch.  Then the discounted price would be (1.00-0.20)($48) = 0.8($48) = $38.40   (answer)</span>
5 0
3 years ago
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