Answer:
b
Step-by-step explanation:
Answer:
$70.34
Step-by-step explanation:
The total before the coupon and tax is:
$54.99 + $21.99 = $76.98
Now apply the 15% coupon:
Since the total price is 100% of the price, when you apply a 15% coupon, you pay 100% - 15% = 85% of the price. We need to find 85% of $76.98
85% * $76.98 =
= 0.85 * $76.98
= $65.43
The price after the 15% coupon, but before the tax, is $65.43
Now the total $65.43 is considered 100% of the price. The tax is 7.5%.
100% + 7.5% = 107.5%
Now we find 107.5% of $65.43
107.5% of $65.43 =
= 1.075 * $65.43
= $70.34
Answer: $70.34
Answer:
The volume of the solid is 19.
unit³
Step-by-step explanation:
The given function is y = x³
The solid is created by revolving R about the line y = 1
We have that when y = 1, x = 1
Taking the end point as x = 2, we have the volume given by the washer method as follows;
![V = \pi \cdot \int\limits^a_b {\left( [f(x)]^2 - [g(x)]^2 \right)} \, dx](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%5Ccdot%20%5Cint%5Climits%5Ea_b%20%7B%5Cleft%28%20%5Bf%28x%29%5D%5E2%20-%20%5Bg%28x%29%5D%5E2%20%5Cright%29%7D%20%5C%2C%20dx)
Where;
a = 1, and b = 2, we have;
g(x) = 1
![V = \pi \cdot \int\limits^{2}_1 {\left( [x^3]^2 - [1]^2 \right)} \, dx = \pi \cdot \left[\dfrac{x^7}{7} + x \right]_1^{2} = \pi \cdot \left[\dfrac{2^7}{7} +2 -\left( \dfrac{1^7}{7} + 1\right)\right] =19\dfrac{1}{7}](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20%5Ccdot%20%5Cint%5Climits%5E%7B2%7D_1%20%7B%5Cleft%28%20%5Bx%5E3%5D%5E2%20-%20%5B1%5D%5E2%20%5Cright%29%7D%20%5C%2C%20dx%20%20%3D%20%5Cpi%20%5Ccdot%20%5Cleft%5B%5Cdfrac%7Bx%5E7%7D%7B7%7D%20%2B%20x%20%5Cright%5D_1%5E%7B2%7D%20%3D%20%5Cpi%20%5Ccdot%20%5Cleft%5B%5Cdfrac%7B2%5E7%7D%7B7%7D%20%2B2%20-%5Cleft%28%20%5Cdfrac%7B1%5E7%7D%7B7%7D%20%2B%201%5Cright%29%5Cright%5D%20%3D19%5Cdfrac%7B1%7D%7B7%7D)
The volume of the solid, V =
unit³ = 19.
unit³
41. A. 30
42. 148 because supplementary angles equal 180
Answer:
B
Step-by-step explanation:
For quadratic expression in this form, the first step is to multiply the number in front of
with the last term, the constant (with the sign in front as well). This is the "multiplied number".
Step 2 is to come up with 2 numbers which when multiplied is equal to the "multiplied number" in step 1 above and also add to the number in front of
.
For this problem, we would need 2 numbers that
- Add up to 27, and
- When multiplied, comes to -90 <em>(18 * -5 = -90)</em>
They already found the 2 numbers as expressed in the form shown
. The 2 numbers are +32 and -5.
<em><u>Do they add up to 27, as required?</u></em>
Yes, 32-5=27
<u><em>Do they come to -90 when multiplied?</em></u>
No, 32 * -5 = -160
Hence, they add up, BUT NOT multiplied.
So the answer choice B is right.