Answer:
θ
∈
{
90
∘
,
210
∘
,
270
∘
,
330
∘
}
step by step explanation:
Factoring the left side of
2
sin
(
θ
)
cos
(
θ
)
+
cos
(
θ
)
=
0
gives
cos
(
θ
)
⋅
[
2
sin
(
θ
)
+
1
]
=
0
Which implies (for θ
∈
[
0
,
360
∘])
either cos
(
θ
)
=
0
→ θ
=
90
∘
or
270
∘
OR
2
sin
(
θ
)
+
1
=
0
→ sin (
θ
)=−
1
2
→
θ
=
210
∘
or
330
∘
→ θ = 210∘ or 330∘
Answer: One DVD is $12 and one book is $1
Step-by-step explanation:
Let the DVD be d and the book be b.
Case 1:
3d + 4b = $40.......(1)
Case 2:
1d + 6b = $18........... (2)
In this equations above, I intend to eliminate variable d, so I'm going to multiply the coefficient of d in (1) to multiply (2)
3 × (1d + 6b = 18)
3d + 18b = 54........ .(3)
Then, subtract (1) from (3)
3d + 18b = 54
- ( 3d + 4b = 40)
3d - 3d + 18b - 4b = 54 - 40
0 + 14b = 14
b = 14/14
b = 1.
Then substitute 1 for b in (2)
1d + 6(1) = 18
d + 6 = 18
d = 18 - 6
d = 12.
(d,b) = (12,1)
Katie has read 32%, so 32%=80 pages. To get the total number of pages, you have to divide 32 and 80 by 8 to get 4% and 10 pages. 4% of the book is 10 pages, and in order to get 100%, you have to multiply by 25(4*25=100) on both sides. Remember, what you do to one side, you do to the other side. That leaves you with 100% and 250 pages. The book is 250 pages long. If she has read 80 pages, you subtract 80 from 250 to find how many pages she has left to read. The difference is 170. Katie has 170 pages left to read.
Answer:
The P-value indicates that the probability of a linear correlation coefficient that is at least as extreme is__3.5%___ which is___significant_(at α=0.05)_ so there _is_ sufficient evidence to conclude that there is a linear correlation between weight and highway fuel consumption in automobiles.
Step-by-step explanation:
Correlation coefficient shows the relation between the <em>weights</em><em></em> and <em>highway fuel consumption amounts</em> of seven types of automobile.
P-value states <em>the significance</em> of this relationship. If the p-value is lower than a <em>significance level</em> (for example 0.05) then the relation is said to be significant.
First off, the underline underneath means plus or minus, since when you take the square root of something, the answer can be negative or positive at the same time
1. 64 is a perfect square. 8 x 8 = 64, therefore it is +- (plus or minus) 8.
2. 45 is not a perfect square, so you can pull out numbers or plug into a calculator and estimate.
Both answers: Since 45 is divisible by 9 and five, you can break a nine into two threes, therefore pull it out, and since the answer is negative, you get:
-3(5)^0.5 (an exponent of one-half or 0.5 means square root)
If you solve by calculator, the answer is ~= (approximately equal to) -6.72
3. Since 90 is not a perfect square, repeat the previous question. 9 can go into 90, therefore you can pull out two threes and are left with: +-3(10)^0.5
Using the calculator, you get ~= +-9.49
