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Luda [366]
2 years ago
11

Bloome’s Flower Shop purchases vases by the caseload. Each case contains 24 vases. On average, 3 vases are usually cracked and c

annot be used. At this rate, how many vases should be expected to be cracked if Bloome’s orders 216 vases?
Mathematics
1 answer:
yan [13]2 years ago
6 0

Answer:

72

Step-by-step explanation:

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Use the given information to find the exact value of the trigonometric function
eimsori [14]
\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}

Half Angle Formula

\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\  \\  \end{gathered}

Answer:

\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}

Checking:

\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{  (3rd quadrant)} \end{gathered}

Also,

\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}

The answer is none of the choices

7 0
11 months ago
Braxton loves to download new music. He originally had 41 songs but plans to purchase 4 new songs each week. He wants to know ho
iren [92.7K]
Original songs he has are 41.
Bought songs per week are 4.
Bought songs in 110 weeks are (4*110) = 440

Total songs he bought altogether
41 + 440
5 0
2 years ago
Read 2 more answers
Fill in the number that makes this sentence true 6x9=(6x5)+(6x)
antiseptic1488 [7]
<span>Fill in the number that makes this sentence true 6x9=(6x5)+(6x)           (6x5)</span>
4 0
2 years ago
3, 12, 48, 192, 768, . . .
Sav [38]
The answer would be the sequence has a common ratio of 4.
The explanation for this would be:
To get the common ratio for get the simplest form of the two numbers, so 12/3 = 4 and 48/12 = 4So we know that their common ratio is 4.
To check:
3 x 4 = 12
12 x 4 = 48
48 x 4 = 192
192 x 4 = 768
7 0
3 years ago
A line segment of length k is divided into 3 equal parts what is the distance between midpoints of the first and third segments
anastassius [24]

Line segment of length k is divided into 3 equal parts.

so first segment is 0-k/3 and third segment is 2/3k-k

so mid-pt of 1st = k/6 and 3rd = 5/6k

so the distance in between = 5/6k-k/6 = 4/6k = 2/3k

4 0
2 years ago
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