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Mathematics

1 answer:

ycow [4]2 years ago

8 0

Step-by-step explanation:

${9}^{ \frac{3}{2} } \times {27}^{ \frac{1}{2} } = {(3)}^{ \frac{3}{2} \times 2 } \times {(3)}^{ \frac{1}{2} \times 3} \\ = {3}^{3} \times {3}^{ \frac{3}{2} } \\ = {3}^{3 + \frac{3}{2} } \\ = {3}^{4\frac{1}{2} } \\ = {3}^{ \frac{9}{2} }$

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2. Find the number of distinct triangles with c=11,b=7,B=18 a.0 b.1 c.2 d. cannot be determined

jok3333 [9.3K]

Answer: Choice C) 2

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Explanation:

Using the law of sines, we get
sin(B)/b = sin(C)/c
sin(18)/7 = sin(C)/11
0.0441452849107 = sin(C)/11
11*0.0441452849107 = sin(C)
0.4855981340177 = sin(C)
sin(C) = 0.4855981340177
C = arcsin(0.4855981340177) or C = 180-arcsin(0.4855981340177)
C = 29.0516679549861 or C = 150.948332045013
There are two possibilities for angle C because of something like sin(30) = sin(150) = 1/2 = 0.5

Those approximate values of C round to
C = 29.05 and C = 150.95

If C = 29.05, then angle A is
A = 180-B-C
A = 180-18-29.05
A = 132.95
Making this triangle possible since angle A is a positive number

If C = 150.95, then angle A is
A = 180-B-C
A = 180-18-150.95
A = 11.05
making this triangle possible since angle A is a positive number

There are two distinct triangles that can be formed.
One triangle is with the angles: A = 132.95, B = 18, C = 29.05
The other triangle is with the angles: A = 11.05, B = 18, C = 150.95
The decimal values are approximate

7 0

2 years ago

In a random sample of 60 shoppers 12 said that they only buy products that are on sale. If there are 3000 shoppers at the mall t

dimulka [17.4K]

Answer:

Number of shopper buy from sale [3,000shopper] = 600 (Approx.)

Step-by-step explanation:

Given:

Number of shopper in mall = 60

Number of shopper buy from sale = 12

Find:

Number of shopper buy from sale if total number number of shopper are 3,000