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bixtya [17]
3 years ago
9

In ABC, if the lengths of sides a and c are 8 centimeters and 16 centimeters, respectively, and the measure of C is 35 degrees,

what is the measure of A to two decimal places
Mathematics
1 answer:
Simora [160]3 years ago
8 0

Answer:

∠ A ≈ 16.67°

Step-by-step explanation:

Using the Sine rule in Δ ABC

\frac{a}{sinA} = \frac{c}{sinC} , substitute values

\frac{8}{sinA} = \frac{16}{sin35} ( cross- multiply )

16 sinA = 8 sin35° ( divide both sides by 16 )

sin A = \frac{8sin35}{16} , thus

∠ A = sin^{-1} ( \frac{8sin35}{16} ) ≈ 16.67° ( to 2 dec. places )

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Suppose a lab need to need to make 400 liters of 39% acid solution, but the only solutions available to the lab are 20% acid and
Maslowich

Answer:

c + d = 400

0.2c + 0.5d = 156

Step-by-step explanation:

Let

c = number of liters of 20% acid solution

d = number of liters of 50% acid solution.

c + d = 400 (1)

0.2c + 0.5d = 400(0.39)

0.2c + 0.5d = 156 (2)

From (1)

c = 400 - d

Substitute c = 400 - d into (2)

0.2c + 0.5d = 156 (2)

0.2(400 - d) + 0.5d = 156

80 - 0.2d + 0.5d = 156

- 0.2d + 0.5d = 156 - 80

0.3d = 76

d = 76/0.3

d = 253.33 liters

Substitute d = 253.33 into (1)

c + d = 400

c + 253.33 = 400

c = 400 - 253.33

c = 146.67 liters

6 0
3 years ago
(a) Find z such that the proportion of observations that are less than z in a standard normal distribution is 0.36. (Enter your
Alisiya [41]

Answer:

a) z = -0.358

b) z = 0.358              

Step-by-step explanation:

We are given a standard normal distribution.

a) We have to find the value of z such that the proportion of observations that are less than z in a standard normal distribution is 0.36.

That is,

P(Z

This value will be calculated with the help of a standard normal table.

From standard normal table we have,

P(z\leq -0.358) = 0.36

Thus, for z equal to -0.358 the proportion of observations that are less than z in a standard normal distribution is 0.36

b) We have to find the value of z such that 36% of all observations from a standard normal distribution are greater than z.

P(Z>z) = 0.36

This value will be calculated with the help of a standard normal table.

= 1 -P( Z > z)=1 - 0.36 = 0.64  

P( z \leq z)=0.64  

Calculation the value from standard normal z table, we have,

P(z \leq 0.358) = 0.64

Thus, 36% of all observations from a standard normal distribution are greater than z equal to 0.358

7 0
3 years ago
60/30 in simplistic form<br><br><br> Need answer quick!!!!!!!!!
makkiz [27]

Answer:

2

Step-by-step explanation:

60/30 is 2

HOpe this helps :D

PLz mark brainliest if correct :D

3 0
3 years ago
A textbook store sold a combined total of 272 biology and math textbooks in a week. The number of math textbooks sold was 50 les
Dovator [93]

Answer:

b = 161, m = 111

Step-by-step explanation:

b + m = 272

m + 50 = b

Substitute

m + 50 + m = 272

2m = 222

m = 111

Plug in for m

b + 111 = 272

b = 161

6 0
3 years ago
Abigail and Grace collected clovers. Abigail collected clovers with
Tcecarenko [31]

Answer:

20

Step-by-step explanation:

To find the least number of leafs that each collection must have, we find the L.C.M of both numbers. So L.C.M of 4 and 5.

The prime factors of 4 = 2²

The prime factors of 5 = 5

So L.C.M of 4 and 5 = 2² × 5 = 20

So, the least number of leafs that each collection can have is 20 leafs.

6 0
3 years ago
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