THERE ARE 4 QUESTIONS BELOW!

1 answer:

5 0

1. $240 in commission. If you add the weekly salary, it would be $635.

2. 35%

3. $8.30

4. $57.96

5. Sales tax on an item is a percent of increase. A discount on an item is a percent decrease. A tip on a bill is a percent increase.

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There are 5 red balls,4 blue balls and n green balls inside a bag.A ball is taken from the bag at random.Given that the probabil

kotegsom [21]

This means that the probability of picking both red and blue balls would have to be 60% or 0.6

$\frac{9}{x} =0.6 \\ 0.6x=9 \\ x=9(0.6) \\ x=15 \\ \frac{n}{15} =0.4 \\ n=0.4(15) \\ n=6$

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3 years ago

0.4(x + 9) = 8.3<br> Find x

Paladinen [302]

Answer:

x = 11.75

Step-by-step explanation:

4 0

3 years ago

Find the exact values of sin θ/2 and cos θ/2 for sin θ = 3/4 on the interval 0° ≤ θ ≤ 90°

timofeeve [1]

Answer:

Step-by-step explanation:

If our interval is between 0 and 90 degrees, that means that our angles are first quadrant angles. Since the formulas for the half angles of sin and cos consider both the positive and negative roots, knowing that we are in QI leaves us using only the principle, or positive, root.

Also, if we know that the sin of angle is 3/4, we can set up a right triangle in QI and find the missing side of that triangle using Pythagorean's Theorem. Sin of an angle is the ratio opposite side/hypotenuse. That means that, according to Pythagorean's Theorem,

$4^2=3^2+b^2$ and

$16-9=b^2$ and

$b=\sqrt{7}$

Now for the forula for the sin of a half-angle:

$sin(\frac{\theta}{2})=\sqrt{\frac{1-cos\theta}{2} }$

Referring to the right triangle we created and found the missing side for, we see that the cosine of that same triangle is $\frac{\sqrt{7} }{4}$

Filling in the formula then:

$sin(\frac{\theta}{2})=\sqrt{\frac{1-\frac{\sqrt{7} }{4} }{2} }$

Get a common denominator on the upper fraction:

$sin(\frac{\theta}{2})=\sqrt{\frac{\frac{4-\sqrt{7} }{4} }{2} }$

Bring up the 2 as 1/2 to multiply and get:

$sin(\frac{\theta}{2})=\sqrt{\frac{4-\sqrt{7} }{8} }$

When you do the exact same thing to find the cos of the half angle, you are using a + sign instead of a - sign under the radical. That gives you as your exact value:

$cos(\frac{\theta}{2})=\sqrt{\frac{4+\sqrt{7} }{8} }$