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Irina-Kira [14]
3 years ago
12

Sin 20.sin 10 as sum or difference

Mathematics
1 answer:
Zielflug [23.3K]3 years ago
6 0

Answer:

see explanation

Step-by-step explanation:

The difference identity for the product is

sinxsiny = \frac{1}{2} [ cos(x - y) - cos(x + y) ], thus

sin20sin10

= \frac{1}{2} [ cos(20 - 10) - cos(20 + 10) ]

= \frac{1}{2} ( cos10 - cos30 )

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3) the product of n and 9​
insens350 [35]

Answer:

9n

Step-by-step explanation:

i mean 9 x n = 9n. straight forward...

8 0
3 years ago
Write an equation in slope-intercept form for the graph of<br> the line shown.<br> (y=mx+b)
Tamiku [17]
The answer for 25 is y=3x+1
The answer for 24 is y=3x+5
4 0
3 years ago
A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 225 vinyl? glov
romanna [79]

Answer:

a)

H₀: ρ₁ ≤ ρ₂

H₁: ρ₁ > ρ₂

b)

Z= \frac{('p_{1} - 'p_{2}) - (p_{1} - p_{2})}{\sqrt{'p(1-'p)[\frac{1}{n_1} + \frac{1}{n_2} ]} } ≈ N(0;1)

c)

p-value < .00001

d)

Reject the null hypothesis.

The population proportion vinyl gloves that leak viruses is greater than the population proportion of latex gloves that leak viruses.

Step-by-step explanation:

Hello!

The objective is to test if the population proportion of vinyl gloves that leak viruses (population 1) is greater then the population proportion of latex gloves that leak viruses (population 2).

Sample 1 (Vinyl)

n₁= 225

Sample proportion 'ρ₁= 0.60

Sample 2 (Latex)

n₂= 225

Sample proportion 'ρ₂= 0.09

Pooled proportion: 'ρ= (x₁+x₂)/(n₁+n₂)= ( 'ρ₁ + 'ρ₂)/2= (0.60 + 0.09)/2= 0.345 ≅0.35

The hypothesis is:

H₀: ρ₁ ≤ ρ₂

H₁: ρ₁ > ρ₂

α: 0.05

The statistic to use is a pooled Z

Z= \frac{('p_{1} - 'p_{2}) - (p_{1} - p_{2})}{\sqrt{'p(1-'p)[\frac{1}{n_1} + \frac{1}{n_2} ]} } ≈ N(0;1)

The critical region is one-tailed to the right (positive), the critical value is:

Z_{1-\alpha } = Z_{0.95} = 1.64

If Z ≥ 1.64, you will reject the null hypothesis.

If Z < 1.64, you will not reject the null hypothesis.

Z= \frac{(0.6 - 0.09) - (0}{\sqrt{0.35(1-0.35)[\frac{1}{225} + \frac{1}{225} ]} } = 11.34

Since the calculated Z- value is greater than the critical value, the decision is to reject the null hypothesis. The population proportion vinyl gloves that leak viruses is greater than the population proportion of latex gloves that leak viruses.

P-value approach:

p-value < .00001

If you compare with the level of signification, you reach the same decision.

I hope it helps!

8 0
3 years ago
CAN SOMEONE HELP ME PLEASE? I’LL GIVE YOU FREE EASY POINTS IF YOU GIVE ME THE RIGHT ANSWER.. NO WRONG ANSWERS PLS!!
Ira Lisetskai [31]

see the attachment..........

3 0
2 years ago
Wendy took a trip from one city to another, a distance of 500 mi. She traveled part of the way by bus, which arrived at the trai
Fynjy0 [20]

<u>Answer- </u>Wendy spent 3 hours on the train

<u>Solution-</u>

The distance between the cities= 500 mi.

She traveled part of the way by bus, and other part by train.

The bus averaged 40 mph, and the train averaged 120 mph.

The entire trip took 6.5 hours.

let d = distance traveled by train

the total distance was given as 500 mi ,

therefore, distance traveled by bus  = (500-d) mi

time = distance/speed

⇒ train traveling time + bus traveling time = 6.5 hrs

⇒ \frac{d}{120} +\frac{500-d}{40} = 6.5

⇒ d + 3(500-d) = 120(6.5)

⇒ d + 1500 - 3d = 780

⇒ 2d = 720

⇒ d = 360  mi

so d = 360 mi by train

⇒ 360/120 = 3 hrs on the train

8 0
3 years ago
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