2 x y`- 3 y=0

It is important that face masks used by firefighters be able to withstand high temperatures because firefighters commonly work i

Salsk061 [2.6K]

Answer:

$(-\infty, 0.2661)$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

n=60 represent the sample size

X=12 represent the number of masks that had lenses pop out at 250°

$\hat p =\frac{12}{60}=0.2$ represent the estimated proportion of masks that had lenses pop out at 250°

p represent the population proportion of masks that had lenses pop out at 250°

Confidence =0.9 or 90%

$\alpha=0.1$ represent the significance level

Confidence interval

On this case we want a interval on this form : $(-\infty,\hat p +z_{\alpha}\sqrt{\frac{\hat p (1-\hat p)}{n}})$

So the critical value would be on this case $z_{\alpha}=1.28$ and we can use the following excel code to find it: "=NORM.INV(1-0.1,0,1)"

We found the lower limit like this:

$0.2 +1.28\sqrt{\frac{0.2 (1-0.2)}{60}}=0.2661$

And the interval would be: $(-\infyt, 0.2661)$

3 0

4 years ago

What is the point that passes through the line Y-5=-3(x-4)

ioda

The point that passes through the line Y-5=-3(x-4) is (-4,7). You are very welcome.

5 0

3 years ago

John ,Rick , and Molli are painting a room together. It takes all of them 16 hours to paint the room to perfection. It takes Joh

CaHeK987 [17]

John's hourly rate is 1/8 of the room per hour.
Rick's hourly rate is 1/2 of the room per hour.
Molli's hourly rate would be 3/8 of the room per hour.

It takes Molli 2 2/3 hours to paint the room alone.

Explanation
Since John paints the entire room (100%=1) in 8 hours, he would paint 1/8 of the room in 1 hour.
Since Rick paints the entire room (100%=1) in 2 hours, he would paint 1/2 of it in 2 hour.

We do not yet know Molli's rate, so we will call it x.

We know that 1/8+1/2+x = 1 hour.

We will use 8 as a common denominator:
1/8+4/8+8x/8 = 1

Adding the numerators,
(1+4+8x)/8 = 1

Multiply both sides by 8:
1+4+8x = 8

Add like terms:
5+8x = 8

Subtract 5 from both sides:
5+8x-5=8-5
8x=3

Divide both sides by 8:
8x/8 = 3/8
x = 3/8

Molli's rate is 3/8.

Since she can paint 3/8 of the room in 1 hour, we can set up the equation
3/8x = 1

Divide both sides by 3/8:
3/8x ÷ 3/8 = 1 ÷ 3/8
x = 1/1 ÷ 3/8 = 1/1 × 8/3 = 8/3
x = 2 2/3

This is the amount of time it takes Molli to paint the entire room.

5 0

3 years ago

PLEASE HELP ANSWER WHAT YOU CAN

igomit [66]

Answer:

1) 20.2 feet

2) 24 miles

I am unsure if this is correct, but I used the Pythagorean theorem to solve your questions.

Step-by-step explanation:

1)

a^2 + b^2 = c^2

13^2 + b^2 = 24^2

b^2 = 24^2 - 13^2

b^2 = 576 - 169 = 407

b = √407 = 20.2

2)

6^2 + 8^2 = c^2

36 + 64 = c^2

100 = c^2

c = 10

10 + 6 + 8 = 24

5 0

4 years ago

Prove that they are equal

Westkost [7]

Step-by-step explanation:

(1-tanx)/(1+tanx) = (1-sin2x)/cos2x

Replace tanx with sinx/cosx:

(1-sinx/cosx)/(1+sinx/cosx)

Multiply numerator and denominator by cosx:

(cosx-sinx)/(cosx+sinx)

Multiply numerator and denominator by cosx-sinx:

(cos^2x-2sinxcosx+sin^2x)/(cos^2x-sin^2x)

For the numerator, since sin2x = 2sinxcosx, and sin^2x + cos^2x = 1, we have 1-sin2x

For the denominator, cos^2x - sin^2x = cos2x

So (1-tanx)/(1+tanx) = (1-sin2x)/cos2x

4 0

3 years ago