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3 years ago

PLZ HELP ASAP

Mathematics

1 answer:

Inga [223]3 years ago

3 0

Answer:

y = -1/3x - 5

Step-by-step explanation:

y - y1 = m(x - x1)

y - (-3) = (-7 + 3)/(6 + 6)(x - (-6))

y + 3 = (-4/12)(x + 6)

y + 3 = (-1/3)(x + 6)

y + 3 = -1/3x - 2

y = -1/3x - 5

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8090 [49]

Answer:

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

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

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

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

And the confidence interval is given by:

(0.123, 0.177)

And for this case the interval contains the value 0.16, so then we can conclude at 5% of significance that the true proportion is not different from 0.16

3 0

3 years ago

In order to remove water from a flooded basement, two pumps, each rated at 40 gallons per minute, are used. After half an hour,

Scrat [10]

Answer:

3600 gallons of water was removed from the basement.

Step-by-step explanation:

Given:

Rate of each pump = 40 gallons/min

We need to find find the number of gallons of water removed from the basement.

Solution:

Now Given:

After half an hour, the one pump burns out.

Now we know that;

1 hour = 60 mins

$\frac12$ hour = $\frac{60}{2}=30\ mins$

Now for 30 mins both the pumps were working and removing the water.

So we can say that;

Water remove for first 30 mins = $40\times2\times30=2400\ gallons$

Also Given:

the second pump finishes removing the water half an hour later.

So we can say that;

Water removed for next 30 mins = $40\times 30\times1 =1200\ gallons$

Now we can say that;

Total water removed from the basement is equal to sum of Water remove for first 30 mins and Water removed for next 30 mins .

framing in equation form we get;

Total water removed from the basement = $2400+1200=3600\ gallons.$

Hence 3600 gallons of water was removed from the basement.

6 0

3 years ago

Find 6 tenths of 80cm

Rzqust [24]

Answer:

6/10 of 80 is 48

7 0

3 years ago

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Express answer in exact form.

Kruka [31]

We know that
the regular hexagon can be divided into 6 equilateral triangles

area of one equilateral triangle=s²*√3/4
for s=3 in
area of one equilateral triangle=9*√3/4 in²

area of a circle=pi*r²

in this problem the radius is equal to the side of a regular hexagon
r=3 in
area of the circle=pi*3²-----> 9*pi in²
we divide that area into 6 equal parts------> 9*pi/6----> 3*pi/2 in²

the area of a segment formed by a side of the hexagon and the circle is equal to 1/6 of the area of the circle minus the area of 1 equilateral triangle
so
[ (3/2)*pi in²-(9/4)*√3 in²]

the answer is
[ (3/2)*pi in²-(9/4)*√3 in²]

6 0

3 years ago

Which one is longer 60 inches or 9 feet please help me.Thanks!

kolezko [41]

9 feet is longer. hope thins helps :-)

5 0

3 years ago

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