Evaluate the expression and express result in scientific notation (4.3 x 10^2)(1.1 x 10^7)

NASA is conducting an experiment to find out the fraction of people who black out at G forces greater than 6. Step 1 of 2 : Supp

Andru [333]

Answer:

The estimate of the proportion of people who pass out at more than 6 Gs is 0.279.

Step-by-step explanation:

Estimate of the proportion of people who pass out at more than 6 Gs.

Number of people who passed out divided by the size of the sample.

We have that:

Sample of 502 people, 140 passed out at G forces greater than 6. So the estimate is:

$p = \frac{140}{502} = 0.279$

The estimate of the proportion of people who pass out at more than 6 Gs is 0.279.

8 0

3 years ago

You know the measure of the exterior angle which forms a linear pair with the vertex angle. Describe two ways you can find measu

aev [14]

Answer:

Step-by-step explanation:

A linear pair are two given angles whose sum is equal to $180^{o}$ .

Let the exterior angle be represented by $x^{o}$ , and the three interior angles of the triangle be represented by $a^{o}$ , $b^{o}$ and $c^{o}$ .

Assume that the vertex angle $c^{o}$ is the linear pair to the exterior angle $x^{o}$ .

i.e $x^{o}$ + $c^{o}$ = $180^{o}$ (sum of angles on a straight line)

Thus,

i. $a^{o}$ + $b^{o}$ = $x^{o}$ (sum of two opposite interior angles is equal to an exterior angle)

⇒ $a^{o}$ = $x^{o}$ - $b^{o}$

Also,

$b^{o}$ = $x^{o}$ - $a^{o}$

But,

$a^{o}$ + $b^{o}$ + $c^{o}$ = $180^{o}$ (sum of angles in a triangle)

⇒ $c^{o}$ = $180^{o}$ - ( $a^{o}$ + $b^{o}$ )

and

$a^{o}$ + $b^{o}$ = $180^{o}$ - $c^{o}$

ii. $a^{o}$ + $b^{o}$ + $c^{o}$ = $180^{o}$ (sum of angles in a triangle)

$a^{o}$ = $180^{o}$ - ( $b^{o}$ + $c^{o}$ )

Also,

$a^{o}$ + $b^{o}$ = $x^{o}$

⇒ $b^{o}$ = $x^{o}$ - $a^{o}$

$c^{o}$ = $180^{o}$ - $x^{o}$

8 0

3 years ago

The realtor and her clients do not know the average home sale price for all of Guelph (500 was actually just a guess). However,

strojnjashka [21]

Answer:

a) The 99% confidence interval would be given by (346.708;453.292)

b) The 99% confidence interval would be given by (338.445;461.555)

Step-by-step explanation:

1) 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".

$\bar X=400$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=80$ represent the population standard deviation

n=15 represent the sample size

2) Part a

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

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that $z_{\alpha/2}=2.58$

Now we have everything in order to replace into formula (1):

$400-2.58\frac{80}{\sqrt{15}}=346.708$

$400+2.58\frac{80}{\sqrt{15}}=453.292$

So on this case the 99% confidence interval would be given by (346.708;453.292)

3) Part b

For this case we don't know the population deviation so we need to use the t distribution instead the normal standard distribution.

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

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

We need to find the degrees of freedom first df=n-1=15-1=14

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,14)".And we see that $t_{\alpha/2}=2.98$

Now we have everything in order to replace into formula (1):

$400-2.98\frac{80}{\sqrt{15}}=338.445$

$400+2.98\frac{80}{\sqrt{15}}=461.555$

So on this case the 99% confidence interval would be given by (338.445;461.555)

4 0

3 years ago

The graph below shows the solution to which system of inequalities?

nlexa [21]

Answer:

Option D.

Step-by-step explanation:

Consider option D. $y\leq \frac{3x}{4}+10\,,\,y\leq \frac{-x}{2}-3$

Take point (0,0)

On putting this point in inequation $y\leq \frac{3x}{4}+10$ , we get

$0\leq 10$ which is true . So, solution is region towards the origin i,e region below the line $y= \frac{3x}{4}+10$ including the line itself .

On putting (0,0) in inequation $y\leq \frac{-x}{2}-3$ , we get $0\leq -3$ which is false , so solution is region away from the origin i.e region below line $y= \frac{-x}{2}-3$ including the line itself .

So, common solution to both the inequations is the shaded part in the given figure .

In other words, we can say that the graph shown in the given figure represents system of equations: $y\leq \frac{3x}{4}+10\,,\,y\leq \frac{-x}{2}-3$

5 0

3 years ago

A spherical water tank holds 7,500 ft3 of water. What is the diameter of the tank?

Alisiya [41]

Answer: 2r=d

d=24.28590063

Step-by-step explanation:

vsphere=4/3pir^3

7500=4/3pir^3

times both sides by 3

22500=4pir^3

divide both sides by 4

5625=pir^3

divide bot sides by pi

1790.4931=r^3

cube root both sides

12.142950=r

2r=d

d=24.28590063 ft

4 0

3 years ago