Solve: 7+42*3^(2-3a)=14*3^-2a+7 A=-3 a=0 a=3 a=no solution

An object is dropped from a bridge and allowed to freefall to the ground. The height of the object over time can be modeled usin

GuDViN [60]

Answer:

3 seconds

Step-by-step explanation:

Complete question:

An object is dropped from a bridge and allowed to freefall to the ground. The height of the object over time can be modeled using h(t)=144-16t2. How many seconds will it take the object to reach the ground? 2 seconds 3 seconds 9 seconds 16 seconds

Given the height of an object modelled by the expression;

h(t)=144-16t²

The object will reach the ground when h(t) = 0

Substitute into the formula

0 = 144 - 16t²

-144 = -16t²

144 = 16t²

Swap

16t² = 144

t² = 144/16

t² = 9

Square root both sides

√t² = ±√9

t = ±3secs

Since the time cannot be negative, hence the object will reach the ground 3 seconds after

8 0

3 years ago

A and B are independent events. P(A) = 0.40 P(B) = 0.30 What is P(A/B)

Lelechka [254]

Answer: Hello mate!

Two independent events, mean that the fact that, if the event A occurred, this has no effect in the probability of the event B to occur after.

For example, a coin flip.

The first result has no effect on the next result.

Then the notation P(A/B) is the probability of the event A when the event B occurred before, but as we know, the fact that the event B occurred before has no effect in it; so:

P(A/B) = P(A) = 0.30

6 0

3 years ago

Read 2 more answers

Cabrina and Dabney are attending a conference. After the conference, Cabrina drives home to Boise at an average speed of 7575 m

kifflom [539]

Answer:

Cabrina's time = 5 hours

Dabney's time = 6.5 hours

Step-by-step explanation:

The data of the exercise are:

Cabrina speed = 75 mph

Daney speed = 60 mph

The sum of their distance is 765 miles, therefore

Cabrina's distance Dabney's distance = 765

Cabrina's distance = x

Dabney's distance = 765-x

The sum of their times is 11.5 hours, therefore

Cabrina's time Dabneys time = 11.5

Cabrina's time = x / 75

Dabney's time = (765-x) / 60

x / 75 (765-x) / 60 = 11.5

Lowest common denominator of 75 and 60 is 300, therefore we have:

330 * x / 75 300 * (765-x) / 60 = 300 * 11.5

4 * x 5 * (- x 765) = 3450

4 * x - 5 * x 3825 = 3450

x = 375

Replacing:

Cabrina's time = 375/75 = 5 hours took

Dabney's time = (765-375) / 60 = 6.5 hours took

7 0

3 years ago

Read 2 more answers

A square room has a tiled floor with 81 square tiles. How many tiles are along an edge of the room?

Sladkaya [172]

Answer:

36 tiles

Step-by-step explanation:

Because the room is square, the numbers of tiles along the edge of the room were multiplied by the same number, meaning that:

81 = x²

So to find x, we must square root both sides of the equation:

$\sqrt{81} = \sqrt{x^2}$

x = 9

So the length of one side is 9 tiles. Now to calculate the circumference, as each side of a square is the same length, we can multiply this number by 4:

9 * 4 = 36

So there are 36 tiles along the edge of the room.

Hope this helps!

4 0

3 years ago

A survey organization has used the methods of our class to construct an approximate 95% confidence interval for the mean annual

lawyer [7]

Answer:

$\bar X = \frac{66000+70000}{2}= 68000$

We can estimate the margin of error with this formula:

$ME= \frac{Upper -Lower}{2}= \frac{70000-66000}{2}= 2000$

And the margin of error is given by:

$ME = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

And we can rewrite the margin of error like this:

$ME =z_{\alpha/2}*SE$

Where $SE= \frac{\sigma}{\sqrt{n}}$

For 95% of confidence the critical value is $z_{\alpha/2}= \pm 1.96$

The Standard error would be:

$SE= \frac{ME}{z_{\alpha/2}}= \frac{2000}{1.96}= 1020.408$

For 99% of confidence the critical value is $z_{\alpha/2}= \pm 2.58$

And the new margin of error would be:

$ME = 2.58* 1020.408 = 2632.653$

And then the interval would be given by:

$Lower = 68000- 2632.653 = 65367.347$

$Upper = 68000+ 2632.653 = 70632.653$

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".

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

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size

Solution to the problem

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

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

The 95% confidence interval is given by (66000 , 70000)

We can estimate the mean with this formula:

$\bar X = \frac{66000+70000}{2}= 68000$

We can estimate the margin of error with this formula:

$ME= \frac{Upper -Lower}{2}= \frac{70000-66000}{2}= 2000$

And the margin of error is given by:

$ME = z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

And we can rewrite the margin of error like this:

$ME =z_{\alpha/2}*SE$

Where $SE= \frac{\sigma}{\sqrt{n}}$

For 95% of confidence the critical value is $z_{\alpha/2}= \pm 1.96$

The Standard error would be:

$SE= \frac{ME}{z_{\alpha/2}}= \frac{2000}{1.96}= 1020.408$

For 99% of confidence the critical value is $z_{\alpha/2}= \pm 2.58$

And the new margin of error would be:

$ME = 2.58* 1020.408 = 2632.653$

And then the interval would be given by:

$Lower = 68000- 2632.653 = 65367.347$

$Upper = 68000+ 2632.653 = 70632.653$

7 0

4 years ago