Round to the nearest place value and write in scientific notation 1,402,941,487

Can the following lengths be

amm1812

I don’t think so because 2 lengths added up HAVE to be greater than the largest length. Hope this helped

3 0

3 years ago

Please help ASAP!!!

slavikrds [6]

Answer:

a) the platform is 110 feet above the ground.

b) It takes 8.69 sec for the rock to hit the ground

Step-by-step explanation:

This situation is modelled by the following function: $f(x) = -5x^2 + 40x + 30\\$

We need to answer the following questions.

a) How high above the ground is the platform?

First we find x using the formula: $x=-\frac{b}{2a}$

we have b = 40 and a = -5

Putting values and finding x

$x=-\frac{b}{2a}\\x=-\frac{40}{2(-5)}\\x=-\frac{40}{-10}\\x=4$

Now putting x=4 in the function to find how high above the ground is the platform

$f(x) = -5x^2 + 40x + 30\\Put\:x=4\\f(4)=-5(4)^2+40(4)+30\\f(4)=-5(16)+160+30\\f(4)=-80+160+30\\f(4)=110$

So, the platform is 110 feet above the ground.

b) How long does it take for the rock to hit the ground? Show all work to receive full credit!

We will factorise the given function $f(x) = -5x^2 + 40x + 30$ to find the time taken to hit the ground.

We can solve the equation using quadratic formula: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

We have a =-5, b=40, c=30

Putting values and finding x

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-40\pm\sqrt{(40)^2-4(-5)(30)}}{2(-5)}\\x=\frac{-40\pm\sqrt{1600+600}}{-10}\\x=\frac{-40\pm\sqrt{2200}}{-10}\\x=\frac{-40\pm46.9}{-10}\\x=\frac{-40+46.9}{-10},x=\frac{-40-46.9}{-10} \\x=-0.69,x=8.69$

So, we get values of x: x = -0.69 and x=8.69

As time cannot be negative, so we take x=8.69

So, It takes 8.69 sec for the rock to hit the ground

3 0

3 years ago

A building inspector believes that the percentage of new construction with serious code violations may be even greater than the

Y_Kistochka [10]

Answer:

The inspector's claim has strong statistical evidence.

Step-by-step explanation:

To answer this we have to perform a hypothesis test.

The inspector claimed that the actual proportion of code violations is greater than 0.07, so the null and alternative hypothesis are:

$H_0: \pi\leq0.07\\\\H_a: \pi>0.07$

We assume a significance level of 0.05.

The sample size is 200 and the proportion of the sample is:

$p=\frac{23}{200}= 0.115$

The standard deviation is

$\sigma=\sqrt{\frac{\pi(1-\pi)}{N} }= \sqrt{\frac{0.07*0.93}{200}}=0.018$

The z-value can be calculated as

$z=\frac{p-\pi-0.5/N}{\sigma} =\frac{0.115-0.07-0.5/200}{0.018} =\frac{0.0425}{0.018}=2.36$

The P-value for this z-value is P=0.00914.

This P-value is smaller than the significance level, so the effect is significant and the null hypothesis is rejected.

The inspector's claim has strong statistical evidence.

7 0

3 years ago

Read 2 more answers

A cylindrical piece of iron pipe is shown below. The wall of the pipe is 0.75 inch thick, and the pipe is open at both ends:

Vadim26 [7]

Answer:

Correct option: fourth one -> 254 cubic inches.

Step-by-step explanation:

The volume of a cylinder is given by the equation:

$Volume = \pi * radius^2 * height$

To calculate the internal volume of the pipe, we should use its internal radius.

The external radius of the pipe is half of the diameter, and the internal radius is the external radius minus the thickness of the pipe, so we have:

$internal\ radius = external\radius - thickness\\internal\ radius = \frac{6}{2} - 0.75\\internal\ radius = 2.25\ in$

Then, using the internal radius in the volume equation, we have that:

$Volume = \pi * 2.25^2 * 16$

$Volume = 254.47\ in3$

So the correct option is the fourth one: Volume is approximately 254 cubic inches.

5 0

3 years ago

Axel lives in Virginia and makes $54,000 a year. If the median annual income in Virginia is $61,233 and the median annual income

rusak2 [61]

Answer:

The answer is Yes Axel will qualify for chapter 7 bankruptcy.

Step-by-step explanation:

To qualify for a Chapter 7 bankruptcy, the debtor must earn less than the state median income on a monthly basis. Here it is given that Axel lives in Virginia and makes $54,000 a year. The median annual income in Virginia is $61,233. So, Axel is earning less than the median income. Hence, he will qualify for chapter 7 bankruptcy.

3 0

4 years ago

Read 2 more answers