Axis of symmetry of y=x^2+6x+7

Complete the chart to find the mean, variance, and standard deviation. Remember to use commas and round numbers to the nearest t

vitfil [10]

Answer: The mean of the data is 433.75, variance of the data is 99667.19 and the standard deviation of the data is 315.7011.

Explanation:

The given data is 900, 35, 500 and 300.

The number of observation is 4.

Formula of mean is,

$\text{Mean}=\frac{\text{Sum of observations}}{\text{Number of observations}}$

$\bar{X}=\frac{900+35+50+300}{4} =433.75$

The formula of variance is given below,

$\sigma^2=\frac{1}{n}\sum{(X-\bar{X})^2}$

$\sigma^2=\frac{398668.75}{4}$

$\sigma^2=99667.19$

The variance of the data is 99667.19

$\sigma=\sqrt{99667.19}$

$\sigma=315.7011$

The standard deviation of the data is 315.7011.

The other information or values of given chart is shown in the attached table.

8 0

3 years ago

Read 2 more answers

Which career would most heavily involve geometric concepts?

LiRa [457]

Answer:

Out of these careers, an engineer would be the most geometric involved career.

Step-by-step explanation:

This answer is true through the process of elimination. A stockbroker focuses on economy in order to choose the right stock. A statistician focuses on graphing and statistics in terms of math. An accountant is focused on simple math in order to deduct and add to the sum of the money. The engineer has to use geometry in order to design plans for constructions.

5 0

3 years ago

If each muffin contains the same amount of cornmeal, how many kilograms of cornbread are in each corn muffin

Diano4ka-milaya [45]

21 cornbread are in each corn muffin

5 0

3 years ago

Read 2 more answers

The angle of elevation from Madison to the top of the Statue of Liberty is 79 degrees. If Madison is standing 58.2 feet from its

lana66690 [7]

To solve this problem you must apply the proccedure shown below:

1. You have the following information given in the problem:

- <span>The angle of elevation from Madison to the top of the Statue of Liberty is 79 degrees.
- Madison is standing 58.2 feet from its base.

-Madison is 5 feet tall.

2. Therefore, you have:

Sin</span>α=opposite/hypotenuse
<span>
Sin(79°)=x/58.2
x=(58.2)(Sin(79°))
x=57.13 ft

3. Now, you can calculate the height of the Statue of Liberty, as below:

height=x+5 ft
height=57.13 ft+5 ft
height=62.13 ft

4. Therefore, as you can see, the answer is: 62.13 ft
</span>

4 0

3 years ago

Read 2 more answers

Find the general solution of the differential equation and check the result by differentiation. (Use C for the constant of integ

atroni [7]

Answer: $y=Ce^(^3^t^{^9}^)$

Step-by-step explanation:

Beginning with the first differential equation:

$\frac{dy}{dt} =27t^8y$

This differential equation is denoted as a separable differential equation due to us having the ability to separate the variables. Divide both sides by 'y' to get:

$\frac{1}{y} \frac{dy}{dt} =27t^8$

Multiply both sides by 'dt' to get:

$\frac{1}{y}dy =27t^8dt$

Integrate both sides. Both sides will produce an integration constant, but I will merge them together into a single integration constant on the right side:

$\int\limits {\frac{1}{y} } \, dy=\int\limits {27t^8} \, dt$

$ln(y)=27(\frac{1}{9} t^9)+C$

$ln(y)=3t^9+C$

We want to cancel the natural log in order to isolate our function 'y'. We can do this by using 'e' since it is the inverse of the natural log:

$e^l^n^(^y^)=e^(^3^t^{^9} ^+^C^)$

$y=e^(^3^t^{^9} ^+^C^)$

We can take out the 'C' of the exponential using a rule of exponents. Addition in an exponent can be broken up into a product of their bases:

$y=e^(^3^t^{^9}^)e^C$

The term e^C is just another constant, so with impunity, I can absorb everything into a single constant:

$y=Ce^(^3^t^{^9}^)$

To check the answer by differentiation, you require the chain rule. Differentiating an exponential gives back the exponential, but you must multiply by the derivative of the inside. We get:

$\frac{d}{dx} (y)=\frac{d}{dx}(Ce^(^3^t^{^9}^))$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*\frac{d}{dx}(3t^9)$

$\frac{dy}{dx} =(Ce^(^3^t^{^9}^))*27t^8$

Now check if the derivative equals the right side of the original differential equation:

$(Ce^(^3^t^{^9}^))*27t^8=27t^8*y(t)$

$Ce^(^3^t^{^9}^)*27t^8=27t^8*Ce^(^3^t^{^9}^)$

QED

I unfortunately do not have enough room for your second question. It is the exact same type of differential equation as the one solved above. The only difference is the fractional exponent, which would make the problem slightly more involved. If you ask your second question again on a different problem, I'd be glad to help you solve it.

7 0

2 years ago