What is the hypotenuse of a right triangle that has legs measuring 6 cm and 8 cm?

What is the value of the 30th percentile for the data set? 6283 5700 6381 6274 5700 5896 5972 6075 5993 5581 5972 6274 6075 5896

Alex17521 [72]

<h2>Answer:</h2>

5896

<h2>Step-by-step explanation:</h2>

Given data set:

6283 5700 6381 6274 5700 5896 5972 6075 5993 5581 5972 6274 6075 5896

To calculate the 30th percentile;

<em>i. Rearrange the given data set in ascending order.</em>

5581 5700 5700 5896 5896 5972 5972 5993 6075 6075 6274 6274 6283 6381

<em>ii. Use the following formula to get the index of the value at the 30th percentile.</em>

N = p(n)

<em>Where;</em>

N = the number of data points at or below the intended percentile.

p = the intended percentile.

n = the number of points in the data.

p = 30 percent = 0.3

n = 14

<em>Substitute these values into the equation;</em>

N = 0.3(14)

N = 4.2

<em>iii. From the calculated index, find the value of the 30th percentile.</em>

If the index is a whole number x, the desired percentile is the average of the values at index x and x+1.

For example if the index is 4, then the desired percentile is the average of the values at index 4 and 5. In our case, that will be;

$\frac{5896+5896}{2}$ = 5896

If the index is a decimal number, it is rounded up to the nearest integer. The value at the rounded index is the desired percentile.

For example, in our case, the index is 4.2 which when rounded up becomes 4.

Therefore, the data point or value at index 4 is the 30th percentile. From the arrangement in (ii) above, that will be 5896. i.e

5581 5700 5700 <u>5896</u> 5896 5972 5972 5993 6075 6075 6274 6274 6283 6381

8 0

3 years ago

Find the value of x. Round to the nearest tenth.

serg [7]

Answer:

Where is the equation?

Step-by-step explanation:

8 0

3 years ago

The volume V of an ice cream cone is given by V = 2 3 πR3 + 1 3 πR2h where R is the common radius of the spherical cap and the c

Nuetrik [128]

Answer:

The change in volume is estimated to be 17.20 $\rm{in^3}$

Step-by-step explanation:

The linearization or linear approximation of a function $f(x)$ is given by:

$f(x_0+dx) \approx f(x_0) + df(x)|_{x_0}$ where $df$ is the total differential of the function evaluated in the given point.

For the given function, the linearization is:

$V(R_0+dR, h_0+dh) = V(R_0, h_0) + \frac{\partial V(R_0, h_0)}{\partial R}dR + \frac{\partial V(R_0, h_0)}{\partial h}dh$

Taking $R_0=1.5$ inches and $h=3$ inches and evaluating the partial derivatives we obtain:

$V(R_0+dR, h_0+dh) = V(R_0, h_0) + \frac{\partial V(R_0, h_0)}{\partial R}dR + \frac{\partial V(R_0, h_0)}{\partial h}dh\\V(R, h) = V(R_0, h_0) + (\frac{2 h \pi r}{3} + 2 \pi r^2)dR + (\frac{\pi r^2}{3} )dh$

substituting the values and taking $dx=0.1$ and $dh=0.3$ inches we have:

$V(R_0+dR, h_0+dh) =V(R_0, h_0) + (\frac{2 h \pi r}{3} + 2 \pi r^2)dR + (\frac{\pi r^2}{3} )dh\\V(1.5+0.1, 3+0.3) =V(1.5, 3) + (\frac{2 \cdot 3 \pi \cdot 1.5}{3} + 2 \pi 1.5^2)\cdot 0.1 + (\frac{\pi 1.5^2}{3} )\cdot 0.3\\V(1.5+0.1, 3+0.3) = 17.2002\\\boxed{V(1.5+0.1, 3+0.3) \approx 17.20}$

Therefore the change in volume is estimated to be 17.20 $\rm{in^3}$

4 0

3 years ago

For 32 hours of work, you are paid $244.80. How much would you receive for 37 hours?

Serga [27]

Answer:

$283.05

Step-by-step explanation:

first divide $244.80 by 32, to find out how much you are making hourly. in this case you are making $7.65 an hour

next, multiply $7.65 by 5, to add the 5 hours, in this case you get $38.25.

next, add $38.25 to $244.80 and you get your answer!

7 0

3 years ago

What is 15 1/2 divided by 2 1/5

IgorLugansk [536]

Answer:

6 1/5

Step-by-step explanation:

8 0

3 years ago

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