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Sauron [17]
3 years ago
15

PLA HELP PLS I NEED TO PASS !! Mendel team built a structure for a competition using wooden spheres and cylinders. The wood they

used weighs 1 g for each 1.4cm ^3. They used 4 spheres and 4 cylinders to build the base of the structure. Each sphere has a radius of 4.45cm. Each cylinder has a radius of 3cm. The base weighs 1700 g. What is the height of the cylinders? Use 3.14 to approximate pi and round your answer to the nearest whole number. Show your work
Mathematics
1 answer:
Ainat [17]3 years ago
6 0
The answer to your question is 22.875
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Consider a discrete random variable x with pmf px (1) = c 3 ; px (2) = c 6 ; px (5) = c 3 and 0 otherwise, where c is a positive
PtichkaEL [24]
Looks like the PMF is supposed to be

\mathbb P(X=x)=\begin{cases}\dfrac c3&\text{for }x\in\{1,5\}\\\\\dfrac c6&\text{for }x=2\\\\0&\text{otherwise}\end{cases}

which is kinda weird, but it's not entirely clear what you meant...

Anyway, assuming the PMF above, for this to be a valid PMF, we need the probabilities of all events to sum to 1:

\displaystyle\sum_{x\in\{1,2,5\}}\mathbb P(X=x)=\dfrac c3+\dfrac c6+\dfrac c3=\dfrac{5c}6=1\implies c=\dfrac65

Next,

\mathbb P(X>2)=\mathbb P(X=5)=\dfrac c3=\dfrac25

\mathbb E(X)=\displaystyle\sum_{x\in\{1,2,5\}}x\,\mathbb P(X=x)=\dfrac c3+\dfrac{2c}6+\dfrac{5c}3=\dfrac{7c}3=\dfrac{14}5

\mathbb V(X)=\mathbb E\bigg((X-\mathbb E(X))^2\bigg)=\mathbb E(X^2)-\mathbb E(X)^2
\mathbb E(X^2)=\displaystyle\sum_{x\in\{1,2,5\}}x^2\,\mathbb P(X=x)=\dfrac c3+\dfrac{4c}6+\dfrac{25c}3=\dfrac{28c}3=\dfrac{56}5
\implies\mathbb V(X)=\dfrac{56}5-\left(\dfrac{14}5\right)^2=\dfrac{84}{25}

If Y=X^2+1, then X^2=Y-1\implies X=\sqrt{Y-1}, where we take the positive root because we know X can only take on positive values, namely 1, 2, and 5. Correspondingly, we know that Y can take on the values 1^2+1=2, 2^2+1=5, and 5^2+1=26. At these values of Y, we would have the same probability as we did for the respective value of X. That is,

\mathbb P(Y=y)=\begin{cases}\dfrac c3&\text{for }y=2\\\\\dfrac c6&\text{for }y=5\\\\\dfrac c3&\text{for }y=26\\\\0&\text{otherwise}\end{cases}

Part (5) is incomplete, so I'll stop here.
8 0
3 years ago
Help me pls it is geometry
Gekata [30.6K]

Answer:

m < b = 76

Step-by-step explanation:

Because b is directly across from the 76 degree angle, that makes them vertical angles, which means they are the same degree I believe.

5 0
2 years ago
Read 2 more answers
A rectangle on a coordinate plane has vertices L(0, 6), M(8,6), N(8,0), and O(0, 0). What are the dimensions of the
solniwko [45]

Answer:

The whole rectangle is in the 1st dimensions.

For how to do this, you need draw it in a grid chart.

5 0
3 years ago
What are the coordinates of M' after triangle MNO is reflected over the y-axis, and rotated 90 degrees clockwise with
exis [7]
(0,-6) because it is reflected and rotated
3 0
3 years ago
Read 2 more answers
This table shows a value that represents an exponential function what is the average rate of change for this function for the in
aliya0001 [1]

Answer:

Option A is correct, i.e. 12.

Step-by-step explanation:

Given is the table of x&y relationship which represents an exponential function.

The average rate of change for a function can be found using the following formula:-

F_average = { f(b) - f(a) } / (b-a)

Given a = 3 and b = 5.

From the table, f(3) = 8 and f(5) = 32.

So, F_average = (32-8)/(5-3)

F_average = 24/2 = 12.

Hence, option A is correct, i.e. 12.

4 0
3 years ago
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