What is b if the area is 140 units

Explain how you can find the LCM of 8 and 10

lions [1.4K]

Answer:

2

Step-by-step explanation:

When trying to find the LCM of two numbers you need to write down all possible ways to multiply any number used to get both 8 and 10. When doing that, the LCM is the smallest number out of both of them.

7 0

3 years ago

Read 2 more answers

Which is the expected value of the random variable with given probability distribution ?

Gnom [1K]

Answer:

Step-by-step explanation:

Let X be the RV we are talking about.

Expected value has different aliases, such as weighted average, mean, expectation, first moment and so on.

Okay, how do we calculate the average first, just sum all the values and divide by number of values. It comes from the basic assumption, which is choosing one of them is equally likely. What I mean by that is quite simple, above process what I talked about is just sum of the numbers times their probabilities. e.g. (a+b+c+d)/4 = a/4 + b/4 + c/4 + d/4. In the example, we assumed that probability of choosing any a, b, c and d is equally likely.

Then, why I use the term weighted average is the generalized situation of average, which is some of the numbers are repetitive. For instance, X can take the values a, b, c and d; however, X can take the value a 3 times more than d, X can take the value b 2 times more than d and c and d occurs with the same frequency at X, Therefore, if we take a sample, it is likely to be a, b, a, c, d, a, b or the permutation of this sample. Therefore the weighted average is 3 * a / 7 + 2 * b / 7 + c / 7 + d /7 or using normal average theorem (a + a + a + b + b + c +d) / 7. First, both of them are equal. Find the distribution and multiply the values with the probabilities of the distribution and sum them up or just add them and divide by number of sample. Second, if you check that, a has more weight, which means a can determine the direction of the average more. That is the logic behind the expected value.

Now, if X is a discrete RV (like in the above example), we know what we are going to do. What if X is a continuous RV ? X could take infinite values therefore if you divide a number with an infinite value, the probability of an individual value X could take is going to be 0. Therefore, we cannot calculate the expected value of chosen values individually; however, we can calculate the expected value of an interval by approximating with Riemann Sum or with a better choice, using integrals. Because, technically using Riemann Sum and quantizing the values and approximating the area of the curve is the same as we did above.

In conclusion, basically if X is a discrete RV and the values X could take is countably infinite,

If X is a discrete RV and the values X could take is finite,

if X is a continuous RV,

3 0

3 years ago

A timeline. 27 B C E to 180 C E PAX ROMANA. 44 B C E The Roman Empire was founded. 80 C E The Colosseum was built. 121 C E Hadri

VARVARA [1.3K]

Answer:

the answer is 41

Step-by-step explanation:

7 0

4 years ago

A onesided test of a hypothesis, based on a sample of size 9, yields a Pvalue of .035. Which of the following best describes t

lana [24]

Answer:

1.86 < t < 2.31

Step-by-step explanation:

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean height actually is higher\lower than an specified value, the system of hypothesis would be:

Null hypothesis: $\mu \leq \mu_o$

Alternative hypothesis: $\mu > \mu_o$

Or like this:

Null hypothesis: $\mu \geq \mu_o$

Alternative hypothesis: $\mu < \mu_o$

If we analyze the size for the sample is < 30 and we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We don't know on this case the calculated value and with the p value we can find it.

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=9-1=8$

Since is a one side test the p value would be:

$p_v =P(t_{(8)}>t_o)=0.035$

And we can find the critical value with the following excel code:

" =T.INV(1-0.035,8)" and we got $t_p =2.09$

And cannot be a lower tail test since all the options have positive values for the statistic. So on this case the best option is:

1.86 < t < 2.31

8 0

3 years ago

The length of a rectangle is 10 m less than three times the width, and the area of the rectangle is 77 m2 . find the dimensions

Anna007 [38]

Let the width be x, the length is then 3x-10
Area of a rectangle is length times width: x(3x-10)=77 => 3x^2-10x-77=0
Factor this quadratic equation: (x-7)(3x+11)=0 =.x=7 or x=-11/3
width cannot be negative, so the only answer is x=7
width is 7m, length is 11m

8 0

3 years ago