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olga2289 [7]
3 years ago
13

Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.

Mathematics
1 answer:
Darya [45]3 years ago
5 0
n;\ n+2;\ n+4-three\ consecutive\ even\ numbers\\\\90 \ \textless \  \dfrac{1}{2}(n+n+2+n+4) \ \textless \  105\\\\90 \ \textless \  \dfrac{1}{2}(3n+6) \ \textless \  105\ \ \ |multiply\ both\ sides\ by\ 2\\\\180 \ \textless \  3n+6 \ \textless \  210\ \ \ |subtract\ 6\ from\ both\ sides\\\\174 \ \textless \  3n \ \textless \  204\ \ \ |divide\ both\ sides\ by\ 3\\\\58 \ \textless \  n \ \textless \  68\\\\Answer:\\60;\ 62;\ 64\ or\ 62;\ 64;\ 66;\ or\ 64;\ 66;\ 68\ or\ 66;\ 68;\ 70.
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For X a binomial random variable with n=5 and p=1/4, answer the following
mash [69]
Recall that for X\sim\mathrm{Bin}(n,p), i.e. a random variable X following a binomial distribution over n trials and with probability parameter p,

\mathbb P(X=x)=f_X(x)=\begin{cases}\dbinom nx p^x(1-p)^{n-x}&\text{for }x\in\{0,1,\ldots,n\}\\\\0&\text{otherwise}\end{cases}

So you have

\mathbb P(X=2)=\dbinom52\left(\dfrac14\right)^2\left(1-\dfrac34\right)^{5-2}=\dfrac{135}{512}\approx0.26

\mathbb P(2\le X\le4)=\displaystyle\sum_{x=2}^4\mathbb P(X=x)
=\dbinom52\left(\dfrac14\right)^2\left(1-\dfrac14\right)^{5-2}+\dbinom52\left(\dfrac14\right)^3\left(1-\dfrac14\right)^{5-3}+\dbinom52\left(\dfrac14\right)^4\left(1-\dfrac14\right)^{5-4}
=\dfrac{375}{1024}\approx0.37

The expected value of X\sim\mathrm{Bin}(n,p) is simply np, while the standard deviation is \sqrt{np(1-p)}. In this case, they are \dfrac54=1.25 and \sqrt{\dfrac{15}{16}}\approx0.97, respectively.
7 0
3 years ago
The ratio of blue jays to Robin's was 6 to 7. If there were 84 Robins, how many blue jays were there?​
Paul [167]

Answer:

72

Step-by-step explanation:

<em>Since the ratio of blue jays to robin's was 6 to 7 then if there were 84 robins how many blue jays were there.</em>

<em>6 to 7 can also be express as 6/7</em>

<em>Thus, we can set up a proportion</em>

<em>6/7 = x/84</em>

<em>Now, we have to solve for x</em>

<em>x = 72</em>

<em>Hence, if there were 84 robin there would be 72 blue jays.</em>

<em />

<u><em>~lenvy~</em></u>

3 0
2 years ago
The product of a number and -3, increased by 8, is 20
natita [175]

answer:

-4

Step-by-step explanation:

-3x+8= 20

-8 -8

-3x = 12

÷-3. = ÷-3

x = -4

3 0
3 years ago
PLEASE HELP ASAP!!!!!!!!!!!
irina [24]

Answer:

132 in^2 but DOUBLE CHECK MY WORK!!!!

Step-by-step explanation:

Break it down into parts ok. So I see a 10x10 square, two 2x4 right triangles and a 4x6 rectangle.

10x10 is 100 in

1/2(2*4) = 4 x 2 = 8 in

6x4 = 24 in

add them together to get 132 in^2

7 0
2 years ago
PLEASE HELP WITH MATH AND BEST GETS BRAINLIEST. PLEASE SHOW WORK.
krek1111 [17]
Well, we know the amount of cups of sugar it calls per 1/2 teaspoon, so all we need to do to find the amount of cups of sugar per teaspoon is multiply by 2, since 1/2 teaspoon * 2 = 1 teaspoon.

2/3 * 2 = 1 1/3

The unit rate is 1 1/3 cups per teaspoon
Hope that helped =)
8 0
3 years ago
Read 2 more answers
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