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4 years ago

The product of three consecutive odd numbers is 6,783. What are the numbers?

1 answer:

7 0

The numbers are 2260, 2261, and 2262. Here’s how i figured it out:
Let x = The smallest numberThe second number is the the first number with one added to it, so it can be represented as x+1.The third number is the first number added 2 to it, so we can say it's x+2.Put this in a equation. The three numbers add together to become 6783, so it will be the sum.6783 = x + x + 1 + x + 2I just replaced the second and third numbers with what I explained above.We also can simplify the expression by combining the like terms to become 6783 = 3x + 3.Subtract 3 on both sides.6780 = 3xDivide by three on both sides to isolate the variable.2260 = xBut, we’re not done yet. Since x is only the starting number, we have to add 1 and 2 to it to get the consecutive numbers. I think you can add, so the three consecutive numbers will be 2260, 2261, and 2262. If you’re not sure then you can add the three numbers together and you will get 6783.I hope this answer helped and if you have any other questions, don’t hesitate to contact me!

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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

Answer to this question?

Readme [11.4K]

A midsegment is given by the formula:
$\frac{x1+x2}{2} , \frac{y1+y2}{2}$

Where x1, x2, y1, and y2 correspond to their respective coordinates. We can do the equation:

$\frac{-3+5}{2} , \frac{-1+3}{2}$
This gets us a midpoint coordinate of (1,1)

As for distance, it will be found by doing:
$\sqrt{(x2-x1)^2+(y2-y1)^2}$
We can do the following:

$\sqrt{(5-(-3))^2+(3-(-1))^2}$
$\sqrt{(8)^2+(4)^2}$
$\sqrt{64+16}$
This simplifies to $4 \sqrt{5}$

:)

5 0

3 years ago

Read 2 more answers

the Galveston-Port Bolivar Ferry takes cars across Galveston Bay. One day, the ferry transported a total of 685 cars over a 5 ho

anastassius [24]

Answer:

137 cars per hour

Step-by-step explanation:

Since there were 685 cars all together you have to do 685 divided by 5 so that you can get your answer of 137 cars per hour

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3 years ago

Taja is a portrait artist. It takes 2 bottles of paint to make 6 paintings or 9 bottles of paint to make 27 paintings. How many

NISA [10]

Answer: 36

Step-by-step explanation:

6/2= 3 & 3x2=6 & 27/9=3 & 3x9=27 so you would multiply 3x12=36 so you would just multiply. and I'm a 6th grader.

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3 years ago

Tamara invests $8000 in two different accounts. The first account has a simple interest rate of 3% and the second account has a

Paraphin [41]

Answer:

$3200 at 3%
$4800 at 2%

Step-by-step explanation:

Interest earned is proportional to the interest rate, so if the interest earned is the same, the amounts invested must be inversely proportional to the interest rates. That is, for the 3% and 2% accounts, the ratio of money invested is 2:3.

In other words, 2/5 of the money ($3200) was invested at 3%, and 3/5 of the money ($4800) was invested at 2%.

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If you need an equation, you can let x represent the amount invested at the highest rate. Then 8000-x is the amount invested at the lower rate. For the interest in the two accounts to be equal, we have ...

3%·x = 2%·(8000-x) . . . . . the amounts of interest earned are the same

3/2·x = 8000 -x . . . . . . . . divide by 2%

5/2·x = 8000 . . . . . . . . . . . add x and simplify

x = 8000·(2/5) = 3200 . . . multiply by the inverse of the x coefficient

8000-x = 8000 -3200 = 4800 . . . . the amount invested at the lower rate

Tamara invested $3200 in the 3% account and $4800 in the 2% account.

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She earned $96 in each account for the year.

8 0

3 years ago