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3 years ago

11

Solve the system of equations by the substation method. Y=4x+5 y=7x+6. Select the correct choice below and if necessary, fill in

the answer box to complete your choice

1 answer:

Tom [10]3 years ago

6 0

The solution to the system of equations is (-1/3, 11/3)

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Solve for the base of a triangle where the height is 16cm and area is 104 cm2. What is the base?

Arturiano [62]

Answer:

13cm

Step-by-step explanation:

104 × 2 = 208

208 ÷ 16 = 13cm

(13 × 16) ÷ 2 = 104cm²

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3 years ago

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Gabriela has dinner at a cafe and the cost of her meal is \$45.00$45.00dollar sign, 45, point, 00. Because of the service, she w

Olegator [25]

The total bill amount before the service fee is given as $45.
We are given that the tip she wants to leave is 15% of the bill amount, this means that:
tip value = 0.15 * 45 = 6.75$

The total bill would be the summation of the original bill and the tip value she left.

Total bill amount = 45 + 6.75 = 51.75$

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3 years ago

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If a circle has a radius of 2.5 inches what is the area of the circle

daser333 [38]

The answer should be 19.63

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3 years ago

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Square of a standard normal: Warmup 1.0 point possible (graded, results hidden) What is the mean ????[????2] and variance ??????

LenaWriter [7]

Answer:

$E[X^2]= \frac{2!}{2^1 1!}= 1$

$Var(X^2)= 3-(1)^2 =2$

Step-by-step explanation:

For this case we can use the moment generating function for the normal model given by:

$\phi(t) = E[e^{tX}]$

And this function is very useful when the distribution analyzed have exponentials and we can write the generating moment function can be write like this:

$\phi(t) = C \int_{R} e^{tx} e^{-\frac{x^2}{2}} dx = C \int_R e^{-\frac{x^2}{2} +tx} dx = e^{\frac{t^2}{2}} C \int_R e^{-\frac{(x-t)^2}{2}}dx$

And we have that the moment generating function can be write like this:

$\phi(t) = e^{\frac{t^2}{2}$

And we can write this as an infinite series like this:

$\phi(t)= 1 +(\frac{t^2}{2})+\frac{1}{2} (\frac{t^2}{2})^2 +....+\frac{1}{k!}(\frac{t^2}{2})^k+ ...$

And since this series converges absolutely for all the possible values of tX as converges the series e^2, we can use this to write this expression:

$E[e^{tX}]= E[1+ tX +\frac{1}{2} (tX)^2 +....+\frac{1}{n!}(tX)^n +....]$

$E[e^{tX}]= 1+ E[X]t +\frac{1}{2}E[X^2]t^2 +....+\frac{1}{n1}E[X^n] t^n+...$

and we can use the property that the convergent power series can be equal only if they are equal term by term and then we have:

$\frac{1}{(2k)!} E[X^{2k}] t^{2k}=\frac{1}{k!} (\frac{t^2}{2})^k =\frac{1}{2^k k!} t^{2k}$

And then we have this:

$E[X^{2k}]=\frac{(2k)!}{2^k k!}, k=0,1,2,...$

And then we can find the $E[X^2]$

$E[X^2]= \frac{2!}{2^1 1!}= 1$

And we can find the variance like this :

$Var(X^2) = E[X^4]-[E(X^2)]^2$

And first we find:

$E[X^4]= \frac{4!}{2^2 2!}= 3$

And then the variance is given by:

$Var(X^2)= 3-(1)^2 =2$

7 0

3 years ago

From a standard deck of 52 cards what is the probability of picking either an eight or a queen

Shtirlitz [24]

In a standard deck of 52 cards, there are four 8's and four queens. The probability of picking an eight is 4/52 or 1/13. Furthermore, the probability of picking a queen from the deck is also 1/13. Since the problem asked for the probability of picking either eight or queen, add the probability of picking queen and eight. The addition gives 2/13.

Thus, the answer is 2/13.

7 0

3 years ago