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3 years ago

What is the solution to 8t - 2 - 9t < 5?

Mathematics

1 answer:

MrRa [10]3 years ago

6 0

Answer:

t > -7

Step-by-step explanation:

8t - 2 - 9t < 5

Combine like terms

- 2 - t < 5

Add 2 to each side

-2-t+2 < 5+2

-t <7

Multiply each side by -1, remembering to flip the inequality

t > -7

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X and y are normal random variables with e(x) = 2, v(x) = 5, e(y) = 6, v(y) = 8 and cov(x,y)=2. determine the following: e(3x 2y

andriy [413]

The result for the given normal random variables are as follows;

a. E(3X + 2Y) = 18

b. V(3X + 2Y) = 77

c. P(3X + 2Y < 18) = 0.5

d. P(3X + 2Y < 28) = 0.8729

<h3>What is normal random variables?</h3>

Any normally distributed random variable having mean = 0 and standard deviation = 1 is referred to as a standard normal random variable. The letter Z will always be used to represent it.

Now, according to the question;

The given normal random variables are;

E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8.

Part a.

Consider E(3X + 2Y)

$\begin{aligned}E(3 X+2 Y) &=3 E(X)+2 E(Y) \\&=(3) (2)+(2)(6 )\\&=18\end{aligned}$

Part b.

Consider V(3X + 2Y)

$\begin{aligned}V(3 X+2 Y) &=3^{2} V(X)+2^{2} V(Y) \\&=(9)(5)+(4)(8) \\&=77\end{aligned}$

Part c.

Consider P(3X + 2Y < 18)

A normal random variable is also linear combination of two independent normal random variables.

$3 X+2 Y \sim N(18,77)$

Thus,

$P(3 X+2 Y < 18)=0.5$

Part d.

Consider P(3X + 2Y < 28)

$Z=\frac{(3 X+2 Y-18)}{\sqrt{77}}$

$\begin{aligned} P(3X + 2Y < 28)&=P\left(\frac{3 X+2 Y-18}{\sqrt{77}} < \frac{28-18}{\sqrt{77}}\right) \\&=P(Z < 1.14) \\&=0.8729\end{aligned}$

Therefore, the values for the given normal random variables are found.

To know more about the normal random variables, here

brainly.com/question/23836881

#SPJ4

The correct question is-

X and Y are independent, normal random variables with E(X) = 2, V(X) = 5, E(Y) = 6, and V(Y) = 8. Determine the following:

a. E(3X + 2Y)

b. V(3X + 2Y)

c. P(3X + 2Y < 18)

d. P(3X + 2Y < 28)

8 0

2 years ago

6300/90???? PLS helpppp

dmitriy555 [2]

Answer: 70

Step-by-step explanation: 6300/90=70 Brainliest please?

4 0

3 years ago

Using the graph as your guide, complete the following statement.

iogann1982 [59]

Answer:

Step-by-step explanation:

The discriminant tells you where the graph of the parabola goes through the x-axis, if at all. If the discriminant is negative there are no real zeros and the parabola does not cross or touch the x-axis; if the discriminant is positive the parabola will go through the x axis in 2 places; if the discriminant is 0 the parabola will touch the x-axis in 1 place. Our discriminant is 0 since the parabola only touches the x-axis but does not go through.

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3 years ago

Read 2 more answers

A bathtub contains 20 gallons of water. After the drain is opened, there are 14 gallons of water remaining after 30 seconds. Usi

Juliette [100K]

6 gallons are lost every 30 second so .2 gallons are lost every second

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3 years ago

Round nine point four two to one decimal place

Alona [7]

Well in order to round 9.42 to the closest whole number we must know that. anything below 5 we round down and 5 and up we round up

So 9.42 becomes 9

of if your wanting to round to the nearest tenth it would be 9.4 you drop the 2 because you rounded down since it was lower than 5.

5 0

3 years ago

What is the solution to 8t - 2 - 9t < 5?​

What is the solution to 8t - 2 - 9t < 5?