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aleksklad [387]
2 years ago
15

a sum of money is divided among ethan June way and Raj in the ratio of 5:6:9 after eating gave $50 to his mother the ratio becom

es 3:4:6 find the amount of money ethan has after giving $50 to his mother​
Mathematics
1 answer:
Natasha_Volkova [10]2 years ago
5 0
The answer you are looking for is 35
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Find the solution(s) to (x- 3) = 49. Check all that apply.
natima [27]

Answer:

B.x= -4 and E. x= 10 are the answers

4 0
2 years ago
Minnie has 4 different stamps. She needs 3 to mail a large letter. How many ways can she pick the 3 that will be used?
timurjin [86]
Number of ways of picking a smaller number out of a bigger number is called combination.
Number of way of picking 3 stamps out of 4 is 4C3 (4 combination 3) = 4! / (3! x (4 - 3)!) = 4! / (3! x 1!) = (4 x 3 x 2 x 1) / (3 x 2 x 1 x 1) = 24 / 6 = 4 ways.
7 0
3 years ago
Let X1 and X2 be independent random variables with mean μand variance σ².
My name is Ann [436]

Answer:

a) E(\hat \theta_1) =\frac{1}{2} [E(X_1) +E(X_2)]= \frac{1}{2} [\mu + \mu] = \mu

So then we conclude that \hat \theta_1 is an unbiased estimator of \mu

E(\hat \theta_2) =\frac{1}{4} [E(X_1) +3E(X_2)]= \frac{1}{4} [\mu + 3\mu] = \mu

So then we conclude that \hat \theta_2 is an unbiased estimator of \mu

b) Var(\hat \theta_1) =\frac{1}{4} [\sigma^2 + \sigma^2 ] =\frac{\sigma^2}{2}

Var(\hat \theta_2) =\frac{1}{16} [\sigma^2 + 9\sigma^2 ] =\frac{5\sigma^2}{8}

Step-by-step explanation:

For this case we know that we have two random variables:

X_1 , X_2 both with mean \mu = \mu and variance \sigma^2

And we define the following estimators:

\hat \theta_1 = \frac{X_1 + X_2}{2}

\hat \theta_2 = \frac{X_1 + 3X_2}{4}

Part a

In order to see if both estimators are unbiased we need to proof if the expected value of the estimators are equal to the real value of the parameter:

E(\hat \theta_i) = \mu , i = 1,2

So let's find the expected values for each estimator:

E(\hat \theta_1) = E(\frac{X_1 +X_2}{2})

Using properties of expected value we have this:

E(\hat \theta_1) =\frac{1}{2} [E(X_1) +E(X_2)]= \frac{1}{2} [\mu + \mu] = \mu

So then we conclude that \hat \theta_1 is an unbiased estimator of \mu

For the second estimator we have:

E(\hat \theta_2) = E(\frac{X_1 + 3X_2}{4})

Using properties of expected value we have this:

E(\hat \theta_2) =\frac{1}{4} [E(X_1) +3E(X_2)]= \frac{1}{4} [\mu + 3\mu] = \mu

So then we conclude that \hat \theta_2 is an unbiased estimator of \mu

Part b

For the variance we need to remember this property: If a is a constant and X a random variable then:

Var(aX) = a^2 Var(X)

For the first estimator we have:

Var(\hat \theta_1) = Var(\frac{X_1 +X_2}{2})

Var(\hat \theta_1) =\frac{1}{4} Var(X_1 +X_2)=\frac{1}{4} [Var(X_1) + Var(X_2) + 2 Cov (X_1 , X_2)]

Since both random variables are independent we know that Cov(X_1, X_2 ) = 0 so then we have:

Var(\hat \theta_1) =\frac{1}{4} [\sigma^2 + \sigma^2 ] =\frac{\sigma^2}{2}

For the second estimator we have:

Var(\hat \theta_2) = Var(\frac{X_1 +3X_2}{4})

Var(\hat \theta_2) =\frac{1}{16} Var(X_1 +3X_2)=\frac{1}{4} [Var(X_1) + Var(3X_2) + 2 Cov (X_1 , 3X_2)]

Since both random variables are independent we know that Cov(X_1, X_2 ) = 0 so then we have:

Var(\hat \theta_2) =\frac{1}{16} [\sigma^2 + 9\sigma^2 ] =\frac{5\sigma^2}{8}

7 0
3 years ago
Which of the following are solutions to the quadratic equation? Check all that
LenKa [72]

Answer:

Step-by-step explanation:

2x2+5x−10=x2+4

Step 1: Subtract x^2+4 from both sides.

2x2+5x−10−(x2+4)=x2+4−(x2+4)

x2+5x−14=0

For this equation: a=1, b=5, c=-14

1x2+5x+−14=0

Step 2: Use quadratic formula with a=1, b=5, c=-14.

x=

−b±√b2−4ac

2a

x=

−(5)±√(5)2−4(1)(−14)

2(1)

x=

−5±√81

2

x=2 or x=−7

Answer:

x=2 or x=−7

5 0
3 years ago
Read 2 more answers
What's 454.895 rounded to the nearest cent?????? Please help me!! I just want to make sure I got the answer right.
Nastasia [14]
454.90, the 5 makes the 9 go up which in turn makes the 8 also go up.
3 0
2 years ago
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