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2 years ago

14

Elisa is 9 years old. When 7 is subtracted from Krista’s age and 1/4 of the difference is taken , the result is equal to Elisa’s

age . How old is Krista?

1 answer:

garri49 [273]2 years ago

8 0

Answer:

43

Step-by-step explanation:

just go backwards so multiply 9 by 4

36

then add 7

43

then to check go 43-7

36-1/4

9

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A local museum charges $25 per adult and $12 per child for admission fees. At the end of a day, the museum made $9,014 in total

Natali [406]

Answer:

There were 172 guests that were children and 278 guests that were adults

Step-by-step explanation:

Step 1: State what is known

It is $25 per adult

It is $12 per child

The made $9014 dollars

There were 450 guests

Step 2: Define equations

25y + 12x = 9014 -----1

x + y = 450 ------------2

Step 3: Rearrange equation 2 for x

x + y = 450

x = 450 - y --------------3

Step 4: Substitute 3 into 1 for y and solve for y

25y + 12(450 - y) = 9014

25y + 5400 - 12y = 9014

13y = 3614

y = 3614/13

y = 278

Step 5: Substitute y = 278 into 3 to solve for x

x = 450 - (278)

x = 172

Therefore 172 children and 278 adults visited the museum

4 0

2 years ago

Lonzell said the function shown in the graph is positive on the interval (−,) and negative on the interval (−,−)open negative 5

Nezavi [6.7K]

Answer:

The positive graph is on the points (-5,-4) and (2,5)

And, negative would be (-4,2)

Step-by-step explanation:

As it seems that fgraph shows positive in the case when it is over x-axis, and negative when it is below y-axis

As on the interval (-1,5)

The graph is below x-axis i.e. on (-1,2)

And, over x-axis i.e. on (2,5)

At this point Lonzell’s is not correct

As on the interval (-5,-1)

The graph is below x-axis i.e. on (-4,-1)

And, over x-axis i.e. on (-5,4)

At this point Lonzell’s is not correct

So,

The positive graph is on the points (-5,-4) and (2,5)

And, negative would be (-4,2)

5 0

2 years ago

In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.02, 0.07, and

Leviafan [203]

Answer:

A. (Table Attached)

B. (See Step 3)

C. 0.06 (See Step 4)

D. NOT independent (See Step 5)

Step-by-step explanation:

<h3 /><h3>STEP 1:</h3>

Name the probabilities:

p₁ = 0.02, p₂ = 0.07, p₃ = 0.91

q₁ = 1-p₁ = 0.98 , q₂ = 1-p₂ = 0.93 , q₃ = 0.09

Let X and Y be the number of bits with high and moderate distortion out of three.

<h3>STEP 2:</h3>

A.

The function will follow multinomial distribution:

$f_{XY}(x,y) = P(X=x, Y=y) = \frac{3!}{x!y!(3-x-y)!} (p_1^x)(p_2^y)(p_3^{3-x-y})$

Substitute the values and make a table.

TABLE IN ATTACHMENT

<h3>STEP 3:</h3>

B.

We calculate marginal distribution by:

$P (X=x)=$ <em>∑</em> $P(X=x,Y=y)$

$fx(x)$ can be found by adding all the probabilities in each row for different value of X

For X=0 , ∑P = 0.94157441

For X=1 , ∑P = 0.057624

For X=2 , ∑P = 0.001176

For X=3 , ∑P =0.000008

<h3>STEP 4:</h3><h3>C.</h3>

The mathematic expectation E is the sum of product of each possibility with its probabiity.

$E(X)=$ <em>∑ </em> $xP(X=x)$

Find E(X):

$E(X)= (0*0.9415744)+(1*0.057624)+(2*0.001176)+(3*0.000008)$

$E(X)=0.06$

<h3>STEP 5:</h3>

Condition probability states:

$P(A|B)=\frac{P(A,B)}{P(B)}$

It can also be written as:

$f_{Y|X=1}(y)=\frac{f_{XY}(1,y)}{f_x(1)}$

Where $f_x(1)\\$ = 0.057624

Calculate the quotient:

$Y|_{x=1}$ = 0 , $f_{Y|_X=1$ = 0.862245

$Y|_{x=1}$ = 1 , $f_{Y|_X=1$ = 0.132653

$Y|_{x=1}$ = 2 , $f_{Y|_X=1$ = 0.000510

$Y|_{x=1}$ = 3 , $f_{Y|_X=1$ = 0

Find the dependency:

$f_{XY}(y)=f_X(x)f_Y(y)$

We found that

$f_{Y|_X=1$ = 0.862245

Calculate $f_Y(1)$ from summing the column from the table

$f_Y(1)=0.17428341+0.007644+0.000084\\f_Y(1)=0.18201141$

Which are not equal.

Conclusion:

X and Y are NOT Independent

7 0

2 years ago

After triangle ace is dilated by a factor of 5, it has an area of 100 square inches. What was its area before dilation?

NISA [10]

Answer:

20in^2

Step-by-step explanation:

Since you multiply the original area of the triangle by the scale factor to get the new area, you can find the original area (before dilation) by dividing the dilated triangle's area by the scale factor. Since 100 is the area of the dilated triangle, and 5 is your scale factor, you do 100/5 to get the area of the triangle before it was dilated.

5 0

1 year ago

1.Write down the short-hand for these two normal distributions. The Verbal Reasoning section has a distribution N( , ) The Quant

IRINA_888 [86]

Answer:

Step-by-step explanation:

4 0

2 years ago