Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is
1 answer:
Answer:
There are 6 red marbles in Bag A.
Step-by-step explanation:
<u>Bag A</u>
Red to white marble ratio is 1:3
White to blue marble ratio is 2:3
If we match the amount of white marbles between both ratios we can put together a three-term ratio.
Red to White 2:6
White to Blue 6:9
Red to White to Blue 2:6:9
Then, the total amount of marbles in bag A is given by:
A= 2·x + 6·x + 9·x
<u>Bag B</u>
B= 1·x + 4·x
White marbles
Since the two bags contain 30 white marbles:
30== 6·x + 4·x=10x ⇒ x=3
Then,
:red marbles in bag A
=2·x=2·3=6
There are 6 red marbles in Bag A.
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Answer:
a) P(-z_0.025 < Z < z_0.025)
For this case we want a quantile that accumulates 0.025 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:
"=NORM.INV(0.025,0,1)"
"=NORM.INV(0.025,0,1)"
And for this case the two values are :
b) P(-z_{\alpha/2} < Z < z_{\alpha/2})
For this case we want a quantile that accumulates of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:
"=NORM.INV(alpha/2,0,1)"
"=NORM.INV(alpha/2,0,1)"
c) For this case we want to find a value of z that satisfy:
P(Z > z_alpha) = 0.05.
And we can use the following excel code:
"=NORM.INV(0.95,0,1)"
And we got
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Part a
P(-z_0.025 < Z < z_0.025)
For this case we want a quantile that accumulates 0.025 of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:
"=NORM.INV(0.025,0,1)"
"=NORM.INV(0.025,0,1)"
And for this case the two values are :
Part b
P(-z_{\alpha/2} < Z < z_{\alpha/2})
For this case we want a quantile that accumulates of the area on the tails of the normal standard distribution, and for this case we can calculate the z value with the following excel codes:
"=NORM.INV(alpha/2,0,1)"
"=NORM.INV(alpha/2,0,1)"
Part c
For this case we want to find a value of z that satisfy:
P(Z > z_alpha) = 0.05.
And we can use the following excel code:
"=NORM.INV(0.95,0,1)"
And we got
Answer:
1) AD=BC(corresponding parts of congruent triangles)
2)The value of x and y are 65 ° and 77.5° respectively
Step-by-step explanation:
1)
Given : AD||BC
AC bisects BD
So, AE=EC and BE=ED
We need to prove AD = BC
In ΔAED and ΔBEC
AE=EC (Given)
( Vertically opposite angles)
BE=ED (Given)
So, ΔAED ≅ ΔBEC (By SAS)
So, AD=BC(corresponding parts of congruent triangles)
Hence Proved
2)
Refer the attached figure
In ΔDBC
BC=DC (Given)
So,(Opposite angles of equal sides are equal)
So,
So, (Angle sum property)
x+x+50=180
2x+50=180
2x=130
x=65
So,
Now,
So,
In ΔABD
AB = BD (Given)
So,(Opposite angles of equal sides are equal)
So,
So,(Angle Sum property)
y+y+25=180
2y=180-25
2y=155
y=77.5
So, The value of x and y are 65 ° and 77.5° respectively
