The answer to the first question is 30.
Answer:
Line of east wedge is: 2x - y = 96
So, Option 1 is correct.
Step-by-step explanation:
The east edge cannot intersect with the west edge means that two lines are parallel.
If the two lines are parallel then they have same slope. We need to find the slopes of given lines and check which line has slope same as slope of west edge.
Slope of west edge.
y = 2x + 5
The standard equation for slope intercept form is:
y = mx+b
where m is the slope. So, m= 2
Now finding line for east edge.
Option 1.
Convert each given equation to standard slope intercept form and find the slope.
2x -y =96
-y = -2x +96
Multiply with -1
y = 2x -96
m = 2
Option 2.
-2x -y = 96
-y = 2x +96
y = -2x-96
m = -2
Option 3
-y-2x =48
-y = 2x +48
y = -2x -48
m = -2
Option 4.
y+2x = 48
y = -2x+48
m = -2
So, only line of Option 1 has slope = 2 which is equal to the slope of west edge.
Line of east wedge is: 2x - y = 96
So, Option 1 is correct.
Answer:
Test statistic Z= 0.13008 < 1.96 at 0.10 level of significance
null hypothesis is accepted
There is no difference proportion of positive tests among men is different from the proportion of positive tests among women
Step-by-step explanation:
<em>Step(I)</em>:-
Given surveyed two random samples of 390 men and 360 women who were tested
first sample proportion
second sample proportion
Step(ii):-
Null hypothesis : H₀ : There is no difference proportion of positive tests among men is different from the proportion of positive tests among women
Alternative Hypothesis:-
There is difference between proportion of positive tests among men is different from the proportion of positive tests among women
where
P = 0.920
Test statistic Z = 0.13008
Level of significance = 0.10
The critical value Z₀.₁₀ = 1.645
Test statistic Z=0.13008 < 1.645 at 0.1 level of significance
Null hypothesis is accepted
There is no difference proportion of positive tests among men is different from the proportion of positive tests among women
Answer:
A = 108 units²
Step-by-step explanation:
The area (A) of a trapezium is calculated as
A = h (b₁ + b₂ )
where h is the height between the 2 bases and b₁, b₂ are the parallel bases
Here h = 24 , b₁ = 8 , b₂ = 1 , then
A = × 24 × (8 + 1) = 12 × 9 = 108 units²
Answer: See below
Step-by-step explanation:
number of yellow pieces/number of blue pieces
= 14/24
= 7/12 --> 7 to 12 --> 7:12
The ratio that represents the number of yellow pieces to the total number of pieces is part-to-whole
number of yellow pieces/total number of pieces
= 14/100
= 7/50 --> 7 to 50 --> 7:50
The ratio that represents the number of blue pieces to the total number of pieces is part-to-whole
= 24/100
= 6/25 --> 6 to 25 --> 6:25