Answer:
Step-by-step explanation:
Hello!
The variable of study is X: Temperature measured by a thermometer (ºC)
This variable has a distribution approximately normal with mean μ= 0ºC and standard deviation σ= 1.00ºC
To determine the value of X that separates the bottom 4% of the distribution from the top 96% you have to work using the standard normal distribution:
P(X≤x)= 0.04 ⇒ P(Z≤z)=0.04
First you have to use the Z tables to determine the value of Z that accumulates 0.04 of probability. It is the "bottom" 0.04, this means that the value will be in the left tail of the distribution and will be a negative value.
z= -1.75
Now using the formula of the distribution and the parameters of X you have to transform the Z-value into a value of X
z= (X-μ)/σ
z*σ = X-μ
(z*σ)+μ = X
X= (-1.75-0)/1= -1.75ºC
The value that separates the bottom 4% is -1.75ºC
I hope this helps!
Answer:
x = 64
Step-by-step explanation:
they give you two angles 56 and 60
add them and subtract from 180
180 - 116 = 64
Answer:
x=12 and y=31
Step-by-step explanation:
First, ( 5x - 7 ) and ( 3x + 17 ) are alternate interior angles, which means they are congruent, or equal:
5x - 7 = 3x + 17
Add 7 to each side:
5x = 3x + 24
Subtract 3x from both sides:
2x = 24
Divide each side by 2:
x = 12
Now we can see that ( 5x - 7 ) and ( 4y + 3 ) are supplementary angles, which means they will add up to 180 degrees:
5x - 7 + 4y + 3 = 180
Substitute 12 in for x to solve for y:
5 ( 12 ) - 7 + 4y + 3 = 180
60 - 7 + 4y + 3 = 180
combine like terms:
( 60 + ( -7 ) + 3 ) + 4y = 180
56 + 4y = 180
Subtract 56 from each side:
4y = 124
Divide each side by 4:
y = 31
Area = L x H
area = 20 x 15 = 300 square feet
